【摘要】：干摩擦碰撞是一類(lèi)重要的非光滑動(dòng)力系統(tǒng),廣泛存在于工程設(shè)計(jì)和機(jī)械制造中。由于干摩擦碰撞的存在,增加了系統(tǒng)的不確定性和研究的復(fù)雜性,使得傳統(tǒng)的動(dòng)力系統(tǒng)研究方法不能直接應(yīng)用到干摩擦碰撞系統(tǒng)中。微分包含理論是研究非光滑動(dòng)力系統(tǒng)的重要工具,且在動(dòng)力系統(tǒng)的控制、多胞系統(tǒng)、脈沖系統(tǒng)中均有所應(yīng)用。本文基于微分包含理論系統(tǒng)分析了皮帶輪上干摩擦碰撞系統(tǒng)的動(dòng)力學(xué)特性,探究了不同參數(shù)引起的分岔現(xiàn)象。結(jié)合微分包含理論分析各種運(yùn)動(dòng)的存在條件,借助C語(yǔ)言和MATLAB進(jìn)行仿真。本文共有六章,主要如下:第一章:本章對(duì)干摩擦碰撞系統(tǒng)的研究背景意義、主要的研究方法、存在的問(wèn)題及微分包含理論在干摩擦碰撞系統(tǒng)中的應(yīng)用進(jìn)行了簡(jiǎn)述,并概述了本文的主要內(nèi)容。第二章:本章給出了集值映射、微分包含理論等相關(guān)的基本定義、定理,主要介紹非光滑動(dòng)力系統(tǒng)微分包含解的存在性和穩(wěn)定性;建立了非光滑系統(tǒng)的運(yùn)動(dòng)模型,推導(dǎo)并計(jì)算出系統(tǒng)中滑膜解存在的必要條件、滑膜指數(shù)及跳躍運(yùn)動(dòng)的跳躍矩陣;最后介紹了Poincaré映射及Poincaré截面圖與周期運(yùn)動(dòng)系統(tǒng)穩(wěn)定性的關(guān)系。第三章:分析了兩種單自由度干摩擦系統(tǒng)的動(dòng)力學(xué)特征,使用凸包的知識(shí)將系統(tǒng)方程微分包含標(biāo)準(zhǔn)化,探究了系統(tǒng)平衡點(diǎn)的穩(wěn)定性;計(jì)算出系統(tǒng)滑膜跳躍運(yùn)動(dòng)的產(chǎn)生條件及系統(tǒng)軌線滑膜、跳躍運(yùn)動(dòng)的范圍,并得出無(wú)外激勵(lì)系統(tǒng)不可能發(fā)生跳躍運(yùn)動(dòng)的結(jié)論;數(shù)值模擬考慮振幅對(duì)滑膜跳躍運(yùn)動(dòng)的影響,仿真出滑膜跳躍分岔圖,發(fā)現(xiàn)了隨著振幅的增大,系統(tǒng)有向跳躍運(yùn)動(dòng)移動(dòng)的趨勢(shì);考慮了外激勵(lì)振幅、頻率對(duì)系統(tǒng)穩(wěn)定性的影響。第四章:分析了雙自由度碰撞系統(tǒng),建立了碰撞的微分方程模型;推導(dǎo)了質(zhì)塊碰撞過(guò)程的轉(zhuǎn)移矩陣、橫截指數(shù),并判斷出碰撞系統(tǒng)中軌線不可能越過(guò)碰撞面;數(shù)值模擬了系統(tǒng)在不同參數(shù)變化下的分岔圖,并發(fā)現(xiàn)了參數(shù)振幅、頻率對(duì)系統(tǒng)的穩(wěn)定性影響較大。第五章:建立了雙自由度干摩擦碰撞系統(tǒng)的微分方程模型,使用凸包和集值映射將方程轉(zhuǎn)化為微分包含標(biāo)準(zhǔn)型;分析了非光滑可能引起系統(tǒng)動(dòng)力學(xué)特征的變化,并推導(dǎo)出干摩擦碰撞過(guò)程中的轉(zhuǎn)移矩陣和跳躍矩陣;數(shù)值仿真出系統(tǒng)的單參分岔圖和雙參分岔圖,探究了不同參數(shù)對(duì)干摩擦碰撞系統(tǒng)的影響。第六章:總結(jié)了本文的主要內(nèi)容并給出了干摩擦碰撞系統(tǒng)中參數(shù)匹配問(wèn)題的進(jìn)一步研究方向。
[Abstract]:Dry friction collision is an important non-smooth dynamic system, which widely exists in engineering design and mechanical manufacturing. Due to the existence of dry friction collision, the uncertainty of the system and the complexity of the research are increased, so the traditional research method of dynamic system can not be directly applied to the dry friction collision system. Differential inclusion theory is an important tool for the study of nonsmooth dynamical systems, and it has been applied in the control of dynamical systems, multi-cell systems and impulsive systems. In this paper, the dynamic characteristics of dry friction collision system on pulley are systematically analyzed based on differential inclusion theory, and the bifurcation caused by different parameters is discussed. Based on the differential inclusion theory, the existing conditions of various motions are analyzed, and the simulation is carried out with the help of C language and MATLAB. There are six chapters in this paper, which are as follows: chapter one: the background significance, the main research methods, the existing problems and the application of differential inclusion theory in dry friction collision system are briefly described in this chapter, the research background, the main research methods, the existing problems and the application of differential inclusion theory in dry friction collision system are briefly described. The main contents of this paper are also summarized. In chapter 2, the basic definitions and theorems of set-valued mapping, differential inclusion theory and so on are given, which mainly introduce the existence and stability of differential inclusion solutions for nonsmooth dynamical systems. In this paper, the motion model of the nonsmooth system is established, and the necessary conditions for the existence of the sliding film solution, the sliding film index and the jump matrix of the jumping motion are derived and calculated. Finally, the relations between the Poincar茅 map and the Poincar茅 section diagram and the stability of the periodic motion system are introduced. In chapter 3, the dynamic characteristics of two kinds of single degree of freedom dry friction systems are analyzed, and the differential inclusion of the system equations is standardized by using convex hull knowledge, and the stability of the equilibrium point of the system is explored. The generating conditions of the jump motion of the slide film and the range of the jump motion of the system are calculated, and the conclusion is drawn that the jump motion cannot occur in the system without external excitation. The numerical simulation takes into account the influence of amplitude on the slip jump motion, and simulates the slip bifurcation diagram. It is found that with the increase of the amplitude, the system moves toward the jump motion, and the influence of the external excitation amplitude and frequency on the stability of the system is considered. In chapter 4, the two-degree-of-freedom collision system is analyzed, the differential equation model of collision is established, the transfer matrix and cross-section index of mass collision process are deduced, and the trajectory of collision system is determined that it is impossible to cross the collision surface. The bifurcation diagrams of the system under different parameters are numerically simulated, and it is found that the amplitude and frequency of the parameters have a great influence on the stability of the system. In chapter 5, the differential equation model of two-degree-of-freedom dry friction collision system is established, and the equation is transformed into differential inclusion standard form by convex hull and set-valued mapping. The variation of the dynamic characteristics of the system caused by non-smoothing is analyzed, and the transfer matrix and jump matrix in dry friction collision are derived. The single-parameter bifurcation diagram and the two-parameter bifurcation diagram of the system are numerically simulated, and the effects of different parameters on the dry friction collision system are investigated. Chapter 6: the main contents of this paper are summarized and the further research direction of parameter matching in dry friction collision system is given.
【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】：2017
【分類(lèi)號(hào)】：O19

