Industrial Gear Box

Rolling bearings in industrial gearboxes

© Copyright SKF 1997 The contents of this publication are the copyright of the publisher and may not be reproduced (even extracts) unless permission is granted. Every care has been taken to ensure the accuracy of the information contained in this publication but no liability can be accepted for any loss or damage whether direct, indirect or consequential arising out of the use of the information contained herein. Publication 4560 E Printed in Denmark on environmentally friendly, chlorine-free paper (Multiart Silk) by Scanprint as


1 Industrial gearboxes – overview

1

2 Bearing types for industrial gearboxes

2

3 Design of bearing arrangements

3

4 Dimensioning the bearing arrangement

4

5 Lubrication and maintenance

5

6 Recommended fits

6

7 Mounting and dismounting bearings

7

8 Application examples

8

Rolling bearings in industrial gearboxes Handbook for the gearbox designer


Foreword This Handbook is intended to provide the gearbox designer with the knowledge required to select bearings for gearboxes and to correctly design gearbox bearing arrangements. Recommendations are given based on experience gained by SKF during decades of cooperation with gearbox manufacturers the world over. General information regarding the selection, calculation, mounting and maintenance of ball and roller bearings is given in the SKF General Catalogue. The questions arising from the use of rolling bearings in industrial gearboxes are dealt with here. Data from the General Catalogue are only repeated here when it has been thought necessary for the sake of clarity. The application examples described comprise proven gearbox designs from major manufacturers which are worthy of note. Grateful thanks are extended to the companies concerned for the provision of the detailed information about their products and the permission to publish.

3

Contents Made by SKF ® stands for excellence. It symbolises our consistent endeavour to achieve total quality in everything we do. For those who use our products, “Made by SKF” implies three main benefits. Reliability – thanks to modern, efficient products, based on our worldwide application know-how, optimised materials, forward-looking designs and the most advanced production techniques.

1 Industrial gearboxes – overview ............................... 9 Types of gearbox ............................................................ 9 Geared transmissions.................................................... 10 Demands made on gearboxes ...................................... 14 Selecting the gears ........................................................ 14 Designing the casing ..................................................... 15

Cost effectiveness – resulting from the favourable ratio between our product quality plus service facilities, and the purchase price of the product.

2 Bearing types for industrial gearboxes .................. 17 Deep groove ball bearings ............................................ 18

Market lead – which you can achieve by taking advantage of our products and services. Increased operating time and reduced down-time, as well as improved output and product quality are the key to a successful partnership.

Angular contact ball bearings ....................................... 20 Cylindrical roller bearings ............................................. 22 CARB™ roller bearings ................................................. 24 Spherical roller bearings ............................................... 26 Taper roller bearings ...................................................... 28 Spherical roller thrust bearings .................................... 30

3 Design of bearing arrangements............................. 33 Shafts and gear wheels in spur gearboxes ................. 33 Shafts in bevel gearboxes ............................................. 44 Shafts in worm gearboxes............................................. 50 Shafts and gear wheels for planetary gearboxes........ 56

4


4 Calculation of bearing arrangement ....................... 65 Bearing loads ................................................................. 65 Determination of external forces .................................. 66 Calculation of bearing loads ......................................... 74 Dimensioning the bearing arrangement ...................... 76

5 Lubrication and maintenance.................................. 91 Grease lubrication.......................................................... 92 Oil lubrication ................................................................. 95 Maintenance ................................................................... 98

6 Recommended fits..................................................103 7 Mounting and dismounting bearings .................... 109 Adjustment of angular contact bearings.................... 109

8 Application examples ............................................. 115

5

The SKF Group – a worldwide corporation SKF is an international industrial Group operating in some 130 countries and is world leader in bearings. The company was founded in 1907 following the invention of the self-aligning ball bearing by Sven Wingquist and, after only a few years, SKF began to expand all over the world. Today, SKF has some 43 000 employees and more than 80 manufacturing facilities spread throughout the world. An international sales network includes a large number of sales companies and some 20 000 distributors and retailers. Worldwide availability of SKF products is supported by a comprehensive technical advisory service. The key to success has been a consistent emphasis on maintaining the

SKF manufactures ball bearings, roller bearings and plain bearings. The smallest are just a few millimetres (a fraction of an inch) in diameter, the largest several metres. In order to protect the bearings effectively against the ingress of contamination and the escape of lubricant, SKF also manufactures oil and bearing seals. SKF's subsidiaries CR and RFT S.p.A. are among the world's largest producers of seals.

6

highest quality of its products and services. Continuous investment in research and development has also played a vital role, resulting in many examples of epoch-making innovations. The business of the Group consists of bearings, seals, special steel and a comprehensive range of other hightech industrial components. The experience gained in these various fields provides SKF with the essential knowledge and expertise required in order to provide the customers with the most advanced engineering products and efficient service.

The SKF house colours are blue and red, but the thinking is green. The latest example is the new factory in Malaysia, where the bearing component cleaning process conforms to the strictest ecological standards. Instead of trichloroethylene, a water-based cleaning fluid is used in a closed system. The cleaning fluid is recycled in the factory's own treatment plant.

SKF has developed the Channel concept in factories all over the world. This drastically reduces the lead time from raw material to end product as well as work in progress and finished goods in stock. The concept enables faster and smoother information flow, eliminates bottlenecks and bypasses unnecessary steps in production. The Channel team members have the knowledge and commitment needed to share the responsibility for fulfilling objectives in areas such as quality, delivery time, production flow etc.

The SKF Engineering & Research Centre is situated just outside Utrecht in The Netherlands. In an area of 17 000 square metres (185 000 sq.ft) some 150 scientists, engineers and support staff are engaged in the further improvement of bearing performance. They are developing technologies aimed at achieving better materials, better designs, better lubricants and better seals – together leading to an even better understanding of the operation of a bearing in its application. This is also where the SKF New Life Theory was evolved, enabling the design of bearings which are even more compact and offer even longer operational life.

7

1 Industrial gearboxes – overview Types of gearbox . . . . . . . . . . 9 Geared transmission . . . . . . 10 Demands on gearboxes . . . 14 Selecting the gears . . . . . . . 14 Designing the casing . . . . . . 15

1 Industrial gearboxes – overview Types of gearbox

Industrial gearboxes – overview Gearboxes are devices for the transmission or translation of movement. In industry gearboxes are used to transform the speeds and torques produced by the prime mover in order that they are appropriate to the machine which is to be driven. The speeds and torques required by the machine are dictated by its use. Prime movers can generally only meet these requirements when combined with gears.

Types of gearbox Gearboxes are characterised by having at least three members: the power input, power take-off and the casing. The casing transmits the support moment to the base. In contrast, a coupling has only two members: the power input and power Gear Torque < M2 M1 >

Power P1 = P2 + Pv

take-off. The coupling housing has no part in the flow of force. The symbols used for power transmission by gearboxes and couplings are shown in figs 1 and 2 .

Fig 1

Fig 2

PV

Rotational speed ≤ n2 n1 >

M1 n1

Pv (with slip) M1 n1 P1 P2

Power P1 = P2 + Pv

n2

M2

Coupling Torque M1 = M2 Rotational speed n1 ≥ n 2

P1

M2

1

P2

n2

9

1 Industrial gearboxes – overview Geared transmissions The main types of power transmission equipment are shown in the following. In addition, there are many combinations, for example bevel/spur gears, spur gears with belt drive input, or variable traction drives combined with a planetary gear.

Types of gearbox Fixed ratio transmissions, shift transmission

Infinitely variable transmissions

Geared transmissions • Spur gears • Planetary gears • Bevel gears • Worm gears • Hypoid gears • Helical gears

Mechanical transmissions • Belt drives • Roller drives • Ratchet gears

Hydraulic transmissions • Hydrostatic transmissions • Hydrodyanmic transmissions

Eccentric drives • Cyclo drives • Harmonic drives

Traction drives • Belt drives • Chain drives

Geared transmissions Geared transmissions are the most commonly used. They transmit power without slip, have high operational reliability and long life, require little maintenance and are characterised by the ability to accept overloading, small size and high efficiency.

●

Gear wheels with straight cut teeth (➔ fig 3 a) are simple in design and can be accurately produced. The axial forces generated by inaccuracies and deformations (twisting) are negligible.

●

Gear wheels with helical teeth (➔ fig 3 b) run more smoothly and can carry heavier loads than those with straight cut teeth. A more elaborate bearing arrangement is required because of the axial forces.

●

The double helix or herringbone (➔ fig 3 c) allows for large tooth widths and can carry particularly heavy loads. The axial forces cancel each other out. Deviations in the helix angle cause axial vibrations.

Spur gears The spur gear is the most well-known and commonly used design of geared transmission. The dimensioning and manufacture of the gear wheels are the easiest to control. Their kinematic behaviour also forms the basis of planetary gears. Spur gears are in rolling contact and, irrespective of tooth type, have parallel axes.

10

1 Industrial gearboxes – overview Geared transmissions Fig 3

1 a

b

●

c

Internal gearing (➔ fig 3 d) has greater load carrying capacity than external because of the favourable osculation, but is more difficult to produce. The bearing arrangement is more complicated. The most frequent use is in planetary gears.

●

Bevel gears

d Spur gear unit a) straight cut teeth b) helical teeth c) double helix d) internal gearing

Bevel gears having spirally cut teeth (➔ fig 4 c) with curved flanks have clear advantages in respect of load carrying capacity. Particularly those with ground teeth are quieter than the types described above. For bevel gears which have to transmit high power, the spiral bevel gears are the most frequently used.

The common characteristic of this type of rolling contact gearing is that the axes of the wheels intersect each other. There are three basic designs categorised by the form of the flank. ●

With straight cut teeth (➔ fig 4 a), the mesh begins and ends across the total tooth width. The noise produced considerably limits the usefulness of straight cut bevel gears.

●

Bevel gears with helical teeth (➔ fig 4 b) have straight flanks. The teeth are usually ground and the mesh is gradual. The total overlap is bigger and the noise behaviour better than with straight cut teeth.

Bevel gear unit a) straight cut teeth b) helical teeth c) spirally cut teeth Fig 4

a

b

c

11

1 Industrial gearboxes – overview Geared transmissions Hypoid gear unit

Fig 5

Worm gears The worm and wheel axes cross each other at a considerable distance and usually at an angle < 90° (➔ fig 6 ). Worm gears are suitable for large single stage speed reduction. Their operation is quiet and vibration damping. The efficiency is lower than that of competing bevel/spur and planetary gears, because of the higher proportion of sliding motion. To reduce the friction, the use of synthetic lubricants is favoured. The most commonly used design is the cylindrical worm paired with a globoid wheel (➔ fig 6 a). The cylindrical worm can be hardened and ground which improves load carrying capacity; it is also freely adjustable in the axial direction so that bearing arrangement and mounting can be simplified. Two other designs – globoid worm with spur wheel (➔ fig 6 b) and globoid worm with globoid wheel (➔ fig 6 c) – are also used. Depending on the flank form, the worm types are classified as follows:

Hypoid gears The pinion axis is displaced so that the axes of this type of bevel gear do not intersect but are crossed (➔ fig 5 ). The wheels of hypoid gears are usually spirally cut. The advantages of this type of gear derive from the larger pinion and thus the smaller circumferential force for the same torque, as well as from the axis displacement which often allows the pinion to be supported at both sides so that the bearing arrangement is stiffer. The noise behaviour is also improved by the sliding motion in the longitudinal direction of the teeth. However, the additional sliding motion increases the friction, wear and risk of smearing and requires the use of hypoid oils with high additive content.

● ● ● ● ●

Worm gear unit a) cylindrical worm with globoid wheel b) globoid worm with spur wheel c) globoid worm with globoid wheel

ZA worm: trapezoidal worm thread in the axial cross section; ZN worm: trapezoidal worm thread in the normal cross section; ZK worm; trapezoidal tool (in normal cross section); ZI worm; evolvent thread in end face cross section; ZC worm: concave worm flanks

Fig 6

a

12

b

c

1 Industrial gearboxes – overview Geared transmissions The ZI and ZC designs are the most popular. The ZI worm can be very accurately ground whilst the favourable osculation conditions of the ZC worm (concave worm, convex wheel) bring load carrying advantages.

Planetary gears From the point of view of the tooth flanks, planetary gears are mostly spur gears. In contrast to the spur gear units so far described, the shafts of which are supported in stationary casings, the planetary gear unit has gear wheels which circulate. They are also referred to as epicyclic gears. In the simplest design (➔ fig 7 ), which is that most commonly used in industry, the sun wheel drives the planetary wheels (when acting as a speed reducer). These are supported in the hollow wheel and drive the planetary carrier from which the power is taken off. Planetary gears have the following important advantages compared with conventional spur gear units: ● ●

●

Fig 7 H

P

Simple planetary gear unit (principle) Z sun wheel P planetary wheel H hollow wheel S planetary carrier

S

Z

1

the volume, weight and centrifugal mass are smaller; the rolling and sliding velocities in the mesh are lower, so that noise is reduced; some of the power is transmitted as coupling power, so that efficiency is higher.

These advantages have led to a continuous increase in the economic importance of planetary gear units in spite of their disadvantages which include more difficult inspection, maintenance and repairs.

13

1 Industrial gearboxes – overview Demands made on gearboxes/Selecting the gears

Demands made on gearboxes The most important demands which must be fulfilled are: ●

●

●

there must be a sufficient safety margin in respect of fatigue and/or requisite life for all components so that the torques and speeds can be reliably transmitted; there must be sufficient cooling even under maximum power transmission conditions; noise emission should not exceed the permitted limits.

In addition to these demands, special requirements in respect of operation and design are dictated by the various applications. Some examples: ●

● ●

● ●

●

● ● ●

● ● ● ● ●

14

radial and/or axial forces on the input and output shafts, e.g. for extruders; external forces on the casing, e.g. in mining; heavy impacts, torque peaks, e.g. when driven by single cylinder combustion engines or when driving bucket excavators; vibrations, e.g. in wire drawing; extreme environmental influences in respect of temperature, dirt, dust, water, e.g. in arctic or tropical open cast mining and in continuous casting plant; seals subjected to pressure, e.g. in submerged gearboxes of dredgers or in mixing equipment in the chemical industry; reversing operation, e.g. for rolling mills; return stop, e.g. for conveyors; operation with little or no clearance and torsional stiffness, e.g. for positioning antennae and for robots; precision, e.g. for printing presses; lubrication with non-flammable lubricants, e.g. in mining; minimum maintenance, e.g. in wind power plant; arrangement, e.g. slip-on gears for converters; accessibility of measuring points to monitor lubrication, temperature, vibrations or torque, e.g. for large plastic extruders.

Selecting the gears To avoid either under or over-dimensioning a gear unit the load and the load carrying capacity of the gear must be able to be determined as accurately and reliably as possible. The size is correctly chosen when a comparison of the load spectrum and the load carrying capacity gives the desired service life. The determination of the load spectrum is a time-consuming and costly exercise calling for considerable measurements. Therefore, dimensioning is usually based on the rated torque of the driven machine, i.e. the operating torque for the most arduous work conditions. For a rolling mill, for example, this is the maximum continuous rolling torque (not the initial entry). The actual loads are higher because of additional external forces, produced by accelerations and vibrations, for example. When calculating the load carrying capacity of the gear wheels, these additional loads are considered by an application factor KA according to DIN 3990. One standard work on the subject lists the following criteria for evaluating the load carrying capacity of gear wheels: ● ● ● ● ● ●

resistance to pitting (tooth flank fatigue), root strength (tooth fracture from fatigue), resistance to scuffing (hot tooth flank welding), wear strength (slow wear of tooth flanks), “grey spot” resistance (fatigue from micro pores on the tooth flanks, and lubricant film formation.

The load carrying capacity which is used as the basis for dimensioning gear wheels is determined in rig tests under standard conditions (partly standardised: FZG test to DIN 51 354).

1 Industrial gearboxes – overview Designing tha casing

Designing the casing The following functions have a decisive influence on the design of the casing: ●

● ● ●

●

forces and supporting moments must be taken up and transmiitted at the same time as the position of the gear wheels and the form of the bearing seatings must be accurately maintained; there must be adequate heat removal; noise radiation must be at a minimum; gear wheels and bearings must be protected against contamination by foreign matter; lubricant loss must be prevented.

1

The increase in load carrying capacity of gear wheels and rolling bearings resulting from design improvements, improved materials and enhanced quality has enabled gearboxes to be downsized or uprated. The higher specific loads, frictional losses and increased noise resulting from this trend mean that the casings must be more stable so as to keep deformations to a minimum, but also that they should have a sufficiently large surface to prevent inadmissible heating and premature lubricant ageing, and should be properly designed with respect to minimising noise so as not to exceed the noise emission limits.

15

2 Bearing types for industrial gearboxes Deep groove ball bearings . 18 Angular contact ball bearings . . . . . . . . . . . . . . . . 20 Cylindrical roller bearings . . 22 CARB™ roller bearings . . . . 24 Spherical roller bearings . . . 26 Taper roller bearings . . . . . . 28 Spherical roller thrust bearings . . . . . . . . . . . . . . . . 30


Bearing types for industrial gearboxes For the support of the shafts and gear wheels of industrial gearboxes, rolling bearings are used almost exclusively. The exceptions are in some specialised areas, such as turbo drives, where hydrodynamic plain bearings are used.

There are many good reasons for this dominance of rolling bearings: ●

● ●

● ● ● ● ● ● ● ● ● ● ● ● ●

good location with minimum radial and axial play enables optimum meshing to be achieved; high specific load carrying capacity with low friction; wide range of internationally standardised products produced in high volumes at reasonable prices and having good availability; can be calculated using reliable load carrying capacity values; little design work for the user; simple arrangement; axially compact so that short and stiff shafts can be used; normal tolerances and surface finishes for shaft and housing seatings; less sensitive to misalignment than plain bearings; ability of radial bearings to accept axial loads; not influenced by direction of load or rotation; low starting torque; no starting problems in intermittent operation; relatively easy to lubricate; favourable behaviour under emergency conditions; economic maintenance.

2

Almost all bearing types are used in industrial gearboxes and almost all the available sizes. In the majority of applications, standard “catalogue” bearings can be used; any variants with respect to clearance or cage design are also generally common, so that the comprehensive range of SKF “catalogue” bearings for general engineering applications covers the needs of gearboxes very well and enables the designer to make an optimum selection. The most important bearing types for gearboxes are described in more detail in the following.

17

2 Bearing types for industrial gearboxes Deep groove ball bearings

18

2 Bearing types for industrial gearboxes Deep groove ball bearings

Deep groove ball bearings Deep groove ball bearings are the most popular of all bearing types and this also applies for gearboxes. The most important characteristics which make them so popular are ●

●

●

● ● ●

they are able to carry radial loads as well as axial loads acting in both directions; they are suitable for high and very high speed operation as their friction is low; they have practically no tendency to smear, i.e. cold welding when the balls are accelerated; they run quietly, particularly if they are lightly preloaded by axial force; they are robust in operation and require little maintenance; they are favourably priced.

These improvements also bring advantages when the bearings are used in gearboxes. In particular the reduced sensitivity to misalignment means that there is no reduction in bearing life under the slight misalignments of up to approximately 3 minutes of arc which are normally encountered. The improved surfaces reduce friction leading to lower running temperatures so that lubrication conditions are improved and bearing life extended.

2

The dominant role for deep groove ball bearings is where shafts have to be located axially and loads are relatively light. This is the case in ● ● ● ● ● ●

Benefits offered by SKF

spur gear units (drive shaft and hollow take-off shaft), multi-ratio gear units (switching spur gear wheels), geared motors worm gear units (worm wheels), planetary gears (drive shaft, planetary carrier) and coupling shafts. In recent years SKF has made a number of improvements to deep groove ball bearings which have resulted in further performance enhancements. The more important include ●

●

●

optimised raceway geometry and finish, reducing friction, running noise and sensitivity to misalignment; improved cages which are more stable, thus increasing reliability at high speeds; improved seals, thus enhancing the sealing efficiency of sealed bearings.

19

2 Bearing types for industrial gearboxes Angular contact ball bearings

20

2 Bearing types for industrial gearboxes Angular contact ball bearings

Angular contact ball bearings The raceways of these bearings are arranged at an angle to the bearing axis (contact angle), so that they are able to carry heavier axial loads than deep groove ball bearings. Sliding movements of the balls are superimposed on their rolling motion, so that the single row bearings require accurate adjustment or a minimum axial load to function properly. Angular contact ball bearings are available in the following designs: ● ●

●

single row, single direction angular contact ball bearings, double row, double direction and paired single row angular contact ball bearings and four-point contact ball bearings, i.e. single row, double direction ball bearings.

