UNIT 13 ROLLING CONTACT BEARING

Structure

13.1 Introduction Objectives

13.2 Materials for Rolling Contact Bearings

13.3 Types of Rolling Contact Bearings 1 3.3.1 Radial Ball Bearing

13.3.2 Angular Contact Ball Bearlngs

13.3.3 Roller Bearings

13.4 Friction in Rolling Bearings

13.5 Basic Static Capacity

13.6 Static Equivalent Load

13.7 Friction Torque Due to Load

13.8 Frictional Torque Due to Viscous Churning of Lubricant

13.9 Heating of Roller Bearing

13.10 Rolling Bearing Geometry

13.1 1 Stress and Deformation in Rolling Element

13.12 Bearing Deflection

13.13 Permanent Deformation in Bearings

13.14 Fatigue of Rolling Bearing

13.15 Selection of Bearing

13.16 Load on Bearing

13.17 Combined Bearing Load

13.18 Bearing Life

13.19 Equivalent Load

13.20 Bearing Dimension Code

1 3.2 1 Summary

13.22 Key Words

13.23 Answers to SAQs

13.1 INTRODUCTION

The idea of a rolling contact bearing is perhaps the oldest and belongs to the age when men moved heavy objects over the rollers. A rolling contact bearing, as it is now understood, is an assembly of balls or rollers which would physically maintain the shaft in radially spaced apart relationship with respect to a usually stationary supporting structure called a housing in which bearing itself is supported. Usually a rolling contact bearing may be obtained as a unit which includes two steel rings each of which has a hardened raceway on which hardened steel balls or rollers roll. One such ball bearing of deep groove type is shown in Figure 13.1. The balls or rollers generally called rolling elements, are usually held in angularly spaced relationship by a cage or separator.

Presently in industry, many different kinds of bearings are used. These are classified as gas film bearings, magnetic bearings, hydrodynamic and hydrostatic bearings. Each of these bearings excels in some specialised field of application. For example, hydrostatic bearings are excellent for applications where size is no restriction, ample supply of pressurised fluid is available and extreme rigidity under heavy loading is required. Self-acting gas bearings are applied where loads are light, speeds are high and gaseous atmosphere exists, rolling contact bearings, however, are not quite so limited in the scope of their application. Thus, these bearings are available from very small size (such as used

Design of Bearings, in internal guidance gyroscope or dental drills running at 300,000 rpm) to very large size Clutches, Brakes (such as 1500 mm outside diameter roller bearing for metal rolling mill). and CAD

The rolling contact bearings have following advantages over other types :

(a) These bearings have very low friction as compared to sliding contact bearings and, therefore, result in less power loss. s

(b) Starting friction is very low and hence can be started on bad.

(c) The deflection of such bearings is less sensitive to load fluctwationthan that of a conventional hydrodynamic bearing.

(d) These bearings can virtually run without lubrication. Howwm, to cool them some lubricant, in a much smaller quantity than for sliding contact bearing, is supplied. This obviously eliminates the expensive lubtricatipg system.

(e) The requirement of shorter axial space is many times an advantage over sliding contact bearing.

(f) Such bearings are less sensitive to change in-load, speed and aperating temperatures.

(g) Most radial bearing can support combination of radial and thrust loads.

It may, nevertheless, be pointed out that all rolling contact bearings will eventually fail due to fatigue of rolling surfaces, no matter how perfcctly they are mounted, kept cool, protected from dirt and moisture and otherwise properly operated.

Objectives

After studying this unit, you should be. able to

classify bearings, w

know materials of rolling contact bearings,

calculate power loss in bearing, and

select bearing for specific purpose from manufacturer's catalogue. . A

13.2 MATERIALS FOR ROLLING CONTAm BEARINGS

, p-

The three elements, vis. inner race, outer race and rolling elements are made in steel. The desired properties of steel for bearings is the capability of beitig hardened to required level which is 61 to 65 RC. The high resistance to wear and good fatigue strength we also the requirement. In many cases, the choice of the material may depend upon process of manufacture. The temperature rise in roller bearings is not much and the bearings are expected to operate at tednperature not higher than 125°C. If however, the temperature is required to be higher than this limit then special treatment to steel is imparted to guarantee the dimensional stability. The care has to be taken in design that the dynamic load capacity (a bearing characteristic to be defined in Section 13.1) is properly modified. A temperature modifying factor is recommended by SKF. The dynamic load capacity is not affected upto 1 50°C but at temperatures 200°C, 250°C and 3W°C, respectively the dynamic load capacities are taken as 90%' 75% and 60% of basic value.

As it will be explained in Section 13.8 the fatigue failure of bearing is initiated below the surface and the cause may be either maximum shearing stress or orthogonal shearing stress which have higher values below th= surface. Perhaps this was the reason that case hardening steels were earlier preferred for bearing elements. Now it has been established that through hardening steels if treated properly can give as good resptts as case hardened steels.

Cr-Ni and Mn-Cr alloy steels with C content of approximately 0.15% are the case Rolling Contact Bearing

hardening steels most commonly used for rolling bearings. Ni-Cr steel (AISI 33 lo), Ni-Mo (AISI 4620) and Ni-Cr-Mo steel (AISI 8620) are some case hardening steels commonly used.

Cr-Mn steel (AISI 521 00 containing; C, 0.95- 1.10, Mn, 0.2-0.5; Cr, 1.3-1.6 as alloying elements) is very commonly used through hardening steel. Both groups of steels can develop hardness in the range of 61 -65 RC.

Cr-Mo steels are recommended in such cases where corrosion is likely occur. These steels do not develop as high hardness as the other two groups and hence bearings will have lower load capacity. Such bearings are further required to have surfaces very finely finished.

The purpose of cage is to keep two neighbouring elements at a proper distance and hold a good amount of grease (in grease lubricated bearings) to keep rollers well lubricated. In certain bearings in which the races can be separated for assembling and dismantling the cage serves the purpose of holding the rollers in position. The cages are made in pressed steel or brass structure centering on rolling elements. The cages that are centred on either of the races are machined and permit conditions of high velocity and acceleration if properly lubricated. The cages are subjected to stresses due to friction and inertia forces and are prone to attack by lubricants and their additives. They are easily attacked by organic solvents, coolants (hydrogenated hydorcarbons and ammonia), etc. For this reason, the material of cages needs consideration for selection. Recent developments have brought polyamide with glass reinforcement in focus for use as cage material. This material can be heat srabilised and easily moulded in required form to obtain a favourable combination of strength and elasticity. Additionally this material is very light and develops very low friction in contact with well lubricated steel surfaces resulting low loss of power. However, polyamide cages are restricted by temperature.

13.3 TYPES OF ROLLING CONTACT BEARINGS

There are several types of bearings, which are used to carry radial and thrust loads. Many of them take the combination of both radial and axial loads. Table 13.1 describes various bearing types. Some of them are described in little greater detail below. For more information the students may refer to bearing manufacturer's catalogue (such as SKF bearing catalogue).

Table 13.1 : Different Types of Bearings

Design of Bearings, Clutches, Brakes

13.3.1 Radial Ball Bearing and CAD Single row deep groove ball bearings are most common in use (Figure 13.1). Most

commercial bearings have inner and outer raceways curved to radii between 5 1.5 and 53% of ball diameter. To assemble these bearings the balls are inserted between the inner and outer rings as illustrated in Figure 13.2. After all the balls have been placed between the rings, the inner one is brought into the position of concentricity with the outer ring, and the separator is then placed on the balls to keep them at constant distance away from each other. The radial deep groove ball bearing has a fairly high load capacity in radial direction and can support a fair proportion of its radial capacity in axial direction too. Sometimes this bearing is used to carry axial load alone. Mostly the outer ring surfaces are flat (part of cylinder) and hence the bearing may support moments also, but only to a small extent. Sometime the outer surface is made spllerical in which case bearing has a tendency to self align and not to Carry any moment. The balls may be shielded or sealed to keep the bearings lubricated and exclude dirt.

Figurk 13.1 : A Deep Groove Ball Bearing

Figure 13.2 : Assembling Deep Groove Ball Bearing

The radial load capacity of a ball bearing may be increased by increasing the number of balls. This is achieved by making ball filling slot in each of the inner and outer races as shown in Figure 13.3. This, however, restricts this bearing to be used against axial load, because of presence of slots.

Double row deep groove ball bearings have similar characteristics as single row bearings but since two rows of balls roll in two pairs of races the diameter of a double groove ball bearing is less than that of a single row ball bearing of comparable load capacity. However, the proper load sharing between the balls would depend a great deal upon the accuracy of manufacture. The instrument of miniature ball bearings have same characteristics as the deep groove ones, except that they are very small in size (9.5 to 28.5 mm in outside diameter and 4.75 to 12.7 mm in bore diameter) and are very carefully manufactured.

Figure 13.3 : Filling Slot Type of Deep Crqove Ball Bearing

13.3.2 Angular Contact Ball Bearings These may be single row or double row bearings. They are meant to carry radial and axial load together or only axial load depending upon the magnitude of the angle of contact. The bearings having large contact angle support heavy thrust. The groove curvature radii are generally 52 to 53% of ball diameter. The contact angle is usually 40". The single row ball bearings of this type are generally used in pairs with ball rotation axes opposing each other (in back-to-back or face-to-face configuration) or parallel to each other (tandem configuration). Figure 13.4 illustrates the mounting of these bearings.

Double row angular contact ball bearing essentially is similar to a dulex pair, with a difference that there is a single inner and single outer ring with a pair of races in each. The balls may be set to rotate either with arrangement as in back-to-back mounted or with the arrangement as in face-to-face mounted duplex pairs of angular contact ball bearings. In thp former configuration it is rigid type while in the latter it is non-rigid type. This type of bearings can take bending moment effectively.

For assembly of shaft and housing which cannot be made perfectly coaxial the self aligning ball bearings are best used. In such bearings the assembly of inner ring and balls can tilt in the outer ring which has spherical inner race. The loss of load carrying capacity which is inlierent in this construction due to non-conforn~ity of outer of outer race way with the balls, is conipensated by having large number of balls in the bearings.

(a) Back-to-Back (b) Face-to-Face (c) Tandem

Figure 13.4 : Angular Contact Ball Bearings used in Pairs, a is Angle of Contact

If the contact angle of angular contact bearings exceeds 45", it is classified as thrust bearing. One can easily imagine that the maximum value this angle can assume is 90°, in which case races will be side ways and balls and cage in the centre. Such a bearing cannot take any radial load.

13.3.3 Roller Bearings Roller bearings have an ideal line contact against the point contact of balls with races. This is the main reason why load carrying capacity of these bearings is higher. Roller bearings, consequently, have large load supporting capacity, they are stiffer and have longer fatigue life than comparable ball bearings. However, in general the roller bearings are costlier.