【參考文獻(xiàn)】

相關(guān)期刊論文 前10條

1 焦云迪;王小靜;白瑞成;聶周;喻廣義;;大比壓油潤(rùn)滑條件下C/C復(fù)合材料的摩擦特性[J];潤(rùn)滑與密封;2017年01期

2 李琳;劉久周;李超;;航空發(fā)動(dòng)機(jī)中的干摩擦阻尼器及其設(shè)計(jì)技術(shù)研究進(jìn)展[J];航空動(dòng)力學(xué)報(bào);2016年10期

3 姜春霞;鄔開(kāi)俊;;一類(lèi)摩擦碰撞振動(dòng)系統(tǒng)動(dòng)力學(xué)行為的數(shù)值研究[J];信息通信;2015年11期

4 王樹(shù)國(guó);陳英;劉大亮;楊昊;翟海峰;;干摩擦下含間隙碰撞振動(dòng)系統(tǒng)的動(dòng)力學(xué)行為分析[J];武漢科技大學(xué)學(xué)報(bào);2011年05期

5 張海濤;丁千;;干摩擦自激振動(dòng)周期解的同倫方法[J];振動(dòng)與沖擊;2011年08期

6 馬飛;杜三明;張永振;;干摩擦磨屑的三維形貌特征研究綜述[J];潤(rùn)滑與密封;2011年01期

7 張有強(qiáng);丁旺才;;干摩擦對(duì)碰撞振動(dòng)系統(tǒng)周期運(yùn)動(dòng)的影響分析[J];振動(dòng)與沖擊;2009年06期

8 許宏文;薛小平;;約束微分包含的Filippov型定理[J];蘭州大學(xué)學(xué)報(bào)(自然科學(xué)版);2009年03期

9 魏艷輝;徐潔瓊;黃龍生;;兩自由度碰撞振動(dòng)系統(tǒng)的Lyapunov指數(shù)譜分析[J];振動(dòng)與沖擊;2009年01期

10 皇甫玉高;李群宏;;一類(lèi)單側(cè)碰撞懸臂振動(dòng)系統(tǒng)的擦邊分岔分析[J];力學(xué)學(xué)報(bào);2008年06期

相關(guān)博士學(xué)位論文 前3條

1 蔡佐威;幾類(lèi)基于微分包含的不連續(xù)系統(tǒng)的動(dòng)力學(xué)研究[D];湖南大學(xué);2014年

2 劉磊坡;微分包含系統(tǒng)的幾類(lèi)控制問(wèn)題研究[D];上海交通大學(xué);2011年

3 秦泗甜;基于微分包含的非光滑動(dòng)力系統(tǒng)分析及其應(yīng)用[D];哈爾濱工業(yè)大學(xué);2010年

，

本文編號(hào)：2446880