齿轮箱的鲁棒优化设计研究

Study of Gearbox's Robust Optimization Design

鲁棒性是指当系统中的不确定性因素发生微小变化时,系统性能的改变程度,而齿轮传动系统在加工装配过程中存在诸多误差,为了提高齿轮传动系统在不确定误差存在的情况下的鲁棒性,提出了齿轮箱的鲁棒优化设计方法。优化设计方法主要包含3个步骤:(1)系统模拟,即建立齿轮箱的动力学模型,从而计算齿轮箱的动态性能,并通过蒙特卡罗模拟的方式计算在不确定因素影响下的齿轮箱的鲁棒性能;(2)构造目标函数,采用目标规划法将多个动态性能、鲁棒性能和质量统一为一个目标函数;(3)目标优化,通过复合形法在约束条件下优化目标函数得到最优解。最后以平行直齿轮的鲁棒优化设计为例说明了提出的鲁棒优化方法,从优化结果的性能可知,鲁棒优化方法相对于传统优化方法能够明显提高齿轮传动系统动态性能的鲁棒性。

The robustness of a system refers to the ability of tolerating unknown perturbations which might affect the system, and there are many errors in the manufacturing or assembly process of gear systems. Therefore, a robust optimization design method of gearbox is proposed considering the uncertain factors. The optimization method contains three steps： （1）system simulation, or in other words, build the dynamic model of gearbox to acquire its dynamic property and calculate the robustness of gearbox using Monte-Carlo method; （2）constructing target function, goal programming method is used to collect mass, dynamic and robust property together to be a comprehensive target function; （3）target optimization, compound form method is used to optimize the comprehensive target function to get the optimum solution. Then, the robust optimization of a parallel spur gear train is given as an example to show how the proposed method works, and from the performance of the optimum solution, it can be concluded that the robustness of the optimum solution of robust optimization is obviously better than that of normal optimization.