Abstract A mathematical model of the motorized spindle taking into account the influence of various fractal parameters is established. Weierstrass–Mandelbrot function (W–M function) shows that the fractal parameters are important that affect the contact characteristics. According to fractal theory, the thermal contact resistance (TCR) between contact surfaces is proposed, and the thermal contact conductance (TCC) verification experiment verifies its accuracy. The key nodes of the motorized spindle are divided and the heat-balance equations are solved. The accuracy of the thermal resistance network model is verified by the temperature–rise experiment. The results show that: the fractal dimension D and the fractal–amplitude coefficient G affect the complexity and contour height of the contact surface; the temperature of each component rises quickly and then remains stable; An increase in the D causes a decrease in the temperature of the nodes and an increase in the G causes an increase in the temperature of the nodes. The influence of fractal parameters on the thermal characteristics of the motorized spindle can not be neglected.

中文翻译：

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基于各种分形参数影响的电主轴热阻网络建模研究

摘要 建立了考虑各种分形参数影响的电主轴数学模型。Weierstrass-Mandelbrot 函数（W-M 函数）表明分形参数是影响接触特性的重要因素。根据分形理论，提出了接触面之间的接触热阻（TCR），并通过接触热导（TCC）验证实验验证了其准确性。划分了电主轴的关键节点，求解了热平衡方程。通过温升实验验证了热阻网络模型的准确性。结果表明：分形维数D和分形幅度系数G影响接触面的复杂度和轮廓高度；各部件温度快速上升后保持稳定；D 的增加导致节点温度的降低，而 G 的增加导致节点温度的增加。分形参数对电主轴热特性的影响不容忽视。