The cylinder roller bearings have rollers as the rolling element placed between the inner and outer rings and separated by softer cage. In a radial roller bearing only one of the rings has guiding flanges and hcnce the bearing cannot take any axial load (Figure 13.5(a)). However, roller bearings having one guiding flange in the opposing rings are also made to make them carry axial loads (Figure 13.5(b)). The edges of the

Rolling Contact Bearing

Design of Clutches, and CAD

Bearings, rollers are often crowned to reduce stresses there. Two or more rows of rollers may be Brakes provided for higher radial load capacity. Bearings for limited radial space are made with

rollers whose lengths are much larger than diameters. Such bearings, called as needle bearing have limited load capacity and are often used to support oscillating shafts. The needless, in many cases, are not even separated by cage and are directly placed on the shaft journal eliminating inner ring.

(a) Without Thrust Flange (b) With Thrust Flange

Figum 3.5 : Cylindrical Roller Bearings

In tapered roller bearings the rollers are frusta of cones. These bearings are capable of carrying both radial and axial loads but are largely used where axial load component predominates (Figure 13.6). Since the inner and outer race contact angles are different in this case, there is a force component which drives the tapered rollers against the guide flange which ultimately results into heating due to friction. Therefore, these bearings are not suitable for high speeds. The angle of contact of bearings is chosen according to load; it being large for lager loads. The radial load carrying capacity of the tapered roller bearings may be increased by combining two or four of them, making two row or four row tapered roller bearings. The inner ring of a tapered bearing is known as cone, while outer is termed cup.

(a) (b) Figure 13.6 : (a) Slngle Row Tapered Roller Bearing and (b) Double Row Tapered Roller Bearlng

Spherical roller bearings have rolling elements having curved generatix in the direction transverse to rotation which conforms closely to inner and outer raceways having spherical surfaces (Figure 13.7). The spherical nature of raceways makes these bearings self-aligning. These bearings, though of high load carrying capacity, have inherently larger friction than cylindrical roller bearings because high sliding between the rollers and raceways may occur. They are specially good against heavy loads and are used for rolling mills, paper mills, power transmission and marine applications.

44 Figure 13.7 : Spherical Roller Bearing

1 - -

Thrust roller bearings with cylindrical, tapered cylindrical and spherical rolling elements Rolling Contact Bearing

are also made mainly to bear axial thrust.

13.4 FRICTION IN ROLLING BEARINGS

It is a well known fact that friction due to rolling of non-lubricated surfaces over each other is considerably less than the dry friction encountered by sliding the identical surfaces over each other. Although the motions of the contacting elements in the rolling contact bearings are quite complicated as compared with that of pure rolling, yet the friction in rolling bearing is far less than that in most sliding contact bearings of comparable size and load carrying capacity. Table 13.2 describes the values of coefficients of friction for various types of rolling bearings, referred to bore diameters. These values, however, are to be used for run-in bearings with good lubrication.

Table 13.2 : Coefficients of Friction of Rolling Contact Bearings

Type of Bearing Coefficient of Friction

Single row deep groove ball bearing 0.001 5

Self-aligning ball bearing 0.001 0

Angular contact ball bearing

Single row 0.0020 Double row 0.0024

Thrust ball bearings 0.00 13

Cylindrical roller bearings 0.001 1

Tapered and spherical roller bearings 0.001 8

Needle ball bearings

Thrust ball bearing 0.00 13

Cylindrical and needle roller bearing 0.0050

The sources of friction in rolling bearings are several. The important of these are listed

I below :

(a) Elastic hysteresis in rolling.

I (b) Sliding due to deformation of contacting elements and/or bearing geometry.

! (c) Spinning of rolling elements.

(d) Gyroscopic pivoted motion of a rolling element.

(e) Viscous friction due to lubricant action.

1 (0 Sliding between cage and rolling elements and between cage and rings. t

(g) Seal friction.

Values of coefficients of friction described in Table 13.2 include all these factors except the seal friction. In more advanced calculation total frictional torque, Mfis calculated. The friction torque is composed of two components. One component is due to load and other is due to viscous churning of oil. Before proceeding to calculate the components of friction torque relevant terms need to be defined.

SAQ 1

(a) Describe materials used for rolling contact bearings.

(b) Name different types of rolling contact bearings and describe radial ball bearing.

(c) What are sources of friction in rolling cotit& bearings?

Design of Bearings, Clutches, Brakes and CAD

13.5 BASIC STATIC CAPACITY

Under load all three element$ (the two races and rolling element) will deform. If the load is increased beyond certain limit the deformation in one of the three elements may turn plastic. However, such load that may cause permanent deformation of any of the elements is never placed on the bearing. A load that will cause a permanent deformation of 0.01% of diameter of rolling element at maximum stressed contact rv ion of any element is called basic static capacity. This subject will again be taken up when stress of deformation will be calculated. The bearing manufacturer's catalogue describes basic static capacity as a bearing characteristic.

The magnitude of basic static capacity, C,, for a ball bearing is calculated from following :

wherefo is a constant whose value can be read from Table 13.3.

i is number of rows of balls.

ti is number of balls in a row.

r is the radius of the ball.

a is the angle of contact.

Factorfo is described in Table 13.3.

Table 13.3 : Factorfo for Basic Static Capacity

Bearing Type fo (N, m) Self aligning ball bearing 13.30 x lo6

Radial and angular contact ball bearing 49.04 x lo6

13.6 STATIC EQUIVALENT LOAD

The bearing is required io carry both radial and axial force components and a load which takes care of both the components is known as static equivalent load. If F, and Fa denote respectively radial and axial force components, then the radial static equivalent load, F,, is calculated from

Here X and Yare factors which have been standardised by Antifriction Bearing Manufacturers Association (AFBMA). These factors are described in Table 13.4.

Table 13.4 : Factors X and Y for Rolling Contact Bearings

* If F, is greater than 0.44 F, the values are not accurate.

13.7 FRICTION TORQUE DUE TO LOAD Rolling Contact Bearing

The load on the bearing will induce proportionate frictional force which maybe related to mean diameter. However, both the radial and axial force component will be responsible for frictional force. The effective force to cause friction is denoted by F, and can be calculated from

For ball bearings the higher value from above equations is to be used while for roller bearing only Eq. (13.3) is applicable for F, is invariable zero. Iff; is effective coefficient friction referred to mean diameter of the bearing then the friction moment due to load will be

The effective coefficient of friction is given by the equation,

F, and C, have already been defined as equivalent static force and basic static capacity. The constants Z and y are described in Table 13.5 for ball bearings. Table 13.6 describes the coefficient of friction,f; for other bearings.

Table 13.5 : Values of Z and y for Ball Bearings

Ball Bearing Type Angle of Contact 2 Y

Deep groove 0 0.00 1 8 0.55

Angular contact 30" 0.0020 0.3

Angular contact 40" 0.0026 0.33

Thrust 90" 0.0024 0.33 , Self aligning 1 0" 0.0006 0.40

Table 13.6 : Effective Coefficient of Frictionj;, for Roller Bearings

Roller Bearing Type F1

Cylindrical 0.0005-0.0006

Spherical 0.0008-0.00 10

Taper 0.0008-0.001 0 1

Higher values off; are used with grease while lower value with oil.

13.8 FIUCTIONAL TORQUE DUE TO VISCOUS CHURNING OF LUBRICANT

It has already been stated that rolling contact bearings do not require any lubrication. However, these bearings are hardly run dry. The lubricant is mainly used to keep the bearings cool. Following three types of lubricant applications are in common use.

Mist Lubrication

In this type the fine particles of lubricant obtained by atomising due to splash occurring somewhere else continuously come in contact with the bearing. Naturally in such a case the power loss due to viscosity of lubricant will be less.

Design of Bearings, Clutches, Brakes and CAD

Oil Bath, Grease Lubricatioq

For bearings operating at dm x N < 3 x 1 0-5 mm x rpm a small amount of grease pressed into bearing is a good measure against heating. This grease is also good for absorbing small shocks due to load or speed fluctuations. Alternatively lubricant may be provided in a bath with care that not more than half of the lowest rolling element must pas through the oil. The greater depth of rolling element into the oil may result in waste of power due to viscous splashing. Whether the grease or oil is used, it should be taken care that they remain chemically inert to the bearing and the bearings are sealed fiom the other side. Besides safeguarding against leakage the seals do not allow dust to enter the bearings.

Flooded or Jet Lubrication

For d,,, x N > 3 x lo5 mm x rpm it is always advisable to run bearings flooded with oil which needs continuous re-circulation. Sometimes a jet of oil under pressure may be directed against the bearing. Though such a method will be very effective in keeping the bearing cool, the power lost in oil churning will be much more than that in other two methods.

For calculating friction torque due to oil churning following formulae are used. Denoting this friction torque by M, vis,

2 -

MlVi, = f2 ( v N ) ~ d i N-m . . . (13.7)

However, if v N I 2 x 1 o - ~ (with v in m2/s)

In above equationsfi is a constant that depends upon type of bearing and methcL of lubrication. v is the kinematic viscosity of the lubricant which has been defined

as ratio of absolute viscosity to the density ofoil . The equations are (9) applicable to oils with specific gravity of 0.9 which is close to moct ns; isbricants. The equations are only approximately true for greases.

The total friction torque in a bearing will be the sum of load torque and viscous torque, i.e.

Mg = ML + M1 V,S . . . (13.9)

Table 13.7 describes the values of factorsfi for broad groupings of bearings. However, for SKF bearings the manufacturer recommends values for different series in the SKF General Catalogue.

Table 13.7 : Values of fi for Various Types of Bearings and Lubrication

Type of Bearlng Mist Oil Bath, Grease Flooded or Jet Lubrication Lubrication Lubrication

(lo3) (lo3) (1 03) Deep groove (single row), self- aligning (double row), thrust ball 0.1-1.0 1.5-2.0 3.0-4.0 bearings Filling slot (single row), angular contact (single row) ball bearings 1 .O 2.0 4.0

Angular contact (double row), ball 2.0 2.0 bearings 8.0

Tapered roller (single row), 1.5-2.0 3.0-4.0 6.0-8.0 spherical roller thrust bearings Cylindrical roller (single row) 1.0-1.5 2.0-3.0 4.0-6.0 bearings Spherical roller (double row), tapered roller (double row) 2.0-3.0 4.0-6.0 8.0-12.0 bearings

Example 13.1 Rolling Contact Bearing

An SKF 6208 Z bearing has 9 balls each of 12 mm diameter. The single row beatjng has following dimensions. Outer diameter, Do = 80 mm, inner diameter, Di =I40 mm. If the bearing is required to carry a radial load, F, = 4.5 kN and an axial load of F, = 1.8 kN, calculate static radial equivalent load and static load capacity of the bearing.

Solution

From Table 13.4 for a radial ball bearing of single row

X= 0.6, Y = 0.5

The radial static equivalent load is calculated from Eq. (13.2)

Using Fr = 4500 N and F, = 1800 N in above equation

F, = 0.6 x 4500 + 0.5 x 1800 = 2700 + 900

. . . (i) The basic static capacity of bearing is calculated from Eq. (13.1)

2 C, = fo in r cos a

from Table 13.3 for radial bearing.

Using i = I , n = 9 , r = 6 x 1 0 - ~ m and a = O

In above equation.

= 15889 N . . . (ii) Example 13.2

If the coefficient of friction referred to bore diameter of the bearing in Example 13.1 is 0.001 5, calculate the power lost in friction if the shaft supported in the bearing rotates at 2000 rpm.

