Two dimensionless parameters controlling the occurrence of stick-slip motion in a 1-DOF system with Coulomb friction

The condition for the occurrence of stick-slip motion is examined analytically based on a 1-DOF system with Coulomb friction which includes seven independent parameters. There exist two dimensionless parameters which control the occurrence of stick-slip motion, one denotes the easiness for the occurrence of stick-slip motion and the other is the damping ratio acting to suppress the motion. A simple non-occurrence inequality of stick-slip motion is derived with the two dimensionless parameters through dimensionless analysis and numerical simulation, which has both high accuracy and high usability. Its validity is confirmed by the comparison with the experimental results reported by Singh.