The improvements made by SKF to single and double row angular contact ball bearings, e.g. reinforcement of the ball set (single row – BE design, double row – A and E designs) to give higher load carrying capacity means that worm gear units can transmit more power and, at the same time, the reduction in friction means that bearing temperature can be lowered. The reduced tolerances for axial clearance and for dimensional and running accuracy which are standard for SKF single row angular contact ball bearings for paired mounting of the CB design, because of the improved location and reduced running noise, are advantageous in low-noise worm gear units such as those required for lifts and escalators.


2

Single direction implies that axial loads acting in one direction only can be accommodated, whereas double direction bearings (and paired single direction bearings, depending on the arrangement) can take axial loads acting in both directions. The single and double row angular contact ball bearings are preferred as locating bearings for worm shafts. Four-point contact ball bearings are used primarily as thrust bearings in high speed spur gear units, where the outer ring is radially free.

21

2 Bearing types for industrial gearboxes Cylindrical roller bearings

22

2 Bearing types for industrial gearboxes Cylindrical roller bearings

Cylindrical roller bearings The special properties of cylindrical roller bearings make them a popular choice for gearboxes and include: ● ● ●

●

●

● ●

high radial load carrying capacity; low friction – the lowest of any roller bearing under purely radial load; suitable for a wide range of operating speeds, including very high speeds, as the cage has the correct combination of roller guidance, strength and sliding friction properties; ability to accommodate moderate axial loads, when they are simultaneously under radial load, via the slid-ing surfaces of the roller end/flange contact, although the increased friction means that lubrication and cooling must be adapted to the conditions; the ease with which lateral displacement can take place within the bearing makes them ideal as non-locating bearings; proven good performance under external radial accelerations; most designs are separable so that mounting and dismounting are simple.

These characteristics make cylindrical roller bearings ideal for the following applications: ●

●

as the non-locating bearings of all high-performance units; the NU design with its flangeless inner ring is perhaps the most used, but also the NJ, NJG and NCF find application; the rings of these bearings need only be axially located at one side, and by mounting the rings with relative axial displacement the bearings can accommodate lateral displacement in both directions. in spur gear units, even where combined radial and axial loads are produced by the helical teeth; the most popular positions are those on the intermediate shaft, as the axial forces from the driven and driving wheels generally act in opposite directions so that the resultant axial load is light.

Practically all improvements made to cylindrical roller bearings by SKF could be considered as tailored to gearbox needs, so that they make an appreciable contribution to increased performance. The main characteristics are ●

●

●

●


the reinforced roller complements and “opened” flanges of the EC design give increased radial and axial load carrying capacity; the logarithmic roller profile ensures an optimum stress distribution over the whole roller length so that edge stresses are avoided even under heavy loads and the permissible misalignments; the refined raceway micro-geometry reduces friction and improves lubricant film formation; newly developed cages ensure proper bearing function over the increased performance range; the standard polyamide cages (designation suffix P) of small bearings have low friction, are elastic and have good sliding properties; the steel window-type cages (designation suffix J) which are standard for medium-sized bearings and can also be fitted to the smaller sizes (to special order) withstand high temperatures and also medium to strong vibrations; the machined brass cages (for gearbox bearings preferably outer ring centred and in two parts, designation suffix MA, or in one piece, suffix MP or ML) are standard for large bearings and can be fitted to other sizes to special order; they can tolerate high speeds and are resistant to vibrations and accelerations.

2

The range of cylindrical roller bearings is large compared with other bearing types. The various flange configurations (NU, NJ, NUP, N and NCF designs) make the bearings suitable for a multitude of applications and the different cage designs extend the usefulness of these bearings. 23

2 Bearing types for industrial gearboxes CARB™ roller bearings

24

2 Bearing types for industrial gearboxes CARB™ roller bearings

CARB™ roller bearings CARB is a completely new type of bearing: a Compact Aligning Roller Bearing. This single row roller bearing, developed by SKF, is characterised by a combination of properties which make it interesting for a multitude of applications: ●

●

● ● ● ●

the ability to compensate for angular misalignments or initial errors of alignment typical of spherical roller bearings; the ability to take up axial displacements in the bearing itself typical of cylindrical roller bearings; the low cross section typical of needle roller bearings; the high radial load carrying capacity imparted by long sphered rollers; the low friction obtained from optimally matched raceway profiles; the quietness of operation.

Because of its many advantages, the CARB makes an ideal non-locating bearing. The points in favour of its use in industrial gearboxes include, in addition its compact design and high radial load carrying capacity even when misaligned, the potential for downsizing or increasing operational reliability or the power rating. The CARB is particularly suitable for the bearing arrange-ments of ● ● ●

SKF has introduced a completely new roller bearing, the CARB. It is the only bearing available which combines the advantages of three different bearing types without, at the same time, incorporating their disadvantages. For gearbox applications, these advantages translate into the following opportunities for enhanced performance. ●

●

●

●

●


Up to 30 % higher load carrying capacity at the bearing position combined with small radial space requirements The low cross section allows downsizing or increased performance Compensation for errors of position and also form of bearing seatings in housings thus allowing machining costs to be reduced Both bearing rings can be mounted with an interference fit so that there will be no wear in the bore and no additional axial loads under conditions of axial displacement Quiet running and little vibration

2

heavily loaded shafts in spur gearboxes, pinion shafts in bevel gearboxes, and planetary gears.

Two versions of CARB are available: a bearing with cage and a full complement bearing.

25

2 Bearing types for industrial gearboxes Spherical roller bearings

26

2 Bearing types for industrial gearboxes Spherical roller bearings

Spherical roller bearings The self-aligning capability (also in operation) of spherical roller bearings makes their use advantageous where shaft bending occurs or where there are errors of alignment between shaft and housing (casing). They are therefore used in all cases where misalignment of the bearing rings would produce inadmissible edge stresses if rigid bearings were used. Additional important characteristics make the spherical roller bearing a reliable “all-rounder” for gearbox applications. These include ●

● ●

the high radial load carrying capacity and the ability to accommodate axial loads acting in both directions; the wide range of dimension series and very wide range of sizes even very large sizes.

The many successful development refinements and the improved characteristics resulting from them explain the popularity of spherical roller bearings for gearboxes (particularly in spur, bevel and planetary gear units).

The design and functional characteristics substantiate the leading position of SKF spherical roller bearings: ● ●

●

●

●

●


long, symmetrical rollers give very high load carrying capacity; the “floating” guide ring between the rows of rollers ensures that the rollers are properly guided (without “wobble”) into the loaded zone and, in cases where axial loads predominate, that the load is correctly carried by the rollers and symmetrically distributed over the roller length; the special form and optimum surface finish of the raceways minimise friction and operating temperature enabling high speed operation; the latest development – the E design – has even higher load carrying capacity as the bearing section is more efficiently exploited; the position of the guide ring above the pitch diameter in the E design favours lubricant film formation between the rollers and guide ring; all SKF spherical roller bearings are fitted with robust metallic cages which perform well even under arduous conditions.

2

27

2 Bearing types for industrial gearboxes Taper roller bearings

28

2 Bearing types for industrial gearboxes Taper roller bearings

Taper roller bearings The tapered form of the raceways makes these bearings eminently suitable for combined radial and axial loads. There is a choice of contact angles so that the appropriate bearing for the particular combination of radial and axial loads can be found. The necessity for functional reasons to use two bearings adjusted against each other enables the force distribution on the rollers to be controlled so that maximum life can be obtained at the same time as the stiffness and guidance of gear shafts can be optimised. The main gearbox applications are ● ● ●

spur gear units with helical teeth, bevel and bevel/spur units and worm gear units.

As taper roller bearings can support very heavy loads, they are always used when the load carrying capacity of other bearings for combined load conditions (deep groove and angular contact ball bearings) is inadequate. Because the raceways are at an angle to the bearing axis, an internal axial force is produced when the bearing is radially loaded, which acts on the housing via the outer ring and can deform it. With larger units (from approximately 90 mm shaft diameter) and specifically high performance requirements, the casing walls are often not sufficiently stiff, so that the use of double row or paired single row taper roller bearings (or spherical roller bearings) is recommended, because the internal axial forces cancel out each other and the casing walls will not be deformed. Paired single row taper roller bearings in a face-to-face arrangement (designation suffix DF) are always used when the preset axial play can be exploited and when adjustment during mounting is to be avoided.

SKF taper roller bearings have a number of advantages which make them suitable for industrial gearboxes. These include ●

●

●


the ideal form and optimum finish of the roller end/guide flange contact enable hydrodynamic lubrication to be achieved and mixed lubrication conditions avoided, so that the critical running-in process normally required when commissioning a gearbox is not needed; the logarithmic raceway profiles guarantee optimum stress distribution over the whole roller length and prevent edge stresses; the improved surface topography of the raceways enhances lubricant film formation and reduces bearing noise.

2

29

2 Bearing types for industrial gearboxes Spherical roller thrust bearings

Spherical roller thrust bearings The special feature of these bearings is their self-aligning capability. This means that their full load carrying capacity can be utilised, in contrast to the very stiff cylindrical roller thrust bearings, even when the bearing washers are slightly out of alignment with each other. The even distribution of load is still maintained when there are small angular misalignments of the seating surfaces. Such misalignments would considerably shorten the life of cylindrical roller thrust bearings. Spherical roller thrust bearings are used in gearboxes, particularly where axial forces are produced by the driven 30

SKF spherical roller thrust bearings have particularly low friction thanks to the special roller end/flange contact geometry. machine, e.g. in extruder gearing and water turbine gearboxes. The bearings are used successfully as thrust bearings for the pinion and worm shafts of large and very heavily loaded bevel and worm gear units.


Marine gearbox with spherical roller bearings, cylindrical roller bearings, fourpoint contact ball bearings and spherical roller thrust bearings


2

31

3 Design of bearing arrangements Shafts and gear wheels in spur gearboxes . . . . . . . . 33 Shafts in bevel gearboxes . . 44 Shafts in worm gearboxes . 50 Shafts and gear wheels for planetary gearboxes . . . . . . 56

3 Design of bearing arrangements Shafts and gear wheels in spur gearboxes

Design of bearing arrangements

It is quite possible that several different bearing types are used in one gearbox, and where combined gear units are concerned, there are several types of gearing. A stepwise approach is therefore appropriate when selecting bearings, taking each shaft in turn so that the different conditions for the individual shafts and gear wheels can be fully considered. The bearing arrangements described in the following are well proven and the conditions specific to a certain shaft are covered. A presentation of the most commonly used bearing series facilitates the initial selection.

Shafts and gear wheels in spur gearboxes Spur gearboxes are generally used to reduce speed. There are three main types which differ in the way they are mounted: stationary units (mounted on the machine base), cartridge units (mounted on the drive shaft of the driven machine) and flanged units (flanged to the casing of the prime mover and/or driven machine).

3

The drive from the prime mover is via a coupling or a belt. The drive is transmitted to the driven machine via a coupling, a quill shaft connection or via a pinion.

Input shafts The input (drive) shafts have the highest speeds and lightest loads provided no additional external loads have to be considered, e.g. belt tension forces. Vibrations and imbalance forces may be produced by the prime mover. It is also necessary to consider the prob33


Bearing arrangement for an input shaft with two cross-located deep groove ball bearings

Bearing arrangement for an input shaft with two taper roller bearings arranged face-to-face

34

lems of high angular accelerations when starting without load as well as operation without load at maximum speed in order to prevent bearing damage caused by the rolling elements sliding on the raceways. There is a danger of this occurring when loads are suddenly applied. The temperature differences and the associated thermal expansions in the radial and axial directions are high for input shafts, as the speed related large power loss and relatively small masses as well as the relatively small surface of the pinion shaft mean that there is insufficient heat removal. The distance between bearings is dictated by the casing and the low torque often means that slim shafts are used. This means that shaft

bending and bearing misalignment must be taken into account, particularly if a belt drive is used. Two deep groove ball bearings arranged for cross location (➔ fig 1 ) provide a cost-favourable bearing arrangement for moderate power requirements. Deep groove ball bearings are suitable for high-speed operation. Because of the low friction, small quantities of oil are adequate for lubrication and cooling so that the collected oil splashed by the gear wheels dipping into the oil bath is generally sufficient. In order to prevent axial clamping of the bearings being caused by thermal expansion of the shaft there should be sufficient axial clearance between the outer ring and the cover. For shaft diameters of up to approximately 90 mm, two taper roller bearings arranged face-to-face (➔ fig 2 ) are advantageous both from technical and cost considerations. The taper roller bearings are adjusted against each other via the cover so that they will have zero clearance when at the operating temperature or, for reasons of stiffness, they may have a slight preload. When determining the initial axial clearance it is necessary not only to consider the temperature differential between shaft and casing but also the deformation of the shaft and, above all, the casing. The casings of larger units are often not stiff enough with respect to the axial forces (tooth force + internal axial forces in the bearings). In such cases bearing adjustment is dif-

Bearing arrangement for an input shaft with two cylindrical roller bearings


Classic locating/nonlocating bearing arrangement with a spherical roller bearing and a cylindrical roller bearing

ficult and shaft guidance is not sufficient-ly accurate. The taper roller bearing arrangement shown is, therefore, not always suitable. Cylindrical roller bearings (➔ fig 3 ) have a high radial stiffness and guide the shaft very accurately without having to be adjusted as taper roller bearings. Axial forces are transmitted via the flanges and roller ends. Because this causes more frictional heat, lubrication and cooling must be particularly good. In order to prevent axial clamping of the bearings when thermal expansion of the shaft takes place, there should be adequate axial play between the flanges. The classical locating/non-locating arrangement (➔ fig 4 ) is more complicated from a design point of view than the cross-located arrangements described above, as the inner and outer rings must be axially located at both sides. However, it has advantages with regard to dimensioning as the axial force is always taken up by a given bearing – in this case the spherical roller bearing – irrespective of the direction of the load. Additionally, displacement of the non-locating bearing is always assured so that there is no risk of axial clamping occurring when the shaft expands. Two NU-design cylindrical roller bearings as radial bearings together with a four-point contact ball bearing as the thrust bearing (➔ fig 5 ) have proved suitable for very high-speed operation (up to n × dm ≈ 1 000 000). For such

high-speed operation the bearings must have ● ●

●

machined brass cages, centred in the outer ring, increased internal clearance: C3 for the cylindrical roller bearings and C4 for the four-point contact ball bearing, and seatings having increased accuracy of form and position (IT4/2).

At high circumferential speeds the bearings will reject normal oil supplies. Therefore, it is necessary to inject oil at high speed (v ≈ 15 m/s) into the gap between cage and inner ring. Oil drainage facilities should be provided at the injection side of the bearings.

3

Bearing arrangement for an input shaft with two cylindrical roller bearings as the radial bearings and a four-point contact ball bearing as the thrust bearing

35


Intermediate shafts

Bearing arrangement for an intermediate shaft with two taper roller bearings arranged face-to-face

36

Intermediate shafts are the most heavily loaded as they are subjected to the forces from two gear meshes. The speeds are moderate. The axial forces on pinion and wheel oppose each other when the direction of the teeth is the same so that they partially balance each other. There are no additional external forces but vibrations may be transmitted from the input or output shafts. As there is no torque acting at the shaft ends, reasonably small diameters can be used enabling a relatively large bearing section to be utilised for the accommodation of the high radial forces. Design limits for the bearing outside diameter are set by the distance between input and output shafts. When using taper roller bearings (➔ fig 6 ) it should be remembered that axial forces are produced even though the load is purely radial. This may lead to axial deformation of the casing. These deformations occur in the central, less stiff region of the casing because of the position of the intermediate shaft, and are larger than for the input shaft. They lead to a change in position of the shaft and can therefore cause inadmissibly high misalignment of the bearings and the mesh. Experience shows that the casing deformations occurring in smaller units with shaft diameters up to 90 mm are generally within acceptable limits. For larger units it is necessary to resort to

other bearing types or arrangements which are less unfavourable in respect of casing deformation. In comparison with input shafts, the axial loading of cylindrical roller bearings used to support intermediate shafts (➔ fig 7 ) is less critical. The axial forces at the gears act in opposite directions and cancel each other out, at least partially, so that the axial load on the bearings is light. Also the speeds are lower so that frictional losses deriving from the axial load remain small. The high radial load carrying capacity of the cylindrical roller bearings is an advantage as the intermediate shaft bearings are heavily loaded. The choice between caged or full complement cylindrical roller bearings is determined primarily by the factors load, speed, lubrication conditions, friction and cost. Compared with the input shaft, there is only a small temperature gradient between the intermediate shaft and the casing. This makes it possible to use spherical roller bearings in a crosslocated arrangement as shown in fig 8 which is simple in design and therefore cost-favourable. There is a wide range of spherical roller bearings available, particularly for medium and large shaft diameters, and there is also a choice of several cross sections for each diameter. It is thus possible to easily find bearings which can support the heavy loads acting on the intermediate shaft but

Bearing arrangement for an intermediate shaft with two cylindrical roller bearings

3 Design of bearing arrangements Shafts and gear wheels in spur gearboxes which have outside diameters within the limits set by the distance between the shafts. A locating/non-locating bearing arrangement as per fig 9 with a spherical roller bearing at the locating side and a CARB as the non-locating bearing offers the possibility of reducing the cross section of the non-locating bearing arrangement, because of the high load carrying capacity of the CARB, so that the available space can be better exploited. In many applications there is a risk that the bearing seating in the housing will be ”hammered out” so that an intermediate sleeve must be incorporated. By using a CARB bearing this is no longer a problem as the outer ring is mounted with an interference fit in the housing, so that a sleeve is not needed.

3

Bearing arrangement for an intermediate shaft with two spherical roller bearings

Bearing arrangement for an intermediate shaft with one spherical roller bearing (locating) and one CARB (nonlocating bearing) Fig 9

37

3 Design of bearing arrangements Shafts and gear wheels in spur gearboxes The locating/non-locating arrangement shown in fig 10 can carry very heavy radial as well as axial loads. Two matched single row taper roller bearings (DF execution) are used for the locating arrangement. In contrast to the cross-located bearing arrangements shown in figs 2 and 6, the internal axial forces of the taper roller bearings compensate each other within the bearing pair and do not deform the casing. The intermediate ring supplied with the bearing pair ensures that there is a minimum axial clearance within the bearings. This is adequate for temperature differentials between shaft and casing of up to 20 °C. To avoid deformation of the thin-walled inner ring as the cover screws are tightened, the length of the centring surface (spigot) of the cover should be chosen to give a preload of approximately 0,01 mm.

Drive (output) shafts Locating/nonlocating bearing arrangement for an intermediate shaft with two matched single row taper roller bearings and one cylindrical roller bearing

38

The conditions for the drive shafts are characterised by high torques and low speeds. The torque calls for a large shaft diameter so that the requisite load carrying capacity can be obtained even when using bearings with low cross sections. There are potential problems with lubrication of the rolling contacts if, because of the low speeds, elastohydrodynamic

(EHD) lubrication, i.e. the formation of a separating lubricant film between rolling elements and raceways, cannot be achieved. Operating bearings under conditions of mixed friction or boundary lubrication will result in wear and shorter bearing life. Besides rotational speed, operating temperature and lubricant viscosity are the most important factors determining EHD lubrication. There is a limit to how high the viscosity of the oil can be because consideration must be paid to the high-speed gears and bearings in the unit. Therefore, a cooling of the gearbox in the region where the low-speed bearings of the drive shaft are situated is often the most effective means of increasing bearing life. Suitable additives in the oil can also contribute to a reduction in wear. Other factors influencing drive shaft bearings depend on the gearbox design: ●

In stationary, base-mounted gearboxes, depending on the type of power take-off, it is necessary to consider the forces of the coupling, the propeller shaft, a pinion or of the directly coupled driven machine (e.g. extruders).

Bearing arrangement for an output shaft with two spherical roller bearings

3 Design of bearing arrangements Shafts and gear wheels in spur gearboxes ●

●

Bearing arrangement for an output shaft of a cartridge-type unit with full complement cylindrical roller bearings of series NCF 29 V

The bearings in cartridge-type gearboxes are subjected to the reactionary forces of the torque support. Additional forces may also be produced as a result of casing deformation. The casings of flanged gearboxes are bolted to the driven machine. The shafts are generally rigidly coupled so that the double support of the output shaft becomes a multiple support in practice. Centring errors of the coupled components produce additional forces in the bearings so that narrower tolerances for the centring should ensure the accuracy of alignment of the bearing arrangement.

The arrangement with spherical roller bearings (➔ fig 11 ) is especially suitable for applications where rough operation, external additional forces, misalignments and shock loads place heightened demands on the bearings. Axial shock loads are taken up by the less sensitive raceways in the absence of flanges on the rings. For cartidge-type gearboxes, the relatively large diameters of the hollow shaft mean that bearings having low cross section are suitable. Fig 12 shows a well-proven bearing arrangement incorporating full complement

cylindrical roller bearings of series NCF 29 V. For lighter loads but with similar diameters, deep groove ball bearings of series 619 can be used in the same arrangement. For heavier loads as well as larger deformations, but still with the same diameters and arrangement, spherical roller bearings of series 239 are appropriate. Deep groove ball and spherical roller bearings have cages and are thus less susceptible to wear when inadequately lubricated than full complement bearings.

