Proceedings of SerbiaTrib '13

3.2. Film Thickness EquationThe film thickness between the skirts and the linergiven by Zhu [9]:h C ety ( t ) cos x eb( t ) et( t )] cos x (6)L 3.3. Reynolds’ Equation ModellingModified 2-D Reynolds equation is given as [2]:2 3 p R 3 p hTS h x h y 6U( ) (7)x x L y y xxwhere x and y are Poiseulle or pressure flowfactors and s is Cuotte or shear flow factor [2][8].The boundary conditions are defined as [4]:pxp 0x p =0 when x 1 ≤ x ≤ x 2p( ,0) p( , L) 0In dimensionless form the 2-D Reynoldsequation is given by [9][4]:20(8) 3 p* R 3 p* hT* Sh*x h*y * (9)x* x* L y* y* x*x*Where by J. H Tripp [8] 1 3( 2) /( 1)][ / h]X y = ( 1/ ) X2212 (h, 1) (hs, 2)2 s 2 s 3 (hs , 2) ( / h)( 1)and is the Peklenik number [10]In order to read the pressure profiles conveniently,the Vogelpohl parameter M v is introduced [4]:21.5M v p*h*The Reynolds equation in terms of the Vogelpohlparameter is given as:2 2 2Mv R Mv . x Mv2 2 (1 / ) ( ) . x* L . y* . x* . x*2 . y R.Mv (1 / ) ( ) FMvG. y* L. y*where(10)2 2 2 2 2 2h* R h* h* R h* 2 20.75 1.5x* Ly* x* Ly*F 2h* h*2h* Rh*1.5 x* x* L y* y* h * h* S * x* x*G 1.5( h * )Mvi ,, jRC. M M C.M ML 2. C 2.C F v i j v il j v i jlv i ji1 , 1, , , 2 , , , ,. * C. (1/ *)M M . x * 2. C 2.C F21 2 i,j3 vi , 1, j vi , l,j1 2 i,j. * C. (1/ *)M M G. y *2. C 2.C F4 vi , 1, j vi , l, j i.j1 2 i,j3.4. Film Thickness in EHL RegimeEHL regime the film thickness includes filmInthickness in the rigid hydrodynamic regime and theelastic surface displacements etc. By consideringthe bulk elastic deformation, the lubricant filmthicknessequation takes the following form [14] h f ( , y) vh eh ;where f(θ ,y ) is neglected. The differentialsurface displacement is [14]:1 p ( x , y ) dydydv E rr( xxy220) ( y0)221 1 (1 v 1) (1 v2) E 2 E1E2 At a specific point (x o , y o )deformation is [4]:1v( x0,y0)Eap(x,y)dxdyr4. RESULTS AND DISCUSSIONthe elasticThe hydrodynamic lubrication and EHL modelsof the piston skirts at 500 rpm are developed afterincorporating the pressure flow and the shear flowfactors. Two different oils having viscosity 0.016Pa.s and 0.1891 Pa.s are used for a comparison andinvestigating the viscosity effects on differentparameters which include film thickness206 13 th International Conference on Tribology – Serbiatrib’13