Improved Dynamic Friction Models for Simulation of One-Dimensional and Two-Dimensional Stick-Slip Motion

Abstract

In many mechanical systems, the tendency of sliding components to intermittently stick and slip leads to undesirable performance, vibration, and control behaviors. Computer simulations of mechanical systems with friction are difficult because of the strongly nonlinear behavior of the friction force near zero sliding velocity. In this paper, two improved friction models are proposed. One model is based on the force-balance method and the other model uses a spring-damper during sticking. The models are tested on hundreds of lumped mass-spring-damper systems with time-varying excitation and normal contact forces for both one-dimensional and two-dimensional stick-slip motions on a planar surface. Piece-wise continuous analytical solutions are compared with solutions using other published force-balance and spring-damper friction models. A method has been developed to set the size of the velocity window for Karnopp’s friction model. The extensive test results show that the new force-balance algorithm gives much lower sticking velocity errors compared to the original method and that the new spring-damper algorithm exhibits no spikes at the beginning of sticking. Weibull distributions of the sticking velocity errors enable maximum errors to be estimated a priori.

Modelling of stick–slip behaviour in a Girling brake using network simulation method

“…Karnopp has used the relation of the dynamic friction force during the slip phase formulated by Coulomb [42]. However, the friction force during the stick phase has been determined on basis of the equilibrium of forces.…”

Dynamic behavior of a smart device on a surface subjected to earthquake motion

“…In this paper, the Tariku and Rogers model is modified and used to model the sticking and sliding behavior of smart devices on an underlying moving surface. The model is validated by comparing its behavior to experimentally measured data.…”

Simulating Two-Dimensional Stick-Slip Motion of a Rigid Body using a New Friction Model

“…Experimentation with various numbers of steps showed that 20 sub-steps produces reasonable answers. To address the second problem, a new criterion is proposed to distribute the friction force using a modification of Tariku and Roger's assumption [5]. The original model proposed by Tariku and Roger [5] assumes that a block accelerates in the direction of the inertial force regardless of its previous velocity direction in the micro-slip region.…”

“…To address the second problem, a new criterion is proposed to distribute the friction force using a modification of Tariku and Roger's assumption [5]. The original model proposed by Tariku and Roger [5] assumes that a block accelerates in the direction of the inertial force regardless of its previous velocity direction in the micro-slip region. They considered the micro-slip region to be that where the magnitude of the sliding velocity is less than 0.1 mm/s [5].…”

“…The original model proposed by Tariku and Roger [5] assumes that a block accelerates in the direction of the inertial force regardless of its previous velocity direction in the micro-slip region. They considered the micro-slip region to be that where the magnitude of the sliding velocity is less than 0.1 mm/s [5]. In this work, the Tariku and Roger assumption is modified as follows: 1) CASE 1, where relative velocity is changing in only one direction, the accelerations of the block are calculated as a function of the magnitude of the accelerations of the surface in each direction, see Eq.…”