Dynamic Field Balancing

TABLE OF CONTENTS AND SEMINAR AGENDA Field Dynamic Balancing Section

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1. INTRODUCTION TO DYNAMIC BALANCING ...................................................... 1-1 2. TYPES OF UNBALANCE ........................................................................................ 2-1 A. Static Unbalance ............................................................................................. 2-2 B. Couple Unbalance .......................................................................................... 2-3 C. Quasi-Static Unbalance .................................................................................. 2-4 D. Dynamic Unbalance ....................................................................................... 2-5 3. TYPES OF BALANCE PROBLEMS ........................................................................ 3-1 A. Rigid Vs Flexible Rotors…………………………………………………… .......... 3-1 B. Critical Speeds……………………………………………………………….......... 3-4 4. HOW TO ENSURE THE DOMINANT PROBLEM IS UNBALANCE……………. ... 4-1 A. Review of Typical Spectra and Phase Behaviors for Common Machinery Problems ................................................................................... 4-1 1. Mass Unbalance ....................................................................................... 4-1 2. Eccentric Rotor .......................................................................................... 4-1 3. Bent Shaft ................................................................................................. 4-3 4. Misalignment ............................................................................................ 4-3 5. Resonance................................................................................................ 4-3 6. Mechanical Looseness/Weakness ........................................................... 4-4 B. Summary of Phase Relationships for Various Machinery ........................ 4-4 1. Force (or Static) Unbalance....................................................................... 4-4 2. Couple Unbalance .................................................................................... 4-4 3. Dynamic Unbalance ................................................................................. 4-4 4. Angular Misalignment............................................................................... 4-6 5. Parallel Misalignment ............................................................................... 4-6 6. Bent Shaft ................................................................................................. 4-6 7. Resonance................................................................................................ 4-6 8. Rotor Rub .................................................................................................. 4-6 9. Mechanical Looseness/Weakness Due to Base/Frame Problems or Loose Hold Down Bolts ....................................................... 4-6 10. Mechanical Looseness Due to a Cracked Frame.................................... 4-6 C. Summary of Normal Unbalance Symptoms .............................................. 4-6 1. Special Characteristics ............................................................................. 4-6 2. Centrifugal Force Due to Unbalance ......................................................... 4-6 3. Unbalance Force Directivity ...................................................................... 4-7 4. Radial/Axial Vibration Comparison .......................................................... 4-7 5. Overhung Rotor Unbalance Directivity ...................................................... 4-7 6. Steadiness & Repeatability of Phase Due To Unbalance ......................... 4-8 7. Resonant Amplitude Magnification ........................................................... 4-8 8. Phase Behavior For Dominant Static,Couple & Dynamic Unbalance ....... 4-8 © Copyright 2001 Techncial Associates of Charlotte, P.C.

Techncial Associates Field Dynamic Balancing


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5. CAUSES OF UNBALANCE .................................................................................... 5-1 A. Assembly Errors ............................................................................................. 5-1 B. Casting Blow Holes ......................................................................................... 5-1 C. Fabrication Tolerance Problems ...................................................................... 5-1 D. Key Length Problems ...................................................................................... 5-1 E. Rotational Distortion ........................................................................................ 5-3 F. Deposit Buildup or Erosion .............................................................................. 5-3 G. Unsymmetrical Design .................................................................................... 5-3 6. WHY DYNAMIC BALANCING IS IMPORTANT .................................................... 6-1 7. UNITS OF EXPRESSING UNBALANCE ................................................................ 7-1 8. VECTORS ............................................................................................................... 8-1 9. DYNAMIC FIELD BALANCING TECHNIQUES ..................................................... 9A. Recommended Trial Weight Size .................................................................... 9B. How a Strobe-Lit Mark On a Rotor Moves When a Trial Weight is Added ........ 9C. Single-Plane Balancing Using a Strobe Light And a Swept-Filter Analyzer .... 9D. Single-Plane Method of Balancing .................................................................. 9E. Balancing in One Run ..................................................................................... 9F. Two-Plane Balancing Techniques .................................................................... 9G. Cross-Effects ................................................................................................... 9H. Single-Plane Method For Two-Plane Balancing .............................................. 9I. Vector Calculations For Two-Plane Balancing .................................................. 9J. Rotor Balancing By Static Couple Derivation .................................................. 9K. Single-Plane Balancing With Remote Phase And A Data Collector ................. 9L. Taking Phase Readings With A Data Collector................................................. 9M. Single-Plane Balancing Using A Data Collector ............................................. 9N. Two-Plane Balancing Using A Data Collector .................................................. 9O. Overhung Rotors ............................................................................................. 9P. Multi-Plane Balancing .................................................................................... 9Q. Splitting Balance Correction Weights .............................................................. 9R. Combining Balance Correction Weights Using Vectors .................................. 9S. Effect of Angular Measurement Errors of Potential Unbalance Reduction ....... 91. Effect of Phase Angle Measurement Errors By Instruments ...................... 92. Effect of Angular Measurement Errors When Attaching Balance Correction Weights .................................................................... 9-

© Copyright 2001 Techncial Associates of Charlotte, P.C.



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10. Balancing Machines - Soft-Bearing Vs Hard-Bearing Machines ................... 10A. Soft-Bearing Machine ................................................................................... 10B. Hard-Bearing Machine ................................................................................ 1011. Recommended Vibration And Balance Tolerances .......................................... 11A. Vibration Tolerances ..................................................................................... 111. Recommended Overall Vibration Specifications .......................................... 112. Synopsis Of Spectral Alarm Band Specifications ......................................... 11B. Balance Tolerances On Allowable Residual Unbalance ................................. 111. ISO 1940 Balance Quality Grades ................................................................ 11a. Application of Tolerances to Single-Plane Problems .......................... 11b. Application of Tolerances to Two-Plane Problems.............................. 11c. Application of Tolerances to Special Rotor Geometries ...................... 11C. How to Determine Residual Unbalance Remaining in a Rotor After Balancing .................................................................................................... 11D. Comparison of ISO 1940 With API and Navy Balance Specifications .......... 11APPENDIX A

Balancing Terminology

APPENDIX B

Weight Removal Charts

APPENDIX C

Conversion Chart for Converting Inches of Flat Stock # 1020 Steel to Ounces of Weight

APPENDIX D

Three-Point Method of Balancing













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CHAPTER 1 INTRODUCTION TO DYNAMIC BALANCING Unbalance has been found to be one of the most common causes of machinery vibration, present to some degree on nearly all rotating machines. Vibration due to an unbalance while the rotor is rotating is the result of a heavy spot located at a radius from the mass centerline producing a centrifugal force. The amount of centrifugal force will be the result of the weight of the heavy spot, the radius of such heavy spot and the speed the rotor is rotating. Thus, unbalance can be described as centrifugal forces that displace the rotors mass center from the rotors rotating center. Another way to state this in general is unbalance is a condition, which exists when vibratory forces or motion is applied to the bearings of a rotor as a result of centrifugal forces, particularly with respect to a rigid rotor. How far and in what manner this displacement takes place will be discussed later in this text. In order to reduce the amount of forces generated by this imbalance there are several factors that we will have to understand. Before a part can be balanced certain conditions must be met. 1.

The vibration must be due to unbalance. A complete vibration analysis needs to be performed to make sure that unbalance is the primary cause of the vibration forces.

2.

We must be able to start and stop the rotor.

3.

We must be able to add or remove weight.

In most instances, weight corrections can be made with the rotor mounted in its normal installation, operating as it normally does. This process of balancing a part without taking it out of the machine is called IN-PLACE BALANCING. Balancing in-place eliminates costly disassembly and eliminates the possibility of damage during the transportation of the rotor. Rotors that are totally enclosed such as some motors, pumps and compressors, can be removed and transported to a balancing machine. The principles of balancing are similar either way. Before we discuss balancing, we should first understand unbalance, where it comes from and what must be done to correct it.



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CHAPTER 2 TYPES OF UNBALANCE Figure 1 helps illustrate unbalance. Here, assuming a perfectly balanced rotor, a 5 ounce (141.75 gram) weight is placed on the rotor at a 10-inch (254 mm) radius. This produces an unbalance of 50 oz-in (36000 gram-mm). Note that the same 5 ounce (141.75 gram) weight placed at 5 inches (127 mm) from the center would produce only a 25 oz-in (18000 gram-mm) unbalance. Figure 2 illustrates the same rotor as that in Figure 1 but with a correction made such that the rotor is balanced by countering the 50 oz-in (36000 gram-mm) original unbalance by placing a correction of 50 oz-in (36000 gram-mm) (by placing an identical weight at a 10 inch (254 mm) radius directly opposite the original weight).

FIGURE 1. ILLUSTRATING UNBALACING

FIGURE 2. BALANCE CORRECTION © Copyright 2001 Techncial Associates of Charlotte, P.C.


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Referring to Figure 3, in a “perfectly balanced rotor”, both the shaft and mass centerlines would coincide with one another with equal mass distribution throughout the rotor.

FIGURE 3. STATIC UNBALANCE As mentioned before, unbalance occurs when the mass centerline does not coincide with the shaft centerline as shown in Figure 3. The mass centerline can be thought of as an axis about which the weight of the rotor is equally distributed. The mass centerline is also the axis about which the part would like to rotate if free to do so. However, if the rotor itself is restricted in it’s bearing, vibration will occur if the shaft and mass centerlines do not coincide. Following below will be a discussion on each of the four major types of unbalance, which include - STATIC, COUPLE, QUASI-STATIC and DYNAMIC UNBALANCE. Each of these types of unbalance will be defined by the relationship between the shaft and mass centerlines of the rotor. A. Static Unbalance Static unbalance is sometimes known as “force unbalance” or “kinetic unbalance”. Static unbalance is a condition where the mass centerline is displaced from and parallel to the shaft centerline as shown in Figure 4. This is the simplest type of unbalance, which has classically been corrected for many years by placing a fan rotor on knife-edges and allowing it to “roll to the bottom”. That is, when the fan wheel is released, if the heavy spot is angularly displaced from the bottom (or 6:00 position), it will tend to roll to the bottom hopefully ending up in the 6:00 position if the rotor was sufficiently free to rotate. So-called correction of this unbalance was then accomplished by placing a weight opposite this location (or at about 12:00).

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FIGURE 4. STATIC UNBALANCE Actually, there are two types of static unbalance as shown in Figure 4A and Figure 4B. In Figure 4A, the unbalance is centered directly above the rotor center of gravity (CG). Figure 4B likewise shows static unbalance, but with equal masses placed at identical distances from the mass centerline and rotor CG on each end. Whether the static unbalance occurs as in either Figures 4A or 4B, each can be corrected by placement of a correction weight in only one plane at the CG, or by attaching two weights with one half the total weight at either end assuming the CG is equidistant from each bearing. NOTE: This text is being written with the assumption that we would be able to attach a weight of suitable size at the appropriate radius. If this cannot be accomplished, then the appropriate amount of weight can be removed from the heavy spot. B. Couple Unbalance Couple unbalance is a condition where the mass centerline intersects the shaft centerline at the rotor center of gravity as shown in Figure 5. Here, a couple is created by placement of equal weights 180° opposite each other and equidistant from the CG in opposite directions. A “couple” is simply two equal and parallel forces acting opposite one another, but not in the same plane. Instead, they are offset from one another, which would tend to rotate the rotor. Significant couple unbalance can introduce severe instability to the rotor causing it to wobble back and forth (like a “seesaw”) with the fulcrum at the rotor CG. Unlike static unbalance, couple unbalance only becomes apparent when the shaft rotates. In other words, if the rotor is placed on knife-edges, it would not tend to rotate no matter what position it is placed since it would be statically balanced. Like static unbalance, couple unbalance likewise causes high vibration at 1X RPM. Unlike static unbalance, couple unbalance will bring about a very different phase behavior, which will be discussed in Section IV. Unlike static unbalance, couple unbalance must be corrected in two planes with corrections 180° opposite each other.

FIGURE 5. COUPLE UNBALANCE © Copyright 2001 Techncial Associates of Charlotte, P.C.


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The axial location of the correction couple will not matter as long as it is equal in magnitude, but opposite in direction to the unbalance couple. For example, looking at Figure 6, placement of the two 5 oz (141.75 gram) weights at an axial distance with 10 inches (254 mm) to the left and right of the CG as shown will create a clockwise couple unbalance. This can be counteracted either by placing identical 5 oz (141.75 gram) weights at a 10-inch (254 mm) distance directly opposite the original weights or by placing 10 oz (283.5 gram) weights at an axial distance only 5 inches (127 mm) from the CG. Only a very few cases will a rotor have true static or true couple unbalance. Normally, an unbalanced rotor will have some of each type. Combination of static and couple unbalance is further classified as “quasi-static” and “dynamic” unbalance.

FIGURE 6. CORRECTION OF COUPLE UNBALANCE C. Quasi-Static Unbalance Quasi-static unbalance represents a specific combination of static and couple unbalance where the static unbalance is directly in line with one of the couple moments as shown in Figure 7. Quasi-static unbalance is that condition where the mass centerline intersects with the shaft, but at a point other than the rotor center of gravity (CG). In Figure 7, the Figures 7A and 7B illustrate quasi-static unbalance. In Figure 7A, the unbalance mass is placed at a location other than the CG which introduces both static and couple unbalance. In reality, Figure 7B represents the same unbalance as that in Figure 7A. The two unbalance masses acting opposite one another close to the CG counteract one another statically, but do not compensate for the unbalance introduced by the unbalance mass on the top left-hand side of the rotor.

FIGURE 7A

FIGURE 7B

FIGURE 7. QUASI-STATIC BALANCE 2-4



Figure 8 illustrates another type of quasi-static unbalance often not even considered by analysts. In this case, assuming you had a perfectly balanced rotor, when this is connected to an unbalanced coupling, a quasi-static unbalance is created. This is a very common type of unbalance since most couplings are not balanced unless they are of great size or speed. Similarly, quasi-static unbalance can be introduced by inserting the wrong size key into the shaft or pump impeller, which again will create both a static and a couple unbalance. In each case, the required correction in addition to a static correction at the same location as the couple component nearest the coupling, key, etc.

FIGURE 8. UNBALANCED COUPLING CAUSING QUASI-STATIC UNBALANCE D. Dynamic Unbalance Dynamic unbalance is the most common type of unbalance and can only be corrected by mass correction in at least two planes. Figure 9 illustrates dynamic unbalance which again is a combination of both static and couple unbalance, but with unbalance masses at different angular positions from one another as shown in Figure 9. Because the unbalance masses are at different angular positions, dynamic unbalance is that condition where the shaft centerline and mass centerline do not intersect with one another, nor are they parallel with one another. As will be pointed out in Section III, dynamic unbalance causes phase differences between the horizontal on one bearing versus the horizontal on the other bearing to be far different from either 0 or 180°. That is, the horizontal phase difference may be 60° or 180°, or most anything. However, if the horizontal phase difference is 60°, the vertical phase difference should be the same as the horizontal within one clock position (+/- 30°).

FIGURE 9. DYNAMIC UNBALANCE © Copyright 2001 Techncial Associates of Charlotte, P.C.


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CHAPTER 3 TYPES OF BALANCE PROBLEMS In order to achieve a satisfactory balance with the minimum number of start-stop operations it not only is important that we recognize the type of balance problem we have (static, couple, quasi-static or dynamic), it should now be obvious that not all balancing can be achieved by balancing in a single correction plane. A guide to determining whether single plane, two plane or multi-plane will be required will be determined by the ratio of the length to diameter of the rotor along with the speed of the rotor. It is also very important to recognize whether the rotor is flexible (one that bows)or rigid (one that maintains it geometric shape.) The L/D ratio is calculated using the dimensions of the rotor exclusive of the supporting shaft. See Table 1. The selection of single plane versus two-plane balancing based on the L/D ratio and rotor speed is offered only as a guide and may not hold true in all cases. Experience reveals that single plane balancing is normally acceptable for rotors such as grinding wheels, singlesheave pulleys, and similar parts even through their operating speed may be greater than 1000 RPM.

TABLE 1 A. Rigid Vs Flexible Rotors Only a few rotors are made of a single disc, but instead they are made of several discs on a common shaft, often times in complex shapes and sizes. This makes it practically impossible to know which disc(s) the heavy spot is located. The unbalance could be in any plane or planes located along the length of a rotor, and it would be most difficult and time consuming to determine where. In addition, it is not always possible to make weight corrections in just any plane. Therefore, the usual practice is to compromise by making weight corrections in the two most convenient planes available. This is possible because any condition of unbalance can be compensated for by weight corrections in any two balancing planes. This is true only if the rotor and shaft are rigid and do not bend or deflect due to the forces caused by unbalance. © Copyright 2001 Techncial Associates of Charlotte, P.C.


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Whether or not a rotor is classified as rigid or flexible depends on the relationship between the rotating speed (RPM) of the rotor and its natural frequency. You will recall that every object including the rotor and shaft of a machine has a natural frequency, or a frequency at which it likes to vibrate. When the natural frequency of some part of a machine is also equal to the rotating or some other exciting frequency of vibration, there is a condition of resonance. A flexible rotor balanced at one operating speed may not be balanced when operating at another speed. If a rotor were first balanced below 70% of the its first critical speed with the correction weights added in the two end planes, the two correction weights added would compensate for all sources of unbalance distributed throughout the rotor. If the rotor were increased to above 70% of the critical speed, the rotor would deflect due to the centrifugal force of the unbalance located at the center of the rotor as shown in Figure 10. As the rotor bends or deflects, the weight of the rotor is moved out away from the rotating centerline creating a new unbalance condition. It would then be necessary to rebalance the two end planes at this new operating speed, and then the rotor would be out of balance at the slower operating speed. The only solution to insure smooth operation at all speeds is to make the balance correction in the actual planes of unbalance, thus a multi-plane balance. This subject will be discussed in greater detail later in the course.

Fig. 10A Rotor with dynamic unbalance, balanced in two planes below critical speed

Fig. 10B Operating above critical speed the rotor deflects due to unbalance in the center

FIGURE 10. ROTOR DEFLECTION DUE TO UNBALANCE ABOVE CRITICAL SPEED

FIGURE 11. ROTOR FLEXURAL MODES

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The rotor in Figure 10 represents the more simple type of flexible rotor. A Rotor can deflect in several ways depending on its operating speed and the distribution of unbalance through out the rotor. Figure 11 illustrates the first, second and third flexural modes a rotor could take while going through the first, second and third criticals. These rotors may require that balance corrections be made in several planes to insure smooth operation through all speed ranges. Whether a flexible rotor requires multi-plane balancing depends on the normal operating speeds of the rotor and the significance of rotor deflection on the functional requirements of the machine. Flexible rotors generally fall into one of the following categories: 1. If the rotor operates at only one speed and a slight amount of deflection will not accelerate wear or hamper the productivity of the machine, then balancing in any two correction planes to minimize bearing vibration may be all that is required. 2. If a flexible rotor operates at only one speed, but it is essential that rotor deflection be minimized, then multi-plane balancing may be required. 3. If it is essential that a rotor operate smoothly over a broad range of speeds where the rotor is rigid at lower speeds and flexible at higher speed, then multi-plane balancing is required. B. Critical Speeds The rotating speed at which the rotor itself goes into bending resonance is called a critical speed. Depending on how many bending modes the rotor goes through is dependant upon the number of operating speeds coincide with the rotors natural frequency. In general, rotors operating below 70% of their natural frequency are considered to be rigid rotors and above 70% of their natural frequency are considered to be flexible rotors. When a rotor bends or deflects due to operating through its critical speed, the weight of the rotor is moved out away from the rotating centerline creating a new unbalanced condition. This rotor could be corrected by rebalancing in the two end planes; however, the rotor would then be out of balance at slower speeds where there is no deflection. The only solution to insure smooth operation at each speed is to make the corrections in the planes of unbalance, thus multi-plane balancing. Remember, any unbalance can be corrected by making corrections in any two balance planes, but only if the rotor is a non-flexible rotor.



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CHAPTER 4 HOW TO ENSURE THE DOMINANT PROBLEM IS UNBALANCE Before analysts begin balancing a machine, they should always ensure that the dominant problem is in fact unbalance before they begin. Vibration consultants commonly report that on over one-half the jobs on which they are requested to balance machinery, they do not in fact perform any balancing, but find other problems requiring different corrective measures instead. An analyst should always employ both spectral and phase behaviors for some of the more common machinery problems, each of which can cause high vibration at 1X RPM, including eccentric rotor, bent shaft, misalignment, resonance and even certain types of mechanical looseness/weakness. While there are still other problems that generate 1X RPM vibration, a review of Table II will help the analyst distinguish which problem is at hand. It should be pointed out that the column entitled “TYPICAL SPECTRUM” in Table II means just that - that is, these spectra are not intended to be all-inclusive. For example, it is quite possible for misalignment to generate only high 1X RPM vibration in certain cases, however, they most often generate a noticeable 2X RPM peak. Therefore, such a spectrum is shown under the “TYPICAL SPECTRUM” column. Following below will be a quick review of Table II pointing out the more common spectral and phase behaviors of the problems shown. Later, a more detailed look will be taken specifically on unbalance symptoms. A.

REVIEW OF TYPICAL SPECTRA AND PHASE BEHAVIORS FOR COMMON MACHINERY PROBLEMS

1. Mass Unbalance: Table II shows that mass unbalance always generates high vibration at 1X RPM. The centrifugal forces caused by unbalance always act in the radial direction, but can sometimes generate high axial vibration in the case of overhung rotors like in Unbalance Case C of Table II. Pure force, or static unbalance, is evidenced by identical phase in the radial direction on both the outboard and inboard bearings supporting the rotor. On the other hand, pure couple unbalance is evidenced by a 180° phase difference in the radial direction between the outboard and inboard bearings (the horizontals will be 180° out of phase with one another as well as the outboard and inboard verticals with one another in pure couple unbalance). Overhung rotors represent a special case of unbalance on which high axial vibration can be generated which is in phase between the inboard and outboard bearings supporting the overhung rotor as shown in Table II. 2. Eccentric Rotor: Like unbalance, an eccentric rotor will generate high vibration at 1X RPM of the eccentric rotor itself with the highest vibration normally being in a direction through the centers of the two rotors as shown in Table II under “ECCENTRIC ROTOR”. However, the main difference between an eccentric rotor and an unbalanced one is with respect to phase behavior-pure unbalance will normally cause the phase difference in the © Copyright 2001 Techncial Associates of Charlotte, P.C.


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horizontal and vertical directions to be about 90° while in the case of an eccentric rotor, the horizontal and vertical phase difference will normally be either approximately 0° or 180° (each of which indicate straight-line motion). One of the problems with an eccentric rotor occurs if one attempts to balance the eccentric rotor. What will often result is that the balance exercise may in fact reduce vibration in one radial direction, but increase it in the other, depending on the amount of eccentricity. 3. Bent Shaft: A bent shaft will most always generate high axial vibration with the greatest component being 1X RPM if bent near the shaft center, but can create a high 2X RPM component if bent near the coupling. One of the things that sets apart bent shaft symptoms from those of unbalance is with respect to phase behavior - a bent shaft will cause axial vibration on the outboard bearing of a rotor to approximately 180° out of phase with respect to that of the inboard rotor bearing, while unbalance will normally cause axial outboard and inboard phase to be about the same. 4. Misalignment: Although misalignment normally generates a 2X RPM component greater than or equal to 30% of the amplitude at 1X RPM, it can sometimes cause only a high 1X RPM component, particularly in the axial direction. However, one of the things that again differentiate it from unbalance is its phase behavior - misaligned shafts will cause phase across the coupling to be approximately 180° different, whereas unbalance will normally cause almost equal phase on either side of the coupling. As Table II shows, angular misalignment is evidenced by a 180° phase change across the coupling in the axial direction whereas parallel, (or offset misalignment), causes a 180° difference in the radial direction across the coupling. Finally, a misaligned bearing cocked on the shaft generates spectra very similar to that of shaft misalignment. However, it can be detected by measuring at each of 4 points in the axial direction on each bearing as shown in Table II. This measurement should show that the phase is almost the same at each of the 4 points around the clock if the bearing is properly oriented. If there is a 180° phase difference across either points 1 and 3, or between 2 and 4 as shown in Table II, a cocked bearing is indicated. 5. Resonance: Resonance occurs when a forcing frequency coincides with a system natural frequency and can cause excessive vibration amplitudes. Even a small amount of unbalance, for example, can be greatly amplified if the rotor is operating at or near a natural frequency. Such a resonant problem is evidenced if the phase changes dramatically for only a small change in speed (Figure 12 shows that a rotor will experience almost a full 180° phase change when its speed passes completely through a natural frequency). At the same time, the amplitude first increases dramatically and then decreases as the rotor passes through the natural frequency (as shown in Table II).



