斜齿轮副结构参数灵敏度分析

以机械传动系统中的斜齿轮啮合为研究对象,在考虑时变刚度、齿侧间隙和啮合误差的情况下,建立了十自由度斜齿轮非线性振动数学模型。以斜齿轮结构参数作为灵敏度分析参数,采用数值分析方法分别研究了斜齿轮系统振动加速度均方根值对齿轮质量、支撑刚度和支撑阻尼的灵敏度。结果表明:主、被动轮横向（y向）振动对各参数敏感度较低,横向振动（x向）与被动轮扭转振动对质量参数、刚度参数、阻尼参数较为敏感,被动轮扭转振动受到阻尼的影响很大,灵敏度在扭转振动固有频率处变化较大。     

行星齿轮传动中齿数对行星轮载荷的影响

从齿轮时变啮合刚度出发，建立了单级2K-H渐开线行星齿轮传动的集中质量参数型振动模型，以行星架作为参考坐标，将齿轮啮合的刚度近似成时变分段线性的弹簧刚度，采用模态叠加的原理，通过系统在刚度变化时的速度以及位移的连续性条件，在时域范围内模拟系统的振动过程。分析了不同齿数齿轮对啮合力的影响，最后得出：在2K-H渐开线行星齿轮传动中，若太阳轮与内齿圈均为行星轮个数的整数倍时，行星轮的均载效果好；太阳轮与内齿圈的齿数不为行星轮个数的整数倍时，行星轮之间出现偏载；系统有数个与初始刚度相关的稳定点的结论。     

Dynamic characteristics analysis of a misaligned rotor-bearing system with squeeze film dampers

In this paper, a dynamic model is established for a two-stage rotor system connected by a gear coupling and supported on ball bearings with squeeze film dampers (SFDs). The nonlinear dynamic behavior of the rotor system is studied under misalignment fault condition. The meshing force of the gear coupling is calculated considering the deformation of the tooth caused by torque transmission and dynamic vibration. The contact force between the ball and race is computed based on the Hertzian elastic contact deformation theory and the elastohydrodynamic lubrication theory. The supported force of SFD is simulated by integrating the pressure distribution derived from Reynolds’s equation. The equations of motion are rewritten in non-dimensional differential form, and the fourth-order Runge-Kutta method is employed to solve the nonlinear dynamic equilibrium equations iteratively. To verify the validity of the dynamic model and the correctness of the numerical solution method, the experimental power spectra of the rotor system under various misalignment degrees are compared with the analytical results. The effects of several important parameters, such as the lubrication of the ball bearing, the centralizing spring stiffness, the radial clearance of SFD, and the misalignment of gear coupling, on the dynamic characteristics of the rotor system are investigated and discussed mainly focusing on the system stability. The response spectra, bifurcation diagrams, and Pointcaré maps are analyzed accordingly. These parametric analyses are very helpful in the development of a high-speed rotor system and provide a theoretical reference for the vibration control and optimal design of rotating machinery.     

Design and Dynamics Simulation of a Novel Double-Ring-Plate Gear Reducer

Three-ring gear reducer , an internal gear planetarytransmission, claims many advantages , including largetransmission ratio, high loading capacity, and compactvolume[1].However ,there still exist some disadvantagesinits application.One is the unbalanced …     

WN 齿轮副耦合振动及动态应力仿真的研究

基于WN弧齿轮传动特征建立了多自由度切．径．轴及系统误差耦合振动动力学模分析型。利用PROE建立齿轮三维实体模型,通过PROE软件和Ansys软件数据接口将WN弧齿轮三维模型导入Ansys软件中进行了3维冲击动力接触模拟分析,利用施加载荷进行了WN弧齿轮的应力分析,仿真出WN齿轮齿面接触的等效应力云图。在ANSYS／LS．DYNA中构建了齿轮钢柔性体动态接触模型,以用于齿轮转动的动态分析,结果表明WN弧齿轮的切向与轴向方向的振动明显大于径向的振动。     