Intermediate gear wheels An internal bearing arrangement is most suitable for intermediate gears as it takes up the least space. Internal bearing arrangements are characterised by rotating outer rings. Therefore, there is rotating outer ring load and stationary inner ring load. This means that the outer rings should have interference fits and the seatings should be very accurately machined in order to keep the rotating inaccuracies – which cause increased friction and additional forces on the bearing cage – to a minimum. With opposing meshes the circumferential forces are added, so that high radial load carrying capacity is required. The axial forces from the

3

Bearing arrangement for an intermediate gear wheel with two cylindrical roller bearings of the NJ design

39


Bearing arrangement for an intermediate gear wheel with two taper roller bearings arranged back-to-back

40

helical teeth oppose each other and partially cancel each other producing a tilting moment on the bearing which can cause misalignment. Two cylindrical roller bearings of the NJ design provide the requisite high radial load carrying capacity in a restricted space as shown in fig 13 . The design of the associated components of the arrangement is simple. The bearing arrangement of helical intermediate gear wheels must be checked for angular misalignment. An unfavourable combination of wheel diameter, pitch and distance between bearings can produce inadmissible values of misalignment. An extended support width (distance between bearing pressure centres) can be achieved using, for example, angular contact ball bearings. Taper roller bearings in a back-toback arrangement (➔ fig 14 ) also increase the support width as well as reducing the influence of the tilitng moment on the misalignment if they are adjusted to zero clearance, or a light preload. Straight cut gear wheels may be supported by a single spherical roller bearing (➔ fig 15 ). The intermediate gear wheels are thus free to align so that a good mesh is achieved. In order to be able to use standard bearings (without lubrication holes in

the inner ring) oil should be supplied at the side. To prevent the supplied oil from being rejected by the bearing, the seal gap at the supply side should not exceed 1 mm.

Shifting gear wheels For reasons of space these gear wheels are supported internally in a similar manner to the intermediate gears. The torque is transmitted in the engaged condition so that the bearings are subjected to the tooth forces. The inner and outer rings rotate but the relative speed is zero. Both rings have rotating load but the rolling elements do not roll. The continuous changes in load under these stationary conditions cause micro-sliding to take place at the rolling element/raceway contacts. As there is no relative rotation of the rings, a ”washboarding” type of wear will be produced in the raceways. This wear can be reduced by using highly viscous lubricating oil containing anti-wear additives. Where the wheels have helical teeth, the axial force produces a tilting moment and consequently a rotating tilting motion which leads to axial movement in the rolling element/raceway contacts. This increases wear. Ball bearings, adjusted to zero clearance, behave favourably as the balls can

Bearing arrangement for an intermediate gear wheel with a single spherical roller bearing

3 Design of bearing arrangements Shafts and gear wheels in spur gearboxes also roll in the axial direction and because the movement is reduced by the clearance-free adjustment. Wear is always load-dependent so that bearings under low specific loads wear less. The washboarding effect is also less prominent as engagement always takes place at new positions so that the wear is evenly spread over the raceway. For the support of shifting wheels, deep groove ball bearings have proved to give good performance (➔ fig 16 ). Bearings with increased radial internal clearance (C3) are used. The clearance-free adjustment via the inner rings produces a contact angle in the bearings of approximately 15°, so that the support width of the bearings is extended. This reduces movement in the relatively stationary bearings under rotating load and thus reduces wear. In addition, the clearance-free back-toback arrangement improves guidance of the wheel. Lubrication of the bearings from the outside is difficult as all components of the arrangement – shaft, bearings and wheel – rotate and because the bearings are partly covered e.g. by the coupling. The most reliable method is to supply oil internally through the shaft.

3

Bearing arrangement for shifting gear wheel with two deep groove ball bearings

41


Demands on the bearings Modern spur gears generally have hardened gear wheels with ground teeth. It is then possible to obtain high performance with relatively little friction and low noise. A prerequisite for this is the use of high-performance bearings, which should have the properties listed in Table 1 . In addition to these general requirements with respect to ball and roller bearings for high-performance gearboxes, other demands deriving from the specific operating conditions at Demands on rolling bearings for spur gears

each particular bearing position must be considered. To make the situation clearer in Tables 2 to 4 , the text has been kept as short as possible.

Table 1 Demand

Required bearing design feature

High load carrying capacity

Optimised rolling element size and number. Logarithmic roller/raceway contact. Good lubricant film formation through low friction and low raceway surface roughness.

High stiffness

Optimised rolling element size and number. Logarithmic roller/raceway contact.

High dimensional and running accuracy

Particularly the inner ring running accuracy should preferably be to tolerance class P6 or better.

Low friction

Low friction in roller end/flange contact for taper and cylindrical roller bearings. Low friction in roller/raceway contact. Lightweight precision cage. Low raceway surface roughness.

Low running noise

High precision of all bearing components.

Demands on input shaft bearings

42

Table 2 Specific operating conditions

Requirements of bearings/steps to guarantee performance

High speed and thus high friction and high operating temperature

Use low-friction bearings. Avoid over-dimensioning. Ensure lubricant supply when starting up cold. Provide good cooling.

Large temperature differential when starting up (slim input shaft heats up more quickly than the better cooled solid casing)

Check required bearing internal clearance; if necessary select bearings with C3 clearance. Ensure axial displacement at non-locating bearing position.

Vibration from drive; imbalance forces

Use bearings with stable cages, e.g. cylindrical roller bearings with steel window-type cages or outer ring centred machined cages, or spherical roller bearings with steel window-type cages.

Idling under light load

Check minimum load. Avoid over-dimensioning. Use bearings with small roller masses where possible. Do not use full complement cylindrical roller bearings. Choose bearing types less susceptible to smearing, e.g. spherical and taper roller bearings.


Bearing selection

●

The following check list will be found useful when selecting bearings in order not to forget any important factors.

● ●

● ●

● ● ●

Adjusted basic rating life Axial load carrying capacity when the flanges of cylindrical roller bearings are under load Friction Stiffness Misalignment

Sufficient play to prevent inadmissible clamping when temperature differentials are large Minimum load Static safety under peak loads

A preliminary choice can be made from the bearing series shown in Table 5 .



Heavy radial loads

Use bearings with high load carrying capacity.

Low to moderate speeds

Check lubricant film formation. If necessary increase viscosity or improve cooling. Use lubricants with wear-reducing additives.

3



Very low speeds

When lubricant film formation inadequate, i.e. a viscosity ratio (actual to required viscosity) κ < 1, use lubricants with suitable EP additives. When κ < 0,5 bearings with cages (not full complement bearings) must be used. When κ < 0,1 reduce the specific bearing load; aim for s0 > 10.

Shock loads from power take-off;deformations

Use robust, self-aligning, spherical roller bearings.

Table 5 Operating conditions

Bearing series normally used Input shaft Intermediate shaft

Demands on intermediate shaft bearings

Output shaft

Intermediate gears

Shifting gears

Light loads

62 63

63 NJ 2 EC

619 160 60

60 62

618/C3 619/C3

Moderate loads

NJ 2 EC 320 X 222 E(CC)

NJ 22 EC 322 222 E(CC)

NCF 29 V 239 CC

NJ 2 EC 320 X

160/C3 60/C3

Heavy loads

322 232 CC 223 E(CC)

NJ 23 EC NJG 23 VH 223 E(CC) 322/DF

230 CC

NJ 3 EC 303 232 CC 223 E(CC)

62/C3

High speeds

NU 2 ECMA/C3 QJ 2 N2MA/C4

Demands on output shaft bearings

Bearing selection

In addition to the bearing series listed above, a CARB can be used as the non-locating bearing for locating/non-locating bearing arrangements

43

3 Design of bearing arrangements Shafts in bevel gearboxes

Shafts in bevel gearboxes Bevel gears are generally speed reduction gears. The high-speed drive shaft is termed the pinion shaft and the slow-speed driven shaft carries the larger bevel gear wheel. The pinion shaft is driven by the motor via a coupling, a spur gear or a belt drive. The power take-off is either via a coupling or with bevel/spur gears via a pinion.

Pinion shafts The pinion is generally supported in an overhung arrangement. In a few cases the pinion is supported between the bearings but it is difficult to design in a bearing with sufficiently high load carrying capacity at the head. The overhung arrangement offers more space. Two taper roller bearings in a backto-back arrangement as shown in fig 17 offer a cost-favourable and axially as well as radially stiff arrangement for small to medium diameter shafts (d < 90 mm). The bearings are adjusted using a shim between the shaft shoulder and the inner ring of the bearing at the input side. The adjustment is determined to give zero clearance when the bearings are in operation and warm or, if required for stiffness reasons, a slight axial prelod. When determining the initial axial clearance the temperature differential between shaft and casing must be considered as well as the deformations of shaft and casing. Bearing arrangement for a bevel pinion shaft with two taper roller bearings arranged back-to-back

44

Oil should be supplied between the two bearings. A baffle plate ensures that both bearings are reliably supplied with lubricant. The oil drain at the cover side reduces the amount of lubricant reaching the seal.


Bearing arrangement for a bevel pinion shaft with two matched single row taper roller bearings arranged face-toface (locating position) and one spherical roller bearing (non-locating position)

For larger shafts, the requisite load carrying capacity can be achieved using a locating/non-locating bearing arrangement as shown in fig 18 . The locating arrangement is at the drive side and consists of two matched single row taper roller bearings (DF execution). The intermediate ring which is supplied with the bearing pair ensures that a minimum axial clearance remains when the bearings are mounted which can cope with temperature differentials between shaft and casing of up to 20 °C. For greater temperature differentials such as may occur, for example, in operation when ambient temperatures are very low, paired bearings with larger axial clearance are required (special execution). In order not to deform the thin-walled intermediate ring when tightening the cover screws, the length of the centring flange (spigot) on the cover should be such that a preload corresponding to approximately 0,01 mm is obtained. The matched taper roller bearings operate as a double row bearing. As the axial load from the pinion dominates, one of the two bearings – depending on the direction of the load – is completely unloaded. Experience shows that this is not a disadvantage when there is little vibration. The non-locating bearing adjacent to the bevel pinion may be either a spherical roller bearing, a cylindrical roller bearing or a CARB.

For one-piece casings, spherical roller bearings offer mounting advantages and they are also relatively insensitive to smearing when loads vary considerably and there are long periods of idling. If cylindrical roller bearings are used, the requisite axial displacement can always take place in the bearing itself so that the outer ring can have an interference fit in the housing, and radial guidance is enhanced. The same is true of CARB (➔ fig 19 ). At this position the bearing will not only enable the axial displacements to be easily accommodated, it will also accept the angular misalignments caused by the off-centre point of action of the tooth forces with no reduction in life. Oil should be supplied to the two taper roller bearings between the outer rings. Experience shows that for small and medium-sized gears (up to approximately d = 150 mm) the non-locating bearing can be adequately lubricated by the oil returning from the locating bearings. For larger gears, however, it is necessary to arrange for a separate oil supply to the non-locating bearing. For spherical roller bearings, the oil should be supplied via the lubrication groove and holes in the outer ring for the best results.

3

Bearing arrangement for a bevel pinion shaft with two single row taper roller bearings arranged back-to-back (locating) and one CARB (nonlocating bearing) Fig 19

45


Bearing arrangement for a bevel pinion shaft with one taper roller bearing as a thrust bearing and one taper roller bearing as a radial bearing (locating position) and one cylindrical roller bearing (nonlocating position)

46

Although the bearing arrangement shown in fig 20 is similar to that in fig 18 , there are considerable functional differences. All roller rows are always under load irrespective of the direction of the axial load. If the direction of axial load is from the pinion tip to the drive input, the taper roller bearing at the cover side with its radially free outer ring will be axially loaded, and the opposing bearing will be radially loaded. If the load direction is reversed then the smaller axial load will act on the inboard bearing which is also under radial load. The taper roller bearing at the cover side will then only be subjected to a minimum axial load by the springs. Because all roller rows are always under load, this arrangement is less sensitive to vibrations than that shown in fig 18 . Mounting is more complex because there is no intermediate ring between the taper roller bearings which have to be adjusted on mounting. The radially free outer ring of the taper roller bearing at the cover side is prevented from turning by an O-ring. A variant of this bearing arrangement incorporates a spherical roller thrust bearing which has a higher load carrying capacity. It replaces the taper roller bearing which only carries axial loads. With respect to lubrication, the same recommendations apply as for the arrangement shown in fig 18 .

Output shafts The gear wheels are generally arranged between the bearings for design reasons. This is also true for the bevel/spur gearboxes. For shaft diameters up to approximately 90 mm, two taper roller bearings mounted back-to-back (➔ fig 21 ) provide a technically advantageous and cost-favourable arrangement. With larger dimensions, the casings are often inadequately stiff with regard to the axial forces (tooth force + internal axial force of the bearings). This makes adjustment of the bearings difficult and shaft guidance is generally not sufficiently accurate. The bearing arrangement with cross location is then not altogether suitable. The axial force from the gear wheel always acts in one direction. As the axial force from the pinion dominates, it is possible that the direction of the resultant axial force will change. This must be taken into consideration when adjusting the mesh. When adjusting the taper roller bearings, the shim at the gear wheel side determines the position of the wheel in the gearbox. The shim at the pinion side is used to set the axial clearance of the taper roller bearings. Oil from the collecting pockets above the bearings runs down at the cover side of each bearing. From there the oil must pass through the bearing and thus lubricate it. Oil retaining plates ensure that there is an adequate supply of oil available even when starting up.

Bearing arrangement for a bevel wheel shaft with two taper roller bearings arranged face-to-face


Bearing arrangement for a bevel wheel shaft with a double row angular contact ball bearing (locating position) and a cylindrical roller bearing (non-locating position)

The locating/non-locating bearing arrangement shown in fig 22 has the advantage, compared with that shown in fig 21 , that no bearing adjustment is required. The bearings are also insensitive to axial deformation of the casing. This will only be subjected to the tooth forces and not to the internal bearing forces, so that there will be less deformation. A double row angular contact ball bearing is used as the locating bearing. Alternatively, single row angular contact ball bearings in matched sets having the same diameters as the double row bearing and being marginally wider can be used for higher load carrying capacity. To determine the position of the gear wheel in the gearbox and to adjust the mesh, a split washer is inserted between the bearing outer ring and the retaining ring. When doing this the bearing can remain on the shaft. A cylindrical roller bearing of the NU design is used as the non-locating bearing at the other side where the radial load is heavier. The locating/non-locating bearing arrangement shown in fig 23 is similar in design and function to that shown in fig 22 . At the locating side, two single row taper roller bearings are arranged face-to-face. Compared with the double row angular contact ball bearing, the taper roller bearings provide higher load carrying capacity and greater stiffness.

Adjustment of the bevel gear wheel is simplified using a special (hookshaped) sleeve. In order to prevent the thin-walled intermediate ring of the paired taper roller bearings from being deformed as the cover screws are tightened, the length of the spigot in the cover should be chosen to give a preload corresponding to approximately 0,01 mm. Oil should be supplied to the taper roller bearings via the lubrication groove and holes in the intermediate ring. To allow an even distribution over the two bearings, an oil drain should be provided at the cover side.

3

Bearing arrangement for a bevel wheel shaft with two matched single row taper roller bearings (locating position) and one cylindrical roller bearing (non-locating position)

47


Demands on the bearings Modern bevel gearboxes usually have hardened gear wheels with ground helical teeth. This enables high power transmission to be achieved with little friction and little noise generation. A prerequisite for this good performance is the use of high-performance ball and roller bearings which should have the properties listed in Table 6 . In addition to these general requirements for bearings for high-performance gearboxes, there are additional requirements which are specific to the actual bearing position.

Demands on rolling bearings for bevel gears

Demands on bevel pinion shaft bearings

48

Bearings for the pinion shaft High radial and axial forces act simultaneously on the pinion shaft. Therefore high radial load carrying capacity is required of the non-locating bearing and high axial load carrying capacity of the locating bearing. Because of the high speed, bearings having low friction should be used. These two requirements are in part contradictory. Experience shows that pinion bearings do not fail from fatigue but are endangered by other influences. From this it is possible to derive the requirements and actions listed in Table 7 .

Table 6 Demand

Required bearing design feature

High load carrying capacity

Optimised rolling element size and number. Logarithmic roller/raceway contact. Good lubricant film formation through low friction and low raceway surface roughness.

High stiffness

Optimised rolling element size and number. Logarithmic roller/raceway contact.

High dimensional and running accuracy

Particularly the inner ring running accuracy should preferably be to tolerance class P6 or better.

Low friction

Low friction in roller end/flange contact for taper roller bearings. Low friction in roller/raceway contact. Low raceway surface roughness.

Low running noise

High precision of all bearing components.

Table 7 Most frequent reason for pinion bearing damage

How to alleviate problem/demands on bearings

Lubrication breakdown

Guarantee lubrication when starting up in the cold state.

Overloading because of too heavy a preload

When selecting bearing size, check the temperature differential between shaft and casing. C3 internal clearance often required.

Inadequate lubricant film generation because of too high operating temperatures

Use low friction bearings. Avoid over-dimensioning. Improve cooling.

Smearing on rollers and raceways caused by roller slip or sliding

Avoid over-dimensioning. Spherical roller bearings are more favourable than cylindrical roller bearings in larger size range (d > 150 mm). When using cylindrical roller bearings aim for small roller diameters; use a full complement bearing.

Wear caused by contaminants

Avoid contaminating the gearbox during production, assembly and in operation.

3 Design of bearing arrangements Shafts in bevel gearboxes To obtain good meshing it is necessary among other things to have a bearing arrangement with high radial and axial stiffness. The locating bearing should therefore have a large contact angle and as small an axial clearance as possible.

Bearing selection When selecting the bearings it is useful to refer to the cheklist given below. ● ● ● ●

Bearings for the output shaft These bearings are predominantly radially loaded so that high radial load carrying capacity is also required of the locating bearing. Because of the slow speeds the risks in respect of thermal behaviour and over-dimensioning compared with the pinion shaft are negligible. The requirements for axial and radial stiffness, for minimum axial clearance and for bearing accuracy correspond to those for the pinion shaft bearings.

●

Adjusted basic rating life Permissible speed Axial and radial stiffness Sufficient bearing clearance in the mounted but cold state to avoid inadmissible preload under conditions of maximum temperature differentials Minimum load

A preliminary selection can be made using the overview of the bearing series commonly used; see Table 8 .

3

Table 8 Bearing arrangement

Bearing selection

Bearing series normally used Bevel pinion shaft Input side Pinion side

Bevel gear wheel/Bevel/spur gear wheel Gear wheel side Opposite side or spur pinion side

Cross location

72 BE 73 BE 313 323 B

72 BE 73 BE 322 332 303 323

Locating bearing(s)

(2×) 72 BECB (2×) 73 BECB 313/DF 322 + 293 E

72 BE 73 BE 323 B 323 B

72 BE 73 BE 322 332 303 323

33 (2×) 72 BECB (2×) 73 BECB 320 X/DF 322/DF

303 + 294 Non-locating bearing

NU 22 EC(/C3) NU 23 EC(/C3) 232 CC(/C3) 223 CC(/C3)

NU 2 EC NU 22 EC NU 3 EC NU 23 EC 223 EC

In addition to the bearing series listed above, a CARB can be used as the non-locating bearing for locating/non-locating bearing arrangements

49

3 Design of bearing arrangements Shafts in worm gearboxes

Shafts in worm gearboxes Generally worm gearboxes are used to reduce speed. There are two main types: one for mounting on the machine base and a cartridge type for mounting on the input (drive) shaft of the machine. The drive from the prime mover is either via a coupling or a belt drive. The power take-off is via a coupling or a quill (hollow) shaft connection. Bearing arrangement for a worm shaft with two angular contact ball bearings in a cross-located arrangement

Worm shafts The heaviest axial loads act on the worm shaft at the same time as speeds are high. Where there is a belt drive, the radial loads will also be heavy.

The temperature differences and the associated thermal expansion in the radial and axial directions are also large in worm gearboxes. Only small masses and surfaces of the worm shafts are available to remove heat. Therefore, there are large temperature gradients from the shaft to the casing and these must be considered when adjusting the bearings. The distance between bearings is dictated by the casing and together with the small torques this often leads to the use of slim shafts. If there is a belt drive, then shaft bending should be calculated so that inadmissible bearing misalignment can be avoided. Two single row angular contact ball bearings in a cross-located arrange50

ment (➔ fig 24 ) offer a cost-favourable, low friction bearing arrangement with low noise for moderate performance and where diameters are small (bearing bore diameter d ≈ 50 mm). The angular contact ball bearings are suitable for high speeds and because of the large contact angle they are also appropriate for predominantly axial loads. The two bearings are adjusted against each other via the cover so that they will have a slight preload when running at the operating temperature. When determining the degree of adjustment it is necessary to consider the temperature differential between shaft and casing, but also casing deformation.

