Elasto-Hydrodynamic Lubrication problem as Differential Algebraic Equations

In this manuscript a computational method to simulate the transient Elasto-Hydrodynamic Lubrication (EHL) of line- contacts tribo-system is presented. The theory behind the developed code is based on the simultaneous addressing of the fluid lubrication dynamics, the solid deformation mechanics and the load approach dynamics into a system of Differential Algebraic Equations (DAEs), which is numerically marched over time with Implicit Runge-Kutta (IRK) methods: constant tribo-system operating conditions were simulated in order to validate the method. The reliability of the proposed approach was demonstrated based on the comparison with respect to empirical benchmarks.