“Vibration analysis based machine unbalance fault detection and correction.”
Siva Shankar Rudraraju
January-May 2005
INDIAN SCHOOL OF MINES DHANBAD, INDIA
INDEX I. Introduction II. Vibration Signal Analysis: In a nutshell
3 4
III. Machine Faults
5
IV. Unbalance: The Problem
6
V. Balancing
8
VI. Experimental Setup
10
VII. Unbalance Detection
12
VIII. Balancing / Removal of unbalance IX. Conclusions & Suggestions X. References
14 18 19
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Introduction
Why do machines vibrate…….?
Every machine component has an inherent capacity to store energy. This energy is stored in certain quantum states which states which are called modes.
When the machine component is excited by an external force, the machine takes up the energy and starts vibrating with various frequencies and corresponding amplitudes. The resultant vibrational state is a superposition of all the individual modes of vibration.
Understanding vibration response. Understanding of a vibrational state can achieved through the analysis of the response signal in time domain and frequency domain.
Time Domain: Domain: Variation of energy with respect to time ( Amplitude vs Time)
Frequency domain: domain: Distribution of energy across various frequencies of vibration. (Amplitude vs Frequency)
Response Signal
Time Domain
Frequency Domain
Energy variation
Energy Distribution
Fourier Transform
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Vibration Signal Analysis: In a nutshell Modern vibration signal analysis is based on frequency domain analysis using sophisticated spectrum analyzers, which are required to perform the Fourier transform of the response signals. The various forms of Fourier transform are
Fourier series: series: Transforms an infinite periodic time signal into an infinite discrete frequency spectrum.
Fourier Integral Transform: Transforms an infinite continuous time signal into an infinite continuous frequency spectrum.
Discrete Fourier Transform (DFT): (DFT): Transforms a discrete periodic time signal into a discrete periodic frequency spectrum.
Fast Fourier Transform(FFT): A Transform(FFT): A computer algorithm for calculating the DFT
Today, FFT analyzers are the preferred choice for obtaining the frequency domain spectrum.
Analysis Methodology
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Machine Faults A fault is an irregularity in the functioning of the equipment which results in component damage, energy losses and reduced efficiency of the machine. The common types of machine faults are:
Unbalance
Shaft misalignment or bent shaft
Damaged or loose bearings
Damaged gears
Faulty of misaligned belt drive.
Mechanical looseness
Increased turbulence
Electrical induced vibration
Fault detection using vibrational analysis involves analysing the vibrational signature for signs of fault. Any predominant fault occurring results in increased vibration level which has energy concentrated at certain frequency levels. The relation of the predominant vibration frequencies with the forcing frequency (input force frequency) gives us an idea about the source of the fault. The increased amplitude of the predominant frequencies indicates the severity of the fault. Standard relations between common faults and corresponding fault signatures are available. For example, fault due to an unbalance mass results in an increased vibrational energy around the forcing frequency (1X RPM), i.e. the predominant frequency is the frequency of rotation of the shaft.
Fig.1.Vibration Signature of an unbalanced shaft rotating at 50Hz
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Unbalance: The Problem
Rotating Machines Rotating machines are becoming increasingly precise and operating at higher speeds due to the progress and demand of modern technology. These machines should offer stable functioning and higher operating efficiencies even under the most severe conditions. The primary factors that degrade the performance of machines operating at a high speed are vibration and accompanying problems such as fatigue and noise. Balancing of rotors is the most fundamental and effective process to prevent vibration of machines, and thus is one of the most indispensable processes in manufacturing and maintenance of rotating machines.
Unbalance Unbalance is a result of uneven distribution of a rotor’s mass and causes vibration to be transmitted to the bearings and other parts of the machine during operation. Imperfect
mass
distribution
can
be
due
to
material
faults,
design
errors,
manufacturing and assembly errors, and especially faults occurring during operation of the machine. By reducing these vibrations, better performance and more costeffective operation can be achieved and deterioration of the machine and ultimately fatigue failure can be avoided. This requires the rotor to be balanced by adding and/or removing mass at certain positions in a controlled manner.
Unbalance may occur due to the following reasons.
The shape of the rotor is unsymmetrical.
Unsymmetrical mass distribution exists due to machining or casting error.
A deformation exists due to a distortion. di stortion.
An eccentricity exists due to a gap of fitting.
An eccentricity exists in the inner ring of a bearing.
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Theory: Vibration due to unbalance Assume that a weight with a mass of m is added to a balanced rotor having a thindisk shape at a distance of r from its center. When this rotor is rotated at a speed of N, the generated centrifugal force is expressed as
P=m.r.ω2
Where ω represents the angular speed of rotation (ω=2πN/60). The centrifugal force P changes its direction as the rotor rotates which repeatedly acts on the bearing and so causes vibration of the whole machine.
Types of Unbalance.
Unbalance in single plane: If the unbalance mass is a concentrated mass present along a single plane, then the unbalance force is present only in that plane.
Unbalance in multiple planes: If the unbalance mass is distributed, then the unbalance forces are acting on multiple planes.
The resultant force can be
obtained by vector summation of the individual forces. These resultant forces can be substituted in place of the individual forces, to simplify the balancing operation.
