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Numerical Estimation of Frictional Torques with Rate and State Friction

In this paper, numerical estimation of frictional torques is carried out of a rotary elastic disc on a hard and rough surface under different rotating conditions. A one dimensional spring- mass rotary system is numerically solved under the quasistatic condition with the rate and state dependent friction model. It is established that torque of frictional strength as well as torque of steady dynamic stress increases with radius and found to be maximum at the periphery of the disc. Torque corresponding to frictional strength estimated using the analytical solution matches closely with the simulation only in the case of high stiffness of the connecting spring. In steady relaxation simulation, a steadily rotating disc is suddenly stopped and relaxational angular velocity and corresponding frictional torque decreases with both steady angular velocity and stiffness of the connecting spring in the velocity strengthening regime. In velocity weakening regime, in contrast, torque of relaxation stress deceases but relaxation velocity increases. The reason for the contradiction is explained.