基于变性法的高阶传动误差设计与分析

传统的弧齿锥齿轮传动误差呈二次抛物线形，易引起齿对间振动和冲击，本提出的高阶传动误差则可以克服这一不足。中给出了基于变性法的高阶传动误差设计的方法和求解过程，得出了变性法的瞬时滚比函数；利用TCA和LTCA，对高阶传动误差设计进行了轮齿接触仿真分析，验证了该设计方法和求解结果。该方法只修正滚比，无需修改齿轮几何参数与加工调整参数并易于实现。对比传统的二次抛物线传动误差，高阶传动误差设计使齿轮副的动态及强度性能均有改进。高阶传动误差的应用为高性能弧齿锥齿轮副的设计提供了新的方法和途径。

On Improving Design of Spiral Bevel Gear with Higher-Order Transmission Error Curve

Fang indicated the theoretical possibility of improving the design of spiral bevel gear by replacing traditional second order transmission error curve with higher order transmission error curve . This paper aims to convert the above mentioned theoretical possibility into a real design method. Section 1 selects eq.(2), a polynomial form, as the mathematical expression of transmission error, whose coefficients a 0, a 1, a 2, a 3 ... are to be determined. Section 2 uses eq.(5) as being more convenient than eq.(2) and shows how to determine the coefficients b 0, b 1, b 2, b 3 ... in eq.(5) by the two equations in eq.(4) of TCA (Tooth Contact Analysis). We can use eq.(6) to compute the instantaneous roll ratio m cp . The determination of m cp makes it quite easy to complete transmission error analysis. Section 3 gives a numerical example. Fig.2 gives the m cp curve. Fig.3 gives respectively transmission error curves and contact patterns for fourth order transmission error analysis (Fig.3a) and second order transmission error analysis (Fig.3b). Fig.4 gives respectively the load distributions for fourth order transmission error analysis (curve a ) and second order transmission error analysis (curve b ). Both Figs.3 and 4 show preliminarily that replacement of second order transmission error curve with fourth order transmission error curve can improve the design of spiral bevel gear.