高速重载人字齿轮传动非线性动力学分析

NONLINEAR DYNAMIC ANALYSIS OF HIGH SPEED AND HEAVY LOAD HERRINGBONE GEAR TRANSMISSION

人字齿轮承载能力强,重合度大,可靠性高,多于高速、重载工况下使用.探究高速重载人字齿轮传动系统非线性动力学特性,可为其设计提供参考.首先,计算齿轮副时变啮合刚度;引入齿侧间隙、间隙非线性函数和综合传动误差,计算时变啮合力;引入轴承游隙,计算轴承受力.随后,建立高速重载人字齿轮传动系统非线性动力学方程,使用4阶Runge-Kutta法对方程求解.最后,探究不同因素对系统动态响应影响.保持系统其他参数不变,分别改变输入转矩、啮合阻尼、齿侧间隙、啮合刚度及激励频率,绘制系统时间−位移图像、时间−速度图像、空间相图、空间频谱图及分岔图,观察系统非线性动力学响应变化趋势,判别系统运动状态.结果表明:在一定范围内,系统稳定性与啮合阻尼、啮合刚度呈正相关关系,与齿侧间隙、输入转矩呈负相关关系;逐渐增大外部激励频率时,系统运动从单周期运动逐渐变为混沌运动,随后又回归单周期运动.为保证系统平稳运行,应合理选取外部激励频率.

Herringbone gears have strong bearing capacity,large contact ratio and high reliability,and are mostly used in high-speed and heavy-load working occasions.Exploring the nonlinear dynamic characteristics of high-speed and heavy-duty herringbone gear transmission system and finding out the stable operation interval of the system can provide reference for its design.Firstly,the time-varying meshing stiffness of gear pair is calculated,and the time-varying meshing force is calculated by introducing the backlash,the nonlinear function of backlash and the comprehensive transmission error.The bearing clearance is introduced to calculate the bearing force.Subsequently,the nonlinear dynamic equation of the high-speed and heavy-duty herringbone gear transmission system is established,and the fourthorder Runge-Kutta method is used to solve the equation.Finally,the influence of different factors on the stability of the system is explored.Keeping other parameters of the system unchanged,the meshing damping,backlash,meshing stiffness and excitation frequency are changed respectively.The time-displacement image,time-velocity image,spatial phase diagram,spatial frequency diagram and bifurcation diagram of the system are drawn.The change trend of nonlinear dynamic response of the system is observed and the motion state of the system is judged.The results show that within a certain range,the stability of the system is positively correlated with meshing damping and meshing stiffness,and negatively correlated with the backlash.When the external excitation frequency is gradually increased,the system motion gradually changes from single-cycle motion to chaotic motion,and then returns to stable single-cycle motion.Therefore,in order to ensure the smooth operation of the system,the external excitation frequency should be reasonably selected.