裂纹齿轮—转子系统振动特性分析

发布时间：2018-04-26 16:34

本文选题：齿根裂纹 + 啮合刚度　；参考：《东北大学》2014年硕士论文

【摘要】：齿轮副是机械设备中最为常用的动力和运动传递装置,其力学行为和工作性能直接影响着机械系统的整体性能和可靠性。由于齿轮的受力情况相当复杂,即使精细设计的齿轮箱也难免出现故障,这种不期望的故障可能导致严重的经济损失甚至危及生命,因而对齿轮的早期故障特征进行分析并尽早识别齿轮早期故障具有重要的工程意义。本文以一个试验台齿轮转子系统为研究对象,建立齿轮副啮合模型及齿轮转子系统有限元模型,探讨齿根裂纹故障对齿轮啮合刚度和系统振动响应的影响,并通过试验对理论结果进行分析和对比。论文的主要研究内容如下：(1)对啮合刚度的三种求解方法,即变形法、能量法和有限元法进行详细的介绍,在传统能量法求啮合刚度的基础上提出改进能量法。通过变形法、改进能量法和有限元三种啮合刚度求解方法的对比表明,有限元法可以考虑更多的实际因素,计算结果较为准确,但计算效率较低。传统的能量法将轮齿视为基圆上的悬臂梁,在轮齿较多或较少时会产生很大的误差,而改进能量法考虑了真实的齿根过渡曲线,将轮齿视为齿根圆上的悬臂梁,更加符合轮齿的形状和受力情况,计算结果更为准确。(2)考虑较为真实的裂纹扩展路径和齿根裂纹对轮齿有效厚度的削弱作用,求解含齿根裂纹的齿轮啮合刚度,分析了裂纹深度、宽度、起始位置和扩展方向对齿轮啮合刚度的影响。研究结果表明,采用直线来模拟裂纹的扩展路径是合理的；在裂纹深度较大时应采用抛物线作为裂纹对轮齿有效厚度削弱的限制线。随着裂纹深度和宽度的增加,啮合刚度的降低幅度增加；随着裂纹起始位置角的增大,啮合刚度的降低幅度减小；随着裂纹扩展方向角的增大,啮合刚度先减小后增大。(3)探讨了齿根裂纹前后系统振动响应的变化以及不同裂纹参数对系统振动响应的影响。研究结果表明,裂纹出现后系统振动响应发生变化,时域波形中出现了以裂纹齿轮转动周期为间隔的周期性冲击,在啮合频率及其谐波附近出现边频,并且冲击、边频以及统计量的幅值随着裂纹深度和宽度的增加而增大,随裂纹起始位置角的增大而减小,随裂纹扩展方向角的增大先增加后减小。(4)考虑由轮齿弹性变形导致的延长啮合效应,基于有限元模型,分析了延长啮合对齿轮啮合刚度和系统振动响应的影响。分析结果表明,考虑延长啮合效应后,单双齿交替时啮合刚度不再是突变的而是渐变的,并且随着扭矩的增大,延长啮合现象越来越显著。另外,考虑延长啮合效应后,系统振动响应的时域和的频域特征也发生改变。(5)通过实验对理论分析进行验证,寻找有效识别早期裂纹故障的方法。研究表明,裂纹出现后,实验和仿真信号的瞬时能量在时间分布上产生周期性冲击,并且随着裂纹深度的增加,冲击能量的幅值越来越大。因而,通过Hilbert瞬时能量的变化可以较为轻松的检测齿轮裂纹故障。
[Abstract]:Gear pair is the most commonly used power and motion transmission device in mechanical equipment, its mechanical behavior and working performance directly affect the overall performance and reliability of the mechanical system. Because the force condition of the gear is quite complex, even the fine design gear box is unavoidable to fail, this undesirable failure may lead to a serious economy. The loss even endangers life, so it is of great engineering significance to analyze the early fault characteristics of the gear and identify the early fault of the gear as early as possible. In this paper, a gear rotor system of a test rig is used as the research object, the gear pair meshing model and the finite element model of the gear rotor system are set up, and the tooth root crack fault on the gear meshing stiffness is discussed. The main research contents of the thesis are as follows: (1) the three methods of solving meshing stiffness, namely, deformation method, energy method and finite element method, are introduced in detail, and the improved energy method is put forward on the basis of the traditional energy method to find the meshing stiffness. The comparison of the three methods of solving the meshing stiffness of the improved energy method and the finite element method shows that the finite element method can consider more practical factors, the calculation result is more accurate, but the calculation efficiency is low. The traditional energy method regards the tooth as the cantilever beam on the base circle, and it will produce great error when the tooth is more or less, and the improved energy method is improved. Considering the true tooth root transition curve, the tooth is regarded as the cantilever beam on the tooth root circle, and the calculation results are more accurate. (2) considering the more true crack propagation path and the tooth root crack to weaken the effective thickness of the tooth, the meshing stiffness of the teeth with the tooth root crack is solved, and the crack is analyzed. The effect of depth, width, starting position and extension direction on the gear meshing stiffness. The results show that it is reasonable to use a straight line to simulate the propagation path of a crack; a parabola should be used as a limiting line to weaken the effective thickness of the tooth when the crack depth is large. With the increase of the crack depth and width, the meshing stiffness is reduced. The reduction of the meshing stiffness decreases with the increase of the starting angle of the crack, and the meshing stiffness decreases first and then increases with the increase of the direction angle of the crack growth. (3) the changes of the system vibration response before and after the tooth root crack and the effect of the different crack parameters on the system vibration response are discussed. The results show that the crack is out of the crack. The vibration response of the system is changed. The periodic impact of the crack gear rotation period appears in the time domain, and the edge frequency occurs near the meshing frequency and its harmonics, and the amplitude of the shock, the side frequency and the statistics increase with the increase of the crack depth and width, and decreases with the increase of the initial angle of the crack. The increase of the direction angle of the crack growth first increases and then decreases. (4) considering the extended meshing effect caused by the elastic deformation of the tooth, the effect of the extended meshing on the gear meshing stiffness and the vibration response of the system is analyzed based on the finite element model. The results show that the meshing stiffness of the single and double teeth alternation is no longer abrupt when the engagement effect is extended. It is a gradual change, and with the increase of torque, the prolonged meshing phenomenon becomes more and more obvious. In addition, the time-domain and frequency domain characteristics of the vibration response of the system are also changed after considering the prolongation of the meshing effect. (5) through the experiment, the theoretical analysis is verified to find a method to effectively identify the early crack failure. The study shows that after the crack appears, the experiment is shown. The instantaneous energy of the simulated signal produces a periodic impact on the time distribution, and the amplitude of the impact energy increases with the increase of the depth of the crack. Therefore, the fault of the gear crack can be easily detected by the change of the instantaneous energy of the Hilbert.

【学位授予单位】：东北大学
【学位级别】：硕士
【学位授予年份】：2014
【分类号】：TH113.1

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