Friction-induced vibration in a two-mass damped system

Abstract

A two degree of freedom mass-spring-damper model on a moving lubricated belt is considered in this paper. The motions of the two masses are coupled through spring and damper and each mass interacts with a moving lubricated belt. The friction model includes the boundary, mixed and hydrodynamic regimes of lubrication contact regimes. Friction coefficient is presented as a function of sliding velocity at each mass interface that includes a combination of linear, exponential and cubic functions to account for relatively large coefficient at low sliding speed, followed by Stribeck effect at low to moderate speed ranges and finally a full hydrodynamic lubrication regime. A set of dimensionless parameters is introduced and system's dynamic response behavior as well as stability are studied for various combination of parameters. The results show that the unstable system response can be quasiperiodic, or periodic in the form of limit cycles away from the origin when the sliding velocity is relatively small. Triple and double periodic behavior is observed in addition to other responses when mass suspended to the ground is larger than the second mass. All responses become asymptotically stable when dimensionless sliding velocity threshold is exceeded. Finally, for a qualitative analysis, the method of averaging is used to solve the nonlinear coupled equations of motion in order to find the amplitude and frequency of steady-state vibration. A comparison between the numerical results from direct time integration and analytical findings shows that approximate solution is acceptable.