Stabilization of frictional sliding by normal load modulation: A bifurcation analysis

TL;DR

This study investigates how periodic normal load modulation affects the stability of low-velocity frictional sliding, demonstrating that vibrations can suppress stick-slip oscillations and mapping the stability conditions through a validated mechanical model.

Contribution

The paper introduces a stability analysis of frictional sliding under normal load modulation, incorporating asperity shear stiffness and validating results with experimental data.

Findings

Normal vibrations stabilize low-velocity sliding against stick-slip.

The mechanical model accurately predicts stability regions.

Large amplitude modulations may destabilize due to non-linear effects.

Abstract

This paper presents the stability analysis of a system sliding at low velocities ($< 100 \mu$m.s$^{-1}$) under a periodically modulated normal load, preserving interfacial contact. Experiments clearly evidence that normal vibrations generally stabilize the system against stick-slip oscillations, at least for a modulation frequency much larger than the stick-slip one. The mechanical model of Bureau {\it et al.} (2000), validated on the steady-state response of the system, is used to map its stability diagram. The model takes explicitly into account the finite shear stiffness of the load-bearing asperities, in addition to a classical state- and rate-dependent friction force. The numerical results are in excellent quantitative agreement with the experimental data obtained from a multicontact frictional system between glassy polymer materials. Simulations at larger amplitude of modulation (typically 20% of the mean normal load) suggest that the non-linear coupling between normal and sliding motion could have a destabilizing effect in restricted regions of the parameter space.