本文選題：圓柱齒輪　切入點(diǎn)：非線性動(dòng)力學(xué)　出處：《蘭州交通大學(xué)》2016年博士論文

【摘要】：齒輪系統(tǒng)是機(jī)械裝備中應(yīng)用廣泛的傳動(dòng)裝置之一,它具有結(jié)構(gòu)緊湊、傳動(dòng)效率高、傳動(dòng)平穩(wěn)等優(yōu)點(diǎn)。齒輪系統(tǒng)的振動(dòng)對(duì)其所在機(jī)械系統(tǒng)的穩(wěn)定性、可靠性和疲勞壽命有重要的影響。研究齒輪振動(dòng)產(chǎn)生的機(jī)理和影響齒輪振動(dòng)的力學(xué)因素,對(duì)于機(jī)械設(shè)備的減振降噪,提高機(jī)械設(shè)備的使用壽命和可靠性具有重要的科學(xué)意義和工程價(jià)值。本文以某車輛系統(tǒng)中使用的單級(jí)直齒圓柱齒輪傳動(dòng)系統(tǒng)為研究對(duì)象,綜合考慮齒輪嚙合時(shí)的齒側(cè)間隙、時(shí)變剛度、綜合傳遞誤差和齒面摩擦等因素,由簡單到復(fù)雜,對(duì)單自由度齒輪扭轉(zhuǎn)振動(dòng)系統(tǒng)、齒輪-轉(zhuǎn)子系統(tǒng)、考慮支承的三自由度齒輪系統(tǒng)和齒輪-轉(zhuǎn)子-軸承等四種系統(tǒng),分別建立不考慮溫度因素和考慮溫度因素兩種情況下的非線性動(dòng)力學(xué)模型,研究系統(tǒng)動(dòng)態(tài)特性。主要研究內(nèi)容如下:1.根據(jù)齒輪系統(tǒng)的特點(diǎn),提出了一種改進(jìn)的胞映射法。該算法根據(jù)胞映射法將所要研究的連續(xù)狀態(tài)空間劃分為離散的胞空間,采用簡單胞映射法建立胞與胞之間的映射關(guān)系,實(shí)現(xiàn)對(duì)胞的初步分組;用逃逸時(shí)間算法,檢驗(yàn)陷胞的真?zhèn)?并對(duì)陷胞的周期性重新分組;通過點(diǎn)映射方法檢驗(yàn)周期胞的真?zhèn)巍Ｔ摳倪M(jìn)胞映射法通過祛除陷胞影響數(shù)值計(jì)算過程,從而得到任意范圍內(nèi)所考察系統(tǒng)的精確吸引域,提高程序的計(jì)算精度,對(duì)于非光滑系統(tǒng)可以避免系統(tǒng)在切換時(shí)出現(xiàn)偽解和胞流擴(kuò)張。2.建立綜合考慮時(shí)變嚙合剛度、齒面摩擦、齒側(cè)間隙和綜合傳遞誤差等因素的單自由度齒輪系統(tǒng)的扭轉(zhuǎn)振動(dòng)動(dòng)力學(xué)模型。通過計(jì)算系統(tǒng)最大幅值波動(dòng)云圖、考察參數(shù)條件下的系統(tǒng)位移時(shí)間映像圖,分析該單自由度齒輪系統(tǒng)在參數(shù)平面內(nèi)的動(dòng)態(tài)特性。結(jié)合系統(tǒng)單初值分岔圖、多初值分岔圖和最大Lyapunov指數(shù)譜,利用改進(jìn)的胞映射法分析不同參數(shù)對(duì)該系統(tǒng)的全局和局部動(dòng)力學(xué)特性的影響。3.基于Blok閃溫理論,推導(dǎo)出齒面接觸溫度隨時(shí)間變化的表達(dá)式,計(jì)算主、從動(dòng)齒輪的齒面閃溫,計(jì)算由齒面接觸溫度變化導(dǎo)致的齒廓變形;根據(jù)Hertz接觸理論,推導(dǎo)出嚙合剛度隨齒面接觸溫度變化的表達(dá)式。構(gòu)建溫度剛度,以便將溫度的影響引入齒輪系統(tǒng)動(dòng)力學(xué)模型。4.建立綜合考慮齒面接觸溫度、時(shí)變嚙合剛度、齒面摩擦、齒側(cè)間隙和綜合傳遞誤差等因素的單自由度直齒圓柱齒輪系統(tǒng)非線性動(dòng)力學(xué)模型。通過計(jì)算不同參數(shù)關(guān)聯(lián)下的齒面最大閃現(xiàn)溫度云圖和齒面閃溫隨嚙合點(diǎn)變化趨勢圖,分析齒面接觸溫度對(duì)系統(tǒng)動(dòng)態(tài)特性的影響。結(jié)合系統(tǒng)單初值分岔圖、多初值分岔圖、相圖和Poincaré映射圖,利用改進(jìn)的胞映射法分析不同參數(shù)對(duì)考慮溫度因素的單自由度齒輪系統(tǒng)局部和全局動(dòng)力學(xué)特性的影響。對(duì)比分析溫度因素對(duì)單自由度齒輪系統(tǒng)的動(dòng)力學(xué)特性的影響。5.將連接在齒輪輸入輸出軸上的電機(jī)等其他部件抽象為與齒輪軸連接的轉(zhuǎn)子,建立齒輪-轉(zhuǎn)子系統(tǒng)非線性動(dòng)力學(xué)模型,計(jì)算系統(tǒng)動(dòng)力學(xué)參數(shù),分析嚙合頻率、時(shí)變剛度和綜合傳遞誤差等因素對(duì)系統(tǒng)非線性動(dòng)力學(xué)特性的影響。將溫度剛度引入該系統(tǒng),建立考慮溫度影響的齒輪轉(zhuǎn)子系統(tǒng)模型,分析系統(tǒng)分岔、混沌運(yùn)動(dòng)及其動(dòng)態(tài)特性。6.考慮主從動(dòng)軸上軸承對(duì)齒輪的作用力及其位移,建立三自由度單級(jí)齒輪系統(tǒng)的扭轉(zhuǎn)振動(dòng)模型,借助分岔圖、最大Lyapunov指數(shù)譜、Poincaré映射圖和FFT頻譜圖等,分析系統(tǒng)的動(dòng)力學(xué)特性。將溫度剛度引入該系統(tǒng),考察系統(tǒng)的動(dòng)態(tài)特性,分析系統(tǒng)的動(dòng)力學(xué)行為。7.建立齒輪-轉(zhuǎn)子-軸承耦合系統(tǒng)的非線性動(dòng)力學(xué)模型,分析系統(tǒng)的分岔與混沌、吸引子共存和動(dòng)態(tài)特性。建立考慮溫度因素的齒輪-轉(zhuǎn)子-軸承耦合系統(tǒng)的非線性動(dòng)力學(xué)模型,分析系統(tǒng)的分岔與混沌、齒面閃溫變化及其動(dòng)態(tài)特性。對(duì)比分析溫度對(duì)該系統(tǒng)動(dòng)力學(xué)特性的影響。研究發(fā)現(xiàn)系統(tǒng)存在Hopf分岔、擦切分岔等多種分岔形式。其中擦切運(yùn)動(dòng)包括齒面擦切和軸承接觸面擦切等多種形式,這些擦邊運(yùn)動(dòng)有的僅改變系統(tǒng)的運(yùn)動(dòng)軌跡而不會(huì)引起系統(tǒng)的運(yùn)動(dòng)形式的拓?fù)涓淖?