【摘要】：本文旨在對含間隙非線性振動系統(tǒng)的動力學(xué)特性進(jìn)行仿真分析,研究各主要參數(shù)改變對系統(tǒng)動力學(xué)特性的影響,得到使系統(tǒng)狀態(tài)較為穩(wěn)定的參數(shù)取值規(guī)律,為一般沖擊振動系統(tǒng)的參數(shù)優(yōu)化作參考。以一個雙質(zhì)體沖擊振動成型機(jī)為研究對象,先將其簡化為動力學(xué)模型,依據(jù)牛頓第二定律列出其動力學(xué)方程并進(jìn)行無量綱化處理,然后用變步長的經(jīng)典四階Runge-Kutta法對系統(tǒng)方程進(jìn)行數(shù)值仿真,將仿真結(jié)果以分岔圖、相平面圖及Poincaré截面圖的形式直觀展示,再借助非線性研究方法及該領(lǐng)域的其他理論對其進(jìn)行分析總結(jié)。主要研究了系統(tǒng)在各主要參數(shù)及激振頻率發(fā)生變化時的周期振動及分岔特性,揭示了周期運(yùn)動經(jīng)由概周期運(yùn)動轉(zhuǎn)化到混沌運(yùn)動的過程,并研究了碰撞恢復(fù)系數(shù)、Hertz接觸剛度比、Hertz接觸阻尼比、系統(tǒng)質(zhì)量比、剛度比、阻尼比、無量綱間隙及阻尼系數(shù)這些主要參數(shù)的改變對系統(tǒng)沖擊振動特性的影響。最后闡述了該研究的實際意義。一般研究中都將碰撞面間的接觸形式看成剛性碰撞,而本文主要以Hertz定律描述這一碰撞力,將兩質(zhì)體間的接觸形式看作彈性碰撞,以便得到更接近實際情況的仿真數(shù)據(jù)。此外給出兩種彈性碰撞模型,一種只考慮碰撞面間剛度對Hertz約束力的影響,而另一種同時考慮碰撞面間剛度和阻尼的影響,分別研究這兩種Hertz約束力作用下系統(tǒng)的動態(tài)響應(yīng)特性,并將其與剛性碰撞模型的仿真結(jié)果進(jìn)行對比,以便選出同時滿足準(zhǔn)確性和高效性的研究方法。仿真結(jié)果顯示,大部分參數(shù)下系統(tǒng)響應(yīng)都隨著激振頻率的增大發(fā)生一次或數(shù)次從周期運(yùn)動到概周期運(yùn)動再到混沌運(yùn)動的轉(zhuǎn)變,系統(tǒng)穩(wěn)定性較差時其間還會夾雜Hopf分岔、邊界激變及多周期間隔陣發(fā)性混沌等復(fù)雜的動力學(xué)行為。要使系統(tǒng)在各參數(shù)下都能處于較穩(wěn)定的振動狀態(tài),需將外激勵頻率盡量保持在中低頻域內(nèi)。此外,三個模型的研究結(jié)論大體一致,因此相關(guān)研究中若只作定性分析可直接使用剛性碰撞模型,若需定量分析則可根據(jù)精度要求選用彈性碰撞模型,從而在得到較高仿真效率的同時保證仿真結(jié)論的準(zhǔn)確性。以上結(jié)論與方法在類似碰撞振動系統(tǒng)的仿真研究中具備通用性,故可在該領(lǐng)域進(jìn)行推廣。
[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.
【學(xué)位授予單位】：蘭州交通大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2016
【分類號】：TH113.1

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