本文關(guān)鍵詞：封閉式行星齒輪傳動(dòng)系統(tǒng)動(dòng)態(tài)特性研究　出處：《山東大學(xué)》2014年博士論文　論文類型：學(xué)位論文

  更多相關(guān)文章： 行星齒輪傳動(dòng) 封閉式 非線性動(dòng)力學(xué) 齒側(cè)間隙

【摘要】：行星齒輪傳動(dòng)系統(tǒng)由于其承載能力大、結(jié)構(gòu)緊湊,廣泛地應(yīng)用于航空航天、船舶、汽車等各個(gè)領(lǐng)域。由于在承受外部激勵(lì)的同時(shí)又承受著自身參數(shù)變化引起的內(nèi)部激勵(lì),行星系統(tǒng)的動(dòng)力學(xué)行為十分復(fù)雜,振動(dòng)和噪聲是影響系統(tǒng)可靠性及壽命的關(guān)鍵因素。因此,要提高機(jī)械系統(tǒng)的安全性及可靠性,亟需針對(duì)機(jī)械傳動(dòng)系統(tǒng)的動(dòng)力學(xué)建模、動(dòng)態(tài)響應(yīng)分析、參數(shù)穩(wěn)定性分析、減振、降噪等動(dòng)態(tài)特征進(jìn)行深入研究。封閉式行星系統(tǒng)作為行星傳動(dòng)的一種,它所傳遞的扭矩可以從多個(gè)路徑傳遞到負(fù)載。因而,封閉式行星傳動(dòng)可承載更大的扭矩,并且結(jié)構(gòu)緊湊,傳動(dòng)比更大,其體積往往比同等額定功率的簡(jiǎn)單行星系統(tǒng)更小。近年來(lái),封閉式行星傳動(dòng)系統(tǒng)以其獨(dú)特的優(yōu)點(diǎn),越來(lái)越多的應(yīng)用在機(jī)械傳動(dòng)領(lǐng)域,對(duì)其開展動(dòng)態(tài)特性研究,可為優(yōu)化設(shè)計(jì)提供理論基礎(chǔ)和指導(dǎo)準(zhǔn)則,具有重要的實(shí)際意義。 本文主要對(duì)一種可實(shí)現(xiàn)功率分流(匯流)的兩級(jí)封閉式行星系統(tǒng)的動(dòng)態(tài)特性進(jìn)行了相關(guān)的研究。在傳動(dòng)系統(tǒng)數(shù)學(xué)模型的建立、固有特性分析、頻響特性分析、系統(tǒng)參數(shù)對(duì)振動(dòng)特性的影響以及實(shí)驗(yàn)研究等方面,取得了一些成果和進(jìn)展。論文的主要內(nèi)容包括以下幾個(gè)方面： 根據(jù)傳動(dòng)系統(tǒng)各個(gè)構(gòu)件的運(yùn)動(dòng)學(xué)關(guān)系,推導(dǎo)了系統(tǒng)各構(gòu)件的相對(duì)位移。在相關(guān)合理假設(shè)的前提下,運(yùn)用集中質(zhì)量法,基于第二類Lagrange方程分別建立了系統(tǒng)的純扭轉(zhuǎn)動(dòng)力學(xué)模型和平移-扭轉(zhuǎn)耦合動(dòng)力學(xué)模型。根據(jù)所建立的兩類動(dòng)力學(xué)模型分析了系統(tǒng)的固有振動(dòng)特性,并依據(jù)固有頻率和振型特征進(jìn)行了歸納和振動(dòng)模式劃分。根據(jù)系統(tǒng)子本征值關(guān)系式,從數(shù)學(xué)意義上證明了振動(dòng)模式劃分的完備性。揭示了行星輪數(shù)目的變化對(duì)系統(tǒng)固有頻率的影響規(guī)律。所建立的模型易于擴(kuò)展,可推廣至任意行星輪數(shù)目和行星傳動(dòng)級(jí)數(shù)的封閉式行星系統(tǒng),具有普遍的指導(dǎo)意義。 對(duì)系統(tǒng)中包含的非線性因素,如時(shí)變嚙合剛度、齒側(cè)間隙及綜合嚙合誤差等進(jìn)行了數(shù)學(xué)意義上的描述,得到非線性、耗散系統(tǒng)的純扭轉(zhuǎn)模型的動(dòng)力學(xué)微分方程組。對(duì)已經(jīng)無(wú)量綱化和去除剛體運(yùn)動(dòng)模式的純扭轉(zhuǎn)模型的非線性動(dòng)力學(xué)微分方程組,利用DFT數(shù)值諧波平衡法將其轉(zhuǎn)化成非線性代數(shù)方程組。為進(jìn)一步求解此方程組,運(yùn)用擬牛頓迭代法(BFS秩2)結(jié)合擬弧長(zhǎng)算法進(jìn)行數(shù)值求解,綜合分析了頻響特性曲線的幅值跳躍、多值性以及不穩(wěn)定解支等典型的非線性特征。通過(guò)變化外激勵(lì)、嚙合剛度、系統(tǒng)阻尼等參數(shù)值,揭示了重要參數(shù)對(duì)兩級(jí)封閉式行星傳動(dòng)系統(tǒng)非線性動(dòng)態(tài)特性的影響規(guī)律。本文為深入研究封閉式行星傳動(dòng)系統(tǒng)的動(dòng)態(tài)特性提供了一種新的方法和途徑。 考慮到由于齒側(cè)間隙屬于強(qiáng)非線性因素,多尺度法不能直接應(yīng)用于齒輪系統(tǒng)非線性動(dòng)力學(xué)模型求解。