Pinpoint calculation of tooth deflection on spur gear by means of method of complex variables in plane elasticity

This paper ineorporated and developed the method originated by AIDA.TERACCHI. and NAGAMUYA. to which a high value is set presently at home andabroad, in which the stress and deflection of tooth on spurgears are calculated by means ofthe method of complex variables in plane elasticity. In this paper, their approximatesolution was developed to become exact solution. The accuracy of the mapping shape oftooth was increased. It was mentioned that the mapping function was expressed by fivefractional terms. with the mapping error being less than 1%m.A calculating principle wasproposed to find out the displacement of contact point in relation to central line of theadjacent gear tooth affecting the quality of mesh of gears directly.The computer programwas made, and according to the computed results.the figures were given so that thedisplacement of the contact point in the normal direction can be calculated conveniently forengineering calculation.     

计算机求解渐开线齿轮齿廓的保角映射函数

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.     

用平面弹性理论的复变函数解法精确确定直齿轮轮齿的挠度

本论文吸取并发展了目前受到国内外普遍注意的由会田俊夫、寺内喜男和永村和照所开创的用平面弹性理论的复变函数解法求直齿轮轮齿的应力和变形的方法,把它们的应力函数的近似解发展为精确解;提高了映射齿形的精度,提出了用五项分式项表达的、映射误差小于1％m的映射函数;提出了求直接影响齿轮啮合质量的啮合点相对于相邻轮齿中线位移的原则;编制了计算程序,并对计算结果进行了分析.     

CALCULATION OF CONFORMAL MAPPING FUNCTION OF THE TOOTH PROFILE ON EVOLVENT GEAR BY COMPUTER

The exact solution of the stress and the displacement on spur gear can be gained by the method of conformal 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 gi yen 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 mid displacement of tooth on evolvent gear.