有的則會(huì)引起系統(tǒng)發(fā)生分岔;該系統(tǒng)中存在大量的吸引子共存現(xiàn)象;系統(tǒng)在誤差較大時(shí)的扭轉(zhuǎn)振幅值較大,而選擇合理的間隙能夠明顯減小系統(tǒng)的扭轉(zhuǎn)振幅;如果綜合傳遞誤差系數(shù)取值也較大,系統(tǒng)的扭轉(zhuǎn)振幅將突然增加,說明綜合傳遞誤差系數(shù)和時(shí)變剛度波動(dòng)系數(shù)具有強(qiáng)烈的非線性耦合影響。研究發(fā)現(xiàn),溫度因素是齒輪系統(tǒng)非線性動(dòng)力學(xué)研究不可忽略的因素。齒面閃溫最低點(diǎn)位于節(jié)點(diǎn)附近;主動(dòng)輪從齒根部分嚙入和齒頂附近即將嚙出時(shí),出現(xiàn)較高的齒面閃溫。隨著頻率和摩擦系數(shù)的增大,齒面最大閃溫隨之增大,且在嚙入和嚙出時(shí)出現(xiàn)的齒面最大閃溫變化幅值也隨之增大;本體溫度對(duì)系統(tǒng)最大振幅的影響較小,而頻率的變化會(huì)引起系統(tǒng)最大振幅的復(fù)雜變化。本文所建立的齒面閃溫計(jì)算方法能夠在一定程度上反映齒輪嚙合時(shí)的溫度變化和滑動(dòng)情況,該方法在計(jì)算齒面溫度變化時(shí)其基本規(guī)律是正確的。本文的研究結(jié)果對(duì)齒輪系統(tǒng)優(yōu)化設(shè)計(jì)及參數(shù)選擇具有一定的參考價(jià)值和理論意義。
[Abstract]:The gear transmission system is one of the most widely used in mechanical equipment, it has the advantages of compact structure, high transmission efficiency, has the advantages of stable transmission. The stability of vibration of gear system on the mechanical system, has an important impact on the reliability and fatigue life of gear vibration. The formation mechanism and influence of gear vibration for mechanical factors. Vibration and noise of mechanical equipment, has important scientific significance and engineering value to improve the life of machinery and equipment use and reliability. Based on a vehicle system in a single-stage spur gear transmission system as the research object, considering the tooth side gear meshing clearance, time-varying stiffness, transmission error and tooth comprehensive surface friction and other factors, from simple to complex vibration system of single degree of freedom gear reverse gear rotor system, considering the three degree of freedom gear system and gear - rotor - bearing support The four systems were established, without considering the temperature factors of the nonlinear dynamics model of two kinds of situations and considering the temperature factors and the dynamic characteristics of the system. The main contents are as follows: 1. according to the characteristics of the gear system, put forward a kind of improved cell mapping method. The algorithm is based on continuous state space division cell mapping method to study for the discrete cell space, mapping relationship between using simple cell mapping method to establish the cell and the cell, to achieve the initial grouping of cells; using the escape time algorithm and test in the cell of authenticity, and the periodical in the cell groups; through the point mapping method test periodic authenticity. The improved cell mapping method the effect of the process of numerical calculation in removing cell, to obtain a precise system of domain of attraction within any range, improve the accuracy of the program, for the non smooth system can avoid system when switching artifacts Solution and cell expansion of.2. is established considering time-varying mesh stiffness, tooth