The object of this fundamental research will be to reveal the effects of variable coefficient of static friction on the static behavior of disc spring. On account of the complex relationship between friction and normal pressure, based on contact mechanics and fractal theory, a model for predicting variable coefficient of static friction of 3 D fractal surface is induced. Then the method proposed by Curti is improved by using the fractal coefficient of static friction to replace the Coulomb's law. The entire deflection range is considered under quasi-static loading condition. The model of disc spring is developed to predict the load-deflection and hysteresis characteristics while contacting with different fractal surfaces. The primary object of this study is to survey the variable static friction coefficient and its effect on the disc spring. Different fractal dimension, constant static friction coefficient and free height of disc spring are considered, and the relative error of the two methods are calculated. The investigation has revealed that the effect of fractal static friction coefficient on the load-deflection and hysteresis characteristics of disc spring is concentrated in the small deflection stage. And the method is universal for disc springs of different dimension on the same surface.

本基础研究的目的是揭示可变静摩擦系数对碟形弹簧静态性能的影响。考虑到摩擦力与法向压力之间的复杂关系，基于接触力学和分形理论，提出了一种预测3D分形表面静摩擦可变系数的模型。然后用静摩擦分形系数代替库仑定律，改进了柯蒂提出的方法。在准静态载荷条件下考虑整个挠度范围。碟形弹簧模型的开发是为了预测与不同分形表面接触时的载荷变形和磁滞特性。这项研究的主要目的是调查可变静摩擦系数及其对碟形弹簧的影响。考虑了不同的分形维数，恒定的静摩擦系数和碟形弹簧的自由高度，并计算了两种方法的相对误差。研究表明，分形静摩擦系数对碟形弹簧的载荷-变形和滞后特性的影响集中在小变形阶段。该方法适用于同一表面上不同尺寸的碟形弹簧。