Friction-Induced Vibration in a Bi-Stable Compliant Mechanism

Niknam Niknam,Farhang Farhang

doi:10.3390/vibration2040018

Niknam Niknam, Farhang Farhang

Open Access

https://doi.org/10.3390/vibration2040018

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Journal: Vibration	Publication Date: Oct 9, 2019
Citations: 1	License type: CC BY 4.0

Affiliation: Southern Illinois University Carbondale

Abstract

This paper investigates friction-induced self-excited vibration in a bi-stable compliant mechanism. A single-degree-of-freedom oscillator, hanged vertically, vibrates on a belt moving horizontally with a constant velocity. The oscillator is excited through the frictional input provided by the belt. The friction coefficient is defined as an exponentially decaying function of the sliding velocity. Due to the specific configuration of spring and damper, the normal contact force is variable. Therefore, the friction force is a function of the system states, namely, slider velocity and position. Employing eigenvalue analysis gives an overview of the local stability of the linearized system in the vicinity of each equilibrium point. It is shown that the normal force, spring pre-compression and belt velocity are bifurcation parameters. Since the system is highly nonlinear, a local analysis does not provide enough information about the steady-state response. Therefore, the oscillating system is studied numerically to attain a global qualitative picture of the steady-state response. The possibility of the mass-belt detachment and overshoot are studied. It is shown that one equilibrium point is always dominant. In addition, three main questions, i.e., possible mass-belt separation, location of stick-slip transition and overshoot are answered. It is proven that the occurrence of overshoot is impossible.

Highlights

Compliant mechanisms are widely employed in various applications due to their potential advantages over conventional mechanisms, from a designing and manufacturing point of view [1]
We investigated the friction-induced vibration in a bi-stable compliant mechanism with large displacement and variable normal contact force
It should be noted that three different velocities, i.e., V = 0.1, 0.33 and 0.5, were chosen to observe Hopf-bifurcation in the global qualitative response

Summary

Introduction

Compliant mechanisms are widely employed in various applications due to their potential advantages over conventional mechanisms, from a designing and manufacturing point of view [1]. Li et al studied friction-induced instability in an asymmetrical archetypal self-excited oscillator by introducing the Stribeck effect, where the damping force does not have a vertical component [19]. This model does not properly represent the viscoelastic behavior in the system. The friction coefficient was defined as a, well-known, exponentially decaying function of the relative velocity in contact interface Such a definition of friction provided an equivalent negative damping, i.e., Stribeck effect, in the system which may have caused instability. Sprag-slip response can be observed in the proposed model when the oscillator experienced self-locking against the sliding surface

Mechanical Model

Linearized Stability

Numerical Results

11. Conclusions