一类离心机振动系统的非线性动力学研究
发布时间：2018-08-17 12:00
【摘要】：具有间隙的碰撞振动是工程机械中经常见到的一种现象,这种现象时而有利,时而有害,我们要怎样趋利避害,这也成为当今机械工程中的一热门研究问题。近年来,国内外的许多专家学者对低自由度的碰撞振动现象进行了深入的研究,对于低自由度系统的分岔混沌问题已取得了很大成果;但对于高自由度结合机械本身的研究稍少。本文就工业上常用的一种离心脱水设备——卧式振动离心机进行了非线性动力学的讨论。全文主要工作如下:简单介绍了离心机自身的发展历史以及工作原理;碰撞振动系统在国内外的研究进展与当前存在的一些主要问题,解释了什么是非线性动力学及其主要研究方法,包括不动点与稳定性的判断依据,分岔现象、Poincaré映射以及混沌现象的概念,为下文非线性动力学的研究做铺垫。将卧式振动离心机的工作过程简化为左右二自由度、左右三自由度以及上下两自由度的碰撞振动系统动力学模型,结合牛顿运动定律和碰撞动量定理知识便可得出该过程的运动微分方程;依据机械工作过程中的边界条件求解了该运动微分方程的解,推导了Poincaré映射及其Jacobi矩阵;根据求解系统方程的过程原理从而应用MATLAB软件进行计算机编程仿真;数值理论研究上述三个物理模型的动力学行为。依据碰撞振动过程中的二维(三维)分岔图和Poincaré映射截面图,结合Jacobi矩阵的特征值越过单位圆的数量以及位置来理论讨论了系统运动状态转迁到混沌的复杂的动力学特征;通过对比分析发现,系统从周期运动转化到混沌的过程中有各种各样的分岔类型,其中包括最常见的Hopf分岔、周期倍化和环面倍化分岔,也有余维二分岔,包括Hopf—Hopf分岔、Hopf—Flip分岔等;对卧式振动离心机而言,根据计算机数值仿真结果可以发现:激励频率w、碰撞间隙b、质量比μm、刚度比μk以及恢复系数R等对系统的动力学行为影响很大;对于离心机而言,选择合适的参数可以降低机器的能耗,提高效率;在正文中给出了发生分岔和混沌时各参数的具体数值,这可为离心机的设计优化制造提供一定的参考依据。
[Abstract]:The impact vibration with clearance is a phenomenon often seen in construction machinery. This phenomenon is sometimes beneficial and sometimes harmful. How to seek advantages and avoid disadvantages has become a hot research problem in mechanical engineering nowadays. In recent years, many experts and scholars at home and abroad have made a deep research on the impact vibration of low degree of freedom, and great achievements have been made on the problem of bifurcation chaos of low degree of freedom system. However, there is little research on the high degree of freedom combined with the mechanism itself. In this paper, the nonlinear dynamics of horizontal vibration centrifuge, a kind of centrifugal dehydration equipment commonly used in industry, is discussed. The main work of this paper is as follows: the development history and working principle of centrifuge itself are briefly introduced, the research progress of impact vibration system at home and abroad and some main problems existing at present are briefly introduced. This paper explains what is nonlinear dynamics and its main research methods, including the judgment basis of fixed point and stability, the bifurcation phenomenon Poincar 茅 map and the concept of chaos phenomenon, which lays the foundation for the study of nonlinear dynamics below. The working process of horizontal vibration centrifuge is simplified as the dynamic model of impact vibration system with two degrees of freedom, three degrees of freedom and two degrees of freedom. The differential equation of motion of this process can be obtained by combining Newton's law of motion and the theorem of collisional momentum, the solution of the differential equation of motion is solved according to the boundary conditions in the process of mechanical work, and the Poincar 茅 map and its Jacobi matrix are derived. According to the process principle of solving the system equation, the computer programming simulation is carried out by using MATLAB software, and the dynamic behavior of the above three physical models is studied by numerical theory. Based on the two-dimensional (three-dimensional) bifurcation diagram and the Poincar 茅 map section of the collision vibration process, the complex dynamic characteristics of the system moving from motion to chaos are discussed based on the number and position of the eigenvalues of the Jacobi matrix over the unit circle. Through comparative analysis, it is found that there are a variety of bifurcation types in the process of system transition from periodic motion to chaos, including the most common Hopf bifurcation, periodic doubling and torus doubling bifurcation, as well as two dimensional bifurcation. Including Hopf-Hopf bifurcation, Hopf-Flip bifurcation and so on; for horizontal vibration centrifuge, According to the computer simulation results, it can be found that the excitation frequency w, the impact clearance b, the mass ratio 渭 m, the stiffness ratio 渭 k and the recovery coefficient R have great influence on the dynamic behavior of the system. Choosing the appropriate parameters can reduce the energy consumption of the machine and improve the efficiency. The specific values of the parameters when bifurcation and chaos occur are given in the text, which can provide a certain reference for the design and optimization of centrifuges.
