一种弧齿锥齿轮传动性能优化方法

 以期望的传动误差曲线为目标，首次提出了弧齿锥齿轮传动误差曲线优化的泛变性(GMR)方法，它是对局部综合法的一种改进。首先讨论了齿面接触印痕和传动误差曲线的计算方法，并在传统局部综合法基础上提出了泛变性局部综合法，给出了该方法的理论基础即局部综合公式和齿面接触方程，接着分析了对弧齿锥齿轮传动性能尤其是传动误差影响最大的两个加工参数即小轮切削速比和三阶变性系数的变化规律，最后对某具体航空弧齿锥齿轮副的传动误差曲线和齿面接触印痕进行了泛变性优化设计。结果表明：当小轮切削速比取0621 9且三阶变性系数取-0021 99时，轮齿接触分析(TCA)实际传动误差曲线比较对称且与期望曲线较好地吻合，而齿面接触印痕几乎没有变化，由此证明泛变性法对传动性能控制的有效性和稳定性。该研究工作对于航空齿轮传动系统具有重要的实际意义。

An Optimization Approach of Transmission Performance of Spiral Bevel Gears

This article proposes a generally modified-roll (GMR) as an improved method of the traditional local synthesis for the optimization of the transmission error function of spiral bevel gears in comparison with the desired curve. It first discusses the formulas of determining the tooth contact pattern and the transmission error function, and then described the basic idea of GMR based on traditional local synthesis, and presents the formulas of local synthesis and tooth contact analysis (TCA) as the basic theory of GMR. The cutting ratio of the pinion and the third-order modified-roll coefficient are the two most sensitive parameters affecting the transmission performance of spiral bevel gears, especially their transmission error function, and the rule governing their variation is analyzed. Finally the transmission error function and contact pattern of a pair of spiral bevel gears in aviation are optimized by the GMR. The results show that the TCA transmission error function is very close to the desired curve when the cutting ratio and the third-order modified-roll coefficient are 0.621 9 and -0.021 99 respectively, and the contact pattern is steady when the two parameters have a fine turning around their reference values at the mean contact point. The conclusions above prove that the GMR is an effective and steady method for the improvement of transmission performance, which is of great significance to the study of gear transmission systems in aviation.