本文選題：齒廓偏差 + “切片法”齒輪嚙合剛度模型　； 參考：《東北大學(xué)》2015年博士論文

【摘要】：齒輪是輪緣上有齒、能夠連續(xù)嚙合傳遞運(yùn)動(dòng)與動(dòng)力的機(jī)械元件,廣泛應(yīng)用于機(jī)械傳動(dòng)系統(tǒng)中。設(shè)計(jì)偏差(齒廓修形)、制造誤差和安裝誤差等因素導(dǎo)致輪齒存在齒廓偏差,齒廓偏差對(duì)齒輪嚙合剛度、傳遞誤差激勵(lì)有一定的影響,進(jìn)而影響齒輪系統(tǒng)的振動(dòng)響應(yīng)和動(dòng)應(yīng)力(齒面接觸動(dòng)應(yīng)力和齒根彎曲動(dòng)應(yīng)力),這將加快齒輪傳動(dòng)系統(tǒng)的劣化過(guò)程,影響齒輪的壽命和可靠性。本課題圍繞誤差齒廓齒輪系統(tǒng)動(dòng)力學(xué)問(wèn)題,建立了考慮齒廓偏差的齒輪嚙合剛度和傳遞誤差激勵(lì)模型、齒輪系統(tǒng)振動(dòng)模型和動(dòng)應(yīng)力計(jì)算模型,分析了齒輪系統(tǒng)在嚙合剛度激勵(lì)和傳遞誤差激勵(lì)下的振動(dòng)特性和動(dòng)應(yīng)力,以及齒輪疲勞可靠性。本文主要工作如下：(1)針對(duì)誤差齒廓的直齒輪和斜齒輪的時(shí)變嚙合剛度、傳遞誤差和載荷分布問(wèn)題,將齒輪沿齒寬方向離散成若干寬度相等的薄片,精確模擬了各薄片輪齒的嚙合過(guò)程,確定齒輪的理論瞬時(shí)接觸線；進(jìn)一步考慮齒廓偏差分布,通過(guò)“切片”思想建立了齒輪嚙合剛度模型,其中“各個(gè)薄片”輪齒可等效為直齒輪齒,分析了齒輪嚙合剛度、傳遞誤差、齒面載荷分布和輪齒有效剛度分布,解決了誤差齒廓齒輪的嚙合剛度激勵(lì)、傳遞誤差激勵(lì)和齒面載荷分布的問(wèn)題。(2)針對(duì)齒輪嚙合動(dòng)力學(xué)模型問(wèn)題,考慮齒輪安裝方位角、主動(dòng)齒輪轉(zhuǎn)向、壓力角、螺旋角、螺旋角旋向等影響因素,忽略齒廓誤差的影響,將齒輪之間的嚙合近似為一個(gè)彈簧,建立了通用的齒輪嚙合彎-扭-軸-擺耦合動(dòng)力學(xué)模型；進(jìn)一步考慮斜齒輪接觸線沿齒寬方向不對(duì)稱,以及含有齒廓偏差的齒輪其載荷沿齒寬方向分布的不均勻性,將齒輪嚙合表示為沿齒寬方向上分布的一系列彈簧的并聯(lián),提出了斜齒輪分布式彎-扭-軸-擺耦合動(dòng)力學(xué)嚙合模型。最后考慮傳動(dòng)軸、軸承的支承作用,建立了齒輪-轉(zhuǎn)子-軸承系統(tǒng)動(dòng)力學(xué)模型。解決了精確模擬斜齒輪和誤差齒廓齒輪系統(tǒng)的嚙合動(dòng)力學(xué)問(wèn)題,為齒輪系統(tǒng)動(dòng)力學(xué)分析奠定了基礎(chǔ)。(3)分別采用單彈簧齒輪嚙合模型和分布式齒輪嚙合模型,建立了齒輪-轉(zhuǎn)子-軸承系統(tǒng)有限元模型,分析了直齒輪、斜齒輪、窄齒面齒輪、寬齒面齒輪、理論齒廓齒輪和誤差齒廓齒輪系統(tǒng)的固有特性和振動(dòng)響應(yīng)特性,驗(yàn)證了齒輪嚙合模型的正確性和適用性。(4)齒輪系統(tǒng)振動(dòng)響應(yīng)分析中,由于齒輪、軸承、傳動(dòng)軸的振動(dòng)變形等作用的影響,將改變齒輪齒廓偏差的分布。齒輪的嚙合力不同于靜力學(xué)中齒輪的嚙合力應(yīng)為齒輪的動(dòng)態(tài)嚙合力。考慮上述因素建立了齒輪嚙合過(guò)程中動(dòng)態(tài)輪齒有效剛度分布、傳遞誤差激勵(lì)模型。齒輪嚙合采用分布式齒輪嚙合動(dòng)力學(xué)模型,建立了齒輪-轉(zhuǎn)子-軸承系統(tǒng)有限元模型,分析了齒輪的振動(dòng)響應(yīng)和動(dòng)態(tài)載荷分布。在此基礎(chǔ)上,以赫茲接觸應(yīng)力作為齒面接觸應(yīng)力的計(jì)算基礎(chǔ),齒廓根部的最大拉應(yīng)力作為齒輪的彎曲應(yīng)力計(jì)算基礎(chǔ),分析了齒輪系統(tǒng)振動(dòng)過(guò)程中齒面接觸動(dòng)應(yīng)力和齒根彎曲動(dòng)應(yīng)力。提出了動(dòng)態(tài)輪齒有效剛度、傳遞誤差激勵(lì)模型以及誤差齒廓齒輪的振動(dòng)響應(yīng)、動(dòng)應(yīng)力計(jì)算模型。(5)在齒輪-轉(zhuǎn)子-軸承系統(tǒng)有限元模型的基礎(chǔ)上,運(yùn)用重要抽樣法分析了基本隨機(jī)變量分布下齒輪接觸動(dòng)應(yīng)力和齒根彎曲動(dòng)應(yīng)力的分布。根據(jù)應(yīng)力-強(qiáng)度干涉模型分析了齒輪的疲勞可靠度和可靠性參數(shù)靈敏度。以靈敏度分析結(jié)果為基礎(chǔ),根據(jù)“反變形”修形理論獲得了齒輪最佳齒廓修形量。
[Abstract]:Gear is a mechanical element that has teeth on the edge of the wheel, and can be continuously meshed to transmit motion and power. It is widely used in the mechanical transmission system. Design deviation (tooth profile modification), manufacturing error and installation error lead to tooth profile deviation in gear teeth. Tooth profile deviation has a certain influence on gear meshing stiffness and transmission error excitation, and then affects teeth. The vibration response and dynamic stress (tooth contact dynamic stress and tooth root bending dynamic stress) will accelerate the deterioration process of the gear transmission system and influence the life and reliability of the gear. In this subject, the gear meshing stiffness and transmission error excitation model, which consider the tooth profile deviation, are built around the dynamic problem of the error Tooth profile gear system. The vibration model and dynamic stress calculation model of the wheel system are used to analyze the vibration characteristics and dynamic stress of the gear system under the excitation and transmission error excitation, as well as the fatigue reliability of the gear. The main work is as follows: (1) the time-varying meshing stiffness, transmission error and load distribution of the spur and helical gear with the error profile, and the distribution of the transmission error and the load will be discussed. The gear is dispersed into a number of thin slices with equal width along the width of the tooth. The meshing process of each tooth is accurately simulated and the theoretical instantaneous contact line of the gear is determined. Further considering the profile deviation distribution, the gear meshing stiffness model is established by the "slice" idea, in which the "each