Solution

Friction torque,

:. Power loss H = Mu o = 0.135 x 209.5

Example 13.3

A roller bearing having a mean diameter of 65 mm carries a radial load of 4500 N and rotates and 10,000 rpm. Calculate the frictional power loss if bearing is lubricated by an oil bath having a kinematic viscosity of 20 x m2/s. 49

Design of Bearings, Solution Clutches, Brakes and CAD The power loss H = Md w, W , where Mfis the frictional torque given by

Eq. (13.9).

The two components of M f will be calculated by using Eq. (1 3.5) and one of Eqs. (1 3.7) and (13.8).

For roller bearing axial load component is zero.

Hence, from Eq. (13.3)

F, = F, = 4500 N . . . (i)

The factorf; for cylindrical roller bearing from Table 13.6, choosing higher value is 0.0006. . . . (ii) Using F, from Eq. (i),f; from Eq. (ii) and dm = 65 mm in Eq. (13.5).

The friction torque due to load

1 M , = ? j ; Fed* : .'

i.e. M,/ = 0.0003 x 4500 x 65 x

= 0.08775 N-m

For the lubricant

v = 20 x m2/s

. . v N = 2 0 x 1 0 ~

Since, V N > z x

(iii)

the viscous torque will be calculated from Eq. (1 3.7)

From Table 13.7,

(For single row cylindrical roller bearing with oil bath lubrication-higher value has been chosen). 3

Substituting& = 3.0, v =.20 x m2/s, N =+04 rpm, dm = 65 mm in Eq. (13.7)

= 0.2822 N-m . . . (iv)

Using MS. (iii) and (iv) the total frictional torque

SAQ 2

(a) Define basic static capacity and static equivalent load for a rolling contact bearing.

(b) How do you calculate power loss in a roller bearing?

Example 13.4

A deep groove ball bearing has following geometrical properties.

Outer diameter Do = 85 mm, Inner diameter, Di = 45 mm, Diameter of ball, 2r = 12 mm, Number of Balls, n = 10, Number of rows i = 1.

The bearing corresponds to SKF 6209 Z whose static load capacity described by manufacturer is 17860 N.

The bearing supports a radial load of 4500 N and an axial load of 1500 N while the shaft runs at 5000 rpm. The bearing is lubricated by an oil bath with kinematic viscosity of 20 x m2/s. Calculate the static capacity of the bearing and compare with the catalogue value. Also calculate the power lost in friction.

Solution

Use Eq. (1 3.1) to calculate static capacity, C,

2 Cs = fo i n r cos a

a, the angle of contact in deep groove ball bearing is zero, i = 1, n = 10, r = 6 mm, fo = 49.04 x 1 o6 from Table 13.3.

. . Cs = 49.04 x lo6 x 1 x 10 x 36 x = 17654.4 N . . . ( i )

The catalogue figure for C, = 17860 N is 1.2% higher than that calculated from Eq. (13.1).

The static equivalent load on bearing, F, is calculated from Eq. (1 3.2)

Fs = XF, + YF,

i t For radial ball bearing, from Table 13.4

L. X = 0.6, Y = 0.5

. . F, = 0.6 x 4500 + 0.5 x 1500 = 2700 + 750

or F, = 3450 N . . . (ii) The factorf; or coefficient of friction is calculated by using Eq. (13.6)

1 From Table 13.5 for a deep groove ball bearing

Friction torque due to load will be calculated from Eq. (13.5)

. . . (iii)

Rolling Contact Bearing

Design of Bearings, Clutches, Brakes and CAD

F, from Eq. (1 3.3),

F, = 0.9 x 1500 - 0.1 x 4500 = 900 N

F, from Eq. (1 3.4)

F, = 4500 N

Higher value of F,, i.e. 4500 N will be used for calculation of MIL.

= 0.108 N-m . . . (iv)

The kinematic viscosity of oil, v = 20 x m2/s and rpm of the shaft, N = 5000.

which is greater than 2 x

Hence, friction torqua due to viscous flow of oil will be calculated using Eq. (1 3.7)

Usef2 = 2.0 x lo3 from Table 13.7, v N = 10- ', d,, = 0.065 m

= 0.118 N-m . . . (v)

Hence, total friction torque

:. Frictional power loss

H = M , / . ( I . )

= 118.5 W

Eqs. (i) and (vi) are Answers.

Example 13.5

. . . (vi)

A single row cylindrical roller bearing has bore diameter of 100 rnm and outside diameter of 180 mm. Its basic static load capacity is 154 kN. The bearing cames a load of 50 kN while shaft rotates at 500 rpm. Calculate the power loss due to friction and viscous churning of oil if the bearing is lubricated by jet lubrication, with oil whose kinematic viscosity is 15 x m2/s.

Solution

For roller bearing axial load component is zero.

Hence, F, = F, = 50000 N from Eq. (1 3.4)

Also the friction torque due to load is given by Eq. (13.5), i.e.

fi is read from Table 13.6, for cylindrical bearing

1; = 0.0006

Rolling Contact Bearing

= 2.1 N-m . . . (i) From Table 13.7 for single row cylindrical bearing under the conditions ofjet lubrication

f2 = 6.0 x 1 o3 (higher value)

Also vN = 15 x x 5000= 75x

I which is greater than 2 x 1 O-3.

Hence, the frictional torque due to viscous flow, Eq. (1 1.7)

. . H = Power lost'in friction = MN o

= 5 x 523.67 = 2.62 kW.

13.9 HEATING OF ROLLER BEARING

The frictional power loss in rolling contact bearings is similar to that discussed in case of sliding contact bearings. The temperature level in this case depends upon :

(a) bearing load,

(b) ' bearing;, speed,

(c) bearing friction torque,

(d) type of lubricant and its viscosity,

(e) bearing housing, and

(f) environment of operation.

Most rolling element bearing in practice operate at temperature levels that are cool and therefore do not require any special consideration regarding thermal adequacy. Under circumstances such as light load and low speed and placement of bearing assembly under stream of air the bearing temperature will not rise. External cooling in many cases of bearing applications may sufficiently keep the bearing cool, although there are examples in which it is not possible to keep the temperature within limits unless detailed analysis of rise of temperature due to each of the reasons stated above is performed and specific measyres taken.

The heat from the rolling bearings is removed through all the three modes of heat transfer, vis. conduction, convention and radiation.

Design of Bearings, In cooling of bearing generally, two types of problem arise. In one case the bearing itself Clutches, Brakes is the source of heat, the external cooling by means of air flow over the housing may be and CAD sufficient to keep the bearing temperature low. For greater rate of heat removal the

surface of bearing housing may be enlarged by providing fins. In other case, the heating of bearing is due to heat source somewhere in the machine. The bearing is cooled by the lubricant in such a situation. The lubricant then has to be cooled in an external heat exchanger or in the sump.

13.10 ROLLING BEARING GE'OMETRY

Before the load carrying capacity and stresses in various bearing elements could be considered, it is essential to understand various geometrical configurations in rolling bearing. Here the various terms will be described for a ball bearing only. Similar terms could, of course, be described for other beaings.

Figure 13.8 illustrates a ball bearing in its simplest form. The mean diameter dm, is average of the inner diameter and outer diameter of the bearing. However, more precisely, mean diameter is the average of inner and outer ring raceway contact diameters, i.e.

Figure 13.8 : Diametral Clearance in a Ball Bearlng

When a bearing is assembled, the rolling elements and raceways could have some clearance between them, as is shown in Figure 13.8. This would be conducive to deformation that would occur in all bearing elements because of the loading of the bearing. The diametral or radial clearance is defined as,

where D is the diameter of rolling element or ball. These clearances vary with bore diameter and bearing tolerances, and have been standardised.

The ratio of diameter of rolling element to that of the raceway in a direction transverse to the direction of rolling is defined as osculation, i.e.

The ratio would be denoted as e, so that D

As it has been shown in Figure 13.8, the radii of inner and outer races are respectively ri Rolling Contact Bearing

and ro the osculation may be unequal for inner and outer contacts. Because of radial clearance a ball bearing will experience an axial play in no load condition. Figure 13.9 shows the inner and outer races pushed to one extreme axial position whereby no end-play is remaining, and the ball-raceway contact assumes an oblique angle. This may be compared with angular contact bearings (Figure 13.4), which are made to have such angular position of contact line to bear the axial load. It can be seen from the Figure 13.9 that the distance between the centers of curvature of the inner and outer raceway is

and since r = eD or ro = eo D and q = ei D

The quantity (eo + ei - 1) is defined as total curvature of the bearing. Again from

Figure 13.9 angle a is defined as the free contact angle and it is easy to see that

In no load condition the two rings will be able to slide relative to each other axially as I shown in Figure 13.9 in one extreme position. The axial displacement between the

centers of curvatures of inner and outer raceway in this position is half of the total permissible play C,.

1 Thus, C, = 2A sin a . . . (13.17)

Figure 13.9 : Inner and m t e r Races Shown Displaced to Axial Extremes

Figure 13.10 demonstrates schematically the contact between two bodies of revolution. It may be noted that while the bodies have point contact, each one of them has two radii in two principal planes. It is shown that body I has a radius rl,, in plane 1 and r / ~ in plane 2 and similarly body II has radii of curvature rill and rln in planes 1 and 2, respectively. A contact between a rolling element and one of the raceways is similar to the situation illustrated here. In case of a ball bearing, the ball will have only one radius of curvature in both planes. If r denotes the radius and p, the curvature then for condition described in Figure 13.10, curvature sum is defined as

and curvature difference, F (p) is defined as

Design of Bearings, Ctutches, Brakes and CAD

Figure 13.10 : Two Bodies of Revolution Incontad

It is easy to see that for a ball inner raceway contact

D rll =- -

2 - r12

rll, = - d i 2 I =- 2 1 ( A - ~ ) , r l 1 2 = e i ~ cos a

2 PI1 = - = PI2 D

l

I

2

Similarly for the ball-outer raceway contact

where

and

, 13.1 1 STRESS AND DEFORMATION IN ROLLING I

ELEMENT

Rolling Contact Bearing

The total load carried by a bearing is shared by a few rolling elements at a time. As an element rolls round the raceway, the load upon it keeps changing from a maximum to zero and then to maximum. It is obviously seen that the load will be compressive in nature. In addition, an element may also be subjected to dynamic load due to its complex motion, e.g. centrihgal force. Analysis of dynamic loads would be too complex to present here.

Strieback calculated maximum compressive load on a ball, during a load cycle. According to his solution, in a ball bearing containing n number of balls and supporting a radial load F,., the maximum load on a ball wo.uId be

5 Fr Pmax = - n cos a

Hertz contact theory provides a solution for contact stresses between the two bodies of revolution. It has been amply clarified in literature on elasticity that in such events of contact the ideal point or line contact does not exist under load. Thus, in case of both ball-inner raceway and ball-outer raceway contacts the region of contact assumes an elliptic shape as illustrated in Figure 13: 1 1. It was explained in Section 13.2.3 that the roller edges are crowned to reduce the stress concentration. Due to this crowning of edges the roller-raceway contact area assumes a shape illustrated in Figure 13.11(c) instead of rectangular shape of Figure 13.1 I (b).

