A Minimum Principle for the Law of Dry Friction, With Application to Elastic Cylinders in Rolling Contact—Part 1: Fundamentals—Application to Steady RollingSource: Journal of Applied Mechanics:;1971:;volume( 038 ):;issue: 004::page 875Author:J. J. Kalker
DOI: 10.1115/1.3408969Publisher: The American Society of Mechanical Engineers (ASME)
Abstract: In Part 1 of the present paper a minimum principle for the Coulomb-Amontons law of friction is derived. This minimum principle is uniform in the sense that no distinction is made between the slip and the no-slip conditions. The principle is applied to the two-dimensional contact problem in which the normal pressure is Hertzian. After discretization, the principle leads to a linear programming problem in the case of steady rolling as considered by Carter [1] and Bentall and Johnson [2]. Good agreement is found with these authors, and the force-creepage law for elastically dissimilar cylinders has been calculated completely. In the case of the nonsteady contact problem, which is treated in Part 2 and in which the traction evolves under the influence of a gross motion and loading program, the principle leads to a time sequence of linear programming problems. Such problems under several restrictions have been treated before by Kalker [3–5], without the aid of minimization techniques. In the present paper these restrictions are all removed. Numerical results are presented.
keyword(s): Rolling contact , Cylinders , Dry-friction whip and whirl , Linear programming , Traction , Force , Pressure , Friction , Motion AND Coulombs ,
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contributor author | J. J. Kalker | |
date accessioned | 2017-05-09T00:47:15Z | |
date available | 2017-05-09T00:47:15Z | |
date copyright | December, 1971 | |
date issued | 1971 | |
identifier issn | 0021-8936 | |
identifier other | JAMCAV-25950#875_1.pdf | |
identifier uri | http://yetl.yabesh.ir/yetl/handle/yetl/147745 | |
description abstract | In Part 1 of the present paper a minimum principle for the Coulomb-Amontons law of friction is derived. This minimum principle is uniform in the sense that no distinction is made between the slip and the no-slip conditions. The principle is applied to the two-dimensional contact problem in which the normal pressure is Hertzian. After discretization, the principle leads to a linear programming problem in the case of steady rolling as considered by Carter [1] and Bentall and Johnson [2]. Good agreement is found with these authors, and the force-creepage law for elastically dissimilar cylinders has been calculated completely. In the case of the nonsteady contact problem, which is treated in Part 2 and in which the traction evolves under the influence of a gross motion and loading program, the principle leads to a time sequence of linear programming problems. Such problems under several restrictions have been treated before by Kalker [3–5], without the aid of minimization techniques. In the present paper these restrictions are all removed. Numerical results are presented. | |
publisher | The American Society of Mechanical Engineers (ASME) | |
title | A Minimum Principle for the Law of Dry Friction, With Application to Elastic Cylinders in Rolling Contact—Part 1: Fundamentals—Application to Steady Rolling | |
type | Journal Paper | |
journal volume | 38 | |
journal issue | 4 | |
journal title | Journal of Applied Mechanics | |
identifier doi | 10.1115/1.3408969 | |
journal fristpage | 875 | |
journal lastpage | 880 | |
identifier eissn | 1528-9036 | |
keywords | Rolling contact | |
keywords | Cylinders | |
keywords | Dry-friction whip and whirl | |
keywords | Linear programming | |
keywords | Traction | |
keywords | Force | |
keywords | Pressure | |
keywords | Friction | |
keywords | Motion AND Coulombs | |
tree | Journal of Applied Mechanics:;1971:;volume( 038 ):;issue: 004 | |
contenttype | Fulltext |