基于NSGA-Ⅱ的斜齿轮宏观参数多目标优化

Multi⁃objective optimization of macro parameters of helical gear based on NSGA⁃Ⅱ

针对齿轮系统在初始设计阶段存在传递误差波动量大,进而导致的振动噪声突出等问题,提出了一种齿轮副宏观参数多目标优化方法。基于势能法和切片法推导出了斜齿轮传递误差解析计算公式,并以齿轮副总重合度最大、传递误差波动量最小和齿轮副总体积最小为优化目标,以齿轮宏观参数为设计变量,以带精英策略的快速非支配排序遗传算法(NSGA-Ⅱ)为优化算法,建立了齿轮系统宏观参数优化模型。以某二级减速齿轮系统为算例,采用优化模型对齿轮副宏观参数进行了优化设计,基于MASTA软件对优化前、后的动力学指标进行了仿真。结果表明,不同工况下,经过宏观参数优化后的齿轮系统啮合传递误差波动量、系统传递误差波动量和轴承座振动位移幅值均得到不同程度的降低,系统动力学性能得到整体改善。

In the initial design stage of gear system,there is a large fluctuation of transmission error,which leads to prominent vibration and noise problems of the system.Aiming at that,a multi-objective optimization method of macro parameters of gear pair is presented.Based on the potential energy method and slicing method,the analytical calculation formula of transmission error of helical gear is derived.Taking the maximum total contact ratio,minimum fluctuation of transmission error(TE),and minimum total volume of gear pair as optimization objectives,the gear macro parameters as design variables,and a fast elitist non-dominated sorting genetic algorithm(NSGA-Ⅱ)as optimization algorithm,the macro parameter optimization model of gear system is established.Taking a two-stage reduction gear system as an example,the macro parameters of the gear pair are optimized by using the optimization model,and the dynamic indexes before and after optimization are simulated based on the software MASTA.The results show that under different working conditions,the fluctuation of meshing TE and system TE as well as the vibration displacement amplitude of bearing seat are reduced in different degrees,and the overall dynamic performance of the gear system is improved.