计入齿面摩擦的行星轮系非线性动力学研究

发布时间：2018-10-08 09:59

【摘要】：齿面摩擦是影响行星齿轮传动系统振动与噪音的关键因素之一。,为明确真实工况下的行星轮系的动力学行为,有必要探究齿面摩擦对系统动力学特性的影响机理。有鉴于此,本文在考虑齿轮副时变啮合刚度、齿侧间隙、静态传递误差等因素的基础上,进一步计及齿面摩擦力的影响,建立计入摩擦效应的直齿行星轮系平移-扭转耦合非线性动力学模型。针对所建的动力学模型,推导轮系运动微分方程,并利用四阶变步长Runge-kutta法求解系统的动力学响应。通过对比有、无计入齿面摩擦效应工况下的轮系动力学响应,揭示齿面摩擦对系统动力学行为的影响机理。在此基础上,进一步开展参数影响分析,以明确设计参数对系统动态特性的影响规律。论文具体内容及贡献简述如下:首先,简要阐述了行星轮系中轴承支承刚度、齿轮副时变啮合刚度、齿轮传动误差、齿侧间隙和齿面摩擦力等非线性因素的计算方法,给出了相关参数的数学描述式,并结合具体案例进行了时变啮合刚度和齿轮传动误差的参数整定。在此基础上,采用集中参数法建立了计入齿面摩擦效应的直齿行星轮系平移—扭转耦合非线性动力学模型,并运用牛顿第二定律推导了系统各传动构件的运动微分方程。其次,对所建的系统运动微分方程进行了降阶和无量纲化处理,进而利用四阶变步长Runge-kutta法求解了系统的动力学方程,获得了行星齿轮系统中各主要构件的稳态响应。在此基础上,对比分析了计入齿面摩擦效应前、后两种工况下太阳轮、行星架和内齿圈的周期响应和动态啮合力。数据表明,齿面摩擦力对系统的非线性运动有一定的抑制作用,会使得系统的振动位移响应和动态啮合力略有减弱。再次,基于上述的动力学分析,开展了参数影响分析的研究。针对有、无摩擦效应两种工况,相继分析了激励频率、啮合阻尼和齿侧间隙对系统非线性行为的影响,初步得到了系统非线性行为的变化规律。此外,进一步研究了时变啮合刚度和静态传动误差对系统动力学响应的影响规律。数据表明,在啮合频率、啮合阻尼和间隙的影响下,齿面摩擦会改变系统进入或者结束混沌运动状态的边界条件。随着齿面摩擦系数的增大,系统会从混沌运动遍历到拟周期、再到单周期的状态。
[Abstract]:Tooth surface friction is one of the key factors affecting the vibration and noise of planetary gear transmission system. In order to clarify the dynamic behavior of planetary gear train under real working conditions, it is necessary to explore the influence mechanism of tooth surface friction on the dynamic characteristics of the system. In view of this, the influence of tooth surface friction is considered on the basis of considering the factors such as gear pair time-varying meshing stiffness, tooth side clearance, static transfer error and so on. A nonlinear dynamic model of transverse-torsional coupling of straight tooth planetary gear train with friction effect is established. According to the dynamic model, the differential equations of gear train motion are derived, and the dynamic response of the system is solved by using the fourth order variable step Runge-kutta method. By comparing the dynamic responses of gear trains without the tooth surface friction effect, the influence mechanism of tooth surface friction on the dynamic behavior of the system is revealed. On this basis, further analysis of the influence of parameters is carried out to clarify the influence of design parameters on the dynamic characteristics of the system. The specific contents and contributions of this paper are summarized as follows: firstly, the calculation methods of nonlinear factors such as bearing support stiffness, gear pair time-varying meshing stiffness, gear transmission error, tooth side clearance and tooth surface friction in planetary gear train are briefly described. The mathematical description of the related parameters is given, and the parameter tuning of the time-varying meshing stiffness and gear transmission error is carried out with a concrete case. On the basis of this, a nonlinear dynamic model of translation-torsional coupling is established by using the lumped parameter method, which takes into account the friction effect on the tooth surface, and the differential equations of motion of each transmission member of the system are derived by using Newton's second law. Secondly, the differential equations of motion of the system are reduced and dimensionless, and the dynamic equations of the system are solved by using the four-order variable step Runge-kutta method, and the steady-state responses of the main components in the planetary gear system are obtained. On this basis, the periodic response and dynamic meshing force of solar wheel, planetary frame and inner gear are analyzed under the latter two working conditions before the tooth surface friction effect is taken into account. The data show that the tooth surface friction can restrain the nonlinear motion of the system to a certain extent and weaken the vibration displacement response and dynamic meshing force of the system. Thirdly, based on the above kinetic analysis, the parameter impact analysis is carried out. In this paper, the effects of excitation frequency, meshing damping and tooth clearance on the nonlinear behavior of the system are analyzed one after another, and the variation law of the nonlinear behavior of the system is preliminarily obtained. In addition, the influence of time-varying meshing stiffness and static transmission error on the dynamic response of the system is further studied. The data show that under the influence of meshing frequency meshing damping and clearance the tooth surface friction will change the boundary conditions when the system enters or ends the chaotic motion state. With the increase of tooth friction coefficient, the system will move from chaotic motion ergodic to quasi-periodic, and then to single-period state.
【学位授予单位】：安徽工业大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：TH132.41

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