【摘要】：具有間隙的碰撞振動是工程機械中經常見到的一種現(xiàn)象,這種現(xiàn)象時而有利,時而有害,我們要怎樣趨利避害,這也成為當今機械工程中的一熱門研究問題。近年來,國內外的許多專家學者對低自由度的碰撞振動現(xiàn)象進行了深入的研究,對于低自由度系統(tǒng)的分岔混沌問題已取得了很大成果;但對于高自由度結合機械本身的研究稍少。本文就工業(yè)上常用的一種離心脫水設備——臥式振動離心機進行了非線性動力學的討論。全文主要工作如下:簡單介紹了離心機自身的發(fā)展歷史以及工作原理;碰撞振動系統(tǒng)在國內外的研究進展與當前存在的一些主要問題,解釋了什么是非線性動力學及其主要研究方法,包括不動點與穩(wěn)定性的判斷依據(jù),分岔現(xiàn)象、Poincaré映射以及混沌現(xiàn)象的概念,為下文非線性動力學的研究做鋪墊。將臥式振動離心機的工作過程簡化為左右二自由度、左右三自由度以及上下兩自由度的碰撞振動系統(tǒng)動力學模型,結合牛頓運動定律和碰撞動量定理知識便可得出該過程的運動微分方程;依據(jù)機械工作過程中的邊界條件求解了該運動微分方程的解,推導了Poincaré映射及其Jacobi矩陣;根據(jù)求解系統(tǒng)方程的過程原理從而應用MATLAB軟件進行計算機編程仿真;數(shù)值理論研究上述三個物理模型的動力學行為。依據(jù)碰撞振動過程中的二維(三維)分岔圖和Poincaré映射截面圖,結合Jacobi矩陣的特征值越過單位圓的數(shù)量以及位置來理論討論了系統(tǒng)運動狀態(tài)轉遷到混沌的復雜的動力學特征;通過對比分析發(fā)現(xiàn),系統(tǒng)從周期運動轉化到混沌的過程中有各種各樣的分岔類型,其中包括最常見的Hopf分岔、周期倍化和環(huán)面倍化分岔,也有余維二分岔,包括Hopf—Hopf分岔、Hopf—Flip分岔等;對臥式振動離心機而言,根據(jù)計算機數(shù)值仿真結果可以發(fā)現(xiàn):激勵頻率w、碰撞間隙b、質量比μm、剛度比μk以及恢復系數(shù)R等對系統(tǒng)的動力學行為影響很大;對于離心機而言,選擇合適的參數(shù)可以降低機器的能耗,提高效率;在正文中給出了發(fā)生分岔和混沌時各參數(shù)的具體數(shù)值,這可為離心機的設計優(yōu)化制造提供一定的參考依據(jù)。
[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.
【學位授予單位】：蘭州交通大學
【學位級別】：碩士
【學位授予年份】：2017
【分類號】：TU601

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