含间隙碰撞系统的动力学研究

发布时间：2018-01-29 06:40

本文关键词： 分岔混沌碰撞振动 Poincaré映射　出处：《兰州交通大学》2013年硕士论文　论文类型：学位论文

【摘要】：含间隙碰撞振动系统是常见的非线性动力学系统，各种机械设备在生产、制造和装配的过程中会发生各种各样的误差，，从而导致机械设备具有间隙；并且在其调试运行过程中，由于碰撞摩擦也会产生间隙。另外，考虑机械设备的各种因素，一些机械设备在设计过程中会预留有间隙，如在啮合齿轮、滚动轴承等系统的有关零部件中也必然会存在间隙，这些间隙是无法消除与避免的。间隙引起设备接触区的接触状态会发生变化,机械设备工作中构件不断出现重复的冲击，碰撞构件发生碰撞会导致构件结构发生局部变形，在碰撞过程中会发生力波的传递对系统的载荷和动态特性影响产生的后果严重。因此，对含间隙振动系统来说，如何去利用它的优点取除它的缺点，对进行碰撞振动动力学优化设计，提高系统的可靠性有十分重要的意义。本文针对此类碰撞系统的三类振动模型情况做了具体的研究。 1.本文研究了三类典型的碰撞振动系统。通过建立碰撞振动系统的力学模型，在对模型进行受力分析，然后用数值分析法对这三个模型的系统周期运动理论推导。以坐标的变换对方程组解耦，用模态矩阵法解出方程组的通解；通过系统周期运动的边界条件结合方程组的通解求的周期中心不动点，从中推导出三类模型系统的解析解、线性化矩阵等一系列结果，然后由计算得到各个系统的Poincaré映射。 2.分析系统发生分岔和混沌的复杂动力学行为，运用Poincaré映射理论进行matlab软件编程找出行系统的稳定性。经数值仿真来验证计算结果的准确性和系统发生分岔与混沌现象，并且给出了线性化矩阵特征值横截单位圆周的趋势图。在数值仿真过程中找到适当的系统参数，研究了各个模型的碰撞振动系统不同情况下，得到了系统通向混沌过程中Poincaré截面图等。 3.由仿真的过程中我们得出一些结论：系统的一些参数如：激励频率、间隙、恢复系数等，这些控制参数的变化对系统运动的影响是非常大的，当它们在临界点处微小的变动就会引起系统运动质的变化。所以，在碰撞振动系统中临界点处系统参数的选择是很重要的，从仿真得到参数的选择对振动系统控制和优化机械设计提供理论参考。
[Abstract]:The collisional vibration system with clearance is a common nonlinear dynamic system. A variety of errors will occur in the process of production, manufacture and assembly of mechanical equipment, which leads to the gap of mechanical equipment. In addition, considering the various factors of mechanical equipment, some mechanical equipment will have clearance in the design process, such as meshing gear. There must also be clearance in the parts of rolling bearing system, which can not be eliminated and avoided. The gap will cause the contact state of the contact area of the equipment to change. The repeated impact of the components in the work of mechanical equipment will lead to the local deformation of the component structure due to the collision of the components. The effect of force wave transmission on the load and dynamic characteristics of the system will be serious in the process of collision. Therefore, for the vibration system with clearance, how to take advantage of its advantages to remove its shortcomings. It is very important to optimize the dynamic design of impact vibration and improve the reliability of the system. In this paper, three kinds of vibration models of the impact system are studied in detail. 1. Three kinds of typical impact vibration systems are studied in this paper. The mechanical model of the impact vibration system is established, and the force of the model is analyzed. Then the periodic motion theory of the three models is deduced by numerical analysis. The equations are decoupled by the transformation of coordinates and the general solutions of the equations are obtained by the modal matrix method. By combining the boundary conditions of the periodic motion of the system with the fixed point of the periodic center obtained by the general solution of the equations, a series of results, such as the analytical solution and the linearization matrix of the three kinds of model systems, are derived. Then the Poincar 茅 map of each system is calculated. 2. The complex dynamical behavior of bifurcation and chaos is analyzed. The Poincar 茅 mapping theory is used to program the stability of the trip finding system with matlab software, and the accuracy of the calculation results and the bifurcation and chaos phenomena of the system are verified by numerical simulation. At the same time, the trend diagram of the linear matrix eigenvalue cross-section unit circle is given. The appropriate system parameters are found in the process of numerical simulation, and the impact vibration system of each model is studied under different conditions. The Poincar 茅 section diagram of the system leading to chaos is obtained. 3. In the course of simulation, we draw some conclusions: some parameters of the system, such as excitation frequency, clearance, recovery coefficient, etc., the change of these control parameters has a great influence on the system motion. When they change slightly at the critical point, the system motion will change. Therefore, it is very important to choose the system parameters at the critical point in the impact vibration system. The selection of parameters from simulation provides a theoretical reference for vibration system control and optimization of mechanical design.
【学位授予单位】：兰州交通大学
【学位级别】：硕士
【学位授予年份】：2013
【分类号】：TH113.1

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