(a) The Elliptic Area of Contact between a Ball and a Raceway

(b) Rectangular Area of Contact between a Roller Raceway

(c) Modified Rectangular-elliptic Area of Contact between Roller and Raceway

Figure 13.11

Design of Bearings, For such cases in which contact area assumes an ellivtic shave with a and b as 1 Clutches, Brakes and CAD

semi-major and semi-minor axes., respectively, the compressive contact stress has been calculated as,

where P is the load acting upon the bodies in contact measured in N as depicted in Figure 13.1 1, and a and b are given as follows :

Above equations have been calculated for steel ball and ring combination for which following constants were assumed :

Modulus of elasticity, E = 2.0 x lo5 MPa

Poisson's ratio, v = 0.3

The values of at and b, have been calculated as functions of F (p), and described in Table 13.8.

The contact deformation has also been determined and for steel ball and ring combination it is given as,

The factor 6, is also a function F (p) and is described in Table 13.8 along with a , and 6,.

Table 13.8 : Factors a,, bl and 61

For a roller and a raceway contact the maximum contact stress is given by Rolling Contact Bearing

where I is the roller length and b is the width of the contact region in mm [Figure 13.1 l(c)]. The factor b has been determined for steel roller ring combination as,

The contact deformation for steel roller and ring is given as

The experimental observations of ball-racewaya combination have revealed that the fatigue failure, which is major cause of bearing failure, initiates below the surface. This i

I may be expected since the surface stresses of high magnitude as presented in this section are of compression type which are not responsible for crack initiation and propagation. On the other hand, it has been confirmed by microscopic examinations that sub-surface shear stresses initiate failure, and as such only shearing stresses are important for design of rolling contact bearings. The mathematical analysis for determination of these stresses is highly complex. It would suffice to give their magnitudes and natures of variation. Two shearing stress components normally maximum shearing stress and orthogonal shearing stress have been calculated. It is however, not very clear as to which of these two shearing stresses is responsible for the fatigue failure, although microscopic observations favour the maximum shearing stress as the cause of failure. Figure 13.12 describes the variation of maximum shearing stress (T,,,) occurring at a depth of h below the point of contact while variation of orthogonal shearing stress (ro) at a depth of k from point of contact is shown in Figure 13.13.

h b and - as Functions of - Figure 13.12 : -

amax, b a

k b 2'0 and - with - Figure 13.13 : Variation of -

Omax b a

Design of Bearings, The depth at which maximum shearing stress occurs gives an idea of the case depth in Clutches, Brakes surface hardened rolling elements of a bearing, naturally the depth of hardened layer in and CAD such cases must be more than the greater of the depth of maximum or orthogonal

shearing stress calculated in above manner.

13.12 BEARING DEFLECTION

In very crude sense only, bearing may be treated as rigid. But truly speaking, in most service conditions, the determination of deflection of bearing becomes very important. In modem machines like aircraft gas turbines, machines tools, inertial gyroscopes, radiotelescopes, etc. the accuracy of operation requires that the bearing deflections be minimised to least and hence their knowledge is a prerequisite of design. The analyses of bearing deflections and those of bearing-shaft-housing system are highly complex. For moderate loads and speeds Palmgren has suggested certain formulae which are described in Table 13.9. These formulae may be used only in cases where extreme accuracy is not essential.

The proper clearance and deflection of non-rigid housing will have to be added to the values obtained from Table 13.9 to obtain the real bearing deflection. Unlike several machine members, the deflectim is a-non-linear function of load. however, deflection of a roller bearing is approximately a linear-function of the loads as 0.9 is very close to 1 .O.

Table 13.9 : Rolling Contact Bearing Deflections

Type of Bearing Radial Deflection (mm) Axial Deflection (mm) under Radial Load (N) under Axial Load (N)

Deep groove ball bearing - 2 - 2 3 3

4.3 x cos a 4.3 x 5 sin a 1 - 1 -

D3 D3

Self-aligning ball bearing - 2 - 2 3 3

4 Pmax sin a cos a 6.9 x 10- - 6 . 9 ~ 1 0 - - 1 - 1 -

D 3 D 3

Thrust ball bearing - 2 3

- 5.2 x sin a 1 -

D3

Roller bearing (line 0.9 0.9 -5 Pmax sins 5 P m a x c o s a 7 . 5 ~ 1 0 - contact at each raceway) 7.5 x 10- -

(I)O.~ (1)Or8

(P,,,,, in N, D and 1 in mm).

One of the methods to reduce the bearing deflection (in particular axial deflection) is to preload the bearings in axial direction so as to create an axial thrust on shaft. When the shaft rotates the load thrust acts against the preload axial thrust whereby some preload deformation is relaxed and then the deformation under load occurs. The effect is similar to the improvement of fatigue behaviour due to residual stress. Figure 13.14 shows how two angular contact ball bearings are used in preloaded condition. A shim between the two bearings is often used as an alternative to sleeve.

Bearings are also preloaded in radial direction, but the purpose of radial preloading is not to eliminate initial large magnitude of deflection. It is done with an aim to bring greater number of rolling elements under load whereby maximum load on a single element is reduced. This in effect will reduce the external bearing deflection. Figure 13.15 shows one method of radialpreloading in which the bore of the bearing and shaft journal have matching taper. In several cases the taper on journal may be eliminated by providing a taper sleeve between bearing and journal.

k Housing 4 Rolling Contact Bearing

! Figure 13.14 : Preloaded Set of Bearings

Figure 13.15 : Radial Preloading of a Roller Bearing

13.13 PERMANENT DEFORMATION IN BEARINGS

Any material, if loaded beyond certain limit stress, would suffer from a permanent or residual deformation. This limit stress is often used to characterise the material (like yield strength). Similarly, if a ball or roller is passed against a raceway at some limit load an indentation or permanent deformation may remain in the rolling element and raceway. The basic static capacity of a bearing has already been defined as a bearing characteristic in Section 13.4.1. The permanent deformation in the bearing could result in stress concentration and excessive vibration leading to eventual failure.

Some plastic or permanent deformation of all loaded surfaces would occur immediately after loading but this would in effect, serve to smoothen the surfaces by removing the irregularities that were left after machining operations.

Palmgren has developed the formulae for residual deformation for ball and roller bearings of steels having hardness between 63.5 and 65.5 RC. These formulae are, however, applicable in close vicinity of compressive yield strength when yielded zone would be very small. Denoting permanent deformation by 6,, Plamgren established that for ball bearing,

and for a roller bearing with line contact between roller and raceway.

y was defined in Eq. (1 3.20), D denotes the diameter of ball or roller and 1 is the length of the roller. It is also assumed that ri = r,-, = r. In above equations upper signs refer to the inner raceway contact while 'lower sign refers to outer raceway contact.

Design of Bearings, Eq. (1 3.25) is modified to take into consideration the number of rows of rolling Clutches, Brakes elements, i. Thus, the equation becomes, and CAD

The basic static capacity, which was defined in Section 13.4.1 as the load that would cause a permanent deformation of 0.001 D is substituted for F, in Eq. (1 3.35) to yield

Cs = 0.2 in P cos a 7" . . . (1 3.36) I

6 s - Divide Eq. (1 3.33)'by Dl substitute - - 1 o - ~ and rearrange the terms D

Use Eq. (13.38) in Eq. (1 3.37), so that

It can be seen that Eq. (13.38) is a same Eq. (13.1) andfo can be calculated.

Eq. (1 3.38) provides a method of calculating basic static capacity of a deep groove ball bearing when its geometry is fully known. Similar equations for other bearings may be derived. It may be noted that the Eq. (1 3.38) and any other which could be derived similarly is applicable to rolling element raceway combination whose surface hardness is between 63.5 and 65.5 RC. Any deviation from this hardness range would require C, to be corrected. SKF ball bearing company has suggested a correction factor for hardness. For elements having a different hardness, the corrected basic static capacity would be

where q, is a conection factor. correlated with hardness as,

where HV is the hardness in Vickers units, and ql is SKF constant described in Table 13.10.

Tmble 13.10 : Values of 11,

Ball on plane (Self-aligning ball bearing)

Ball on groove (Deep groove ball bearing)

Roller on roller (Radial roller bearing)

Roller on plane (Thrust bearing)

The static capacity described above is much less than the static fracture load of the bearing elements. It is generally regarded that the fracture load would be greater than 8 C,.

Permanent deformation resulting into a single indentation in the ring or depression in the rolling element will highly impdr the bearing operation. However, if the load exceeds C, over several revolutions then the whole surface of the rolling elements would be

uniformly deformed and this situation would not be very much harmhl. Still it is I

1 customary to apply a factor of safety on the basic static capacity of a bearing, so as to avoid any permanent deformation. In Section 13.4, static equivalent load, F, was defined

I

t by Eq. (1 3.6). The factor of safety, n', is defined as

I

r cs n =- -

For different types of services, the factor n' must exceed certain minimum as described by Table 13.1 1 .

k Table 13.11 : Factors of Safety

Rolling Contact

Type of Service Minimum n'

Smooth shock free operation 0.5

Ordinary service 1 .O

Sudden shocks and high requirements for smooth running 2.0

b Basic static load rating is often used by the manufacturers to characteris'e the bearing and I is a means for bearing selection. However, for very 1 bearings or those used in instruments, this criterion

small bearings such as a needle is difficult to apply because the

quantity 0.01% of D becomes extremely small. For such bearings the load for fracture . with a factor of safety is used for selection.

Example 13.6

If for the SKF 6208 Z bearing which has a balls placed in a single row, each of diameter 12 mm the inner and outer raceway diameters are di = 47.998 m, and do = 72.0019 mm, respectively and groove radii are r, = ro = 6.25 mm calculate the static load capacity. The outer and bore diameter of bearing are Do = 80 mm, Dl = 40 mm. The radial load F, = 45 kN and gxial,load, F, = 1.8 kN. Assume ball hardness is 65 RC. Calculate the factors of safety.

Solution.

(This problem is same as Example 13.1 with additional data about the raceways Example 13.1 was solved using Eq. (1 3.5) and C, = 15889 N was obtained).

Use do = 72.001Vinm, di = 47.98 mm and D - 12.00 mm in Eq. (13.1 1) to obtain q '$

radial clearance 3 3

C = 72.0019 - 47.998 - 2 x 12 = 0.0038 mm

From Eq. (1 3.14)

From Eq. (13.16)

= cos-' 0.9962

or a = 4.9965'

Use Eq. (13.20) to calculate y

D c o s a 1 2 ~ 0 . 9 9 6 ~ 2 Y = - -

dm (72.0019 + 47.98)

Design of Bearings, Cluteba, Brakes and CAD

Since dm = do + dl 2

. . y = 0.1992 . . . (i) From Eq. (13.38) the static capacity of the bearing

I

wherei= 1 , n = 9 , D = 12 mm,r=6.25 mm, y =0.1992

= 3665.088 x 4.474 x 0.9962 = 16336.64 N . . . (ii) While using Eq. (13.38) negative sign before y has been taken so that lower value of Cs will be obtained. Apparently value of Cs at Eq. (ii) is 3.2% higher than that obtained in Example 13.1.

