【摘要】：本文根據(jù)非線性動(dòng)力學(xué)的相關(guān)理論,利用定性和定量的方法對(duì)含真實(shí)時(shí)變剛度、真實(shí)靜態(tài)傳動(dòng)誤差、齒面摩擦以及齒側(cè)間隙的齒輪傳動(dòng)系統(tǒng)的非線性動(dòng)力學(xué)特性進(jìn)行了研究,論文主要內(nèi)容如下： 1.建立了包含真實(shí)時(shí)變剛度、真實(shí)靜態(tài)傳動(dòng)誤差以及齒面摩擦等在內(nèi)的齒輪扭轉(zhuǎn)振動(dòng)模型。假設(shè)輪齒在嚙合線上勻速運(yùn)動(dòng)和摩擦系數(shù)為常數(shù),推導(dǎo)出嚙合過(guò)程中摩擦力的表達(dá)式,并考慮齒輪傳動(dòng)中的時(shí)變參數(shù)——嚙合剛度和靜態(tài)傳動(dòng)誤差,將其代入到齒輪副扭轉(zhuǎn)振動(dòng)模型中,推導(dǎo)出了系統(tǒng)的動(dòng)力學(xué)微分方程。 2.針對(duì)所建立的齒輪非線性動(dòng)力學(xué)模型分別應(yīng)用解析法和數(shù)值法進(jìn)行求解分析。在應(yīng)用解析方法之前,利用簡(jiǎn)單的傅里葉級(jí)數(shù)表達(dá)時(shí)變剛度和靜態(tài)傳動(dòng)誤差,并應(yīng)用高次多項(xiàng)式擬合分段非光滑的輪齒間隙函數(shù),推導(dǎo)出系統(tǒng)分別在主共振和1/2亞諧共振情況下的幅頻函數(shù),揭示了系統(tǒng)的一些非線性現(xiàn)象,如亞諧響應(yīng),跳躍和分岔。針對(duì)真實(shí)時(shí)變參數(shù)下的離散動(dòng)力學(xué)模型,應(yīng)用數(shù)值法分析系統(tǒng)的動(dòng)態(tài)響應(yīng)以及參數(shù)的變化對(duì)系統(tǒng)動(dòng)力學(xué)行為的影響,發(fā)現(xiàn)齒面摩擦在節(jié)點(diǎn)附近的局部范圍引起動(dòng)態(tài)傳動(dòng)誤差和動(dòng)態(tài)嚙合力的突變和附加振動(dòng),齒輪的轉(zhuǎn)速、負(fù)載力矩以及阻尼等參數(shù)對(duì)系統(tǒng)的動(dòng)態(tài)響應(yīng)也都具有不同程度影響。 3.應(yīng)用數(shù)值法對(duì)輪齒的沖擊-碰撞動(dòng)力學(xué)進(jìn)行了探索研究。引入考慮能量損耗的非線性彈簧-阻尼接觸模型,將輪齒嚙合過(guò)程簡(jiǎn)化為兩側(cè)彈性碰撞的連續(xù)動(dòng)力學(xué)模型,應(yīng)用接觸碰撞理論、非線性理論和數(shù)值方法研究了系統(tǒng)的穩(wěn)態(tài)響應(yīng)及能量損耗的頻率分岔,數(shù)值結(jié)果表明系統(tǒng)具有非常復(fù)雜的動(dòng)力學(xué)特性,隨著參數(shù)的變化發(fā)生了周期分叉和擦邊分叉。 4.通過(guò)齒輪傳動(dòng)實(shí)驗(yàn)測(cè)得一對(duì)標(biāo)準(zhǔn)參數(shù)的直齒圓柱齒輪的動(dòng)態(tài)傳動(dòng)誤差,從原始實(shí)驗(yàn)數(shù)提取穩(wěn)態(tài)響應(yīng)的頻譜特性,與理論分析得到的結(jié)果進(jìn)行對(duì)比,驗(yàn)證了理論模型的有效性。
[Abstract]:Based on the theory of nonlinear dynamics, the nonlinear dynamic characteristics of gear transmission system with real time-varying stiffness, real static transmission error, tooth surface friction and tooth side clearance are studied by qualitative and quantitative methods. The main contents of the thesis are as follows: 1. The torsional vibration model of gears including real time-varying stiffness, real static transmission error and tooth surface friction is established. Assuming that the uniform speed motion and friction coefficient of the gear teeth are constant on the meshing line, the expression of friction force in the meshing process is derived, and the time-varying parameters in the gear transmission, meshing stiffness and static transmission error, are taken into account. The dynamic differential equation of the system is derived by inserting it into the torsional vibration model of the gear pair. 2. The nonlinear dynamic model of gear is solved by analytic method and numerical method respectively. Before applying the analytical method, the time-varying stiffness and static transmission error are expressed by simple Fourier series, and the piecewise nonsmooth gear clearance function is fitted with higher order polynomial. The amplitude-frequency functions of the system in the case of main resonance and 1 / 2 subharmonic resonance are derived respectively. Some nonlinear phenomena of the system such as subharmonic response jump and bifurcation are revealed. For the discrete dynamic model with real time-varying parameters, the dynamic response of the system and the influence of the parameters on the dynamic behavior of the system are analyzed by numerical method. It is found that the local range of tooth surface friction causes the sudden change and additional vibration of dynamic transmission error and dynamic meshing force, and the parameters of gear rotation speed, load moment and damping have different effects on the dynamic response of the system. 3. The impact-impact dynamics of gear teeth are studied by numerical method. In this paper, a nonlinear spring-damping contact model considering energy loss is introduced. The meshing process of gear teeth is simplified as a continuous dynamic model of elastic impact on both sides, and the contact collision theory is applied. Nonlinear theory and numerical method are used to study the steady state response of the system and the frequency bifurcation of energy loss. The numerical results show that the system has very complex dynamic characteristics, and the periodic bifurcation and erasure bifurcation occur with the change of parameters. 4. The dynamic transmission errors of a pair of straight cylindrical gears with standard parameters are measured by gear transmission experiments. The spectral characteristics of steady state response are extracted from the original experimental data, and compared with the results obtained by theoretical analysis, the validity of the theoretical model is verified.
【學(xué)位授予單位】：中南大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2011
【分類號(hào)】：TH132.41

【引證文獻(xiàn)】

相關(guān)碩士學(xué)位論文 前2條

1 白國(guó)慶;TY型商用車細(xì)高齒變速箱動(dòng)態(tài)特性仿真及分析[D];太原理工大學(xué);2012年

2 吳偉傳;基于沉樁負(fù)載的液壓振動(dòng)樁錘齒輪傳動(dòng)系統(tǒng)動(dòng)態(tài)特性研究[D];中南大學(xué);2012年

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本文編號(hào)：2391958