Bearing Ratings & Life Equations

Timken Training

AGENDA

• Load Ratings

• Single-Row Life Equations

• Multiple-Row Life Equations

2

BEARING RATING & BEARING LIFE

Bearing Rating:

• Describes the expected load a part can carry

• Determined by geometry and material of bearing

• A variable used to calculate estimated life (L10)

Bearing Life:

• Estimated time bearing will run before predetermined amount of damage occurs

• Determined by application conditions, bearing rating, and bearing performance enhancements

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Bearing Ratings

BEARING LOAD RATINGS

• Timken ratings are calculated based on algorithms developed inter-company or through ISO

• Validated through:

• Testing under reference conditions

• Practical experience in customer applications

• International Bearing Performance Audit samples bearings to ensure they meet the established rating.

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TIMKEN BEARING TESTING

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DYNAMIC LOAD RATING

• Used for estimating the life of a rotating bearing.

• Symbol is C90 or C(90) for radial rating

• Symbol is Ca90 or Ca(90) for thrust rating

• The load that 90% or more of a large group of bearings could survive for 90 million revolutions before a 0.01in2 (6mm2) spall develops.

• Rating verified by testing at given reference conditions

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DYNAMIC LOAD RATING REFERENCE CONDITIONS

• Load: Fr = 150% C90

• Speed: S = 500 RPM

• Lubrication: Oil viscosity = 33 cSt @ 55° C (155 SUS at 130° F)

• Temperature: T = 55° C (130° F)

• Setting: 150° load zone

• Alignment: < 0.0005 radians

• Fatigue spall size: 6 mm2 (0.01 in2)

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• Timken ratings based on C90 yet many ratings are

published as C1

• To convert C1 to C90

• Using C1 in L10

equation

901

9010

3

1

C86.3C

C90C

sRevolution 101P

CL 6

310

110

BEARING RATINGS

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BEARING RATINGS

• C1 is a theoretical number. The bearing should never be loaded to this magnitude.

• “Working” load range is 1/3 of the C1 rating.

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D N cos L ZM H = 1516

107

54

90 C

• Rating Equations: Radial Capacity

H = Geometry dependent factor

M = Material constant

Z = Number of bearing rows in

assembly

L = Effective roller contact length

= 1/2 Included cup angle

N = Number of rollers per rating row

D = Mean roller diameter

D

Leff

TIMKEN DYNAMIC RADIAL RATING – TRB, MOST CRB AND MOST SRB

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• Rating Equations: Radial Capacity

bm = material factor and manufacturing quality. Current factor is 1.1.

fc = geometry, accuracy, and material factor

i = number of rows in a bearing

Lwe = effective roller length

= nominal contact angle of a bearing [deg]

Z = number of rollers in a single/multi-row bearing

Dwe = roller diameter

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294

3

9

7

1 cos wewecm DZiLfbC

D

L

ISO 281 DYNAMIC BEARING RATING – SOME CRB, SOME SRB, BALL

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Bearing Life Calculations: Single Row Bearings

WHAT IS BEARING “LIFE”?

• Multiple bearing damage modes exist

• Industry standardization of bearing life prediction needed

• Fatigue damage mode chosen as standard approach

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SINGLE BEARING FATIGUE LIFE

• A single bearing’s fatigue life is the time until a spall of a predefined area forms on a bearing contact surface due to fatigue

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CONTACT STRESS

Point Contact Line Contact

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CONTACT AND SUBSURFACE STRESS

Subsurface Stress

Contact Stress

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SUBSURFACE ORIGINATED FATIGUE CRACK EXAMPLES

Probable crack propagation paths

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BEARING POPULATION FATIGUE LIFE

L10 life:

• The number of hours (or revolutions) that 90% of a group of (apparently identical) bearings will meet or exceed, under a given set of conditions, before specified fatigue damage occurs

L = Fatigue Life of a rolling element bearing

10 = 10% of population with damage (reliability)

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WEIBULL DISTRIBUTION OF BEARING FATIGUE LIFE

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WEIBULL CUMULATIVE DISTRIBUTION FUNCTION

F(N) = Fraction failed by life N

N0 = Minimum life for any member

(often N0=0)

NA = Characteristic Life

(63.2% failure point where NA = N)

= Weibull slope

(1.5 for Timken roller bearings)

AN

NN

eNF

0

1)(

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WEIBULL STATISTICS OVERVIEW

• Bearings tested under identical loading conditions will have different lives.

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CATALOG L10 LIFE CALCULATIONS: GENERALIZED EQUATION

• Generally calculated from one of the following formulas:

speed

const

loadequiv

capacityL

loadequiv

capacityL

exp

hrs

exp

revs

.

.

.

,10

,10

capacity = Dynamic load rating equiv. load = Dynamic equivalent load speed = Bearing speed exp = Load-life exponent const. = Conversion factor

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CATALOG L10 LIFE CALCULATIONS: GENERALIZED EQUATION - TERMS

• Dynamic Load Rating (“capacity”) • This can be based on 1 million (C1 or Ca1)

or 90 million (C90 or Ca90) revolutions

• It can be radial (C1 or C90) or axial (Ca1 or Ca90)

• Dynamic Equivalent Load (“equiv. load”) • Can be Dynamic Equivalent Radial Load or Dynamic

Equivalent Axial Load, but it must match the rating (radial or axial)

• Units must also match those of the rating

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CATALOG L10 LIFE CALCULATIONS: GENERALIZED EQUATION - TERMS

• Bearing Speed (“speed”)

• Units are Revolutions Per Minute (RPM)

• Using this and the constant, the equation converts from revolutions to hours

• Exponent (“exp”)

• 10/3 for roller bearings

• 3 for ball bearings

• Constant (“const.”)