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6. Mechanical Looseness/Weakness: Table II shows three different types of mechanical looseness, one of which is lesser known, but causes high radial vibration predominantly at 1X RPM which again causes a spectrum almost identical to an unbalance vibration spectrum as shown under mechanical looseness “Type A”. Type A looseness is caused by a looseness or weakness of machine feet, base plate, foundation, loose hold-down bolts at the base, distortion at the frame or base, etc. Again, the thing which sets it apart from unbalance is its phase behavior. Referring to “MECHANICAL LOOSNESS Type A” in Table I note that a problem is evidenced between the base plate and its base by a 180° phase change between these two sections. In other words, when a phase measurement is taken, if everything is moving together as it should, the phase should be almost identical as one moves his probe in the vertical direction from the foot to the baseplate, and then down to the base. One of the most important points about this type of looseness/weakness problem is that even if one is able to temporarily correct the problem by balancing and alignment procedures, the vibration will likely reoccur when even the least bit of unbalance or misalignment symptoms return. They must first correct the looseness/weakness problem, then balance or align if any further correction measures are still required. B. SUMMARY OF PHASE RELATIONSHIPS FOR VARIOUS MACHINERY Section A above summarized the typical spectral and phase relationships for some of the more common machinery problems. One of the most important points that this section hopefully made was that the key parameter that helped differentiate one problem from another was phase. Therefore, because of the importance of phase, following below will be a summary showing how phase generally behave for each particular problem scenario (see Table II):

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1.

Force (or “static”) unbalance is evidenced by nearly identical phase in the radial direction on each bearing of a machine.

2.

Couple unbalance shows approximately a 180° out-of-phase relationship when comparing the outboard and inboard horizontal, or the outboard and inboard vertical direction on the same machine.

3.

Dynamic Unbalance is indicated when the phase difference is well removed from either 0° or 180° but importantly is nearly the same in the horizontal and vertical directions. That is, the horizontal phase difference could be almost anything ranging from 0° to 180° between the outboard and inboard bearings; but the key point is that the vertical phase difference should be almost identical to the horizontal phase difference (+/- 30°). For example, if the horizontal phase difference between the outboard and inboard bearings is 60°, and dominant problem is dynamic unbalance, then the vertical phase difference between these two bearings should also be about 60° (+/- 30°). If the horizontal phase difference varies greatly from the vertical phase difference when high 1X RPM vibration is present, this strongly suggests the dominant problem is not unbalance.

4.

Angular misalignment is indicated by approximately a 180° phase difference across the coupling, with measurements in the axial direction. © Copyright 2001 Techncial Associates of Charlotte, P.C.


W E O OV , T

FIGURE N A O CHANGE D

N

T

I Techncial Associates Field Dynamic Balancing

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A


5.

Parallel misalignment causes radial phase differences across the coupling to be approximately 180° out of phase with respect to one another.

6.

Bent shaft causes axial phase on the same shaft of a machine to approach a 180° difference when comparing axial measurements on the outboard with those on the inboard bearing of the same rotor.

7.

Resonance is shown by exactly a 90° phase change at the point when the forcing frequency coincides with a natural frequency, and approaches a full 180° phase change when the machine passes through the natural frequency (depending on the amount of damping present).

8.

Rotor rub causes significant, instantaneous changes in phase.

9.

Mechanical looseness/weakness due to base/frame problems or loose hold-down bolts is indicated by nearly a 180° phase change when one moves the probe from the machine foot down to its baseplate and support base.

10.

Mechanical looseness due to a cracked frame, loose bearing or loose rotor causes phase to be unsteady with widely differing phase measurements from one measurement to the next. The phase measurement may noticeably differ every time you speed up the machine.

C. Summary of Normal Unbalance Symptoms Sections A and B above summarized how the analyst can ensure that the dominant problem is unbalance. Following below will be a more detailed look at the symptoms normally present when some type of unbalance is the major problem: 1. Special Characteristics - unbalance is always indicated by high vibration at 1X RPM of the unbalanced part. Normally, this 1X RPM vibration will dominate the spectrum. In fact, the amplitude at 1X RPM will normally be greater than or equal to 80% of the overall amplitude when the problem is limited to unbalance (may be only 50% to 80% of the overall if other problems exist in addition to unbalance). 2. Centrifugal Force Due to Unbalance - Mass unbalance produces centrifugal forces proportional to the following equation:

4-6



FC = mrω2 = g

Wr (386)(16)

C

2πn

2

(EQUATION 1)

60

2

2

F = .000001775 Un = .00002841 Wrn C

where: Fc u w r n

= Centrifugal Force (lb) = Unbalance of Rotating Part (oz-in) = Weight of Rotating Part (lb) = eccentricity of the rotor (in) = Rotating Speed (RPM)

For example, assuming a sample rotor with a 1 oz (28.35 grams) unbalance at an 18 inch (457.2 mm) radius (U= 18 oz-in) (12,962 gram-mm) turning 6000 RPM. FC = (.000001775)(18 oz-in)(6000 RPM)2 F

C

= 1150 lbs (from centrifugal force due to unbalance alone)

That is, only a 1 oz (28.35 gram) unbalance on a 3 foot (914.4 mm) diameter wheel turning 6000 RPM would introduce a centrifugal force of 1150 lbs (521.6 kg) that would have to be supported by the bearings in addition to the static rotor weight they must support. Importantly, note that the centrifugal force varies with the square of RPM (that is, tripling the speed will result in an increase in unbalance vibration by a factor of 9 times). 3. Unbalance Force Directivity - Mass unbalance generates a uniform rotating force that is continually changing direction, but is evenly applied in all radial directions. As a result, the shaft and supporting bearings tend to move in somewhat a circular orbit. However, due to the fact that vertical bearing stiffness is normally higher than that in the horizontal direction, the normal response is a slightly elliptical orbit. Subsequently, horizontal vibration is normally somewhat higher than that in the vertical, commonly ranging between 1.5 and 2 times higher. When the ratio of horizontal to vertical is higher than about 5 to 1, it normally indicates problems other than unbalance, particularly resonance. 4. Radial/Axial Vibration Comparison - When unbalance is dominant, radial vibration (horizontal and vertical) will normally be quite higher than that in the axial direction (except for overhung rotors). 5. Overhung Rotor Unbalance Directivity - Generally causes high 1X RPM vibration in both the axial and radial directions. Overhung rotors most often have both static and couple imbalance, which will normally require correction in at least two planes. © Copyright 2001 Techncial Associates of Charlotte, P.C.


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6. Steadiness & Repeatability of Phase Due to Unbalance - Unbalanced rotors normally exhibit steady and repeatable phase in radial directions. When the rotor is trim balanced, phase can begin to “dwell” back and forth under a strobe light as you achieve a better and better balance, particularly if problems other than unbalance are present. 7. Resonant Amplitude Magnification - The effects of unbalance may sometimes be amplified by resonance. Only a slight unbalance vibration can increase by a factor of 10 up to as much as 50 times if the rotor is operated at or near resonance with a system natural frequency. 8. Phase Behavior for Dominant Static, Couple and Dynamic Unbalance - Figure 13 illustrates typical phase measurements for a machine which has either static (Table A), couple (Table B) or dynamic (Table C) unbalance. Static Unbalance Phase - Table A shows a machine having dominant static unbalance. Note that the horizontal phase difference between the #1 and #2 bearings is about 5° (30° minus 25°) compared to a vertical phase difference of about 10° (120° - 110°). Similarly, over on the pump, the horizontal phase difference at positions 3 and 4 is about 10° and the vertical phase difference is about 15°. Couple Unbalance Phase - Table B illustrates typical couple unbalance phase readings. Note the 180° phase difference between positions 1 and 2 horizontal (210° - 30°), and the 175° phase difference between positions 1 and 2 vertical (295° - 120°). Dynamic Unbalance - Table C illustrates typical behavior for dynamic unbalance. Note that the horizontal phase difference between outboard and inboard bearings can be anything from 0° to 180°. However, whatever the phase difference in horizontal, the phase difference in the vertical should then be almost identical (within one clock position or +/- 30°). In the Figure 13 example in Table C, note the 60° phase difference between positions 1 and 2 in both the horizontal and vertical directions; while over on the pump at positions 3 and 4, the 10° difference in the pump horizontal readings compared to the 5° difference in the vertical (170° 165°). Key Point About Unbalance Phase Behavior - Whatever the phase difference between the outboard and inboard horizontal phase measurements on a rotor, the vertical phase difference between outboard and inboard bearings must be about the same (within +/- 30°), or the dominant problem is not unbalance. If, for example, the horizontal phase difference on a motor between its outboard and inboard bearings were 30°, while the outboard and inboard vertical phase difference was approximately 150°, an analyst would likely waste much time and effort if he attempted to balance the rotor.

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TABLE A

TABLE B

TABLE C

FIGURE 13 TYPICAL PHASE MEASUREMENTS WHICH WOULD INDICATE EITHER STATIC, COUPLE OR DYNAMIC UNBALANCE © Copyright 2001 Techncial Associates of Charlotte, P.C.


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CHAPTER 5 CAUSES OF UNBALANCE There are a variety of causes of unbalance. These can be summarized as follows: A. Assembly Errors - Sometimes occur after assembly when the mass center of rotation of one part does not line up with the mass center of rotation of the part to which it was assembled. For example, even if both a pump impeller and the pump shaft were separately precision balanced and then assembled, this can happen if the pump impeller had been balanced on a balancing shaft that fit its bore within 1 mil, but then was mounted on the shaft which itself allows a clearance of over 3 mils. This would shift the mass of the impeller/shaft rotor away from the shaft center which would throw the assembly out of balance, or at least cause it to have noticeably more unbalance than that when each part was separately balanced. B. Casting Blow Holes - Cast parts occasionally will be left with blow holes within them that might not be detectable by visual inspection means. Depending on the diameter of the rotor as well as its speed, this can throw it considerably out of balance. C. Fabrication Tolerance Problems - A common problem with parts such as a sheave deals with stack up of clearance tolerance. In this case, since the bore of the sheave is necessarily larger than that for the shaft diameter, when a key or setscrews is employed, the take-up in clearance shifts the rotating centerline of the sheave away from that of the shaft on which it is mounted. D. Key Length Problems - Use of no key or the wrong size of key can cause noticeable unbalance problems. Mr. Ralph Buscarello of Update International points out the great importance of employing a half-key (full key length, but half-key depth) when balancing couplings, impellers, sheaves, etc. Figure 14 helps explain why this is important. Mr. Buscarello recommends that a tag like the one shown in the figure should be attached to the finish balanced rotor any time a machine part is to be balanced and then mounted on a shaft. For example, if the coupling shown in Figure 14 had a “B” dimension of about 4 inches (101.6 mm) and an “A” dimension of 8 inches (203.2 mm), Mr. Buscarello recommends a final key length of about 6 inches [1/2 X (8 + 4) inches] or 152.4 mm [1/2 X (203.2 + 101.6) mm]. To further illustrate, assume a machine is to be outfitted with a 1/4" X 1/4" X 6" (6.4 mm X 6.4 mm X 152.4 mm) key, then both the coupling and the shaft should be outfitted with1/4" X 1/8" X 6" (6.4 mm X 6.4 mm X 152.4 mm) keys when balancing. Also assume this coupling is perfectly balanced, weighs 5 lbs (2.3 kg), will operate at 1800 RPM and will be mounted on a 4" (101.6 mm) shaft diameter. The following will illustrate the effect of not using the proper half-key:



5-1

Coupling outfitted with a 1/4" x 1/8" x 4" key (a)

Final key weight = (1/4" x 1/4" x 6" ) x .238 lb/in3 x 16 oz/lb = 1.698 oz (6” key)

(b)

Weight of 4" long key = (1.698)(4) = 1.132 oz (4" key) 6

(c)

Unused key weight if used only 4" half-key = 1.698 - 1.132 = .283 oz (unused half-key weight) 2

(d)

Distance of Key CG from shaft center = 2" radius + (1/2 x 1/8") = 2.0625"

(e)

So, if 6" half-key rather than a 4" half-key used, unbalance introduced when you insert 6" full key will be: 2.0625" x .283 lb. = .584 oz-in (unbalance introduced by wrong half-key length used to balance the coupling).

Then, referring to the ISO balance tolerance table shown in Figure 54 (on page 11-16), let us see how this would affect an otherwise perfectly balanced coupling installed on a rotor turning 1800 RPM. Assuming the coupling weight of 5 lbs and the unbalance of .584 oz-in introduced by the key, this corresponds to a residual unbalance of .1168 oz-in/lb which equals .0073 lbin/lb. Referring to Figure 54 at 1800 RPM, this would degrade the perfectly balanced coupling down to an ISO Balance Quality G 40, or one with a poor balance quality grade. Of course, if no half-key were used at all when balancing the coupling, this would introduce even more unbalance to the system. And, one of the real problems with this being a coupling is that the weight would be overhung from the motor bearing meaning that it could introduce considerable couple unbalance. This fact is often overlooked, particularly when dealing with couplings, most of which are not even factory balanced unless specifically requested by the end user.

Figure 14 SUGGESTED TAG THAT SHOULD ACCOMPANY FINISH BALANCED KEYED ROTOR (Ref. “Practical Solutions to Machinery and Maintenance Vibration Problems”, Update International).

5-2



E. Rotational Distortion - Sometimes, a part might be well balanced, but might distort when rotating due to stress relieving or thermal distortion. Parts fabricated by welding process or shaped by pressing, drawing, bending and so forth will sometimes have high internal residual stresses. If not relieved during the fabrication, they may begin doing so over a period of time when operating, distorting slightly and taking on a new shape. This can throw the rotor out of balance. In addition, some machines have problems with thermal distortion caused by such problems as uneven thermal expansion of parts when brought up to operating temperatures. This sometimes mandates that the rotor be balanced at its normal elevated operating temperature. F. Deposit Buildup or Erosion - Fan or impeller wheels are often thrown well out of balance due to buildup of deposits of dirt or other foreign matter brought into them by the pumping fluid or air. When small pieces of these deposits break away, it can sometimes introduce serious unbalance. On the other hand, some high-speed centrifugal compressor rotors are susceptible to erosion from small droplets of water traveling at very high speeds which impact the impeller rotors. This can cause uneven erosion of impeller surfaces and eventually can introduce considerable unbalance. G. Unsymmetrical Design - Unbalance can be introduced if good symmetry is not maintained in all parts. For example, rotor windings on electric motors are sometimes difficult to keep symmetrical; the thickness in sheaves sometimes vary from on side to the other; the density of coating finishes sometimes varies around the rotor periphery. Other problems can affect rotor symmetry, each of which can detrimentally affect rotor balance. In summary, all of the above causes of unbalance can exist to some degree in a rotor. However, the vector summation of all unbalance can be considered as a concentration at a point termed the “heavy spot”. Balancing, then, is the technique for determining the amount and location of this heavy spot so that an equal amount of weight can be removed at this location or an equal amount of weight added directly opposite.



5-3

CHAPTER 6 WHY DYNAMIC BALANCING IS IMPORTANT The forces created by unbalance can be among the most destructive forces in rotating machinery if left uncorrected. Not only will these forces damage the bearing but they have been know to crack foundations, break welds, etc. In addition, the vibration displacement due to unbalance can be detrimental to product quality in many applications. The amount of force created by unbalance depends on the speed of rotation and the weight of the heavy spot. Figure 15 represents a rotor with a heavy spot (W) located at some radius (R) from the rotating centerline. If the unbalance weight, radius and machine RPM are known, the force (F) generated can be found using the following formula: F = 1.77 x (RPM/1000)2 x ounce-inches

(EQUATION 2)

In this formula the unbalance is expressed in oz-inches and (F) is the force in pounds. The constant 1.77 is required to make the formula dimensionally correct. When the unbalance is expressed in terms of gram-inches, the force (F) in pounds can be found by using the following formula: F = 1/16 x (RPM/1000)2 x gram-inches

(EQUATION 3)

For unbalance expressed in gram-mm, the force (F) in kg can be calculated using the following formula: F = 0.001 x (RPM/1000)2 x gram-mm

(EQUATION 4)

From these formulas it can be seen that the centrifugal force due to unbalance actually increases by the square of the rotor RPM. For example, from Figure 16 we see that the force created by a 3 ounce weight attached at a radius of 30 inches (90 oz-in unbalance) and rotating at 3600 RPM is over 2000 lbs (907 kg). By doubling the speed to 7200 RPM, the unbalance force is increased to over 8000 pounds (3630 kg). From this we can see, especially on high-speed machines, a small amount of unbalance can create a tremendous amount of force.



6-1

CHAPTER 7 UNITS OF EXPRESSING UNBALANCE Units of unbalance in a rotating work piece is normally expressed as the product of the unbalance weight (lbs., oz., grams, etc.) and its distance from the rotating centerline (inches, mm, etc.), see Figure 15. The units for expressing unbalance are generally oz-inches, graminches, gram-mm, etc. For example, a 1 oz (28.35 gram) weight located at 10" (254 mm) from the rotating centerline would be 10 oz-inches, (7200 gram-mm) and a 2 oz (56.7 gram) weight located 6" (152.4 mm) from the rotating centerline would be 12 oz-in (8641 gram-mm). Figure 16 represents other examples of unbalance expressed as the product of weight and distance.

FIGURE 15. THE FORCE DUE TO UNBALANCE CAN BE FOUND IF THE UNBALANCE WEIGHT (W), RADIUS (R) AND ROTATING SPEED ARE KNOWN

FIGURE 16. CENTRIFUGAL FORCE EXERTED BY UNBALANCE (OZ-IN) AT VARIOUS SPEEDS © Copyright 2001 Techncial Associates of Charlotte, P.C.


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UNBALANCE UNITS

FIGURE 17. UNITS OF UNBALANCE ARE EXPRESSED AS THE PRODUCT OF THE UNBALANCE WEIGHT AND ITS DISTANCE FROM THE ROTATIONAL CENTER

7-2



CHAPTER 8 VECTORS Scalar quantities such as mass, time, volume, or force may be represented by a length of a single line in any arbitrarily chosen direction. A quantity, which has both magnitude and direction, is called a vector quantity. Describing a vector is giving it magnitude (length) and direction. Unbalance forces generate a magnitude equivalent to a certain number of ounces of weight or ounce-inches and an angular direction with respect to a reference point on the rotor, can be represented by a vector. It should be apparent that unbalance forces that tend to move the rotor away from its axis of rotation cause a certain magnitude. These forces and their exact location on the rotor cannot be measured directly. However, their effects on the rotor and/or bearing supports can be measured. An unbalance vector, then, can be described as a straight line whose length is proportional to the amount of unbalance and the angular direction measured from a reference point. The combined effect of several unbalances or balance weights can be determined by vector calculations. Examples of several vectors are shown in Figures 18. In Figure 18A, vectors are drawn to represent the radial location of weights. The length of the vector represents the radius in inches. Figure 18B vectors are shown to represent the weight in ounces. In Figure 18C, the vectors represent the amount of unbalance in ounce-inches. Balancing vectors are used to represent the amount and angular location of unbalance, as well as to measure the effect of trial weight when solving balancing problems.



8-1

FIGURE 18A. VECTOR RADIUS (LENGTH)

FIGURE 18B. VECTOR WEIGHT

FIGURE 18C. VECTOR UNBALANCE (RADIUS X WEIGHT) FIGURE 18 8-2



CHAPTER 9 DYNAMIC FIELD BALANCING TECHNIQUES Generally, it is best to balance a good majority of rotating machines in place since it can be done under the actual operating conditions and speed which exist during operation, in its own bearings and on its own foundation. In addition, balancing in-place eliminates the possible damage to the rotor during disassembly and transportation to a balancing machine. Following will be information on what techniques should be mastered in order to best accomplish field balancing using portable balancing equipment. Information on recommended techniques on performing field balancing including singleplane, two-plane, multi-plane and over-hung rotors will be discussed. In addition, instructions will be provided on directly related topics such as how to properly size trial weights, how to split balance correction weights when is not possible to place a single weight at the angular location specified by the solution, and how to vectorially combine the effects of several weights into one correction weight of just the right size and at just the right location. To begin with we will be discussing balancing using the vector method of balancing. Although there are many instruments with balancing programs in them on the market today, the mastering of the vector solution will give us a very good understanding of the effects that we should get and how to read the vector to determine if we made an error in our weight selection and location. We will later discuss the use of instruments with built in balancing programs. Although it is possible to balance any object with amplitude alone, we will begin our discussion of balancing using conventional vectors, both amplitude and phase. At the end of this chapter you will find the instructions for balancing using just the amplitude, called the Four Point Method of Balancing. A.

Recommended Trial Weight Size

It is important that the size of the trial weight be carefully chosen as well as the location at which the trial weight will be placed. If the trial weight is too large, damage may be done to the machine if the trial weight happens to be installed at or close to the rotor heavy spot producing even more vibration, particularly if the rotor is operating above critical speed. On the other hand, if the trial weight is too small, it may bring about no significant change in amplitude or phase that can cause significant error when calculations for the proper correction weight and location are made.



9-1

As a general rule, a trial weight should produce either/or both a 30% change in amplitude or a 30° phase change. In order to provide a sufficiently large trial weight effect, but without risking damage to the rotor, it is recommended that a trial weight which will produce an equivalent unbalance force at each bearing of about 10% of the rotor weight supported by each bearing should be installed. Therefore, referring to Equation (1), a similar equation can be derived to help the analyst choose a proper trial weight: FC =.000001775 Un2 = .00002841 Wrn2

(EQUATION 1 Repeated)

Solving for U: U = 563,380 FC n2

(EQUATION 5)

Now, assuming the trial weight should cause a 10% effect (.10 X U), TW = .10 X U = .10 (563,380) W = 56,338 W (with W=Bearing Load at this point) n2 n2 In order to make the equation easier for the analyst to use, double the constant (56,338) so that W can be considered the full rotor weight. Therefore, TW= 112,676W n2

(EQUATION 6)

Where: TW = Recommended Trial Weight Effect (oz-in) W = Weight of Rotating Part (lb) n = Rotating Speed (RPM)

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Now, if the radius at which the trial weight will be placed is known, the trial weight size that should be employed can be calculated as per the following: TW = U = mr Therefore: m = TW r Where:

(EQUATION 7)

m = Trial Weight Size (oz or grams) r = Radius at which Trial Weight will be placed (in) TW = Trial Weight Effect (oz-in or gram-in)

An example will serve to illustrate the use of these equations: Example - The rotor shown in Figure 19 is to be balanced. It has a weight of 453.6 kg., operates at 1800 RPM and has a 24" (609.6 mm) diameter wheel. To determine the recommended trial weight size (oz), TW = 112,676 W = (112,676)(1000) = 34.78 oz-in n2 (1800)2 (at 12" radius) Then, m = TW = 34.78 = 2.90 oz (Record trial weight size) r 12 The centrifugal force that would be developed by this 2.90 oz (82.2 gram) trial weight is: 2

Centrifugal Force = (.000001775)(34.78 oz-in)(1800) = 200.0 lb.



9-3

FIGURE 19. EXAMPLE ROTOR TO BE BALANCED is operated. In addition, the machine casings and inspection doors should be closed before operation in case the trial weights do accidentally come off the rotor. If it is not possible to close the casing or inspection door, a shield should be placed between the machine and the analyst for protection. The analyst and all others should place themselves to the side of the machine away from direction of rotation when the machine is operated. When attaching temporary clips or set-screwed trial weights, attempt to fasten these so that the centrifugal force is working for you to hold the weights (for example, if an analyst desires to attach a balance clip to fan blades, fasten them on the inside of the blades so that the throat rests against the blades inside surface). Finally, it is a good idea to identify the location of the trial weights by marking them in case they do happen to come off. B.

