Investigation of the closed form solutions and new algorithm for two-dimensional frictional system

The closed form solutions for two-dimensional Coulomb frictional systems are proposed in path coordinated system. The system will stick when the dimensionless force ratio F>1 and the position and time for sticking have also been presented, which could be utilized to predict the moment when stick commence accurately. There exist sharp bending corner, characterized by fierce slip direction variation, in the trajectory of system when F>1 and the initial launch angle θ is very large, which denotes an opposite initial direction between external force and slip and this kind of sharp bending corner is very close to the slip/stick transition position. Numerical difficulties is introduced by slip/stick transitions and sharp bending corner on the trajectories when traditional numerical integration methods are employed to solve the responses of two-dimensional Coulomb frictional system. If the time step size is sufficient small, the time varying external excitation forces can be treat as constant and thus all those closed form solutions can be employed to propose a new numerical frictional algorithm, which can be utilized to analyze the microslip, wear and energy dissipation for rough contacting surfaces represented by multi-nodes model. © 2016 Journal of Mechanical Engineering.