考虑摩擦和间隙的轮齿冲击行为建模与分析
发布时间：2018-12-26 10:23
【摘要】：本文根据非线性动力学的相关理论,利用定性和定量的方法对含真实时变刚度、真实静态传动误差、齿面摩擦以及齿侧间隙的齿轮传动系统的非线性动力学特性进行了研究,论文主要内容如下： 1.建立了包含真实时变刚度、真实静态传动误差以及齿面摩擦等在内的齿轮扭转振动模型。假设轮齿在啮合线上匀速运动和摩擦系数为常数,推导出啮合过程中摩擦力的表达式,并考虑齿轮传动中的时变参数——啮合刚度和静态传动误差,将其代入到齿轮副扭转振动模型中,推导出了系统的动力学微分方程。 2.针对所建立的齿轮非线性动力学模型分别应用解析法和数值法进行求解分析。在应用解析方法之前,利用简单的傅里叶级数表达时变刚度和静态传动误差,并应用高次多项式拟合分段非光滑的轮齿间隙函数,推导出系统分别在主共振和1/2亚谐共振情况下的幅频函数,揭示了系统的一些非线性现象,如亚谐响应,跳跃和分岔。针对真实时变参数下的离散动力学模型,应用数值法分析系统的动态响应以及参数的变化对系统动力学行为的影响,发现齿面摩擦在节点附近的局部范围引起动态传动误差和动态啮合力的突变和附加振动,齿轮的转速、负载力矩以及阻尼等参数对系统的动态响应也都具有不同程度影响。 3.应用数值法对轮齿的冲击-碰撞动力学进行了探索研究。引入考虑能量损耗的非线性弹簧-阻尼接触模型,将轮齿啮合过程简化为两侧弹性碰撞的连续动力学模型,应用接触碰撞理论、非线性理论和数值方法研究了系统的稳态响应及能量损耗的频率分岔,数值结果表明系统具有非常复杂的动力学特性,随着参数的变化发生了周期分叉和擦边分叉。 4.通过齿轮传动实验测得一对标准参数的直齿圆柱齿轮的动态传动误差,从原始实验数提取稳态响应的频谱特性,与理论分析得到的结果进行对比,验证了理论模型的有效性。
[Abstract]:Based on the theory of nonlinear dynamics, the nonlinear dynamic characteristics of gear transmission system with real time-varying stiffness, real static transmission error, tooth surface friction and tooth side clearance are studied by qualitative and quantitative methods. The main contents of the thesis are as follows: 1. The torsional vibration model of gears including real time-varying stiffness, real static transmission error and tooth surface friction is established. Assuming that the uniform speed motion and friction coefficient of the gear teeth are constant on the meshing line, the expression of friction force in the meshing process is derived, and the time-varying parameters in the gear transmission, meshing stiffness and static transmission error, are taken into account. The dynamic differential equation of the system is derived by inserting it into the torsional vibration model of the gear pair. 2. The nonlinear dynamic model of gear is solved by analytic method and numerical method respectively. Before applying the analytical method, the time-varying stiffness and static transmission error are expressed by simple Fourier series, and the piecewise nonsmooth gear clearance function is fitted with higher order polynomial. The amplitude-frequency functions of the system in the case of main resonance and 1 / 2 subharmonic resonance are derived respectively. Some nonlinear phenomena of the system such as subharmonic response jump and bifurcation are revealed. For the discrete dynamic model with real time-varying parameters, the dynamic response of the system and the influence of the parameters on the dynamic behavior of the system are analyzed by numerical method. It is found that the local range of tooth surface friction causes the sudden change and additional vibration of dynamic transmission error and dynamic meshing force, and the parameters of gear rotation speed, load moment and damping have different effects on the dynamic response of the system. 3. The impact-impact dynamics of gear teeth are studied by numerical method. In this paper, a nonlinear spring-damping contact model considering energy loss is introduced. The meshing process of gear teeth is simplified as a continuous dynamic model of elastic impact on both sides, and the contact collision theory is applied. Nonlinear theory and numerical method are used to study the steady state response of the system and the frequency bifurcation of energy loss. The numerical results show that the system has very complex dynamic characteristics, and the periodic bifurcation and erasure bifurcation occur with the change of parameters. 4. The dynamic transmission errors of a pair of straight cylindrical gears with standard parameters are measured by gear transmission experiments. The spectral characteristics of steady state response are extracted from the original experimental data, and compared with the results obtained by theoretical analysis, the validity of the theoretical model is verified.
【学位授予单位】：中南大学
【学位级别】：硕士
【学位授予年份】：2011
【分类号】：TH132.41
本文编号：2391958
[Abstract]:Based on the theory of nonlinear dynamics, the nonlinear dynamic characteristics of gear transmission system with real time-varying stiffness, real static transmission error, tooth surface friction and tooth side clearance are studied by qualitative and quantitative methods. The main contents of the thesis are as follows: 1. The torsional vibration model of gears including real time-varying stiffness, real static transmission error and tooth surface friction is established. Assuming that the uniform speed motion and friction coefficient of the gear teeth are constant on the meshing line, the expression of friction force in the meshing process is derived, and the time-varying parameters in the gear transmission, meshing stiffness and static transmission error, are taken into account. The dynamic differential equation of the system is derived by inserting it into the torsional vibration model of the gear pair. 2. The nonlinear dynamic model of gear is solved by analytic method and numerical method respectively. Before applying the analytical method, the time-varying stiffness and static transmission error are expressed by simple Fourier series, and the piecewise nonsmooth gear clearance function is fitted with higher order polynomial. The amplitude-frequency functions of the system in the case of main resonance and 1 / 2 subharmonic resonance are derived respectively. Some nonlinear phenomena of the system such as subharmonic response jump and bifurcation are revealed. For the discrete dynamic model with real time-varying parameters, the dynamic response of the system and the influence of the parameters on the dynamic behavior of the system are analyzed by numerical method. It is found that the local range of tooth surface friction causes the sudden change and additional vibration of dynamic transmission error and dynamic meshing force, and the parameters of gear rotation speed, load moment and damping have different effects on the dynamic response of the system. 3. The impact-impact dynamics of gear teeth are studied by numerical method. In this paper, a nonlinear spring-damping contact model considering energy loss is introduced. The meshing process of gear teeth is simplified as a continuous dynamic model of elastic impact on both sides, and the contact collision theory is applied. Nonlinear theory and numerical method are used to study the steady state response of the system and the frequency bifurcation of energy loss. The numerical results show that the system has very complex dynamic characteristics, and the periodic bifurcation and erasure bifurcation occur with the change of parameters. 4. The dynamic transmission errors of a pair of straight cylindrical gears with standard parameters are measured by gear transmission experiments. The spectral characteristics of steady state response are extracted from the original experimental data, and compared with the results obtained by theoretical analysis, the validity of the theoretical model is verified.
【学位授予单位】：中南大学
【学位级别】：硕士
【学位授予年份】：2011
【分类号】：TH132.41
【引证文献】
相关硕士学位论文 前2条
1 白国庆;TY型商用车细高齿变速箱动态特性仿真及分析[D];太原理工大学;2012年
2 吴伟传;基于沉桩负载的液压振动桩锤齿轮传动系统动态特性研究[D];中南大学;2012年
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