GENERALISED COMPUTATIONAL ANALYSIS OF CONTACT FATIGUE INITIATION

Transcription

1 UNIVERSITY OF MARIBOR FACULTY OF MECHANICAL ENGINEERING NAFEMS/FENET GENERALISED COMPUTATIONAL ANALYSIS OF CONTACT FATIGUE INITIATION M. Šraml, Z. Ren,, J. Flašker ker,, I. Potrč, M.Ulbin Zurich, June 22

2 CONTENTS OF THE PRESENTATION 1. INTRODUCTION OF THE FATIGUE OF METAL MATERIAL 2 2. MODELLING OF CONTACT FATIGUE OF MECHANICAL ELEMENTS 3. PROPOSED GENERAL MODEL OF CONTACT FATIGUE OF MECHANICAL ELEMENTS 4. APPLICATION: CONTACT FATIGUE OF SPUR GEARS DETERMINATION OF NiN 5. CONCLUSIONS, FURTHER WORK

3 INFLUENTIAL FACTORS ON OPERATIONAL STRENGTH 3 LOADS DIMENSIONING MANUFACTURING OPERATIONAL STRENGTH Measurement Simulation Strength Manufacturing Damage determination Chemical analysis Geometry Material Geometry Load Connections Stiffness Weigth Cutting shaping Non-cutting Standard testing Heat treatment Joining technics Surface protection Prototype manufacturing EVALUATION TESTING

4 FATIGUE ANALYSIS 4 Total Life Crack Initiation Crack Growth = Detail A + N TL N i N g

5 stage I (initiation) Fatigue crack initiation (detail A) stage II (crack growth) F Dynamic loading 5 t HOW? micro-structural changes growth and coalescence of microscopic cracks macro-cracks complete failure of structure WHERE? stress concentracion inclusions, short cracks stable propagation of dominant cracks in the direction of max. stress concentracion

6 Stress RESPONSE OF A MATERIAL TO CYCLIC LOADING Elastic shakedown Plastična ustalitev Plastic shakedown materiala Ratchetting 6 Purely elastic deformation Deformation p 3. 1 k 3.1k p 4k p > 4 k * k k k fatigue limit of the material in pure shear p max. Hertzian pressure

7 METHODS OF ANALYSES AND USED TOOLS THEORETICAL BACKGROUND (S-N N analysis, damage-tolerant criteria, theory of damage accumulation, ε-n N analysis) PHYSICALLY-EXSPERIMENTALLYSPERIMENTALLYLY RESULTS (microstructural changes in the material structure fatigue damage initiation ) 7 CONNECTION: Numerical analysis of contact stresses, determination of loading cycles, fatigue analysis) NUMERICAL MODELLING (MSC/NASTRAN, PATRAN, FATIGUE, Hertz, Trenje,, Contact 96)

8 METHODOLOGY OF MODELLING CONTACT FATIGUE 8 LOADING GEOMETRY MATERIALS CONTACT METHODS FOR DETERMINATION OF LOADING CYCLES AT CONTACT LOADING STRESS, STRAIN CYCLES CRITICAL PLANE APPROACH MICRO - MACRO APPROACH ELASTIC SHAKEDOWN LIMIT MODEL OF CRACK INITIATION LIFE PREDICTION INITIATION LIFE TIME Ni FRACTURE MECHANICS - LEFM Ng

9 Contact fatigue damage Case: GEARS Fatigue cracks due to rolling contact fatigue process 9 FATIGUE DAMAGE - PITTING

10 Contact fatigue damage Case: the RAIL 1 Shear plastic deformation at the layer under the contact surface FATIGUE CRACKS

