416 書名： Essentials of Mechanical Engineering Design, 1/E 作者： Shigey Mischke Budynas 書號： MX0398.

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書名： Essentials of Mechanical Engineering Design, 1/E作者： Shigey Mischke Budynas書號：MX0398

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8-2 Bearing lifeCommon life measure:

• Number of revolutions of the inner ring (outer ring stationary) until the first tangible evidence of fatigue

• Number of hours of use at a standard angular speed until the first tangible evidence of fatigue

Rate life (90%)-minimum life, L10 life and B10 lifeMedian life is the 50% (or average life)

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In above equation:

a=3 for ball bearing

a=1/3 for roller bearing

a

DDDa

RR nLFnLC /1/110 )60()60(

Catalog rating lb or kN

Rating life in hours

Rating speedrpm

Desired life

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Reliability set x=L/L10 by Weibul distribution Minimum

value of the variate

Characteristic parameter

corresponding to the 63.2121

percentile value of the variate

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Along a constant reliability contour (BD)

Along load line (AB)

But FB=C10

B 0

0

1/0 0

1/

1/0 0

exp

1( )(ln )

( )1

( )(ln )

b

D

bB

D

aD DB D D

bR

D

x xR

x

x x xR

x xF F F

x x xR

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Equivalent load

Axial load

Radial load

V=1 when inner ring rotate

V=1.2 when outer ring rotate

V=1 for self aligning bearing

Common expression

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C0 : basic static load rating

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K

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Damage done by equivalent loads Fe1,Fe2 and Fe3 is

In general form

Eq. 8-10 can be written as

→

→

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332211

332211

332211

equals alsoK and

and

lL

Kl

L

Kl

L

KLFlFlFK

LFLFLFK

lFlFlFLF

ae

ae

ae

ae

ae

ae

ae

ae

aeeq

aeq

For continue load

0dFdDD

dFdD

a

a

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31cot389.0Kαis the half the include cup angle

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Location of reactions

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Relating load, life and reliability

Solve for xD gives

xD=L/L10

For Weibull model: x0=0, θ=4.48,b=3/2

For roller bearing:

a

D

bDD F

CRxxx )()1)(( 10/1

00

210/3103/2 )()1(48.4D

DD F

CRx

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Timken:

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Outline of design assessment:

1. Bearing reliability for the load imposed and life expected

2. Shouldering on shaft and housing satisfactory

3. Journal finish, diameter and tolerance compatible.

4. Lubricant type according to manufacturer’s recommendations; lubricant paths and volum supplied to keep operating temperature satisfactory

5. Preloads, if required, are supplied

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Bearing Reliability

For x0=0, θ=4.48, b=3/2

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8-11 Lubrication

Elastohydrodynamic lubrication

Purpose of the antifriction-bearing lubricant:

1. To provide a file of lubricant between the sliding and rolling surfaces.

2. To help distribute and dissipate heat.

3. To prevent corrosion of the bearing surfaces.

4. To protect the parts from the entrance of foreign matter.

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Preloading

Alignment

Enclosures