由于目前对椭圆锥齿轮的研究主要是进行传动原理及特性、齿形设计、加工制造分析以及传动实验等研究，而对其轮齿承载能力的研究相对较少。结合微分几何理论和齿轮啮合原理，在椭圆锥齿轮平面当量节曲线的基础上，获得传动过程中的压力角变化关系。对啮合过程进行受力分析，并推导轮齿所受切向力及法向力的计算公式。建立椭圆锥齿轮强度的连续计算方法，讨论齿面接触应力和齿根弯曲应力随主动轮转角的变化规律。判断啮合过程中最薄弱轮齿的位置，分析了模数、齿数和偏心率3个基本参数对接触应力及弯曲应力的影响，并通过与传统直齿锥齿轮强度计算法的对比分析，验证了椭圆锥齿轮强度连续计算法的正确性。

Based on the plane equivalent pitch curve of elliptical bevel gear，the pressure angle in the transmission is acquired with differential geometry and gear meshing theories. The force analysis in the meshing process is performed and the formulas of tangential force and normal force on the gear teeth are derived. A method to calculate elliptical bevel gear’s strength in a successive way is established and the regulation of the tooth surface contacting stress and the root bending stress changing with the angle of driving gear is discussed. Then the position of the weakest tooth is determined and the influence of basic parameters including module，number of teeth and eccentricity ratio on contacting stress and bending stress is analysed. Comparing with traditional calculation for spur bevel gear，the exactness of this successive strength calculation method is verified.

国家自然科学基金资助项目(50875269，51275537)