人字齿轮直线型对角修形设计及成形磨原理

Design and Form Grinding Principle of Linear Triangular End Relief for Double Helical Gears

为了降低承载传动误差波动产生的振动激励,提出了成形磨人字齿轮直线型对角修形优化设计。根据ISO对角修形定义,计算齿顶、齿根修形起始线在旋转投影面上的螺旋角,将修形曲线设计为直线型,给定最大修形量,确定对角修形的齿面方程。利用齿面接触分析和轮齿承载接触分析,以工作载荷下人字齿轮承载传动误差波动量最小为优化目标,采用遗传算法优化对角修形参数。确定以目标修形齿面法向偏差的平方和最小的目标函数,以螺旋角、模数、压力角为设计变量,采用遗传算法分别对齿顶和齿根修形区域进行逼近,从而实现对角修形的成形磨加工。结果表明,人字齿轮直线型对角修形可以将承载传动误差波动量降低到36.65%;采用三截面砂轮成形磨的理论误差控制在1μm以内,获得较高的齿面精度;试验人字齿小轮齿的检测结果控制在4级精度以内,并进行了齿轮副的滚检试验,从而验证该方法的有效性。

In order to reduce the vibration excitation caused by the fluctuation of loaded transmission error,an optimization design of linear triangular end relief of double helical gears based on form grinding is proposed.According to the ISO definition of triangular end relief,the helix angle of starting line of modification at the tooth top and tooth root on the rotating projection plane is calculated,the modification curve is designed as linear,and the tooth surface equation of triangular end relief is determined by giving the maximum modification amount.Based on tooth contact analysis(TCA)and loaded tooth contact analysis(LTCA),the loaded transmission error of double helical gears under working load is calculated.The optimization objective was to minimize the fluctuation of the loaded transmission error,and triangular end relief parameters are optimized by genetic algorithm.The objective function is established to minimize the sum of squares of normal deviation of the modified target tooth surface.The helix angle,modulus and pressure angle are taken as design variables,and the tooth top and tooth root modification regions are approximated by genetic algorithm respectively,so as to realize the form grinding of triangular end relief.The results show that the fluctuation of loaded transmission error can be reduced to 36.65%by linear triangular end relief of double helical gears.The theoretical error of form grinding with three-section grinding wheel is controlled within 1μm,and high accuracy is obtained.The test results of pinion for the double helical gears are controlled within grade 4 accuracy,and the contact patterns rolling test of gear pair is also performed,which verify the effectiveness of the proposed method.