摘 要

城轨是城际轨道交通和城市轨道交通的简称兼统称，齿轮箱是双馈直线驱动电动机的关键部件，由于城轨所处环境和所受载荷的特殊性，造成了齿轮箱的高故障率。通过对城轨齿轮箱的转动装置设计优化，可以保证其设计质量，降低故障率，提高城轨整体运行的可靠性。基于齿轮动力学理论和Lagrange方程，运用集中参数法建立了某两级传动城轨齿轮箱的纯扭转动力学模型。将城轨齿轮传动系统中齿轮的弹性模量、质量密度、工作齿宽和分度圆直径视为随机变量，根据随机摄动理论推导了系统特征值统计特征的表达式。应用随机摄动法研究了齿轮物理参数和几何参数随机变异时系统固有频率的统计特征，定量分析了各参数随机变异对系统固有频率的影响。根据城轨齿轮传动系统的结构模型，以传动系统各构件扭转位移均值和体积最小为优化目标，以影响传动系统动态性能和可靠性的参数为优化设计变量，以传动系统的可靠度、参数随机性对可靠性的影响、以及各轮齿正常啮合的条件和强度等为约束条件，建立了用于城轨齿轮传动系统可靠性概率优化设计的数学模型。对系统优化问题的求解方法进行了探讨。

关键词：城轨；齿轮箱；动力学

Abstract

Urban rail transit is the abbreviation of intercity rail transit and urban rail transit.Gearbox is the key component of doubly fed linear drive motor.Due to the particularity of urban rail transit environment and load, the high failure rate of gearbox is caused. By optimizing the design of the rotating device of the urban rail gearbox,the design quality can be guaranteed, the failure rate can be reduced,And it can improve the reliability of the overall operation of urban rail. According to the theory of gear dynamics and Lagrangian equation,the pure torsional dynamic model of a two-stage transmission urban rail transit gearbox is established by using lumped parameter method. The elastic modulus, mass density,working tooth width and pitch circle diameter of gears in urban rail transit gear transmission system are regarded as random variables, and the statistical expression of eigenvalues of the system is derived according to the random perturbation theory. The statistical characteristics of natural frequency of gear system with random variation of physical and geometric parameters are studied by using random perturbation method,and the influence of random variation of each parameter on natural frequency of gear system is quantitatively analyzed. According to the structural model of urban rail transit gear transmission system,the optimization objective is to minimize the torsional displacement and volume of each component of the transmission system,the parameters affecting the dynamic performance and reliability of the transmission system are taken as the optimization design variables, and reliability of the transmission system, the effect of parameter stochasticity on reliability., and the normal meshing condition and strength of each gear tooth are taken asthe constraint conditions The mathematical model of reliability probability optimization design for urban rail transit gear transmission system is established. The solution method of system optimization problem is discussed.

Key words: urban rail transit; gearbox; dynamics