How A Strobe-Lit Mark on a Rotor Moves When a Trial Weight Is Moved

Figure 20 shows an important concept about how a phase reference mark moves relative to the movement of a trial weight. This often confuses analysts, but really is a simple concept if one takes a close look. In Figure 20A, a rotor is shown with the key weight at the top (or 0°). Most analysts will put their phase reference mark in line with the key weight or some other convenient reference point, but it really does not matter exactly where the reference mark is applied. If the pickup is located at point A, the 90° position, and has a zero response time (no electronic lag), the strobe light will flash when the heavy spot is at the 90° position, and the phase mark will be seen at the top or 0° position. Now please refer to Figure 20B where the weight has been moved 90° clockwise to point B at the 180° position. Again, note that the phase mark is still at the 0° location, or 180° away from point B where the trial weight is now located. If the strobe light now flashes when B is at the pickup (90° position), this means that point A written on the rotor is at the 0° position while the phase mark is over at the 270° position (180° away from the heavy spot). Note what happened. The weight was moved 90° clockwise, but the phase mark moved 90° counterclockwise. The direction of rotation does not matter. You get the same results. The point is this: If you want to move a phase reference mark clockwise, move the trail weight counterclockwise and vise versa. The reference mark always will shift in a direction opposite a shift of the heavy spot; and the angle that the reference mark shifts is equal to the angle that the heavy spot has shifted.

9-4



Instruments used to measure phase may or may not have an electronic lag, however, the effects will still be the same as discussed above. The fact that the phase shift is predictable can be used and the lag figured once the trial weight effect has been calculated. This will be discussed in more detail under “Balancing in One Run” later in this text.

FIGURE 20A. TRIAL WEIGHT AT LOCATION A (90° CLOCKWISE FROM PHASE REFERENCE MARK)

FIGURE 20A. TRIAL WEIGHT MOVED TO LOCATION B (180° CLOCKWISE FROM PHASE REFERENCE MARK)

FIGURE 20. HOW A STROBE-LIT REFERENCE MARK MOVES WHEN A TRIAL WEIGHT IS MOVED

C.

Single-Plane Balancing Using A Strobe Light And A Swept-Filter Analyzer

At the start of a balancing problem we have no idea how large the heavy spot is, nor do we know where on the part it is located. The unbalance in the part at the start of our problem is called the ORIGINAL UNBALANCE, and the vibration amplitude and phase readings that represent the unbalance are called our ORIGINAL READINGS. In the beginning we must tune our analyzer to a frequency of 1X RPM at which time our strobe light will flash at a rate equal to 1X RPM. When in the filtered mode on the analyzer, this flashing strobe will appear to “freeze” the rotor and our reference mark will appear to be stopped. For example, the part in Figure 21 has an original unbalance of 5.0 mils (127 microns) at 120°. Once the original unbalance has been noted and recorded, the next step is to change the original unbalance by adding a TRIAL WEIGHT to the part. The resultant unbalance in the part will be represented by a new amplitude and phase of vibration. The change caused by the trial weight can be used to learn the size and location of the original unbalance, or where the trial weight must be placed to be opposite the original unbalance heavy spot, and how large the trial weight must be to be equal to the original heavy spot.



9-5

FIGURE 21. THIS ROTOR HAS AN ORIGINAL UNBALANCE OF 5.0 MILS (127 microns) AND 120° PHASE By adding a trial weight to the unbalanced part, one of three things might happen: 1) First, if we are lucky, we might add the trial weight right on the heavy spot. If we do, the vibration will increase, but the reference mark will appear in the same position it did on the original run. To balance the part, all we have to do is move the trail weight directly opposite its first position, and adjust the amount of the weight until we achieve a satisfactory balance. 2) The second thing that could happen is that we could add the trial weight in exactly the right location opposite the heavy spot. If the trial weight were smaller than the unbalance, we would see a decrease in vibration, and the reference mark would appear in the same position as seen on the original run. To balance the part, all we would have to do is increase the weight until we reached a satisfactory vibration level. If the trial weight were larger than the unbalance, then its position would now be the heavy spot, and the reference mark would shift 180°, or directly opposite where it was originally. In this case, all we would have to do to balance the part is reduce the amount of the trial weight until we achieved a satisfactory level. 3) The third thing that can happen by adding a trial weight is the usual one where the trial weight is added neither at the heavy spot, nor opposite it. When this happens, the reference mark shifts to a new position, and the vibration amplitude may change to a new amount. In this case, the angle and direction the trial weight must be moved, and how much the weight must be increased or decreased to be equal and opposite the original unbalance heavy spot, is determined by making a VECTOR DIAGRAM.

9-6



D.

Single-Plane Vector Method Of Balancing

A vector is simply a line whose length represents the amount of unbalance and whose direction represents the angle of the unbalance. For example, if the vibration amplitude is 5.0 mils (127 microns) and the phase reference mark position is 120°, the unbalance can be represented by a line with an arrowhead (a vector) 5.0 divisions long pointed at 120° as illustrated in Figure 22. To simplify drawing vectors, polar coordinate graph paper like that shown is normally used. The radial lines, which radiate from the center, or origin, represent the angular position of the vector and are scaled in degrees increasing in the clockwise direction. The concentric circles with a common center at the origin are spaced equally for plotting the length of vectors. When a trail weight is added to a part, we actually add to the original unbalance. The resultant unbalance will be at some new position between the trail weight and original unbalance. We see this resultant unbalance as a new vibration amplitude and phase reading. In Figure 22, our ORIGINAL unbalance was represented by 5.0 mils (127 microns) and a phase of 120°. After adding a trial weight, Figure 23A, the unbalance due to both the ORIGINAL PLUS THE TRIAL WEIGHT is represented by 8 mils (203 microns) and a phase of 30°. These two readings can be represented by vectors. Using polar graph paper, the ORIGINAL unbalance vector is plotted by drawing a line from the origin at the same angle as the reference mark, or 120°, as shown in Figure 22. A convenient scale is selected for the length of the vector. In this example, each major division equals 1.0 mil (25.4 microns). Thus, the ORIGINAL unbalance vector is drawn 5 major divisions in length to represent 5 mils (127 microns). The vector for the ORIGINAL unbalance is labeled “O”. Next, the vector representing the ORIGINAL PLUS THE TRIAL WEIGHT unbalance is drawn to the same scale at the new phase angle observed. For our example, this vector will be drawn 8 major divisions in length to represent 8.0 mils (203 microns) at an angular position of 30° that was the new phase angle. The ORIGINIAL PLUS THE TRIAL WEIGHT vector is labeled “O + T” in Figure 23A. These two vectors, together with the known amount of trial weight, are all that’s needed to determine the required balance correction - both weight amount and location.

FIGURE 22 AN UNBALANCE OF 5 MILS (127 Microns) AT 120° CAN BE REPRESENTED BY A VECTOR DRAWN 5 DIVISIONS LONG AND POINTING AT 120° © Copyright 2001 Techncial Associates of Charlotte, P.C.


9-7

A B FIGURE 23. THE SINGLE-PLANE VECTOR SOLUTION To solve the balancing problem, the next step is to draw a vector connecting the end of the “O” vector to the end of the “O + T” vector as illustrated in Figure 23 B. This connecting vector is labeled “T” and represents the difference between vectors “O” and “ “O + T” (O + T) - (O) = T. Thus, vector “T” represents the effect of the trial weight alone. By measuring the length of the “T” vector using the same scale used for “O” and “O + T”, the effect of the trial weight in terms of vibration amplitude is determined. For example, vector “T” in Figure 3B is 9.4 mils (239 microns) in length. This means that the trial weight added to the rotor produced an effect equal to 9.4 mils (239 microns) of vibration. This relationship can now be used to determine how much weight is required to be equivalent to the original unbalance, “O”. The correct balance weight is found following the formula: Correction weight = Trial weight x O (EQUATION 8) T For our example, assume that the amount of trial weight added to the rotor in Figure 21 is 10 grams. From the vector diagram, Figure 23B, we know that “O” = 5.0 mils (127 microns) and “T” = 9.4 mils (239 microns). Therefore:

or

Correction weight = 10 grams x 5 mils = 5.3 grams 9.4 mils Correction weight = 10 grams x 127 microns = 5.3 grams 239 microns

To balance a part, our objective is to adjust vector “T” to make it equal in length and pointing directly opposite the original unbalance vector “O”. In this way, the effect of the correction weight will serve to cancel out the original unbalance, resulting in a balanced rotor. Adjusting the amount of weight according to the correct formula will make vector “T” equal in length to the “O” vector. The next step is to determine the correct angular position of the weight. The direction in which the trial weight acts with respect to the original unbalance is represented by the direction of vector “T”. See Figure 23B. Vector “T” can always be thought of as pointing away from the end of the “O” vector. Therefore, vector “T” must be shifted by the included angle (O) between vector “O” and vector “T” in order to be opposite vector “O”. Of course, in order to shift vector “T” the required angle, it will be necessary to move the trial weight by the same angle. From the vector diagram, Figure 23B, the measured angle (O) between “O” and “T” is 58°. Therefore, it will be necessary to move the weight 58°. 9-8



Remember, the trial weight is moved from its position on the part through the angle determined by the vector diagram. This is not an angle from the reference mark, but is the angle from the initial position of the trial weight to the required position. To determine which direction we must move the weight, i.e., clockwise or counterclockwise, you will recall from our experiment in Figure 20 that the reference mark shifts in a direction opposite a shift of the heavy spot. Therefore, the following rule should be used to determine which direction the weight must be shifted: Always shift the trial weight in the direction opposite the observed shift of the reference mark from “O” to “O + T”. Thus if the reference mark shifts counterclockwise from “O” to “O + T”, the trial weight must be moved in a clockwise direction. Or, if the observed phase shift is clockwise, then the weight must be moved counterclockwise. This rule applies regardless of the direction of rotation of the rotor. By following these instructions carefully, the part should now be balanced. However, very small errors in measuring the phase angle, in shifting the weight, and adjusting the weight to the proper amount can result in some remaining vibration still due to unbalance.

FIGURE 24 UNBALANCE CAN BE FURTHER REDUCED BY MAKING A VECTOR DIAGRAM USING THE NEW “O+T” VECTOR ALONG WITH THE ORIGINAL “O” VECTOR If further correction is required, simply observe and record the new amplitude and phase of vibration. For example, assume that the balance correction applied according to the vector diagram in Figure 24 resulted in a new amplitude reading of 1.0 mil (25.4 microns) and a new phase reading of 270°. Plot this new reading as a new “O+T” vector on the polar graph paper along with the original unbalance vector “O” as shown in Figure 24. Next, draw a line connecting the end of the original “O” vector to the end of the new “O+T” vector to find the vector “T”. Measure the length of the new “T” vector. In the example, Figure 24, “T” = 5.9 mils (150 microns). Using the new value for vector “T” proceed to find the new balance correction weight using the familiar formula: CORRECT WEIGHT = TRIAL WEIGHT X O T © Copyright 2001 Techncial Associates of Charlotte, P.C.


9-9

Remember that the value for the trial weight applied to this formula is the amount of weight presently on the rotor and not the value of the trial weight applied on the first trial run. In this example, the original trial weight was 10 grams; however, this was adjusted to 5.3 grams as a result of our first vector solution, Figure 23. Therefore, to solve for the new correct weight the formula becomes: CORRECT WEIGHT = 5.3 grams X 5.0 mils = 4.5 grams 5.9 mils or CORRECT WEIGHT = 5.3 grams X 127 microns = 4.5 grams 150 microns To determine the new location for the correction weight, measure the included angle between the original vector “O” and the new “T” vector. In the example, Figure 24, this measured angle is approximately 5°, and since the phase shift from “O” to the new “O+T” is clockwise, the weight must be shifted 5° counterclockwise. Applying this new balance correction should further reduce the unbalance vibration. This procedure may be repeated as many times as necessary using the new “O+T” and trial weight value, but always using the original “O” vector. E.

Balancing in One Run

At the start of a balancing problem, we have no way of knowing exactly how much weight is required or where the weight must be added to balance the part. However, once a part has been balanced, it is possible to determine how much and where weight must be added (or removed) to balance the unit or similar units in the future - in only one run. We have learned that the amplitude of vibration is directly proportional to the unbalance weight. Further, we also know how much vibration will result from a given amount of unbalance. We have also learned that the phase of the reference mark moves in a direction opposite the shift of the heavy spot. Should it be necessary to rebalance this rotor or a like rotor in the future, it will be a simple matter to determine the amount of correction weight needed. We may find that we have many like rotors in our plant and this “One Run Balancing” will save extensive hours attempting to balance rotors. An unbalance constant can be worked out for any rotor. After you have successfully balanced the part the first time using the 4-step or vector method, simply divide the final balance weight by the original amplitude of vibration. For example, if the original amplitude of vibration was say, 12 mils (305 microns), and after balancing you note that a correction weight of 18 grams has been added, then this rotor has an unbalance constant or rotor sensitivity of:

or

9-10

18 grams = 1.5 grams/mil 12 mils 18 grams = 0.059 grams/micron 305 microns © Copyright 2001 Techncial Associates of Charlotte, P.C.


If this rotor requires rebalancing in the future, the amount of balance weight needed can easily be determined by simply multiplying the new original amplitude times the constant of 1.5 grams/mil. In addition to the UNBALANCE WEIGHT/VIBRATION AMPLITUDE constant, there is another constant relationship, which can be determined for finding the location of the unbalance. The position of the heavy spot in a rotor relative to the vibration pickup is defined as the “FLASH ANGLE” of the system. The flash angle of a rotor is the angle, measured in the direction of shaft rotation, between the point where the vibration pickup is applied and the position of the heavy spot when the strobe light flashes. See Figure 25.

FIGURE 25. FLASH ANGLE The reference mark has nothing to do with this relationship since it can be placed anywhere on the rotor. The reference mark simply allows us to see the position of the rotor when the strobe light flashes. To find the flash angle for a part, proceed as follows: 1. Note the original unbalance readings and proceed to balance the part using the vector or 4-step method. 2. After the rotor has been balanced successfully, stop the work piece and turn it until the reference mark is in the same position observed under the strobe light on the original run. 3. With the rotor in this position, note the location of your applied balance weight. This represents the location of the original “light spot” of the rotor. Of course, 180° away or directly opposite the original light spot is the original “heavy spot”. 4. Following the direction of shaft rotation, note the angle between the point where the vibration pickup is applied and the position of the heavy spot. This measured angle is the “flash angle”. © Copyright 2001 Techncial Associates of Charlotte, P.C.


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After the weight constant and flash angle for a part have been learned, it is a simple matter to rebalance the part in the future. The information learned by balancing one rotor can be used for other rotors. The RPM, pickup location and machine configuration (i.e. mass, stiffness, etc.) must be the same each time. To balance a part in “one run” proceed as follows: 1. Operate the machine and record the unbalance data - amplitude and phase. 2. Stop the machine and turn the rotor until the reference mark is in the same position observed under the strobe light. 3. With the rotor in this position, measure off the flash angle from the pickup in the direction of shaft rotation to find the heavy spot of the rotor. 4. Next, multiply the unbalance constant times the amplitude of unbalance vibration to find the amount of weight, which must be either removed from the heavy spot or added on the light spot directly opposite. F.

Two-Plane Balancing Techniques

Two-plane balancing is done in much the same manner as single-plane balancing. There are, however, a number of balancing techniques commonly in use, which will yield good results depending upon the type of unbalance problem encountered. The choice of balancing techniques will depend on several factors, such as unbalance configuration, length-to-diameter ratio, balance speed compared to operating speed of the rotor, rotor flexibility and amount of cross-effect. Two-plane balancing techniques are: 1. Separate single-plane approach - used when the rotor length-to-diameter ratio is large. 2. Simultaneous single-plane approach - used when the rotor length-todiameter ratio is large and the original unbalance vector indicates a predominantly static or dynamic unbalance configuration. 3. Force/Couple Derivation - used on overhung rotor configuration and some standard rotors. 4. Two-Plane Vector Calculations a) Graphical method b) Using an automatic balancing instrument or programmable handcalculator.

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G. Cross-Effects Two-plane balancing requires special attention because of “cross-effects”. “Cross-effect, sometimes called “correction plane interference”, can be defined as the effect on the unbalance indication at one end of a rotor caused by unbalance at the opposite end. Cross-effect can best be explained by assuming the rotor in Figure 26A is perfectly balanced. Adding an unbalance in the right correction plane, Figure 26B, results in a vibration reading at the right bearing of 5.0 mils (127 microns) at 90°. At the left bearing a vibration of .66 mils (17 microns) is also noted with a phase of 300°. This vibration is due to cross-effect. That is, the vibration at the left bearing is caused by the unbalance in the right correction plane.

FIGURE 26. CROSS-EFFECTS To see what this does to two-plane balancing, note that an unbalance added in the left correction plane, Figure 26C, changes the amount and phase of vibration at the right bearing to 6.4 mils (163 microns) at 120°. © Copyright 2001 Techncial Associates of Charlotte, P.C.


9-13

Because of cross-effect, the unbalance indications observed at each end of a rotor do not truly represent the unbalance in their respective planes. Instead, each indication will be the resultant of unbalance in the associated correction plane plus cross-effect from the opposite end. At the start of a balancing problem, there is no way of knowing the amount and phase of cross-effect. In addition, the amount and phase of cross-effect will be different for different machines. H.

Single-Plane Method for Two-Plane Balancing

Cross-effect must be taken into consideration when balancing in two planes. There are many ways to do this. The most popular way is to treat each correction plane problem using the nearest bearing for the vibration readings. With this procedure, each plane is balanced individually, one at a time. 1. Observe the amplitude and phase of vibration at both bearings and select the bearing with the most vibration to balance first. 2. Using the single-plane vector method described earlier, proceed to balance the end having the highest vibration by making weight corrections in the nearest correction plane. 3. After the first plane has been successfully balanced, observe and record the new amplitude and phase data for the second end. These amplitudes and phase readings are the “original” readings for starting the second plane balancing operation. Balancing the first end will usually result in a new set of readings at the second end because the unbalance in the first correction plane creating cross-effect has been removed. 4. Using the new data, proceed to balance the second end using the standard single plane vector technique. 5. After the second plane has been balanced, you will likely find that the first plane has changed. This is due to the fact that the cross-effect of unbalance in the second plane to the first plane (which was originally compensated for in the first plane) has now been eliminated. In any case, if the change is an increase to an unacceptable level, the first correction plane must be rebalanced. Therefore, observe and record the new unbalance data for the first plane and using this data as your original reading, proceed to rebalance. Do not disturb the previously applied balance corrections. Start with a new trial weight and rebalance as a new problem. 6. If the cross-effect is especially severe, this procedure may have to be repeated several times, alternately balancing first one end and then the other end until both ends are balanced to an acceptable level. Each time correction planes are changed, a new problem is started using the new original readings. Do not disturb the previous corrections.

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The single-plane vector method for two-plane balancing is a good example of where knowing the “flash angle” and weight constant of the rotor would be most helpful in reducing the number of balancing runs. After balancing the first end, this information can be learned and used for all subsequent balancing operations needed to reduce the unbalance at each end of the rotor. In some cases, extremely severe cross-effect may be encountered to make two-plane balancing very difficult using the single-plane vector method. Some systems may reveal cross-effect where unbalance in one correction plane has great effect on the indicated vibration at the bearing furthest away instead of the closest bearing. When this happens, the cross-effect is said to be greater than 100%. The rotor configurations in Figure 27 will often have cross-effect greater than 100%. When this is encountered, one solution might be to simply “switch” correction planes. For example, referring to the rotor in Figure 27A, balance in correction plane “X” using the vibration readings at bearing “B”, and balance in correction plane “Y” using the vibration readings at bearing “A”. A special procedure is outlined later for balancing overhung rotors such as that illustrated in Figure 27B.

A

B

FIGURE 27 THE ROTOR CONFIGURATION SHOWN WILL OFTEN HAVE VERY LARGE CROSS-EFFECTS

I.

Vector Calculations For Two-Plane Balancing

If it were not for cross-effect, two-plane balancing could be accomplished in only three balancing runs or start-stop operations by making trial weight additions in both balancing planes at the same time, and constructing vector diagrams to get the proper solution. Unfortunately, cross-effect is always present to some degree. Therefore, you can expect to use many balancing runs to get a good balancing using the single plane vector technique. However, some machines may require from one-half hour to a full day for only one start-stop operation. On such machines, it would be most helpful to be able to minimize the number of balancing runs. When a considerable amount of time is required to start and stop a machine, or where severe cross-effect is encountered, the balancing problem can be greatly simplified by using the TWO-PLANE VECTOR METHOD.



9-15

In brief, the two-plane vector solution makes it possible to balance in two planes with only three start-stop operations. First, the original unbalance readings are recorded at the two bearings of the machine. Next, a trial weight is added to the first correction plane and the resultant readings at both bearings are again recorded. Finally, the trial weight is removed from the first correction plane and a trial weight added to the second correction plane. With this weight in the second plane, the resultant readings at both bearings are again noted and recorded. Using the data recorded from the original and two trial runs, together with the known amount and location of the trial weights, a series of vector diagrams and calculations make it possible to eliminate the cross-effect of the system, and find both the amount and location of balance weight needed in each correction plane. The two-plane vector solution requires from 15-30 minutes to complete. Therefore, it is essential that the data used be as accurate as possible. The most important readings taken are phase measurements. It is suggested that a phase reference card be used. This card can be made from a piece of vector paper and attached to cardboard of other stiff material. The center is cut out so that it may be held up to the center of shaft and the phase mark read directly. Other means such as a plastic phase reference card may be used. The calculation data sheet in Figure 28 has been developed for the two-plane vector calculation to serve as a guide and simplify recording of data. The Roman Numerals in the far left column correspond to the steps outlined in the detailed procedure below. The NEAR END (N) refers to the bearing observed; and the FAR END (F) refers to the opposite bearing and correction plane. Phase measurements for both the near end and far end must be taken using the same reference mark and phase reference card. The procedure is as follows:

9-16

1.

With the machine operating at the balancing speed and your analyzer filter properly tuned to a frequency that is equal to 1X RPM, observe and record the original phase for the near end (Item #1); the original amplitude for the near end (Item #2); the original phase for the far end (item #3), and the original amplitude for the far end (Item #4).

2.

Stop the machine and add a trial weight in the NEAR END correction plane. Record in (Item #5) the angular position of the trial weight in degrees clockwise from the reference mark. (For example, with the trial weight in the position shown in Figure 29, we would record 240°.) Enter the amount of the trial weight as (Item # 6).



FIGURE 28. TWO-PLANE VECTORS CALCULATION DATA SHEET © Copyright 2001 Techncial Associates of Charlotte, P.C.


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FIGURE 29. RECORD THE POSITION OF THE TRIAL WEIGHT IN DEGREES FROM THE REFERENCE MARK. HERE THE WEIGHT IS AT 240° 3.

With the trial weight in the near end correction plane, operate the rotor at balancing speed. Observe and record the new phase for the near end (Item #7); the new amplitude for the near end (Item #8); the new phase for the far end (Item #9); and the new amplitude for the far end (Item #10).

4.

Stop the machine and REMOVE the near end trial weight. Using the same weight or different weight if you prefer, add a trial weight at the far end correction plane. Record as (Item #11) the position of the weight in degrees clockwise from the reference mark (as viewed from the near end). Record the amount of this trial weight as (Item #12).

5.

With the trial weight in the far end, again operate the rotor at the balancing speed. Observe and record the new phase reading for the near end (Item #13); and new amplitude for the end (Item #14); the new phase reading for the far end (Item #15); and the new amplitude for the far end (Item #16).

6.

Using polar graph paper, construct vectors N, F, N2, F2, N3 and F3 by drawing each at the observed phase angle, and to a length corresponding to the measured amplitude of vibration. For example, the vectors in Figure 30 have been drawn from the sample data in Figure 28. NOTE: For accuracy, use the largest scale possible for constructing your vectors.

FIGURE 30 9-18



7.