The radial static equivalent load Fs is calculated from Eq. (13.6) and using Table 13.6. The value was obtained as

F, = 3600 N in Example 13.1

Factor of safety from Eq. (1 3.4 1 )

. . . (iii)

From Table 13.1 1 it can be seen that this factor of safety is high even' for shock loading.

Eqs. (ii) and (iii) are the Answers.

SAQ 3

(a) How a rolling contact bearing kept cool in practice?

'(b) Describe geometry of rolling bearing by a sketch.

(c) Write expression for stress in a ball of ball bearing and in a roller of roller bearing under a load P.

(d) Show by sketch how are the bearings on shaft preloaded axially and radially.

13.14 FATIGUE OF ROLLING BEARING

Fatigue is a very important consideration in designs of rolling contact bearing. The life of a bearing is generally described in number of revolution it can make before failure. - - Bearing manufacturers generally describe the life of a bearing in number of hours. The bearing life would be governed by the life of the weakest of its elements. From Section 13.8 it can be seen that inner raceway contact is stressed to higher stress level than outer. Therefore, failure of inner race way contact is a general trend. In case ofball

, bearings, since the ball is free to spin, it is not subjected to maximum stress at the same Rolling Contact Bearing

I point and consequently it is the inner raceway that fails frequently. In case of roller bearing also chance of failure of roller are less than that of inner raceway because the

t raceway undergoes more number of cycles of load than roller in one revolution.

It was pointed out that some steels of strain ageing type posses definite fatigue limit below which they can undergo infinite number of load cycles. But the steels used for bearings do not have such limits. These steels have some finite life at each stress level, though this life could be much larger. The bearing failures due to several reasons, like inadequate lubrication, misalignment, ingress of abrasive and attack of corrosive atmosphere may be successfully avoided if proper care is taken during design stage and operation. Nevertheless, the bearing failure would eventually take place possibly after several million revolutions.

The fatigue in bearing element takes place due to variation of contact stress which in effect are shearing stresses. The surface cracks are first generated into which the lubricating oil may enter. When surface is conipressed the pressure of such ingressed oil will break open the surface crack creating a pit. The bearing elements (particularly inner raceway) have been found to develop pits. The details of pits found in bearing inner raceway are illustrated in Figure 13.16. Undoubtedly the fatigue cracks appearing on the surface of bearing element originate from the points of maximum or orthogonal shearing stress. The crack initiation can be delayed by improving strength at depth where these

I stresses are highest. This can be achieved by case hardening treatment. It is of interest to ! note that pitting is a common phenomenon in gear failure and it was shown that gear

i teeth surfaces are under contact stresses.

A B C D E F G xxx i V

Figure 13.16 : Typical Fatigue Pit in Bearing Element (a) Along the Rolling Direction, and (b) Transverse to Rolling

The statistical nature of fatigue was highlighted in unit on fatigue.

This presents an impossibility to assign a single life to a bearing at a given load. If a population of identical bearings is tested in fatigue under identical conditions the bearings would fail at all the number of cycles. If any bearing surviving N, cycles is regarded to have survived prescribed number of cycles, then those which fail before reaching Ns cycles are failures. If out of m number in given population of bearings, m, number of bearings has survived, then probability of survival, P,,, is defined as,

And probability of failure is

Design of Clutches, and CAD

Bearings, The bearing life is plotted as function of the probability of survival in Figure 13.17. A Brakes life Nlo corresponds to 90%prs or 1 0 % ~ ~ . The bearing manufactures generally use either

Nlo or N50 as "rating life" to characteristics their bearings. Weibull has shown that thep, and N,, the two variables of Figure 13.9 are related through,

prs = exp. (- K N:) . . . (13.44)

Here K and q are the constants of bearing under given operating conditions. Experiments have shown that Eq. (13.44) fits well into observations for 0.07 Ip, 50.93, i.e. between N7 and Ng3 whereas region of interest for most bearings is between Nlo'and NbO. Weibull has further determined that q assumes a value of 1.1 11 for ball bearings and a value of 1.125 for roller bearings.

Robabillty of survival, Pr,

Figure 13.17 : Bearing Life as a Function of Probability of Sunrival

It will be quite logical to assume that

1 In - = f (z, N, z ) . . . (13.45)

Prs

where T is shearing stress at depth z and N is the life of the bearing in million cycles. Lundberg has expressed relationship between Nand D as

where indices t and t' are yet undermined, A I is a material constant and 4, is the function of bearing geometry. P is the load on bearing element that would fail after N million cycles. The load to cause failure after N = 1 million cycle is defined as dynamic capacity

39 3 1 of bearing element. Thus, by replacing N = 1 ' by 1 and P by Cd the dynamic capacity in Eq. (13.46),

substituting C'd from Eq. (13.47) in Eq. (13.46)

t - has been determined for ball and roller bearing respectively as 3 and 4. Detailed 39 analysis has been performed and values of constants in Eq. (13.47) determined. Thus, for ball bearings with point contact

I For roller bearings and for bearing with line contact

The geometric characteristics of the bearing have already been defined. The upper signs are used for inner raceway while lower signs for outer raceway. The hardness of material must lie between 61.7 and 64.5 RC. Apparently dynamic capacity of the inner raceway

I will be lower and hence it would decide the life of bearing.

t This must be understood here that definition of Cd is related to the single element and

1 what will be desired is the dynamic load capacity of the whole bearing. Call this capacity as Cd. The situation is similar to that existed for Eq. (13.25) in which P,,, was load on 1 one rolling element whereas F, was the radial load on the whole bearing. Therefore, Eq. (1 3.25) can be used to correlate Cd and Cd.

n cos a Thus. Cd = Ci -

5

Example 13.7

A heavy duty bearing required to cany a radial load of 19 kN has following dimensions

Do=215, D i = lO0,ri=ro= 18.161, D=34.925,di= 122.556, do = 192.434 (all in mm), n = 8

Calculate basic static capacity and dynamic capacity of the bearing.

Solution

Use do = 192.434 mm, di = 122.556 mm and D = 34.925 mm in Eq. (13.1 1) to obtain radial clearance

C = 192.434 - 122.556 x 34.925 = 0.028 mm

From Eq. (1 3.14)

A = r o + r i - D

= 2 x 18.161 - 34.925 = 1.397 mm

From Eq. (13.16)

a = cos-I (1 - &) 0.028

= c o s (1 - ) = c o s (0.99) 2 x 1.397

or a = 8.12"

Use Eq. (1 3.20) to calculate y

v = D cos a

d m = 92'434 + 22'556

= 157.495 [Eq. (1 3.1 O)] 2

34.925 x 0.99 Y = = 0.22

157.495

Design of Bearings, Clutches, Brakes and CAD

U s e i = l , n = 8 , D = 3 4 . 9 2 5 m m , r = 18.161 mm,y=0.22inEq.(13.39)to calculate basic capacity.

= 2.828 x 8 x (34.9251~ 2 x 18.161 (1 - 0.22) 5 2 x 18.161 - 34.925

1' cos a

= 123027.6 N . . . (i) Use Eq. (13.49) to calculate dynamic capacity of one rolling element

= 47515.4 N

Use n = 8, cos a = 0.99 Cn from (ii) in Eq. (1 3.5 1)

n cos a C, = ci -= 475 15.4 8 x 0.99 5 5

. . . (ii)

In Eq. (13.49) upper sign between 1 and y relates to inner raceway. Apparently if lower sign (which relates to outer raceway) is used the magnitude of Cd will be higher. Hence, the dynamic capacity of bearing will be taken as 75264.4 N.

(i) and (ii) are the Answers.

Example 13.8

A certain ball bearing is characaterised as N l o = 10' revolutions. It is desired that the bearing should have 95% reliability. What life may be expected for this reliability?

Solution

Reliability is often used an alternative to probability of survival. Thus, Nlo = I 08, p, = 0.9. The problem is what will be NS forp, = 0.95. From Eq. (13.44)

. . . (i)

q = 1.1 1 1, substitutep, = 0.9, N, = 10' in (i)

Rolling Contact Bearing

or In K = - 2.25 - 20.465 = - 22.175

or K = 1.365 x lo-''

Now substitutep, = 0.95, q = 1 .l11 and K from (ii)

N5 = 0.523 x 10' . . . (iii)

13.15 SELECTION OF BEARING

The analyses of stresses and deflections of rolling element given so far by no means are complete and conclusive. It is expected that by this time the reader must have realised that rolling contact bearings are subjected to a vei;f large number of applications of contact stresses and varying deformations. Such analyses are useful for designers of bearings. The design of rolling contact bearing has become a specialised branch whereas a general designer has to choose a bearing for his design of a machine from available stock and line of manufacturer. The bearing manufacturers publish data about their products and also suggest methods for selection of bearings for any desired purpose. These methods of selection may differ in detail from manufacturer to manufacturer, yet the general approash remains same.

Bearing ratings are described in terms of either the radial or thrust load for a specified number of hours of life, based upon certain inner race rpm. All the bearing manufacturers do not seem to be agreeable for a particular standard for hours of life or for inner race rpm. Some base the life of a bearing in number of hours at an arbitrary rpm (e.g. a bearing will have a life of 300 hours at 500 rpm) while other fix the life at some level and specify the load rating at various speeds. For example, SKF bearing catalogue describes that life of a bearing will be 100 hours at 200 rpm when bearing loading ratio will be 1.05, while if loading ratio is 1.03 then life will be 200,000 hours at same rpm. The loading ratio in this case is the bearing index and is defined as the ratio of dynamic load capacity to radial bearing load.

Another point of disagreement among the manufacturers is the life expectancy of probability of survival. Some base the lives of their bearings on 10% survival probability while others base on 50% probability of survival, (Nlo and NSo in Figure 13.17). There are other manufacturers who use other probabilities of survival but majority of them lies between Nlo and NSo. SKF bearings are designated to have N10 life and it may be calculated from Eq. (13.48). With slight difference Eq. (13.48) is written again as

and

3

N = (%) for ball bearings

N = (s$ for roller bearings

[%) is defined as bearing loading ratio.

The procedure of bearing selection described here is based upon recommendations made in SKF catalogue No. 2000 EIII and the tables of bearing are also from SKF (India) manufacture range. The bearing manufacturers prodide the students with the bearing catalogue on request.

