On regularities of contact interaction of surfaces with regular microrelief (plane problem)

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We consider plane contact problems with a limited contact area for elastic bodies with a regular microrelief (RMR) applied to their surfaces. It is assumed that Flamant’s solution to the problem of the action of a concentrated normal force on the boundary of an elastic half-plane can be used to determine the stress-strain state of bodies. When modeling the contact interaction, a calculation scheme was used in which one of the bodies is considered as a rigid punch, and the second is considered as an elastic half-plane with a composite modulus of elasticity. The single-parameter families of punches with RMR are considered, the parameter of which is the number of microprotrusions. The regularities of contact interaction of punches with RMR and elastic half-plane were investigated by the method of computational experiment. Based on the established patterns, a method for approximate calculation of load distribution between RMR elements, as well as assessment of contact pressure, sizes of actual contact areas and average final gaps on microprotrusions is proposed.

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作者简介

А. Bobylev

Lomonosov Moscow State University

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Email: abobylov@gmail.com
俄罗斯联邦, Moscow

参考

  1. Schneider Yu.G. Operational properties of parts with regular microrelief. SPb.: SPb GITMO (TU), 2001. 264 p. (in Russian)
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  4. Goryacheva I.G., Tsukanov I.Y. Analysis of Elastic Normal Contact of Surfaces with Regular Microgeometry Based on the Localization Principle // Front. Mech. Eng. 2020. V. 6. Article 45. https://doi.org/10.3389/fmech.2020.00045
  5. Tsukanov I.Y. On the Contact Problem for a Wavy Cylinder and an Elastic Half-Plane // Mech. Solids. 2022. V. 57. № 8. P. 2104–2110. https://doi.org/10.3103/S002565442208026X
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  7. Bobylev A.A. Application of the Conjugate Gradient Method to Solving Discrete Contact Problems for an Elastic Half-Plane // Mech. Solids. 2022. V. 57. № 2. P. 317–332. https://doi.org/10.3103/S0025654422020029
  8. Bobylev A.A. Algorithm for Solving Discrete Contact Problems for an Elastic Strip // Mech. Solids. 2022. V. 57. № 7. P. 1766–1780. https://doi.org/10.3103/S0025654422070068
  9. Muskhelishvili N.I. Some Basic Problems of the Mathematical Theory of Elasticity. Dordrecht: Springer Netherlands, 1977. 732 p.
  10. Bobylev A.A. On the Positive Definiteness of the Poincaré–Steklov Operator for Elastic Half-Plane // Moscow University Mechanics Bulletin. 2021. V. 76. № 6. P. 156–162. https://doi.org/10.3103/S0027133021060029
  11. Bobylev A. A. The Unilateral Discrete Contact Problem for a Functionally Graded Elastic Strip // Moscow University Mechanics Bulletin. 2024. V. 79. № 2. P. 56–68. https://doi.org/10.3103/S0027133024700080
  12. Bobylev A.A. Algorithm for Solving Unilateral Discrete Contact Problems for a Multilayer Elastic Strip // J. Appl. Mech. Tech. Phys. 2024. V. 65. № 2. P. 382–392. https://doi.org/10.1134/S0021894424020202
  13. Bobylev A.A. Algorithm for Solving Discrete Contact Problems for an Elastic Layer // Mech. Solids. 2023. V. 58. № 2. P. 439–454. https://doi.org/10.3103/S0025654422100296

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2. Fig. 1. Profiles of the basic stamp P7b (a) and microprotrusions of the stamps of the P7s family (b).

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3. Fig. 2. Profiles of stamps P7(16) (a) and P7(64) (b).

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4. Fig. 3. Dependence of the relative value of the actual stamp contact area on the external load parameter s = L1Q( f ) (the curve numbers correspond to the stamp numbers Pn(Q)).

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5. Fig. 4. Dependence of the stamp upset on the external load parameter dy = L2Q( f ) (the curve numbers correspond to the stamp numbers Pn(Q)).

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6. Fig. 5. Dependence of the stamp rotation angle on the external load parameter jz = L3Q( f ) (the curve numbers correspond to the stamp numbers Pn(Q)).

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