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Balancing “Balancing means a process of restoring a rotor which has unbalance to a balanced state by adjusting the mass distribution of the rotor” Unbalance is caused by the displacement of the mass centerline from the rotor's axis by an eccentricity in the distribution of the rotor mass. In simpler terms, due to centrifugal force, the "heavy" point of a rotor exceeds the centrifugal force exerted by the light side of the rotor and pulls the entire rotor in the direction of the heavy point. Balancing is the correction of this phenomenon by the removal or addition of mass to the component to compensate for centerline error.
Why Balancing is required? required? An unbalanced rotor causes the following foll owing problems.
The whole machine vibrates.
The performance of a rotating machine deteriorates.
Abrasion of bearings may shorten the life of the machine.
Machine may fail in the worst case.
Noise produced due to excessive vibration.
Types of Balancing
Static Balancing Dynamic Balancing
Static balancing balancing involves installing the component into a balancing machine and measuring the "heavy" point in relation to the centerline, while the part is rotating. If the required balance correction is at a single axial point on the rotor the balance is said to be "Single-Plane". Single plane balancing is adequate for rotors which are short in length, such as pulleys and fans.
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Dynamic balancing balancing is required for components or assemblies of significant length. Rotors with some axial length can have two "heavy" points at opposing ends of the component, acting independently on the mass center line. In order to balance the component, both planes must be corrected for center line error. Dynamic balancing is required for components such as shafts and multi-rotor assemblies.
Balance correction is typically done per customer supplied specifications. Test Devices can perform balance correction on materials ranging from plastics to aerospace superalloys, by the following methods: •
Abrasive Material Removal - Grinding equipment is used to remove mass at the appropriate location.
•
Drilling or Milling Material Removal - Drills are used to plunge to specified depths at the appropriate location.
•
Mass Addition - Mass is added by the addition of epoxy, welding metal strips, or by adding mechanical hardware (set screws, washers, etc.) if provisions are included in the design.
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Experimental Setup The experimental setup for unbalance fault detection and diagnosis can be broadly classified into two categories:
Fault generator.
Vibration analysers.
Fault generator generator is the SpectraQuest Machine Fault Simulator (MFS) unit. MFS comprises of a shaft rotor assembly driven by an AC motor. MFS comprises facilities to introduce various machine faults like rotor unbalance, misalignment, faulty bearings, damaged gear box and faulty belt drive.
Fig.2.MACHINE FAULT SIMULATOR (MFS)
Bearing
Rotor Unbalance
Gear Box Belt Drive
Fig.3. Various possible fault locations in MFS unit.
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Vibration Analysers: Analysers: The following hardware was used for vibration signal acquisition & processing. The signal acquired was further processed in signal analysis software.
Hardware: 1. Portable vibration meter 2. Larson Davis 2900B spectrum analyser 3. Oros 25 FFT analyser
Larson Davis 2900B Analyser
Software:
Oros 25 FFT analyser
1. Oros analysis software 2. Larson Davis RTA utility
Real time analysis Utility
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Unbalance Detection
A machine without faults has a vibration signature which has low energy distribution across a wide frequency range. The exact frequency distribution of energy depends on the dynamics and working condition of the specific equi pment.
Fig.4. Vibration signature obtained on the bearings of the MFS uni t running at 20 Hz without any faults. From above figure it can be seen that non-faulty equipment has a low energy distribution across a wide frequency range.
On introducing an unbalance fault by adding a small additional weight, the vibration signature changes significantly. The energy (amplitude) at the forcing frequency (1X shaft RPM) shows substantial increase. A comparative representation of the vibration signature obtained with and without unbalance at different RPM is presented b elow.
Balanced Rotor
Unbalanced Rotor
Fig.5. Comparison of vibration signatures of balanced and unbalanced rotor of MFS unit running at 20 Hz.
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Balanced Rotor
Unbalanced Unbalanced Rotor
Fig.6. Comparison of vibration signatures of balanced and unbalanced rotor of MFS unit running at 40 Hz.
Balanced Rotor
Unbalanced Rotor
Fig.7. Comparison of vibration signatures of balanced and unbalanced rotor of MFS unit running at 50 Hz. Thus from above study we can observe that during unbalance fault the vibration spectra has higher energy (vibration amplitude) concentration at the predominant frequency (1XRPM). Also the increase in vibration amplitude (from balanced to unbalanced rotor) increases with the i ncrease in rotor RPM.
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Balancing / Removal of Unbalance
Single plane balancing When the unbalance mass is a concentrated mass in a single plane then the corrective measure taken to restore the balance of the rotor constitute single plane balancing.
In Single Plane balancing, the unbalanced centrifugal force is neutralized by an equivalent opposite force generated by a correction weight.
To simulate an unbalance in the rotor, we add a small unbalance weight (=7gm), at a distance (10cm) from the rotation axis. Now we attempt to rectify this unbalance by using vibration analysis, described below.
Procedure of Single Plane Balancing Step 1: Measurement of the overall vibration using portable vibration meter. meter . The overall vibration level showed a substantial increase from the normal working vibration level. This is an indication of the presence of a fault.