The same type of arrangement but using two steep-angled taper roller bearings (➔ fig 25 ) can carry heavier loads than that with the angular contact ball bearings for the same shaft diameter. Therefore, taper roller bearings are preferred for higher performance gearboxes and for medium to large diameters. When determining the degree of adjustment, it must be remembered that taper roller bearings are axially stiffer than angular contact ball bearings and are therefore more sensitive to excessive preload. It is thus advisable to aim at zero clearance when the bearings are running at the operating temperature. When starting up (worm already warm, casing still cold) a slight preload will be pre-

Bearing arrangement for a worm shaft with two taper roller bearings arranged face-to-face

3 Design of bearing arrangements Shafts in worm gearboxes Bearing arrangement for a worm shaft with two matched angular contact ball bearings (locating position) and one cylindrical roller bearing (nonlocating position)

sent which experience shows can be tolerated when lubrication is good. The locating/non-locating bearing arrangement (➔ fig 26 ) is more costly from a design point of view and because a third bearing is involved but it has the following advantages: ● ●

●

higher load carrying capacity (e.g. for belt tension forces); if paired angular contact ball bearings are used, no individual adjustment is required; axial displacement at the non-locating bearing position is guaranteed.

ed single row taper roller bearings (DF execution) as shown in fig 27 . The intermediate ring which is supplied with the bearing pair ensures that there is a minimum axial clearance in the mounted condition, which is sufficient for temperature differentials between shaft and casing of up to 20 °C. In order not to deform the thin-walled intermediate ring when the cover screws are tightened, the spigot (centring shoulder) in the cover should have a length such that a preload corresponding to approximately 0,01 mm can be obtained.

3

A further performance increase can be obtained by replacing the pair of angular contact ball bearings by two matchBearing arrangement for a worm shaft with two matched taper roller bearings (locating position) and one cylindrical roller bearing (non-locating position)

51

3 Design of bearing arrangements Shafts in worm gearboxes Bearing arrangement for a worm shaft with a taper roller bearing as the radial bearing and a spherical roller thrust bearing as the thrust bearing (locating position) and a cylindrical roller bearing (nonlocating position)

The bearing arrangement shown in fig 28 is particularly suitable when the axial load in one direction predominates, as for example in lifting gear. The spherical roller thrust bearing takes the dominant axial load as well as the axial force produced in the taper roller bearing, which in this case is only subjected to radial load. If the axial load changes direction, then the taper roller bearing takes the radial as well as the axial load, while the spherical roller bearing is spring loaded to give the minimum axial load required for the correct motion of the rollers. Both bearings are adjusted via the cover. When determining the axial clearance it is necessary to consider the temperature differential between shaft and casing. Bearing arrangement for a worm shaft for maximum loads with two radial spherical roller bearings and two spherical roller thrust bearings

52

The advantages of this bearing arrangement are the very high load carrying capacity in the one direction and also that all three bearings are always under load. Bearing noise is then particularly low and the bearings are less sensitive to vibration. Fig 29 shows a bearing arrangement for maximum loads and shocktype operation as encountered, for example, in rolling mills when the rolls are set. The radial forces are taken up by two radial spherical roller bearings mounted as non-locating bearings, whilst the axial forces act on the spherical roller thrust bearings which have radial freedom in the casing. The axial clearance of the spherical roller thrust bearings is obtained by adjusting the

3 Design of bearing arrangements Shafts in worm gearboxes width of the spacer sleeve. The springs ensure that the requisite minimum load is applied to the bearing which is relieved of axial load.

Worm wheel shafts

Fig 30: Bearing arrangement for a worm wheel shaft with two deep groove ball bearings in a crosslocated arrangement

The high torques on the worm wheel shafts require large shaft diameters. As speeds are slow, the load carrying capacity of low cross section bearings (light series) is adequate. Because of the low speeds, lubrication of the worm wheel bearings by oil spray is usually not sufficient and special arrangements must be made for lubricant supply. An oil wiper on the worm wheel or separate grease lubrication of the bearings have been found to give good results.

vide adequate lubrication for the bearings they are greased and a gap-type seal is provided on the inboard side. The arrangement shown in fig 31 with two taper roller bearings is intended for heavier loads than that shown in fig 30 but is otherwise similar. It should be remembered when using taper roller bearings that – in contrast to deep groove ball bearings – the axial adjustment of the bearings will influence the radial guidance of the worm wheel. Therefore, the casing must be sufficiently stiff so that it will not be deformed (beaten out) under load. This would otherwise lead to too large a bearing clearance and inadmissible alterations to the mesh.

Fig 32: Bearing arrangement for a worm wheel shaft with two cylindrical roller bearings

3

Fig 31: Bearing arrangement for a worm wheel shaft with two taper roller bearings arranged faceto-face

In most cases the worm wheel has a globoid form and requires accurate axial guidance, but it must also be possible for the axial position of the mesh to be changed. Two deep groove ball bearings in the cross-located arrangement shown in fig 30 generally have adequate load carrying capacity and are very cost-favourable. The adjustment of the mesh and the bearings is made via the covers. The mesh should preferably be adjusted via the one cover first and then the bearing clearance via the other cover. The temperature of the slowly rotating worm wheel shaft is usually low, so the bearings can be adjusted to almost zero clearance. To keep the oil level down and still pro-

When two cylindrical roller bearings (➔ fig 32 ) of the NJ or NCF (full complement) design are used, the radial guidance of the worm wheel is not influenced by any axial adjustment, so that setting the mesh is simplified. However, axially loaded cylindrical roller bearings are particularly susceptible to wear, so that it is important that they are adequately supplied with lubricant of sufficient viscosity (κ > 0,5) and that the specific bearing load is not too high (s0 > 10).

53

3 Design of bearing arrangements Shafts in worm gearboxes Bearing arrangement for a worm wheel shaft with a double row angular contact ball bearing (locating position) and a cylindrical roller bearing (nonlocating position)

The design of the locating/non-locating bearing arrangement shown in fig 33 is more complex since all bearings rings have to be axially located at both sides. The double row angular contact ball bearing (alternatively two matched single row angular contact ball bearings) guides the worm wheel axially with practically no clearance, so that adjustment is not required. The inner ring without flanges of the cylindrical roller bearing (NU design) allows free axial displacement at the non-locating side.

Bearing selection

Demands on the rolling bearings

The commonly used bearing series are listed in Table 11 to facilitate a preliminary choice.

The demands on the rolling bearings are derived from the specific operating conditions at each bearing position. They are briefly summarised in Tables 9 and 10 .

54

The following checklist may be helpful when selecting the bearings. ● ● ●

● ● ●

Adjusted basic rating life Permissible speed Maximum preload when starting up for the maximum temperature differential Zero clearance or slight preload at the operating temperature Misalignment Static safety under shock loads

3 Design of bearing arrangements Shafts in worm gearboxes Table 9 Specific operating conditions


Specifically heavy axial loads

Use bearings with large contact angle to take up the axial load.

Need for clearance-free operation and quiet running

Aim for slight preload when running at the operating temperature. When adjusting or selecting initial bearing clearance remember the expected temperature differential.

Large temperature differentials during start-up (slim worm shaft heats up faster than cooled casing)

When adjusting remember the expected temperature differential to avoid inadmissible preloads.

High operating temperatures; the use of lubricants with large proportion of additives which are chemically aggressive to plasticwhen aged

For gearboxes which operate constantly, or mainly (high frequency of use) at high operating temperatures (> 80 °C) and which must also have a long service life (> 20 000 hours) bearings fitted with metal cages should be used.



Accurate axial guidance of worm wheel

Adjust bearings to zero axial clearance.

Very slow speeds

With inadequate lubricant film formation corresponding to a viscosity ratio (actual to required viscosity) of κ < 1 use lubricants with suitable EP additives. When κ < 0,5 only use bearings with cages (not full complement bearings). When κ < 0,1 reduce the specific bearing load; aim for s0 > 10.

Table 11 Operating conditions

Bearing series normally used Worm shaft

Demands on worm shaft bearings

Demands on worm wheel shaft bearings

Bearing selection

Worm wheel shaft

Light loads

72 BEP 73 BEP

618 619 160

Moderate loads

313 (2×) 73 BECBM + NJ 2 ECJ 313/DF + NJ 3 ECJ

60 62 32 + NU 10 (2×) 72 BECBM + NU 2 ECJ

Heavy loads

293 E + 303 + NU 3 ECJ 294 E + 313 + NU 3 ECJ (2×) 293 E + (2×) 230 CC

320 X NCF 29 V NJ 2 ECJ

In addition to the bearing series listed above, a CARB can be used as the non-locating bearing for locating/non-locating bearings arrangements

55

3

3 Design of bearing arrangements Shafts and gear wheels for planetary gearboxes

Shafts and gear wheels for planetary gearboxes Planetary gearboxes usually come as cartridge-type or flanged units and more seldom for mounting on the base. Power input and also output from the sun wheel is almost exclusively via couplings so that the sun wheel can centre itself in the planetary wheels. Power take-off via the planetary carriers is either via a coupling or, for the cartridge-type units via a hollow shaft connection.

Sun wheels The sun wheel meshes with several planetary wheels, so splitting the power. The arrangement is always symmetrical so that with straight-cut teeth, the reaction forces on the sun wheel bearings should cancel each other out theoretically. In practice, however, this is not the case. The even distribution of load over all the planetary wheels is influenced by many factors. The most important are the design (radial alignment of the sun wheel), the accuracy of manufacture, and the specific load. When the load is heavy the relative deviation in the load distribution will be smaller because of deformation. Because of the ability of the sun wheel to align radially and/or the high manufacturing precision common today, the bearing forces resulting from the uneven load distribution are so small that they can be neglected when selecting the sun wheel bearings. At high Bearing arrangement for an input shaft with two deep groove ball bearings

56

speeds, it is even sensible to subject deep groove ball bearings to a minimum axial load by springs, in order to prevent them from rotating without load, and to achieve smooth running. Fig 34 shows the bearing arrangement of the input shaft which incorporates two deep groove ball bearings in a cross-located bearing arrangement. Transmission of the torque from the input shaft to the sun wheel is via a toothed coupling. This allows the sun wheel to adjust easily and the load distribution will be good as a result. The sun wheel shaft shown in fig 35 is also supported by two deep groove ball bearings, but these are in a locating/non-locating bearing arrangement. The springs acting on the outer ring of the non-locating bearing subject both bearings to axial load. This increases the smooth running of the bearings, particularly at high speeds and under vibrating conditions.


Bearing arrangement for a sun wheel with two deep groove ball bearings

Bearing arrangement for a planetary wheel with a needle roller and cage assembly

Planetary wheels The conditions for the planetary wheels are characterised by heavy radial load from the forces of two meshes as well as by the infuence of radial accelerations and the mass inertia forces resulting from these. Bearings having high radial load carrying capacity are needed, and their cages should be able to endure the mass forces. An internal bearing arrangement is suitable for the planetary wheels as it takes up the least space. This means rotating load for the outer ring and point load on the inner ring. Thus, the outer rings must have interference fits and the seatings must be accurately machined in order to keep the rotating inaccuracy – which leads to increased

friction in the bearings and additional forces on the cages – to be kept as small as possible. The specifically heavy radial loads, the rotating outer rings, and not least, the mass inertia forces cause high friction. Therefore special demands are placed on the lubrication and cooling of the planetary wheel bearings. The least space is taken up by a needle roller and cage assembly as shown in fig 36 . This very cost-favourable bearing arrangement is very suitable for small units (up to approximately 50 mm between shafts) as well as for light loads or short periods of operation as, for example, with small lifting gear. The pins and bores of the planetary wheels serve as bearing raceways. Recommendations regarding raceway hardness and design are given in the section ”Recommended fits” (➔ page 106). The planetary wheel is axially guided by thrust washers. These are secured on the planetary carrier so that they cannot turn. The bearing arrangement shown in fig 37 with two cylindrical roller bearings of the NJ design offers the advantages of very high radial load carrying capacity and very high accuracy as well as high rupture strength in respect of the cage forces if window-type cages are used. The planetary wheel is guided axially by the flanges of the cylindrical roller bearings. To prevent the bearings from being axially clamped, the intermediate ring on the pin should be at least 1 mm wider than the retaining ring in the bore of the wheel. Even though the two cylindrical roller bearings are virtually immediately adjacent to each other, it is not necessary to resort to special bearings for paired mounting (DR execution). Modern manufacturing methods mean that standard bearings differ only slightly in their cross section (bore and outside diameters + internal clearance) from each other. When using two bearings per wheel the deviation will, at the most, cause a slight angular misalignment which is largely compensated for by deformation, so that any effect on the mesh or the load carrying capacity of the bearings is negligible.

3

57

3 Design of bearing arrangements Shafts and gear wheels for planetary gearboxes Bearing arrangement for a planetary wheel with two cylindrical roller bearings

Bearing arrangement for a planetary wheel with two cylindrical roller bearings without outer ring

To achieve the maximum load carrying capacity in the limited space, the bearing outer rings can be dispensed with, as shown in fig 38 . Cylindrical roller bearings of the RN design are used. The wheel is guided axially by the flange rings and the inner ring flanges. The dimensions of the rings are not standardised and should be agreed with the bearing manufacturer. Recommendations regarding design of the raceways in the wheel bore will be found in the section “Recommended fits” (➔ page 106). Another way to increase load carrying capacity is to use full complement cylindrical roller bearings as shown in fig 39 . In this case, a special double row bearing without outer ring is used. Bearing arrangement for a planetary wheel with a double row full complement cylindrical roller bearing without outer ring

58

The design provides very high load carrying capacity in a small space. However, full complement cylindrical roller bearings cause more friction and are susceptible to wear. They are not suitable for high normal accelerations. Therefore, this bearing arrangement is more appropriate for short-term operation, also with heavy load shocks, rather than for constant operation. A typical application area is that of mobile gear units. The use of a spherical roller bearing to support a planetary wheel, as shown in fig 40 , allows the wheel to adjust to the mesh. When the planetary carriers deform, so that the overhung pins become misaligned, the mesh is improved by the use of a self-aligning Bearing arrangement for a planetary wheel with one spherical roller bearing

3 Design of bearing arrangements Shafts and gear wheels for planetary gearboxes bearing arrangement, when compared to a rigid bearing arrangement incorporating more than one bearing. The advantage of this self-alignment can also be exploited at high speeds and correspondingly small tooth forces, as there is not much deformation in the tooth contact and the mesh will be good. The easy adjustment of the mesh is also an advantage when the wheels are wide. The smaller theoretical load carrying capacity of the single spherical roller bearing as compared with rigid arrangements where two or more bearings are used is partly compensated for by the even distribution of load over the two rows of rollers. Because of its exceptionally high load carrying capacity compared with other roller bearings and its low cross section, the CARB is eminently suitable for planetary gear bearing arrangements (➔ fig 41 ). Its insensitivity to angular misalignment is particularly important for correct meshing in this case. The planetary wheel can align itself so that even meshing is obtained across the whole tooth width. The favourable distributon of the tooth forces thus obtained has a positive influence on the life of the gearbox.

Fig 41

Planetary wheel bearing arrangement with one CARB

3

59


Planetary carriers To achieve equal power splitting in planetary gear units, it is possible to avoid the need for an additional bearing support for the planetary carrier if the following conditions apply: ●

●

Planetary gearbox of cartridge type with two deep groove ball bearings supporting the planetary carrier

60

the planetary carrier is not subjected to load from the output shaft or the torque support; the weight of the planetary carrier is negligible.

The planetary carrier centres itself under load via the planetary wheel meshes. Fig 42 shows a gearbox where the planetary carrier of the high-speed stage is not supported by bearings. It

centres itself via the planetary wheels in the hollow shaft (housing) and on the supported sun wheel. This multiple centring is only possible if manufacturing precision is adequate.

3 Design of bearing arrangements Shafts and gear wheels for planetary gearboxes The casing is supported by the planetary carrier of the slow-speed stage. The two deep groove ball bearings in a cross-located arrangement are under load from the restoring force of the torque support and from the weight of the gearbox. The resultant bearing forces are generally small and the rotational speed low so that the load carrying capacity of deep groove ball bearings is usually sufficient. The planetary carrier with take-off shaft shown in fig 43 is supported by two full complement cylindrical roller bearings. This arrangement enables additional forces from the power takeoff to be accommodated.

Bearing arrangement for planetary carrier with two full complement cylindrical roller bearings

3

61


Demands on the rolling bearings The special requirements placed on the bearings for planetary gearboxes are derived from the particular conditions pertaining at the various bearing positions. A brief summary is given in Tables 12 to 14 .

Bearing selection The following list may be found useful to check that the chosen bearings satisfy the demands. ● ● ● ● ●

Adjusted rating life Permissible radial acceleration Permissible speed Friction and cooling Adequate bearing play to prevent inadmissible preload at the maximum operating temperature (sun wheel) or under interference fits (planetary wheel)

Demands on sun wheel bearings

Demands on planetary wheel bearings

62



Light loads; idling

Use of deep groove ball bearings preferred to avoid over-dimensioning.

Requirements for clearance-free operation and quiet running

Adjust deep groove ball bearings axially by springs.

Large temperature differentials when starting up (slim sun wheel shaft heats up more quickly than the casing which is better cooled)

Particularly where casings are solid and/or well cooled use deep groove ball bearings with internal clearance to C3.



Heavy radial loads

Use roller bearings with high load carrying capacity. If lubricant film formation is also inadequate, corresponding to a viscosity ratio (actual to required) of κ < 1 use lubricants with suitable EP additives. When κ < 0,5 only use bearings with cages (not full complement bearings). When κ < 0,1 reduce the specific bearing load; aim for s0 > 10.

Radial accelerations resulting from movement of the planetary wheels around the axis of rotation of the sun wheel

Check cage stresses by calculating mass inertia forces. Pay consideration to mass inertia forces of planetary wheel when calculating bearing life.

Increased friction caused by mass intertia forces and rotating outer rings (rotating inaccuracy)

Ensure adequate lubricant supply and cooling. Use heat-stable lubricants. For gearboxes which continuously, or frequently (high frequency of use) operate at high tempeatures (> 80 °C) and which should also have long service life (> 20 000 hours) bearings with metallic cages should be used.

Deformation of planetary wheel by two meshes on opposite sides

For thin-walled planetary wheels (wall thickness < 3 × modulus) take into account the influence of the tension band load distribution on the loaded zone of the bearing (FEM calculation).

3 Design of bearing arrangements Shafts and gear wheels for planetary gearboxes ●

●

Deformation of planetary wheel when wall thickness small; influence on the load distribution in the bearing Static load safety in respect of load shocks

A preliminary bearing selection can be made by referring to the most frequently used bearing series listed in Table 15 .



Very slow speeds with additional loads from the drive

Use preferably bearings with small cross section. When κ < 1 use lubricants with suitable EP additives. When κ < 0,5 only use bearings with cages (not full complement bearings). When κ < 0,1 reduce the specific bearing load; aim for s0 > 10.

3

Table 15 Operating

Bearing series normally used Planetary wheels Sun wheels

Demands on planetary carrier bearings

Bearing selection

Planetary carriers

Low radial accelerations or short operation periods

NJ 23 ECP NCF 30 V NJG 23 VH 230 CC 232 CC 223 E(CC)

60, 62, 63

618, 619 NCF 18 V, NCF 29 V 239 CC

Moderate radial accelerations and continuous operation

NJ 3 ECMA NJ 23 ECMA 230 CC 232 CC 223 E(CC)

60, 62, 63

618, 619 NCF 18 V, NCF 29 V 239 CC

High radial accelerations

NJ 2 ECML NJ 3 ECML NJ 23 ECML 223 CCJA/VA405

60, 62, 63

618, 619 NCF 18 V, NCF 29 V 239 CC

In addition to the bearing series listed above, a CARB can be used for planetary wheels

63

4 Calculation of bearing arrangements Bearing loads . . . . . . . . . . . . 65 Determination of external forces . . . . . . . . . . . . . . . . . . 66 Calculation of bearing loads . . . . . . . . . . . . . . . . . . . 74 Dimensioning the bearing arrangement . . . . . . . . . . . . . 76 Life calculation . . . . . . . . . 76 Static safety factor . . . . . . . 79 Axial load carrying capacity . . . . . . . . . . . . . . . 79 Minimum load . . . . . . . . . . 80 Normal acceleration and cage load carrying capacity 80 Friction and cooling . . . . . . 81 Permissible speeds . . . . . . 82 Internal clearance and preload . . . . . . . . . . . . 83 Adjustment values for single row angular contact bearings . . . . . . . . 85

4 Calculation of bearing arrangements Bearing loads

Calculation of bearing arrangements Following the preliminary selection of bearing type, it is necessary to determine all the external forces acting on a gear unit and from them to calculate the bearing loads. For the final selection of bearing size (and execution) several criteria must be observed, the most important of which is bearing life. 4

Bearing loads ●

To calculate the bearing loads it is first necessary to determine all the external forces acting on the shaft/bearing system. The following are external forces: ● ● ● ● ●

tooth forces, mass inertia forces from radial accelerations in planetary gears, coupling and propeller shaft forces, belt forces, and weights of shafts and gear wheels.

