基于Kriging模型和遗传算法的齿轮修形减振优化

针对齿轮修形优化时计算啮合刚度计算量大、计算精度低、操作繁琐等问题，提出一种基于Kriging模型和遗传算法的齿轮减振修形优化算法.以典型直齿轮传动为例开展齿轮修形优化，通过拉丁抽样建立Kriging模型，解决齿轮修形优化的多响应和隐式函数的问题，通过Kriging预测的啮合刚度与有限元法的对比可知，时变啮合刚度函数各参数的误差最大值为7.79×10-5,1.20×10-3及1.30×10-4，验证了Kriging多响应预测啮合刚度函数的精确性.将Kriging预测函数代入直齿轮啮合传动的动力学微分方程，采用遗传优化算法时将齿轮动态传动误差响应波动最小作为优化目标，得到最优的齿轮修形参数.算例表明:相比于ISO(International Standardization Organization)修形和未修形的齿轮，该算法的减振效果最好，验证了基于遗传算法与Kriging模型对齿轮进行修形优化的正确性、高效性.相比于直接采用有限元法进行齿轮修形优化，该算法计算时间由26.91d减小为2.24h，证明了该算法计算效率的优越性. 

Vibration reduction optimization of gear modification based on Kriging model and genetic algorithm

To solves the problems of large computation, low precision and complicated operation during optimization of gear modification, an algorithm for optimization of gear modification was proposed based on Kriging model and genetic algorithm. Taking spur gear drive as the research object, optimization of gear modification was carried out. Firstly, in order to solve the problems of multiple responses and implicit function during optimization of gear modification, Kriging model was established by using Latin sampling method. Compared with the gear engaged stiffness of Kriging prediction and finite element, it was shown that the maximum errors of predicted stiffness parameters were 7.79×10-5, 1.20×10-3 and 1.30×10-4 respectively, therefore, the precision of Kriging multiple prediction was validated. Secondly, Kriging prediction was applied to dynamical differential equation of spur gear, and then fluctuation of dynamic transmission error was regarded as the goal of genetic algorithm optimization, so optimal parameters of gear modification was obtained. Example showed that the proposed method was better than ISO(International Standardization Organization) modification and no modification, therefore, the efficiency and correctness of the gear modification by using genetic algorithm and Kriging model was validated. Compared with gear modification by using finite element directly, the cost time of the proposed method changed from 26.91d to 2.24h, so the computational efficiency of the proposed method was verified.