11 Contact fatigue damage Case: the ROLLING BEARING 11 CONTACT FATIGUE: inner ring of the rolling bearing

12 EXISTING MODELS and IMPROVEMENTS OF NUMERICAL MODELLING OF CONTACT FATIGUE EXISTENT NEW STRESS ANALYSIS SURFAFE AND SUBSURFACE CONTACT STRESS ANALYSIS: CONTACT FATIGUE 12 DRAWBACKS: FATIGUE ANALYSIS LIFE PREDICTION Statical stress analysis Global state of material Time and place of fatigue damage initiation HARD TO ESTABLISH N i INFLUENCE OF OPERATIONAL CONDITIONS Hertzian boundary conditions, friction ε- N ANALYSIS: METHOD FOR FATIGUE CRACK INITIATION and CRITICAL PLANE APPROACH ADVANTAGES: Time depended loading cycles Local state of material Material models PREDICTION OF FATIGUE DAMAGE INITIATION N i

13 MODELLING OF ROLLING-SLIDING CONTACT 13 Rolling direction H τ yx σ y a a τ xy σ x z y σ z Finite element method continuum mechanichs Hertzian theory of contact Homogeneous eous, elastic material model

14 General model of contact fatigue 14 p(x), q(x) E* = MPa ν* =,3 Material: 42CrMo4 n'=,19, K'=2278 MPa σ m = 846 MPa σ Y = 6 MPa H 2a yi µ =,;,1;,2;,3;,4;,5 p =155 MPa 2a=,5476mm y x Determination of the rolling-contact loading cycle, for fatigue analysis

15 Influence of the friction coefficient on the contact stresses 15 1,9,8 p =155 MPa 2a=,5476 mm,7,6 Tresca/p,5,4,3,2,1 µ=, µ=,1 µ=,2 µ=,3 µ=,4 µ=,5,5,1,15,2,25,3,35,4,45 y i (mm)

16 Tre s c a/p Tresca/p Tresca/p,7,6,5,4,3,2,1,8,7,6,5,4,3,2 Loading cycles at rolling-sliding contact čas t µ =, p =155 MPa 2a=,5476mm y 1 y 2 =, mm =,25 mm y 3 =,533 mm y 4 =,852 mm y 5 =,1212 mm y 6 =,1619 mm y 7 =,278 mm y 8 =,2596 mm y 9 =,3181 mm y 1 =,3842 mm µ =,3 p =155 MPa 2a=,5476mm 16, čas t

17 ,3,2,1 Loading cycles at rolling-sliding contact µ =, p = 155 MPa 2a =,5476 mm 17 Tauxy/p τ xy /p -,1 -,2 -,3,4,3 čas t y 1 y 2 y 3 y 4 y 5 y 6 y 7 y 8 =, mm =,25 mm =,533 mm =,852 mm =,1212 mm =,1619 mm =,278 mm =,2596 mm y 9 =,3181 mm y 1 =,3842 mm Tauxy/p τ xy /p,2,1 -,1 -,2 čas t µ =,3 p = 155 MPa 2a =,5476 mm

18 Critical plane approach: Dang Van s fatigue theorem 18 τ a ( τ () t, σ () t ) a h t = t 2 t = t t 3 t = t 1 τ DV 1 τ e τ = τ a σ a e DV h * * τ DV 2 σ h τ / e a DV τ e τ = a σ τ a DV h e τ τ DV1 DV 2 τ τ a a () t + a σ () t DV () t a () DVσ h t < τ e h > τ e a DV = τ e σ / 2 e σ / 3 e = 3 2 2τ σ e σ e e

19 µ =. Results: critical plane approach,35,3,25 τ/p τ DV MATERIAL LINE = τ a () t + a σ () t DV h 19 σ h /p,2,15,1,5 -,8 -,7 -,6 -,5 -,4 -,3 -,2 -,1,1 µ =.3,4,35 τ/p,3,25,2,15,1 σ h /p,5 -,8 -,6 -,4 -,2,2,4 a DV =,3 k = 31 MPa 155_y1 155_y2 155_y3 155_y4 155_y5 155_y6 155_y7 155_y8 155_y9 155_y1

