Sensitivity Analysis of Helical Gears with Tooth Surface Modification to Applied Torque and Gear Misalignment

斜齿轮修形对负载扭矩和啮合错位的敏感性

¹ Shaanxi Engineering Laboratory for Transmissions and Controls, Northwestern Polytechnical University, Xi’an 710072, China
² China Shipbuilding Industry Corporation 703 Institute, Harbin 150078, China
³ Key Laboratory of Road Construction Technology and Equipment of Ministry of Education, Chang'an University, Xi'an 710064, China

Received: 5 December 2017

Abstract

The numerical calculation model of time-varying mesh stiffness, static transmission error and composite mesh error of modified helical gears is developed based on loaded tooth contact analysis (LTCA) model. To minimize the fluctuation of vibration excitation force, the optimal modification parameters of three modification methods under designed applied torque and ideal tooth contact condition are determined, and the effects of three modification methods on time-varying mesh stiffness, static transmission error and composite mesh error are analyzed. In order to analyze the sensitivity of the three modification methods to applied torque and gear misalignment, the effects of applied torque in wide range and gear misalignment on vibration excitation force and dynamic transmission error are investigated. The results show that the difference of time-varying mesh stiffness, static transmission error, composite mesh error of helical gears with different modifications methods are obvious. However, the fluctuation of vibration excitation force of helical gears is reduced significantly. When the applied torque is higher than the designed applied torque, the three modification methods show a great reduction of system vibration. When the applied torque is too low, the vibration of modified helical gears is larger than unmodified ones. Meanwhile, the resonance speed of the helical gears is slightly lower. With the increase of gear misalignment, the resonance speed becomes lower correspondingly and the effect of the three modification methods on the reduction of vibration excitation force is not obvious any more. The results can provide effective reference for establishing robust optimization method for tooth surface modification.

摘要

基于齿面承载接触分析方法，建立了修形斜齿轮时变啮合刚度、静态传递误差和综合啮合误差计算模型。以系统振动激振力波动量最小为目标，确定了设计负载扭矩和理想啮合状况下3种修形方式的最佳修形参数，并分析了3种修形方式对斜齿轮时变啮合刚度、静态传递误差以及综合啮合误差的影响。通过考察宽范围负载扭矩和啮合错位影响下的修形斜齿轮系统振动激振力和动态传递误差，分析了3种修形方式对负载扭矩和啮合错位的敏感性。研究表明：采用不同修形方式的斜齿轮时变啮合刚度、静态传递误差以及综合啮合误差差别较大，然而系统振动激振力波动量均得到了显著降低。当负载扭矩大于设计扭矩时，3种修形方式仍有较好减振效果。当负载扭矩过小时，3种修形方式的齿轮系统振动将大于未修形齿轮系统，且共振转速略有降低。随着啮合错位量的增加，系统共振转速逐步降低，且3种修形方式的减振效果均逐渐降低，直至不再具有减振效果。研究结果可为进一步建立齿面修形稳健设计方法提供有效参考。