内平动齿轮传动几何参数的优化设计

Geometrical Parameters Optimizition Design of Internal Parallel Moving Gears Transmission

为了解决内平动齿轮传动设计中几何参数,特别是变位系数确定困难、计算过程繁琐和计算结果精度不高等问题,探讨渐开线少齿差行星齿轮传动优化设计的方法,采用机械优化设计理论,运用CAD建立了内平动齿轮传动变位系数和啮合角的优化求解数学模型,在优化软件LINGO平台上编程实现了计算过程的自动化和几何参数的优化,得到了一齿差和二齿差内平动齿轮传动变位系数和啮合角的最优值,并结合工程实例,验证了该方法的优越性。计算结果表明:一齿差内齿轮副最小啮合角为53.2°,二齿差最小啮合角为39.3°;一齿差内齿轮副的外齿轮最好采用标准齿轮,内齿轮采用变位系数为0.577的正变位,二齿差内齿轮副的内、外齿轮均须采用正变位,有时变位系数大于1。

In order to solve the difficult problem in determining geometric parameters, especially modification coefficient, calculating cumbersome and low accuracy of calculation results, this paper provides a method for optimization design for planetary gear train with a small tooth difference. Applying the theory of mechanical optimization design and CAD method, the mathematical models to optimize the modification coefficient and working pressure angle are built. Based on the optimization software LINGO the automatic calculation and geometric optimization are achieved. The accurate optimized values of modification coefficient and working pressure angle for internal engaged gear with one tooth difference and two teeth difference are obtained. Combining some engineering design instances, the advantages of this method are embodied. Calculation results indicate that in the intemal gear pair with one tooth difference the minimum working pressure angle is 53.2°, with two teeth difference the minimum working angle is 39.4°. And it indicates that in the internal gear pair with one tooth difference the extemal gear should be standardized and intemal gear should be modified with the modification coefficient being 0. 577. When it comes to the internal gear pair with two teeth difference the modification coefficients of external and internal gear both should be above zero, and sometimes larger than one.