An analysis of the force distribution over the bearings must then be made. There is a choice of method: ●

fying assumptions and models; advanced methods where bearings, shafts and in part also housings (casing) are considered as a nonrigid system; these methods involve extensive calculations and require the use of sophisticated computer programs available in house at SKF.

Where experience is available from the same or similar designs it is still the custom to use the conventional methods for comparative calculations. Because of the greater information obtained using the sophisticated methods it is recommended that they be applied for new designs and also when conducting damage analysis. Please contact SKF for assistance.

conventional methods based on the beam model, suitable for manual calculations and the corresponding computer programs (included in the SKF CADalogue and ADAM software); these methods rely on simpli-

65

4 Calculation of bearing arrangements Determination of external forces

Determination of external forces Tooth forces The magnitude of the tooth forces is dependent upon the torque which is to be transmitted. As the torque is the fundamental criterium on which all calculations are based, and consequently also the evaluation of the bearing arrangement, it should be determined as accurately as possible, e.g. by measuring or based on experience. Additional forces caused by inaccuracies in the mesh which come from the manufacturing process, or by shocks originating from the input or output drives, are taken into account by selecting an application-related minimum life. When calculating the forces for spur, bevel and planetary gears (➔ fig 1 ), tooth friction is ignored. Friction is only taken into account for hypoid and worm gears where there is a larger proportion of sliding friction. In the following equations the index 1 is used for the driving wheel and the index 2 for the driven wheel. The peripheral force Kp depends on the torque or power and can be obtained from

Kp =

Symbols K tooth force acting at right angles to the tooth flank, N Kp tangential component of K (= peripheral force), N Ka component of K acting parallel to the shaft axis (= axial force), N component of K acting at right Kn angles to the shaft axis (= normal force), N M torque to be transmitted by gear wheel, Nmm W power to be transmitted by gear wheel, kW r pitch radius (mean radius for bevel gear wheels), mm n rotational speed of gear wheel, r/min α angle of engagement, degrees β angle of inclination, degrees δ half cone angle of bevel gear wheels, degrees γ pitch of worm, degrees Z number of teeth µ coefficient of friction of tooth flanks of hypoid and worm gears η degree of efficiency for hypoid and worm gears

M W = 9,5517 × 106 r nr

For spur and bevel gears, the gear ratio is

Tooth forces Fig 1

Kp

n1 r Z = 2 = 2 n2 r1 Z1

r K Ka Kn

66

4 Calculation of bearing arrangements Determination of external forces Spur gear For straight cut spur gear units (➔ fig 2 )

For spiral cut or curved bevel gear units (➔ fig 5 ) the equations shown in Table 1 should be used. As the equations

Ka = 0 Ka2 = Kn1

Kn = Kp tan α

Kn2 = Ka1 and for spiral cut spur gear units (➔ fig 3 )

also apply to bevel gear units where the shafts are at right angles to each other, it is sufficient in this case to calculate the forces acting on the driving wheel, as this will also determine the forces on the driven wheel. Where the teeth are straight cut, the forces Kn and Ka always act in the directions shown in fig 4. For spiral cut or curved teeth, the forces may act in the opposite direction, depending on the angles α, β and δ. In this case, the calculated values for Kn and Ka are negative.

Ka = Kp tan β

Kn = Kp

tan α cos β

Bevel gear units For straight cut bevel gear units (➔ fig 4 ) Ka1 = Kp tan α sin δ1 Kn1 = Kp tan α cos δ1 Ka2 = Kp tan α sin δ2

4

Kn2 = Kp tan α cos δ2 Tooth forces of straight cut

Fig 3

Fig 2 Kp

Kp

Tooth forces of helical cut spur gears

β Ka Kn

Kn

r

Tooth forces of straight cut

r

Fig 4

Fig 5 Kp

Kp

Tooth forces of helical cut bevel gears

β

δ

Ka

Ka Kn

Kn r

r

67

4 Calculation of bearing arrangements Determination of external forces Tooth forces for helical and curve toothed bevel gears

Table 1 Driving wheel

Ka1 =

Kp (− sin β cos δ1 + tan α sin δ1) cos β

Kn1 =

Kp (sin β sin δ1 + tan α cos δ1) cos β

Ka1 =

Kp (sin β cos δ1 + tan α sin δ1) cos β

Kn1 =

Kp (− sin β sin δ1 + tan α cos δ1) cos β

Driven wheel

Ka2 =

Kp (sin β cos δ2 + tan α sin δ2) cos β

Kn2 =

Kp (− sin β sin δ2 + tan α cos δ2) cos β

Ka2 =

Kp (− sin β cos δ2 + tan α sin δ2) cos β

Kn2 =

Kp (sin β sin δ2 + tan α cos δ2) cos β

Tooth forces for hypoid gears

Table 2 Driving wheel

Ka1 = K (− cos α sin β1 cos δ1 + sin α sin δ1 + µ cos β1 cos δ1) Kn1 = K (cos α sin β1 sin δ1 + sin α cos δ1 − µ cos β1 sin δ1)

Ka1 = K (cos α sin β1 cos δ1 + sin α sin δ1 − µ cos β1 cos δ1) Kn1 = K (− cos α sin β1 sin δ1 + sin α cos δ1 + µ cos β1 sin δ1)

Driven wheel

Ka2 = K (cos α sin β2 cos δ2 + sin α sin δ2 − µ cos β2 cos δ2) Kn2 = K (− cos α sin β2 sin δ2 + sin α cos δ2 + µ cos β2 sin δ2)

Ka2 = K (− cos α sin β2 cos δ2 + sin α sin δ2 + µ cos β2 cos δ2) Kn2 = K (cos α sin β2 sin δ2 + sin α cos δ2 − µ cos β2 sin δ2)

68

4 Calculation of bearing arrangements Determination of external forces Hypoid gear units As can be seen from fig 6 , the two shafts of a hypoid gear unit do not lie in the same plane. Therefore, the angle of inclination β1 of the driving wheel is not the same as β2 of the driven wheel. The wheels are so chosen that β1 is larger than β2. The directions of the peripheral forces Kp1 and Kp2 do not coincide, in contrast to spur and bevel gear units. For hypoid gears, the ratio is

As (cos β2/cos β1) > 1, the pitch radius of the pinion is greater for a given ratio and a given size of the wheel which the pinion engages than is the case for a bevel gear unit. The peripheral force Kp1 which acts on the pinion is obtained from M1 r1

The tooth force which acts vertically on the tooth flank is obtained from K =

Kp1 cos α cos β1 + µ sin β1

tan γ =

h 2 π r1

where h in mm is the pass height of the worm on the partial cylinder and r1 in mm the pitch radius of the worm. Generally, the worm drives the worm wheel and the following calculation is for this case. Index 1 refers to the worm and index 2 to the worm wheel (➔ fig 7 ). The tooth forces are obtained from

Kp1 =

4

M1 r1

Ka1 = Kp1

and the peripheral force for the large wheel from Hypoid gears

Worm gear units When calculating worm gears it is common practice to take the angle of pitch γ instead of the angle of inclination β. The following equations can be used γ = 90 − β

n1 Z r cos β2 = 2 = 2 × n2 Z1 r1 cos β1

Kp1 =

The forces Ka and Kn are obtained using the equations shown in Table 2 , taking into account the requirements for the direction of the spiral cut and of rotation.

cos α cos γ − µ sin γ cos α sin γ + µ cos γ

= Kp1 cot γ η Tooth forces of worm gears

Kp2 = K (cos α cos β2 + µ sin β2) Fig 6

Fig 7

Kn1 Kp1

r1

Kp2 Ka1 Ka2 Kn2

r2

69

4 Calculation of bearing arrangements Determination of external forces

Kn1 = Kp1

= Kp1

sin α cos α sin γ + µ cos γ tan α [sin2 γ (1 − η) + η] sin γ

As can be seen from fig 7 the forces acting on the worm wheel are determined by calculating the forces on the worm as follows Kp2 = Ka1; Ka2 = Kp1; Kn2 = Kn1 The reduction ratio for worm gear units is Z n1 = 2 n2 Z1 where Z1 is the number of passes of the worm and Z2 the number of teeth of the worm wheel. Planetary gear units The determination of the forces is shown for the most common type of planetary gear, i.e. with parallel shafts and toothed pinion. Using the following equations it is of no importance for the determintion of the speeds and torques which of the three parts is connected to the drive, the power take-off, or the stationary part (casing), or whether all three parts are in motion and transmit power. The calculation starts with the basic ratio u, which is the ratio of the rolling

Construction of planetary gearbox (schematic)

pitch radius of the hollow wheel R and its planetary wheel to that of the sun wheel and its planetary wheel. The magnitude of the radius s, which for corrected toothing must not be (R + r) /2, does not matter here. The advantage of this method is that the various types with double planetary wheels can be calculated in a simple manner. The same equations can be used for all planetary gear units of types I to III (➔ fig 8 a), which are equivalent to the simple unit (➔ fig 8 b). It should be remembered that the values of R, s and r to be inserted in the equation for u correspond to the lever of the three parts which act on the assumed double lever in the planetary wheel (thus, R is not always the radius of the hollow wheel, s not always the radius of the planetary wheel and r not always the radius of the sun wheel). The basic ratio is obtained from

u =

R (s − r) (R − s) r

For normal toothing (s − r) = (R − s) is valid so that

u =

R r

Fig 8 type I

type II

R

R S

r

type III

R

R S

r

simple unit

S

S r r

a

70

b

4 Calculation of bearing arrangements Determination of external forces If the symbols R, s and r are inserted for the different equivalent planetary units according to fig 8 a, the the upper equation for u is again valid.

Torques: Ms = Mr + MR = (u + 1) Mr

= (

Speeds:

1 + 1) MR u

nr = (u + 1) ns − u nR

nR =

Mr =

(u + 1) ns − nr u

MR = u Mr =

n + u nR ns = r u+1 Speeds of the planetary wheels about their own axes a) for simple planetary gear units

= (ns − nr) = (nR − nr)

R R−s

u M u+1 s

Tooth forces: The peripheral force is obtained from

Kp = npl = (nr − ns)

1 1 M = M u R u+1 s

Mr Mr or Kp = R Zpl r Zpl

where Zpl = number of planetary wheels.

r s−r

4

For straight cut teeth 1

s−r R−s + r R

b) for double planetary units type I:

Ka = 0 Kn = Kp tan α and for spiral cut teeth Ka = Kp tan β

npl = (nR − nr) = (ns − nr)

R R−r s s−r

Kn = Kp

tan α cos β

type II:

npl = (nR − ns) = (ns − nr)

R R−s r s−r

type III: npl = (nR − nr)

r R−r

= (nR − ns)

s R−s 71

4 Calculation of bearing arrangements Determination of external forces Fig 9

Fig 10

FG M

S1

r

ϕ Kr

a S2

FG

Cardan shaft forces

Inertia forces from the radial acceleration The rotation of the planetary carrier about its own axis causes inertia forces on the planetary wheels which must be considered when calculating the bearing load if speeds are high. For the inertia (gyratory) force on a planetary wheel F = m rs ω2 where F = inertia force, N m = mass of planetary wheel, kg rs = radius of centre of gravity of rotating planetary wheel, m ω = angular velocity of the planetary carrier

(= π30n ), s s

−1

ns = rotational speed of the planetary carrier, r/min

Coupling and propeller shaft forces When selecting and designing torquetransmitting couplings, it is desirable that no reactionary forces act on the shaft/bearing system. Even though this is not completely possible, because of inaccuracies governed by manufacture or deviations when aligning the coupled shafts, and not least because of deformations, it may still be assumed that the coupling forces are negligible in comparison to the tooth forces. With propeller shafts, forces are produced when the torque is transmitted. These forces rotate with the rotation of the shaft and change periodically (➔ fig 9 ). For two bearings, the fol-

72

lowing radially acting pair of maximum forces should be used for calculations

FG max =

M tan ϕ a

where FG max = maximum, periodically changing force, N M = torque to be transmitted, Nmm a = distance between bearings, mm ϕ = bending angle of joint, degrees As FG max is the maximum of the periodically changing force, an approximate average force can be obtained from Fm = 0,75 FG max assuming that the bearings are only subjected to load caused by the joint forces. If the bearings are also subjected to other forces then the following approximation applies

Fm =

1 2 Fmin + F 3 3 max

Fmin = forces other than the joint force which act on the bearings, N Fmax = all forces acting on the bearing, including the joint force FG max, N As the bending angle ϕ changes there will be a compensation in length of the propeller shaft which, because of friction, will produce an axial force

Belt forces

4 Calculation of bearing arrangements Determination of external forces Table 3 Type of belt drive

Preload factor f at peripheral speed (m/s) <5 5 to 20

> 20

Kr = f Kp = f

Flat belts

3 to 4

2,5 to 3,5

2 to 3

V belts

1,5 to 2,5

1,5 to 2,5

1,5 to 2,5

Toothed belts

1,1 to 1,3

1,1 to 1,3

1,1 to 1,3

Preload factor

where Kr = resultant belt force, N Kp = peripheral force, N M = torque, Nmm f = tensioning factor r = radius of belt pulley, mm

Forces from the torque support

where M = torque, Nmm rm = mean radius of the sliding profile, mm µ = coefficient of friction ϕ = angle of bending, degrees As this axial force only acts during certain periods – namely when the bending angle changes – it should be taken into account for the time it acts when calculating the life, or if the change in angle occurs when the shaft is not rotating, it should be included in the calculation of the static safety factor s0.

Belt forces Torque support forces

M r

Appropriate values of tensioning factor, depending on the peripheral speed, can be obtained from Table 3 .

M µ cos ϕ rm

Fa =

Kr produced by the belt (➔ fig 10 ) can be calculated using

The gear unit may be driven by a belt and power take-off may also be via a belt. The radial force acting on the shaft Fig 11

K1

In cartridge-type gear units, the bearings on the output shaft are subjected not only to the tooth forces, but also to forces from the reaction to the torque and from the weight (➔ fig 11 ). The force K1 acting on the output shaft bearings can be obtained from

4 K1 =

M a +G l l

where K1 = force acting on the bearings, N M = reaction torque (for simplicity it can be taken as being equal to the torque of the output shaft), Nmm G = weight of gear unit including motor and base plate, N l = distance between torque support and output shaft, mm a = distance between torque support and centre of gravity, mm When calculating bearing load it should be remembered that the force K1 is introduced via the bearing outer rings from the casing.

Weights of shafts and gears G K2 a l

The weights of shafts and gears are generally negligible compared with the tooth forces. They should not be ignored, however, when dealing with vertical units as they act axially and may constitute a considerable part of the total bearing load – particularly in large units.

73

4 Calculation of bearing arrangements Calculation of bearing loads

Calculation of bearing loads Once the external forces have been determined it is possible to calculate the bearing loads. It is sensible to divide the forces, as shown in fig 12 , into three vertically acting components. The forces act at the pressure centres of the bearings. For deep groove ball bearings, cylindrical roller bearings and spherical roller bearings, the pressure centre is at the geometric centre of the bearing. For single row angular contact ball bearings and taper roller bearings, the distance between the pressure and geometric centres of the bearing will be found for each bearing in the SKF General Catalogue. If a shaft is supported in a double row angular contact bearing, or in two single row angular contact bearings arranged back-to-back, plus an additional bearing, and if the distance between the bearings is relatively small, under a load consisting of a radial force component Kn and an axial component Ka, the position of the line of action of the radial force Fr acting on the bearing pair or bearings will influence the distribution of the external load over the three rows of rolling elements. The distance ax of the line of action can be determined approximately from the diagram in fig 13 in relation to the contact angle of the bearing and the load ratio Fa/Fr. A more realistic determination of the load distribution over the three rows

Forces acting at the bearing positions when an external force is applied at a point between the pressure centres

can be made by taking into account the resilience of the shaft and bearings. This can be done with the inhouse computer programs developed by SKF.

The external force acts on the shaft between the pressure centres of the bearings The bearings with pressure centres I and II at a distance l corresponding to fig 12 are loaded by a force K acting in any direction. The force is divided into the components Kp, Kn and Ka. For the forces acting vertically at the bearing positions

F1 I =

l−a r Kn − K l l a

F1 II =

a r K + K l n l a

and for the forces acting horizontally

F2 I =

l−a Kp l

F2 II =

a K l p

Position of the force produced by double row and paired single row angular contact bearings

Fig 12

Fig 13

Kp

r

Ka = Fa

F1I FrI

Kn

Kn FrII

F2I

F2II

Fr

0,5

F1II II

0

ax

K

Ka

I

b

Fa

0,4

Ball bearings

0,3

Roller bearings

0,2 0,1

a

0

l

74

0

0,2 0,4 0,6 0,8

1

1,2 1,4 1,6 1,8 2 Fa cotα Fr

4 Calculation of bearing arrangements Calculation of bearing loads The resultant radial load s for the bearings can then be determined using

and for the horizontally acting forces

Fr I = √ F1 I2 + F2 I2

F2 I =

a−l Kp l

F2 II =

a K l p

Fr II = √ F1 II2 + F2 II2 The axial force Fa acts on one of the two bearings – the locating bearing – in addition to the radial forces. When the bearing is not a single row angular contact bearing, Fa = Ka. In single row angular contact bearings under radial load, an axial force will be induced which must be taken into account when calculating the equivalent dynamic bearing load. Details will be found in the SKF General Catalogue.

The external force acts on the shaft away from the pressure centres of the bearings The force K is also divided into three components: Kp, Kn and Ka. According to fig 14 , for the bearing forces acting vertically

F1 I =

a−l r Kn − K l l a

F1 II =

a r Kn − K l l a

Forces acting at the bearing positions when an external force is applied at a point outside the pressure centres Fig 14 Kp F2I I

Ka

FrI

K

F1II

F1I

Kn

FrII II

The resultant radial loads acting on the bearing can then be obtained, as before, from Fr I = √ F1 I2 + F2 I2 Fr II = √ F1 II2 + F2 II2 Once the radial load Fr and the axial load Fa have been determined, the equivalent dynamic bearing load P and then the bearing rating life L10h can be determined following the instructions given in the SKF General Catalogue. The conventional determination of the bearing load described here is based on many simplifying assumptions in order to permit manual calculation. More realistic results are obtained if the deformation of bearings, shafts and possibly also of the casing can be taken into account. This can be done using the sophisticated SKF computer programs available in house. For shaft systems supported at three or more positions it is imperative that deformations are considered, as the conventional methods often lead to rather unrealistic results. Even for statically determinate doubly supported shafts, it is advisable to calculate using the more sophisticated methods when the application limits for a new design are being evaluated, or when additional information is required on bearing and gear displacements and misalignments, or on rolling element loads and stresses in the rolling contact, rather than the approximate life.

4

r

F2II Fa l a

75

4 Calculation of bearing arrangements Dimensioning the bearing arrangement

Dimensioning the bearing arrangement The bearing size and execution required for a given bearing arrangement are determined based on the following criteria: ● ● ● ● ● ● ● ● ●

life static load carrying capacity axial load carrying capacity minimum load normal acceleration and cage load carrying capacity friction and cooling speed capability internal clearance and preload adjustment values for single row angular contact bearings.

A more reliable selection can be made by calculating the adjusted rating life L10ah which also takes into account lubrication. The calculation requires information regarding the viscosity of the lubricant to be used and the bearing operating temperature in addition to the load and speed. By calculating the adjusted rating life it is also possible to determine whether the lubricant is suitable and whether cooling would give better results. A determination of the adjusted rating life is also helpful for the following reasons. ●

In many cases bearing size is simply selected on the basis of the calculated life. The list above and the following comments serve to show that for reliable performance of the bearing, a number of other criteria should be considered in addition to the calculated bearing life. ●

Life calculation The Lundberg and Palmgren theory of bearing fatigue life forms the basis for bearing life calculations. The life equations derived from the theory are to be found in the SKF General Catalogue. Their use for gearbox bearing calculation will be discussed here. Bearing life can be calculated with greater accuracy and reliability, the more accurately the operating conditions are known or can be determined. To calculate the basic rating life L10h according to ISO it is only necessary to know the basic dynamic load rating of the bearing, the equivalent bearing load and the rotational speed. Important influences such as lubricant film formation in the bearing and lubricant cleanliness are not considered in the L10h calculation. In spite of this, if experience of similar bearing arrangements is available and the other parameters which affect bearing life, but which are not considered in the calculation are reasonably constant, a basic rating life calculation may be sufficient to determine the appropriate bearing size.

