An Elasto-plastic Contact Solving Method for Two Spheres
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ISSN 1860-2134
An Elasto-plastic Contact Solving Method for Two Spheres Jizhong Zhao1
Qianhua Kan1
Peilin Fu1
Guozheng Kang1
Ping Wang2
1
( Applied Mechanics and Structure Safety Key Laboratory of Sichuan Province, School of Mechanics and Engineering, Southwest Jiaotong University, Chengdu 610031, China) (2 Key Laboratory of High-speed Railway Engineering, Ministry of Education, Southwest Jiaotong University, Chengdu 610031, China)
Received 20 November 2019; Accepted 18 March 2020 c The Chinese Society of Theoretical and Applied Mechanics 2020
ABSTRACT The traditional Hertz contact theory has been widely used in solving contact problems. However, it is only applicable to the elastic contact, and cannot truly reflect the contact stress distribution and contact radius in the elasto-plastic contact. In this work, based on the Hertz contact theory, a fast solving method is proposed to calculate the contact stress distribution and contact radius in the elasto-plastic contact between two spheres. It is assumed that the elastic contact only occurs at the outer edge of contact patch and its contact stress distribution satisfies the Hertz contact theory, and the contact stress distribution at the inner edge of contact patch can be superimposed by a constant contact stress and several small ellipsoidal contact stress distributions. Moreover, based on the equivalent relation between the resultant force of contact stress and the normal external load, the contact radius in the elasto-plastic contact can be solved. Finally, an elasto-plastic contact example of two spheres is given based on the power-law hardening material model, and the influences of material parameters, contact radii and normal external loads on the accuracy of the proposed method are discussed by comparing the differences between the numerical results by finite element method and the predicted ones by the proposed method. It is shown that the proposed method can accurately calculate the maximum contact stress and contact radius in the elasto-plastic contact, and the relative errors of both maximum contact stress and contact radius are within ± 5%. To sum up, the proposed fast solving method can be applied to perform the elasto-plastic contact analysis in engineering practice.
KEY WORDS Elasto-plastic contact, Hertz contact theory, Contact stress distribution, Contact radius, Finite element simulation
1. Introduction Contact problems exist widely in the field of engineering, such as bearing transmission contact [1–3], wheel/rail contact [4–6], gear engagement contact [7], etc. The Hertz contact theory was proposed firstly to solve the contact problems of elastic bodies, which assumed that the contact stress was distributed in a semi-ellipsoidal shape and the normal deformation was a paraboloid [5, 8]. Subsequently, over the past decades, based on the Hertz contact theory, research on elastic contact problems has been gradually deepened, especially in the fields of rail transit and mechanical engineering, which greatly promoted the perfection and developme
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