thin slice" tooth can be equivalent to the straight tooth. Gear meshing stiffness, transmission error, tooth surface load distribution and tooth effective stiffness distribution, solving the problem of meshing stiffness excitation, transmission error excitation and tooth surface load distribution. (2) considering gear meshing dynamics model, the gear position angle, active gear steering, pressure angle, spiral angle, spiral angular rotation are considered. By ignoring the influence of the tooth profile error, the meshing between gears is approximated to a spring, and a general dynamic model of gear meshing bending torsion axis pendulum coupling is established, and the asymmetry of the helical gear contact line along the direction of the tooth width and the distribution of the gear with the tooth profile deviation along the direction of the tooth width are considered. The gear meshing is expressed in parallel with a series of springs distributed along the direction of the tooth width. A distributed bending torsional axis swing coupling dynamic meshing model of helical gear is proposed. Finally, considering the bearing function of the drive shaft and bearing, the dynamic model of the gear rotor bearing system is set up. The accurate simulation of the helical gear and the error Tooth profile gear system is solved. The problem of meshing dynamics has laid the foundation for the dynamics analysis of the gear system. (3) the finite element model of the gear rotor bearing system is established by using the single spring gear meshing model and the distributed gear meshing model, and the spur gear, the helical gear, the narrow tooth face gear, the wide tooth face gear, the theoretical tooth profile gear and the error Tooth profile gear system are analyzed. The inherent characteristics of the system and the vibration response characteristics verify the correctness and applicability of the gear meshing model. (4) in the analysis of the vibration response of the gear system, the distribution of the gear profile deviation will be changed by the influence of the vibration and deformation of the gear, bearing, and the transmission shaft. The meshing force of the gear is different from the meshing force of the gear in the statics. On the basis of the above factors, the effective stiffness distribution of the dynamic gear teeth in the gear meshing process and the transfer error excitation model are established. The gear meshing dynamic model is used for the distributed gear meshing, and the finite element model of the gear rotor bearing system is established, and the vibration response and the dynamic load distribution of the gear are analyzed. Taking the Hertz contact stress as the basis for calculating the contact stress of the tooth surface, the maximum tensile stress of the root of the tooth profile is used as the basis of the calculation of the bending stress of the gear. The contact dynamic stress and the bending stress of the tooth root are analyzed in the vibration process of the gear system, and the effective stiffness of the dynamic gear, the transfer error excitation model and the error Tooth profile gear are put forward. The vibration response and dynamic stress calculation model. (5) on the basis of the finite element model of the gear rotor bearing system, the distribution of the contact dynamic stress and the tooth root bending dynamic stress under the basic random variable distribution is analyzed on the basis of the finite element model of the gear rotor bearing system. The fatigue reliability and the reliability parameter sensitivity of the gear are analyzed according to the stress intensity interference model. Based on the results of sensitivity analysis, the optimal profile modification of gear is obtained based on the theory of "reverse deformation".
【學(xué)位授予單位】：東北大學(xué)
【學(xué)位級(jí)別】：博士
【學(xué)位授予年份】：2015
【分類號(hào)】：TH132.41

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