20 Example of determining the critical areas for fatigue damage due to cyclic contact loading p =155 MPa, 2a=,5476 mm on the contact surface (y 1 ) MATERIAL LINE 2,5,45 τ/p,4,35,3 µ =, 155 y1 µ =,3 µ =,5 155_3_y1 155_5_y1,25,2,15,1 σ h /p -1 -,8 -,6 -,4 -,2,2,4,5

21 Initiation of fatigue damage - ε-n N method 21 ' ε f ε 2 = σa E + ε 2 p = σ ' f E ' b ' ( 2N ) + ε ( 2N ) TOTAL DEFORMATION f f f c ε c 1 ε 2 p = ε ' f ( 2N ) c [ plastic part] f σ ' f E LCF HCF b 1 ' σ σ a f = E E b ( 2N ) [ elastic part] f loading cycles 2N f

22 Results: number of cycles for contact fatigue crack initiation 22 1,E+8 1,E+7 1,E+6 1,E+5 N i 1,E+4 1,E+3 1,E+2 1,E+1 Method of analyses: ε-n Plasticity correction: Neuberjeva Tresca_µ=, Tresca_µ=,1 Tresca_µ=,2 Tresca_µ=,3 Tresca_µ=,4 Tresca_µ=,5 1,E+,15,3,45 y i (mm)

23 Summary PROPOSED GENERAL NUMERICAL MODEL OF CONTACT FATIGUE OF MECHANICAL ELEMENTS 23 loading cycles at rolling-sliding contact, friction coefficient, different methods of analysis (ε-n, SWT,, Morrow), components of stress tensor, Neuber s plasticity correction, determination of the number of loading cycles for the fatigue damage initiation

24 Example: Contact fatigue of spur gears 24 Contact fatigue of spur gears ω 1 substitutional model D E C ω 2 B A Rolling Sliding Characteristic points and operational conditions on the gear tooth flank p(x), q(x) H A B C D E

25 The main parameters influencing contact fatigue at spur gears Hertzian pressure Substitutional radius Contact length Friction Coeficient A p [MPa] 142 * A R A [mm] 3,8999 2a,1843 µ A,188 AB p [MPa] 1148 * R [mm] 5,8198 AB 2a,2251 µ AB,975 AB B p [MPa] 1453 * R B [mm] 7,2562 B 2a,3555 µ B,175 C p [MPa] 1352 * R C [mm] 8,3821 C 2a,3821 µ C D p [MPa] 1325 * R D [mm] 8,7289 D 2a,39 µ D,14 E p [MPa] 1 * R [mm] 7,6637 E 2a,2584 µ E,868 E 25 E CRITICAL AREA for pitting - area of negative specific sliding D ψ 2 B C rolling A + + B C D - - ψ 1 E A sliding Specific sliding

26 Relations on the tooth flank 26,15,1,5 Rolling direction Sliding direction µ A B C D E -,5 -,1 -,15 Coefficient of friction course on the tooth flank (points A-E) σ H [MPa] Hertzian pressure 6 Tangential component of the contact pressure 4 2 D E A AB B C -2-4

27 Duration of loading cycle 27 ϕ u O 1 ω 1 Pinion z 1 =16, x 1 =.182, d 1 =72 mm, d a1 =82.45 mm moment of rotation: T=183.4 Nm Rotational velocity: n=2175 min -1 α T 1 S X A B C Gear z 2 =24, x 2 =.171, d 2 =18 mm, d a1 = mm D E Engagement angle: T 2 ϕ u = 38,26 ω 2 Engagement time: t u = 5,86 ms

28 ,2 1 Tresca /τ n 28,8,6,4,2 Loading cycles at rolling-sliding contact (point B - negative specific sliding) -,2,2 -,2 t σ 1 /σ n t y 1 y 3 y 5 y 7 y 2 y 4 y 6 y 8 -,4 y 9 y 1 -,6 -,8-1 -1,2

