Nihon Kikai Gakkai ronbunshu (Sep 2020)
Numerical analysis of fluid lubrication in line contact by using the MPS method
Abstract
The fluid film lubrication problem is usually solved using classical Reynolds equation-based modeling to predict fluid film behavior such as pressure distribution and oil film thickness, which requires pressure boundary conditions at the locations of film formation and separation. When applying the classical approach to practical applications like rolling element bearings, it is difficult to specify boundary conditions at appropriate locations in order to solve the Reynolds equation due to complex geometry, unknown amount of oil lubricant around contacts, and interaction between multiple lubricated contacts. A general approach to solve the Navier-Stokes equations for predicting the fluid film behavior is proposed here using the moving particle simulation (MPS) method, which is a meshless, Lagrangian, particle-based method suitable to model moving or deforming boundaries, multiphase fluids, free surfaces, and complex geometry. When applying the MPS method to the micron-scale fluid film lubrication problem, calculating the viscous term is the key to ensure accuracy and robustness because the viscous forces are dominant over the other forces and affect the numerical stability. This study uses three different algorithms of the MPS method: (1) the semi-implicit MPS method, (2) the implicit MPS method, and (3) the explicit MPS method. They are employed by using virtual surface particles to enhance the robustness of the calculation of the pressure Poisson equation, and a sub-time step method enables the use of large time steps for calculating the viscous term explicitly. The proposed methods are applied to a plane Poiseuille flow and a fluid film lubrication in line contact, and show good agreement with analytical solutions of the velocity profile and the pressure profile respectively by using an appropriate initial particle distance and time step. A parametric study covering a wide range of initial particle distance and time step size reveals the stability conditions based on Courant number. The result confirmed that the implicit MPS method provides the best accuracy and stability, whereas the explicit MPS method is the best in terms of computational cost.
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