基于分形理论的结合面法向接触刚度模型

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摘要基于修正的分形理论，以尺度系数定义微凸体大小，在充分考虑微凸体接触变形过程的基础上，对赫兹接触模型进行补偿修正，建立了结合面法向接触刚度模型，研究了法向接触刚度与分形维度之间的关系，并进行了仿真；以螺栓结合面为实验对象，采用结构函数法获取分形参数，进而求出结合面法向接触刚度值并录入有限元模型，在此基础上应用m+p噪声振动测试系统开展模态实验，通过对比理论模态与实验模态的振型和固有频率来验证理论模型的正确性；实验和仿真结果表明：理论模型和实验模型前8阶模态的振型一致，前8阶固有频率误差在-10.2%～-1%以内。

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关键词 ：分形, 结合面, 法向接触刚度, 模态实验

Abstract：A joint surface normal contact stiffness model was established.The model was based on the modified fractal theory and the size of asperity was defined by the scaling factor.Considering the contact deformation process of asperity, an error compensation method was used to correct the Hertz contact model.Numerical simulation was carried out to obtain the relations between normal contact stiffness and the fractal dimension.A bolt joint surface experiment was carried out to verify the correctness of the theoretical model.Firstly, according to the measured fractal parameters of the bolt joint surface, normal contact stiffness was solved.Then a modal experiment was carried out by using m+p noise and a vibration testing system.Finally, the results of the experiment and the finite element simulation were compared.The experiment results show that the first 8 modal shapes of the theoretical model and the experimental model are the same, and the error of the natural frequencies are within the range of -10.2%—-1%.

Key words： fractal joint surface normal contact stiffness modal experiment

收稿日期: 2017-07-18 出版日期: 2019-04-15

引用本文:

陈虹旭，董冠华，殷勤，谭峰，殷国富 . 基于分形理论的结合面法向接触刚度模型[J]. 振动与冲击, 2019, 38(8): 218-224.
CHEN Hongxu DONG Guanhua YIN Qin TAN Feng YIN Guofu. A normal contact stiffness model of joint surface based on the fractal theory. JOURNAL OF VIBRATION AND SHOCK, 2019, 38(8): 218-224.

链接本文:

http://jvs.sjtu.edu.cn/CN/ 或 http://jvs.sjtu.edu.cn/CN/Y2019/V38/I8/218

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