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.
Highlights
Friction-induced vibration is usually known as self-excited vibration by friction producing unwanted phenomena such as vibration, noise, and fatigue
The minimal model has been widely used to explain the dynamic instability induced by the negative friction-slope and mode-coupling instability [10,11,12,13]
A stability analysis based on linear eigenvalue analysis was performed and stability boundaries in the parameter space were derived for the equilibrium of the system
Summary
Friction-induced vibration is usually known as self-excited vibration by friction producing unwanted phenomena such as vibration, noise, and fatigue. A stability analysis based on linear eigenvalue analysis was performed and stability boundaries in the parameter space were derived for the equilibrium of the system. Their nonlinear stick-slip oscillations at the unstable steady-sliding equilibrium have been demonstrated by solving discontinuous differential equations using several different friction models such as the smoothing [10]. In this scenario, the determination of the dynamic instability in the parameter space is valid when steady-sliding exists, and the resulting nonlinear motion in this space can be reasonably found
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