计算机求解渐开线齿轮齿廓的保角映射函数

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Calculation of Conformal Mapping Function of the Tooth Profile on Evolvent Gear by Computer

摘要: 平面弹性理论的复变函数保角映射解法可以求得齿轮的应力和位移的精确解.而相应于各种不同参数的轮齿齿廓的保角映射函数的求得却是比较困难的.以往均采用试算法,这是费时且昂贵的.作者编制了求解保角映射函数的计算机程序,并通过大量的计算证明这一程序是成功的,所取得的映射函数是精确的.从而解决了保角映射法求解渐开线齿轮应力和位移应用于实际工程计算的主要障碍.

Abstract: The exact solution of the stress and the displacement on spur gear can be gained by the method of con formal mapping of complex variables in plane elasticity.But it is difficult to get the comformal mapping function for the tooth profile with different parameters.They used to be obtained through trial method.This is time-consuming and expensive.In this paper a computer program is drawn up for the conformal mapping function.A large amount of calculation has given proof of its success and of the precision of the mapping function: thereby the main obstacle has been removed for the practical application of the conformal mapping method to the stress and displacement of tooth on evolvent gear.

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