Step 2: Analysis of frequency spectra using the Larson Davis 2900B analyser and Oros 25 FFT analyser. The vibration spectra showed predominant frequency at the shaft rotation frequency (30 Hz).
Fig.8. Vibration Spectra of MFS unit with unbalance
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Observation Shaft rotation frequency=30Hz Highest frequency Peak in vibration spectra at 30.0781Hz Vibration level in vibration spectra at 30.0781Hz, Vunbalance = 1.35 mm/s Next high frequency peaks at 60Hz,90Hz,120Hz 60 Hz,90Hz,120Hz (1XRPM,2XRPM,3XRPM)…. (1XRPM,2XRPM,3XRPM)….
Step 3: Adding Trial Weight Add a trial weight W (=5.1gm), at any position on the rotor at a distance R from the rotation axis. Then obtain the vibration spectra again.
Fig.9. Vibration Spectra of MFS unit with trial weight, W. Observation Highest frequency Peak in vibration spectra at 30.0781Hz Vibration level in vibration spectra at 30.0781Hz, V0 = 2.26 mm/s Next high frequency peaks at 60Hz,90Hz,120Hz 60 Hz,90Hz,120Hz (1XRPM,2XRPM,3XRPM)…. (1XRPM,2XRPM,3XRPM)….
Step 4: Add the Trial Weight at 180 0 Remove the trail weight and add it at 180 0 on the other side of the rotor, at the same distance R form the rotation axis. Again obtain the vibration spectra. . Observation Highest frequency Peak in vibration spectra at 30.0781Hz Vibration level in vibration spectra at 30.0781Hz, V180 = 0.785 mm/s Next high frequency peaks at 60Hz,90Hz,120Hz 60 Hz,90Hz,120Hz (1XRPM,2XRPM,3XRPM)…. (1XRPM,2XRPM,3XRPM)….
Step 5: Calculate the correction weight and position. The correction weight and position is determined by geometrically representing the forces.
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The following procedure is followed to determine the unbalance. 1. Draw a circle of radius Vunbalance, with centre O. 2. With centre A, draw an arc AX of radius V0. 3. With centre B, draw an arc BY of radius V180. 4. Let the point of intersection be P, Join OP. 5. OP is the geometric representation of the unbalance force produced only due to the trial weight, W. 6. Correction weight, Wcorrection=
ΟΑ × W ΟΡ
7. Location of unbalance is at an angle ∠ΑΟΡ (or - ∠ΒΟΡ ) from the initial location of the trial weight, W. Add the balance weight at an angle +/- ∠ΒΟΡ from the initial location of W. 8. Determine one of the positions (T) from +/- ∠ΒΟΡ , which has minimum level of vibration at shaft rotation frequency (30.0781Hz). The location of the actual unbalance is diagonally opposite to this minimum vibration position (T). The correction weight should be added at position T.
A
OA- Initial Unbalance AX- V0 (trial weight 00) BY- V180 (trial weight 1800) OP- Unbalance due to W
O
X
Y P B
Fig.10. Geometric representation of the unbalance forces
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Calculation W=5.1 gm OA=1.35 From diagram, OP=1.00 Correction weight, Wcorrection=
1.35 × W 1.00
= 6.885 gm.
0
∠ΒΟΡ = 40
Minimum vibration level is obtained at -400 from the position (00) of the trial weight.
So this is the location of the correction mass. And diagonally opposite is the original single plane unbalance in the rotor.
Result The calculated correction mass (6.885gm) is close to the initially introduced unbalance (7gm).
The results obtained from the Larson Davis 2900B analyser were cross checked with the more advanced Oros 25 multi channel analyser and Oros software. Both results showed good agreement.
After balancing the overall vibration level substantially decreased.
Fig.11. Vibration signature of balanced rotor MFS unit
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Conclusions
Vibration signature analysis backed by good signal analysers (Like Larson Davis 2900B, Oros 25) results in excellent machine fault detection and correction.
Various
balancing
experiments
conducted
with
different
unbalance
configurations using vibration analysis resulted in excellent balancing. This lead to drastic reduction in the overall vibration l evels.
Suggestions
Unbalance fault detection in presence of other machine faults can be performed, as in actual working conditions multi-fault condition exists.
The present balancing method should be extended to include multi plane balancing and flexible rotor balancing.
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References
1. Steve Goldman, “Vibration Spectrum Analysis – A Practical Approach”, Second Edition, Industrial Press Inc. 2. Keith Mobley, “Vibration Fundamentals”, Newnes. 3. Thompson, W.T., “Theory of Vibration with Applications”, Prentice Hall, New Jersey, 1972. 4. Madhujit Mukhopadhyay, “Vibrations, Dynamics and Structural Systems”, Oxford & IBH Publishing Company Pvt. Ltd., New Del hi, 2000. 5. Alan V.Oppenheim & Ronald W.Schafer, “Discrete-Time Signal Processing”, Pearson Education Signal Processing Series, 2002. 6. Larson Davis 2900B User Manual and Training Guide 7. Oros 25 User Manual 8. Other technical resources on the Internet.
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