【学位授予单位】：兰州交通大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：TU601
[Abstract]:The impact vibration with clearance is a phenomenon often seen in construction machinery. This phenomenon is sometimes beneficial and sometimes harmful. How to seek advantages and avoid disadvantages has become a hot research problem in mechanical engineering nowadays. In recent years, many experts and scholars at home and abroad have made a deep research on the impact vibration of low degree of freedom, and great achievements have been made on the problem of bifurcation chaos of low degree of freedom system. However, there is little research on the high degree of freedom combined with the mechanism itself. In this paper, the nonlinear dynamics of horizontal vibration centrifuge, a kind of centrifugal dehydration equipment commonly used in industry, is discussed. The main work of this paper is as follows: the development history and working principle of centrifuge itself are briefly introduced, the research progress of impact vibration system at home and abroad and some main problems existing at present are briefly introduced. This paper explains what is nonlinear dynamics and its main research methods, including the judgment basis of fixed point and stability, the bifurcation phenomenon Poincar 茅 map and the concept of chaos phenomenon, which lays the foundation for the study of nonlinear dynamics below. The working process of horizontal vibration centrifuge is simplified as the dynamic model of impact vibration system with two degrees of freedom, three degrees of freedom and two degrees of freedom. The differential equation of motion of this process can be obtained by combining Newton's law of motion and the theorem of collisional momentum, the solution of the differential equation of motion is solved according to the boundary conditions in the process of mechanical work, and the Poincar 茅 map and its Jacobi matrix are derived. According to the process principle of solving the system equation, the computer programming simulation is carried out by using MATLAB software, and the dynamic behavior of the above three physical models is studied by numerical theory. Based on the two-dimensional (three-dimensional) bifurcation diagram and the Poincar 茅 map section of the collision vibration process, the complex dynamic characteristics of the system moving from motion to chaos are discussed based on the number and position of the eigenvalues of the Jacobi matrix over the unit circle. Through comparative analysis, it is found that there are a variety of bifurcation types in the process of system transition from periodic motion to chaos, including the most common Hopf bifurcation, periodic doubling and torus doubling bifurcation, as well as two dimensional bifurcation. Including Hopf-Hopf bifurcation, Hopf-Flip bifurcation and so on; for horizontal vibration centrifuge, According to the computer simulation results, it can be found that the excitation frequency w, the impact clearance b, the mass ratio 渭 m, the stiffness ratio 渭 k and the recovery coefficient R have great influence on the dynamic behavior of the system. Choosing the appropriate parameters can reduce the energy consumption of the machine and improve the efficiency. The specific values of the parameters when bifurcation and chaos occur are given in the text, which can provide a certain reference for the design and optimization of centrifuges.
【学位授予单位】：兰州交通大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：TU601
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