【摘要】：齒面摩擦是影響行星齒輪傳動系統(tǒng)振動與噪音的關鍵因素之一。,為明確真實工況下的行星輪系的動力學行為,有必要探究齒面摩擦對系統(tǒng)動力學特性的影響機理。有鑒于此,本文在考慮齒輪副時變嚙合剛度、齒側間隙、靜態(tài)傳遞誤差等因素的基礎上,進一步計及齒面摩擦力的影響,建立計入摩擦效應的直齒行星輪系平移-扭轉耦合非線性動力學模型。針對所建的動力學模型,推導輪系運動微分方程,并利用四階變步長Runge-kutta法求解系統(tǒng)的動力學響應。通過對比有、無計入齒面摩擦效應工況下的輪系動力學響應,揭示齒面摩擦對系統(tǒng)動力學行為的影響機理。在此基礎上,進一步開展參數(shù)影響分析,以明確設計參數(shù)對系統(tǒng)動態(tài)特性的影響規(guī)律。論文具體內(nèi)容及貢獻簡述如下:首先,簡要闡述了行星輪系中軸承支承剛度、齒輪副時變嚙合剛度、齒輪傳動誤差、齒側間隙和齒面摩擦力等非線性因素的計算方法,給出了相關參數(shù)的數(shù)學描述式,并結合具體案例進行了時變嚙合剛度和齒輪傳動誤差的參數(shù)整定。在此基礎上,采用集中參數(shù)法建立了計入齒面摩擦效應的直齒行星輪系平移—扭轉耦合非線性動力學模型,并運用牛頓第二定律推導了系統(tǒng)各傳動構件的運動微分方程。其次,對所建的系統(tǒng)運動微分方程進行了降階和無量綱化處理,進而利用四階變步長Runge-kutta法求解了系統(tǒng)的動力學方程,獲得了行星齒輪系統(tǒng)中各主要構件的穩(wěn)態(tài)響應。在此基礎上,對比分析了計入齒面摩擦效應前、后兩種工況下太陽輪、行星架和內(nèi)齒圈的周期響應和動態(tài)嚙合力。數(shù)據(jù)表明,齒面摩擦力對系統(tǒng)的非線性運動有一定的抑制作用,會使得系統(tǒng)的振動位移響應和動態(tài)嚙合力略有減弱。再次,基于上述的動力學分析,開展了參數(shù)影響分析的研究。針對有、無摩擦效應兩種工況,相繼分析了激勵頻率、嚙合阻尼和齒側間隙對系統(tǒng)非線性行為的影響,初步得到了系統(tǒng)非線性行為的變化規(guī)律。此外,進一步研究了時變嚙合剛度和靜態(tài)傳動誤差對系統(tǒng)動力學響應的影響規(guī)律。數(shù)據(jù)表明,在嚙合頻率、嚙合阻尼和間隙的影響下,齒面摩擦會改變系統(tǒng)進入或者結束混沌運動狀態(tài)的邊界條件。隨著齒面摩擦系數(shù)的增大,系統(tǒng)會從混沌運動遍歷到擬周期、再到單周期的狀態(tài)。
[Abstract]:Tooth surface friction is one of the key factors affecting the vibration and noise of planetary gear transmission system. In order to clarify the dynamic behavior of planetary gear train under real working conditions, it is necessary to explore the influence mechanism of tooth surface friction on the dynamic characteristics of the system. In view of this, the influence of tooth surface friction is considered on the basis of considering the factors such as gear pair time-varying meshing stiffness, tooth side clearance, static transfer error and so on. A nonlinear dynamic model of transverse-torsional coupling of straight tooth planetary gear train with friction effect is established. According to the dynamic model, the differential equations of gear train motion are derived, and the dynamic response of the system is solved by using the fourth order variable step Runge-kutta method. By comparing the dynamic responses of gear trains without the tooth surface friction effect, the influence mechanism of tooth surface friction on the dynamic behavior of the system is revealed. On this basis, further analysis of the influence of parameters is carried out to clarify the influence of design parameters on the dynamic characteristics of the system. The specific contents and contributions of this paper are summarized as follows: firstly, the calculation methods of nonlinear factors such as bearing support stiffness, gear pair time-varying meshing stiffness, gear transmission error, tooth side clearance and tooth surface friction in planetary gear train are briefly described. The mathematical description of the related parameters is given, and the parameter tuning of the time-varying meshing stiffness and gear transmission error is carried out with a concrete case. On the basis of this, a nonlinear dynamic model of translation-torsional coupling is established by using the lumped parameter method, which takes into account the friction effect on the tooth surface, and the differential equations of motion of each transmission member of the system are derived by using Newton's second law. Secondly, the differential equations of motion of the system are reduced and dimensionless, and the dynamic equations of the system are solved by using the four-order variable step Runge-kutta method, and the steady-state responses of the main components in the planetary gear system are obtained. On this basis, the periodic response and dynamic meshing force of solar wheel, planetary frame and inner gear are analyzed under the latter two working conditions before the tooth surface friction effect is taken into account. The data show that the tooth surface friction can restrain the nonlinear motion of the system to a certain extent and weaken the vibration displacement response and dynamic meshing force of the system. Thirdly, based on the above kinetic analysis, the parameter impact analysis is carried out. In this paper, the effects of excitation frequency, meshing damping and tooth clearance on the nonlinear behavior of the system are analyzed one after another, and the variation law of the nonlinear behavior of the system is preliminarily obtained. In addition, the influence of time-varying meshing stiffness and static transmission error on the dynamic response of the system is further studied. The data show that under the influence of meshing frequency meshing damping and clearance the tooth surface friction will change the boundary conditions when the system enters or ends the chaotic motion state. With the increase of tooth friction coefficient, the system will move from chaotic motion ergodic to quasi-periodic, and then to single-period state.
【學位授予單位】：安徽工業(yè)大學
【學位級別】：碩士
【學位授予年份】：2017
【分類號】：TH132.41

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