surface friction, the torsional vibration dynamic model of single degree of freedom gear system with backlash and integrated transmission error and other factors. By calculating the maximum amplitude fluctuation of cloud system parameters under the condition of displacement time map, analysis of dynamic characteristics the parameter plane of the single degree of freedom gear system. Combined with the system of a single initial bifurcation diagram, multiple initial bifurcation and the maximum Lyapunov exponent spectrum, analysis the influence of different parameters on the system of global and local dynamics of the.3. Blok flash temperature theory based on cell mapping method is improved, is derived. The tooth contact temperature change over time to calculate the main driven gear tooth surface, the flash temperature, calculate the temperature change caused by tooth contact tooth surface deformation; based on Hertz contact theory, the meshing stiffness with the tooth surface contact temperature is derived The change of expression. In order to construct temperature stiffness, the influence of temperature into the gear system dynamics model of.4. is established considering the tooth contact temperature, time-varying mesh stiffness, tooth surface friction, single degree of freedom gear system nonlinear dynamic model of gear backlash and transmission error and other factors. Through the calculation of different parameters of tooth surface maximum flash temperature charts and surface flash temperature trends with the meshing point changes, influence analysis of tooth contact temperature on the dynamic characteristics of the system. Combined with the system of a single initial bifurcation diagram, multiple initial bifurcation diagram, phase diagram and Poincar maps, analysis of the influence of different parameters on the consideration of local and global free single the degree of gear system dynamics characteristics of temperature factors using the cell mapping method improved. Comparative analysis of effect of temperature on the dynamic characteristics of single degree of freedom gear system.5. will be connected to the gear The input on the output shaft of the motor and other components are abstracted as rotor is connected with the gear shaft, a gear nonlinear dynamics of rotor system model, system dynamics calculation parameters, analysis of meshing frequency, time-varying stiffness and transmission error of comprehensive factors such as nonlinear dynamic characteristics of the system. The temperature stiffness is introduced into the system, the establishment of gear the rotor system model considering the influence of temperature, analysis the bifurcation, chaotic motion and dynamic characteristics of.6. driving force and its displacement considering the shaft bearing of the gear, we establish three degree