基于遗传算法的双圆弧谐波齿轮的优化与分析

Optimization and Analysis of Double-circular-arc Harmonic Gear based on Genetic Algorithm

双圆弧谐波齿轮传动过程中产生的"双共轭"现象对谐波传动的承载能力有重要影响,为此,提出了一种基于遗传算法的针对谐波齿轮啮合时的"双共轭"区间的优化方法。首先,运用包络法求解柔轮的理论共轭齿廓;然后,以两段共轭齿廓的贴合程度为目标,建立了一种基于遗传算法的双圆弧谐波齿轮参数优化模型。使用此模型对柔轮参数进行优化设计,结果发现,该优化方法能对较多的参数进行优化且可以减少计算时间。对优化后的参数进行单参数敏感度分析,发现目标函数对凸齿圆弧半径、凹齿圆弧半径及齿厚比的敏感度低。因此,可以通过适当放宽低敏感度参数和控制高敏感度参数尺寸误差的方式来控制柔轮制造的精度并增加双圆弧谐波齿轮啮合时的"双共轭"区间。

The"dual-conjugated"phenomenon is generated in the process of the double-circular-arc harmonic transmission,which has an important influence on the carrying capacity of harmonic gear transmission.Therefore,an optimization method based on genetic algorithm to optimize the"dual-conjugated"interval is proposed.Firstly,based on the theoretical conjugate tooth profile of the flexspline obtained by the envelope method,then,one parameter optimization model(based on genetic algorithm)of double-circular-arc harmonic gear is established,which taking the fit degree of the two conjugate tooth profiles as the optimized goal.By using this model,the parameters of the flexspline are optimized quickly.The results show that this optimization method can optimize more parameters contemporary and reduce the calculation time.Through analyze the single parameter sensitivity of the optimized parameters,it is found that the objective function has a low sensitivity to the arc radius of convex and concave tooth,and the tooth thickness ratio.Therefore,to control the manufacturing accuracy of the flexspline and increase the"dual conjugate"interval,one of the useful way is that relax the size error of low sensitivity parameters and control the size error of high sensitivity parameters appropriately.