Tangential stiffness model of the joint surface considering contact angles between asperities based on fractal theory

IF 4.4 2区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Applied Mathematical Modelling Pub Date : 2025-03-12 DOI:10.1016/j.apm.2025.116088

Yongchang Li, Guangpeng Zhang, Zhenyang Lv, Ke Chen

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引用次数: 0

Abstract

Based on fractal theory, the tangential contact model for a joint surface, taking into account the contact angle between asperities, was developed by incorporating Gorbatikh's contact angle probability distribution function. Mathematical expressions for the stages of a single asperity and the entire joint surface were derived. The quantitative effects of fractal parameters, friction coefficient, material properties, normal and tangential loading forces, and repeated loading on tangential stiffness were analyzed theoretically, and a dedicated testing platform was constructed to validate the accuracy of the model. The results show that the proposed model enhances stiffness prediction accuracy. The increase in contact stiffness is primarily determined by the fractal dimension and the number of repeated loadings. Tangential contact stiffness initially increases and then decreases with the fractal dimension D, reaching its maximum value when D = 2.6. Multiple loadings significantly improved stiffness, which gradually stabilized. After three loading cycles, the stiffness reached over 90 % of the maximum value, stabilizing at 1.21 times the initial loading stiffness when D > 2.6. This study provides a systematic analysis of the quantitative effects of various factors on tangential contact stiffness, offering both a theoretical foundation and practical guidance for optimizing the assembly process.

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来源期刊

Applied Mathematical Modelling 数学-工程：综合

CiteScore

9.80

自引率

8.00%

发文量

508

审稿时长

43 days

期刊介绍： Applied Mathematical Modelling focuses on research related to the mathematical modelling of engineering and environmental processes, manufacturing, and industrial systems. A significant emerging area of research activity involves multiphysics processes, and contributions in this area are particularly encouraged. This influential publication covers a wide spectrum of subjects including heat transfer, fluid mechanics, CFD, and transport phenomena; solid mechanics and mechanics of metals; electromagnets and MHD; reliability modelling and system optimization; finite volume, finite element, and boundary element procedures; modelling of inventory, industrial, manufacturing and logistics systems for viable decision making; civil engineering systems and structures; mineral and energy resources; relevant software engineering issues associated with CAD and CAE; and materials and metallurgical engineering. Applied Mathematical Modelling is primarily interested in papers developing increased insights into real-world problems through novel mathematical modelling, novel applications or a combination of these. Papers employing existing numerical techniques must demonstrate sufficient novelty in the solution of practical problems. Papers on fuzzy logic in decision-making or purely financial mathematics are normally not considered. Research on fractional differential equations, bifurcation, and numerical methods needs to include practical examples. Population dynamics must solve realistic scenarios. Papers in the area of logistics and business modelling should demonstrate meaningful managerial insight. Submissions with no real-world application will not be considered.