Bearing Ratings & Life Equations. Timken Training

Transcription

1 Bearing Ratings & Life Equations Timken Training

2 AGENDA Load Ratings Single-Row Life Equations Multiple-Row Life Equations 2

3 BEARING RATING & BEARING LIFE Bearing Rating: Bearing Life: Describes the expected load a part can carry Determined by geometry and material of bearing A variable used to calculate estimated life (L10) Estimated time bearing will run before predetermined amount of damage occurs Determined by application conditions, bearing rating, and bearing performance enhancements 3

4 Bearing Ratings

5 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. 5

6 6 TIMKEN BEARING TESTING

7 DYNAMIC LOAD RATING Used for estimating the life of a rotating bearing. Symbol is C 90 or C (90) for radial rating Symbol is Ca 90 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 0.01in 2 (6mm 2 ) spall develops. Rating verified by testing at given reference conditions 7

8 DYNAMIC LOAD RATING REFERENCE CONDITIONS Load: F r = 150% C 90 Speed: S = 500 RPM Lubrication: Oil viscosity = C (155 SUS at 130 F) Temperature: T = 55 C (130 F) Setting: 150 load zone Alignment: < radians Fatigue spall size: 6 mm 2 (0.01 in 2 ) 8

9 BEARING RATINGS Timken ratings based on C 90 yet many ratings are published as C 1 3 To convert C 1 to C 90 C C C 3.86C Using C 1 in L 10 equation L 10 3 C1 10 P Revolution s 9

10 BEARING RATINGS C 1 is a theoretical number. The bearing should never be loaded to this magnitude. Working load range is 1/3 of the C 1 rating. 10

11 TIMKEN DYNAMIC RADIAL RATING TRB, MOST CRB AND MOST SRB Rating Equations: Radial Capacity 7 10 C = H M Z L cos 5 N D H M Z L N D = Geometry dependent factor = Material constant = Number of bearing rows in assembly = Effective roller contact length = 1/2 Included cup angle = Number of rollers per rating row = Mean roller diameter L eff D 11

12 ISO 281 DYNAMIC BEARING RATING SOME CRB, SOME SRB, BALL Rating Equations: Radial Capacity C b m = material factor and manufacturing quality. Current factor is 1.1. f c = geometry, accuracy, and material factor i = number of rows in a bearing L we = effective roller length = nominal contact angle of a bearing [deg] Z = number of rollers in a single/multi-row bearing D we = roller diameter bm fc we cos we il Z D L D 12

13 Bearing Life Calculations: Single Row Bearings

14 WHAT IS BEARING LIFE? Multiple bearing damage modes exist Industry standardization of bearing life prediction needed Fatigue damage mode chosen as standard approach 14

15 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 15

16 CONTACT STRESS Point Contact Line Contact 16

17 CONTACT AND SUBSURFACE STRESS Contact Stress Subsurface Stress 17

18 SUBSURFACE ORIGINATED FATIGUE CRACK EXAMPLES Probable crack propagation paths 18

19 BEARING POPULATION FATIGUE LIFE L 10 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) 19

20 20 WEIBULL DISTRIBUTION OF BEARING FATIGUE LIFE

21 WEIBULL CUMULATIVE DISTRIBUTION FUNCTION F ( N ) 1 e N N N A 0 F(N) = Fraction failed by life N N 0 = Minimum life for any member (often N 0 =0) N A = Characteristic Life (63.2% failure point where N A = N) = Weibull slope (1.5 for Timken roller bearings) 21

22 WEIBULL STATISTICS OVERVIEW Bearings tested under identical loading conditions will have different lives. 22

23 CATALOG L 10 LIFE CALCULATIONS: GENERALIZED EQUATION Generally calculated from one of the following formulas: L 10, revs L 10, hrs capacity equiv. load capacity equiv. load exp exp const. speed capacity = Dynamic load rating equiv. load = Dynamic equivalent load speed = Bearing speed exp = Load-life exponent const. = Conversion factor 23

