基于雅可比旋量模型的行星齿轮传动系统三维偏差分析方法

Three-dimensional Tolerance Analysis of Planetary Gearboxes Based on Jacobian-Torsor Model

行星齿轮传动系统装配时各零件的偏差累积影响齿轮啮合状态,导致其系统振动噪声性能劣化。行星齿轮传动系统属于刚性多体装配,在控制偏差时,传统尺寸链方法无法有效表征间隙和形位公差耦合下的结构偏差及其三维空间传递。基于雅可比旋量模型和蒙特卡洛统计仿真方法,建立行星齿轮传动的间隙和形位公差等偏差源的三维旋量分量约束方程模型,提出装配体串联化偏差传递路径等效方法,计算目标特征偏差参数的分布,并获得各个偏差源的敏感度和贡献度,形成从设计公差到装配偏差的完整三维偏差分析方法。以实际数值案例进行计算,实现装配质量预测和偏差溯源,为齿轮传动系统公差优化设计提供指导。

The accumulation of deviations of each part during the assembly of planetary gear train affects the gear contact pattern and the vibration of the system.The conventional dimensional chain method cannot effectively characterize the clearance deviations and form tolerances and their three-dimensional transfer due to high stiffness of the parts.In this paper,based on Jacobian-Torsor model and Monte-Carlo statistical simulation method,a three-dimensional torsor component constraint model of deviation sources in planetary gear transmission is established.The distribution of target deviation parameters by tandemizing the deviation transmission path of the assembly is calculated.The sensitivity and contribution of each deviation source to that of the assembled structure is defined.A three-dimensional deviation analysis method from design tolerance to assembly deviation for planetary gearboxes is proposed.The deviation prediction for typical planetary gearboxes is conducted to verify the reasonability of the established model.The results show that the assembly quality can be predicted and the deviation relationship between the assembled structures and parts can be determined quantitatively,which may provide guidance for tolerance optimization design.