Transient elastohydrodynamic point contact analysis using a new coupled differential deflection method Part 1: Theory and validation

Abstract

The paper presents a transient analysis technique for point contact elastohydrodynamic (EHL) lubrication problems using coupled elastic and hydrodynamic equations. Full coupling is made possible by use of a novel differential de¯ection formulation. The way in which the differential de¯ection is incorporated into the overall solution method for a point contact is discussed. A range of spatial and temporal discretization methods are incorporated and compared. The method is validated under transient conditions by a detailed comparison with published work produced using a different, independent method incorporating a moving roughness feature.A comparison of the results with different discretization methods leads to the conclusion that spatial central differencing with a Crank±Nicolson temporal discretization is the most effective ®nite difference scheme, and this is generally equivalent to the ®nite element discretization given in detail in the paper. A comparison of the results produced for moving rough surfaces suggests that the ®nite element formulation is preferred. NOTATIONheight of the surface feature de®ned by equation (12) (m) E 0 effective modulus of elasticity (Pa) f i, j pressure coef®cient in the differential de¯ection equation (m ¡1 ) F factor determining timestepˆU UDt=Dx h ®lm thickness (m) h 0 constant in the ®lm thickness equation (3) (m) L Moes and Bosma non-dimensional parameterˆaE 0 ‰2Z 0 U U=…E 0 R R †Š 1=4 M Moes and Bosma non-dimensional parameterˆ‰w=…E 0 R R 2 †Š‰E 0 R R=…2Z 0 U U †Š 3=4 n c number of neighbouring mesh points in discretization N i shape function p pressure (Pa) p hz maximum pressure in Hertzian contact (Pa) Pˆp=p hz in Figs 4 to 7 R x , R y radii of relative curvature in axis directions (m) R R 2R x R y =…R x ‡ R y † (m) u total de¯ection of the surfaces perpendicular to the xy plane (m) U U, V V mean surface velocities in axis directions (m/s) w load (N) W b width of surface feature de®ned by equation (12) (m) x, y coordinates in the contact plane (m) x b x coordinate of the centre of the ridge feature (m) Z parameter in the viscosity equation (5) a=‰w ln…Z 0 =k †Š a pressure viscosity coef®cient (Pa ¡1 ) g coef®cient in the density equation (6) (Pa ¡1 ) Dt timestep (s) Dx, Dy mesh spacing in coordinate directions (m) Z viscosity (Pa s) The MS was Downloaded from Z 0 viscosity at ambient pressure (Pa s) k coef®cient in the viscosity equation (5) (Pa s) l coef®cient in the density equation (6) (Pa ¡1 ) x slide±roll ratio r density (kg/m 3 ) r 0 density at ambient pressure (kg/m 3 ) s x , s y¯o w coef®cients in axis directions (m s) t 0 non-Newtonian shear stress parameter (Pa) f surface roughness feature (m) w coef®cient in the viscosity equation (5) (Pa ¡1 )

Contact fatigue initiation and tensile surface stresses at a point asperity which passes an elastohydrodynamic contact

“…The model was verified against the results by Holmes et al [68] for a ball on disk contact with a transverse ridge passing with the lubrication entrainment speed. Holmes et al [68] validated their model against Venner [73].…”

“…C1c are plotted against the number of nodes in the rolling direction, . Holmes et al [68] show in a similar graph for a point contact that the solutions for the film thickness converge with increasing node numbers. Based on Fig.…”

“…C1. a) Model validation against Holmes et al [68] for transverse ridge passing a rolling sphere with parameters in Table C1. Convergence study for spatial resolution of h in b) and p in c) for rolling smooth cylinder.…”

“…Holmes et al [68] investigated the influence of spatial and time resolution for the transient problem of a spherical contact over-rolling a transvers ridge. The accuracy of the present model was evaluated similarly; see Appendix C. Based on the analyses, the selected space resolution with 201 • 97 nodes in the -directions together with 402 time steps for the overrolling sequence was judged as a sufficiently good compromise between accuracy and simulation time.…”

“…Holmes et al [68] validated their model against Venner [73]. The reference models were temperature independent.…”