考虑齿顶修缘的直齿轮—转子系统非线性动力学特性研究

发布时间：2018-08-06 16:48

【摘要】：齿轮转子系统是旋转机械的主要传动系统,是各种设备中应用最广的动力传递装置。由于制造、安装误差和轮齿变形等因素,齿轮在啮合过程中难免产生振动和冲击,齿廓修形是优化接触、弥补误差、降低振动和冲击的有效手段。本文基于ANSYS软件建立考虑齿顶修缘的准静态直齿轮副啮合有限元模型,输出时变啮合刚度和静态传递误差。在此基础上,基于MATLAB软件建立直齿轮副啮合动力学模型,与转子有限元模型耦合形成直齿轮-转子系统弯扭轴摆全自由度有限元模型。考虑时变啮合刚度、静态传递误差、扭转激励以及齿侧间隙,对直齿轮-转子系统进行模态分析以及动力学特性分析。主要内容如下： (1)基于ANSYS软件,在准静态下建立直齿轮副啮合有限元模型,对其进行静力学分析,在仅考虑轮齿变形的前提下,计算不同扭矩作用下考虑齿顶修缘的齿轮的时变啮合刚度和静态传递误差,为直齿轮-转子系统动力学特性分析提供数据支持。通过分析得出不同加载扭矩将引起啮合刚度和静态传递误差整体幅值的变化,而齿顶修缘能够缓和单双齿交替区的突变,使啮合频率的高频成分幅值发生变化。 (2)建立直齿轮副啮合动力学模型,与转子有限元模型耦合形成直齿轮-转子有限元模型。假定啮合刚度为定值,对静态传递误差作用下的系统响应进行求解得出静态传递误差的基频、高频成分分别激起幅频响应的有关弯扭耦合的主共振峰和超谐波共振峰。考虑时变啮合刚度的影响,对系统施加定值扭转激励,分析表明时变啮合刚度的基频成分也将使系统产生基频以及倍频成分。另外由于时变啮合刚度和正弦扭转激励相互影响,系统将产生啮合频率及其倍频、转频以及啮合频率与转频的和频、差频等复杂的频率成分。 (3)考虑齿顶修缘条件下的时变啮合刚度和静态传递误差,分析不同扭矩下不同修缘量对系统振动响应的影响。齿顶修缘能够降低除共振峰处的动力学响应幅值,抑制加速度幅值波动,减少振动和冲击,并且不同扭矩对应的最优修缘量不同,随着齿顶修缘量的增加振动响应幅值并不是持续降低。 (4)考虑齿侧间隙,建立仅考虑扭转自由度的动力学模型,分析不同系统参数下齿侧间隙对系统动力学特性的影响。随着齿侧间隙的增大,系统硬式非线性特性以及双边冲击状态逐渐消失,均呈现为“软化曲线”。随着阻尼的增大系统幅频响应幅值逐渐减少,硬式非线性特性和共振峰处的跳跃现象逐渐消失。随着扭转激励的增大系统幅频响应幅值逐渐增大,硬式非线性特性逐渐显著。由于齿侧间隙对振动响应的影响依赖于系统参数,对于本文所研究的齿轮-转子系统,考虑齿侧间隙情况下系统的幅频响应未出现跳跃现象。本文通过数值仿真方法,主要对考虑齿顶修缘的直齿轮-转子系统进行动力学特性研究,研究结果可为直齿轮-转子系统的动态响应计算以及结构设计提供理论依据。
[Abstract]:Gear rotor system is the main transmission system of rotating machinery. It is the most widely used power transmission device in all kinds of equipment. Because of the factors such as manufacturing, installation error and gear tooth deformation, the gear is unavoidable to produce vibration and impact during the meshing process. The tooth profile modification is an effective means to optimize contact, make up error, reduce vibration and impact. The ANSYS software establishes the finite element model of the quasi static spur gear pair, which considers the tooth top repair edge, and the time-varying meshing stiffness and the static transmission error. On this basis, based on the MATLAB software, the meshing dynamic model of the spur gear is established and coupled with the rotor finite element model to form the full degree of freedom finite element model of the bending and torsion axis swing of the spur rotor system. Considering the time-varying meshing stiffness, static transmission error, torsional excitation and tooth side gap, the modal analysis and dynamic characteristic analysis of the spur gear rotor system are carried out. The main contents are as follows:
(1) based on the ANSYS software, the finite element model of the spur gear meshing is established under the quasi static state, and the statics analysis is carried out. The time-varying meshing stiffness and the static transmission error of the gear with the tooth top repair edge are calculated under the condition of only the tooth deformation, which provides the data support for the dynamic characteristics analysis of the spur gear rotor system. The analysis shows that the different loading torque will cause the change of the overall amplitude of the meshing stiffness and the static transmission error, and the tooth top repair edge can ease the mutation of the single and double teeth alternation zone, and make the high-frequency component amplitude of the meshing frequency change.
(2) establish the meshing dynamic model of the spur gear, coupled with the rotor finite element model to form the finite element model of the spur gear rotor. Assuming the meshing stiffness as the fixed value, the system response of the static transmission error is solved to get the basic frequency of the static transmission error and the main resonance of the amplitude frequency response of the high frequency component to the amplitude frequency response. Considering the influence of time-varying meshing stiffness, considering the influence of time-varying meshing stiffness, the fixed value torsion excitation is applied to the system. The analysis shows that the basic frequency component of the time-varying meshing stiffness will also make the system produce fundamental frequency and frequency doubling component. And complex frequency components such as frequency and frequency, frequency difference.
(3) considering the time varying meshing stiffness and the static transmission error under the tooth top repair edge, the influence of the different trimming amount on the vibration response of the system under different torque can be analyzed. The tooth top repair edge can reduce the amplitude of the dynamic response except the resonance peak, restrain the fluctuation of the acceleration amplitude, reduce the vibration and impact, and the optimal trimming amount corresponding to the different torque is not. The amplitude of vibration response does not decrease continuously with the increase of tooth margin.
(4) considering the tooth side gap, a dynamic model which only considers the torsional degree of freedom is established, and the influence of the tooth side gap on the dynamic characteristics of the system is analyzed under the different system parameters. With the increase of the tooth side gap, the hard nonlinear characteristics and the bilateral impact state gradually disappear, all of which are now "softening curves". With the damping increasing the system amplitude The amplitude of the frequency response is gradually reduced, the hard nonlinear characteristics and the jumping phenomenon at the resonance peak gradually disappear. With the increase of the torsional excitation, the amplitude of the amplitude frequency response of the system increases gradually, and the hard type nonlinear characteristic is gradually obvious. There is no jumping phenomenon when the amplitude frequency response of the system is taken into account.
In this paper, the numerical simulation method is used to study the dynamic characteristics of the spur rotor system, which considers the tooth top repair edge. The results can provide the theoretical basis for the dynamic response calculation and the structure design of the spur gear rotor system.
【学位授予单位】：东北大学
【学位级别】：硕士
【学位授予年份】：2013
【分类号】：TH132.41

【参考文献】