Construct vector A by drawing a line connecting the end of vector N to the end of vector N2. See Figure 31. You will note on the data form in Figure 28 that vector A is designated A = (N2). This notation is given to indicate the direction of vector A and means that vector A is pointing from the end of vector N towards the end of vector N2. This direction is very important for finding the angle of vector A, (Item #17). The angle of vector A is found by transposing vector A back to the origin of the polar graph as illustrated in Figure 31. A parallel ruler or set of triangles can be used to accurately transpose vector A parallel back to the origin. For our example, the angle of vector A is 201° and is entered as (Item #17). The amplitude of vector A, (Item #18) is found by simply measuring its length using the same scale selected for vectors N, F, N2, etc. From our example, Figure 31, vector A = 7.6 mils (193 microns). Following the same procedure used to find the angle and amplitude of vector A, proceed to find the values for vector B = (F3); ∝ A = (F2); and B = (N3). Enter these values on the data form as (Items #19 through Items #24).

FIGURE 31 (Figure repeated for convenience of reader)



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8.

Do the calculations as indicated to find the values for (Items #25 through Items #32). Note that the numbers indicated in the “Calculation Procedures” column of the data sheet are all referring to Item Numbers. Thus 25 = 21-17 means that the value of Item #25 is found by subtracting the value of (Item #17) from the value of (Item #21).

NOTE: During the calculations, you may find that some of your answers will be negative (-) angles or angles larger than 360°. A negative angle, say -35°, may be converted to an equivalent positive angle by subtracting the angle from 360°. Thus 360°- 35°= 325°. An angle which is larger than 360° is converted to one less than 360° by subtracting 360° from the angle. For example, 463° - 360°= 103°. 9.

Construct vectors ∝ N and BF in the same way and to the same scale used for vectors N, F, etc. The angle and length of vector ∝ N are obtained from your calculated data, (Items #31 and #32) to construct vector BF.

10. Following the same procedure used to construct vectors A, B, etc., in step 7 above,proceed to construct vector C = (N BF) and vector D = (F ∝ N). Find and enter the values for vectors C and D, (Items 33 through 36). 11. Calculate the values for (Items #37 and #38) following the same procedure outlined for (Items #25 through #32) in step 8 above. 12. Using a new sheet of polar graph paper, construct the UNITY VECTOR (U), 1.0 unit long at an angle of 0°. Note that the values for the unity vector have already been entered on the data form as (Items #39 and #40). The unity vector is always 1.0 unit at 0° for all two-plane vector problems. A suggested scale for the unity vector is 1.0 unit = 2.5 inches. (63.5 mm) See Figure 32. NOTE: Do not confuse the UNITY VECTOR scale with that used to designate the amplitude of vibration for vectors N, F, N2, etc. The unity vector can be thought of as a dimensionless vector. This is why it is suggested that a separate sheet of graph paper be used, to help avoid confusion.

FIGURE 32. UNITY VECTOR PLOT 9-20



13.

On the same graph paper with the unity vector, construct vector ∝B using the same scale selected for the unity vector. The values for ∝B are obtained from your calculated data, (Items #37 and #38). Remember, the value of vector ∝B (Item #38) is expressed in units. Therefore, in the sample, Figure 32, ∝B = 0.22 units long at an angle of 311°.

14.

Following the same procedure used to construct vectors A, B, etc, in step 7, construct vector E =(∝ ∝B U). Find and enter the values for vector E, (Items #41 and #42). Remember to measure the length of ∝B, (Item #42) using the same unity scale.

15.

Calculate the values for (Items 43 through #54), following the same procedure outlined in step 8 above. (Items #51 and #52) Represent the position and amount of the balance weight needed for the NEAR END correction plane. The angles for locating the balance weights are clockwise from the reference mark.

16.

Before applying the new balance correction weights as indicated by (Items #51 through #54), it is suggested that a graphic check of your solution be made as outlined below. This check will reveal whether or not any errors have been made in the solution. A.

On a new sheet of polar graph paper, construct vector O-A from your calculated data (Items #43 and #44); and construct vector O/B from (Items #45 and #46). For the length of vectors, use the same scale selected for your original vectors N, F, N2, etc.

B.

Calculate the amplitude and angle values for vector Ο/BB. Amplitude = (Item #50 x Item #24); and the angle = (Item #49 + Item #21).

C.

Calculate the amplitude and angle values for vector Ο-∝ A. Amplitude = (Item #40 x Item #22); and the angle = (Item (#47 + Item #21).

D.

Using the calculated values, proceed to construct vectors ∅ BB and ∅ A to the same scale used for ∅ B and ∅ A. See Figure 33.

E.

Construct vector X by adding vector ∅ A and ∅ BB. This is done by completing the parallelogram as shown in Figure 34. The diagonal of this parallelogram is vector X that should be equal in length but directly opposite the original N vector.

F.

Construct vector Y by adding vectors ∅ /B and ∅ -∝ A, again by completing the parallelogram. Vector Y should be equal in length and directly opposite your original F vector. See Figure 34.

G.

If vectors N and X or vectors F and Y are not equal and opposite, this indicates that an error has been made in the solution.



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FIGURE 33. GRAPHIC CHECK SOLUTION

FIGURE 34.

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17.

If the graphic check indicates that your solution has been done correctly, proceed to make the balance corrections as indicated in step 15. Be sure the trial weight added in step 9 has been removed.

18.

With the balance corrections applied, operate the rotor and check to be sure the vibration has been reduced to an acceptable level.



19. If the applied corrections significantly reduced the unbalance, yet further correction is required, observe and record the new unbalance data - amplitude and phase - for the near and far ends. Enter this data as items 1 through 4 on a new two-plane vector data sheet. Also enter on the new form those items marked by an asterisk (*) from the original data (i.e. items 5, 6, 11, 12, 17, 18, 19, 21, 25, 26, 27, 28, 41 and 42). Now, simply recalculate items 29 through 36 and 43 through 54 to find the additional balance corrections required. Do not disturb your previous corrections. Here also, the GRAPHIC CHECK can be performed to verify that your solution is correct before applying the additional corrections. The procedure for applying further balance corrections can be of great value if this rotor should require rebalancing any time in the future. Simply attach the vibration pickups in the same position used during the original balancing, and take phase readings using the same reference mark. Enter the new unbalance data on the data sheet as items 1 through 4. From the original balance data, enter those items marked by an asterisk (*) and simply recalculate to find the new required balance corrections. In summary, once the two-plane vector calculation has been worked successfully for a particular rotor, this rotor can be balanced in two-planes in the future in only one run. J.

Rotor Balancing By Static Couple Derivation

The static-couple method is a multi-plane (3 plane) balancing technique frequently used for balancing large turbo-rotors. This procedure, referred to here as STATIC COUPLE DERIVATION, is based on the premises that: Any condition of rotor unbalance can be identified as either static unbalance, couple unbalance or a combination of static and couple unbalance. For a condition of combined static and couple unbalance, the static and couple unbalance components can be vectorially derived and corrected separately. By correcting for a portion of the derived static unbalance in a reference at or very near the plane which includes the rotor center of gravity, the static unbalance responsible for the first rigid (structural) resonance as well as the first rotor critical will be minimized. Further, by correcting the couple unbalance in reference planes near the ends of the rotor, the second rigid mode and second rotor critical will be minimized. Although the static-couple derivation technique is clearly a compromise approach and may not prove effective for all flexible rotor balancing, experience reveals that this technique does produce satisfactory results when applied to slow-speed balancing of large turbo-generator rotors. However, the application is by no means limited to multi-plane balancing of flexible rotors, such as large motor armatures and industrial fans.



9-23

One argument for this procedure, even when applied to two-plane balancing problems, is that deriving the static and couple unbalance components allows balancing to be performed in two reference planes simultaneously - without fighting annoying cross-effect. Others prefer this method for in-place balancing of high-speed equipment which must pass through resonant points during startup and coast down. By locating static and couple trial weights with the aid of phase-lag information, the result will nearly always be a reduction in vibration. The procedure of balancing by STATIC-COUPLE DERIVATION can be illustrated using a typical dynamic unbalance problem with original readings of: Original Right (OR) = 6 mils (152 microns) at 30° Original Left (OL) = 8 mils (203 microns) at 130° 1)

Using polar-coordinate graph paper, construct vectors OR and OL to the same scale. See Figure 35.

2)

Connect the end of vector OR to the end of vector OL and find the mid-point of the intersecting line.

3)

Draw a line from the origin to the midpoint of the interconnecting line. This vector represents the original static unbalance So . For the example, Figure 35, SO = 4.6 mils (117 microns) at 90°. The divided interconnecting line further represents the couple unbalance, with CR representing the couple component acting on the right side and CL representing the couple component on the left. In Figure 35, the couple unbalance vectors have been transposed parallel through the origin revealing CR = 5.4 mils (137 microns) at 343° and CL = 5.4 mils (137 microns) at 163°.

With the static and couple unbalance vectors derived, either the static or the couple unbalance can be corrected first, whichever is preferred. Or, since true static corrections will not influence the couple and vice versa, with a little care both the static and couple corrections can be carried out simultaneously. However, for simplification, the following example illustrates the correction of the static unbalance first followed by correction of the couple unbalance. 4)

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With the original static unbalance vector (SO) derived as illustrated in Figure 35, proceed to apply a static trial weight. A static trial weight can be applied as a single weight in the reference plane that includes the rotor center-of-gravity (C.G.) as illustrated by the examples in Figure 36.



FIGURE 35. STATIC COUPLE DERIVATION UNBALANCE VECTORS DETERMINED GRAPHICALLY

FIGURE 36. STATIC TRIAL/CORRECTION WEIGHT LOCATIONS If it is not possible to add or remove balance weight at the center plane of the rotor, the static correction can be divided and added in-line at the end planes as shown in Figure 36B. Figure 36 also illustrates that the static-couple technique can be applied to non-symmetrical rotors as long as the moments created by the trial and correction weights are equal about the rotor center of gravity. This may require that balance weights be adjusted to compensate in each plane. © Copyright 2001 Techncial Associates of Charlotte, P.C.


9-25

For example, assume that a static trial weight of 50 grams (T.W. = 50 grams) has been added at the center reference plane, resulting in new unbalance reading of: (O + T)R = 3.6 mils (91 microns) at 313° (O + T)L = 7.8 mils (198 microns) at 176° 5)

On polar graph paper, construct vectors (O + TR) and (O + TL) to the same scale used for OR and OL. See Figure 37.

6)

Connect the end of vector (O +TR) to the end of vector (O + TL) and find the midpoint of this interconnecting line.

7)

Draw a line from the origin to the midpoint of the interconnecting line. This vector represents the original-plus-trial static unbalance (SO + T). From Figure 37, SO + T =2.9 mils (74 microns) at 202°. NOTE: It is significant to note in Figure 37 that the interconnecting line joining (O + TR) and (O + TL) is equal in length and parallel to the interconnecting line in Figure 35. This indicates that the static trial weight has been located in the reference plane which includes the center of gravity, and the couple unbalance has not been disturbed. Determining that static and couple trial weights do not disturb one another is important, particularly when working both static and couple solutions simultaneously.

FIGURE 37. VECTOR DIAGRAM SHOWING RESULTS OF ADDING TRIAL WEIGHT

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FIGURE 38. VECTOR DIAGRAM SHOWING STATIC PART OF COMPUTATION 8).

With vectors SO and SO + T derived from Figures 35 and 37, a standard single-plane vector solution can be completed to correct for the static unbalance. This vector is shown in Figure 38. The resultant vector ST = 6.3 mils. From this the correct weight can be calculated. CW =TW X O T = 50 grams X 4.6 mils 6.3 mils = 36.5 grams or CW = 50 grams x 117 microns 160 microns = 36.5 grams The included angle between SO and ST is 25°, and the direction of phase shift from SO to SO + T is clockwise. Thus, the 50 gram trial weight should be reduced to 36.5 grams and shifted 25° counterclockwise to correct for the static unbalance.

9).

Repeat steps 5 through 8 above as required to reduce the static unbalance to acceptable limits. If the static unbalance was completely corrected, the result would be equal amplitudes by opposite (180°) phase readings, indicating that only the couple unbalance remains. For the example given in Figure 35, eliminating the static unbalance would result in a couple unbalance with readings of: CR = 5.4 grams at 343° CL = 5.4 grams at 163°



9-27

10)

The derived or resultant couple unbalance is corrected by applying trial weights in the form of a “couple” as illustrated in Figure 39. The vector calculations can be carried out using measurements from either the right or left side. When a trail weight or correction weight is applied at one end, simply apply an equal weight at the other end - 180° away.

11)

Using trial and correction weights in the form of a couple, proceed to balance for the couple unbalance using standard vector methods.

FIGURE 39. COUPLE UNBALANCE CORRECTIONS When the static-couple technique is used for slow speed balancing of turbo-generator rotors or other flexible rotors, a common practice is to divide the final static correction over several reference planes along the length of the rotor instead of concentrating the entire correction at the C.G. reference plane. This practice is based on the assumption that the static unbalance of the rotor will not all be concentrated at the center, but will generally be distributed along the entire rotor. Thus, if the static unbalance of the entire rotor was corrected by a single weight in the center, this would very likely over compensate for unbalance at the center, resulting in excessive deflection at the rotor bending critical speed and excessive unbalance vibration at normal operating speeds. In some cases, the static balance may be distributed equally among the number of reference planes available. In other cases, a measure of rotor run-out is used as the criteria for determining static correction distribution. If there is no run-out, the weight may be divided evenly. If run-out exceeds a particular value, then a higher percentage of the static correction might be applied to the center plane with less added at the end planes. K. Single-Plane Balancing With Remote Phase And A Data Collector The use of a programmable “Data Collector” used in a Predictive Maintenance Program and loaded with a Balancing Program has become a very successful method of balancing. Even though this technology has made it very easy to collect and store the data, and even perform the balancing correction data, the setup of this instrument and a good understanding of balancing effects is still the most important part of obtaining good results. There are several Data Collectors on the market today with down-loadable balancing programs, both single plane as well as two-plane. They may include other functions of balancing such as “Splitting Weights”, “Combining Weights”, “Safe Trail Weight Calculations”, “Static-Couple Solutions” and “Result Storage” for rebalancing of like rotors in “One-Run”.

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It will not be the intent in this text to describe in detail the operation of each of the various Data Collector balancing programs but instead to give a general overview of them and the application practice to successfully balance rotors. During the practical work exercise that is performed during the formal training, each data collector or the data collector balancing programs of choice will be demonstrated and used to solve balancing programs. The previous chapters of this manual have gone into some detail on the principles of balancing. Although the data may be obtained in a different manner, these principles of balancing still remain in effect except the one that will be noted, especially in respect to which direction we move our weights. When using a data collector there will be different methods of collecting or viewing the phase readings as well as the amplitude readings. Figure 40 shows a typical setup using a Data Collector when performing balancing operations.

FIGURE 40. FIELD BALANCING SETUP USING A PORTABLE DATA COLLECTOR All of the Data Collectors have a menu selection for selecting the type of balancing you want to perform. The menus of each and the way they are accessed may be different but essentially each data collector will perform the same functions.



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As we remember from our earlier lessons, before we attempt to balance a rotor a complete analysis needs to be performed to insure that the vibration is indeed occurring at a frequency equal to 1X RPM of the rotor. Using our data collector, we can take readings in all three directions, i.e. Horizontal, Vertical and Axial at each bearing location. This can be accomplished either in the “Route Mode” or “Analysis” (Off-Route) mode. In addition, we also need to capture phase readings at these locations to assist us in determining that we have predominate vibration due to unbalance. L. Taking Phase Readings With a Data Collector Taking phase readings with a Data Collector is somewhat different than that which was discussed in the earlier chapters of this text. With most Data Collectors we have the option of taking phase readings with a Strobe Light, a Photocell, a Laser-Tach or a Keyphasor (Proximity Probe). Following will be the method in which the phase is calculated using the Data Collector with a reference pickup. Using a tach pulse from a photocell, laser-tach or proximity probe connected to the Data Collector and a vibration pickup the vibration signal is obtained from the transducer and the phase obtained from the reference pickup. The phase angle is determined from the difference in time between the tach pulse and the positive peak amplitude of the vibration signal. This difference is expressed as a ratio that is multiplied by 360 degrees to give us the phase difference. This is done internally in the Data Collector. This method of phase measurement is more accurate than the hand-held strobe light method since the instrument measures the phase angle within very accurate tolerances, whereas the strobe methods include human error in attempting to accurately read the angular position of the reference mark. Figure 40 shows a typical setup where a piece of reflective tape will cause the light from the photocell to reflect back to provide a 1X RPM speed reference pulse and phase angle. M. Single-Plane Balancing Using Data Collector 1.

MOUNT TRANSDUCER Mount the transducer in the direction with the highest amplitude of vibration. This will usually be the horizontal direction due to less support stiffness provided in this direction. For our example, Figure 40, the transducer is mounted in the horizontal direction at bearing A to accomplish a balance in plane 1 (the plane nearest the C.G.).

2.

INSTRUMENT SETUP From the main menu selection, select instrument configurations, select the transducer, sensitivity, type of reference pickup and which unit of measure will be used. Do not change units of measurement once the balancing program has started as the phase will differ based on the unit of measure. For example, there is a 90° phase difference between a velocity reading and a displacement reading.

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Select the Single Plane Balancing Program. Depending on the instrument you will be using you may have to select the direction the weight will be moved, i.e. with rotation or against rotation. Some programs let you choose while others only go with rotation and still others go only against rotation. Again, your exact instrument operation will be covered in the “hands on” exercises. 3.

ESTIMATE TRIAL WEIGHT This program feature calculates a trail weight size when the rotor weight (weight of all rotating parts including the shaft, pulley, impeller, etc.), the run speed (rotational speed of the rotor to be balanced), and the radius (distance from the center of the shaft that the trial weight is to be placed) are entered. Obtain a trial weight as per this step and set aside for balancing.

Note: It is important that an accurate set of scales be used for weighing all weights. 4.

COLLECT ORIGINAL MEASUREMENTS Select the “Acquire Data for Single Plane”. Enter a rotor description at this point for identifying if you should select to save this data for future balancing. Take the original readings. The instrument will record the RPM, the amplitude and the phase. This reading should be taken two or three times do ensure that the readings are stable. Once you are satisfied that the readings are stable, store these readings.

5.

ATTACH THE TRIAL WEIGHT Turn the rotor off and attach you measured trail weight. Make sure the trial weight is secure on the rotor and rotate the rotor by hand if possible to ensure that the trial weight does not strike any parts of the machine or housing. Select trial weight data entry information on the data collector. Enter the amount of the weight and the location of the weight in angular direction from the reference mark. The trial weight can be placed at any location but for simplicity reasons we place it a 0°. Again, the weight can be placed anywhere on the rotor but the location must be entered into the data collector. Depending on the instrument you are using, you must enter this information as a direction in degrees with rotation. In addition, with some instruments the degrees are measured from the leading edge of the reference tape, while others are measured from the trailing edge. Always look at the rotor in the same direction when placing the trial weight so as not to get confused when measuring the degrees.

6

MEASURE NEW VIBRATION WITH TRIAL WEIGHT

Start the rotor and measure the resultant reading. Observe the reading before storing the data to insure that this trial weight has had an effect of at least a 30% change in phase and/or amplitude. If this change is not noted, stop the rotor and increase the size of the trial weight. © Copyright 2001 Techncial Associates of Charlotte, P.C. 9-31 Techncial Associates Field Dynamic Balancing

7.

ORIGINAL CORRECTION WEIGHT Shut the machine down and remove the trail weight. It is always a good idea to mark the location of this weight for reference if you should forget where it was. Advance to the next menu selection on the data collector, you will now see the new weight amount and placement location in degrees. Make the weight addition/removal in the location indicated on the instrument making sure you place it in the direction indicated, i.e. with rotation or against rotation.

8.

SPLITTING WEIGHTS If the angular location for a single weight cannot be achieved due to an obstruction or void (if the program directed the analyst to place the correction weight between blades or spokes) the “Split Vectors” portion of the software can “split” the single weight vectorially into two weights that can then be attached in two more convenient locations.

9.

MEASURE NEW VIBRATION WITH ORIGINAL CORRECTION WEIGHT Start the rotor and select and measure new vibration with the original correction weight added. Compare this vibration level to your balance criteria. If the resulting vibration amplitude is within quality tolerance, stop the rotor and permanently attach the original correction weight. If not within tolerance, select “Trim Balance” for new weight addition or removal and location.

10

TRIM BALANCE After taking the new readings and obtaining your trim weight readings, weigh the weight to the desired size. Stop the rotor and add the weight to the proper location as indicated on the instrument, again making sure that the weight is placed at the proper location and direction. Do not remove the original correction weight. Start the rotor and compare the new vibration amplitude with your balance quality standards. If the new readings are with in tolerance, balancing is now complete. If the readings still are not within balance quality standards, the trim program can be repeated as often as necessary. Remember, always leave the balance weights on the rotor that were placed there in previous runs.

11

COMBINE CORRECTION WEIGHTS If more than one weight is used to achieve a satisfactory balance tolerance the weights can be combined. Select the “Add Vectors” selection in your balance program. Enter the weight amount and angular location for any two weights. The combined vector sum and angle is noted as the “Sum”. If only two correction weights were used, this single final correction weight will replace them and can be attached as one weight, instead of two, except where you have had to do a vector split. If more than two correction weights were used, the weights can be combined in steps, i.e., start by combining two weights vectorially, then

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combining this vector sum with the next weight, etc. until all weights are combined into a single weight. This process must be done very carefully since the final balance results can be greatly affected if inaccurate weight amount and angles are entered. After combining weights, it is recommended that the rotor be re-tested for balance with the single weight and additional corrections made if required. 12

SECURLEY FASTEN FINAL CORRECTION WEIGHTS If measurements are now in compliance throughout the machine with balance and vibration specs, the analyst should take great care to securely fasten permanent correction weights; or if they desire, remove weight at locations 180° away from the final correction weights. If possible, secure these weights in such a manner that if they do happen to be thrown off, they will not be thrown into areas where personnel might be stationed.

13

REPEAT VIBRATION MEASUREMENTS AT ALL MACHINE LOCATIONS (BOTH DRIVER AND DRIVEN) Complete vibration measurements should next be captured at each location on both the driver and driven machine components. Ensure not only that the unbalance problem has been resolved, but also that other problems have not been introduced (or have now “surfaced” since the dominating unbalance problem has been resolved). Also, ensure that balancing in one direction on Plane 1 has not now caused an increase in vibration at other locations and directions. For example, eccentric rotors will often cause vibration to go up in the vertical direction when balancing in the horizontal or vice versa. This can also sometimes be caused by looseness and/or resonant problems.

N. Two-Plane Balancing Using A Data Collector When a second plane is balanced, it involves more than just two single plane balancing exercises. When balancing is “performed” in two or more planes, one must consider something known as “cross-effect” which is also sometimes known as “corrective plane interference”. This can be defined as the change of unbalance indication on one orrection plane caused by unbalance in the other correction plane. For example, if a rotor were perfectly balanced on both the left and right planes and a trial weight was placed on the left plane, the trial weight would cause vibration not only in the left plane, but also in the right. For example, it may cause 5 mils (127 microns) of vibration on the left plane and increase the vibration on the right from almost nothing up to say 1 or 2 mils (25 or 50 microns). Then, if the same trial weight is moved over to the right plane, it might cause 1 or 2 mils (25 or 50 microns) additional vibration back to the left plane. This is known as cross-effect. Because of such cross-effect, unbalance indications observed on any one plane do not truly represent the unbalance in just that plane. Instead, each measurement will be a combination of the unbalance in that particular plane plus the cross-effect transmitting into this plane from other planes. When one begins a balancing exercise, he does not know the amount and the phase of cross-effect, but he must take this into account if he is to successfully balance the machine. This will be covered in the following sections. © Copyright 2001 Techncial Associates of Charlotte, P.C. 9-33 Techncial Associates Field Dynamic Balancing

1

DETERMINE IF THE DOMINANT PROBLEM IS UNBALANCE First, and foremost, determine if the real problem is unbalance using the analysis procedures outlined early in this text. It is not unusual to find that more than 50% of the times an analyst will be asked to balance a machine he will find the dominant problem to be something else. This procedure should include a complete set of measurements that can be used as “before” balance measurements and later compared to “after” measurements.