Design of Bearings, Clutches, Brakes and CAD

Gear Accuracy d Gear Service k Error in pitch and form less Shock free rotary

1.05-1.1 1-1.2 than 0.025 mm machines

Reciprocating 1.2-1.5 machines

Error in pitch and form Machines subjected to .5-3.0 1.1-1.3 between 0.025 to 0.125 mm heavy shock loads

Type of Belt f V-belt 2-2.5

Single leather belts with jockey pulleys 2.5-3.0

Single leather belts, rubber belts, balata belts 4-5

Rolling Contact Bearing

roller

Bearing Type Fa (SKF Bearing) - 5 e

Fr X Y

Deep groove ball bearing Series EL, R, 60,62, 63, 64, RLS, RMS, EE

- Fa = 0.025 1 0

cs I

= 0.04 = 0.07 = 0.13 = 0.25 = 0.50

Angular contact ball 1 0 bearings series 72 B, 73 B Self-aligning ball bearings

135, 126 I 1.8 127,108 1 1.8

Spherical roller 23024 C-23068 CA 1 2.9 24024 C-24080 CA 1 2.3 24122 C-24128 C ! 1.9 241 30 C-24172 CA 1 1.8 24176 CA-24192 CA 1 1.9 22205 C-22207 C 1 2.1

Taper roller 30203-30204 1 0 05-08 1 0 32206-32208 1 0

Table 13.14 : Factors X

bearing without a guiding flange or lip would not be able to carry any axial thrust (Table 13.1 and Section 13.2.3). SKF recommended that choosing of a roller bearing to carry axial thrust must be referred to them.

Thrust ball bearings cannot carry any radial load (Table 13. I) and they are also not included in Table 13.14. Spherical roller thrust bearings can carry radial loads to a maximum extent of 55% of the simultaneously acting thrust load. For such a bearing the equivalent thrust load is obtained from

P=F ,+1 .2F r . . . (13.56)

13.18 BEARING LIFE

The basic dynamic capacity C d , of a bearing has been defined as constant load on bearing that will result in bearing lye of I million revolutions (Section 13.1). The information on load carrying capacity in SKF catalogue is based upon life attained or exceeded by 90% of the bearings (Nlo life). This is called the nominal life and for majority of bearings actual life is much longer than nominal. The life in working hours may be calculated from

L,, = N x lo6

. . . (13.57) 60 x ( I P ~ )

where N is life in number of millions of cycles given by Eqs. (13.52) and (13.53). To choose a bearing one would first be required to fix the life of the bearing that would be expected when bearing is placed in the machine. This life is a function of type of

and Y

Cylindrical roller bearings are not included in Table 13.1 4. Generally a cylindrical

e

0.22

0.24 0.27 0.3 1 0.37 0.44

1.14

0.34 0.34

0.23 0.29 0.35 0.37 0.35 0.32

0.34 0.37 0.37

Fa > e - Fr

X

0.56

0.35

0.65 0.65

0.67 0.67 0.67 0.67 0.67 0.67

0.4 0.4 0.4

Y

2

1.8 1.6 1.4 1.2

1

0.57

2.80 2.80

4.4 3.5 2.9 2.7 2.9 3.1

1.75 1.6 1.6

Design of Bearings, Clutches, Brakes and CAD

machine and its service. Table 13.15 gives the indication of life for bearings with respect to the machines and service. This table has been adopted from SKF Catalogue No. 189.

Table 13.15 : Expected Bearing Life in Working Hours

S1. No. Class of Machines Lh (Hours) I I

Instruments and apparatus that are used only seldom : demonstration apparatus; mechanisms for sliding door.

Aircraft engines.

, Machines used for short periods or intermittently and whose breakdown would not have serious consequences; hand tools; lifting tackles; hand operated machines; agricultural machines; cranes in erecting shops; domestic machines.

Machines working intermittently and whose breakdown would have serious consequences : Auxiliary machinery in power stations; conveyor plant for flow production, lifts; cranes for piece goods; machine tools used infrequently.

Machines for use eight hours per day and not fully utilized : stationary electric motors, general purpose gear units. 1 12,000-20.000 1

- - - -

6. Machines for use eight hours per day and filly utilised. 20,000-30,000 I I

Machines for engineering industry generally, cranes for bulk goods; ventilating fans; counter shafts.

1 20,000-30,000 1 Machines for continuous use 24 hours per day. Separators; compressors; pumps; mine hoists; stationary electric machines; machines in continuous operation on board naval vessels.

Machines required to work with a high degree of reliability 24 hours per day : Pulp and paper making machinery; public power plants; mine pumps; water works; machines in continuous operation on board merchant ships.

13.19 EQUIVALENT LOAD

Under actual operations the load on the bearing may not be constant through entire period. For example, loads F , , F2, etc. may act on bearing N 1 , N2 number of cycles. An effective load F,, can be calculated which acting for N,, number of cycles will have same effect as the loads F , , F2, etc. acting for N I , N2, etc. number of cycles. The equivalent load is calculated from

13.20 BEARING DIMENSION CODE

In design practice it is very common to refer to a bearing by a four digit number like SKF 621 or SKF 0205. The bearing is described by following dimensions :

(a) the bore or inner diameter, d,

(b) the outside diameber, D,

(c) the width, B, and

(d) the comer radius, r

The AFBMA recommends a four digit code for bearing. The last two digits represent a number which is one fifth of the bore diameter of the bearing in mm for this number being 04 or greater. Thus, for a 0205 bearing the inner diameter is 25 mm. It may be understood that the bearing may have different outside diameters and widths for the same inside diameter. The first digit in the code represents the relative with while the second digit represents the relative outside diameter. Seven widths in increasing order are represented by digits 0, 1, 2, 3,4, 5 and 6. Seven outside diameters in increasing order are represented by digits 8,9,0, 1,2,3, and 4. Figure 13.18 shows the dimensions codes for a bore of 75 mm. The first two digits in the figure are only indicative of increasing width and outside diameters.

Figure 13.18 : AFBMA Bearing Number Code Illustrated for Ball Bearings of Bore of 75 mm

IS0 has modified the scheme of dimension. Outside diameter is designated by a number series 7,8,9,0, l , 2 , 3 and 4 (in order of ascending diameter) for a standard bore size. Within each diameter series different widths are designated by number series 8,0, 1,2,3, 4 ,5 ,6 and 7 (in order of increasing width). Most manufacturers have now started designating their bearings according to IS0 dimension plan.

Example 13.8

An SKF 6205 ball bearing has dynamic capacity Cd = 10.8 kN. This bearing is used to support a shaft which rotates at 300 rpm and cames a radial load F, = 3600 N and an axial load of F, = 1500 N. Calculate the expected life of bearing in hours. Static capacity of bearing C, = 6.95 kN. Assume rotating inner race.

Solution

The equivalent load on bearings is calculated by using Eq. (13.2).

P = X F r + Y F a

Fa Factors X and Yare read from Table 13.14. First the ratio - has to be checked F,

(I- 1500 - 0.4167 Fr 3600

Fa It is seen from Table 13.14 that 7 is between 0.13 and 0.25. Even for first value

of 0.13, e = 0.3 1 and thus 2~ for the bearing is greater than e. Hence, X and Y will F,

be selected from second column of Table 13.14. Thus, X = 0.56, but Y will have to be interpolated between 1.4 and 1.2. To be on the safer side the higher value of Y = 1.4 can be chosen. Now using Eq. (13.6)

Rolling Contact Bearill

Design o l Bearings, Clutches, Brakes and CAD =2016+2100=4116N

Now use Eq. (13.52) to calcdlate number of revolution in millions to failure

3 N = ( = (-1 = 18.065 million revolutions

The expected life in number of hours from Eq. (13.57)

N x lo6 18.065 x lo6 L , =

- - 60 x (rpm) 60 x 300

Example 13.9

A belt driven shaft can have journal diameter d such that 25 I d I 30 mm. The radial load, F, = 4000 N while axial, load, F, = 1000 N . The bearing is required to last for 1500 hours at 350 rpm. Check if any of the following bearing is suitable.

Bearing Bore, d cs c d

SKF 6305 25 mm 11.4 kN 17.3 kN

SKF 6406 30 mm 29.85 kN 33.5 kN

Solution

(a) Check for the bearing 6305 whose d = 25 mm

Fu Fa - lies between 0.07 and 0.13 for which corresponding - values are 0.27 cs F,

Fa and 0.3 1 in Table 13.14. Hence, - < e so that X and Y values will be Fr

selected from first column.

X=1.0, Y=O

Hence, equivalent bearing load from Eq. (1 3.6)

P = F r = 4 0 0 0 N

The effective load on bearing in a belt drive is calculated fiom Eq. (13.55)

p e , = f x P

The factor f is chosen from Table 13.13. Assuming V-belt

f = 2

. . P,, = 2 x 4000 = 8000 N

Using above value for P and Cd = 17300 N from given table, in Eq. (13.53) the expected life of bearing in million revolutions

3

= 10.1 13 million revolutions

The expected life in number of hours, Eq. (13.57)

or L,, = 48 1.57 hours

The life in number of hours is much less than the desired life of 1500 hours. Hence, bearing 6305 is not suitable. . . . (i)

(b) Check for the bearing 6406 whose d = 30 mm

5- --- loo0 - 0.25 F,. 4000

Fa From Table 13.14, - lies between 0.25 and 0.04 and corresponding e cs

Fa values are 0.22 and 0.24 so that - > e and hence Xand Y values will be Fr

selected from second column in Table 13.14.

Fa - Fa - By interpolation between - - 0.025 and - - 0.04 cs c.7

. . = 2 x 4 128 (taking f = 2 as in first case)

= 8256 N

From Eq. (1 3.52) with Cd = 33500 N

N = (~~~~~ - = 66.81 million cycles.

Hence, from Eq. (1 3.57), expected life in hours.

L, = 66.81 x lo6

= 3181.4 hours 60 x 350

This is greater than required life of 1500 hours. Hence, the bearing 6406 is suitable,

d = 3 0 m m . , . (ii) (i) and (ii) are Answers.

Example 13.10

It is required to select bearings for the pinion shaft of a gear drive shown in Figure 13.19. Strength calculation of shaft resulted in journal diameter, on left hand side of the shaft of 28.5 mm and shoulder filled radius of 2.0 mm. The load calculation due to power transmission result in a radjal load of 2000 N on the

Rolling Contact Bearing

Design of Bearings, Clutches, Brakes and CAD

bearing. There is dead axial load of 750 N on the shaft. The shaft rotates at 1000 rpm. Select the bearing for LHS journal and comment if same could be used for RHS journal also. The drive is running a pump.

Figure 13.19 : Pinion Shaft

Solution

The effective load is calculated by using Eq. (13.54). Assuming that gear is precision finished so that error in pitch and form is less than 0.025 mm, factorsfk andfJ are read from Table 1 3.12 as

For reciprocating pump.

It must be noted that drive correction factor has been applied on the gear tooth load coming upon the bearing. Since the axial dead load is not derived from the gear, the drive correction factors are not applied upon F, which remains as 750 N. If however, axial load were effected from gear drive the correction factorsh andfd would have been applied on the equivalent bearing load.

At this stage since the bearing has not been selected, the basic static capacity, C, is

Fa unknown. The radio - cannot be calculated and hence values of X and Y from cs

Table 13.14 cannot be chosen. The X and Y values are tentatively chosen as X = 0.56 and Y = 1.8.

Hence, using Eq. (1 3.6), the equivalent load on bearing

P = 0 . 5 6 ~ 3 3 0 0 + 1,8x750=3198 N . . . (i)

From Table 13.1 a single row deep groove ball bearing can take load in axial direction to the extent of 70% of radial load. A deep groove ball bearing in the present case will be a good proposition.