29 ,2 29 1,8,6,4,2 τ xy /τ n Loading cycles at rolling-sliding contact at point B (negative specific sliding) -,2 t y 1 y 3 y 2 y 4 -,4 y 5 y 6 -,6 y 7 y 8 -,8 y 9 y 1-1 Case designation Pr1 Pr2 Pr3 Pr4 Pr5 Pr6 Pr7 Pr8 Case description Average M achine and Shot Peened Average M achine Good M achine and Nitrided Polished Average M achine and Nitrided Polished and Shot Peened Shot Peened Poore M achined

30 Critical plane approach 3 Dang Van_B_y1 Dang Van_B_y3 Dang Van_B_y5 Dang Van_B_y7 Dang Van_B_y9 Dang Van_B_y2 Dang Van_B_y4 Dang Van_B_y6 Dang Van_B_y8 Dang Van_B_y1,35,3 τ/p B a DV =,3 k = 31 MPa,25,2 τ DV = τ a () t + a σ () t DV h,15,1,5 -,8 -,7 -,6 -,5 -,4 -,3 -,2 -,1,1 σ h /p B -,5

31 Results: fatigue crack initiation 31 Analysis of contact fatigue of the pinion (point B) - Number of Loading Cycles for Crack Initiation Ni Tresca stresses, ε-n analysis method, Neuber s plasticity correction N i = KU_Pr1 KU_Pr2 KU_Pr3 KU_Pr4 KU_Pr5 KU_Pr6 KU_Pr7 KU_Pr8,5,1,15,2,25,3,35 y i (mm)

32 Comparison: MODEL OF FATIGUE CRACK INITIATION ALONG SLIP BANDS q(x) p(x) Mura & Nakasone 32 Contact surfaces U 2 x y H h 2e U 1 2e- length of dislocation pile-up, crystal grain size, respectively, h - slip band width; U 1, U 2 - velocity H depth of the fatigue crack initiation, mesured from the contact surface FATIGUE CRACK INITIATION ALONG SLIP BANDS this is the idealization case, valid for homogeneous material model, without inclusions N i = f (place and mode of initiation, boundary conditions, stress field at the dislocations, irreversibility of the dislocations, shear stresses along slip bands, microstructure of material etc.) N i = (Glodež, 1996) EXPERIMENTS: (D. Dudely, 1996): N i =

33 ACHIVED GOALS OF THE PRESENTED WORK GENERAL MODEL FOR LIFE PREDICTION OF CONTACT FATIGUE CRACK INITIATION AT CONTACT LOADING, BASED ON THE CRITICAL PLANE APPROACH. 33 MODEL OF FATIGUE DIMENSIONINGIONINGING AT ROLLING-SLIDING CONTACT LOADING - the initiation of fatigue damage N i Application of the proposed new model: CONTACT FATIGUE OF TOOTH FLANKS

34 FURTHER WORK recommendations APPLICABILITY OF THE PROPOSED MODEL FOR DIFFERENT APPLICATIONS OF CONTACT FATIGUE (gears, wheel-rail, rolling bearings etc.) Additional loading conditions: lubrication, different material structure, inclusions, contact surface topography, contact temperature, residual stresses etc. Numerical modelling of micromechanical behaviour and their changes throughout the process of contact fatigue Experimental determination of required fatigue-material parameters, which will be needed for further developing of present numerical model. Models for prediction the total life (N( TL = N i + N g ) 34

35 Fatigue initiation analysis of gears (UP-TO DATE) OPERATING PITCH PITTING SPALLING EXPERIMENTAL MODELLING OF EARLY DETECTING OF FATIGUE DAMAGE AT GEARS 35 LOADING CYCLES MICROPITTING PITTING NEURAL NETWORKS- MODELS FILLET Batista A.C. et al. RENAULT (a) Carbonitrided surface of gear tooth flank (b) Additional mechanical treatment: shot-peening Ni Stabio et al. FIAT-Torino