Chapter 7 Rolling Contact Bearing-2

8/10/2019 Chapter 7 Rolling Contact Bearing-2

1/33

7.2 Loading and Failure Styles

(1) Axial load Fa

Well-distributed on all rolling

elements (such as ball, or roller).

(2) Radial load FrNo load on the upper semi,

uneven distributed load on the

lower semi.

F05Fr/Zif Point contact

F04.6Fr/Zif Line contact

ZNumber of rolling elements

1. Load distribution of rolling contact bearing


2/33

Generally, the acting point of the radial load Frcan be

regarded as the middle point of width of bearing. =0

But for the angular contact ball bearing, and tapered roller

bearing, this rule is not valid. 0

If the span of the shaft is very small, the modeling error

could be significant.(2) Calculation of axial load

For the deep groove ball bearing

If the resultant force on the shaft is FA,

Fa=FA(the axial load of bearing withstanding FA);Fa=0 (the axial load of bearing not withstanding FA).

(1) Briefness of radial load

2. Load calculation of rolling contact bearing


3/33

FS1.25Frtan

Type of

bearing

Angular contact ball bearing Tapered rollerbearing

70000C(=15) 70000AC(=25) 70000B(=40) 30000

Fs eFr 0.68Fr 1.14Fr Fr/(2Y)

The factor ecan be found in a bearing dictionary.

The factor Yis the factor of axial dynamic load. See Table 7-7.

Table 7-5 Formulas of calculating the additional axial load

But for the angular contact bearing, the radial load will

generate additional axial load Fs.


4/33

The additional axial load path is from the outer race, to the balls,

to the inner race and shaft.

So we need to use the angular contact ball bearing in pair.

Face to face


5/33

Before calculating the axial load Fa1and Fa2, we need to consider

Fs1, Fs2and working axial load FA. There are two cases:

Fa2=Fs1+FA

And the left bearing is relaxed,

where it is only applied by

additional axial force. So, we

have Fa1=Fs1

(1) If Fs1+FA>Fs2,

The shaft has an inclination of moving rightwards. We assume

the right bearing is already fixed, so the shaft can not move. The

right bearing has been pressed. Based on the force equilibrium,

we have


6/33

(2) If Fs1+FA


7/33

The main failure types of rolling contact bearing include:Fatigue pitting on the surfaces of raceway and rolling element;

Plastic deformation of bearing;

Abrasive wear.

(1) Fatigue pitting

The surfaces of race and rolling element are applied by

fluctuating load.

After a large number of cycles of loading, fatigue pitting may

occur.

If fatigue pitting happens, the vibration, noise and heat loss will

increase very significantly.

3. Failure types and calculation principles


8/33

(2) Plastic deformation

Overloaded static force or impact will cause plastic

deformation. The failure is sometimes referred to as brinelling.

If plastic deformation happens, the starting torque, vibrationand noise will increase very rapidly, and the positioning

precision of bearing will decrease.


9/33

(3) Abrasive wear

Poor sealing and lubrication may cause abrasive wear, which

may produce noise and vibration.

The positioning error of bearing will decreases.


10/33

(4) Calculation principles

1) Common situation -- Fatigue life (pitting)

2) Low speed situation -- Checking the static strength

3) High speed -- Calculating the fatigue life, and checking the

limiting speed

(5) Performance parameters of bearing

1) Basic static load rating C0(C0r, C0a)

The load that bearing can withstand without permanent

deformation of any component.

2) Basic dynamic rating C (Cr

, Ca

)

The load to which the bearings can be subjected while achieving a

rated life (L 10) of 106revolutions.

3) Limiting speed (nlim)

For an instance, 6317, nlim

=5000r/min.


11/33

7.3 Strength Features and Life Design

Fatigue pitting is a statistical phenomenon with considerable

spread of the actual life of a group of bearings of a given design.

The rated life is the standard means of reporting the results of

many tests of bearings of a given design.

It represents the life that 90%of the bearings would achieve

successfully at a rated load.

It also represents the life that 10% of the bearings would not

achieve.