of freedom gear torsional vibration model of the system, the bifurcation diagram, the largest Lyapunov exponent, Poincar maps and FFT spectrum. Analysis of dynamic characteristics of the system. The temperature stiffness is introduced into the system, the dynamic characteristics of the system, the.7. dynamic behavior analysis system to establish gear - rotor - bearing coupling The nonlinear dynamic model of the system, bifurcation and chaos analysis system, attractors and dynamic characteristics. The nonlinear dynamics model is established by considering the temperature factors of the gear rotor bearing system, bifurcation and chaos analysis system, surface flash characteristics and its dynamic changes in temperature. Comparative analysis of the influence of temperature on the dynamic characteristics of the system. The study found that the system has a Hopf bifurcation, tangent bifurcation and other clean forms. The clean cut bifurcation motion including tooth cutting and rubbing contact surface clean cut and other forms, these edge movement some only change the system's motion trajectory without causing the movement of the system in the form of topology changes, some will cause the system bifurcation; a large number of attractors phenomenon exists in the system; the system is greater in torsion of large amplitude error, and the choice of reasonable gap torsion can obviously reduce the system If the transmission error amplitude; comprehensive coefficient is larger, the torsion amplitude system will suddenly increase, indicating that transmission is strongly influenced by the nonlinear coupling coefficient and the time-varying stiffness fluctuation coefficient. It is found that the temperature factors are nonlinear dynamics of gear system research can not be ignored. The surface flash temperature lows in the node near the driving wheel; from the root of meshing and tooth meshing is near the top, high surface flash temperature. With the increase of frequency and coefficient of friction of tooth surface, maximum flash temperature increases, and the meshing and meshing tooth surface when the maximum flash temperature change amplitude increases smaller; the body temperature affects the system maximum amplitude, and frequency variation will cause complex changes of the system maximum amplitude. Calculation method of tooth surface of the flash temperature can reflect the temperature when the gears are engaged in a certain extent The basic law of the method is correct when calculating the change of tooth surface temperature. The results of this study have some reference value and theoretical significance for gear system optimization design and parameter selection.

【學(xué)位授予單位】：蘭州交通大學(xué)
【學(xué)位級(jí)別】：博士
【學(xué)位授予年份】：2016
【分類號(hào)】：TH132.41
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本文編號(hào)：1662146