Solution of nonlinear friction forces when friction interfaces constrained to complex contact motions

A numerical method was developed and used to calculate the nonlinear friction force by tracing the trajectory of the relative motion of the moving contact point when friction interfaces constrained to complex contact motions. The calculated results display that when the contact motion is ellipse, the results of the friction forces calculated by the numerical method is more accurately; the difference of the phase between the normal motion and the tangential motion can not be ignored when calculating the contact friction forces because this difference of the phase has a great effect on the transit of the contact state, the numerical value of the friction forces and the shape of the hysteresis loop; when friction interfaces constrained to three-dimensional motion, the coupling of the normal motion with the tangential motions of two directions must be considered simultaneous. This numerical method can be used to solve friction forces when friction interfaces constrained to one-dimensional motion, two-dimensional motion and even three-dimensional motion, so it is a very convenient method to calculate the nonlinear friction forces during solve the vibration responses of the structures with dry friction damping.