The rated life is thus typically referred to as the L 10life at the

rated load.

If load increase, the life of bearings decreases. See Fig. 7-10.

Basic dynamic load rating C: The constant load that bearings

can endure under the 106revolutions.

1. Life of bearings

2. Basic dynamic load rating


12/33

The basic dynamic load rating indicates the performance ofresisting fatigue pitting.

By experimentswe have10 constantP L C

Ball bearing 3

10Roller bearing

3Equivalent dynamic load, P

For the radial bearings, it refers to the radial basic load rating Cr;

For the thrust bearings, it refers to the axial basic load rating Ca;

Cr, and Cacan be found in a bearing dictionary.

Basic dynamic load rating

Fig. 7-10 Life and equivalent dynamic load of rolling bearings

3. Life calculation of bearing


13/33

10P L C

If the equivalent dynamic load of bearings is given

we can have the rated life of bearings, L 10. That is

6

10 10C

L revP

6

1010

10 16670

60 60h

L C CL h

n P n n P

If the rotational speed of bearings is given

we can have the rated life of bearings, L 10h. That is

If the equivalent dynamic load Pand the design life L his given

we can calculated the allowable dynamic load rating C. That is

16670

hL n

C P

we can specify the number of bearing based on C.

C C.


14/33

Table 7-6 Recommended design life of bearings


15/33

Basic dynamic load rating Cincludes radial basic dynamic

load rating Crand axial basic dynamic load rating Ca.

If the radial load Frand axial load Faare applied on therolling bearings, they have to be transferred into equivalent

dynamic load P.

Equivalent dynamic loadP

can be calculated by

( )d r aP f XF YF

X

Factor of radial dynamic load, see Table 7-7;YFactor of axial dynamic load, see Table 7-7;

fdFactor of impact load, including the vibration and shock,

see Table 7-8.

4. Equivalent dynamic load


16/33

Table 7-7 Xand Yfor calculating the equivalent dynamic load

of rolling contact bearing

TypesFa/C0r

e

Single row bearing Double row bearing

Fa

/Fr

e Fa

/Fr

>e Fa

/Fr

e Fa

/Fr

>e

X Y X Y X Y X Y

Deepgroove

ball

bearing

60000

0.014 0.19

1 0 0.56

2.30

1 0 0.56

2.30

0.028 0.22 1.99 1.99

0.056 0.26 1.71 1.71

0.085 0.28 1.55 1.55

0.11 0.30 1.45 1.45

0.17 0.34 1.31 1.31

0.28 0.38 1.15 1.15

0.42 0.42 1.04 1.04

0.56 0.44 1.00 1.00

In the relative axial load Fa/Cor, Coris the radial static load rating,

which can be found in a bearing dictionary; If the value of Fa/Coris an

arbitrary value, an linear interpolation is needed.


17/33

TypesFa/C0r

e


Fa/Fre Fa/Fr>e Fa/Fre Fa/Fr>e

X Y X Y X Y X Y

Angular contact

ball bearing

=15

70000

0.015 0.38

1 0 0.44

1.47

1

1.65

0.72

2.39

0.029 0.40 1.40 1.57 2.28

0.058 0.43 1.30 1.46 2.11

0.087 0.46 1.23 1.38 2.00

0.12 0.47 1.19 1.34 1.93

0.17 0.50 1.12 1.26 1.82

0.29 0.55 1.02 1.14 1.66

0.44 0.56 1.00 1.12 1.63

0.58 0.56 1.00 1.12 1.63

=25

, 70000 -- 0.68 1 0 0.41 0.87 1 0.92 0.67 1.41

=45 -- 1.14 1 0 0.36 0.57 1 0.55 0.67 0.93


18/33

TypesFa/C0r

e


Fa/Fre Fa/Fr>e Fa/Fre Fa/Fr>e

X Y X Y X Y X Y

Double row

angular contact

ball bearing

=30

- 0.80 -- -- -- -- 1 0.78 0.63 1.24

4-point contact

bearing =30

-- 0.95 1 0.66 0.60 1.07 -- -- -- --

Tapered roller

bearing 3000--

1.5 tan

1 0 0.40

0.4cot

1

0.45

cot 0.67

0.67

cot

Self-aligning

bearing-- 1.5 tan -- -- -- -- 1

0.42

cot 0.65

0.65

cot

Thrust selfaligning roller

bearing

-- 1/0.55 -- -- 1.20 1.00 -- -- -- --

The values of eand Yare decided by the contact angle , also can be

found in a bearing dictionary.


