本文關(guān)鍵詞： 分岔 混沌 碰撞振動(dòng) Poincaré映射　出處：《蘭州交通大學(xué)》2013年碩士論文　論文類型：學(xué)位論文

【摘要】：含間隙碰撞振動(dòng)系統(tǒng)是常見的非線性動(dòng)力學(xué)系統(tǒng)，各種機(jī)械設(shè)備在生產(chǎn)、制造和裝配的過程中會(huì)發(fā)生各種各樣的誤差，，從而導(dǎo)致機(jī)械設(shè)備具有間隙；并且在其調(diào)試運(yùn)行過程中，由于碰撞摩擦也會(huì)產(chǎn)生間隙。另外，考慮機(jī)械設(shè)備的各種因素，一些機(jī)械設(shè)備在設(shè)計(jì)過程中會(huì)預(yù)留有間隙，如在嚙合齒輪、滾動(dòng)軸承等系統(tǒng)的有關(guān)零部件中也必然會(huì)存在間隙，這些間隙是無(wú)法消除與避免的。間隙引起設(shè)備接觸區(qū)的接觸狀態(tài)會(huì)發(fā)生變化,機(jī)械設(shè)備工作中構(gòu)件不斷出現(xiàn)重復(fù)的沖擊，碰撞構(gòu)件發(fā)生碰撞會(huì)導(dǎo)致構(gòu)件結(jié)構(gòu)發(fā)生局部變形，在碰撞過程中會(huì)發(fā)生力波的傳遞對(duì)系統(tǒng)的載荷和動(dòng)態(tài)特性影響產(chǎn)生的后果嚴(yán)重。因此，對(duì)含間隙振動(dòng)系統(tǒng)來(lái)說，如何去利用它的優(yōu)點(diǎn)取除它的缺點(diǎn)，對(duì)進(jìn)行碰撞振動(dòng)動(dòng)力學(xué)優(yōu)化設(shè)計(jì)，提高系統(tǒng)的可靠性有十分重要的意義。本文針對(duì)此類碰撞系統(tǒng)的三類振動(dòng)模型情況做了具體的研究。 1.本文研究了三類典型的碰撞振動(dòng)系統(tǒng)。通過建立碰撞振動(dòng)系統(tǒng)的力學(xué)模型，在對(duì)模型進(jìn)行受力分析，然后用數(shù)值分析法對(duì)這三個(gè)模型的系統(tǒng)周期運(yùn)動(dòng)理論推導(dǎo)。以坐標(biāo)的變換對(duì)方程組解耦，用模態(tài)矩陣法解出方程組的通解；通過系統(tǒng)周期運(yùn)動(dòng)的邊界條件結(jié)合方程組的通解求的周期中心不動(dòng)點(diǎn)，從中推導(dǎo)出三類模型系統(tǒng)的解析解、線性化矩陣等一系列結(jié)果，然后由計(jì)算得到各個(gè)系統(tǒng)的Poincaré映射。 2.分析系統(tǒng)發(fā)生分岔和混沌的復(fù)雜動(dòng)力學(xué)行為，運(yùn)用Poincaré映射理論進(jìn)行matlab軟件編程找出行系統(tǒng)的穩(wěn)定性。經(jīng)數(shù)值仿真來(lái)驗(yàn)證計(jì)算結(jié)果的準(zhǔn)確性和系統(tǒng)發(fā)生分岔與混沌現(xiàn)象，并且給出了線性化矩陣特征值橫截單位圓周的趨勢(shì)圖。在數(shù)值仿真過程中找到適當(dāng)?shù)南到y(tǒng)參數(shù)，研究了各個(gè)模型的碰撞振動(dòng)系統(tǒng)不同情況下，得到了系統(tǒng)通向混沌過程中Poincaré截面圖等。 3.由仿真的過程中我們得出一些結(jié)論：系統(tǒng)的一些參數(shù)如：激勵(lì)頻率、間隙、恢復(fù)系數(shù)等，這些控制參數(shù)的變化對(duì)系統(tǒng)運(yùn)動(dòng)的影響是非常大的，當(dāng)它們?cè)谂R界點(diǎn)處微小的變動(dòng)就會(huì)引起系統(tǒng)運(yùn)動(dòng)質(zhì)的變化。所以，在碰撞振動(dòng)系統(tǒng)中臨界點(diǎn)處系統(tǒng)參數(shù)的選擇是很重要的，從仿真得到參數(shù)的選擇對(duì)振動(dòng)系統(tǒng)控制和優(yōu)化機(jī)械設(shè)計(jì)提供理論參考。
[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.
【學(xué)位授予單位】：蘭州交通大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2013
【分類號(hào)】：TH113.1

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相關(guān)期刊論文 前1條

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