24 CATALOG L 10 LIFE CALCULATIONS: GENERALIZED EQUATION - TERMS Dynamic Load Rating ( capacity ) This can be based on 1 million (C 1 or C a1 ) or 90 million (C 90 or C a90 ) revolutions It can be radial (C 1 or C 90 ) or axial (C a1 or C a90 ) 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 24

25 CATALOG L 10 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 L 10 life units (hours or revolutions) 25

26 L 10 LIFE CALCULATIONS: SPECIFIC BEARING TYPES Cylindrical Roller Bearings Tapered Roller Bearings Spherical Roller Bearings 26

27 L 10 LIFE CALCULATIONS: CYLINDRICAL ROLLER BEARINGS Variables: Dynamic Radial Equivalent Load C (or C 1 ), Rating for 1 million revolutions L L 10, hrs 10, revs C P 1 C P 1 10/3 10/3 16,667 S [million revs] [hours] 27

28 L 10 LIFE CALCULATIONS: CYLINDRICAL ROLLER BEARINGS If the C 90 rating is used, the constant changes accordingly when calculating L 10 life in hours: L10, hrs C P 90 10/3 90x10 S 6 / 60 [hours] C P 90 10/3 1.5x10 S 6 [hours] 28

29 L 10 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 C 1 ) The 10/3 load-life relationship is no longer as appropriate at these load levels 29

30 L 10 LIFE CALCULATIONS: TAPERED ROLLER BEARINGS Variables: P, Dynamic Equivalent Radial Load (unless loading is axial only) C 90, Rating for 90 million revolutions 10/3 6 C90 1.5x10 10, P S L hrs [hours] 30

31 L 10 LIFE CALCULATIONS: TAPERED ROLLER BEARINGS If only axial load is applied, the variables become: P a Dynamic Equivalent Axial Load C a90 Axial rating for 90 million revolutions 10/3 6 C , a x L hrs Pa S [hours] 31

32 L 10 LIFE CALCULATIONS: SPHERICAL ROLLER BEARINGS Variables: Dynamic Equivalent Radial Load C (or C 1 ) Rating for 1 million revolutions L L 10, hrs 10, revs C P 1 C P 1 10/3 10/3 16,667 S [million revs] [hours] 32

33 L 10 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 C 1 ) The 10/3 load-life relationship is no longer as appropriate at these load levels 33

34 Other Considerations

35 CONCLUSIONS FROM THE CATALOG L 10 LIFE EQUATIONS Roller Bearings: 10/3 C constant L10, hrs P S [hours] 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 35

36 ADVANCED USE OF L 10 LIFE: SYSTEM LIFE Multiple-Bearing Systems Applications typically consist of more than a single bearing row The L 10 life of the system is the time at which 90% of the bearings in the system would not have had any damaged bearings System L 10 life is always lower than any individual bearing L 10 lives within that system L 10, system 1 L 10, A 3 / 2 1 L 10, B 3 / 2 1 L 10, n 3 / 2 2 / 3 36

37 Bearing Life Calculations - Multiple- Row Bearings

38 TIMKEN BEARING PRODUCTS TDO TDI 38

39 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 L 10 life for fixed position 6. Repeat steps 4-5 for the float position 39

40 BEARING LIFE CALCULATION A B C Fixed Float 40

41 FIXED BEARING LIFE CALCULATION Timken Method: Evaluate life based on heaviest loaded single row Assumes row A is the heaviest loaded row Use C 90(1)A, the single row rating L 10 A C 90 P 1 A The L 10 system life for two-row bearing is: L 10( AB) A 1 L 10 A L 10B S

42 FLOAT BEARING LIFE CALCULATION Timken Method: Evaluate life based on the total radial load, F r The two rows of the float position share the load equally Therefore the dynamic equivalent radial load is equal to the radial reaction, so: P C = F rc L 10C C 90 F 2 rc C S 6 Note: Use C 90(2)C, the two row rating C 90(2) 2 X C 90(1) C 90(2) = 1.74 X C 90(1) 42

43 FLOAT BEARING LIFE CALCULATION C 90(2) 2 X C 90(1) C 90(2) = 1.74 X C 90(1) 43

44 BEARING RATINGS & LIFE EQUATIONS QUESTIONS? 44

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