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    A Minimum Principle for the Law of Dry Friction, With Application to Elastic Cylinders in Rolling Contact—Part 1: Fundamentals—Application to Steady Rolling

    Source: Journal of Applied Mechanics:;1971:;volume( 038 ):;issue: 004::page 875
    Author:
    J. J. Kalker
    DOI: 10.1115/1.3408969
    Publisher: 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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      A Minimum Principle for the Law of Dry Friction, With Application to Elastic Cylinders in Rolling Contact—Part 1: Fundamentals—Application to Steady Rolling

    URI
    http://yetl.yabesh.ir/yetl1/handle/yetl/147745
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    contributor authorJ. J. Kalker
    date accessioned2017-05-09T00:47:15Z
    date available2017-05-09T00:47:15Z
    date copyrightDecember, 1971
    date issued1971
    identifier issn0021-8936
    identifier otherJAMCAV-25950#875_1.pdf
    identifier urihttp://yetl.yabesh.ir/yetl/handle/yetl/147745
    description abstractIn 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.
    publisherThe American Society of Mechanical Engineers (ASME)
    titleA Minimum Principle for the Law of Dry Friction, With Application to Elastic Cylinders in Rolling Contact—Part 1: Fundamentals—Application to Steady Rolling
    typeJournal Paper
    journal volume38
    journal issue4
    journal titleJournal of Applied Mechanics
    identifier doi10.1115/1.3408969
    journal fristpage875
    journal lastpage880
    identifier eissn1528-9036
    keywordsRolling contact
    keywordsCylinders
    keywordsDry-friction whip and whirl
    keywordsLinear programming
    keywordsTraction
    keywordsForce
    keywordsPressure
    keywordsFriction
    keywordsMotion AND Coulombs
    treeJournal of Applied Mechanics:;1971:;volume( 038 ):;issue: 004
    contenttypeFulltext
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