76

Bearings operating at high speeds but which are lightly loaded are negatively influenced by high temperatures and large inertia forces. Lubricant film formation is promoted at high speeds and an adjusted rating life calculation can show that a smaller bearing can be used than would be suggested by a basic rating life calculation, so that friction as well as inertia forces will be reduced. The reliability of the bearing arrangement will be enhanced. Slowly rotating bearings operating under heavy loads are subject to deformations with correspondingly high proportions of sliding in the rolling contact and are susceptible to wear. The slow speeds mean that lubricant film formation will be poorer, and the adjusted rating life calculation will lead to the choice of bearings having higher load carrying capacity. This will mean that the specific bearing loads will be lighter, deformations and wear will be reduced, and reliability enhanced.

Contamination has a considerable effect on the life of gearbox bearings. The influence of contamination can be calculated using the SKF New Life Theory. The fatigue load limit is also considered when calculating the adjusted rating life L10aah according to the New Life Theory so that it is possible to design an arrangement for infinite life.

4 Calculation of bearing arrangements Dimensioning the bearing arrangement The following parameters are considered when calculating L10aah: ● ● ● ● ● ● ●

dynamic load rating of the bearing, fatigue load limit of the bearing, equivalent dynamic bearing load, rotational speed, lubricant viscosity, operating temperature and cooling, and contamination and sealing.

Calculations according to the New Life Theory are particularly suitable for making parametric studies to determine the influence of the different factors. It should be noted that the various factors have a strong influence on each other, and such calculations are only meaningful when the operating conditions are exactly known. When bearing life calculations for the selection of bearing size are made, only those results obtained using one and the same method should be compared. When determining a suitable life it is necessary to consider how the gearbox is to be used. The requisite basic rating life is dependent on the type

and size of the driven machine, on the length of service and on demands regarding operational reliability. If no experience is available then the guideline values for the requisite basic rating life L10h given in Table 4 can be used. In similar applications, the drives of large machines are generally subjected to more arduous conditions than the drives of smaller machines because of stronger shock loads and larger defomations. This should be taken into consideration when choosing the guide-line value from Table 4. When bearing arrangements are intended for very slow rotational speeds and/or are to have a very short life, the requisite basic dynamic load rating of the bearing is very small. This can lead to an unsuitable bearing being chosen which will give inadequate static safety, or the formation of only an inadequate lubricant film, or to the overloading and consequent deformation of the associated components. If, in addition to the requisite life, a minimum requisite value of the static safety factor s0 is also to be considered, this Table 4

Gearbox application

L10h (operating hours)

Machines and equipment infrequently used: Household appliances Agricultural machinery Medical equipment

300 to 3 000

Machines used for brief periods or intermittently: Cranes Lifts and elevators Construction machinery

3 000 to 10 000

Machines for daily (8 hour) use: Machine tools Woodworking machines Fans Conveyor drives Centrifuges

10 000 to 30 000

Machines for 24-hour use: Rolling mills Compressors Pumps Barges

30 000 to 50 000

Machines for 24-hour operation where high reliability is required: Cement mills Rotary furnaces Power generating plant Large-size open cast mining equipment Wind and water turbines Ocean-going ships

50 000 to 100 000

4

Guideline values for the requisite basic rating life L10h for gearboxes for various applications

77

4 Calculation of bearing arrangements Dimensioning the bearing arrangement should be based on the κ value (ratio of actual to required viscosity). The decision not only depends on the operating speed therefore, but also on the viscosity at the operating temperature and on the mean bearing diameter. Table 5 contains recommendations as whether the bearing selection should be based on the requisite life or on the static safety, taking the value of κ into account. Thus ●

●

●

when κ < 0,1 no life should be given; the material will fatigue under conditions of small κ, but the operational reliability and service life will not depend on fatigue but on other factors which are indirectly accounted for by the static safety factor s0.

when κ > 0,5, the static safety factor s0 should be checked in addition to the requisite life; when κ ≤ 0,5 then the static safety factor s0 must be considered;

Selection criteria

Table 5 Viscosity ratio κ over incl.

Bearing selection based on fatigue life

static safety factor

L10h

L10ah

L10aah

s0

0,1

−

−

−

+

0,1

0,5

−

o

+

+

0,5

1

+

+

+

o

+

+

+

o

1 Symbols + recommended – not appropriate o can also be used

Guideline values for the static safety factor s0

78

Table 6 Bearing type

Type of operation Rotating, Rotating, statically brief shock loaded loads nrel = 0 nrel > 0

κ < 0,1

κ = 0,1 to 0,5

Ball bearings

2

2

10

5

0,5

Roller bearings

3,5

3

10

5

1

Full complement cylindrical roller bearings

–

3

20

10

1

Rotating at very slow speeds under load

Stationary


Static safety factor

●

The basic static load rating C0 is used to select bearing size in the following cases: ●

●

● ●

when the bearing rotates at a relative speed of 0 (bearing arrangements of shifting gears) under load (rotating static load); when the bearing rotates and must, in addition to the normal loads, take up heavy shock loads for a fraction of a revolution (e.g. rolling mill drives); when the bearing rotates very slowly under constant load; when the bearing is stationary and is under constant load or is subjected to shock (short duration) loads, e.g. in mobile gearboxes.

●

●

light axial load, when 0,1 < κ ≤ 0,5: Fa max = 0,05 Fap, when 0,5 < κ ≤ 1: Fa max = 0,1 Fap, when 1 < κ ≤ 2: Fa max = 0,2 Fap, where Fap is the maximum permissible axial load at κ ≥ 2 there is an adequate supply of a CLP oil which offers good protection against wear the arrangements for oil supply and drainage are designed so that wear particles will not collect in the bearing

The guideline values of the static safety factor s0 for different bearing types given in Table 6 are valid when there is adequate lubrication using a CLP oil to DIN 51 517 which offers good protection against wear. Bearing selection based on the static safety factor s0 is described in the SKF General Catalogue.

4

Axial load carrying capacity The axial loads acting on rolling bearings are considered when calculating the equivalent dynamic and static bearing loads, see SKF General Catalogue. However, the axial load carrying capacity of cylindrical roller bearings is primarily determined by the load carrying ability of the sliding surfaces of the roller ends and flanges and is very strongly dependent on the lubrication and cooling. When calculating the permissible axial load according to the SKF General Catalogue, a viscosity ratio κ ≥ 2 is presupposed. When κ is smaller friction and wear will increase. Based on experience these effects can be kept at an acceptable level for slowly rotating gearbox bearings if the fol-lowing favourable conditions pertain

79


Minimum load In order for bearings to perform correctly they must always be subjected to a given minimum load. This will prevent the rolling elements from sliding on the raceways which would lead to smearing and premature bearing failure. This minimum bearing load can be calculated using the information given in the SKF General Catalogue. When this minimum load is constantly applied, there will be practically no sliding in the bearings. This load can be applied rather easily to thrust bearings, e.g. by springs, even when they are idling, but may be more difficult to arrange for radial bearings. In cases where the weights of shaft and gears are insufficient for the minimum load requirements, the risk of sliding can at least be reduced if the following recommendations are respected. ●

●

●

●

●

● ●

Use ball bearings, taper roller bearings or spherical roller bearings where possible (full complement cylindrical roller bearings are most at risk). Use bearings with small rolling elements – in critical cases at the expense of basic rating life. Keep bearing internal clearance small and – if at all possible – apply a preload. Avoid metallic contact in the rolling element/raceway contacts (ensure adequate supply of lubricant having sufficient viscosity; if necessary use bearings with black oxidised rolling elements). Ensure high accuracy of position and form of the associated components and use bearings of correspondingly high precision. Avoid vibrations wherever possible. Limit periods of idling under insufficient load as far as possible.

Experience shows that idling under insufficient load in gearboxes cannot always be avoided. The bearings which are most susceptible to damage under such conditions are large cylindrical roller bearings (d > 150 mm) as well as full complement cylindrical roller bearings. Often the bearings are damaged during test running without load.

80

The development of smearing – the typical damage caused during idling – and its prevention are being studied. SKF application engineers will gladly provide information on the latest research results.

Normal acceleration and cage load carrying capacity The movement of a planetary gear bearing is made up of a guidance or locating movement, resulting from the rotation of the planetary carrier, and a relative movement resulting from the bearing turning in the planetary carrier. In comparison with bearings mounted in stationary housings, the guidance and coriolis accelerations cause additional inertia forces to act on the planetary gear bearings. The mass of the planetary gear and the associated bearing rings produces a force as a result of the normal guidance acceleration which the bearing arrangement must also accommodate. These accelerations also mean that the masses of the rolling elements and cage will exert additional forces as well as the bearing itself. These additional inertia forces act on the rolling elements, bearing rings and, to a high degree, also the bearing cage. It is thus possible that a bearing will fail not from fatigue but because of cage fracture. The additional forces increase the sliding friction in the contacts which guide the rolling elements and cage. In full complement cylindrical roller bearings, because of the normal acceleration, the rollers are in contact with each other, so that friction increases and lubricant film formation is hindered. As a result the risk of scuffing or seizure is increased. SKF has specially developed computer programs for the calculation of the cage carrying capacity and also for how much the friction will be increased by the additional forces as well as the risk of seizure for full complement cylindrical roller bearings.

4 Calculation of bearing arrangements Dimensioning the bearing arrangement An estimate of the permissible normal acceleration for the bearing and cage designs most frequently used for planetary gears can be made using the following equation and catalogue data

Friction and cooling Bearing friction depends on the following factors: ● ● ●

an ≤ ka

●

dm0,8 g × 103 C0

● ●

where an = permissible normal acceleration ka = a factor (➔Table 7 ) dm = mean bearing diameter = 0,5 (d + D), mm C0 = basic static load rating, N

load, speed, bearing type, bearing size, lubricant properties (viscosity in operation), and lubricant quantity.

The total frictional resistance in a bearing is made up of ● ●

● ● ●

rolling and sliding friction in the rolling element/raceway contacts, sliding friction in the rolling element/ cage contacts (rolling element guidance), sliding friction in the cage/bearing ring contact (cage guidance), friction in the lubricant, and sliding friction of the rubbing seals in sealed bearings.

4

Friction influences heat generation and consequently bearing operating temperature. In gearboxes, the gears produce more friction than the bearings. When making arrangements for cooling, therefore, it is necessary to consider the total friction in the gearbox.

Factor ka

Table 7 Bearing type

Bearing design

Factor ka for circulating oil lubrication with good cooling

for oil bath lubrication without special cooling

Cylindrical roller bearings

ECP ECJ ECM ECMR ECMA ECMP ECML

120 170 150 400 700 1 400 1 800

40 50 50 150 250 500 600

Spherical roller bearings

E CC CC/VA405

250 600 1 400

100 200 500

81

4 Calculation of bearing arrangements Dimensioning the bearing arrangement Operating temperatures in the gearbox (and thus the bearings) should preferably not exceed 100 °C and definitely not be higher than 150 °C for the following reasons: ● ● ●

●

High lubricant viscosity enhances lubricant film formation. The lubricant ages more slowly, the lower the temperature. The dimensional changes in the bearing rings and rolling elements resulting from micro-structural changes in the material are smaller, the lower the temperature. The temperature differential across a bearing is smaller, the lower the temperature, so that preset bearing clearance or preload will not change as much.

The power loss resulting from the bearing friction can be calculated using information given in the SKF General Catalogue. Heat is removed from a bearing by conduction, convection, radiation and by the lubricant. If circulating oil lubrication is to be used, the requisite quantity of oil can be calculated from

Q = 0,039

NR Ta − Te

where Q = requisite quantity of oil (oil flow rate), l/min NR = power loss, W Ta = oil temperature at exit, °C Te = oil temperature at inlet, °C By experience, approximately 1/3 of the power loss is dissipated by the oil and 2/3 through heat conduction, convection and radiation. A value of 10 °C can be assumed for the temperature difference (Ta – Te). The guideline values obtained using the equation below have been found to be good estimates of the oil flow rates.

where Q = oil quantity (oil flow rate), l/min f = factor depending on bearing type and duty = 0,00003 for radial ball bearings, and radial roller bearings for moderate duty = 0,00005 for radial roller bearings in general = 0,00001 for thrust bearings, radial roller bearings with rotating outer ring and planetary gear bearings D = bearing outside diameter, mm B = bearing total width (radial bearings) or height (thrust bearings), mm The guideline values for the oil flow rate are generally on the safe side. For small bearings only very small quantities are required and it is difficult to arrange for a correct supply, particularly when the temperature varies. Often, the oil from pockets which capture oil will be sufficient. As there is a risk with forced oil circulation that the leads and nozzles become blocked it is recommended that either at least 0,25 l/min is supplied to each bearing, or supply pumps should be used which allow larger supply cross sections even where oil quantities are small and pressures high.

Permissible speeds When considering the operating speed, the speed ratings quoted in the SKF General Catalogue should be used as a reference. Bearing speeds which are higher than 70 to 80 % of the catalogue speed ratings are considered high. In such cases the following influences must be specially taken into consideration. ●

●

Q = fDB

82

The heat produced as a result of the friction increases bearing temperature; lubrication (viscosity, type of lubricant, lubricant supply) and cooling must be checked. As the heat loss via the casing is usually good, the temperature differential from inner to outer ring is larger, and a bearing having increased internal clearance (e.g. to C3) is required.

4 Calculation of bearing arrangements Dimensioning the bearing arrangement ●

To ensure proper performance of the bearing (no slip and proper rolling motion of the rolling elements) a correspondingly higher minimum load is required.

The maximum permissible speeds are much higher than the speed ratings (see SKF General Catalogue, factor fn). This also applies to gearbox bearings, so that the maximum permissible speeds for deep groove ball bearings, cylindrical roller bearings (with cage), angular contact ball bearings and fourpoint contact ball bearings are twice the speed ratings. If operating speeds are to exceed the speed ratings by more than 50 %, however, it is not only necessary to consider the points outlined above but also the following points. ●

●

●

●

Use oil jet lubrication with a jet speed of approximately 15 m/s. The oil should be directed at the inner ring raceway or the gap between cage and inner ring. Particularly stable cage designs should be chosen, e.g. one-piece outer ring centred machined brass cages (window-type), designation suffix ML, for cylindrical roller bearings. Minimise the vibrations produced in the complete drive system. This means using bearings with increased accuracy of dimensions and form and associated components with correspondingly high accuracy. Take into account the critical bending and torsional vibrations when designing the gearbox shafts.

In cases where bearings fitted with special cages or with increased accuracy are required, it is advisable to contact the SKF application engin-eering service.

●

●

●

4 When calculating the clearance in operation it must be rememberd that the clearance range quoted in the General Catalogue will be reduced when the bearing is mounted with interference fits and by the temperature differential from inner to outer ring. The Normal bearing clearance is sufficiently large so that if the fits are as normally recommended and operating conditions are normal, a sensible operational clearance will be obtained. In gearboxes, unusual operating conditions (e.g. in the cases below) often require the use of bearings with greater than Normal internal clearance to C3 or C4. In such cases it is advisable to check the operational clearance. ●

Internal clearance and preload The clearance in a bearing in operation is important with regard to proper performance of the bearing and to proper load distribution on the rolling elements. The following conditions should be aimed for when the bearings have reached their operating temperature.

For radial roller bearings in gearboxes (e.g. cylindrical, spherical and double row taper roller bearings) a slight radial internal clearance is favourable as the bearings and associated components (shaft, casing) usually have high radial stiffness. Radial preload combined with the deviations from form normally tolerated in gearboxes, or combined with unexpected differences in temperature would increase the risk of inadmissibly high additional stresses occurring which would overload the bearing. For single row taper roller bearings, although they have high radial stiffness, an axial preload can always be allowed if it can be expected that bearing overloading can be avoided by the casing walls ‘‘giving” in the axial direction. For ball bearings zero clearance is best; a slight preload is less critical for ball bearings than for the much stiffer radial roller bearings.

●

Bearings mounted inside gears for which an interference fit for the outer ring is required. This will further reduce internal clearance. Bearings on high-speed slim shafts which will heat up much more rapidly than the casing. The temperature differential across the bearing will then be particularly large.

83

4 Calculation of bearing arrangements Dimensioning the bearing arrangement ●

Gearboxes where the casing is well cooled. Again there will be a large temperature differential across the bearings. Examples include gearboxes operating out of doors where ambient temperatures are low and gearboxes having thick-walled or fan-cooled casings.

The operational clearance (mounted bearings which have reached the operating temperature) can be calculated by following the scheme shown in Table 8 .

Calculation of operational clearance

Bearing (designation): .......................... Tolerances (shaft/housing bore): ..........................

low

high

Radial clearance (µm) 1 Bearing bore (deviation ∆dmp) 2 Shaft (deviation) 3 Theoretical interference (+) or clearance (−): Zth = Point 2 − Point 1 4 Expected interference Z = Zth − smoothing1) 5 Expansion of inner ring:

.......... .......... .......... ..........

.......... .......... .......... ..........

..........

..........

.......... .......... .......... ..........

.......... .......... .......... ..........

..........

..........

.......... .......... ..........

.......... .......... ..........

..........

..........

15 Radial clearance in operation (Point 13 − Point 14)

..........

..........

Axial clearance (µm) for double row angular contact bearings 11a Total axial clearance reduction (Point 11 × cot α) 12a Axial internal clearance before mounting (min/max) 13a Axial internal clearance after mounting (Point 12a − Point 11a) 14a Thermal expansion:

.......... .......... ..........

.......... .......... ..........

..........

..........

..........

..........

el = 6 7 8 9 10

(solid shaft)

el =

d/F [1 − (di/d)2] 1 − (d/F)2 (di/d)2

E/D [1 − (D/Da)2] 1 − (D/Da)2 (E/D)2

Z

Total radial clearance reduction (Point 5 + Point 10) Radial internal clearance before mounting (min/max) Radial internal clearance after mounting (Point 12 − Point 11) Thermal expansion: et = 1,1 dm

eta = 1,1 dm

∆t 100

(µm, with dm in mm)

∆t cot α 100

(µm, with dm in mm)

15a Axial clearance in operation (Point 13a − Point 14a) 1)

84

Z

(hollow shaft)

Bearing outside diameter (deviation ∆Dmp) Housing bore (deviation) Theoretical interference (+) or clearance (−): Zth = Point 6 − Point 7 Expected interference: Z = Zth – smoothing1) Compression of outer ring: eA =

11 12 13 14

d Z F

For guideline values for smoothing see Table 9.

4 Calculation of bearing arrangements Dimensioning the bearing arrangement Guideline values for smoothing of mating surfaces

Table 9 Nominal diameter over incl

Smoothing

mm

µm

–

50

4

50

100

6

100

–

8

Adjustment values for single row angular contact bearings Single row angular contact bearings (angular contact ball bearings, taper roller bearings) are adjusted axially on mounting. The adjustment values (axial clearance or preload) are based on the operating conditions when the bearing is under load and has reached its operating temperature. Light preload is recommended for gearbox bearings and provides the following advantages compared with clearance: ● ● ● ● ●

accurate shaft guidance, increased stiffness, extended calculated and service lives, quiet running, and compensation for settling movements in operation.

As the bearings have to be adjusted on mounting, i.e. in an unloaded condition at ambient temperature, the changes produced when the bearings are in operation must be considered when determining the adjustment values. The main influences are those of temperature and deformations.

Influence of temperature on the adjustment of angular contact bearings The inner rings of bearings mounted on gearbox shafts are generally hotter than the outer rings. This will reduce the set clearance or increase the set preload. The influence of temperature on the adjustment can be calculated using the following equation provided both shaft and casing are of steel or a material with the same thermal behaviour ∆a = 11 × 10−6 [0,5 (dmA T∆A cot αA + dmB T∆B cot αB) ± T∆m L] where Da

dm L α

T∆A, T∆B T∆m

= reduction in axial internal clearance caused by temperature differential, mm = mean bearing diameter = 0,5 (d + D), mm = mean distance between bearings (➔ fig 15 ), mm = contact angle of bearing, degrees (cot α = 1,5/e; for values of bearingdependent factor e see SKF General Catalogue) = temperature differential from inner to outer ring across bearings A and B, °C = temperature differential from shaft to casing, °C

4

The plus sign is used for bearings arranged face-to-face, the minus sign for bearings arranged back-to-back.

