Celtic Stone Dynamics Revisited Using Dry Friction and Rolling Resistance

J Awrejcewicz,G Kudra

doi:10.1155/2012/781573

Abstract

The integral model of dry friction components is built with assumption of classical Coulomb friction law and with specially developed model of normal stress distribution coupled with rolling resistance for elliptic contact shape. In order to avoid a necessity of numerical integration over the contact area at each the numerical simulation step, few versions of approximate model are developed and then tested numerically. In the numerical experiments the simulation results of the Celtic stone with the friction forces modelled by the use of approximants of different complexity (from no coupling between friction force and torque to the second order Padé approximation) are compared to results obtained from model with friction approximated in the form of piecewise polynomial functions (based on the Taylor series with hertzian stress distribution). The coefficients of the corresponding approximate models are found by the use of optimization methods, like as in identification process using the real experiment data.

Highlights

For small contact area between two bodies the sliding friction force opposes the sliding relative velocity and can be successfully modelled by the use of classical one-dimensional Coulomb friction law
Contensou [1] noticed that relative normal angular velocity is important for dynamics of some mechanical systems, where contact between two bodies or spin is relatively large
The present work aims at the development of the coupled approximate model of dry friction force and torque as well as the rolling resistance for elliptic contact area

Summary

Introduction

For small contact area between two bodies the sliding friction force opposes the sliding relative velocity and can be successfully modelled by the use of classical one-dimensional Coulomb friction law. We will refer to coupled model of friction force and torque as Coulomb-Contensou fritction model This direction of research led to the second-order Padéapproximants [3], more accurate and suitable for qualitative analysis. A three-dimensional friction model for circular areas but with the coupling between friction and rolling resistance, where rolling resistance is a result of distortion of contact stress distribution, is developed in the work [4]. In the work [6] the coupled friction model for circular contact area with central symmetry of contact stress distribution (without rolling resistance) was approximated by the use of Taylor expansion of the velocity pseudo po-. The present work aims at the development of the coupled approximate model of dry friction force and torque as well as the rolling resistance for elliptic contact area

Mathematical modeling of the Celtic stone

Model of normal stress distribution

Hertz contact and piecewise polynomial approximation

Other approximant models

Concluding remarks