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求解共轭曲面的主曲率主方向是共轭曲面原理的一个基本问题。针对常规计算方法涉及中间变量多,求解过程繁琐,容易出错问题,给出了一种数值微分的计算方法。以空间交错轴传动准双曲面齿轮为例,建立了大小轮啮合坐标系,推导了大小轮共轭齿面方程,计算了共轭齿面的主曲率主方向。对常见的LITVIN法、诱导曲率法与数值微分法进行了对比分析。表明数值微分方法求解共轭曲面主方向和主曲率过程清晰明了,易于编程计算,且结果准确。
Solving the principal direction of the principal curvature of the conjugate surface is a basic problem of the principle of the conjugate surface. Aiming at the problems that conventional calculation methods involve many intermediate variables, the solution process is cumbersome and error-prone, a numerical calculation method of numerical differentiation is given. Taking spatially interlaced shaft-driven hypoid gears as an example, the meshing coordinate system of large and small wheels was established. The conjugate tooth surface equation of large and small wheels was deduced and the main principal curvature direction of conjugate tooth flanks was calculated. The common LITVIN method, inductive curvature method and numerical differential method were compared and analyzed. It shows that the numerical differential method is clear and easy to solve for the principal direction and principal curvature of the conjugate surface, and is easy to program and calculate with accurate results.