Machine Design Databook Episode 3 part 3 ppt

The approximate rating life in millions of revolutionsfor ball bearing The equivalent radial load for radial and contact ball bearings under combined constant radial and axial loads The

The equivalent dynamic load used in Eq (23-177a) is

given by

life in millions of revolutions (L)

The Eq (23-178b) can be written as

The simplified form of Eq (23-179b)

The basic dynamic load rating from Eq (23-180a)

m ¼ life exponent

¼ 3.0 for ball bearing

¼ 10/3 for roller bearing

23-42a and 23-42b can be determined from Fig 23-53.

C can be obtained from manufacturer’s catalogue.

where

axial load for axial bearings

X ¼ radial factor

Y ¼ axial/thrust factor The values of X and Y can be found in tables of the manufacturer’s catalogue (e.g FAG catalogue).

60n

C F



C F

ð23-179bÞ

DESIGN OF BEARINGS AND TRIBOLOGY 23.95

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FIGURE 23-53 Nomogram chart for determining c/p for ball and roller bearings (ISO-R281) (Note: Information on thecalculation of load rating C and equivalent load P can be obtained from ISO Recommendation R281 Values of C for varioustypes of bearing can be obtained from the bearing manufacturers.)

ROLLER BEARINGSBALL BEARINGS

Speed

rev/min Loadratio

C/P

Rating lifehoursLh

MillionrevolutionsL=L10

Speedrev/min Loadratio

C/P

Rating life

hoursLh

MillionrevolutionsL=L10

1520

30

400003000020000

1000080006000400030002000

1000800600400300200

1008060403020

1086

54321.0

200300400500600700800900100015002000300040005000600070008000900010000150002000030000400005000060000700008000090000100000150000200000

2000015000

100009000800070006000500040003000

2000180015001200

1000900800700600500400300200150

1009080706050403020

1.0 1.0234682

1.5

10203040506080100200300400500765

3

4

8001000200030004000500080001000020000

8910

300000200000150000

100000900008000070000600005000040000300002000015000

1000090007000600050004000300020001500

1000900800700600500400300200

The value of index of dynamic stressing, fL, can be

DESIGN OF BEARINGS AND TRIBOLOGY 23.97

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The value of speed factor, fn, can be obtained from

Eq (23-179b)

The equivalent dynamic load for deep groove ball

bearings with increased radial clearance

ffiffiffiffiffiffiffiffi

3n

s

ffiffiffiffiffiffiffiffi 100 3n

r

ð23-181bÞ

TABLE 23-45

q

Speed, Speed Speed, Speed Speed, Speed Speed, Speed Speed, Speed Speed, Speed

n, rpm factor,fn n, rpm factor,fn n, rpm factor,fn n, rpm factor,fn n, rpm factor,fn n, rpm factor,fn

DESIGN OF BEARINGS AND TRIBOLOGY 23.99

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TABLE 23.46

Speed, Speed Speed, Speed Speed, Speed Speed, Speed Speed, Speed Speed, Speed

n, rpm factor,fn n, rpm factor,fn n, rpm factor,fn n, rpm factor,fn n, rpm factor,fn n, rpm factor,fn

LIFE ADJUSTMENT FACTORS

An adjusted fatigue life equation for a reliability of

(100-n) percent

which accounts for reliability, R, is calculated from

the Weibull distribution.

The adjusted fatigue life for non-conventional

materi-als and operating conditions.

For values of X and Y, refer to Table 23-39 and also

to bearing tables given in FAG catalogue For values

of X and Y of deep groove ball bearings with increased radial clearance, refer to Table 23-47b.

where

¼ 3 for radial ball bearings of good quality as per AFBMA

¼ 0.2 to 2.0 for normal bearing materials

¼ 2.0 for most common material, AISI 52100

conditions

¼ 1 for well and adequately lubricated bearings

< 1 for other adverse lubricating conditions and temperatures.

TABLE 23-47a

Normal Bearing Standard clearance Bearing clearance C3a Bearing clearance C4a

aC3, C4Standard for a radial clearance that is larger than normal

Values of factor faare given in Table 23-47b

DESIGN OF BEARINGS AND TRIBOLOGY 23.101

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Reliability R, % Ln Adjustment factor,a1

From Eq (23-177a), an adjusted fatigue life equation

ISO 281

An adjusted fatigue life equation, which accounts for

variation in vibration and shock, speed, environment,

From Eq (23-186a), the basic equivalent load rating,

Fig 23-54 shows the plot of relative life vs probability

minimum life), which indicates a 10% probability of

failure, i.e 90% of the loaded bearings will survive

23-54 indicates median life with a 50% probability

of failure, which is also known as average life From

indicates only 50% of the bearings will survive this

longer life.

For life curves of ball bearings as per SKF and New

Departure (ND) and Needle-bearings

C F

Smooth operation free from shock Machinery with no impact:

Electric motors, machine tools, air conditioners 1–1.2Normal operation Machinery with light impact:

Air blowers, compressors, elevators, cranes, paper making machines 1.2–1.5Operation accompanied Machinery with moderate impact:

by shock and vibration Construction machines crushers, vibration screens, rolling mills 1.5–3.0

DESIGN OF BEARINGS AND TRIBOLOGY 23.103

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BASIC DYNAMIC LOAD RATING OF

BEARINGS AS PER INDIAN STANDARDS

Radial Ball Bearing

The basic dynamic load rating for radial and angular

contact ball bearings.

