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Theoretical Model for Friction-Induced Vibration of Ball Joint System under Mode-Coupling Instability

A theoretical model for the friction-induced vibration in ball joint systems is proposed. In a ball joint system, a small contact area is formed on the surface of the ball due to clearance between the ball and hemispherical cup. To analyze the dynamic instability induced by friction in the ball joint system, the dynamic beam-on-socket model with nonconformal contact under three-dimensional rotation was theoretically proposed. The results from stability analysis revealed that the mode-coupling type instability occurred for the lower bending modes at a specific combination of rotation components as well as an increase in the friction coefficient. In particular, the spinning component was essential in generating the mode-coupling instability between the doublet bending modes of the beam.