基于赫兹约束的振动系统动力学研究

发布时间：2018-09-09 10:47

【摘要】：本文旨在对含间隙非线性振动系统的动力学特性进行仿真分析,研究各主要参数改变对系统动力学特性的影响,得到使系统状态较为稳定的参数取值规律,为一般冲击振动系统的参数优化作参考。以一个双质体冲击振动成型机为研究对象,先将其简化为动力学模型,依据牛顿第二定律列出其动力学方程并进行无量纲化处理,然后用变步长的经典四阶Runge-Kutta法对系统方程进行数值仿真,将仿真结果以分岔图、相平面图及Poincaré截面图的形式直观展示,再借助非线性研究方法及该领域的其他理论对其进行分析总结。主要研究了系统在各主要参数及激振频率发生变化时的周期振动及分岔特性,揭示了周期运动经由概周期运动转化到混沌运动的过程,并研究了碰撞恢复系数、Hertz接触刚度比、Hertz接触阻尼比、系统质量比、刚度比、阻尼比、无量纲间隙及阻尼系数这些主要参数的改变对系统冲击振动特性的影响。最后阐述了该研究的实际意义。一般研究中都将碰撞面间的接触形式看成刚性碰撞,而本文主要以Hertz定律描述这一碰撞力,将两质体间的接触形式看作弹性碰撞,以便得到更接近实际情况的仿真数据。此外给出两种弹性碰撞模型,一种只考虑碰撞面间刚度对Hertz约束力的影响,而另一种同时考虑碰撞面间刚度和阻尼的影响,分别研究这两种Hertz约束力作用下系统的动态响应特性,并将其与刚性碰撞模型的仿真结果进行对比,以便选出同时满足准确性和高效性的研究方法。仿真结果显示,大部分参数下系统响应都随着激振频率的增大发生一次或数次从周期运动到概周期运动再到混沌运动的转变,系统稳定性较差时其间还会夹杂Hopf分岔、边界激变及多周期间隔阵发性混沌等复杂的动力学行为。要使系统在各参数下都能处于较稳定的振动状态,需将外激励频率尽量保持在中低频域内。此外,三个模型的研究结论大体一致,因此相关研究中若只作定性分析可直接使用刚性碰撞模型,若需定量分析则可根据精度要求选用弹性碰撞模型,从而在得到较高仿真效率的同时保证仿真结论的准确性。以上结论与方法在类似碰撞振动系统的仿真研究中具备通用性,故可在该领域进行推广。
[Abstract]:The purpose of this paper is to simulate and analyze the dynamic characteristics of the nonlinear vibration system with gaps, study the influence of the main parameters on the dynamic characteristics of the system, and obtain the law of parameter values which make the system state more stable. It is a reference for parameter optimization of general shock vibration system. In this paper, a double mass shock vibration molding machine is studied, which is simplified as a dynamic model, and its dynamic equations are listed according to Newton's second law and processed in a dimensionless manner. Then the system equation is simulated by the classical four-order Runge-Kutta method with variable step size. The simulation results are displayed directly in the form of bifurcation diagram, phase plane diagram and Poincar 茅 section diagram. Then the nonlinear research method and other theories in this field are used to analyze and summarize it. In this paper, the periodic vibration and bifurcation characteristics of the system are studied when the main parameters and exciting frequencies change, and the process of transforming the periodic motion from almost periodic motion to chaotic motion is revealed. The effects of the main parameters such as Hertz contact damping ratio, system mass ratio, stiffness ratio, damping ratio, dimensionless clearance and damping coefficient on the impact vibration characteristics of the system are studied. Finally, the practical significance of the study is expounded. In general, the contact form between collision planes is regarded as a rigid collision. In this paper, the collision force is described by Hertz's law, and the contact form between two objects is regarded as elastic collision, so as to obtain the simulation data which is closer to the actual situation. In addition, two kinds of elastic collision models are given, one is considering the effect of the stiffness between the collision planes on the Hertz binding force, and the other is considering the influence of the stiffness and damping of the collision plane at the same time. The dynamic response characteristics of the two Hertz binding systems are studied and compared with the simulation results of the rigid collision model in order to select a research method that satisfies both accuracy and efficiency. The simulation results show that the response of the system changes from periodic motion to almost periodic motion to chaotic motion once or several times with the increase of exciting frequency under most parameters, and the Hopf bifurcation will be included in the system when the stability of the system is poor. Boundary shock and multi-periodic interval paroxysmal chaos and other complex dynamical behaviors. In order for the system to be in a stable vibration state under various parameters, it is necessary to keep the external excitation frequency in the medium and low frequency domain as far as possible. In addition, the conclusions of the three models are generally the same, so the rigid collision model can be used directly in the qualitative analysis, and the elastic impact model can be selected according to the precision requirement in the quantitative analysis. Therefore, the accuracy of the simulation results is guaranteed while obtaining higher simulation efficiency. The above conclusions and methods are universal in the simulation of similar impact vibration systems, so they can be popularized in this field.
【学位授予单位】：兰州交通大学
【学位级别】：硕士
【学位授予年份】：2016
【分类号】：TH113.1

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