Single row radial contact groove ball

bearings and single and double

row-angular contact groove ball bearings

Double row radialcontact groove ballbearings

Single row anddouble row self-aligning ball bearings

Single row radial contactseparable ball bearings(magneto bearings)

Note: Values of fcfor intermediate values of D0wcos=Dpware obtained by linear interpolation IS: 3824 (Part 1)–1983

DESIGN OF BEARINGS AND TRIBOLOGY 23.105

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The approximate rating life in millions of revolutions

for ball bearing

The equivalent radial load for radial and contact ball

bearings under combined constant radial and axial

loads

The basic rating life for a radial ball bearing which is

based statistically

Adjusted rating life

The adjusted rating life for a reliability of (100-n)

percent

The adjusted rating life for non-conventional

materi-als and operating conditions

The adjusted rating life for non-conventional

materi-als and operating conditions, and for a reliability of

(100-n) percent.

Radial roller bearings

The basic dynamic radial load rating of radial roller

bearings

The equivalent radial load for radial roller bearings

axial loads

The equivalent radial load for radial roller bearings

The basic rating life in millions of revolutions for

radial roller bearings

For adjusted rating life for roller bearings

C P

revolutions (i.e., the number of revolutions resulting in 10% failure).

accor-dance with Eqs (23-187), (23-188), and (23-190).

TABLE 23-51

Radial contact groove ball bearings

Single row radial contact

separable ball bearings (magnetic

bearings)

Note: Values of X, Y and e for intermediate ‘relative axial loads’ and/or contact angles are obtained by linear interpolation IS: 3824 (Part 1), 1983

aPermissible maximum value depends on bearing design (internal clearance and raceway groove depth)

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THRUST BEARINGS

Ball bearings

The basic dynamic axial load rating for a single-row,

single- or double-direction thrust ball bearing

Z ¼ number of balls carrying load in one direction.

TABLE 23-52

bearings for use in Eq (23.195)

Note: Values of fcfor intermediate value

of Dwcos=Dware obtained by linear

interpolation IS: 3824 (Part 2) 1983

 6¼ 0

IS: 3824 (Part 2) 1983

Bearings with two or more rows of balls

The basic dynamic axial load rating for thrust ball

bearings with two or more rows of similar balls

carrying load in the same direction

DESIGN OF BEARINGS AND TRIBOLOGY 23.109

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Dynamic equivalent axial load

The equivalent load for thrust ball bearings with

 6¼ 908 under combined constant axial and radial

loads

The equivalent axial load for thrust bearing with

 ¼ 908 which can support axial loads only

Basic rating life

The basic rating life in millions of revolutions for a

thrust ball bearings

single row bearing formulae from Eqs (23-199)

Table 23-54 are obtained by linear interpolation or extrapolation.

Single direction bearingsa Double direction bearings

Note: For thrust bearings > 458 Values for  ¼ 458 are shown to permit interpolation of values for  between 458 and 508

aFa=Fr e is unsuitable for single direction bearings IS: 3824 (Part 3) 1983

Adjusted rating life

The adjusted rating life of (100-n) percent

For other adjusted rating life with modification if

required

Roller bearings

The basic dynamic axial load rating for single row,

single- or double-direction thrust roller bearing

Z ¼ number of rollers carrying load in one direction.

aApplicable for 458 <  < 608;bApplicable for 608 <  < 758;cApplicable for 758 <  < 908

Note: Values of fcfor intermediate values of Dwc=Dpwor Dwcos=Dpware obtained by linear interpolation IS: 3824 (Part 4) 1983

DESIGN OF BEARINGS AND TRIBOLOGY 23.111

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Bearing with two or more rows of rollers

The basic dynamic axial load rating for thrust roller

bearings with two or more rows of rollers carrying

load in the same direction

The equivalent axial load for thrust roller bearings

radial load

The equivalent axial load for thrust roller bearings

The basic rating life in millions of revolutions for

thrust roller bearings

Adjusted rating life

The Eqs (23-192), (23-193) and (23-194) for adjusted

rating life with appropriate modification to suit the

roller thrust bearings are repeated here

Variable bearing load and speed

are calculated from the appropriate single row bearing Eqs (23-207) and (23-208).

with Eqs (23-207), (23-208), and (23-210).

r

ð23-213aÞ

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi P

The mean effective load Fm under linearly varying

The equivalent dynamic load for the varying load

which acts in a radial direction only for radial

bear-ings and in a axial direction only for thrust bearing.

In the direction and magnitude of load changes with

equivalent load’s Eq (23-119).