2

MOUNT TRANSDUCERS Mount a transducer securely at each bearing in the radial direction of the highest 1X RPM vibration. This will normally be in the horizontal direction due to less support stiffness than that provided by the vertical direction. In any case, both transducers must face the same direction on both the outboard and inboard bearing housings. Two transducers are recommended to avoid having to move one transducer between the two bearings. For identification purposes they will be referred to as “left” and “right” transducers.

3

MOUNT PHOTO-TACH AND REFLECTIVE TAPE Mount photo-tach and place reflective tape on the machine using the recommended directions given below. The three quantities needed to balance are the frequency, amplitude and phase at 1X RPM. The accelerometer will provide the amplitude and frequency information to the data collector. A photo-tach is connected to the data collector to provide phase information by sensing the reflective tape each time it passes by the photo-tach during each shaft revolution. The photo-tach can be targeted to any portion of the rotating shaft supporting the rotor to be balanced. The reflective tape can be mounted on any exposed, clean surface which rotates with the shaft including a coupling, sheave, flywheel or the shaft itself. If there is an option, it is usually best to mount it on a part with a larger diameter with a continuous, unbroken surface (i.e., not on a broken surface such as a gear). Large diameters will give better accuracy for angular measurements. The photo-tach itself can be targeted on the tape at right angles to the shaft, or it can even be targeted in a direction along the shaft axis, (for example, on the fan wheel itself in a direction parallel to the shaft). However, the best positioning choice for the phototach will normally be with it facing upwards looking at the target surface from below. Then, should the photo-tach fall off during operation, it will not likely strike the rotating member. In addition, if this convention is adopted, the analyst will be able to remember how the photocell was positioned (the photo-tach position must be the same in order to make meaningful comparative phase measurements). If the photo-tach is moved, it will change the resultant phase readings for all subsequent measurements by the angular amount it was altered when moved. Check for triggering of the photo-tach by slowly rotating the shaft by hand and noting if the red LED photo-tach indicator goes out as the reflective tape passes the photo-tach indicating triggering is taking place.

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4

INSTRUMENT SETUP From the main setup menu, select instrument configuration. Choose the units that you will use for balancing, i.e., g’s, in/sec or mils. Also make sure that the sensitivity of the transducer you are using in properly set. It is recommended that the same type of transducer with the same sensitivity is used on both locations. If you are not using a two-channel instrument, it is suggested that the cable from these transducers be connected to a selector switch and then to the instrument. This will allow switching from the left and right transducer without switching cables.

5

ESTIMATE TRIAL WEIGHT From the menu, select estimate trial weight. This selection will calculate a trial weight size when the rotor weight (weight of all rotating parts including the shaft, pulley, impeller, etc.), the run speed (rotation speed of the rotor to be balanced), and the radius (distance from the center of the shaft to the point where the trial weight is to be placed) are entered, Obtain a trial weight as per this step and set aside for use during the balancing.

6

COLLECT ORIGINAL READINGS From the main balancing menu select Begin New Balance. Enter a rotor description and notes if so desired. Start the rotor and select to begin original reading for the left plane. It is suggested that this reading be taken two or three times to make certain that you are getting repeatable data. Upon the completion of this data collection, switch to the right plane and take the data from the right plane.

7

ATTACH TRIAL WEIGHT Since this is a two-plane balance, a trial weight must be put in both the leftand right correction planes, and vibration readings taken from both transducers while the trial weights are at each location. To accomplish this, first stop the rotor and attach the trial weight to the “left” rotor plane. Record the amount of the trial weight and its angular location, (with or against rotation depending on instrument), from the reflective tape. Note that even though the weight can be placed at any location on the rotor it is recommended that the trial weight be placed at 0° making sure that you are reading the leading edge or trailing edge of the reflective tape depending on your instrument . If the trial weight cannot be placed at 0°, measure the angle between the reflective tape and the trial weight and enter that value. See Figure 41 for angular measurement conventions. Use the trial weight from Step 5. Always look at the rotor from the same direction when measuring this trial weight angle and any correction weight angles. Start the rotor and measure the new “right” vibration using the right transducer. Insure measurement repeatability. Now, switch to the left transducer and measure the new “left” vibration and phase. Store this information. Stop the rotor and remove the “left” plane trial weight. Attach a trial weight to the “right” rotor correction plane.



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Enter the amount and location of this weight. It is recommended this weight be the same size as the left trial weight and be placed at the same angle that the left trial weight had been located. If this cannot be done, enter the amount and angular location of the actual position. Remember to always look at the rotor from the same direction when measuring angles. Making sure that you are switched to the “left” transducer, measure and store the new “left” vibration and phase. Then, switch to the “right” transducer and measure and store the new “right” vibration and phase. Note during this procedure a significant change of at least 30% amplitude and/or phase is needed for accurate correction weight calculations. If this amount of change was not achieved, increase the trial weight size and repeat the procedure. 8

ORIGINAL CORRECTION WEIGHT

Shut the machine down and remove the “right” trial weight. Select correction weight readout on the instrument. Both the “left” and the “right” correction weight should be displayed. Obtain the proper correction weights and attach at their proper locations in the “left” and “right” correction planes. Remember to always view the angle from the same direction. 9

SPLITTING WEIGHTS

If the angular location for a single correction weight cannot be achieved due to an obstruction or void (as if between blades or spokes), the “Split Vector” portion of the software can “split” the single weight vectorially into two weights that can then be attached in two more convenient locations.

FIGURE 41. ANGULAR MEASUREMENT CONVENTIONS 9-36



Enter the number of equally spaced positions where split weights could be attached, the amount and angular position of the weight to be split. The result is two weights (Amt 1 and Amt 2) with the weight and angular location of each noted. Note the reflective tape or reference position is considered Position 1, and both weights must be added to the rotor to replace the original un-split single weight. Repeat this procedure for both correction weights if needed. 10

MEASURE NEW VIBRATION WITH ORIGINAL CORRECTION WEIGHTS

Start the machine with correction weights from Step 8 in both the “left” and “right” correction planes. Select the menu selection to measure “new” vibration making sure that the proper transducer has been selected. Measure both the “new” vibration and phase for both the “left” and “right” planes. Insure that these reading are stable. Stop the rotor. Compare this vibration to your balance criteria. If the vibration is within tolerance, permanently attach the correction weights. If the vibration is not in tolerance, stop the rotor and select “Trim Balance” to access the new weight and location for further correction. 11

TRIM BALANCE

The trim balance screen list both the “left” and “right” corrections weight size and angular location. Obtain trim weights equal to these and attach to the rotor in their correct angular location in their respective “left” and “right” correction planes at their correct angular location. Do not remove the original correction weights from Step 8 and use the weight splitting technique of Step 9 if needed. Start the rotor and measure the new “left” transducer and “right” transducer vibration with both correction and trim weights in place. Check for measurement repeatability. Stop the rotor. Compare the results to your balance criteria. If within tolerance, the balance is complete. If not within tolerance, repeat the trim procedures list above. This procedure can be repeated as often as necessary, however, always leave on the previous attached correction weights. 12

COMBINE CORRECTION WEIGHTS

If more than one weight is used in each (left and right) correction planes, the weights can be combined by using the “Add Vector” function. Note only the weights in each plane may be combined. That is, only the weights in the “left” plane can be combined to make one “left” correction weight and only the weights in the “right” plane can be combined to make a single “right” correction weight. The “left” and “right” correction weights cannot be combined. Enter the weight amount and angular location (in degrees from the reference tape) for any two weights in the same plane. The combined vector sum and combined vector angle are noted as the sum on the screen. If any two correction weights were used, this single final correction weight will replace them and can be attached as one weight instead of two. If more than one correction weight was used, the weights can be combined in steps starting by combining two weights vectorially, then combining that combined vector sum with the next weight, etc., until all weights in the same plane are combined to a single weight. This process must be done very carefully as the final balance results can be © Copyright 2001 Techncial Associates of Charlotte, P.C.


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greatly affected if inaccurate weight amounts and angles are entered. After combining weights it is recommended that the rotor be re-tested for balance with the “left” and “right” combined weights in place. Additional balance corrections may be required. 13

SECURELY FASTEN CORRECTION WEIGHTS

If measurements are now in complince throughout the machine with balance and vibration specs, the analyst should take care to securely fasten permanent correction weights or, if he desires, remove weight at locations 180° away from the final correction weights. If possible, secure these weights in such a manner that if they do happen to be thrown off, they will not be thrown into areas where personnel might be stationed. 14

REPEAT VIBRATION MEASUREMENTS AT ALL LOCATIONS (BOTH THE DRIVER AND DRIVEN).

Complete vibration measurements should next be captured at each location on both the driver and driven machine components. Ensure not only that the unbalance problem has been resolved, but also that other problems are not now indicated. Also, ensure that balancing in one direction on Plane 1 has not now caused an increase in vibration at other locations and directions. O. Overhung Rotors Overhung rotors are machine configurations like that shown in Figure 42 where the fan wheel to be balanced is outboard of its two supporting bearings. This configuration is very often found with machines such as blowers, pumps, etc. The planes where balance corrections are made do not necessarily respond to standard single and two-plane balancing techniques. In addition, the unbalance planes alone will create a couple unbalance proportional to the distance of the unbalance plane from the rotor C.G. Therefore, when attempting to balance overhung rotors, the analyst needs to take into account both static and couple unbalance forces, and treat the accordingly.

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FIGURE 42. EXAMPLE SETUP FOR BALANCING AN OVERHUNG ROTOR When balancing an overhung rotor, one of the two following procedures should be taken: 1

BALANCING OVERHUNG ROTORS BY CLASSIC SINGLE-PLANE STATICCOUPLE METHOD:

Figure 42 helps explain methods of balancing overhung rotors. Classically, Bearing A is most sensitive to static unbalance whereas the bearing farthest from the fan wheel to be balanced (Bearing B) is most sensitive to couple unbalance. Since Plane 1 is closest to the rotor center of gravity (C.G.), static corrections should be made in this plane while measuring the response on Bearing A. On the other hand, measurements should be made on Bearing B when making couple corrections in Plane 2. However, placing a trial weight in Plane 2 will destroy the static balance achieved at Bearing A. Therefore, in order to maintain the static balance at Bearing A, a trial weight placement which will generate a couple must be used. Thus, a trial weight of identical size should be placed in Plane 1 at an angle 180° opposite the trial weight in Plane 2. Therefore, either the data collector can be used using single-plane balance software or the single-plane graphic technique previously explained can be successfully employed on many overhung rotors, particularly if the ratio of rotor length-to-diameter (L/D) is less than approximately .50 (where L is length of the rotating component on which correction weights will be placed and D is the diameter of this component. See Figure 42. © Copyright 2001 Techncial Associates of Charlotte, P.C.


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Following below will be a description of this classic single-plane balancing technique for overhung rotors. a.

SET UP DATA COLLECTOR OR SPECTRUM ANALYZER INSTRUMENT

The data collector, photo-tach and transducer should be set up as previously described under Sections K & L and Figure 40 showing the two-plane balancing procedure. Alternatively, the analyst may wish to employ either a swept-filter analyzer that drives a strobe light, or a spectrum analyzer which will fire a photo-tach for phase measurements. b.

TAKE INITIAL MEASUREMENTS

Take initial measurements of 1X RPM amplitude, frequency and phase before adding any trial weights. Measurements should be taken on both the outboard and inboard bearings in both vertical and horizontal directions. The radial direction measurement having the highest amplitude will normally be employed for initial balancing (however, after correcting unbalance in the radial direction, measurements will have to taken in the other directions to ensure amplitudes in all directions likewise acceptable). c.

DETERMINE IF THE DOMINANT UNBALANCE PROBLEM IS STATIC OR COUPLE UNBALANCE

Looking at the amplitude and phase measurements taken on both bearings in the radial and horizontal directions, determine if the problem is dominated by either static or couple unbalance. If phase differences between the outboard and inboard bearings are between 90° and 180° in both the vertical and horizontal directions, the dominant problem will be couple unbalance. On the other hand, if these differences are both anywhere from 0° to approximately 40°, a static unbalance is dominant. Of course, phase differences ranging from approximately 40° to 140° are truly dynamic balance once again with a combination of static and couple. If the problem appears to be mostly couple unbalance, use couple unbalance procedures outlined below. However, if the problem appears to be predominantly static or dynamic unbalance, employ static balance procedures. For now, we will assume that the problem is mostly static. d.

MAKE A SINGLE-PLANE STATIC BALANCE

Referring to Figure 22, use single-plane techniques taking measurements on bearing A and placing trial and correction weights in Plane1.

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e.

DETERMINE IF RESULTANT VIBRATION AMPLITUDES MEET REQUIRED CRITERIA

After completing the single-plane static balance using Plane 1, repeat vibration measurements on both the outboard and inboard bearings in each direction (including axial) and ensure that amplitudes now meet allowable criteria. f.

IF CONSIDERABLE COUPLE UNBALANCE NOW REMAINS, CONTINUE WITH SINGLE-PLANE BALANCE FROM BEARING B

Overhung rotors often have large cross-effects which means that single-plane balancing from Plane 1 will often cause high vibration on bearing B. Therefore, the analysts will perform another single-plane balance, this time making their measurements from bearing B farthest from the component to be balanced. When they arrive at the single-plane correction weight solution, they should place this weight in Plane 2; and then place an identical size correction weight in Plane 1 180° away from the weight location in Plane 2. g.

DETERMINE IF AMPLITUDES NOW MEET ALL CRITERIA

After completing the single-plane couple correction, the analyst must again make measurements in horizontal, vertical and axial directions on each bearing and determine that all amplitudes now meet allowable criteria. Often, further balancing must be done at this point beginning with another single-plane balance using Bearing A and Plane 1 which might possibly be followed by another couple balance correction. h.

IF ALLOWABLE CRITERIA CANNOT BE MET IN ALL THREE DIRECTIONS OF EACH BEARING, PROCEED TO TWO-PLANE BALANCE PROCEDURE OUTLINED BELOW

Sometimes, this single-plane approach will not successfully reduce amplitudes below allowable criteria in all three direction on each bearing, particularly if the L/D ratio is greater than .5 or if the component to be balanced is located far away from the closest bearing. If this happens, two-plane techniques outlined below will have to be taken.



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2.

BALANCING OVERHUNG ROTORS BY CLASSIC TWO-PLANE STATIC-COUPLE METHOD:

Due to the significant cross-effects that are often present in overhung rotors, two-plane balance correction techniques often are more successful than those employing singleplane methods. However, one of the problems with two-plane methods is that it can sometimes be a little confusing on deciding which bearing is the left and which is the right bearing; similarly, which plane is the left and which is the right plane? (Some data collectors refer to these as the near and far planes as opposed to left and right; terminology does not matter - only that the analysts remain consistent in their convention.) Referring to Figure 42, when using two-plane techniques, Bearing A will be considered the bearing closest to the overhung rotor while Bearing B will be closest to the pulley. Similarly, Plane 1 will be on the inboard side of the wheel closest to the bearings whereas Plane 2 will be outboard. Here again, a static/couple solution will be employed when the two-plane correction weight calculations are completed. Since most overhung rotors are so sensitive to static unbalance, only the static correction will be placed when this static/ couple solution is obtained. Then, after trim balancing, if considerable couple unbalance remains, the analyst will proceed to correct this as well. They should follow the procedure outlined below: a.

SET UP INSTRUMENTS AS OUTLINED IN TWO-PLANE BALANCING METHOD AND FIGURE 42

Here again, this same procedure can be used with either data collectors, sweptfilter analyzers or real-time analyzers. However, if using either a swept-filter or realtime analyzer, the analyst should have a two-plane calculator program that is capable of providing static/couple solutions. b.

TAKE INITIAL MEASUREMENTS ON BOTH BEARINGS

Here again, 1X RPM amplitude, frequency and phase should be measured in horizontal, vertical and axial directions on both the outboard and inboard bearings. c.

COMPLETE A TWO-PLANE BALANCING PROCEDURE, BUT DO NOT YET PLACE BALANCE CORRECTION WEIGHTS

A two-plane balance procedure like that outlined in Section L should be employed, but final correction weights not put in place. Instead, when the trial weights, sizes and locations are calculated for each plane, the analyst should ask for a static/ couple solution and should initially only make the static correction. For example, it the static solution called for 1 oz (28.35 grams) in Plane 1 whereas the couple solution called for a 2 oz (56.70) grams correction in Planes 1 & 2 180° opposite one another, make only the static correction at this point.

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d.

DETERMINE IF AMPLITUDES NOW MEET ALLOWABLE CRITERIA After making the static correction in Plane 1, see if amplitudes in all three directions on each bearing are now within compliance with allowable criteria. If not, trim as required. Again, when the two-plane corrections are determined, ask for the static/ couple solution and once again, make only the static correction. Most of the time, the problems are resolved at this point. However, if considerable couple unbalance still remains, complete another two-plane procedure asking for the static/couple solution - this time making the couple correction called for, and not the static correction.

e.

DETERMINE IF AMPLITUDES NOW MEET ALLOWABLE CRITERIA After each of the two trials making these static corrections and the single trial making the couple correction, compare amplitudes in horizontal,vertical and axial directions on both the outboard bearings with allowable criteria. A small percentage of the time, the couple correction will throw the static balance back off. If this is the case, it may require one more static correction before the rotor is successfully balanced.

P. MULTI-PLANE BALANCING When a rotor is rigid and running well below its first critical speed, it can be balanced successfully by employing two-plane methods. In this case, the correction weights can be placed in any two planes as long as they satisfy both the static and the couple unbalance problems. However, when this rotor is operated at a speed roughly 70% of critical, it will often experience noticeable bending, particularly as it gets closer and closer to its critical. In this case, it becomes a “flexible” rotor. In addition, multi-plane balancing may be required on long rotors (high L/D ratios) which again are subject to bending due to the effect of unbalance forces, Figure 44 helps illustrate why a rotor operating near critical speed will likely require multi-plane balancing. Note the different mode shapes the rotor will take when passing through the first, second and third critical speeds. When such a rotor approaches critical, the internal bending moments producing great deflection will have to be counterbalanced by placement of correction weights in three or more planes. In these cases, it may be required that one perform a two-plane balance at speeds significantly below critical and when it is operating as a rigid rotor. Then, the rotor can be brought up to the desired operating speed and balanced once again, but this time employing multi-plane techniques. In these cases, it will be most important to know whether the rotor is operating near its first, second or third critical speed since the mode shapes will dictate how many planes require correction weights. Most often, if the rotor speed approaches 70% of critical, it will require multi-plane balancing. Software has been developed for many of today’s data collectors that will allow multi-plane balancing.



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FIGURE 43. BALANCING USING A PHOTOCELL Make sure to check the instrument set up to know if you are measuring the angle with or against rotation. Also, always view the rotor from the same direction.

FIGURE 44 MODE SHAPE DURING FIRST, SECOND, AND THIRD CRITICAL SPEEDS FOR A SIMPLY SUPPORTED ROTOR

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Q. SPLITTING BALANCE CORRECTION WEIGHTS 1.

Splitting Weights Using Data Collector Software:

Often, when balancing pumps, blowers, centrifuges and other machines having rotating blades or vanes, balance calculations will call for correction weights to be placed between vanes or blades. In these cases, many of today’s data collectors and balance machines can help the analysts determine how they can place smaller correction weights on two adjacent vanes which will give the same effect as would the one correction weight which was specified to be installed between the two vanes. In these cases, the analyst will be asked by the software to enter the number of vanes, the amount of the single correction weight for which the software calls, and the angle at which the software specifies the correction weight to be placed. The software, will then calculate the size of the two correction weights, assuming that the correction weights will be installed at the same radius as the single weight would have been. If it is not possible to install them at the same radius, the following formula should be invoked to determine the ultimate correction weight size based on the new radius: Where: Wc rc Wn rn

2.

Wc rc = Wn rn

(Equation 9)

= Correction weight size specified by Software (oz or gram) = Radius at which W was to be installed (in) = New correction weight size to be installed at new radius r (oz or gram) = New radius at which W is to be installed (in)

Manual Formula for Splitting Weights (see Figure 45):

Figure 45 is provided for those situations in which an analyst does not have a software to calculate “split weight”. Figure 45 shows two equations solving for CW1 and CW2 that are calculated correction weight sizes that would be installed on each of two vanes rather than CWR that was specified to be installed between vanes. An example is provided which will help explain the use of the two equations given in Figure 45 (Equations 10 and 11). In this example, a fan wheel with six blades is shown in Figure 45A with a required correction weight of 1 oz (28.35 grams) to be installed at an angle of 75° (this places it 15° clockwise of Blade 1 and 45° counter-clockwise of Blade 2 as shown in Figure 46). When the example is solved in Figure 47, it shows that the singular correction weight of 1 oz (28.35 grams) at 75° is equivalent to one correction weight of .816 oz (23.13 grams) on Blade 1 and another weight of .299 oz (8.48 grams) on Blade 2.



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3.

Splitting weights using the graphic vector method:

As an example, we are going to be using a fan with 6 blades evenly spaced at 60° as shown in Figure 47. After adding a trial weight on blade #1, the vector diagram directs us to move the weight 75° clockwise and adjust the weight to 20 grams. As you can see, there is no blade 75° clockwise to which we can add the required balance weight. Therefore, we must add weights on the adjacent blades which will provide the required result. The problem now is to find how much weight must be added on each blade.

FIGURE 45. HOW TO SPLIT ONE CORRECTION WEIGHT INTO TWO EQUIVALENT CORRECTION WEIGHTS 9-46



FIGURE 46. WEIGHT CORRECTIONS ARE MADE TO BLADES #2 AND #3 TO PRODUCE THE NEEDED RESULTANT CORRECTIONS To find the amount of weight required on blades #2 and #3, we will construct a vector diagram. On a sheet of polar graph paper, mark off the angular position of blades #2 and #3 as shown in Figure 47A. Next draw a vector representing the required correction weight, Figure 47B. The angular position of this vector is 75° clockwise from blade #1 and 20 grams in length as dictated by our vector calculations. Now, complete the parallelogram as shown in Figure 47C by drawing a line from the end of vector CW, parallel to blade #3 until is intersects blade #2; and draw a line from the end of vector CW parallel to blade #2 until it intersects blade #3. To find the amount of weight required on blade #3, simply measure the length of vector OA using the same scale used for vector CW. Similarly, measure vector OB to find the amount of weight needed on blade #3. In Figure 47D, vectors OA and OB show that 16.3 grams are needed on blade #2 and 6.0 grams are needed on blade #3. Of course, these are required weights added at the same radius as the original trial weight on blade #1. Note that the two weights total more than 20 grams. This is normal as the two will always total more than the resultant vector CW. R. Combining Balance Correction Weights Using Vectors After balancing a rotor in two planes using the single plane vector method, you may find that 2, 3 or more balance weights have been added in a correction plane as a result of repeated balancing to eliminate cross-effect. Instead of permanently correcting for each of these smaller weights, it is often more convenient to combine these weights so only one permanent correction weight must be added. Any number of balance correction weights in a given plane can be combined into a single weight by constructing a vector diagram.



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FIGURE 47. VECTOR SOLUTION FOR “SPLITTING” WEIGHTS For example, consider the three balance weights on the rotor in Figure 48A. To combine these weights, their amounts and angular positions must be known. First, draw a vector representing balance weight #1. See Figure 48B. For convenience, we have selected the largest weight for #1 and have constructed its vector at 0° . The length of this vector corresponds to the amount of weight, 25 grams. Next, from the end of the #1 balance weight vector, construct a vector 10 grams in length representing balance weight #2 as shown in Figure 48C. Note that the vector for balance weight #2 is drawn at an angle of 30° clockwise from balance weight #1. Now, from the end of the #2 balance weight vector, construct the vector for #3 that is 5 grams in length. See Figure 48D. This vector is constructed at an angle 45° clockwise from balance weight vector #1. After vectors have been constructed for each balance weight as shown, construct vector R by drawing a line from the origin (O) to the end of the last balance vector as shown in Figure 48D. This vector R is the resultant and represents the amount and position of a single weight whichwill be equivalent to the three balance weights. From vector R, we see that a weight of 38 grams located at a position 13° clockwise from balance weight #1 is required. will be equivalent to the three balance weights. From vector R, we see that a weight of 38 grams located at a position 13° clockwise from balance weight #1 is required. © Copyright 2001 Techncial Associates of Charlotte, P.C. 9-48 Techncial Associates Field Dynamic Balancing

FIGURE 48 S. Effect of Angular Measurement Errors on Potential Unbalance Reduction Two types of angular measurement errors can occur, each of which can have detrimental effects on the amount of unbalance reduction achievable. The first type includes phase measurement errors made by the instruments themselves and the second type includes errors by the analyst in placing the balance correction weights at the specified angular locations on the rotor. Each of these will be separately discussed. 1.

