锥齿轮传动机构的优化设计

Optimum Design of Bevel Gear Drive Mechanism

以锥齿轮副的体积和最小为目标,以锥齿轮齿面许用接触应力和齿根许用弯曲应力为性能约束条件,以小锥齿轮齿数、齿轮副模数、齿轮副齿宽因数等设计变量为边界条件,建立数学模型,对轴交角为90°的锥齿轮传动机构进行优化设计。在优化设计中,结合实例采用惩罚函数法构造适应度函数,取小齿轮的复合齿形因数为4.80。应用Matlab优化工具箱fmincon函数编制遗传算法.m格式文件,对目标函数进行求解。程序运行结束后,对设计变量采用遗传算法进行离散变量优化,获得齿轮副各个变量的最优解。通过实例确认,锥齿轮传动机构的优化设计效果良好,具有可行性和实用性,为齿轮传动机构的多目标优化设计提供了参考。

Taking the minimum volume of the bevel gear pair as the target,taking the permissible contact stress on the bevel gear tooth surface and the permissible bending stress on the tooth root as performance constraints and taking the design variables such as the tooth number of bevel pinion,gear pair modulus,gear pair tooth width coefficient,etc.as the boundary conditions,a mathematical model was established to optimize the design of the bevel gear drive mechanism with a crossed axes angle of 90°.In the optimum design,a penalty function method was used in combination with an example to construct the fitness function,and the compound tooth form factor of the pinion was 4.80.The Matlab optimization kit fmincon function was used to compile the.m format file in genetic algorithm to solve the objective function.At the end of the program run,the genetic algorithm was used to optimize the discrete variables for the design variables and obtain the optimal solution of each variable of the gear pair.It is confirmed by example that the optimum design of the bevel gear drive mechanism can possess sound performance,feasibility and practicability,and provides a reference for the multi-objective optimal design of the gear transmission mechanism.