高速柔性行星齿轮传动系统耦合动力学机理与设计方法研究

High-speed flexible planetary gear transmission systems are widely used in helicopters, cars, etc, whose dynamic performance is affected by the high speed, flexibility, and the unsteady operating condition (variable speed process, driven/load torque fluctuation, etc.) synthetically. However, the investigation is few in coupling dynamic mechanism for the high-speed flexible planetary gear transmission system and the effective design method has not been proposed, resulting in poor dynamic performance and easy failure. Therefore, considering the components (gear housing, ring, etc.) flexibility, drive and load dynamic characteristics, and the effect of unsteady operating condition, the coupling dynamic model is constructed for high-speed flexible planetary gear transmission system. Based on this model, the stability under lasting large perturbation, coupling dynamic characteristics and parameter sensitivity are investigated for high-speed flexible planetary gear transmission system, constructing the instability criterion and obtaining the main parameters affecting system dynamic performance and the parameter limit ranges for system stability. Furthermore, in order to reduce the system dynamic load, vibration, and weight, considering the bidirectional constraint relationship between the flexible components (gear housing, etc.) parameters and the gear dynamic load, the main parameters are optimized comprehensively in the limit ranges for system stability. Thereby, a kind of coupling dynamic design method is constructed for the high-speed flexible planetary gear transmission system, laying the foundation of dynamic performance improvement for transmission systems, such as the main reducer in helicopter, and so on.

高速柔性行星齿轮传动广泛应用于直升机、汽车等装备，其动力学性能受到系统高速、柔性和非稳态工况（变速、驱动/负载转矩波动等）的综合影响。但目前高速柔性行星齿轮传动系统耦合动力学机理研究不足，从而无法提出有效的设计方法，导致其动力学性能差且易失效。鉴于此，综合考虑箱体、齿圈等构件柔性、驱动/负载动态特性以及非稳态工况的影响，建立高速柔性行星齿轮传动系统耦合动力学模型，研究持续大扰动下的系统稳定性、系统耦合动态特性及参数影响规律，建立系统失稳判别方法，获得影响系统动力学性能的主要参数（齿轮参数和箱体等结构参数）及其稳定极限范围。进而以减小系统动载荷和振动并减轻系统重量为目标，考虑箱体等柔性构件参数与齿轮动载荷的双向耦合约束关系，对主要参数在稳定极限范围内进行综合优化，据此选择系统设计参数。从而建立一种高速柔性行星齿轮传动系统耦合动力学设计方法，为直升机主减速器等传动系统的动力学性能提升奠定基础。

建立了每个齿轮考虑6个自由度的行星齿轮传动系统集中参数动力学模型。建立了状态方程形式的柔性齿圈、行星架有限元缩聚模型，该模型考虑了行星架刚体转动引起的离心力、惯性力和柯氏力。建立了电机动态载荷模型。在以上部件模型的基础上，运用集中参数-有限元混合建模方法，将各子结构模型耦合建立了高速柔性行星齿轮传动系统耦合动力学模型，该模型可用于变速、匀速、变载荷等瞬稳态工况。基于此模型，分析了高速柔性行星齿轮传动系统在恒速、变速过程的动力学特性，并提出了动力学性能改进方案。建立了基于TSPDR（trajectory-based stability preserving dimension reduction，基于轨迹的保稳降维方法）的齿轮传动系统稳定性分析方法，该方法包括四个步骤：第一步，通过数值计算的方法得到系统运动轨迹；第二步，通过互补群惯性中心-相对运动方法（complementary cluster center of inertia-relative motion, CCCOI-RM）降维；第三步，定义稳定裕度；第四步，求解临界值。研究了齿轮传动系统稳定性、系统耦合动态特性及参数影响规律。通过参数相关性分析识别出影响系统性能的敏感结构参数，在此基础上建立了系统减振抗冲性能优化模型，采用NSGA-Ⅱ多目标遗传算法进行参数优化，有效降低了系统瞬时动载荷，提升了系统的动力学性能。搭建了高速柔性行星齿轮传动系统耦合动态特性实验台，采用高动态测试系统获得了传动系统的耦合动态特性，验证了高速柔性行星齿轮传动系统的耦合动力学模型和理论分析结果。最后将本项目研究方法、成果用于直升机、风电、采煤机、汽车传动系统的设计与分析。