NUMERICAL INVESTIGATION OF STEADY WEAR PROCESS

1. NUMERICAL INVESTIGATION OF STEADY WEAR PROCESS Páczelt István University of Miskolc, Department of Mechanics , Miskolc, Hungary 2-nd Hungarian-Ukrainian Joint Conference on SAFETY-RELIABILITY AND RISK OF ENGINEERING PLANTS AND COMPONENTSKYIV, September 19-21, 2007.

2. A contact problem

3. Linear elastic contact problems Contact conditions

4. Signorinicontact conditions Frictionconditions: In adhesion subregion In slip subregion

5. Contact stresses

6. Clasification of mechanical wear processes

7. Factors influencing dry wear rates

8. Modified Archard wear model

9. Problem classification 1. Rigid body wear velocities allowed, contact area fixed-steady states present

10. 2.Rigid body wear velocities allowed, contact area evolving in time due to wear-quasi steady states

11. 3.No rigid body wear velocities allowed- steady states corresponding to vanishing wear rate and contact pressure (wear shake down).

12. Initial gap g= g_0 =0.05 mm, • Beam side a_0=10 mm, b_0=25 mm, lenght L=300 mm. • Load F_0=10 kN, AB distance (a) =150mm, • Relative velocity v_r=50 mm/s • Coefficient of Winkler foundation= 0.0000002 mm/N

13. The wear parameters are: beta=0.0025, a=b=1 • coefficient of friction mu=0.3 • In initial state: (u1_n beam displacement in vertical direction without body 2.) • def1, def2 are vertical displacement of body 1 and 2 in the contact.

14. Initial state:

15. In the time t=0.8 sec

16. In the time t=1200*dt=1200*0.001=1,2 sec

17. In the time t=2,4 sec

18. In the time= 3,6 sec

19. In the time= 7,8 sec

20. In the time=12 sec

21. Inthe time=60 secHere p_n= 1*10e-7 that is practically p_n is equal to zero.

22. 4. Oscillating sliding contacts (fretting process)

23. Type of investigated mechanical systems The analysis of the present investigation is referred to such class of problems when • the contact surface does not evolve in time and is specified • the wear velocity associated with rigid body motion does not vanish and is compatible with the specified boundary conditions

24. [1] Páczelt I, Mróz Z. On optimal contact shapes generated by wear, Int. J. Num. Meth. Eng. 2005;63:1310-1347. [2] Páczelt I, Mróz Z. Optimal shapes of contact interfaces due to sliding wear in the steady relative motion, Int. J. Solids Struct 2007;44:895-925. [3] Pödra P, Andersson S. Simulating sliding wear with finite element method, Tribology Int 1999;32:71-81. [4] Öqvist M. Numerical simulations of mild wear using updated geometry with different step size approaches, Wear 2001;49:6-11. [5] Peigney U. Simulating wear under cyclic loading by a minimization approach, Int. J. Solids Struct 2004;41: 6783-6799. [6] Marshek KM, Chen HH. Discretization pressure wear theory for bodies in sliding contact, J. Tribology ASME 1989; 111:95-100. [7] Sfantos GK, Aliabadi MH. Application of BEM and optimization technique to wear problems, Int. J. Solids Struct 2006;43:3626-3642. [8] Kim NH, Won D, Burris D, Holtkamp B, Gessel GC, Swanson P, Sawyer WG. Finite element analysis and experiments of metal/metal wear in oscillatory contacts, Wear 2005;258:1787-1793. [9] Fouvry S. et al. An energy description of wear mechanisms and its applications to oscillating sliding contacts, Wear, 2003;255:287-298

25. The generalized wear volume rate Generalized friction dissipation power

26. The generalized wear dissipation power For one body For two bodies q>0 where the control parameterq usually is

27. The relative tangential velocity on • sliding velocity at the interface • wear velocity are the relative translation and rotation velocities induced by wear

29. The generalized wear dissipation power Wear rate vectors: . Relative velocity:

30. The global equilibrium conditions forbody 1 are

32. Constrained minimization • Problem PW1: Min • Problem PW2: Min • Problem PW3: Min subject to

33. Major results of our investigation: • Question: What kind of minimization problem generates contact pressure distribution corresponding to the steady wear state? • Answer: Must be used: min

34. Main assumption: • We shall consider only the generalized wear dissipation power and the resulting optimal pressure distribution. • It will be shown that for q=1, the optimal solution corresponds to steady state condition.

35. Congruency conditions • In stationary translation motion: • In rotation with constant angular velocity: the case of annular punch:

36. The Lagrangian functional is Introducing the Lagrange multipliers and

37. From the stationary condition we obtain The equations are highly nonlinear !

38. Special case 1 • the contact pressure is • the wear rate equals • the wear volume rate is

39. Special case2: translation and rotation SCx=60 mm,SCy=80 mm

42. Special case 3:Block-on-disk wear tests

43. Results At steady wear state (q=1)

44. Contact pressure distribution for anticlockwise disk rotation

45. Vertical wear rate distribution for clockwise disk rotation

46. Normal contact shape for different values of friction coefficient, q=1

47. Vertical contact shape for different values of friction coefficient, q=1

48. Steady state normal and vertical wear rate distributions

49. Special case 4:ring segment-on-disk wear tests .

50. Initial contact pressure distribution (anticlockwise rotation).