Definition of distance between bearings Fig 15 L

A

L

B

Face-to-face arrangement

A

B

Back-to-back arrangement

85

4 Calculation of bearing arrangements Dimensioning the bearing arrangement If the value of the temperature differential T∆ is not known from experience or measurements, the following guideline values can be used:

Influence of deformations on the adjustment of angular contact bearings When considering deformations it should be remembered that the total resilience is influenced not only by the resilience of the bearings but also by the elasticity of the associated components, the fits and the elastic deformations of all other components through which the forces pass, including the gearbox support. The effects of the different stiffnesses of the associated components can be represented in preload force/preload path diagrams. The three preload force/preload path diagrams shown in Diagrams 1 to 3 show the influence of casing stiffness

T∆ = 5 to 10 °C for slowly rotating gearbox shafts T∆ = 10 to 20 °C for intermediate shafts and moderate speeds T∆ = 20 to 30 °C for slim high-speed shafts T∆ = 30 to 40 °C for high-speed input shafts and well-cooled gearboxes

Preload force/preload “path” diagrams for a bearing arrangement (Design 1)

Diagram 1 Preload force F0 Bearing B

Bearing A Bearing position A total

Bearing position B total

Ka F01

δ a1

Axial displacement δa

δ1


Diagram 2 Preload force F0 Bearing B

Bearing A Bearing position A total


Ka F02

δ a2 δ2= δ1

86

Axial displacement δa

4 Calculation of bearing arrangements Dimensioning the bearing arrangement Diagram 3 Preload force F0

Bearing B

Bearing A


Bearing position A total


Ka F01 = F03 Axial displacement δa

δ a3 δ3

on the axial displacement δa for the pinion shaft shown in fig 16 as a result of the external force Ka. In all three cases, the bearing stiffness and the external force Ka are the same. The casing in case 1 is very stiff whereas the casings in cases 2 and 3 are less stiff. Cases 2 and 3 differ only in the preload. Whereas in case 2 the preload path d is kept constant with respect to case 1, for case 3, the preload force F0 is the same as for case 1. Irrespectively of whether the preload path or the preload force is kept constant, the axial displacement δa will change depending on the casing stiffness. Thus it is imperative that the total resilience at the bearing positions is taken into account when determining

the preload in order to limit the axial displacement. Using the application example shown in fig 17 (a bevel/spur gear) the choice of adjustment (axial clearance, zero clearance or preload) will be discussed. The locating bearings for the bevel pinion shaft have axial clearance because the temperature differential from shaft to casing is relatively large as the speed is high and the pinion shaft has a small mass. Also the bearings are arranged in the (hook-shaped) sleeve and this arrangement is relatvely stiff in the axial direction. The intermediate shaft bearings and those on the output (power take-off) shaft can be either clearance-free or – Fig 16

B

A

4

Pinion shaft bearing arrangement

Ka δa

87


Bevel/spur gearbox bearing arrangements

depending on casing stiffness – even be adjusted to preload. The reason for this is that the speeds are low (less frictional heat), the masses of the shafts are relatively large, and the axial stiffness of the casing is lower. In fact, because of the axial forces generated in the bearings, the casing tends to deform (bulge). Influence of adjustment on bearing life The adjustment has different effects on the life of the two bearings shown in

Influence on bearing life of preload and clearance

Diagram 4 Life

Bearing A

Bearing B

Preload

88

Clearance

fig 16 . Whereas the life of bearing A which is subjected to the external force Ka immediately drops with increasing preload, bearing B will achieve its maximum life when it has a slight preload. Diagram 4 shows qualitatively the dependence of bearing life on preload and clearance. From this it will be seen that the stiffness does not increase very much with increasing preload whereas there is a risk that bearing life will be shortened and there will be increased friction and heat. Thus it is advisable to choose the adjustment so that when under load and at the operating temperature the bearing arrangement will have virtually zero clearance. An adjustment to give a distinct preload should only be chosen if the operating conditions (loads, temperatures, deformations) are accurately known, so that the preload force can be determined using sophisticated computer programs.

4 Calculation of bearing arrangements Dimensioning the bearing arrangement When selecting the bearings therefore, not only must the complete bearing designation (cage design, bearing clearance) be established, but information regarding adjustment values, oil flow rates and minimum load must also be given to production and assembly as well as to the end user, so that proper bearing performance can be guaranteed.

4

89

5 Lubrication and maintenance Grease lubrication . . . . . . . . 92 Oil lubrication . . . . . . . . . . . 95 Maintenance . . . . . . . . . . . . . 98

5 Lubrication and maintenance

Lubrication and maintenance Rolling bearings will only perform reliably when they are adequately lubricated. The lubricant prevents intermetallic contact between rolling elements, raceways and cage and also protects the bearing surfaces against corrosion. The importance of lubrication can be seen from the fact that of all premature bearing failures, some 80 to 90 % are caused by faulty lubrication and/or contamination. Long experience indicates that the same estimate holds true for gearbox bearings.

The task of the gearbox designer to choose the most suitable method of lubrication as well as the most suitable lubricant is made more difficult because of the different and varying demands on lubrication which exist for one and the same gearbox. Generally, the lubrication must not only be appropriate for the bearings but also for the gears. Additionally, the operating conditions for the individual bearings in a gearbox are often very different. One type of lubrication can be the optimum for high-speed, lightly loaded bearings, but unsuitable for heavily loaded bearings which rotate slowly. The operating temperature, which has a significant influence on the quality of the lubrication, is often not only dependent on the

5

load and speed but is also affected by changes in ambient temperature. Since, generally, only one method of lubrication and one lubricant are to be used for a gearbox, the optimum will never be achieved. To find the best compromise all the demands regarding lubrication and lubricant properties must be weighed against each other. The explanations and recommendations given in the following may be helpful.

91

5 Lubrication and maintenance Grease lubrication

Grease lubrication

Greases

The most important advantages of grease lubrication are:

The following properties must be considered when selecting an appropriate grease.

●

● ● ●

●

good protection against corrosion as the grease adheres well to the bearing surfaces; the efficiency of seals against external contaminants is reinforced; there is little risk of leakage; reliable lubricant supply – particularly when operation is intermittent – as the grease is retained at the bearing position; freedom from maintenance for lubricated-for-life bearings.

From this it is possible to define the main areas where grease lubrication can be employed in gearboxes. It is used mostly for small units and particularly for geared motors, and the gears are also grease lubricated. Small gearboxes may often be used in varying positions (horizontal, vertical or inclined at an angle). In such cases lubricant supply is more reliable if grease is used rather than oil bath lubrication. Sealing arrangements can also be simpler if grease is used. The life requirements are often very moderate for small units and if they are only used for short periods at a time, they will require no maintenance, being literally lubricated for life. For oil bath lubricated vertical gearboxes it is sensible to grease the upper bearings as the amount of oil splashed up is generally inadequate. The grease can be retained in position by baffle plates.

Base oil viscosity Generally speaking, the base oil viscosity of a grease can be used to calculate the adjusted rating life Lna, see SKF General Catalogue. This viscosity, ν, should preferably be greater than the required viscosity ν1, both viscosities being at the bearing operating temperature. Consistency Greases of consistency 2 and 3 are generally used for rolling bearing lubrication. Greases with lower consistency are easier to pump; those with higher consistency are easier to retain at the bearing position. At low temperatures soft greases of consistency 0 or 1 may be used, but special grease supply arrangements must then be made (e.g. 100 % grease fill, or a central lubrication unit and short relubrication intervals). For gearboxes subjected to vibrations or which are arranged vertically, a consistency 3 grease with high mechanical stability is preferable. When ‘‘gearbox greases” are used for small gearboxes, lubrication is a type of ‘‘dip” lubrication. The greases have a consistency of 0 or 00. Temperature range The expected operating temperature should lie within the temperature range permitted for the grease. When the temperature is too low, the grease will not have sufficient lubricating properties and when it is too high, ageing will be accelerated. An increase of 15 °C halves the original relubrication interval. Load carrying ability and wear protection For heavily loaded bearings (C/P < 10, e.g. bearings on the intermediate and output shafts) or in cases where a fully separating lubricant film is not present (κ < 1), EP greases are used. As the effect of some EP additives may be detrimental to bearing life, it is advisable to contact the lubricant supplier for recommendations.

92

5 Lubrication and maintenance Grease lubrication Protection against corrosion Usually gearboxes are well protected against the penetration of water. Nevertheless the presence of water or moisture cannot be completely prevented as differences in temperature allow condensation to form. Since any water in the rolling contacts of a bearing will quickly destroy the bearing surfaces, only greases having good rust inhibiting properties should be used.

thickener of the old and new greases are compatible. When a combination of oil and grease lubrication is used (e.g. grease lubricated bearings and oil lubricated gears) the lubricants should also be compatible with each other if negative results are to be avoided. This is particularly important when synthetic gear oils and mineral oil based bearing greases are used.

Oil bleed A grease must bleed oil to allow the formation of a lubricant film in the rolling contact. At low temperatures considerable bleeding is advantageous to ensure lubricant supply. At very slow speeds grease will be pushed away from the raceways and will no longer participate in bearing lubrication. Oil will not bleed to the raceways so that starvation will occur in the rolling contact. Consequently, oil lubrication is to be preferred for very slow speed operation. A much more moderate oil bleed is preferred at higher temperatures (> 80 °C) in order to give long relubrication intervals. Miscibility If, for some reason, it is necessary to change to another grease it should be checked whether the base oil and

5 SKF greases

93

5 Lubrication and maintenance Grease lubrication

SKF greases The SKF range of lubricating greases covers nearly all the requirements for gearbox bearing lubrication. These quality greases were specially developed for bearing lubrication. The most important technical data will be found in the SKF General Catalogue. Table 1 gives recommendations regarding the particular suitability of the various greases for different gearbox applications. Methods of grease lubrication The selection of the lubrication method is basically governed by the relubrication interval which can be determined using the information given in the SKF General Catalogue. ●

●

Suitable SKF lubricating greases for gearbox bearings

94

In cases where the relubrication interval is longer than the expected service life of the bearings a single grease fill will suffice. This presupposes that the grease can be retained in the bearings and that any oil bled from the grease cannot escape through openings below the bearings. Lubrication for life has only been found suitable for small and medium-sized bearings (bearing outside diameter up to 240 mm). Manual relubrication using a grease gun is suitable when relubri-

●

cation intervals are in the range one week to six months and the quantities required are up to 500 g. This means that manual relubrication can be used for bearings with outside diameters up to 420 mm. For larger bearings (D > 420 mm), larger quantities of grease (G > 500 g), or shorter relubrication intervals than one week, a continuous supply of grease is more reliable and also more economic. This is also true where the number of bearings to be grease lubricated is large.

When designing the grease supply, care should be taken to ensure that grease cannot escape at the supply side of the bearing, i.e. that it is compelled to pass through the bearing. At the opposite side of the bearing, the emerging used grease will prevent contaminants from entering the bearing. For double row bearings, the most efficient method is to supply the grease via the lubrication holes in the outer ring or, for paired taper roller bearings, through the lubrication holes in the intermediate ring.

Table 1 SKF grease Designation

Use, properties

LGMT 2

Small bearings (outside diameter D up to approx. 62 mm) Light to moderate loads Moderate temperatures up to 80 °C (max 120 °C) Low friction, quiet, good protection against corrosion

LGMT 3

Medium-sized bearings (outside diameter > 62 mm up to approx. 240 mm) Moderate loads Moderate temperatures up to 100 °C (max 120 °C) Multi-purpose grease, good protection against corrosion

LGEP 2

Heavily loaded roller bearings Moderate temperatures up to 80 °C (max 110 °C) Good protection against corrosion

LGEM 2

Heavily loaded roller bearings at low speeds Moderate temperatures up to 90 °C (max 120 °C) Water repellant

LGLT 2

Small, lightly loaded bearings at high speeds Low temperatures down to −20 °C Low friction, water repellant

LGHQ 3

High temperatures above 80 up to 150 °C Moderate loads Moderate speeds Water repellant

5 Lubrication and maintenance Oil lubrication

Oil lubrication Gearbox bearings are generally oil lubricated when the gears are to be oil lubricated and it is simpler to use a single lubricant. The use of oil lubrication for bearings has the following advantages: ●

●

●

●

●

oil can remove heat when bearings operate at high speeds and high temperatures; at very slow speeds and under heavy loads, oil penetrates to the bearing surfaces more easily than grease; less maintenance is required in respect of supplying oil to the bearing position than for grease lubrication, so that operational reliability is enhanced; the intervals between oil changes are longer than the grease relubrication intervals, particularly for medium and large-sized bearings; changing oil is simpler than changing grease.

Lubricating oils The following lubricant properties should be considered when selecting the oil. Viscosity Preferably the viscosity of the oil ν should be greater than the required oil viscosity ν1, both viscosities being at the bearing operating temperature (see under adjusted rating life in the SKF General Catalogue). When determining the appropriate viscosity for the different bearing requirements (speeds, temperatures etc.) in a gearbox, as well as for gear lubrication, it is advisable, if κ values < 1 are found for some of the positions, to err on the side of higher viscosity for the compromise solution. The intention is to improve the lubrication conditions for the heavily loaded bearings rotating at slow speed at the expense of generating more friction, because of the higher viscosity, in the high speed bearings. The operating viscosity and lubricant film formation can be influenced by selecting an oil of the appropriate viscosity class, but also by cooling.

Load carrying ability, wear protection EP oils (lubricating oils CLP to DIN 51 517) are preferred for the lubrication of spur, bevel and planetary gearboxes. As some EP additives have a detrimental effect on bearing life and EP oils also have varying load carrying ability and wear protection properties, it is advisable to contact the lubricant supplier for recommendations regarding the particular application. Protection against corrosion, behaviour in presence of water The rust inhibiting lubricating oils CLP to DIN 51 517 provide enhanced protection against corrosion as they have good surface wetting properties. Free water in the rolling contact is extremely damaging even when the actual amounts are very small. This is particularly true of bearings where the proportion of sliding is high (e.g. heavily loaded spherical roller bearings and all bearings subjected to centrifugal force). It is thus desirable that the oil will emulsify the small quantities of water which cannot be avoided. Behaviour in presence of air At moderate to high speeds there is a danger of air becoming mixed into the oil (foaming). Gear oils should be capable of expelling dispersed air and should not be able to form a stable foam.

5

Ageing Lubricating oils oxidise as a result of external influences, mainly high temperatures and exposure to air. This oxidation is catalysed (accelerated) in the presence of some metals such as copper or iron (wear particles). Antioxidant additives will slow down the process. Synthetic lubricating oils are more resistant to oxidation than mineral oils, but are not always as good in respect of lubricant film formation. Synthetic oils are used for worm gears because of lower friction, and for gears which are to be used in a wide range of temperatures, e.g. wind turbine gears.

95


Oil lubrication methods When selecting the method of lubrication the first aim should be to ensure a reliable supply of lubricant to the bearings. The oil mist inside a gearbox is not sufficient as bearings in modern gearboxes are heavily loaded and under conditions of lubricant starvation will wear and fatigue prematurely. The most used methods are described in the following.

Oil supply and return ducts for oil bath lubrication

96

Oil bath lubrication This method is commonly used for gears operating at peripheral speeds of up to 15 m/s. The oil level should reach the centre of the lowest rolling element. Greater depths mean losses because of churning and higher friction. This is often accepted for small and medium-sized vertical gears (for oscillation and agitation, and submerged units) where the bearings may be fully submerged. Bearings which are arranged above the surface of the oil must be supplied with oil which is captured by oil pockets or grooves where the oil running down

the casing walls is collected. The feed to the bearings should be designed to lead the oil through the bearings before it flows back to the sump. If the feed is on the seal or cover side, then the drainage should be laterally displaced and should be positioned sufficiently high so that the oil must pass through the bearings but at the same time, any surplus oil can run off without impinging on the seals. This also supports oil circulation and exchange at the bearing position on the cover side, thus improving cooling (➔ fig 1 ). If there is a risk that insufficient oil will be caught by the oil pockets, the oil supply can be improved by providing baffle plates or wipers. Bearings with asymmetrical cross section which dip into oil have a pumping action by virtue of their design, and this can contribute to cooling. Appropriate feed and return ducts should be provided.


Circulating oil Circulating oil lubrication should be considered above all when ● ● ● ●

●

●

circulating oil is to be used for the gears, the oil is to be used for heat removal, speeds are high to prevent rapid ageing of the oil, oil bath lubrication will not provide enough oil for the bearings, e.g. on vertical or inclined shafts, very large quantities of oil are required for oil bath lubrication because of the size of the gearbox, or the oil is to be continuously ‘‘freshened” by filtration or centrifuging.

●

●

●

When designing for oil circulation the following points should be remembered.

Oil jet lubrication

To guarantee that the bearings are lubricated right at the start, the oil supply leads must be dimensioned to provide oil even when the gearbox is first started up. There is otherwise a risk that oil will only arrive at positions where the feed cross section is larger (e.g. for the gears). To prevent the oil nozzles from becoming blocked they should have an opening diameter of at least 1,5 mm. Where oil pressures are high a suitable throttle length can be used to limit the oil flow. The throttle should be positioned immediately in front of each bearing, so that larger and thus more reliable oil lead diameters can be used with high oil pressures. Bearings operating at high speeds produce turbulence which rejects the oil. Care must be taken to see that the oil can actually enter the bearing at the feed side. Double row bearings are usually best lubricated via the lubrication holes in the outer ring (or paired single row taper roller bearings through the holes in the intermediate ring). For single row bearings the oil should preferably be supplied at the cover side.

5 Oil jet lubrication At very high speeds (n × dm > 106) oil jet lubrication must be used. As shown in fig 2 , the oil should be injected in the gap between inner ring and cage at high speed (v ≈ 15 m/s). Rejected oil must be able to run off between the bearings so that heat can be removed without excessive losses.

97

5 Lubrication and maintenance Maintenance

Maintenance

Monitoring lubrication

Gearbox bearing maintenance consists basically of monitoring the operating conditions in the gearbox and of monitoring the condition of the bearings themselves. This preventive maintenance should enable early identification of any malfunction so that remedial action can be taken. Such action should either prevent premature ending of the bearing service life or, at least, enable bearing replacement to be planned so that downtime costs can be minimised.

Lubricant supply and lubricant quality should be checked. To check the lubricant supply, simple means are available, e.g. a dip stick for oil bath lubrication. For circulating oil lubrication, on the other hand, complex systems are required to check the oil pressure, flow rate and temperature at each lubrication position, and include an alarm system. When choosing the monitoring arrangements lubricant supply relibility should be weighed against the costs which would occur in the event of a

For for analysis of used oil

Table 2 Machine: ............................................................. Type: ................................................................... No.: ...................................................................... Location: ............................................................

Oil:........................................................................ Oil quantity in system: ....................................... Sample taken, date:............................................ Sample taken by: ................................................

Property or guideline value

Test method (Standard)

Unit

Analysis result for used oil

Data for new oil

Colour, appearance

Visual inspection

–

..................

..................

Smell

–

–

..................

..................

Density at 15 °C

DIN 51 757

kg/m3

..................

..................

Kinematic viscosity at 40 °C at 80 °C at 100 °C

DIN 51 562

mm2/s .................. .................. ..................

.................. .................. ..................

Acid number

DIN 51 588, Part 1

mg KOH/g

..................

..................

Water content

ISO 3733

% wt/wt

..................

..................

Solid contaminants > 3 µm (quantity + type)

e.g. IR analysis DIN 51 451

% wt/wt

..................

..................

Four ball test

DIN 51 350, Part 4

N

..................

..................

Special test(s):

...............................................................................................................................................

Remarks:

...............................................................................................................................................

Characteristic

Deviation from new oil As new slight

moderate

large

very large

Ageing Contamination Recommended action:

............................................ Test date

98

.........................................................................................................................

................................................ Test carried out at

.............................................................. Tested by (Signature)

5 Lubrication and maintenance Maintenance blockage. Oil quality can be monitored by measuring the temperature in the oil bath, in the return duct and in the bearings either continuously or at regular intervals. This allows the operating viscosity to be evaluated. Additionally, regular analysis of the used oil is recommended (according to the scheme shown in Table 2 , for example). The results should always be compared to a similar analysis of the fresh oil.

Monitoring load The power consumption of the drive is sometimes used as a measure of the load, but this is not suitable for monitoring bearing loads, as the peak loads are very much smoothed in the recording. Better information is obtained by measuring torque and measuring stress at the root of the gear teeth. A reliable bearing load measurement can only be obtained by using special force measuring bearings equipped with strain gauges. As this method is very expensive, it is generally only used for new developments or during damage analysis.