本文通過(guò)分析時(shí)變嚙合剛度和齒側(cè)間隙兩類非線性因的特點(diǎn),推導(dǎo)了包含兩類非線性因素的綜合表達(dá)式,使多尺度法能合理應(yīng)用于兩級(jí)封閉式行星系統(tǒng)非線性模型,并且以此推導(dǎo)了系統(tǒng)主共振幅值的近似解析表達(dá)式。對(duì)系統(tǒng)相對(duì)嚙合相位關(guān)系進(jìn)行了深入的研究,推導(dǎo)了任意兩對(duì)齒輪副的相對(duì)嚙合相位�；诙喑叨冉平馕鼋獗磉_(dá)式,揭示了系統(tǒng)結(jié)構(gòu)、相對(duì)嚙合相位以及系統(tǒng)重合度等幾何參數(shù)對(duì)振動(dòng)特性的影響規(guī)律。 構(gòu)建了兩級(jí)封閉式行星傳動(dòng)系統(tǒng)的實(shí)驗(yàn)平臺(tái)。通過(guò)實(shí)驗(yàn)?zāi)B(tài)分析測(cè)試了傳動(dòng)系統(tǒng)的頻響函數(shù),獲得了系統(tǒng)的固有頻率；實(shí)驗(yàn)測(cè)試結(jié)果與理論分析結(jié)果對(duì)比表明：本文基于集中質(zhì)量法建立的行星傳動(dòng)系統(tǒng)純扭轉(zhuǎn)動(dòng)力學(xué)模型和平移-扭轉(zhuǎn)耦合動(dòng)力學(xué)模型是合理的。 通過(guò)本文的研究揭示了系統(tǒng)設(shè)計(jì)參數(shù)對(duì)動(dòng)態(tài)特性的影響規(guī)律,為封閉式行星傳動(dòng)系統(tǒng)的動(dòng)態(tài)設(shè)計(jì)提供了理論依據(jù),對(duì)提高我國(guó)封閉式行星系統(tǒng)的設(shè)計(jì)水平有較大的理論意義和實(shí)際應(yīng)用價(jià)值。 本課題得到國(guó)家自然科學(xué)基金(51175299)及山東省自然科學(xué)基金(ZR2010EM012)的支持。
[Abstract]:Planetary gear transmission system due to its high bearing capacity, compact structure, widely used in aerospace, shipbuilding, automobile and other fields. Due to the internal incentive under the external incentive and bear their own parameters caused by the change of the planet, the dynamic behavior of the system ten is complex, the noise and vibration is a key factor affecting system reliability and life. Therefore, to improve the safety and reliability of the mechanical system dynamics modeling, need for mechanical transmission system, dynamic response analysis, vibration analysis, parameter stability, in-depth study of noise reduction. The dynamic characteristics of the closed planetary system as a planetary transmission, it can load the torque transmitted from multiple paths transfer to the closed planetary transmission. So it can carry more torque, and compact structure, the transmission ratio is bigger, its volume more often than the same power rating is simple The planetary system is smaller. In recent years, closed planetary transmission system has more and more applications in the field of mechanical transmission because of its unique advantages. Its dynamic characteristics can provide theoretical basis and guidance for optimal design, and has important practical significance.