The life of a bearing under variable load and variable

speed, taking into consideration life adjustment

The basic load rating for a required bearing life in case

where

revo-lutions.

n ¼ total number of revolutions in a complete cycle

DESIGN OF BEARINGS AND TRIBOLOGY 23.113

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Electric motors

For household appliances 1.5–2.0

Medium-sized standard cars 3.0–4.0

Outer bearings of locomotives 4.0–5.5

Inner bearings of locomotives 4.5–5.5

Ship propeller thrust blocks 2.9–3.6

Ship propeller shaft bearings 6.0

General engineering

Medium-sized universal gears 3.0–4.0

Large mechanical stirrers 3.5–4.0

Milling cutters and cutter shafts 3.0–4.0

Machines for working of wood and plastics 3.0–4.0

The expression for reliability (R) as per Weibull

three-parameter

reliability (R) for bearings.

The reliability (R) of bearing using Weibull

two-parameter for tapered roller bearings.

Another form of reliability (R) equation for bearing

using Weibull two-parameter

Weibull two-parameter equation for reliability is

obtained from Eq (23-225a) by putting b ¼ 1.17

Weibull equation for the distribution of bearing

rating life based on reliability.

The relation between the design or required values

according to the Timken Engineering is given by

x ¼ life measure

 ¼ Weibull characteristic of life measure

b ¼ Weibull exponent/shape parameter

R ¼ exp

L

ð23-222bÞ where

R ¼ reliability corresponding to life L

m ¼ scale constant

R ¼ exp

L

DESIGN OF BEARINGS AND TRIBOLOGY 23.115

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The basic dynamic capacity or specific dynamic

capacity of bearing corresponding to any desired life

L at the reliability R

Another equation connecting catalog radial load

(R).

m ¼ an exponent which varies from 3 to 4

R ¼ reliability

30000 20000 10000 7000 3000 2000 1000 700 500 300 200 100 70 50 30 20

0.200.300.400.500.701.00

THE EQUIVALENT DYNAMIC LOAD FOR ANGULAR CONTACT BALL BEARINGS

FIGURE 23-57 Angular contact ball bearings mounted on a single shaft

Thrust load to be used in equivalent load calculationCondition of load Bearing A (Fig 23-57) Bearing B (Fig 23-57)

Probability of failure, F(percent)

FIGURE 23-58 Reduction in life for reliabilities greater than 90% (Courtesy: Tedric A Harris, Predicting Bearing Reliability,Machine Design, Vol 35, No 1, Jan 3, 1963, pp 129–132)

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An expression for tapered roller bearings connecting

The radial equivalent or effective load when the cup

rotates in case of tapered roller bearing (Fig 23-50)

the tapered roller

The net thrust on the tapered roller bearing when the

The radial equivalent load when the cup rotates in

case of tapered roller bearing (Fig 23-50)

The radial equivalent load when the cone rotates in

case of tapered roller bearing (Fig 23-50)

thrust rating of bearing

¼ 1:5 for radial bearings

¼ 0:75 for steep-angle bearings

THE EQUIVALENT DYNAMIC LOAD FOR TAPERED ROLLER BEARINGS

The radial equivalent load on bearing A according to

The radial equivalent load on bearing B according to

DIMENSIONS, BASIC LOAD RATING

CAPACITY, FATIGUE LOAD LIMIT AND

MAXIMUM PERMISSIBLE SPEED OF

ROLLING CONTACT BEARINGS

Deep groove ball bearings—Series 02, Series 03, Series

04

Self-aligning and deep groove ball bearings—Series

02, Series 03, Series 22 (FAG) and Series 23 (FAG)

Refer to Tables 23-60, 23-61, and 23-62 respectively.

Refer to Tables 23-63, 23-64, 23-65 and 23-66 respectively.

A B

FIGURE 23-59 Two taper roller bearings mounted on a single shaft

Thrust load to be used in equivalent load calculationCondition of load Bearing A (Fig 23-59) Bearing B (Fig 23-59)

The thrust factors Y and Yeare taken from Table 23-39 and 23-47a

DESIGN OF BEARINGS AND TRIBOLOGY 23.119

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Single row angular contact ball bearings—Series 02

and Series 03

Double row angular contact ball bearings—Series 33

(FAG)

Cylindrical roller bearings—Series 02, Series 03,

Series 04, Series NU 22 (FAG), Series NU 23 (FAG)

Tapered roller bearings—Series 322, Series 02 (22)

and Series 03 (23)

Single thrust ball bearings—Series 11, Series 12, Series

13 and Series 14

Double thrust ball bearing-Series 522 (FAG)

Selection of bearing size

NEEDLE BEARING

LOAD CAPACITY

For various types of needle roller bearings and for

some of their characteristics

The capacity of needle bearing at 3000 h average life

The load capacity of needle bearing based on the

projected area of the needle-rollers

The load capacity of needle bearing is also calculated

from formula

PRESSURE

The pressure for wrist pin rocker arm and similar

oscillating mechanism is given by

The rotary motion pressure may be computed from

the relation

Check for total circumferential clearance from formula

For dimensions, design data and sizes for needle

bearings.

Refer to Tables 23-67 and 23-68.

Refer to Table 23-69.

Refer to Tables 23-70, 23-71, 23-72, 23-73, and 23-74.

Refer to Tables 75, 76, 76A, 76B and 77.

23-Refer to Tables 23-78, 23-79, 23-80, and 23-81.