考虑齿顶修缘的齿轮-转子系统振动响应分析

Vibration Response Analysis of a Geared Rotor System Considering the Tip Relief

考虑齿轮齿顶修缘,基于ANSYS软件建立了直齿轮啮合有限元模型,基于该模型确定了未修缘以及不同修缘量下的时变啮合刚度和静态传递误差,并将其引入齿轮-转子系统的有限元模型,分析了齿顶修缘对系统振动响应的影响。研究表明:随着齿顶修缘量的增加,时变啮合刚度以及静态传递误差在啮入点以及单双齿啮合区交替处的突变减少;在一定转速内,系统振动响应的幅值降低,但在某些临界转速附近反而有增大的趋势;当齿轮啮合频率等于系统固有频率或分频时会出现共振峰,在某些修缘量情况下一些分频对应的共振峰消失,研究结果可为修形齿轮的动态响应计算和结构设计提供理论依据。

Considering the tip relief, a finite element model （FEM） of a spur gear pair in mesh is built by ANSYS software. Time-varying mesh stiffness and static transmission error with different amounts of tip relief are calculated based on the FEM. Then a finite element model of a geared rotor system is developed by considering the effects of the time-varying mesh stiffness and static transmission error, and the effect of the tip relief on the system vibration response is analyzed. The results show that as the amount of the tip relief on the gear increases, the saltation of the time-varying mesh stiffness and static transmission error decreases at the position of approach action and transition mesh region from the single-tooth to the double-tooth. The vibration amplitude significantly decreases at certain speeds, but it has an increase tendency in the vicinity of some critical speeds. A resonance peak appears when the gear mesh frequency is equal to the natural frequency or its fractional frequency; however, some resonance peaks corresponding to some fractional frequencies disappear at some amounts of the tip relief.