A mixed lubrication simulation model of conical piston ring with outer steps liner system was set up by considering the influence of the piston ring size,elastic and roughness,and the lubricating oil viscosity.Based on the finite difference method and the integral method,one dimensional average Reynolds equation was solved respectively,and the oil film thickness,pressure and friction of whole working cycle were got.The calculation results show that,the integral method has faster speed in solving Reynolds equation,and the application framework is simple and clear.However,the derivation of the integral method is influenced by the type line of piston ring,and the finite difference method is unrelated with the type line of piston ring.The difference of the oil film thickness by two algorithms is large due to adopting different oil film rupture boundaries when piston ring running up,and the Reynolds boundary conditions for the finite difference method are more accurate on the determination of boundary compared with the half Sommerfeld boundary conditions for the integral method.