Numerical analysis of fluid lubrication in line contact by using the MPS method
Numerical analysis of fluid lubrication in line contact by using the MPS method
复制标题
DOI：
10.1299/transjsme.20-00241
复制
发表时间：
2020
期刊：
影响因子：
--
通讯作者：
H. Negishi;Hironori Fujihara;Hidenao Takahashi;Kazuya Shibata;K. Maniwa;Shingo Obara
中科院分区：
文献类型：
--
作者：
H. Negishi;Hironori Fujihara;Hidenao Takahashi;Kazuya Shibata;K. Maniwa;Shingo Obara
流体膜润滑问题通常采用基于经典雷诺方程的模型来预测流体膜的压力分布和油膜厚度等行为，这需要在膜形成和分离位置有压力边界条件。当将经典方法应用于滚动轴承等实际应用时，由于复杂的几何形状、接触点周围的润滑油量未知以及多个润滑接触之间的相互作用，很难在适当的位置指定边界条件以求解雷诺兹方程。本文提出了一种求解用于预测流体膜行为的Navier-Stokes方程的一般方法，即移动粒子模拟（MPS）方法，该方法是一种无网格、拉格朗日、基于粒子的方法，适用于模拟移动或变形边界、多相流体、自由表面和复杂几何形状。将MPS方法应用于微米尺度的液膜润滑问题时，粘性项的计算是保证精度和鲁棒性的关键，因为粘性力对其他力起主导作用，影响数值稳定性。本研究使用了三种不同的MPS方法：(1)半隐式MPS方法，(2)隐式MPS方法，(3)显式MPS方法。它们通过使用虚拟表面粒子来增强压力泊松方程计算的鲁棒性，并且子时间步长方法可以使用大时间步长来显式计算粘性项。将所提出的方法应用于平面泊泽维尔流和线接触液膜润滑，通过适当的初始粒子距离和时间步长，分别与速度分布和压力分布的解析解具有较好的一致性。通过对大范围初始粒子距离和时间步长的参数化研究，揭示了基于Courant数的稳定性条件。结果表明，隐式MPS法具有最好的精度和稳定性，而显式MPS法在计算成本方面是最好的。
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.