• A units conversion constant to convert:

• Rating based upon 1 million or 90 million revolutions

• Speed from RPM to revolutions/hour

• L10 life units (hours or revolutions)

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L10 LIFE CALCULATIONS: SPECIFIC BEARING TYPES

• Cylindrical Roller Bearings

• Tapered Roller Bearings

• Spherical Roller Bearings

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L10 LIFE CALCULATIONS: CYLINDRICAL ROLLER BEARINGS

• Variables:

• Dynamic Radial Equivalent Load

• C (or C1), Rating for 1 million revolutions

revs][million

[hours]667,16

3/10

1,10

3/10

1,10

P

CL

SP

CL

revs

hrs

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L10 LIFE CALCULATIONS: CYLINDRICAL ROLLER BEARINGS

• If the C90 rating is used, the constant changes accordingly when calculating L10 life in hours:

[hours]105.1

[hours]60/1090

63/10

90

63/10

90,10

S

x

P

C

S

x

P

CL hrs

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L10 LIFE CALCULATIONS: CYLINDRICAL ROLLER BEARINGS

• To avoid slippage, a minimum load should be maintained • Bearings with cage: P/C 0.02

• Full-complement: P/C 0.04

• Certain cylindrical roller bearings can carry some axial load • Engineering guideline - the axial load should not exceed

10% the radial load

• Applied load (P) should not exceed 1/3 of the load rating (C or C1) • The 10/3 load-life relationship is no longer as

appropriate at these load levels

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L10 LIFE CALCULATIONS: TAPERED ROLLER BEARINGS

• Variables:

• P, Dynamic Equivalent Radial Load (unless loading is axial only)

• C90, Rating for 90 million revolutions

[hours]105.1 63/10

90,10

S

x

P

CL hrs

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L10 LIFE CALCULATIONS: TAPERED ROLLER BEARINGS

• If only axial load is applied, the variables become:

• Pa – Dynamic Equivalent Axial Load

• Ca90 – Axial rating for 90 million revolutions

[hours]105.1 6

3/10

90,10

S

x

P

CL

a

ahrs

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L10 LIFE CALCULATIONS: SPHERICAL ROLLER BEARINGS

• Variables:

• Dynamic Equivalent Radial Load

• C (or C1) – Rating for 1 million revolutions

revs][million

[hours]667,16

3/10

1,10

3/10

1,10

P

CL

SP

CL

revs

hrs

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L10 LIFE CALCULATIONS: SPHERICAL ROLLER BEARINGS

• To avoid slippage, a minimum

load should be maintained • P/C 0.02

• Spherical roller bearings can carry axial load • Review the thrust load factor “e” • Engineering guideline = ¼ thrust to radial load

• Applied load (P) should not exceed 1/3 of the load rating (C or C1) • The 10/3 load-life relationship is no longer as

appropriate at these load levels

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Other Considerations

CONCLUSIONS FROM THE CATALOG L10 LIFE EQUATIONS

Roller Bearings:

2 X Load = 1/10 Life

1/2 Load = 10 X Life

+23% Load = ½ Life

2 X Speed = 1/2 Life

1/2 Speed = 2 X Life

[hours]

3/10

,10

S

constant

P

CL hrs

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ADVANCED USE OF L10 LIFE: SYSTEM LIFE

• Multiple-Bearing Systems

• Applications typically consist of more than a single bearing row

• The L10 life of the system is the time at which 90% of the bearings in the system would not have had any damaged bearings

• System L10 life is always lower than any individual bearing L10 lives within that system

3/2

2/3

,10

2/3

,10

2/3

,10

,10

111

nBA

systemLLL

L

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Bearing Life Calculations - Multiple-Row Bearings

TDO TDI

TIMKEN BEARING PRODUCTS

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TWO-ROW LIFE CALCULATION PROCEDURE

1. Determine applied forces

2. Calculate bearing reactions

3. Check thrust condition for fixed position

4. Determine dynamic equivalent radial load for fixed position

5. Calculate bearing L10 life for fixed position

6. Repeat steps 4-5 for the float position

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BEARING LIFE CALCULATION

A

Fixed Float

B C

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FIXED BEARING LIFE CALCULATION

• Timken Method:

• Evaluate life based on heaviest loaded single row

• Assumes row A is the heaviest loaded row

• Use C90(1)A, the single row rating

• The L10 system life for two-row bearing is:

SP

CL

A

A

A

6310

190

10

105.1

32

23

10

23

10

)(10

11

BA

AB LLL

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FLOAT BEARING LIFE CALCULATION

• Timken Method:

• Evaluate life based on the total radial load, Fr

• The two rows of the float position share the load equally

• Therefore the dynamic equivalent radial load is equal to the radial reaction, so: PC = FrC

• Note: Use C90(2)C, the two row rating

C90(2) 2 X C90(1)

C90(2) = 1.74 X C90(1)

SF

CL

rC

C

C

6310

290

10

105.1

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FLOAT BEARING LIFE CALCULATION

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C90(2) 2 X C90(1) C90(2) = 1.74 X C90(1)

QUESTIONS?

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BEARING RATINGS & LIFE EQUATIONS