误差齿廓齿轮系统动力学特性研究及疲劳可靠性分析

发布时间：2018-05-25 08:49

本文选题：齿廓偏差 + “切片法”齿轮啮合刚度模型　；参考：《东北大学》2015年博士论文

【摘要】：齿轮是轮缘上有齿、能够连续啮合传递运动与动力的机械元件,广泛应用于机械传动系统中。设计偏差(齿廓修形)、制造误差和安装误差等因素导致轮齿存在齿廓偏差,齿廓偏差对齿轮啮合刚度、传递误差激励有一定的影响,进而影响齿轮系统的振动响应和动应力(齿面接触动应力和齿根弯曲动应力),这将加快齿轮传动系统的劣化过程,影响齿轮的寿命和可靠性。本课题围绕误差齿廓齿轮系统动力学问题,建立了考虑齿廓偏差的齿轮啮合刚度和传递误差激励模型、齿轮系统振动模型和动应力计算模型,分析了齿轮系统在啮合刚度激励和传递误差激励下的振动特性和动应力,以及齿轮疲劳可靠性。本文主要工作如下：(1)针对误差齿廓的直齿轮和斜齿轮的时变啮合刚度、传递误差和载荷分布问题,将齿轮沿齿宽方向离散成若干宽度相等的薄片,精确模拟了各薄片轮齿的啮合过程,确定齿轮的理论瞬时接触线；进一步考虑齿廓偏差分布,通过“切片”思想建立了齿轮啮合刚度模型,其中“各个薄片”轮齿可等效为直齿轮齿,分析了齿轮啮合刚度、传递误差、齿面载荷分布和轮齿有效刚度分布,解决了误差齿廓齿轮的啮合刚度激励、传递误差激励和齿面载荷分布的问题。(2)针对齿轮啮合动力学模型问题,考虑齿轮安装方位角、主动齿轮转向、压力角、螺旋角、螺旋角旋向等影响因素,忽略齿廓误差的影响,将齿轮之间的啮合近似为一个弹簧,建立了通用的齿轮啮合弯-扭-轴-摆耦合动力学模型；进一步考虑斜齿轮接触线沿齿宽方向不对称,以及含有齿廓偏差的齿轮其载荷沿齿宽方向分布的不均匀性,将齿轮啮合表示为沿齿宽方向上分布的一系列弹簧的并联,提出了斜齿轮分布式弯-扭-轴-摆耦合动力学啮合模型。最后考虑传动轴、轴承的支承作用,建立了齿轮-转子-轴承系统动力学模型。解决了精确模拟斜齿轮和误差齿廓齿轮系统的啮合动力学问题,为齿轮系统动力学分析奠定了基础。(3)分别采用单弹簧齿轮啮合模型和分布式齿轮啮合模型,建立了齿轮-转子-轴承系统有限元模型,分析了直齿轮、斜齿轮、窄齿面齿轮、宽齿面齿轮、理论齿廓齿轮和误差齿廓齿轮系统的固有特性和振动响应特性,验证了齿轮啮合模型的正确性和适用性。(4)齿轮系统振动响应分析中,由于齿轮、轴承、传动轴的振动变形等作用的影响,将改变齿轮齿廓偏差的分布。齿轮的啮合力不同于静力学中齿轮的啮合力应为齿轮的动态啮合力。考虑上述因素建立了齿轮啮合过程中动态轮齿有效刚度分布、传递误差激励模型。齿轮啮合采用分布式齿轮啮合动力学模型,建立了齿轮-转子-轴承系统有限元模型,分析了齿轮的振动响应和动态载荷分布。在此基础上,以赫兹接触应力作为齿面接触应力的计算基础,齿廓根部的最大拉应力作为齿轮的弯曲应力计算基础,分析了齿轮系统振动过程中齿面接触动应力和齿根弯曲动应力。提出了动态轮齿有效刚度、传递误差激励模型以及误差齿廓齿轮的振动响应、动应力计算模型。(5)在齿轮-转子-轴承系统有限元模型的基础上,运用重要抽样法分析了基本随机变量分布下齿轮接触动应力和齿根弯曲动应力的分布。根据应力-强度干涉模型分析了齿轮的疲劳可靠度和可靠性参数灵敏度。以灵敏度分析结果为基础,根据“反变形”修形理论获得了齿轮最佳齿廓修形量。
[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".
【学位授予单位】：东北大学
【学位级别】：博士
【学位授予年份】：2015
【分类号】：TH132.41

【相似文献】