Assume that the unit runs for eight hours per day but not fully utilised. From Table 13.15 against item 5, the bearing is required to have life of 12000-20000 hours. Choosing the lower value and using Eq. (13.58)

N = 60 I2O0 O0 = 720 million cycles

1 o6 . . . (ii)

Using Eqs. (i) and (ii) in Eq. (1 3.52)

I

Rolling Contact Bearing

Cd = P ( N ) 3

I

or Cd = 3 198 (720): = 28662 N . . . (iii)

Tables 13. I 6 and 13.1 7 describe SKF bearings of 64,62 and 63 series. The bearing of 6406 will have bore of 30 mm and will be nearest to 28.5 mm which is iournal diameter required from strength calculations. The dynamic capacity of 6406 bearing from Table 13.16 is 33550 N which is in excess of required Cd at (iii) corresponding static capacity of 6406 bearing is 23200 N, so that

It is seen from Table 13.14 that the value of 2 lies between 0.025 and 0.04. Also cs

Fa Fu - has been calculated as 0.227. By observation it appears that - is nearly Fr Fr

equal to e and hence from first columns of Table 13.14, X = 1 and Y = 0 can be used.

Hence, equivalent bearing load

P = F,= 3300 N

Hence, using Eq. (13.53)

I

C, = 3300 (720)j = 29571 N . . . (v)

which is less than Cd of 6406 bearing which from Table 13.16 is 33350 N.

Hence, SKF 6406 bearing will be chosen for LHS journal of the shaft. The symmetric positions of LHS and RHS journals with respect to the pinion will

. . . (vi)

most advantageous in which case the load on RHS bearing wil1 be same as that on LHS bearing. Hence, the identical bearings can be used on RHS journal.

The dimensions of 6406 bearing from Table 13.16 are :

Inner diameter or bore, d = 30 mm

Outer diameter, D = 90 mm

Width, B = 23 mm

Radius at comers, r = 2.5 mm

Permissible speed = 800 rpm

The bearing comer radius of 2.5 mm is also suitable as the radius of 2.0 mm at the fillet in the shaft was prescribed.

13.21 SEATING BEARING ON SHAFT

The fillet radius must be less than bearing comer radius as shown in Figure 13.20(a). If two radii are equal than contact at the fillet will occur which is highly undesirable for

the fillet radius is less than bearing comer radius than the st the shoulder and it will have a tendency to ride over the situations are not permissible and alternative is shown in

Design of Bearings, Clutches, Brakes and CAD

(a) Bearing Corner Radius Greater (b) Bearing Corner Radius Less than Shaft Fillet Radius than or Equal to Shaft Finet Radius

(c) Alternative Arrangement for Condition of (b)

Figure 13.20

Any change in journal diameter, as in this case must be examined on calculation of shaft strength. Presently nothing has been said about the bearing housing and hence outer diameter and width are not examined. In some cases the outer diameter can become an important criterion particularly if the outer diameter of bearings on adjacent parallel shafts start interfering.

Note : The reader is advised to go through recommendations of bearing manufacturers for fits and tolerances,.sealing and lubrication, mounting and dismounting of bearings. SKF Catalogue No. 2000 I11 and No. 189 describe there aspects.

Dimensional and running accuracy of bearings has been standardised, IS0 covers a wide range from normal tolerance class 0 to tolerance classes 6 and 5. The corresponding SKF tolerance classes designated as P6 and P5 are described in manufacturers catalogue. Special tolerance classes for very accurate machines like machine tools are also available from SKF.

Table 13.16 and 13.17 describe data on SKF bearing designated as per AFBMA practice. Other tables describe IS0 standard practice. It can be seen that in IS0 practice all possible outer diameter and widths for a given bearing are described at one place.

78 Figure for Table 13.16

Table 13.16 : SKF Bearing Series 64 and 63 Rolling Contact Bearing

One Sideplate Two Sideplates One Seal Two Seals 1

Maximum Permissible

Speed rPm

10000 10000 8000 8000 6000 6000 6000 5000 5000 5000 4000 4000 4000 3000 3000 3000

16000 16000 13000 13000 10000 10000 10000 8000 8000 8000 6000 6000 6000 5000 5000 5000

Bearing D No. mm

6403 17 6404 20 6405 25 6406 30 6407 35 6408 40 6409 45 6410 50 6411 55 6412 60 6413 65 6414 70 6415 75 6416 80 6417 85 6418 90

6303 17 6304 20 6305 25 6306 30 6307 35 6308 40 6309 45 6310 50 631 1 55 6312 60 6313 ,65 63 14 70 .6315 75 6316 80 6317 85 63 18 90

D mm

62 72 80 90 100 110 120 130 140 150 160 180 190 200 210 225

47 52 62 72 80 90 100 110 120 130 140 150

. 160 170 180 190

B mm

17 19 21 23 25 27 29 31 33 35 37 42 45 48 52 54

14 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43

R mm

2.0 2.0 2.5 2.5 2.5 3.0 3.0 3.5 3.5

. 3.5 3.5 4.0 4.0 4.0 4.0 5.0

1.0 1.0 1.0 1.0 1.5 1.5 1.5 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.5 2.5

Basic

Static N

11000 15600 19000 23200 30500 37500 44000 50000 60000 67000 76500 102000 1 10000 120000 1 32000 146000

6300 7650 10400 14600 17600 22000 30000 35500 42500 48000 55000 63000 72000 80000 88000 98000

Capacity

Dynamic N

18000 24000 28000 33500 43000 50000 60000 68000 78000 85000 93000 1 12000 120000 127000 137000 146000

10600 12500 16600 22000 26000 32000 4 1500 48000 56000 64000 72000 81500 900000 96500 104000 1 12000

Design of Bearings, Clutches, Brakes and CAD

Rolling Contact Bearing

Speed Limit Basic Capacity Fatigue

d D B Load rpm with Designation mm mm mm Dynamic Static Limit

N N N Grease Oil

6011.5 2,5 8 2,8 319 106 4 67000 80000

623 3 10 4 488 146 6 60000 70000

6 1 814 4 9 2,5 540 180 7 63000 75000 604 12 4 806 280 12 53000 63000 624 13 5 975 305 14 48000 56000 634 16 6 11 10 380 16 43000 50000

6 1 815 5 11 3 63 7 255 1.1 53000 63000 625 16 5 11 10 380 16 43000 50000 635 19 6 1720 620 26 36000 43000

6 1 816 6 13 3,5 884 345 15 48000 , 56000 626 19 6 1720 620 26 36000 43000

6 1 817 7 14 3,5 956 400 17 45000 53000 607 19 6 1720 620 26 38000 45000 627 22 7 3250 1370 57 32000 38000

6 1 818 8 16 4 1330 570 24 40000 48000 608 22 7 3250 1370 57 36000 43000

6 1 819 9 1430 640 27 38000 45000 l7 1 47 609 24 3710 1660 7 1 32000 38000

629 26 8 4620 1960 83 28000 34000

61 800 10 19 5 1380 585 25 36000 43000 6 1900 22 6 1950 750 32 34000 40000 6060 26 8 4620 1960 83 30000 36000 16100 28 8 4620 1960 83 28000 34000 6200 30 9 5070 2360 100 24000 30000 6300 3 5 1 1 8060 3400 143 20000 26000 1

61801 12 2 1 5 1430 670 28 32000 38000 61901 24 6 2250 980 43 30000 36000 600 1 28 8 5070 2360 100 26000 32000 16101 30 8 5070 2360 100 26000 32000 620 1 32 10 6890 3100 132 22000 28000 6301 3 7 12 9750 4150 176 19000 24000

6 1802 15 24 5 1560 800 34 28000 34000 6 1902 28 7 4030 2040 8 5 24000 30000 16002 3 2 8 5590 2850 120 22000 28000 6002 32 9 5590 2850 120 22000 28000 6202 35 11 7800 3750 160 19000 24000 6302 42 13 11400 5400 228 17000 20000

61803 17 26 5 1680 930 39 24000 30000 6 1903 30 7 4360 2320 98 22000 28000 16003 3 5 8 6050 3250 137 19000 24000 6003 35 10 6050 3250 137 19000 24000 6303 40 12 9560 4650 200 17000 20000 6403 47 14 13500 6550 275 16000 19000 6403 62 17 22900 10800 455 12000 15000

Design of Bearings, Clutches, Brakes - -J K. A r,

Table 13.19 : Deep Groove Ball Bearing I S 0 Designation (20 mm to 55 mm Bore)

ano LAU (Stared Designations are Normal SKF)

Designation

61804 6 1904 16004 6004 6204* 6304* 6404*

6 1805 61905 16005 6005 6205* 6305* 6405*

61806 I 6 1906 16006 6006 6206' 6306* 6406*

61807 6 1907 16007 6007 6207, 6307, 6407*

61808 61908 16008 6008 6208* 6308* 6408*

61809 61909 16009 6009 6209* 6309* 6409*

61810 61910 16010 6010 6210* 6310* 6410*

6181 1 6191 1 1601 1 601 1 6211* 631 I* 6411.

d mm

20

25

30

35

40

I 45

50

55

D mm

32 37 42 42 47 52 57

37 42 47 47 52 62 80

42 47 .

55 55 62 72 90

47 55 62 62 72 80 100

52 62 68 68 80 90 110 1 58 68 75 75

' 85 100 120

65 72 80 80 90 110 130

72 80 90 90 100 1 20 140

Basic Capacity Fatigue Speed Limit rpm B Load with

Dynamic Static Limit N N N Grease Oil

7 2700 1500 63 19000 24000 9 6370 3650 156 18000 22000 8 6890 405C 173 17000 20000 12 9360 5000 212 17000 20000 14 12700 6550 280 15000 I80W 15 15900 7800 335 13000 16000 19 30700 15000 640 10000 18000

7 4360 2600 125 17000 20000 9 6630 4000 176 16000 19000 8 7610 4750 212 14000 17000 12 1 1200 6550 275 15000 18000 15 14000 7800 335 12000 15000 17 22500 1 1600 490 11000 14000 2 1 35800 19300 815 9000 11000

7 4490 2900 146 15000 18000 9 7280 4550 212 14000 17000 9 1 1200 7350 310 12000 15000 13 13300 8300 355 12000 15000 16 19500 11200 475 1000 13000 19 28100 16000 670 8000 11000 23 43600 23600 1000 8500 1000

7 4750 3200 166 13000 16000 10 9560 6200 290 11000 14000 9 12400 8150 375 10000 13000 14 15900 10200 440 10000 13000 17 25500 15300 655 9000 11000 21 33200 19000 81 5 8500 1000 25 55300 31000 1290 70000 8500

7 4940 3450 186 11000 14000 12 13800 9300 425 10000 13000 9 1300 9150 440 9500 12000 15 16800 11600 490 9500 12000 18 30700 19000 800 8500 10000 23 41000 24000 1020 7500 9000 27 63700 1530 4 6700 7000 1 36500 1 7 6050 4300 228 9500 12000 12 10100 6700 285 9000 11000 10 15600 10800 520 9000 11000 16 20800 14600 640 9000 1 1000 19 33200 21600 915 7500 9000 25 52700 31500 1340 6300 8000 29 76100 45000 1900 6000 7000