19/33

Table 7-8 Factor of impact load

Load pattern Examplesfd

Uniform load or

slight impact

Electrical motor, water pumping,

ventilator and steam turbine1.0-1.2

Medium impact

Vehicles, machine tool, crane,

metallurgical machinery, andinternal combustion engine

1.2-1.8

Great impact

Crusher, rolling machine, vibrating

screen, construction machinery, and

Oil drilling machine

1.8-3.0


20/33

If Fa/Freor Fa/Fr>e, Xand Yhave different values.

For the single row radial bearing or angular contact bearing,if Fa/Fre, Y=0, P=fdFr. That means the axial loads

contribution to the equivalent dynamic load can be ignored.

For the deep groove and angular contact ball bearings, e

keeps positively proportional to the ratio of Fa

/Cor

.

The ratio of Fa/Corindicates the relative magnitude of axial

load, and effects the values of eby the value of contact angle.

For cylindrical roller bearing and needle bearing, Pr=fdFr.

For thrust bearing,P

a=fdF

a.

5. Instructions on calculating equivalent load


21/33

If the load and speed are variable, we calculate the bearing life by

kkm ananann .....2211

m

kkk

m

n

PanPanPanP

...222111

1 1 1 2 2 2

16670 16670

( ) ...h m m k k k

C CL

n P n a P n a P n a P

nmMean rotational speed;

P1,P

2, ,P

kEquivalent dynamic loads at different working situation;

n1, n2, , nk

Rotational speeds at different equivalent dynamic load;

a1, a2, , ak

Percentages of time among different working situation.

6. Bearing life under varying speed and varying load

PmMean equivalent dynamic load;


22/33

L 10life indicates 90%probability that selected bearing would

carry its rated dynamic load for the specified number of design

hours.

That leaves a 10% probability that any given bearing would

have a lower life.

Certain applications call for greater reliability, such as

aerospace, military, instrumentation, and medical fields.

It is desirable to be able to adjust the expected life of a

bearing for higher reliability.

na 1 2 3 10L a a a L

7. Adjustment of life rating for reliability

a1Adjustment factor for reliability, see Table 7-10;

a2Adjustment factor for life;

a3Adjustment factor for working situation;

a2, and a3are proposed by the bearing producer.


23/33

Reliability,%

40 50 60 70 80 90 95 96 97 98 99

a1

ball 7.01 5.45 4.14 2.00 1.961 0.62 0.53 0.44 0.33 0.21

roller 6.84 5.34 4.07 2.98 1.95

Table 7-10 Adjustment factor for reliability


24/33

To avoid the plastic deformation, we need to check the static

strength of rolling contact bearings. We have0 0 0C S P

C0(radial C0r, axial C0a)Basic static load rating, which canbe found in the bearing dictionary.

S0Safety factor; if requiring high precision and smooth

rotation or great impact, S0=1.2-2.5; if the opposite condition,

S0=0.5-0.8; commonly, S0=0.8-1.2.

P0Equivalent static load.

For the bearings with 0 , P0r=max(X0Fr+Y0Fa, Fr)

X0Radial static load factor;

Y0

Axial static load factor;

X0, Y0can be found in the bearing dictionary.

For the radial bearings with =0, P0r=Fr;

For the thrust bearings with =90, P0a=Fa;

For the thrust self-aligning roller bearings, if Fr0.55Fa,

P0a=Fr+2.7Fa.

8. Static strength of rolling contact bearings


25/33

Exceeding speed limits may result in excessively high operating

temperature due to friction between the cages supporting the

rolling elements.