Monitoring temperature An indication of incipient bearing damage will be given quite late by the temperature, and at low speeds there may be no indication at all. Therefore, measuring bearing temperature is only appropriate for condition monitoring of bearings at high speeds, and then only as an indication of trends. To be of any use, the temperature should preferably be measured directly on the bearing rings. Temperature measurements of bearings, gearbox and oil are very suitable for monitoring the operating viscosity of the oil. This allows important deductions to be made with respect to the operating conditions.

Monitoring wear Under favourable operating conditions (adequate lubricant film thickness and clean lubricant) bearings will operate practically without wear. Where there is a clear indication that particles of bearing steel are among the wear particles the conclusion is that a bearing has already become damaged. It is

then recommended that the gearbox be inspected to determine the source of the wear and to take remedial action to prevent further damage. Wear particle analysis also enables gear wear and seal efficiency to be monitored.

Monitoring vibrations Bearings in operation generate slight noise even when in perfect condition. This running noise could be listened to by holding a wooden stick to the housing and to the ear. In the past this was one of the most reliable monitoring methods in spite of human failings such as limited frequency spectrum, subjective judgements and inability to relate frequencies heard to causes. With the methods and equipment available today diagnoses can be made and condition monitoring is effective. Suitable proven procedures are: ●

●

comparative measurements on similar gearboxes under the same operating conditions, allowing differences to be observed, and/or trend measurements on one gearbox at given intervals, again allowing differences to be noticed.

5 SKF has developed special measuring techniques as well as the requisite equipment allowing a broad spectrum of vibrations to be monitored and making it possible to analyse the type and magnitude of incipient damage in a bearing. The more important items of equipment and associated software are described in the following. SKF VIB Pen This very handy vibration measuring probe (dimensions 150 × 20 × 18 mm; mass 80 g) can measure vibration velocities of 0,1 to 99,9 mm/s in the fre-quency range 10 to1 000 Hz. It is poss-ible to determine whether the machine vibrations are in the range allowed according to ISO 3945. Bearing dam-age can only be identified when it is in an advanced stage using this method. However, as inadmissible vibrations will considerably shorten bearing life, the VIB Pen is a simple and reliable instrument for maintenance personnel to monitor operating conditions. 99


SKF SEE Pen The SEE Pen measures differences in vibration acceleration with time in the frequency range 250 to 350 Hz. The signals in the high frequency band which are measured, evaluated and recorded using the SEE (Spectral Emitted Energy) method are only produced by ‘‘damaged” bearings. The indications may be for lubricant starvation, contamination or actual bearing damage. Thus the SEE Pen is an ideal complement to the VIB Pen (both have the same dimensions) to give simple and reliable bearing condition monitoring. Here too, trend measurements give the optimum evaluation.

e

SKF Picolog This compact, breast-pocket size apparatus combines the measuring capabilities of the VIB and SEE Pens and can also be used for ‘‘enveloping”. The peaks of the enveloped bearing noise are evaluated. The distance between peaks enables the bearing component which is damaged to be identified. Up to 500 recorded measurements and alarm levels can be stored and downloaded on to a PC. Evaluations can be made using PRISM2 Jr. software. The Picolog is an excellent tool for bearing condition monitoring.

-

-

SKF Microlog This portable equipment (mass 2 kg) can be used for frequency analysis and gives optimum evaluation in the low and high-frequency range (SEE). The Microlog is a powerful data log with a display panel. The PRISM2 software permits a variety of evaluation methods to be used, e.g.waterfall diagrams, storage of critical frequencies, determination of alarm levels etc. The Microlog can be used with handheld sensors or with permanently installed sensors. As it records electrical signals, it can be used to measure not only vibration velocities and accelerations but also distances, pressures and temperatures.

100

SKF Multilog This is a system for plant monitoring with permanently installed sensors and is more powerful than the SKF Microlog. It can be used for the continuous monitoring of rolling bearings and machines. In practice, the SEE method indicates incipient bearing damage earlier and more clearly than other methods. This is particularly true when the damage consists of micro cracks and/or cold welding (lubricant starvation) in the rolling contact. Because of the early warning, the user has time to plan bearing replacement.

Photograph (from left to right) SKF Thermo Pen, SKF Picolog, SKF SEE Pen, SKF VIB Pen (upper), SKF Tachometer (lower), SKF Oil Check, SKF Stethoskop, SKF Microlog


5

101

6 Recommended fits

Recommended fits The rings of rolling bearings deform elastically under load and adapt themselves to their seatings. To be able to fully exploit the load carrying capacity and accuracy of the bearings, the bearing rings must be supported with sufficient firmness and accuracy by the associated components. Where the load rotates with respect to the ring, the ring should have an interference fit on or in its seating (shaft, housing or gear). This prevents a loosening of the bearing fit and the ring will not ‘‘wander” under load. Fretting corrosion will also be prevented. It is not possible to provide a sufficiently tight fit for the ring simply by clamping it axially.

The selection of fits is dealt with in detail in the SKF General Catalogue. The following recommendations complement the catalogue information, giving the usual, proven tolerances for high-performance gearboxes for the most common case, i.e. rotating inner ring load and stationary outer ring load (➔ Table 1 ).

6

The recommendations given in Tables 2 and 3 are for special cases which differ from the above, but which are typical of certain types of gear.

103

6 Recommended fits Recommended fits, form and position tolerances for gearbox bearings Table 1 Bearing type

Shaft tolerances (for solid steel shafts and rotating inner ring load) Shaft diameter (mm) ≤18 (18) (40) (100) (140) (200) (280) to to to to to to 40 100 140 200 280 500

Deep groove ball bearings (for light loads P ≤ 0,06 C)

Housing tolerances (for steel, spheroidal graphite or grey cast iron and stationary outer ring load) >500

Housing bore diameter (mm) Bearing ≤300 (300) >500 arrangement to 500

j5

k5

k5

k6

k6

m6

m6

m6

J6 G6

J6 G7

H7 F7

Locating Non-locating

j6

k6

k6

m6

m6

n6

p6

p6

J6

J6

H7

Cross located

j5

k5

k5

m5

m5

m5

–

–

J6

J6

H7

Locating

double row (series 33 D) k5

k5

m5

m5

–

–

–

–

J6

J6

H7

Locating

k5

k5

m5

m5

n6

–

–

–

approx. 1 mm radial clearance (locate to prevent turning)

Thrust bearing

Cylindrical roller bearings (N, NU, NJ designs)

k5

k5

m5

m5

n6

p6

p6

r6

J6

J6

H7

–

Spherical roller bearings

k5

k5

m5

m5

n6

p6

p6

r6

J6 G6

J6 G7

H7 F7

Locating Non-locating

Taper roller bearings single row (adjusted via the outer ring)

k6

k6

m6

m6

n6

p6

p6

–

J6

J6

H7

Cross located

double row, paired single row

k5

k5

m5

m5

n6

p6

p6

r6

J6

J6

H7

Locating

Thrust ball bearings

h6

h6

h6

h6

h6

g6

g6

g6

G7

G7

F7

Thrust bearing

Spherical roller thrust bearings

j6 (for all diameters)

Angular contact ball bearings single row (adjusted via the outer ring) double row, paired single row (series 32, 33, 70 BG, 72 BG, 73 BG)

Four-point contact ball bearings

approx. 1 mm radial clearance

Form and position tolerances, surface roughness Cylindricity

IT5/2 (for all diameters)

Rectangularity

IT5 (for all diameters)

Permissible surface roughness Rz (µm)

4

4

4

6,3

6,3

6,3

6,3

10

8

When shaft tolerances p6 and r6 are used, use of the oil injection method will ease dismounting

104

10

16

Thrust bearing

6 Recommended fits

Housing tolerances for special cases Table 2 Case

Housing tolerance Housing bore diameter (mm) < 300 (300) > 500 to 500

Deep groove ball bearings and spherical roller bearings as non-locating bearings with rotating inner ring load and stationary outer ring load and a temperature differential > 10 °C from outer ring to housing (e.g. when heating via the shaft, high speed operation, very solid housings, low environmental temperatures)

G7

F7

E8

a) axial displacement of outer ring in housing required, e.g. with thermal expansion of shaft and axially stiff housing

G6

G7

F7

b) axial displacement of outer ring not required, e.g. when thermal expansion of shaft is compensated by elastic deformation of housing without overloading bearings

J6

J6

H7

a) locating bearing

G6

G7

F7

b) non-locating bearing

J6

J6

H7

Locating bearings and cylindrical roller bearings under oscillating outer ring load, e.g. when weight and tooth force act in different directions. Special steps have to be taken when mounting in one-piece (non-split) housings (e.g. heating the housing)

JS6

JS6

JS7

Deep groove ball bearings and spherical roller bearings, cross located, with rotating inner ring load and stationary outer ring load

Cylindrical roller bearings of NUP design with rotating inner ring load and stationary outer ring load

Shaft tolerances ➔ Table 1

6

105

6 Recommended fits

Tolerances for bearings mounted in gear hubs Table 3 Bearing type

Bearing arrangement

Shaft tolerance Shaft diameter (mm) < 120 (120) (250) to to 250 315

Housing tolerance Housing bore diameter (mm) < 120 (120) > 250 to 250

Deep groove ball bearings

Shifting gear (inner and outer rings rotate at same speed)

j5

js6

k6

M61)

M61)

N61)

Planetary gear, intermediate gear (outer ring rotates, inner ring stationary)

h5

h6

h6

M61)

M61)

M61)

Spherical roller bearings Cylindrical roller bearings

Planetary gear, intermediate gear (outer ring rotates, inner ring stationary)

h5

h6

h6

N6

P61)

R61)

Cylindrical roller bearings

Planetary gear, intermediate gear (rotating inner and outer ring load)

see Table 1

N61)

P61)

R61)

Cylindrical roller bearings Planetary gear, intermediate gear without outer ring (planetary gear rotates, inner ring stationary)

h5

h6

h6

G62)

F62)

F62)

Cylindrical roller bearings Planetary gear, intermediate gear without inner ring (outer ring rotates)

f62)

e62)

e62)

N6

P6

R6

Needle roller and cage assemblies

g52)

g52)

–

G62)

G62)

–

Planetary gear, intermediate gear

1)

C3 internal clearance required

2)

For raceways on the planetary pins and in gear hubs, the deviation from circularity should be < 25 % of actual diameter tolerance; the deviation from cylindricity should be < 50 % of actual diameter tolerance; the surface roughness should be Ra ≤ 0,2 µm and Rz ≤ 1 µm; hardness should be 58 to 64 HRC and the case depth when finish machined should be Eht = 0,5 √Dw – 0,5 ≥ 0,3 mm, with Dw = rolling element diameter in mm

Measuring a distance for adjustment of taper roller bearings

106

6 Recommended fits

6

107

7 Mounting and dismounting bearings Adjustment of angular contact bearings . . . . . . . . .109

7 Mounting and dismounting bearings Adjustment of angular contact bearings

Mounting and dismounting bearings Rolling bearings are precision products which must be carefully handled when they are being mounted if they are to perform properly. Equal care must be taken when dismounting if the bearings are going to be re-used.

Basically, there are three things to remember when mounting: ●

●

●

cleanliness, to prevent damage to the raceways by contamination and corrosion; accuracy of all associated components, to avoid additional forces arising from deformations and to avoid imprecise running; the force used to mount and dismount should not be applied via the rolling elements and cage; direct blows should be avoided so that indentations and initial damage to the raceways are prevented.

The SKF General Catalogue contains more detailed instructions regarding mounting and dismounting based on the above requirements. A comprehensive selection of SKF tools, equipment and maintenance products are presented in publication 4100 “SKF Bearing Maintenance Handbook”. SKF also offers various training courses and seminars for personnel involved in mounting and dismounting.

Adjustment of angular contact bearings When mounting angular contact bearings (angular contact ball bearings, taper roller bearings) in gearboxes, particular attention should be paid to the adjustment of the bearings as this determines not only the performance of the bearings themselves but also the guidance of the shafts and consequently the load carrying ability of the gears. The calculation of the adjustment value is described in the section ‘‘Dimensioning rolling bearings” (➔ Section 4). The choice of adjustment method depends on whether the bearings are to be adjusted to axial clearance or to preload.

7

109


Adjustment of taper roller bearings arranged face-to-face to axial clearance First it is necessary to determine the zero clearance condition as accurately as possible. This is rather difficult for taper roller bearings on horizontal shafts, as the weight of the shaft and gears displaces the outer rings axially because of the taper angle, so that the clearance-free roller end/flange contact, which is decisive for the adjustment, is difficult to achieve. The procedure described in the following is well proven and is very much simpler and more reliable. A device is used to swing the gear shaft into the vertical position for the adjustment (➔ fig 1 ). ●

● ●

● ●

Adjustment of taper roller bearings arranged face-to-face with axial clearance

●

Mount the inner rings on the shaft (take care that the rings abut the shoulders correctly). Push the outer rings over the roller and cage assemblies. Place the shaft with bearings in the gearbox which should be horizontally positioned Mount the top of the casing. Screw down the cover at one side of the casing. Tilt the casing so that the shaft is supported via the bearing by the cover.

●

●

●

The weight of the shaft and gears acts as a measuring load on the lower bearing. The upper bearing is free of clearance as soon as all the rollers rotate about their own axes when the shaft is rotated. A limited range of matched single row taper roller bearings (DF execution) is available. The bearing pairs are supplied with an appropriate intermediate ring, so that adjustment is not required. The user can also match single row taper roller bearings himself; the requisite width of the intermediate ring, taking into consideration the fit, is determined as follows. ● ●

Fig 1 ●

a

x

Rotate the shaft by hand (if necessary by turning the input or output shaft) and press the outer ring of the upper bearing downwards in its seating until all the rollers in the bearing turn about their own axes. The bearing arrangement is now free of clearance. The requisite length of the spigot in the cover is determined from a = x – s where s is the required axial clearance. Mount the finish machined cover with shims (if necessary).

●

Mark the bearing components as shown in fig 2 using an electric pen. Place bearing A on three gauge blocks (➔ fig 3 ). Apply the measuring load: 300 N for bearings with outside diameter up to and including 240 mm 500 N for bearings with outside diameter over 240 mm. Turn outer ring 1A by hand so that the rollers abut the flange of the inner ring 1A.

Fig 2

a=x–s s = requisite axial clearance

1B

1B

1

C

1A

110

Marking of bearing components

1A

7 Mounting and dismounting bearings Adjustment of angular contact bearings Fig 3

FB =

Measuring load

F

Gauge block

Measuring the standout F

● ●

Measure the standout FA at three points using the gauge blocks. Calculate the average value of FA from FA =

● ●

FA1 + FA2 + FA3 (mm) 3

Repeat the above procedure for bearing B. Calculate the average value of FB from

●

FB1 + FB2 + FB3 (mm) 3

Determine the width of the intermediate ring from C = FA + FB + ∆a (mm) where ∆a = maximum axial clearance according to Table 1 or for special bearings, the maximum value of the special clearance. The following tolerances apply to the width C of the intermediate ring: 0/–0,04 mm for bearings with outside diameter D ≤ 140 mm and 0/–0,06 mm for berings with outside diameter D > 140 mm

The axial clearance values given take into account the clearance reduction caused by the interference fit when the shaft tolerances (also given in Table 1 ) are applied. These tolerances are required for rotating inner ring loads which are moderate to heavy. The outer ring with its point load should have a seating to tolerance J6 or H7.

Maximum standard axial clearance of matched taper roller bearings Table 1

Maximum standard axial clearance ∆a before mounting

Bearing bore diameter d over incl.

Shaft tolerance

mm

–

mm

Bearings of series 329 320 X

330

331

302,322

332

303,323

313 (X)

– 30 40

30 40 50

k5 k5 m5

– 0,200 0,220

0,120 0,140 0,160

– – 0,220

– 0,160 0,180

0,140 0,160 0,180

0,150 0,170 0,170

0,170 0,180 0,200

0,100 0,110 0,120

50 65 80

65 80 100

m5 m5 m5

0,250 0,270 0,310

0,180 0,200 0,230

0,240 0,290 0,390

0,200 0,240 0,270

0,200 0,220 0,270

0,190 0,220 0,260

0,220 0,260 0,300

0,140 0,170 0,170

100 120 140

120 140 160

m5 m5 n6

0,330 0,370 0,430

0,280 0,300 0,330

0,400 0,400 0,400

0,300 – –

0,280 0,300 0,330

0,300 – –

0,340 0,390 0,430

0,190 0,220 0,240

160 180 190

180 190 200

n6 n6 n6

0,430 0,430 0,450

0,370 0,400 0,400

– – –

– – –

0,370 0,400 0,400

– – –

0,450 0,500 0,500

– – –

200 225 250

225 250 280

p6 p6 p6

0,500 0,500 0,600

0,450 0,500 0,550

– – –

– – –

0,450 0,500 0,550

– – –

0,550 0,600 –

– – –

280 300 340

300 340 360

p6 p6 p6

0,700 0,700 0,750

0,600 0,650 0,750

– – –

– – –

0,600 0,650 –

– – –

– – –

– – –

7

111


Principle of force/path measurement

There will be virtually no reduction in clearance from any deformation of the outer ring. If looser fits are chosen, then the axial clearance value will be slightly larger when the bearing is mounted. If a tighter fit is used then it is advisable to check that the bearing will not be axially preloaded.

basis or a collective method based on tolerances has not found acceptance in gearbox applications as there is excessive scatter of the preload force when these methods are used. However, the friction torque can be used indirectly for adjustment as will be seen from the following.

Adjustment of taper roller bearings arranged face-to-face to preload

●

When adjusting bearings which are to have a preload it is necessary to achieve a certain preload force. If the preload distance (path) method is to be used, it is first necessary to measure the force and displacement in the mounted condition. This is the only way to be able to take housing resilience into account when determining the appropriate distance. Fig 4 shows the principle of a force/distance measurement. Diagram 1 shows the result of such measurements. The characteristic curve has been extrapolated (broken line) for small loads because the measurements are not sufficiently accurate under such light loads. Using the characteristic curve the desired preload can be set by fitting a shim or spacer ring. The adjustment of taper roller bearings using the friction torque as a

●

The friction torque of the two bearings which are to be adjusted against each other is measured in a rig for a given preload force and at a defined measuring speed and recorded. After mounting the bearings in the gearbox, the preload force is applied by inserting shims until the recorded friction torque is obtained. The speed and lubrication conditions when the torque is measured must be the same as when the original recorded measurements were made.

This method is advantageous particularly when large numbers of bearings are to be adjusted if it is easier to measure torque than force at the assembly position.

Adjustment of taper roller bearings arranged back-to-back To ensure sufficient accuracy, the bearing rings should always be mount-

Fig 4

Recorded force/ path diagram for shaft/bearing/ housing system Diagram 1

Axial force Axial load

S

Axial preload path s

112

7 Mounting and dismounting bearings Adjustment of angular contact bearings Fig 5

●

●

●

Bearing V X B

●

Spacer ring (shim)

X =

● ●

Bearing H

●

Adjustment of taper roller bearings arranged back-to-back on pinion shaft

●

ed against a fixed abutment face which is at right angles to the shaft axis. For taper roller bearings arranged back-toback, therefore, a shim (spacer ring) is inserted between one of the two bearings and a shaft shoulder. The following procedure allows the shim to be fitted without having to mount and dismount bearing V; this would be rather difficult because of the requisite interference fit of the bearing on the shaft. ● ●

Measurement of standout Z

Rest the shaft with bearing H and casing in a vertical position on the face of the pinion (➔ fig 5 ). Turn the casing by hand so that the rollers of bearing H abut the inner ring flange. Measure the standout X at three points (dial gauge). Calculate average standout X.

●

Determine reduction in axial clearance ∆p taking into account the shaft fit from

= ∆r 0,4

1,5 (mm) e

7

where ∆p = reduction in axial clearance, mm ∆r = radial interference, mm e = bearing-related calculation factor, see bearing tables in SKF General Catalogue

Fig 6

Z

Z1 + Z2 + Z3 (mm) 3

∆p = ∆r 0,4 cot α

Mount outer ring of bearing H in the casing. Mount the inner ring with roller and cage assembly of bearing H on the pinion shaft and introduce the shaft into the casing.

Measuring load

Lay bearing V on measuring plate (➔ fig 6 ). Apply measuring load: 300 N for bearings with outside diameter D up to and including 240 mm 500 N for bearings with outside diameter D > 240 mm. Rotate the outer ring of bearing V by hand so that the rollers abut the inner ring flange. Measure the standout Z at three points (dial gauge). Calculate average standout Z.

Z =

●

X1 + X2 + X3 (mm) 3

●

Determine width B of shim for a given adjustment of the pinion bearing arrangement using B = X + Z + ∆p ± ∆a (mm)

Bearing V Measuring plate

where + ∆a is the desired axial clearance and − ∆a is the desired preload.

113

Industrial Gear Box

Recommend Documents