Minimal Model for Sprag-Slip Oscillation as Catastrophe-Type Behavior

Abstract

The infinite spragging force can be produced by a spring inclined with a constant angle in a frictional sliding system. The ensuing oscillation is called the sprag-slip oscillation. This sprag-slip oscillation is re-examined by using the minimal nonlinear dynamic model with the variable angle of the inclined spring. Nonlinear equilibrium equation is converted into the novel polynomial form. This simple but more realistic sprag model shows that the infinite spragging force is not realistic and the catastrophic static deformation in the steady-sliding state can occur. It indicates that the ‘sprag’, termed by Spurr, can be described by this catastrophic characteristic of the frictional sliding system.

Keywords

• sprag-slip
• Painleve paradox
• friction-induced vibration
• catastrophe
• cusp catastrophe