高重合度斜齿轮多齿对啮合的补偿修形设计与分析

Design and Analysis of Compensation Modification for Multi-Pair Contact of High-Contact-Ratio Helical Gears

为准确计算齿面修形量以降低承载传动误差波动幅值,考虑齿轮传动过程中不同啮合区之间轮齿承载变形的变化规律,提出了高重合度斜齿轮多齿对啮合的补偿修形设计方法。基于标准齿面在设计载荷下的承载传动误差波动幅值大小和方向,预设修形齿面的几何传动误差;通过优化几何传动误差控制齿面修形量大小,实现轮齿不同啮合区的精确补偿修形;建立齿向改进修形齿面模型,以齿条刀具附加转角和齿向修形参数为优化变量,采用快速非支配排序遗传算法(NSGA-II)基于承载传动误差幅值最小确定齿面最佳修形量。研究结果表明:啮合齿对变化引起不同啮合区之间轮齿承载变形的变化是承载传动误差幅值波动的主要原因;齿面补偿修形后,承载传动误差幅值大幅下降,在设计负载下,承载传动误差幅值几乎降到零;改进修形也能够有效补偿不同啮合区之间轮齿承载变形的差异,同时避免了边缘接触,降低了齿轮副的振动与噪声。

To accurately calculate the amount of the tooth surface modification to reduce the amplitude of load transmission error(ALTE),considering the load-bearing deformation of the teeth between different meshing areas in the process of gear meshing,a design method of compensation modification for multi-pair contact of high contact ratio helical gears is proposed.The transmission error of modified tooth surface is predesigned based on the magnitude and direction of ALTE of the standard tooth surface under the design load,and the precise compensation modification in different meshing areas of the tooth is realized by optimizing the TE to control the value of the tooth surface modification.The model of a further longitudinal modified tooth surface is established,and the additional angle of rack cutters and the parameters of the longitudinal correction are taken as the optimization variables.The optimal tooth surface modification values are determined by the fast elitist non-dominated sorting genetic algorithm(NSGA-II)based on the minimum ALTE.The results show that the change of load-bearing deformation caused by the change of meshing pairs is the main cause for the fluctuation of the ALTE.After the tooth surface compensation modification,the ALTE decreases greatly,and under the designed load,the ALTE drops to almost zero.The further longitudinal correction can also effectively compensate the difference of tooth deformation between different meshing areas of the teeth,avoiding the edge contact,and reducing the vibration and noise of gears.