弧齿锥齿轮复合传动误差设计与分析

Design and Analysis of Hybrid Transmission Error of Spiral Bevel Gears

为了降低承载传动误差高阶谐波引起的噪声,本文提出了弧齿锥齿轮复合传动误差设计。借助优化方法确定了工作载荷下承载传动误差波动量最小和几何传动误差对称性的局部综合参数,从而获得机床调整参数。借助轮齿接触分析方法,通过计算对称抛物线传动误差在5个关键点处的小轮转角和传动误差幅值,确定一个啮合周期内的简谐函数表达式,根据啮合转换点的连续相切条件计算两侧抛物线传动误差曲线系数,进而获得完整的3段传动误差曲线。采用逆轮齿接触分析方法,获得3段传动误差所对应的小轮基本滚比和高阶变性系数。算例结果表明:在轻载条件下啮合转换点处的夹角为180°,可实现啮合齿对的平稳过渡,减小换齿冲击;在工作载荷下能够降低承载传动误差的高阶谐波幅值;通过设置3段高阶变性系数可实现复合传动误差的磨齿加工。

This paper proposes the design of hybrid transmission error(HTE)of spiral bevel gears to reduce the noise caused by high order frequency of loaded transmission errors.The local synthetic parameters with minimum fluctuation of loaded transmission error(LTE)and symmetry of geometric transmission error under working load were determined through optimization to obtain the machine-tool setting for spiral bevel gears.The pinion rotation angle and transmission error amplitude of symmetric parabola transmission error(PTE)at five key points were calculated through tooth contact analysis(TCA)to determine the harmonic function expression within a meshing period;the higher order parabolic coefficients of transmission error curves on both sides of the harmonic function were calculated according to the condition of continuous tangent at the meshing transfer point;the basic roll ratio and high order modified coefficient of pinion,corresponding to three-segment transmission error,were obtained by using reverse tooth contact analysis method.The numerical results show that stable meshing among tooth pairs can be realized and the meshing impact can be reduced under an intersection angle of 180°at transfer points under light loads;the high-frequency amplitude of the loaded transmission error can be reduced by the composite transmission error design under the working load.The gear grinding of compound transmission error can be realized by setting the high order modified roll coefficient of three-segment transmission error.