EFFECT OF PHASE ANGLE MEASUREMENT ERRORS BY INSTRUMENTS THEMSELVES. Table III shows the best possible ratio of unbalanced reduction for various degrees of error when measuring the phase angle of unbalance: Referring to Table III, note that if the instrument makes a phase measurement of 30° that the maximum possible unbalance reduction during this trial or trim run is by a ratio of only 2:1 (i.e., if the initial was 10 oz (283.5 grams), it will not allow



9-49

one to go below 5 oz (141.7 grams) during this trial). And it should be pointed out that this assumes just the right balance weight was employed. Similarly, a phase measurement error of only 7.5° using the correct weight will not allow more reduction than by a factor of 8 times. If such errors can be kept below +/- 2º, considerably higher reduction ratios are possible. Therefore, this points out the importance of using instruments that have very good phase resolution capability down to +/- 2º if possible. Strobe light instruments with the analyst attempting to interpret phase angles do allow this phase measurement precision (usually fortunate to be within 10º to 15º). Therefore, instruments with the capability of measuring remote phase with a reference pickup are recommended since many of them do have this measurement resolution capability. Use of such remote phase instruments will often allow the machine to be balanced in much fewer runs. TABLE III. BEST POSSIBLE RATIO OF UNBALANCE REDUCTION FOR VARIOUS DEGREES OF PHASE ANGLE MEASUREMENT ERROR

2.

EFFECT OF ANGULAR MEASUREMENT ERRORS WHEN ATTACHING BALANCE CORRECTION WEIGHTS

The analyst should take great pains to correctly locate the balance correction weights as closely as possible to the angular locations called for by the software or graphical solution. Of course, when attempting to balance some fan wheels or pump impellers and wanting to place such weights on the blades, the analyst may have to invoke the “split weight” capability if the solution calls for weight placement between blades. In any case, they should not just attempt to “ball park” either the weight size or angular location. Figure 49 illustrates the relationship of how errors in attaching correction weights will cause unnecessary residual unbalance to remain that should have been removed. For example, looking at Figure 49, a vector that would be directly opposite the initial unbalance of 100 grams was required. However, the analyst made a 10° error when attaching the correction mass of 100 grams. Therefore, the figure shows that a residual unbalance of 17.4 grams would be left in place. This residual unbalance will be indicated in the next run as 17.4 grams at 85°, which is nearly at right angles to the initial unbalance. Table IV shows the amount of residual unbalance error for varying degrees of correction weight angular error.

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FIGURE 49 RESIDUAL UNBALACNE DUE TO AN ERROR WHEN ATTACHING A BALANCE CORRECTION WEIGHT

TABLE IV RESIDUAL UNBALANCE AMOUNT ERROR FOR VARIOUS DEGREES OF ERROR WHEN PLACING CORRECTION WEIGHTS



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CHAPTER 10 BALANCING MACHINES - SOFT SOFT-BEARING Vs Vs HARD-BEARING MACHINES Figure 50 shows the distinctly different approaches taken by soft and hard bearing balancing machines in the attempt of each design to provide a relatively constant amplitude and phase lag throughout their operating speed range. These differences and some of the attributes of each will be discussed below.

FIGURE 50 COMPARSION OF PHASE LAG ANGLE AND DISPLACEMENT AMPLITUDES VERSUS ROTATIONAL SPEED IN SOFT-BEARING AND HARD-BEARING BALANCING MACHINES © Copyright 2001 Techncial Associates of Charlotte, P.C.


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A

Soft-Bearing Balancing Machines Figure 51 illustrates the motions of an unbalanced rotor suspended in a softbearing machine having flexible supported bearings. The soft-bearing balancing machine gets its name from the fact that it supports the rotor to be balanced on bearings that are free to move in at least one direction, usually horizontal, perpendicular to the rotor axis as shown in Figure 51. Referring to Figure 50, the natural frequency of the rotor and bearing system occurs at one-half or less of the lowest balancing speed. Therefore, when the rotor is brought up to balancing speed, the phase lag angle and vibration displacement amplitude have stabilized and can be measured with accuracy. Until recently, a direct indication of unbalance was only possible on soft-bearing machines after calibrating the indicating system for any particular rotor by making several calibration runs with calibration weights of known size attached to the rotor in specific correction planes (calibration settings will vary from one rotor to the next due to different mass and distribution of the mass since displacement of the principle axis of inertia in the balancing machine bearings depends on rotor mass bearing and suspension mass, rotor moments of inertia and the distance between bearings). However, in recent years, new technical developments have overcome many of the soft-bearing machine calibration problems making it possible to obtain accurate vibration before the first spin-up of the rotor, and also making it possible to provide updated calibration of the system just minutes before actually correcting and checking a rotor.

FIGURE 51 MOTION OF AN UNBALANCED ROTOR AND BEARING IN A “SOFT-BEARING” BALANCING MACHINE WITH FLEXIBLE SUPPORTED BEARINGS 10-2



In addition, this updated calibration also provides a built-in means of verifying and validating the fact that the machine is responding properly. These newer techniques involve several steps. First, the balance machine operator will dial in several geometric parameters that are specific to each rotor. Then, the softbearing machine will apply several predetermined calibrated forces against the bearing supports with the rotor at rest. Then, transducers mounted on the balance machine will sense the response of the rotor to the applied forces and will determine the rotor sensitivity (oz-in/mil or gr-in/mil of vibration). Then, the calibration can be checked by cross checks to verify the apparent level. The balance machine is switched into the “mils” mode, and a direct measurement of the actual vibration is obtained. One-half of this value will be multiplied by the rotor weight to provide a cross check with the actual balance level. B

Hard-Bearing Balancing Machines Figure 52 shows a typical hard-bearing machine along with some of the dimensions which must be dialed into its analog (or digital) computer. Hardbearing machines have similar construction to soft-bearing machines, except that their bearing supports are significantly stiffer in the horizontal direction. This results in a horizontal resonance which is several orders of magnitude higher than that for a comparable soft-bearing balancing. The natural frequency of the rotor in a hard-bearing machine is normally designed to occur a 3X greater than the maximum balancing machine. Referring to Figure 50, the hard-bearing machine is designed to operate at speeds well below the natural frequency in an area where the phase lag angle is constant and practically zero, and where the vibration displacement amplitude, though small, is directly proportional to the centrifugal forces produced by unbalance.

FIGURE 52 TYPICAL HARD-BEARING MACHINE WITH PERMANENTLY CALIBRATED INSTRUMENTATION. ROTOR DIMENSIONS a, b, c AND r1, r2 ARE DIALED DIRECTLY INTO THE ANALOG (OR DIGITAL) COMPUTER. © Copyright 2001 Techncial Associates of Charlotte, P.C.


10-3

Recall that centrifugal force is proportional to the following formula: FC = mrω2 = g C

Wr (386)(16)

2

2πn

2

(EQUATION 12)

60 2

F = .000001775 Un = .00002841 Wrn C

(EQUATION 1 Repeated)

where: Fc U W r n

= Centrifugal Force (lb) = Unbalance of Rotating Part (oz-in) = Weight of Rotating Part (lb) = eccentricity of the rotor (in) = Rotating Speed (RPM)

Since the centrifugal force (Fc) for a given amount of unbalance (Wr) at a given speed is always the same whether this unbalance occurs in a small or large rotor, the output from the sensing elements attached to the balancing machine bearing supports remains proportional to the centrifugal force resulting from unbalance in the rotor (remember that W in this equation is the unbalance weight, not the rotor weight; r is the radius at which this unbalance weight is acting). This output will depend only on the speed and amount of unbalance (Wr). Therefore, the use of calibration masses is not required to calibrate the machine for a given rotor.

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CHAPTER 11 RECOMMENDED VIBRATION VIBRATION AND BALANCE TOLERANCES A.

Vibration Tolerances

Today’s condition monitoring programs are recognizing that two sets of vibration tolerance specifications need to be developed for their rotating equipment(1) Overall Vibration Specifications; and (2) Spectral Band Alarm Specifications. That is, a number of standards have been written through the years by a number of professional organizations and individual corporations concerning allowable overall vibration. However, spectral analysis particularly within the last few years has proven time after time that serious problems can occur with certain components such as bearings and gears which can have little or no real effect on a change in the overall vibration itself, but will noticeably affect certain areas of the spectrum (in fact, in the final stages of deterioration, rolling element bearings can actually cause amplitude to drop). Therefore, procedures have been developed which will help the analysts break up the spectrum into a number of bands, thereby allowing them to set much higher alarm levels for problems that cause high vibration such as unbalance affecting 1X RPM, but much lower amplitudes for those things which can withstand significantly less vibration such as rolling element bearings. Unfortunately, although there are hundreds of plants and installations that have condition monitoring software that will allow the user to specify such spectral alarm bands, very few sites are effectively using them since there is very little information available on how they should properly do so. While setting such spectral alarm bands is not the purpose of this paper on field balancing, and since space considerations do not allow complete publication of a paper by the author on this subject, the following sections under vibration specifications will at least introduce this topic, hoping that the reader will gain an appreciation of how important properly specifying these bands is to his entire condition monitoring program.



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1.

Recommended Overall Vibration Specifications Much work continues today on establishing standards for allowable overall vibration. Some of the better known standards now available include: a) ISO 2372 - “Mechanical Vibration of Machines with Operating Speeds from 10 to 200 Revolutions per Second” - Basis for specifying evaluation standards (measurements made on structure). b) ISO 3945 - “Mechanical Vibration of Large Rotating Machines with Speeds Ranging from 10 to 200 Revolutions per Second” – Measurement and evaluation of vibration severity in situ (measurements made on structure at various elevations). c) ISO 7919 - “Mechanical Vibration of Non-Reciprocating Machines” Measurements on rotating components and evaluation (measurements made on shafting). d) ANSI S2.44, Part 1 - 1986, “Measurements and Evaluation of Mechanical Vibration of Non-Reciprocating Machines as measured on rotating shafts, “American National Standards Institute”, NY (1986). e) AGMA Standard, “Specifications for Measurement of Lateral Vibration on High Speed Helical and Herringbone Gear Units”, Standard 426.01. f) API 610 “Centrifugal Pumps for General Refinery Services”, 1971, American Petroleum Institute, Washington, DC. g) API 617, “Centrifugal Compressors for Refinery Services”, 4th Edition 1979, American Petroleum Institute, Washington, DC. h) API 670, “Non-Contacting Vibration and Axial Position Monitoring System”, 1976, American Petroleum Institute, Washington, DC. i) MIL STD-167-1 (Ships) 1974, “Mechanical Vibrations of Shipboard Equipment”, US Government Printing Office, Washington, DC. j) MIL-M-17060B (SHIPS) 1959, “Military Specifications - Motors, Alternating Current, Integral Horsepower” (Shipboard Use), US Government Printing Office, Washington, DC.

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Some attempts have been made to provide overall vibration criteria based on the type of machine and its drive configuration (centrifugal pump, direct coupled fan, belt driven fan, turbine/generator, etc.), and on its mounting (isolated versus non-isolated). It is recognized that there is often a significant difference in the amount of vibration for one machine type versus another. For example, a reciprocating air compressor obviously has significantly frequency, forcing frequencies of the machine itself, machine center of gravity relative to the placement of isolators, etc. Thus, it is important that users of today’s predictive maintenance hardware and software take into account the type of machine and its mounting when they begin to specify alarm levels of overall vibration for each machine that they will input into the computer database. In addition, it is important for users to know how their particular predictive maintenance data collector and software system measures overall vibration. Some systems have a fixed frequency range which is completely independent of any frequency range chosen on any particular spectrum. In fact, this overall measurement is completely independent from the spectra measurement parameters specified for the data collector (Fmax, # lines, # averages, etc.). In these cases, the analog time waveform is used as the basis for computing the overall vibration. In other data collector systems, the overall is computed directly from the spectra themselves using the following formula: (EQUATION 13)

The danger with the latter technique of calculating overall vibration is that significant vibration can possibly be occurring outside the maximum frequency (Fmax) that was specified by the analyst. There would be no way one could be aware of this if the overall were not computed from the time waveform. For example, if a user specified a maximum frequency of 30,000 CPM and, unknown to him, there was a very large peak out at 60,000 CPM with an amplitude of .50 in/sec (12.7 mm/sec), the data collector may only display an overall of about .20 in/sec (5.1 mm/sec) whereas the true overall may be up on the order of .60 in/sec (15.2 mm/sec). Thus, it is most important for the analyst to know how the overall is computed and, if given the option, one should choose the analog time waveform technique. © Copyright 2001 Techncial Associates of Charlotte, P.C.


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If they still wish to know the total RMS energy within the spectrum as calculated by the above equation, they could possibly specify one of the spectral alarm bands that would go all the way from the low end up to the high end of the spectrum since the RMS energy in each one of the bands is calculated using the same formula within the software of most condition monitoring vendors. Table V is offered as a specification which takes into account the various machine types, how they are mounted and where measurements are taken when specifying peak velocity overall alarm levels. This table assumes that the data collector has used the analog time waveform technique to compute the overall peak velocity. In addition, this overall “peak” velocity assumes an actual measurement of RMS vibration multiplied by 2 since most all data collectors and analyzers today actually take RMS measurements and multiply them by this mathematical constant when displaying so-called “peak” velocity. Note that each of three “ratings” is provided in Table V including “GOOD”, “FAIR” and “ALARM. After reviewing of all spectra captured on a machine, if no problems are found, the first two columns (“GOOD” and “FAIR”) are offered to give the analyst a general feel for the overall condition of each machine based on the highest overall level measured on their machine. However, even if the highest overall in the machine is still within the “GOOD” range, it is still possible for the machine to be in alarm, depending on what frequencies were generated and the amplitudes of those frequencies. That is where the spectral alarm bands come into play to ferret out the “apparently good condition” machines from those that truly have problems. 2. Synopsis of Spectral Alarm Band Specifications Written, tabulated procedures have been developed to help the analyst specify spectral alarm bands for a series of machine types and configuration using those types of predictive maintenance software systems which allow the spectrum to be broken up into 6 individual bands. Each of these bands can be set at any span of frequencies and at any alarm level for each individual band as chosen by the analyst. Again, please note that a complete paper has been prepared by the author on this subject. However, due to space considerations and due to the fact that the purpose of the paper is instruction and specifications for balancing, only a portion of the procedure can be presented within this paper. Therefore, Table VI is a portion of a complete set of tables that has been developed to specify these spectral alarm bands. Importantly, like the Table V overall alarm table, this Table VI spectral alarm band table assumes casing measurements of peak velocity using instruments which measure RMS and convert them to peak levels by electronic multiplication of amplitudes by 1.414. Also of importance is the fact that Table VI specifies spectral bands whose alarm levels are compared to the total power within the band (so-called “power bands”). That is, the amplitude for each band is computed by summing the amplitudes of each of the FFT lines as per the earlier equation. Therefore, it is not necessary for any individual peak to equal or exceed the level of any of these alarm bands for the band alarm itself to be violated. Instead, it is only necessary that the total RMS content of the band as computed equal or exceed this band alarm specification. 11-4



Table VI shows how spectral alarm bands are set up for several different types of machines including “general machines with rolling element bearings and without vanes” (Type A), “general machines with sleeve bearings and without vanes” (Type B), “special gearbox high frequency points with known number of teeth” (Type C), and “special gearbox high frequency points with unknown number of teeth” (Type D). A number of other machine types are covered in the remainder of the complete spectral alarm band tables that are in the referenced paper. When using Table VI, the analyst first should identify the particular machine type looking beneath the overall alarm specification in Table V, and find the overall alarm for this particular machine type. This will be used as direct input into the spectral alarm band specs of Table VI. If this particular machine type is not included in Table V, the user should either refer to the manufacturer of the machine, or other similar vibration severity charts, or use alarm levels for another machine type that most closely resembles the particular machine. Please refer to the entries under the first column of Table VI. “BAND LOWER FREQUENCY” specifies at what frequency each band should begin, whereas “BAND HIGHER FREQUENCY” shows where each band should end (for example, “from 0 to 1000 CPM”). In general, no gaps should be left between bands, nor should bands overlap one another (although some analysts using power bands sometimes extend one band from the beginning to the end of a complete spectrum in order to have the system calculate the “Spectral Overall Level”, and then compare this to the overall level provided separately by their instrument). Next, the column entry entitled “BAND ALARM” specifies how high to set the alarm level of each band. Notice that many of the cases described in Table VI have the “BAND LOWER FREQUENCY” set at 1% of F max rather than at 0 CPM. The reason for this is that data collectors and spectrum analyzers most always have built-in “noise” within the first 1 to 3 FFT lines, particularly when data from an accelerometer are electronically integrated to velocity. In fact, some instruments have been know to display “peaks” with so called “amplitudes” over 2.0 in/sec (50.8 mm/sec) within these first 3 FFT lines. If Fmax is properly specified, this most always is “garbage data” which can be neglected. Therefore, Band 1 will never begin within these first 3 lines in Table VI. Each of the cases specify the maximum frequency (Fmax which is always given along with the case title). Therefore, each case will tell where to set both the frequency range and alarm level of each band, and will describe what each band covers (i.e., bearing defect frequencies, gear mesh frequencies, etc.) Case A will be discussed in detail to illustrate the alarm band specification technique, whereas only highlights of each remaining case will be given. Then, several examples will follow the discussion to further illustrate how these techniques should be applied. A detailed explanation will be given on how to use Case A on “general rolling element bearing machines without rotating vanes” in order to give a detailed example on how to use the remainder of this portion of the alarm band tables. Also, an example showing how spectral alarm bands are specified for a pump is shown in Figure 53. © Copyright 2001 Techncial Associates of Charlotte, P.C.


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Note the special points called “1.0” and “2.0” which evaluate electrical problems and note the slightly different band setup for the pump spectra at positions 3 and 4 versus that for the motor at positions 1 and 2. The remaining three cases on this page of Table VI will be handled in like manner. However, it should be pointed out that Cases C and D specify particular gearbox high frequency points which are taken in addition to standard measurements on the gearbox.

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TABLE V CRITERIA FOR OVERALL CONDITION RATING (PEAK OVERALL VELOCITY, IN/SEC)* 1. 2. 3. 4. 5.

Assuming Machine Speed = 600 to 60,000 RPM. Assuming Measurements by Accelerometer or Velocity Pickup securely mounted as Close as Possible to Bearing Housing. Assuming Machine Is Not Mounted on Vibration Isolators (for Isolated Machinery - Set Alarm 30% - 50% Higher). Set Motor Alarms the Same as that for the Particular Machine Type unless Otherwise Noted. Consider Setting Alarms on Individual External Gearbox Positions about 25% Higher than that for a particular Machine Type.

MACHINE TYPE COOLING TOWER DRIVES Long, Hollow Drive Shaft Close Coupled Belt Drive Close Coupled Direct Drive COMPRESSORS Reciprocating Rotary Screw Centrifugal With or W/O External Gearbox Centrifugal - Integral Gear (Axial Meas.) Centrifugal - Integral Gear (Radial Meas.) BLOWERS (FANS) Lobe-Type Rotary Belt-Driven Blowers General Direct Drive Fans (with Coupling) Primary Air Fans Vacuum Blowers Large Forced Draft Fans Large Induced Draft Fans Shaft-Mounted Integral Fan (Extended Motor Shaft) Vane-Axial Fans MOTOR/GENERATOR SETS Belt-Driven Direct Coupled CHILLERS Reciprocating Centrifugal (Open-Air) - Motor & Compressor Separate Centrifugal (Hermetic) - Motor & Impellers Inside LARGE TURBINE/GENERATORS 3600 RPM Turbine/Generators 1800 RPM Turbine/Generators CENTRIFUGAL PUMPS Vertical Pumps (12' - 20' Height) Vertical Pumps ( 8' - 12' Height) Vertical Pumps ( 5' - 8' Height) Vertical Pumps ( 0' - 5' Height) General Purpose Horizontal Pump - Direct Coupled Boiler Feed Pumps - Horizontal Orientation Piston Type Hydraulic Pumps - Horizontal Orientation (under load) MACHINE TOOLS Motor Gearbox Input Gearbox Output Spindles: a. Roughing Operations b. Machine Finishing c. Critical Finishing

GOOD

FAIR

ALARM 1

ALARM 2

0 - .375 0 - .275 0 - .200

.375 - .600 .275 - .425 .200 - .300

.600 .425 .300

.900 .650 .450

0 - .325 0 - .300 0 - .200 0 - .200 0 - .150

.325 - .500 .300 - .450 .200 - .300 .200 - .300 .150 - .250

.500 .450 .300 .300 .250

.750 .650 .450 .450 .375

0 - .300 0 - .275 0 - .250 0 - .250 0 - .200 0 - .200 0 - .175 0 - .175 0 - .150

.300 - .450 .275 - .425 .250 - .375 .250 - .375 .200 - .300 .200 - .300 .175 - .275 .175 - .275 .150 - .250

.450 .425 .375 .375 .300 .300 .275 .275 .250

.675 .650 .550 .550 .450 .450 .400 .400 .375

0 - .275 0 - .200

.275 - .425 .200 - .300

.425 .300

.675 .450

0 - .250 0 - .200 0 - .150

.250 - .400 .200 - .300 .150 - .225

.400 .300 .225

.600 .450 .350

0 - .175 0 - .150

.175 - .275 .150 - .225

.275 .225

.400 .350

0 - .325 0 - .275 0 - .225 0 - .200 0 - .200 0 - .200 0 - .150

.325 - .500 .275 - .425 .225 - .350 .200 - .300 .200 - .300 .200 - .300 .150 - .250

.500 .425 .350 .300 .300 .300 .250

.750 .650 .525 .450 .450 .450 .375

0 - .100 0 - .150 0 - .090

.100 - .175 .150 - .225 .090 - .150

.175 .225 .150

.250 .350 .225

0 - .065 0 - .040 0 - .025

.065 - .100 .040 - .060 .025 - .040

.100 .060 .040

.150 .090 .060

*NOTE: The “ALARM 1” and “ALARM 2” overall levels given above apply only to in-service machinery which has been operating for some time after initial installation and/or overhaul. They do not apply (and are not meant to serve as) Acceptance Criteria for either new or rebuilt machinery.

R-200002-PK © Copyright 2001 Techncial Associates of Charlotte, P.C.


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TABLE VI 11-8



FIGURE 53 © Copyright 2001 Techncial Associates of Charlotte, P.C.