In this paper, a power split (bus) can realize the dynamic characteristics of two stage closed planetary system is studied. The mathematical model of the transmission system is established, the inherent characteristics of analysis, frequency response analysis, influence of system parameters on vibration characteristics and experimental research, made some achievements and progress. The main contents of this paper include the following aspects:
According to the kinematics of each component of the transmission system, the formulas of relative displacement of each component of the system. In the premise of reasonable assumptions, using the lumped mass method, the system dynamics model of pure torsion and translational torsional coupling dynamic model was established based on the Lagrange equation of the second kind. According to the two kinds of the dynamic model analysis the natural vibration characteristics of the system, and based on the natural frequency and vibration characteristics were summarized and classified. According to the vibration mode of system eigenvalue equation, mathematically proved that the complete classification of the vibration modes. The influences of planetary gear changes in the number of the natural frequency of the system. The model is easy to expansion of the closed planetary system can be extended to an arbitrary number of planet gears and planetary gear series, has a universal significance.
The nonlinear factors included in the system, such as time-varying meshing stiffness, backlash and meshing error are mathematically described by nonlinear dynamic differential equation group, pure torsion model of dissipative system. The nonlinear dynamic differential of pure torsion model has dimensionless and remove the rigid motion model of the equations, using DFT numerical harmonic balance method is transformed into nonlinear algebraic equations. In order to further solve the equations, using the quasi Newton method (BFS rank 2) combined with the pseudo arclength algorithm for numerical solution, a comprehensive analysis of the amplitude frequency response curve of the jump, multi value and unstable solution support etc. the typical nonlinear characteristics. By changing the external excitation, the meshing stiffness, damping and other parameters, reveals the important parameters of rule two grade influence dynamic characteristics of nonlinear planetary transmission system in this paper. A new method and way is provided for the thorough study of the dynamic characteristics of the closed planetary transmission system.
Considering the backlash belongs to the strong nonlinear factors, the method of multiple scales cannot be directly applied to solve the nonlinear dynamic model of gear system. Through the analysis of time-varying meshing stiffness and backlash of two kinds of nonlinear factors, including two kinds of nonlinear factors are the comprehensive expression, make the method of multiple scales can be applied reasonably in two grade nonlinear planetary system model, and deduced the approximate analytical expressions of the amplitude of the primary resonance of the system. The system of relative meshing phase are studied, the formulas of relative phase of any two meshing gear pair. The approximate analytic expressions based on multi-scale, reveals the system structure, the relative meshing phase and system the coincidence degree of geometrical parameters on vibration characteristics are studied.
Build the experimental platform of two stage closed planetary transmission system. The frequency response function of transmission system was tested by experimental modal analysis, the natural frequency of the system; comparing test results with the results of theoretical analysis. Based on the lumped mass method of planetary transmission system dynamics model of pure torsion and translational torsional coupling dynamics model based on the reasonable.
The influence of system design parameters on dynamic characteristics is revealed through the research in this paper, which provides a theoretical basis for dynamic design of closed planetary transmission system, and has great theoretical significance and practical application value for improving the design level of closed planetary system in China.
The project has been supported by the National Natural Science Foundation (51175299) and the natural science foundation of Shandong (ZR2010EM012).

【學(xué)位授予單位】：山東大學(xué)
【學(xué)位級(jí)別】：博士
【學(xué)位授予年份】：2014
【分類號(hào)】：TH132.425

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