Most catalogs list limiting speed for each bearing.

A given bearing will have a lower limiting speed as loads

increase.

The allowable speed ncan be estimated by

1 2 limn f f n

nlimLimiting speed of bearing;f1Factor of load varying, see Table 7-11;

f2Factor of load distribution, see Table 7-12.

9. Limiting speed of bearing

Table 7 11 Factor of load varying f


26/33

Table 7-11 Factor of load varying, f1

Factorforloadvarying

f1

Value of P/C

1Self-aligning ball bearing;

2Self-aligning roller bearing;

3Tapered roller bearing;6Deep groove ball bearing;

7Angular contact ball bearing;

NCylindrical roller bearing.

Table 7-12 Factor of load distribution, f2

Contact angle


27/33

We mount a pair of single-row angular contact bearing or

cylindrical bearing in the way of face-to-faceor back-to-back.

In the calculating process, we regard the pair of bearing as a wholebearing, satisfying that,

For angular contact ball bearing0.72 1.62r r rC C C

For tapered roller bearing 7/9

2 1.71r r rC C C

Their basic static load ratings are0 0

2r r

C C

Their limiting speeds are lim lim0.6 0.8n n

CrBasic dynamic load rating of single bearing;

C0rBasic static load rating of single bearing;

nlimLimiting speed of one bearing.

10. Calculations of angular contact bearings used in pair


28/33

A pair of bearings 30308 are mounted as shown below. The applied

radial force Fr1=6000N, and Fr2=4000N, and the axial workingload FA=2500N. Try to find the axial load of each bearing.

Example 1

FS1

FS2

FA

1 2

Fr1 Fr2

11. Examples of bearing life design


29/33

Solutions:

(1) Additional axial load FsFor the left bearing:

For the right bearing:

11

60001724

2 2 1.74

rs

FF N

Y

Pointing rightward

22

40001149

2 2 1.74

rs

FF N

Y

Pointing leftward

From a bearing dictionary, we have =125710.

So we have Y=0.4cot =0.4cot 12

5710=1.74.

(2) Axial load Fa

Because Fs1+FA-Fs2=1724+2500-1149=3075N>0, the shaft has an

inclination of moving rightward. The right bearing is pressed,

and the left bearing is relaxed.

1 1 1724a sF F N 2 1 4224a s AF F F N

FS1 FS2

FA

1 2

Fr1 Fr2

See Table 7-5

See Table 7-7

Example 2


30/33

Example 2

Analysis the feasibility of mounting a pair of bearings 30309onto a

worm shaft. If it is not correct, please propose your improvement.

Question: Given that radial supporting forcesF

r1=1800N,Fr2=520N, the axial load on worm shaft FA=4100, shown below.

The rotational speed of worm n=1440r/min. Oil lubrication is

required. The design life of bearings L=11000h. It is under a

sizeable impact (Factor of impact load fd=1.3.)

FS2 FS1

FA

2 1

Fr2Fr1

Solutions:


31/33

Solutions:(1) Calculation of bearing life

From a bearing dictionary, the basic dynamic load rating

C=64800N, basic static load rating C0=61200N. Under oillubrication, the limiting speed nlim=5000r/min. the contact angle

=125710. e=1.5tan =1.5 tan 125710=0.34.

1) Additional axial load Fs

0.4cot 0.4cot12 57 10Y

11 1800 517

2 2 1.74r

s FF NY

2

2

520149

2 2 1.74

rs

FF N

Y

2) Axial loadF

a

Fs2+FA-Fs1=149+4100-517=3732>0, so the shaft has an inclination

of moving rightward. That is the right bearing is pressed, and the

left bearing is relaxed. So we have

Fa1

=Fs1

+FA

=4249N

Fa2=Fs2=149N

FS2 FS1

FA

2

1

Fr2Fr1


32/33

4) The bearing life is


33/33

4) The bearing life is10

6 6310 10 64800

4913h

Chapter 7 Rolling Contact Bearing-2

Documents

Transcript of Chapter 7 Rolling Contact Bearing-2