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That is, one set of measurements should be taken on the gearbox using either Case A or B, depending on whether the gearbox is outfitted with rolling element (Case A) or sleeve (Case B) bearings. Then, a second set of measurements should be taken at various gearbox points close to each mesh, with a much higher Fmax on this second measurement up to 3.25X gear mesh frequency as shown in Table VI. Therefore, the spectra having lower Fmax which are given in Tables A or B will detect problems such as misalignment, unbalance, looseness, etc., which are concentrated within lower frequencies; and the special high frequency point specified by Cases C and D will look much higher for the presence of gear problems which commonly show up at gear mesh frequency, 2X gear mesh frequency and even one-half harmonics of gear mesh frequency up to 5.5X gear mesh frequency. When taking measurements up to these high Fmax frequencies, the analyst is cautioned to read the notes under Cases C and D concerning mounting of the accelerometer. When getting up to frequencies which exceed 360,000 CPM or more, the analyst may have to stud mount the accelerometer and may even have to employ special high frequency accelerometers. Case A - General Rolling Element Bearing Machine without Rotating Vanes Case A on Table VI applies to both the driver and driven components of a wide range of general rotating process and utility machines which are outfitted with rolling element bearings (ball, roller or needle bearings). Before entering Table VI, refer to Table V to obtain the alarm level of overall peak velocity for your machine type. Then, determine the type of rolling element bearings. For common rolling element bearings Case A specifies a spectrum with a maximum frequency (Fmax) of approximately 40X RPM (for example, for a nominal speed of 1800 RPM, set Fmax at approximately 72,000 CPM as in the example of Figure 53). However, for tapered roller bearings (Timken cup and cone arrangement, or equivalent) or for special roller bearings, Case A specifies a maximum frequency of approximately 50X RPM. The reason for the higher Fmax for these bearing types is the fact that, with their particular geometries, they inherently have higher calculated rolling element bearing defect frequencies. Also note in Case A that if the speed is from 500 to 999 RPM, Fmax should be set at 60X RPM. The reason for this is to ensure that the spectra designed for this machine will detect a rolling element bearing in only the second of four failure stages through which it will normally pass rather than waiting late in the life of the bearing before problems are detected. Referring to Table IV for “Rolling Element Bearings”, note that the natural frequencies of bearing components will be excited during this second stage. Since these natural frequencies normally range from 30,000 to 120,000 CPM for most bearings, it is important to keep Fmax sufficiently high to detect these when excited. Please note that it is not necessary to specify Fmax at exactly 40X or 50X RPM, but should be somewhere in this vicinity (certainly not less than 30X RPM). If one sets FMAX too low it can cause a spectrum to completely miss potentially serious developing bearing wear, particularly during earlier stages. On the other hand, if Fmax is set too high, this can result in poor frequency resolution that can cause the user to misdiagnose problems, since they do not have sufficiently precise frequency resolution to properly identify such frequency components as true running speed harmonics versus bearing defect frequencies and vibration from adjacent machines. Also, if one sets Fmax too high, 11-10



this can cause potentially valuable information on subsychronous vibration to be “buried” at the left-hand side of the spectrum. In general, the rule of thumb is to keep Fmax as low as you can “without missing anything important”. Referring to Case A in Table VI, note that each one of the bands has a specific purpose and zone of coverage. For example, Band 1 ranges from subsynchronous vibration (below 1X RPM) up through operating speed. Bands 2 and 3 cover 2X and 3X RPM, respectively. Band 4 will include fundamental bearing defect frequencies for most rolling element bearings. Similarly, Bands 5 and 6 will include bearing defect frequency harmonics as well as natural frequencies of bearing components for most common rolling element bearings. Now, referring back to Table VI, note that Band 1 extends from 1% of Fmax to a frequency at 1.2X RPM. In the case of the example 1800 RPM machine having Fmax at 72,000 CPM as previously discussed, Band 1 would extend from 720 to 2160 CPM. The Band 1 alarm spec calls for 90% of the overall level, thus, if the overall alarm were .300 in/sec (7.6 mm/sec) (from table V), then the Band 1 alarm would be set at .270 in/sec (6.9 mm/ sec) for this machine. Similarly, Table VI specifies the frequency range of Band 2 to extend from 1.2 to 2.2X RPM (in the 1800 RPM case, this would extend from approximately 2160 to 3960 CPM). The Band 2 alarm spec calls for 50% of the overall alarm (thus from the example .300 in/sec (7.6 mm/sec) overall, Band 2 would be set at .150 in/sec) (3.8 mm/sec). Finally, Bands 3 through 6 are specified similarly (note that fixed alarm levels are specified for Bands 4 through 6, independent of the overall alarm for that machine type since bearing frequencies exceeding these fixed amplitudes should be considered serious, no matter what the machine, particularly when more than one harmonic defect frequency is present). The fixed alarm levels specified for Bands 4 thru 6 should work out satisfactorily for the great majority of machines. However, some users might have to drop these considerably, particularly if they have high vibration path impendence, slow moving machinery such as paper machines or calendar rolls. Here again, this is a case where the alarm band and overall level refinement procedure discussed and illustrated in a later section of the paper will to be put into play. Finally, if readers find that they need additional information on how to properly specify spectral alarm bands, they can get in touch with Technical Associates and acquire the complete paper. This paper is also given along with complete instruction on how it should be used along with examples in vibration seminars offered by Technical Associates.



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B. Balance Tolerances On Allowable Residual Unbalance Balance specification are provided by a number of sources. These include each of the following: 1)

ISO 1940 “Balance Quality of Rotating Rigid Bodies” (same as ANSI S2.19-1975); The International Standards Organization (ISO); Geneva 20, Switzerland.

2)

NEMA MG1-12.06 “Balance of Motors” 1971; National Electrical Manufactures Association.

3)

NAVY MIL STD - 167-1 (SHIPS) 1974, “Mechanical Vibrations of Shipboard Equipment”; U S Government Printing Office, Washington, DC

4)

NAVY MIL - M - 17060B (SHIPS) 1959, “Military Specification - Motors, Alternating Current, Integral Horsepower” (Shipboard Use).

5)

SAE ARP 1136, “Balance Classification of Turbine Rotor Blades”; Society of Automotive Engineers, Inc. “SAE”; Warrendale, PA.

6)

API 610, Centrifugal Pumps for General Refinery Service”, 1971; American Petroleum Institute, Washington, DC (API offers vibration and balance standards for many types of rotating equipment).

A discussion will first be provided on balance quality as per ISO 1940. Then, a comparison of ISO 1940 will be made with standards provided by the Navy and API. 1.

ISO 1940 Balance Quality Grades

Dynamic balancing is the process of attempting to align the mass and shaft centerlines so that the rotor will rotate with an absolute minimum of unbalanced centrifugal force. Since there is no such thing as a perfectly concentric rotor with perfectly fitting concentric parts that are supported with perfectly fitting concentric bearings, there will always be some degree of residual unbalance in each rotor. Residual unbalance, sometimes called final unbalance, is the unbalance of any kind that remains after balancing. Calculations can be performed when balancing a rotor to determine the degree of residual unbalance (this will be covered in Section 2 which will follow). During the 1950’s, a small group of experts active within the balancing field got together and began to formulate discussions on how a set of balance standards could be developed so that one could numerically determine to what quality his rotor is balanced in comparison with other similar rotors.

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Several years of intensive study ensued, culminating with this group joining “Technical Committee 108 on Shock and Vibration” of the International Standards Organization (ISO). Later, the group name was changed to “Sub-Committee 1 on Balancing and Balancing Machies” (ISO TC-108/SC1). Request were made by the committee to groups throughout the world to submit more and more data on balance qualities achieved. Finally, ISO Standard No. 1940 was issued entitled “Balance Quality Requirements of Rigid Rotors” which, after a period of time, was also adopted as “S2.19” by The American National Standards Institute (ANSI). Some of the more important points of this standard are summarized below. Table VII provides each of the balance quality grades as per ISO1940 delineated by “Balance Quality Grade”. Beside each quality grade G number is a listing of various rotor types, grouped according to these quality grades. As Table VII states, the list of rotor types is meant to include general examples and is not meant to be all-inclusive. Please note that beside each quality grade number in Table VII is a column entitled “eper x ω”. It shows that each quality grade number represents the maximum permissible orbital velocity (eper x ω) of the center of gravity in mm/sec around the shaft axis (ω) expressed in radians/sec. For example, referring to quality grade G 6.3, this grade allows an orbital velocity of: 6.3 mm/sec, RMS = .248 in/sec, RMS = .351 in/sec peak. Figure 54 provides the ISO “Permissible Residual Unbalance” bands for each rotor group as a function of the maximum service speed (RPM). This graph is used to establish the actual residual unbalance tolerance (called “Uper”) in terms of lb-in/lb or gram-in/gram. Therefore, this tolerance specifies the permissible residual unbalance per unit of rotor weight (rotor weight includes all portions of a machine which are in fact rotating, not the total weight of the entire machine assembly). For example, a small motor may have a total static weight of 20 lbs. (9 kg), whereas the weight of its rotor alone is only 10 lbs. (4.5 kg). It is the 10 lb. (4.5 kg) rotor weight which should be employed when using these residual unbalance guidelines. Referring again to Figure 54, note that each of the balance quality grades incorporates four bands except for those in the very upper or lower extremes of the graph. These unofficial bands might be considered (from top to bottom in each grade) as “sub-standard”, “fair”, “good” and “precision”. Therefore, the graph permits some adjustment to individual circumstances within each quality grade. Importantly, the difference in permissible residual unbalance between the bottom and top edge of each grade is a factor of 2.5. For critical applications, one should employ the lower band within each grade. © Copyright 2001 Techncial Associates of Charlotte, P.C.


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It is important to point out that the tolerances recommended in Figure 54 apply only to rigid rotors. Recommendations for flexible rotor tolerances are contained in ISO 5343 entitled “Criteria for Evaluating Flexible Rotor Unbalance” which must be read in conjunction with ISO 1940 and ISO 5406 entitled “The Mechanical Balancing of Flexible Rotors”. Looking again at Figure 54, note that in general, the larger the rotor mass, the greater the permissible unbalance; while the higher the RPM, the lower the allowable residual unbalance. Also, note that when obtaining the residual unbalance from the left-hand vertical axis, it will be expressed in units of (for example) lb-in/lb. As note (2) below Figure 54 states, to obtain this in units of oz-in/lb, multiply by a value of 16. For example, referring to Figure 54, if you had a 10 lb rotor turning at 1000 RPM and wanted to single-plane balance it to the “precision” level of G 2.5 (lowest of the four G 2.5 bands), this would correspond to a permissible residual unbalance of .00065 lb-in/lb which equals .0104 oz-lb/lb of rotor weight. Therefore, if this were a single-plane problem, the total allowable residual unbalance would be .0104 X 10 lb = .104 oz/in total in this one plane (had it been a two-plane problem, the permissible residual unbalance would have been .0052 oz-in/plane if this were a symmetric rotor centered between bearings as per note (1) below Figure 54). Following below will be a discussion on how ISO applies to both single-plane and twoplane problems with standard rotors of symetric design centered between bearings, as well as how it applies to rotors of various other geometries (including overhung rotors). a.

Application of Tolerances to Single-Plane Problems: A single-plane rotor is normally considered to be “disc shaped” requiring only one correction plane which may be sufficient if the distance between the bearings is large and the disc has small axial run-out. The entire tolerance provided in Figure 54 will be allowed for the single plane. If the couple unbalance (referred to the bearing planes) exceeds one-half the total rotor tolerance, the rotor may require two-plane balance.

b.

Application of Tolerances to Two-Plane Problems: In general, one-half of the permissible residual unbalance is applied to each of the two correction planes provided each of the following three conditions is met:

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1)

The rotor CG is located within the mid-third of the bearing span;

2)

The distance between correction planes is greater than 1/3 of the bearing span, and the correction planes are between bearings;

3)

The correction planes are approximately the same distance from the CG, having a ratio no greater than 1.5.



TABLE VII BALANCE QUALITY GRADES FOR VARIOUS GROUPS OF REPRESENTATIVE RIGID ROTORS IN ACCORDANCE WITH ISO 1940 AND ANSI S2.19-1975 © Copyright 2001 Techncial Associates of Charlotte, P.C.


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FIGURE 54

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FIGURE 55 (1OF 2) © Copyright 2001 Techncial Associates of Charlotte, P.C.


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FIGURE 55 (2 OF 2)

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c.

Application of Tolerances to Special Rotor Geometries Figure 55 is provided to show how ISO 1940 tolerances can be applied to rotors of special geometries that do not meet each of the three conditions stipulated above in Section b. For example, rotor A at the top of the figure shows a rotor with widely spaced inboard (between bearings) correction planes; rotor B has each of two overhung rotors outboard of each of the bearings; rotor C shows a classic overhung rotor with each of two corrections planes on the single wheel which is outboard of each of its bearings; whereas rotor D is situated between bearings, but away from the bearing span mid-point. Note that permissible tolerances (Uper) are stipulated on Figure 55 for each of these rotor geometries.

Following below are several examples which help illustrate how ISO 1940 tolerances are applied to various rotor types and geometries:



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C

How to Determine Residual Unbalance Remaining in a Rotor After Balancing

When field balancing, you must know when to determine that the job is complete. This will be not only when low vibration levels are achieved but also when the rotor is balanced within allowable specifications. To know this, you must determine the residual unbalance remaining in the rotor. This can be accomplished by following the procedure below; a.

Make original measurements of amplitude and phase and graph this to scale on polar coordinate paper. Call this vector the “O” vector.

b.

Attach a trial weight and document the trial weight size (oz) and radius (in) to which it is attached. (mr = trial weight size X trial weight radius.

c.

After attaching the trial weight, spin the rotor and measure amplitude and phase. Graph this on the polar graph paper as the “O + T” vector.

d.

Draw a vector called “T” from the end of vector “O” to the end of vector “O + T”. Vector T represents the effect of the trial weight alone. Measure the length of vector T to the same scale as that used for vectors “O” and “O + T”. Using this scale, determine the equivalent vibration level (mils).

e.

Calculate Rotor Sensitivity as per the following equation:

Rotor Sensitivity = (Trial Wt. Size) (Trial Wt. Radius) oz-in/mil Trial Weight Effect f.

Calculate Residual Unbalance using the equation shown below. If Residual unbalance is not brought within tolerances, trim balance using current correction weight as the trial weight for the trim run. Continue trim balancing until Residual Unbalance is reduced within required balance tolerances.

Residual Unbalance = Rotor Sensitivity X Vibration amp. after Bal. (oz-in) (oz-in/mil) (mils)



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Example (see Figure 54) Given: Required ISO Balance Quality = G 2.5 Rotor Weight = 100 Rotor speed = 800 RPM Amplitude after balancing = 2.0 mils Therefore, Required Uper = 1.76 oz-in total (single-plane) a.

Original reading = 10 mils @ 240º = “O” vector.

b.

Trial weight of 3 oz is attached in the balance plane at a 6 inch radius (mr = 3 oz X 6 in =18 oz-in)

c.

Trial run reading = 8 mils @ 120º = “O + T” vector

d.

Effect of trial weight alone = T = 15.5 mils (From Figure 54)

e.

Rotor Sensitivity = 18 oz-in = 1.16 oz-in 15.5 mils mil

f.

Residual Unbalance = (1.16 oz-in) (2.0 mils) =2.32 oz-in mil (not with specs) Continued balancing and reduced vibration to 1.0 mil Residual Unbalance = (1.16 oz-in)(1.0 mil) = 1.16 oz-in mil (in compliance)

D

Comparison of ISO 1940 with API and Navy Balance Specifications:

In general, the author has not found ISO tolerances to be sufficient tight. Recall that they were initially developed in the 1950’s when much less was know about the detrimental effect of vibration on machine life. Therefore, when using the ISO 1940 tolerances, the author has found much greater success by going one quality grade better than that called for by ISO 1940 guidelines that is given in Table VIII.

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FIGURE 56 STANDARD SINGLE-PLANE VECTOR SOLUTION Prior to the development of ISO 1940, the United States Navy had developed a balancing standard for its noise reduction program on submarines. This standard was known as NAVSEA STANDARD ITEM 009-15 and the Navy MIL STD-167-1 (SHIPS) 1 May 1974 prescribed the following balance tolerances: For Rotor Service Speeds Below 150 RPM, Uper

= 0.177 W

For Rotor Service Speeds Up to 1000 RPM, Uper

= 4000 W 2 N

For Rotor Service Speeds Above 1000 RPM, Uper = 4W N Where: Uper

= Permissible residual unbalance in oz-in

W

= Rotor weight (lbs)

N

= Maximum service speed (RPM)



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The American Petroleum Institute (API) finally adopted the third of the above standards that are written on a variety of machines. Therefore, the API standards are equal to those of the Navy MIL-STD-167-1 (SHIPS) 1 May 1974. Examples Comparing Navy and ISO Standards: Example 4.

Blower Requiring Two-Plane Balancing Machine Type = Blower Machine Class. = ISO G 6.3 from Table VII Blower Speed = 2000 RPM Rotor Weight = 1000 lbs (including fan wheel, shaft & sheave)

a)

Navy Uper = 4W = (4)(1000) =2 oz-in/plane N 2000

b)

ISO Grade G 6.3 (From Figure 52) Uper = (.0012 lb-in)(16 oz)(1000 lb) =19.2 oz-in total = 9.6 oz-in/plane lb lb 2 Planes

Example 5.

Fractional HP Electric Motor Requiring Two-Plane Balancing Machine Type = Fractional HP Electric Motor Machine Class.= ISO G 2.5 from Table VII Machine Speed = 1780 RPM Rotor Weight = 5 lbs (Total Motor Static Weight = 8 lb)

a)

Navy Uper = 4W =(4)(5) =.0112 oz-in/plane N 1780

b)

ISO Grade G 2.5 (from Figure 52) Uper = (.00062 lb-in)(16 oz)(5 lb) = .0496 oz-in total =.0248 oz-in/plane lb lb 2 planes

Based on Examples 4 and 5 along with a number of other test examples comparing Navy and ISO standards, one will see that the ISO tolerances are noticeably more lenient than those of the Navy. In some cases, the Navy Specs, written for submarine noise protection, may sometimes be difficult for the average balance shop to achieve. On the other hand, those of ISO are almost always too lenient.

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APPENDIX A

BALANCING TERMINOLOG TERMINOLOGY Y ISO A general vocabulary on vibration and shock is given in ISO 2041. NOTE:

Terms in italics in the definitions are themselves defined elsewhere in this vocabulary. Italicized terms that are defined separately are separated by an asterisk.

ISO 1940-1, Mechanical vibration – Balance quality requirements of rigid rotors – Part 1: Determination of permissible residual unbalance. ISO 2041, Vibration and shock – Vocabulary. ISO 2953, Balancing machines – Description and evaluation. Acceptability limit: That value of an unbalance parameter which is specified as the maximum below which the state of unbalance of a rotor is considered to be acceptable. Amount indicator: On a balancing machine, the dial, gauge or meter with which a measured amount of unbalance or the effect of this unbalance is indicated. Amount of unbalance:

Quantitative measure of unbalance of a rotor (referred to a plane), without referring to its angular position. It is obtained by taking the product of the unbalance mass and the distance of its center of gravity from the shaft axis.

NOTE: 1.

Units of unbalance are, for example, gram-millimeters and ounce-inches.

2.

In certain countries, the terms “weight” and “mass” are used interchangeably.

Angle indicator: Device used to indicate the angle of unbalance.



A-1

Angle of unbalance:

Given a polar coordinate system fixed in a plane perpendicular to the shaft axis and rotating with the rotor, the polar angle at which an unbalance mass is located with reference to the given coordinate system.

Angle reference generator:

In balancing, a device used to generate a signal which defines the angular position of the rotor.

Angle reference marks: Marks placed on a rotor to denote an angle reference system fixed in the rotor; they may be optical, magnetic, mechanical or radioactive. Axis of rotation:

Instantaneous line about which a body rotates

NOTES: 1.

If the bearings are anisotropic, there is no stationary axis of rotation.

2.

In the case of rigid bearings, the axis of rotation is the shaft axis, but if the bearings are not rigid, the axis of rotation is not necessarily the shaft axis.

Balance quality grade:

For rigid rotors, the product of the specific unbalance and the maximum service angular velocity of the rotor, (See ISO 1940-1).

Balance tolerance; maximum permissible residual unbalance Uper: In case of rigid rotors, that amount of unbalance with respect to a plane (measuring plane or correction plane) which is specified as the maximum below which the state of unbalance is considered to be acceptable. Balancing: Procedure by which the mass distribution of the rotor is checked and, if necessary, adjusted to ensure that the residual unbalance or the vibration of the journals and/or forces on the bearings at a frequency corresponding to service speed are within specified limits. Balancing machine:

Machine that provides a measure of the unbalance in a rotor and which can be used for adjusting the mass distribution of that rotor mounted on it so that the once-per-revolution vibratory motion of the journals or the force on the bearings can be reduced if necessary.

Balancing machine accuracy: Limits within which the amount and angle of unbalance can be measured under specified conditions.

A-2



Balancing machine minimum response: Measure of the machine’s ability to sense and indicate a minimum amount of unbalance under specified conditions. Balancing machine sensitivity: Of a balancing machine under specified conditions, the increment in unbalance indication expressed as indicator movement or a digital reading per unit increment in the amount of unbalance. Balancing run (on a balancing machine): Run consisting of one measuring run and the associated correction process. Balancing speed: Rotational speed at which a rotor is balanced. Bearing support: Part, or series of parts, that transmits the load from the bearing to the main body of the structure. Bias mass: The mass added to a mandrel (balancing arbor) to create a desired unbalance bias. Calibration: Process of adjusting a machine so that the unbalance indicator(s) read(s) in terms of selected correction units in specified correction planes for a given rotor and other essentially identical rotors: it may include adjustment for angular location if required. Calibration mass: A known mass used a)

in conjunction with a proving rotor, to calibrate a balancing machine, and

b)

on the first rotor of a kind, to calibrate a soft-bearing balancing machine for that particular rotor and subsequent identical rotors.

Calibration rotor: Rotor (usually the first of a series) used for the calibration of a balancing machine. Center of gravity: The point in a body through which the resultant of the weights of its component particles passes, for all orientations of the body with respect to a gravitational field. NOTE: - If the field is uniform, the center of gravity coincides with the center of mass. Center of mass:

That point associated with a body which has the property that an imaginary particle placed at this point, with a mass equal to the mass of a given material system, has a first moment with respect to any plane equal to the corresponding first moment of the system.



A-3

Centrifugal (rotational) balancing machine: Balancing Machine that provides for the support and rotation of a rotor and for the measurement of once-per-revolution vibratory forces or motions due to unbalance in the rotor. Claimed minimum achievable residual unbalance: The value of minimum achievable residual unbalance stated by the manufacture for his machine, and measured in accordance with the procedure specified in ISO 2953. Compensating (null-force) balancing machine: Balancing machine with a built-in calibrated force system which counteracts the unbalance forces in the rotor. Compensator:

Facility into a balancing machine which enables the initial unbalance of the rotor to be nulled out, usually electrically, so speeding up the process of plane setting and calibration.

Component correction: Correction of unbalance in a correction plane by mass addition or subtraction at two or more of a predetermined number of angular locations. Component measuring device: Device for measuring and displaying the amount and angle of unbalance in terms of selected components of the unbalance vector. Controlled initial unbalance: Initial unbalance which has been minimized by individual balancing of components and/or careful attention to design, manufacture and assembly of rotor. Correction (balancing) plane: Plane perpendicular to the shaft axis of a rotor in which correction for unbalance is made. Correction mass: A mass attached to a rotor in a given correction plane for the purpose of reducing the unbalance to the desired level. NOTE:

The same correction can be effected by removing mass from the opposite side of the rotor.

Correction plane interference (cross-effect): Change in balancing machine indication for one correction plane of a given rotor, which is observed for a certain change in unbalance in the other plane.

A-4



Correction plane interference ratios: Interference ratios IAB and IBA of two correction planes A and B of a given rotor are defined by the following relationships. I AB =

UAB UBB

Where UAB and UBB are the unbalances referring to planes A and B respectively, caused by the addition of a specified amount of unbalance in plane B: I BA =

UBA UAA

Where UBA and UAA are the unbalances referring to planes B and A respectively, caused by the addition of a specified amount of unbalance in plane A. Counterweight: NOTE:

Weight added to a body to reduce a calculated unbalance at a desired place. Such weights may be used to bring an asymmetric body to a state of balance or to reduce bending moments within a body, e.g., crankshafts.

Couple unbalance:

That condition of unbalance for which the central principal axis intersects the shaft axis at the center of gravity.

NOTES: 1.

The quantitative measure of couple unbalance can be given by the vector sum of the moments of the two dynamic unbalance vectors about a certain reference point in the plane containing the center of gravity and the shaft axis.

2.

If static unbalance in a rotor is corrected in any plane other than that containing the reference point, the couple unbalance will be changed.

Couple unbalance interference ratio: The interference ratio ISC = USIUC. Where US is the change in static unbalance indication of a balancing machine when a given amount of couple unbalance UC is introduced into the rotor. NOTE:

This ratio is generally used in the testing of single-plane balancing machines and may be expressed as a percentage by multiplying it by the maximum distance between the test plane on a proving rotor.