7 6240 4750 250 9000 11000 12 14600 10400 500 8500 loo00 10 16300 1 1400 560 8500 loo00 16 2 1600 16000 710 8500 10000 20 35100 23200 980 7000 8500 27 6 1800 38000 1600 6300 7500 3 1 87100 52000 2200 5300 6300

9 8320 6200 325 8500 10000 13 15900 11400 560 8000 9500 1 1 19500 14000 695 7500 9000 18 28100 2 1200 900 7500 9000 21 43600 29000 1250 6300 7500 29 7 1500 65000 1900 5600 6700 33 99500 62000 2600 5000 6000

Rolling Contact Bearing

Fatigue Speed Limit rpm Basic Capacity d D B Load with

Designation mm mm Dynamic Static Limit

I N N N Grease Oil

61812 60 78 10 8710 6700 365 7500 9000 61912 85 13 16500 12000 600 7500 9000 16012 95 I I 19900 15000 735 6700 8000 6012 95 18 29600 23200 980 6700 8000 6212 110 22 47500 32500 1400 6000 7000 63 12 130 21 8 1900 52000 2200 5000 6000 6412 150 35 108000 69500 2900 4800 5600

61813 65 85 10 1 1700 9150 490 7000 8500 61913 90 13 17400 13400 680 6700 8000 16013 100 I I 2 1 200 16600 830 6300 7500 6013 100 18 30700 25000 1060 6300 7500 6213 120 23 55900 40500 1730 5300 6300 63 13 140 3 92300 60000 2500 4800 5600 6413 160 37 119000 78000 3150 4500 5300

61814 70 90 10 12100 10000 540 6700 8000 61914 100 16 23800 18300 900 6300 7500 16014 110 13 28 100 25000 1060 6000 7000 6014 110 20 37700 3 1000 1320 6000 7000 6214 125 24 60500 45000 1900 5000 6000 63 14 150 3 5 104000 68000 2750 4500 5300 6414 180 42 143000 10400 3900 3800 4500

61815 75 95 10 12500 10800 585 6300 7500 61915 105 16 24200 19300 965 6000 7000 16015 115 13 28600 27000 1140 5600 1700 1 6015 115 20 39700 33500 1430 5600 6700 6215 130 66300 49000 2040 4800 56UQ :: 1

'

63 15 160 114000 76500 3000 4300 5000 1 6415 190 45 153000 114000 41 50 I 3600 I 4300

61816 80 100 10 12400 10800 585 6000 7000 6t916 110 16 25 100 20400 1020 5600 6700 16016 125 14 33200 3 1500 1320 5300 6300 6016 125 22 47500 40000 1660 5300 6 300 6216 140 26 70200 55000 2200 4500 5300 6316 1 70 39 124000 86500 3250 3800 4500 6416 200 48 163000 125000 4500 3400 4000

61817 85 , 110 13 19500 16600 880 1 5300 6300 61917 120 18 3 1900 30000 1250 5300 6300 16017 130 14 33800 33500 1370 5000 6000 6017 130 22 49400 43000 1760 5000 6000 621 7 150 28 83200 64000 250 4300 5000 63 17 180 4 1 133000 96500 3550 3600 4300 641 7 210 52 174000 137000 4750 3200 3800

61818 90 115 13 19500 17000 915 5300 6300 61918 125 18 33200 3 1500 1230 5000 6000 16018 140 16 4 1600 39000 1560 4800 5600 601 8 140 24 58500 50000 1960 4800 6218 160 30 95600 73500 2800 3800 :::: 1 6318 190 43 143000 108000 3850 3400 4000 6418 225 54 186000 150000 5000 3000 3600

61819 95 120 13 19900 17600 930 5000 6000 61919 130 18 3380 33500 1430 4800 5600 16019 145 16 42300 4 1 500 1630 4500 5300 6019 145 24 60500 54000 2080 4500 5300 6219 170 32 108000 81500 3000 6319 200 45 153000 118000 4150

- - - -- -

Design of Bearings, Clutches, Brakes and CAD

Table 13.21 : Deep Groove Ball Bearing IS0 Designation (100 rnrn to 160 rnrn Bore)

Designation

61820 6 1920 16020 6020 6220 6320

61821 61921 1602 1 602 1 622 1 632 1

6 1822 6 1922 16022 6022 6222 6322

61824 61924 16024 6024 6224 6324

6 1826 6 1926 16026 6026 6226 6326

61828 61928 16028 6028 6228 6328

61830 61930 16030 6030 6230 6330

61 832 61932 16032 6032 6232 6332

SAQ 3

(a) A certain ball bearing has single row in which 12 balls of 16 mm diameter are arranged. Calculate the basic statics capacity. From Table 13.16 find out the bearing closest to the given bearing.

(b) If in the bearing of Example 13.1 the diameter of grooved surface on inner raceway di = 58.986 mm and that of outer raceway do = 91.014 mm and radius of grooves on both raceways ro = r, = 8.32 mm, calculate the basic static capacity. If a factor of safety of 2 is to be provided what radial load the bearing can carry?

d mm

100

105

---- 110

120

130

D mm

125 140 150 150 180 215

130 145 1 60 160 190 225

140 150 170 170 200 240

150 165 180 180 215 260

165 1 80 200 200 230

B mm

13 20 16 24 34 47

13 20 18 26 36 49

16 20 19 28 3 8 50

16 22 19 28 40 55

18 24 22 33 40

140

150

160

58

18 24 22 33 42 62

20 28 24 35 45 65

20 28 25 38 48 68

280

175 190 210 210 250 300

190 210 225 225 270 320

200 220 240 240 290 340

Basic

Dynamic N

19900 42300 44200 60500 124000 174000

20800 44200 52000 72800 133000 182000 w

28100 43600 57200 8 1900 143000 203000

291 00 55300 60500 85200 146000 208000

37700 65000 79300 106000 156000 '

Fatigue Load Limit N

950 1630 1700 2040 3350 4750

1000

Capacity

Static N

18300 4 1500 44000 54000 93000 140000

19600 44000 5 1000 65500 104000 153000

26000 45000 57000 73500 118000 180000

2800 570000 64600 80000 118000 186000

43000 67000 81500 1000

132000 229000

39000 66300 80600 111000 165000 251000

48800 88400 92300 125000 174000 276000

49400 92300 99500 143000 186000 276000

216000

46500 72000 86500 108000 150000 245000

6 1000 93000 98000 125000 166000 285000

64000 98000 108000 143000 186000 285000

2800

4000 3800 3600 3600 3000 2600

3600 3400 3200 3200 2600 2400

3400 3200 3000 3000 2400 2200

Speed with

Grease

4800 4500 4300 4300 3400 3000

4500

6300

1660 2280 2700 3350 4150 7100

1960 2900 3050 3900 4900 7800

2000 3050 3250 4300 5300 7650

Limit rpm

0 1 1 -

5600 5300 5000 5000 4000 3600

5300

2200

3400 3200 3000 3000 2400 2000

3000 2800 2600 2600 2000 1900

2800 2600 2400 2400 1900 1800

5000 4800 4800 3800 3400

5000 4800 4500 4500 3600 3200

4500 4300 4000 4000 3400 3000

4300 4000 3800 3800 3200

1700 4300 I860 ~ 4000 2400 3650 5100 ---- 1250 1660 2040 2400 4000 5700

1290 2040 2200 2750 3900 5700

1660 2280 2700 3350 4150

4000 3200 2800

4300 4000 3800 3800 3000 2600

3800 3600 3400 3400 2800 2400

3600 3400 3200 3200 2600

(c) Calculate the dynamic capacity of the bearing in above two problems.

(d) A shaft driven by a V-belt drive is supported in two end bearings, each being SKF 6418. The reaction at both ends is 15200 N and shaft additionally carries an axial load of 3650 N. What life in hours the bearings is expected to have if shaft rotates at 100 rpms.

(e) If the shaft in above problem is driven by a gear which has error in pitch and form between 0.025 and 0.125 mm while the reactions at ends and axial load remain same, what bearing life is expected? Assume that shaft drives a rotary machine in a shock free operation.

(f) A shaft of diameter 75 mm is supported in bearings which are 1 m apart. The shaft carries a flat pulley on which runs a flat rubber belt. The drive is used for conveyor belt which works intermittently. The sum of the belt tensions on two sides is 10000 N in horizontal plane while pulley weighs 1000 N. The shaft runs at 100 rpm. The journal diameter can be close to 60 mm. Calculate reactions at the bearing ends, effective load on bearing life, in million cycles and dynamic capacity of the bearing required. Choose a proper bearing and calculate its factor of safety. Check if this factor of safety is within limits.

(g) ( i ) Out of four elements of a rolling contact bearing the one subjected to highest stress level for same number of cycles is

(a) Outer race

(b) Inner race

(c) Cage

(d) Rolling element

(ii) Which of the following causes of failure cannot be avoided by proper design practice?

(a) Fatigue

(b) Inadequate, lubrication

(c) Ingress of dust

(d) Corrosion of bearing elements

13.20 SUMMARY

Roller bearings have very low friction as compared to sliding contact bearings. Inner race, outer race and rolling elements of rolling bearings are made of steel. There are several types of bearings, which are used to carry radial and thrust loads. Single row deep groove ball bearings are most common in use. Under load all three elements (the two races and rolling element) will deform. If the load is increased beyond certain limit the deformation in one of the three elements may turn plastic. The bearing is required to carry both radial and axial force components and a load which takes care of both the components is known as static equivalent load. Rolling contact bearings do not require any lubrication. Lubrication is mainly used to keep the bearings cool. The total load carried by a bearing is shared by a few rolling elements at a time. Fatigue is a very important consideration in designs of rolling contact bearing. The life of a beanng is generally described in number of revolution it can make before failure. Bearing is normally specified by four digit number.

Rolling Contact Bearing

Design of Clutches, and CAD

Bearings, Brakes 13.21 KEY WORDS I

Rolling Contact Bearing : Rolling contact bearing is an assembly of balls or rollers which would physically maintain the shaft in radially spaced apart relationship with respect to a usually stationary supporting structure called a housing in which bearing itself is supported.

Static Equivalent Load : The static equivalent load may be defined as static radial load (in case of radial ball or roller bearings)

Life of a Bearing

or axial load (in case of thrust or roller bearings) which, if applied, would cause the same total I permanent deformation at the most nearly stressed ball (or roller) and race contact as that which occurs under the actual conditions of loading. 1

: The life of an individual ball (or roller) bearing may be defined as the number of revolutions (or hours at some given constant speed) which the - . - bearing runs before the first evidence of fatigue develops in the material of one of the rings or any of the rolling elements.

Reliability of Bearing : The reliability is defined as the ratio of the number -

of bearings which have successfully completed L million revolutions to the total number of bearings under test.

13.22 ANSWERS TO SAQs

SAQ 1

(a) C, = 38540 N, 19270 N

(b) Cd=24165 N

(c) 945.27 hours

(d) 3890 hours

(e) 5099 N, 25495 N, 48 million cycles, 92536 N, SKF 6413, d = 65 mm, D = 160mm, B = 3 7 m m , r = 3 . 5 mm,f:s. = 15.