中文摘要：

不考虑润滑剂影响，针对理想渐开线直齿圆柱齿轮，研究存在齿面磨损时齿轮啮合刚度的计算方法。基于齿轮共轭啮合原理计算滚齿加工条件下的齿廓曲线。根据 Timoshinko 梁理论，考虑轮齿弯曲变形、剪切变形、压缩变形、齿轮基体变形和赫兹接触变形，计算齿轮啮合刚度。针对运行过程中的齿面磨损，提出轮齿等弧长离散方法，分析齿面磨损对离散微元短梁的截面面积、截面面积矩和实际接触齿宽的影响，计算分析存在均匀磨损、微点蚀和宏观点蚀等齿面磨损时的齿轮啮合刚度。结果表明，100μm深的均匀磨损导致的啮合刚度变化不到2‰；齿面产生15%的微点蚀时，啮合刚度变化在10%以内，啮合刚度对早期齿面磨损不敏感。本研究为计及齿面磨损的齿轮动力学建模提供了一条技术路径。

英文摘要：

Without considering the effect of lubricant, a computational method of mesh stiffness of a gear pair with tooth surface wear is developed for ideal cylindrical spur gear. The coordinates of tooth profile curves processed by a hobbing machine are obtained according to conjugate engagement theory. Based on the theory of Timoshenko beam, the mesh stiffness is calculated in consideration of bending, shearing and compressing, contacting and fillet-foundation deformation. Discrediting the tooth profile curve according to the equal-arc method is proposed aimed at wear of gear teeth in running process, and then effects of tooth wear on the cross-sectional area, area moment of inertia and real width of contact of a short discrete beam element are taken into account to calculate and analyze mesh stiffness with uniform wear, pitting and micro-pitting. The results show that the decrease of mesh stiffness caused by 100μm uniform wear is less than 2‰ and 15% micro-pitting results in a less than 10% variation of mesh stiffness. Mesh stiffness is not sensitive to early wear of gear teeth. This study is useful to improve the accuracy of dynamic modeling of a gear pair with tooth surface wear.