基于齿轮动态激励和弹流润滑的多目标优化

Multi objective optimization based on dynamic incentives and elastohydrodynamic lubrication of gear

依据齿轮啮合动态激励基本原理和弹性流体动力润滑理论,建立同时追求齿轮啮合时变刚度激励最小、齿间最小油膜厚度最大(倒数最小)及齿轮传动总体积最小的约束多目标优化设计数学模型。对现有的用于两目标优化设计的粒子群优化方法加以改进,给出了约束3目标优化设计方法。利用Matlab编制优化程序,并对范例进行分析计算。优化过程及结果表明,采用较多的齿数,在小于1的范围内采用较大的正变位系数,适度采用较大的压力角可以增大轮齿啮合综合刚度谱图中基频谐波的幅值,有效地提高齿轮传动系统抵抗内部激励振动的能力及性价比。

According to the fundamental of gear mesh dynamic incentives and elastohydrodynamic lubrication theory,this paper establishes a mathematical model of constraint multi objective optimization,which seeks the minimum of time-varying stiffness excitation of gear mesh,the maximum of minimum oil film thickness（the minimum reciprocal） in tooth space,and the minimum of total volume of transmission at the same time.This paper improves present particle swarm optimization of two-objective optimization and shows a design of constraint three-objective optimization.It also programs optimization by Matlab and analyzes examples.The optimization process and result show that,in less than one range,when more number of teeth,larger positive modification coefficient and appropriate pressure angle are adopted,the amplitude of fundamental harmonic in the tooth mesh spectrogram of synthetical stiffness is enlarged,and the capacity and cost performance are increased effectively while the gear powertrain system resists vibration of internal incentives.