A-5

Critical speed: Characteristic speed at which resonance of a system is excited. NOTE:

Depending on the relative magnitudes of the bearing stiffness and mass and the rotor stiffness and mass, the significant effect at a critical speed may be the motion of the journals or the flexure of the rotor (see flexural critical speed, and rigid-rotor-mode critical speed).

Cycle rate: The number of starts and stops that a balancing machine, for a given rotor having a specified moment of inertia and for a given balancing speed, can perform per hour (without damage to the machine) when balancing the rotor. Design axis:

Axis about which parts and assemblies are designed and about which it is intended that the body be balanced.

Differential test masses: Two masses, representing different amounts of unbalance, added to a rotor in the same transverse plane at diametrically opposed positions. NOTES: 1.

Differential test masses are used, for example, in cases where a single test mass is impractical.

2.

In practice, the threaded portion and the height of the head of the test mass are kept constant. The diameter of the head is varied to achieve the difference in test mass.

3.

The smaller of the two differential test masses is sometimes called the “tare” mass, the larger the “tare-delta” mass.

Differential unbalance:

The difference in unbalance between the two differential test masses.

Direct reading balancing machine: A balancing machine which can be set to indicate unbalance in terms of angular position and in units of mass such as grams (or ounces) in any two balancing planes without requiring individual calibration for the first rotor of a kind. Dummy rotor:

A-6

In a balancing procedure, an attachment of adequate stiffness and of the same dynamic characteristics (center-of mass location, mass and moments of inertia) as the rotor, or part of a rotor, it replaces.



Dynamic (two-plane balancing machine: Centrifugal balancing machine that furnishes information for performing two-plane balancing. NOTE: Dynamic balancing machines are sometimes used to accomplish single-plane balancing. Dynamic unbalance:

That condition in which the central principle axis is not parallel to and does not intersect the shaft axis.

NOTE: The quantitative measure of dynamic unbalance can be given by two complementary unbalance vectors in two specified planes (perpendicular to the shaft axis) which completely represent the total unbalance of the rotor. Equivalent nth modal unbalance: The minimum single unbalance Une equivalent to the nth modal unbalance in its effect on the nth principal mode of the deflection configuration. Field balancing:

The process of balancing a rotor in its own bearings and supporting structure rather than in a balancing machine.

NOTE: Under such conditions, the information required to perform balancing is derived from measurements of vibratory forces or motions of the supporting structure and/or measurements of other responses to rotor unbalance. Field balancing equipment: Assembly of measuring instruments for providing information for performing balancing operations on assembled machinery which is not mounted in a balancing machine. Flexible rotor: Rotor not satisfying definition 2.2 because of elastic deflection. Floor-to-floor time: Time including the time for all necessary balancing runs and measuring runs, together with the times for loading and unloading. Foundation:

Structure that supports the mechanical system.

NOTE: In the context of the balancing and vibration of rotating machines, the term foundation is usually applied to the heavy base structure on which the whole machine is mounted Gravitational (non-rotating) balancing machine: Balancing Machine that provides for the support of a rigid rotor under non-rotating conditions and provides information on the amount and angle of the static unbalance. © Copyright 2001 Techncial Associates of Charlotte, P.C.


A-7

Hard-bearing (force-measuring, below resonance) balancing machine: Machine having a balancing speed range below the natural frequency of the suspension-and-rotor system High speed balancing (relating to flexible rotors): Procedure of balancing at a speed where the rotor to be balanced cannot be considered to be rigid. Inboard rotor:

A two-journal rotor which has its center of mass between the journals, without having significant mass outside the journals.

NOTE: For a precise description of the rotor, it may be necessary to state the positions of the center of mass and of the correction planes indexing:

Incremental rotation of a rotor about its journal axis for the purpose of bringing it to a desired position.

Index balancing (as applied to multipart rotor assemblies): A procedure whereby each part of a multipart rotor assembly is corrected within itself for the unbalance errors in it, and caused by it, by indexing one part of the assembly with respect to the remainder. NOTES: 1.

Index balancing is normally carried out by balancing a multipart rotor to within desired limits, indexing a specific part through 180° with respect to the remainder and correcting half the indexing unbalance in each part.

2.

If 180° indexing is not possible, other angles can be used: in that case, however, vector calculations may be required.

Indexing unbalance:

NOTE:

The change in unbalance, indicated after indexing two components of an unbalanced rotor assembly in relation to each other, which is usually caused by individual component unbalance, run-out of mounting (locating) surfaces, and/or loose fits.

Given repeatability of the interface fit. The change in unbalance measured in one component after indexing by 180° is twice the error in or resulting from the mating component.

Initial unbalance: Unbalance of any kind that exists in the rotor before balancing. Journal:

A-8

That part of the rotor which is in contact with or supported by a bearing in which it revolves. © Copyright 2001 Techncial Associates of Charlotte, P.C.


Journal axis:

Mean straight line joining the centroids of cross-sectional contours of a journal.

Journal center:

Intersection of the journal axis and the radial plane of the journal where the resultant transverse bearing force acts.

Local mass eccentricity (for distributed mass rotors): For small axial elements cut from a rotor perpendicular to the shaft axis. The distance of the center of mass of each element from the shaft axis. Low speed balancing (relating to flexible rotors): Procedure of balancing at a speed where the rotor to be balanced can be considered to be rigid. Mandrel; balancing arbor: Machined shaft on which work is mounted for balancing. Mass centring:

The process of determination of the rotor’s principal axis of inertia followed by the machining of journals, centers or other reference surfaces to bring the axis of rotation, determined by these surfaces, into close proximity with the principal axis.

Mass eccentricity: The distance of the center of mass of a rigid rotor from the shaft axis. Master rotor:

A calibration rotor with provision for adding calibration masses at a known location and used for periodically checking the calibration of a balancing machine.

Measuring plane: Plane perpendicular to the shaft axis in which the unbalance vector is determined.



A-9

Measuring run (on a balancing machine): A run consisting of the following steps. a)

mechanical adjustment of the machine, including the drive, tooling and/or adaptor.

b)

setting of the indicating system.

c)

preparation of the rotor for the balancing run.

d)

acceleration of the rotor.

e)

measurement of the unbalance.

f)

deceleration of the rotor.

g)

any further operations necessary to relate the readings obtained to the actual rotor being balanced.

h)

any other required operation, e.g., safety measures.

NOTES: 1.

In the case of mass production balancing, steps a) and b) are usually omitted from the initial measuring run. For subsequent measuring runs, steps a), b) and c) are omitted in all cases.

2.

A measuring run is sometimes referred to as a check run.

Mechanical adjustment: of a balancing machine, the operation of preparing the machine mechanically to balance a rotor. Method of correction:

Procedure by which the mass distribution of a rotor is adjusted to reduce unbalance, or vibration due to unbalance, to an acceptable value. Corrections are usually made by adding material to, or removing it from, the rotor.

Minimum achievable residual unbalance Umar: The smallest value of residual unbalance that a balancing machine is capable of achieving. Minimum achievable residual specific unbalance Uemar: the smallest value of residual specific unbalance that a balancing machine is capable of achieving under given conditions. Modal balancing: Procedure for balancing flexible rotors which affects only the nth principle mode of the deflection configuration of a rotor/bearing system.

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Modal balance tolerance: With respect to a mode, that amount of equivalent modal unbalance that is specified as the maximum below which the state of unbalance in that mode is considered to be acceptable. Multiple-frequency vibration: Vibration at a frequency corresponding to an integral multiple of rotational speed. NOTE: This vibration may be caused by anisotropy of the rotor, non-liner characteristics of the rotor/bearing system, or other causes. Multi-plane balancing:

Nodal Bar:

As applied to the balancing of flexible rotors, any balancing procedure that requires unbalance correction in more than two correction planes.

A rigid bar coupled through bearings to a flexibly supported rigid rotor, its motion being essentially parallel to that of the shaft axis.

NOTES: 1.

2.

Its function is to provide correction plane separation by locating the motion transducer at centers of rotation corresponding to centers of percussion located in connection planes. A motion transducer so located has minimum correction plane interference ration.

nth modal unbalance: The unbalance which affects only the nth principal mode of the deflection configuration of a rotor/bearing system. Overhung (outboard) rotor: A two-journal rotor with significant mass located outside the journals. Parasitic mass: Of a balancing machine, any mass, other than that of the rotor being balanced, that is moved by the unbalance force(s) developed in the rotor. Perfectly balanced rotor: An ideal rotor which has zero unbalance. Permanent calibration: That feature of a hard-bearing balancing machine that permits it to be calibrated once and for all, so that it remains calibrated for any rotor within the capacity and speed range of the machine. Plane separation: Of a balancing machine, the operation of reducing the correction plane interference ratio for a particular rotor. Plane separation (nodal) network: Electrical circuit, interposed between the motion transducers and the unbalance indicators, that performs the plane separation function electrically without requiring particular locations for the motion transducers © Copyright 2001 Techncial Associates of Charlotte, P.C.


A-11

Polar correction: Correction of amount of unbalance in a correction plane by mass addition or subtraction at a single angular location. Practical correction unit: Unit corresponding to a unit value of the amount of unbalance indicated on a balancing machine. For convenience, it is associated with a specific radius and correction plane and is commonly expressed as units of an arbitrarily chosen quantity such as drill depths of given diameter, weight, lengths of wire solder, plugs and wedges. Principal axis location:

The axis location defined by the offset of the center of mass from the design axis and the tilt angle of the principal axis from the design axis.

Principal inertia axes:

The coordinate directions corresponding to the principal moments of inertia lxixj (I = j).

For each set of Cartesian coordinate directions at a given point, the values of the six moments of inertia I xixj (I,j =1,2,3) of a body are in general unequal: for one such coordinate system, the moments I xixj (i = j) vanish. The values of Ixixj (i = j) for this particular coordinate system are called the principal moments of inertia and the corresponding coordinate directions are called the principle axes of inertia. NOTES: 1.

Ixixj =∫ j m Ixixj =∫ (r2 –xi2) dm, if I = j m

where r2 = x12 +x22 + x32 xi, xj are Cartesian coordinates.

A-12

2.

If the point under consideration is the center of mass of the body, the axes and moments are called central principal axes and central principal moments of inertia respectively.

3.

In balancing, the term principal inertia axis is used to designate the central principal axis (of the three such axes) most nearly coincident with the shaft axis of the rotor, and is sometimes referred to as the balance axis of the mass axis.



Production rate:

Reciprocal of floor-to-floor time.

NOTE:

The rate is normally expressed in pieces per hour.

Proving (test) rotor: Rigid rotor of suitable mass designed for testing balancing machines and balanced sufficiently to permit the introduction of exact unbalance by means of additional masses with high reproducibility of the magnitude and angular position. Quasi-rigid rotor:

Flexible rotor that can be satisfactorily balanced below where significant flexure of the rotor occurs.

Quasi-static unbalance: That condition of unbalance for which the central principal axis intersects the shaft axis at a point other than the center of gravity. Reference plane: Any plane perpendicular to the shaft axis to which an amount of unbalance is referred. Residual (final) unbalance:

Unbalance of any kind that remains after balancing.

Resonance balancing machine:

Resultant unbalance force:

Machine having a balancing speed corresponding to the natural frequency of the suspension and rotor system.

Resultant force of the system of centrifugal forces of all mass elements of a rotor referred to any point on the shaft axis, provided that the rotor revolves about the shaft axis.

NOTE: The resultant unbalance force always lies in the plane containing the center of gravity of the rotor and the shaft axis. Resultant unbalance moment: resultant moment of unbalance forces: The resultant moment of the system of centrifugal forces of all mass elements of the rotor about a certain reference point in the plane containing the center of gravity of the rotor and the shaft axis. NOTES: 1.

The angle and the magnitude of the resultant moment depend in general on the position of the reference point.

2.

There exists a certain position of the reference point in which the magnitude of the resultant moment reaches its minimum (center of unbalance).

3.

The resultant moment is independent of the position of the reference point in the case where the resultant unbalance force is zero.



A-13

Rigid free-body balancing:

Procedure by which the mass distribution of a rigid free-body is checked and, if necessary, adjusted to ensure that the principal axis location is within specific limits.

Rigid free-body unbalance:

On a balancing machine the condition that exists in any rotating rigid-free-body, when rotary motion is imparted about its spin axis as a result of centrifugal force(s).

NOTE: 1.

The rotating motion of the principal axis may be cylindrical or conical or a combination of both.

Rigid rotor: A rotor is considered to be rigid when its unbalance can be corrected in any two (arbitrarily selected) planes (see 4.9). After the correction, its residual unbalance does not change significantly (relative to the shaft axis) at any speed up to the maximum service speed and running under conditions which approximate closely to those of the final supporting system. NOTE: A rotor which qualifies as a rigid rotor under one set of conditions, such as service speed and initial unbalance, may not qualify as a rigid under other conditions Rigid-rotor-mode critical speed: Speed of a rotor at which there is maximum motion of the journals and where that motion is significantly greater than the flexure of the rotor Rigid free-body:

System of particles with rigid internal connections and no external constraints.

Rotating rigid free-body: Rigid free-body rotating about an axis. NOTE:

The rotation axis is not stationary if it is not a central principle axis.

Rotor: Body, capable of rotation, generally with journals which are supported by bearings. NOTE: The term rotor is sometimes applied to, for example, a disk-like mass that has no journals (e.g. a fly wheel). In the sense of the definition of 2.1, such a disk-like mass becomes a rotor for the purpose of balancing only when it is placed on a shaft with journals (see 2.4).

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(Rotor) flexural critical speed: Speed of a rotor at which there is maximum flexure of the rotor and where that flexure is significantly greater than the motion of the journals. (Rotor) flexural principle mode: For undamped rotor/bearing systems, that mode shape which the rotor takes on at one of the (rotor) flexural critical speeds. Self-balancing device:

Equipment which compensates automatically for changes in unbalance during normal operation.

Sensitivity switch: A control used to change the maximum amount of unbalance that can be indicated in a range or scale, usually in steps of 10.1 or smaller. Service speed:

Rotational speed at which a rotor operates in its final installation or environment. The definitions in this clause apply to unbalance in rigid rotors. They may also be applied to flexible rotors, but because unbalance in such rotors changes with speed, any values of unbalance given for those rotors must be associated with a particular speed.

Setting:

Of a hard-bearing balancing machine, the operation of entering into the machine information concerning the location of the correction planes, the location of the bearings, the radii of correction, and the speed if applicable.

Shaft axis: The straight line joining the journal centers. Single-plane (static) balancing: Procedure by which the mass distribution of a rigid rotor is adjusted to ensure that the residual static unbalance is within specified limits. NOTE: Single-plane balancing can be carried out on a pair of knife edges without rotation of the rotor but is now more usually carried out on centrifugal balancing machines. Single-plane (static) balancing machine: Gravitational or centrifugal balancing machine that provides information for performing two-plance balancing. Soft-bearing (above-resonance) balancing machine: Machine having a balancing speed above the natural frequency of the suspension-and-rotor system.



A-15

Specific unbalance: The amount of static unbalance U divided by the mass M of the rotor. NOTES: 1.

The specific unbalance is numerically equivalent to the mass eccentricity .

2.

In the case of a rotor with two correction planes, specific unbalance sometimes refers to the unbalance in one plane divided by the rotor mass allocated to that plane

Static unbalance: That condition of unbalance for which the central principal axis is displaced only parallel to the shaft axis. NOTE: The quantitative measure of static unbalance can be given by the resultant of the two dynamic unbalance vectors. Swing Diameter:

Maximum work-piece diameter that can be accommodated by a balancing machine.

Test mass: A precisely defined mass used in conjunction with a proving rotor to test a balancing machine. NOTES: 1.

The use of the term “test weight” is depreciated: the term “test mass” is accepted in international usage.

2.

The specification for a test mass should include its mass and its center-of-mass location, the aggregate effect of the errors in these values should not have a significant effect on the test results.

Test plane: A plane perpendicular to the shaft axis of a rotor in which test masses may be attached. Thermally induced unbalance: That change in condition exhibited by a rotor if its state of unbalance is significantly altered by its changes in temperature. Trial mass: a mass selected arbitrarily (or prior experience with similar rotors) and attached to a rotor to determine the rotor response. Traverse test: Test by which the residual unbalances of a rotor can be found (see ISO 1940-1) or which a balancing machine may be tested for conformance with the claimed minimum achievable residual unbalance Umar. A-16



Two-plane (dynamic) balancing: Procedure by which the mass distribution of a rigid rotor is adjusted to ensure that the residual dynamic unbalance is within specified limits. NOTE: A trial mass is usually used in “trial and error” balancing or field balancing where conditions cannot be precisely controlled and/or precision measuring equipment is not available. Unbalance: That condition which exists in a rotor when vibratory force or motion is imparted to its bearings as a result of centrifugal (See clause 3) NOTES: 1.

The term unbalance is sometimes used as a synonym for amount of unbalance or unbalance vector.

2.

The term imbalance is sometimes used in place of unbalance, but this is depreciated.

3.

Unbalance will in general be distributed throughout the rotor but can be reduced to: a)

static unbalance and couple unbalance described by three unbalance vectors in three specified planes, or

b)

dynamic unbalance described by two unbalance vectors in two specified planes.

Unbalance bias of a mandrel (balancing arbor): added to a balancing arbor. NOTE:

A known amount of unbalance

Biasing a balancing arbor generally serves the purpose of either compensating for the residual unbalance that run-out of the balancing arbor’s rotor mounting surface causes when this single balancing arbor is used in balancing a series of rotors of the same mass or introducing a specified unbalance at a specific angular position for the purpose of balancing parts which, after being removed from the balancing arbor, are to have a specified unbalance.

Unbalance couple:For the case where the resultant unbalance force is zero, the resultant couple of the system of centrifugal forces of all mass elements of the rotor.



A-17

Unbalance force: In a rotor referred to a correction plane, the centrifugal force at a given speed (referred to the shaft axis) due to the unbalance in that plane. Unbalance mass: That mass which is considered to be located at a particular radius such that the product of this mass and its centrifugal acceleration is equal to the unbalance force. NOTE: The centrifugal acceleration is the distance between the shaft axis and the unbalance mass multiplied by the square of the angular velocity of the rotor, in radians per second. Unbalance moment:

Moment of a centrifugal force of a mass element of a rotor about a certain reference point in the plane containing the center of gravity of the rotor and the shaft axis.

Unbalance reduction ratio (URR): The ratio of the reduction in the unbalance by a single unbalance correction to the initial unbalance. Where:

URR = U1 - U2U2 = 1 U1 U1

U1 is the amount of initial unbalance U2 is the amount of unbalance remaining after one correction. NOTES: 1.

The unbalance reduction ratio is a measure of the overall efficiency of the unbalance correction.

2.

The ratio is usually given as a percentage.

Unbalance vector: Vector whose magnitude is the amount of unbalance and whose direction is the angle of unbalance. Vertical axis freedom:

Freedom of a horizontal balancing machine bearing carriage or housing to rotate by a few degrees about the vertical axis through the center of the support.

Vector measuring device: Device for measuring and displaying the amount and angle of unbalance in terms of an unbalance vector, usually by means of a point or line. Vibration transducer plane: Plane perpendicular to the shaft axis in which the vibration transducer in located.

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APPENDIX B

WEIGHT REMOVAL CHARTS



B-1

B-2





B-3

B-4





B-5

B-6





B-7

B-8





B-9

B-10





B-11

B-12





B-13

B-14





B-15

B-16





B-17

B-18





B-19

B-20





B-21

B-22





B-23

B-24





B-25

B-26





B-27

B-28





B-29

B-30





B-31

APPENDIX C

CONVERSION CHART FOR CONVERTING INCHES OF FLAT FLAT STOCK #1020 STEEL TO OUNCES OF WEIGHT



C-1

C-2





C-3

C-4



APPENDIX D

THREE-POINT METHOD OF BALANCING The following procedure outlines a three-point method for balancing rotors where the use of a reference pickup or strobe light to read phase is not practical or possible. This three-point method is often preferred to the familiar two-point method because it does determine the location of the balance correction weight. This may be particularly important where it may be necessary to divide balance weights between adjacent blades of a fan or similar rotor. 1.

With the rotor operating at normal speed, measure and record the original vibration amplitudes as O’. For our example : O’ = 6 mils (152 micron)

2.

Draw a circle with a radius equal to O’, as shown in Figure 1. For our example this circle will have a radius of O’ = 6 mils (152 micron)

FIGURE 1

3.

Stop the rotor. Mark on the rotor three (3) points; “A”, “B” and “C” approximately 120° apart. These three points on the rotor need not be exactly 120° apart, however, the precise angles of separation, whatever they may be, must be known. In our example we will not position our test weights equally spaced, just to show that this can be done.



D-1

In our example, Figure 2, point “A” is our starting point and is thus considered 0°. Mark the respective positions of points “A”, “B” and “C” on the original circle as shown in Figure 2.

FIGURE 2 4.

Select a suitable trial weight and attach at position “A” on the rotor. Refer to the formulas for calculating a safe trial weight as required. For our example, trial weight (TW) = 10 ounces (283.5 grams)

5.

Start the rotor and bring to normal operating speed. Measure and record the new vibration amplitude as O’ + T1. For our example O’ + T1 = 4 mils (102 micron)

6.

Using point “A” on our original circle as the center point, draw a circle with a radius equal to O’ + T1. For our example, this circle will have a radius of O’ + T 1 = 4 mils (102 micron), as shown in Figure 3.

7.

D-2

Stop the rotor and move the trial weight to position “B”.



FIGURE 3 8.

Start the rotor and bring to normal operating speed. Measure and record the new vibration amplitude as O’ + T2. For our example: O’ + T2 = 8 mils (203 micron).

9.

Using point “B” on our original circle as the center point, draw a circle with a radius equal to O’ + T2. For our example, this circle will have a radius of O’ + T 2 = 8 mils (203 micron), as shown in Figure 4.

10.

Stop the rotor and move the trial weight to position “C”.

11.

Start the rotor and bring to normal operating speed. Measure and record the new vibration amplitude as O’ + T3. For our example, this circle will have a radius of O’ + T3 = 11 mils (279 micron).

12.

Using point “C” on our original circle as the center point, draw a circle with a radius equal to O’ + T3.



D-3

FIGURE 4 For our example, this circle will have a radius of O’ + T3 = 11 mils (279 micron), as shown in Figure 5.

FIGURE 5 Note from Figure 5 that the three circles drawn from points “A”, “B” and “C” intersect at a common point “D”.

D-4



13.

Draw a line from the center “O” of the original circle to point “D”, as shown in Figure 6. Label this line “T”.

14.

Measure the length of line “T”, using the same scale used in drawing the circles.

For our example, this line “T” is 5.25 (133 mm) as measured in Figure 6.

FIGURE 6 15.

Calculate the amount of the balance correction weight, using the formula: CW = TW (O’/T) Where: CW TW O’ T

= Correct Weight = Trial Weight = The Original Unbalance Reading = The measured Resultant Vector

For our example problem, the solution is found as follows: CW = TW (O’/T) CW =10 oz. X (6.0/5.25) CW =11.4 oz.

CW = TW (O’/T) CW = 283.5 grams X (152 /133) CW = 323 grams



D-5

16.

Using the protractor, measure the angle between line “T” and line “OA”, as shown in Figure 7. THIS MEASURED ANGLE IS THE ANGULAR LOCATION OF THE CORRECT WEIGHT, LOCATED RELATIVE TO POINT “A” ON THE ROTOR.

FIGURE 7 For our example problem, this angle is measured to be 41°. 17.

Stop the rotor and remove the original trial weight from point “C”.

18.

Attach the correct weight calculated in Step 15 above to the rotor at the angular position determined from Step 16.

For our example problem, the calculated correct weight of 11.4 oz. (323 grams) is added to the rotor at an angular position 41° clockwise from position “A” on the rotor, as shown in Figure 8.

FIGURE 8 With the balance correction weight calculated and located on the rotor in accordance with the above instructions, the rotor should now be balanced.

D-6



Dynamic Field Balancing

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