点接触的行星齿轮传动误差理论分析与试验研究

Point contact theory based on "Local Conjugate Principle" has more advantages, such as improving the gear practical transmission performance,than ones on traditional"Global Conjugate Principle". Point contact theory is being a generally accepted belief in industrial community and usually realized by tooth surface modification. Planetary gear trains is complicated multibody and multicontact transmission system with a sun gear,a ring gear and several planet gears, and related theory about the elaborate transmission system such as Transmission Error and Tooth Surface Modification have not a deep research previously. The transmission error character of planetary gear trains will be studied in this project. The modification quantity of planet gear is calculated and assigned depending on transmission error curve which is predesigned by working condition. Then planetary gear trains on point contact theory is realized. The multibody, multicontact and nonlinear dynamics of transmission system will be studied in the paper.Under existing conditions,a testing platform is set up to measure data of transmission error,vibration and noise with modified planet gear , desirable involute(non-modification surface) sun gear and ring gear.Through analysis the transmission error data on spatial domain, the main factors which bring about the system transmission error will be analyzed, and the inner relationship between the transmission error， the vibration and the noise will be studied, so as to provide the new theoretical basis and the engineering value to improve the transmission stationarity, restrain the vibration and noise, and enhance the loaded capacity of the planetary gear system.

基于"局部共轭"思想的点接触原理的齿轮，可以克服基于传统"完全共轭"思想的诸多弊端，提高齿轮的实际传动性能，工业界对此已普遍接受并采用齿面修形实现该原理。行星齿轮传动系统含有太阳轮、行星轮和内齿轮，是一种典型的多体多接触复杂传动系统，相关理论呈现出更加复杂的内容。本课题研究行星轮系传动误差特点，根据实际工况预先设计行星齿轮传动误差曲线，将其分配到行星轮的修形量中，实现点接触理论的行星齿轮传动形式，对传动系统进行多体多接触分析和非线性动力学理论研究。在现有条件的基础上，搭建一个行星轮修形，其余齿轮为标准渐开线齿廓的点接触行星传动试验平台，对传动系统中的传动误差、振动和噪声等参数进行测量，对传动误差数据进行空域分析，分析影响系统的传动误差的主要因素，研究传动误差与振动、噪声之间的内在联系，为点接触行星齿轮系统传动平稳性的提高、振动和噪声的抑制、承载能力的增强提供新的理论依据和工程价值。

针对行星齿轮使用工况，提出点接触传动原理，研究对行星齿轮传动误差的影响，提高传动系统的传动性能。主要研究如下：对点接触公式含有摩擦系数进行了理论分析，并且与线接触齿轮副进行对比，安装误差不可避免的情况下，线接触最大接触应力明显恶化。研究了齿廓修形原理和修形系数的计算方法，以鼓型齿为例研究了点接触齿面TCA，研究修形系数对其传动误差和接触印痕的影响，进一步给出了用MatLab计算修形齿面的方法。给出了含有n个行星齿轮多点多接触TCA建模方法，并且针对该非线性方程组难以求解，给出采用行星齿轮相位差的简化计算方法，对行星轮不同布置位置给出了相位差和TCA求解方法。根据加工刀具对行星齿轮各个轮齿的齿面点啮合方程进行推导，特别是铲形轮采用包络的方法进行修形齿面反求，预置不同的修形系数的修形方案，得到其中心轮修形后的齿面方程。分析行星齿轮拓扑结构，采用完全笛卡尔坐标法对行星齿轮内外啮合、转动副进行约束分析，采用行星齿轮多体动力学研究行星齿轮运动系统构件的运动参变量。搭建了行星齿轮双鼓修形磨齿试验台，并且进行了滚检及噪声试验；进行了行星齿轮振动噪声实验，对修形前后的齿轮进行对比，在载荷增加时，修形行星齿轮振动噪声呈下降趋势。