Stiffness and damping characteristics of lubricated ball bearings considering the surface roughness effect. Part 1: theoretical formulation

The stiffness and damping characteristics of isothermal, elastohydrodynamically lubricated point contact problems are evaluated numerically considering the surface roughness effect and variation in viscosity with pressure. A set of equations under steady-state and dynamic conditions is derived from the classical Reynolds equation using the linear perturbation method. The elasticity equation and steady-state Reynolds equation are solved simultaneously using the finite difference method with the successive over-relaxation scheme, whereas the dynamic pressures are found after solving the set of perturbed equations using the previously obtained steady-state pressures. The load capacity is obtained from the steady-state pressure distribution. The stiffness and damping coefficients of the contact are determined using the dynamic pressures. Then the overall stiffness and damping matrices of the ball bearing are obtained from the load distribution, coordinate transformation, and compatibility relations.