基于MLP法的磁浮列车非线性系统的稳定性分析

以磁浮列车的垂向运动为研究对象,研究其非线性系统的稳定性。选取气隙值、电流值为磁浮列车悬浮系统的广义坐标,依据拉格朗日-麦克斯韦方程建立磁浮列车非线性悬浮系统的动力学模型,得到的振动方程是三阶的强非线性负刚度微分方程。应用MLP法求得系统的共振永年项条件,并对初始方程进行了数值计算,得到了磁浮列车在空载、满载、过载情况下的悬浮系统振动时间响应曲线和相图,结果表明:随着列车质量的增加,列车初始位移增加,但列车启动后50 s的时间内,系统振动趋于稳定。     

Backlash analysis of a new planetary gearing with internal gear ring

Due to low carrying capacity and short life of current ring reducer, we proposed a new planetary gearing with internal gear ring, which consisted of two stages. One was an involute planetary drive and the other was an N-type planetary drive with small teeth difference. The kinematic calculation was conducted based on the analysis of structural composition and working principle. Formulas of backlash calculation for the new planetary gearing were derived by using probabilistic theory and the analytical model was created at the same time. Then, main factors that affect the systematic backlash were introduced and the effects of manufacture error, misaligments and roller bearing parameters on the distribution of backlash were presented. The influence of gear backlash on systematic return difference was performed based on the backlash mathematic model proposed. The results show that the backlash is a little large, of which the backlash of bearing takes a greater part than two gearing stages. So we presented some practical methods to reduce the systematic backlash.     

斜齿轮啮合刚度的计算

根据梅泽清彦(umezawa)斜齿轮振动模型，改进后得出齿轮传动中斜齿轮啮合刚度的计算公式，为齿轮传动动态特性的研究打下基础。     

列表叠加法计算行星轮系的转速

大多数“机械原理”教材都使用转化机构法来研究行星轮系的转速。章介绍使用列表叠加法来计算行星轮系的转速,此法将行星轮系的运动看成是两段运动的叠加。同时还论证了此法的理论依据并指出此法的缺陷。     

Finite element analysis of dynamic response and structure borne noise of gearbox

A dynamic finite element method combined with finite element mixed formula for contact problem is used to analyze the dynamic characteristics of gear system. Considering the stiffness excitation, error excitation and meshing shock excitation, the dynamic finite element model is established for the entire gear system which includes gears, shafts, bearings and gearbox housing. By the software of I-DEAS, the natural frequency, normal mode, dynamic time-domain response, frequency-domain response and one-third octave velocity grade structure borne noise of gear system are studied by the method of theoretical modal analysis and dynamic response analysis. The maximum values of vibration and structure borne noise are occurred at the mesh frequency of output grade gearing.     

一种高速列车-轨道三维空间耦合动力学模型

研究目的：基于车辆-轨道耦合动力学理论分析方法,建立一种高速列车-轨道三维耦合动力学模型,并明确列车-轨道耦合模型与单节车辆-轨道耦合模型在高速列车-车九道耦合动力学性能分析中的差异。创新要点：建立一种高速列车-轨道三维耦合动力学模型,模型中考虑列车的纵向动力学行为以及车间连接装置对列车中不同车辆动态响应的影响,并基本明确完善的列车-轨道耦合模型在高速列车-轨道耦合动力学性能分析中的重要性。重要结论：单节车辆-轨道耦合模型会过高地估计高速列车在运营过程中的振动响应和动力学性能指标,而完善的列车-轨道耦合动力学模型的计算结果则更加接近实际情况。     

Finite element analysis of internal gear in high-speed planetary gear units

The stress and the elastic deflection of internal ring gear in high-speed spur planetary gear units are investigated. A rim thickness parameter is defined as the flexibility of internal ring gear. Six evenly spaced linear springs are used to describe the fitting status between internal ring gear and the gearcase, The finite element model of the whole internal ring gear is established by means of Pro/E and ANSYS. The loads on meshing teeth of internal ring gear are applied according to the contact ratio and the load-sharing coefficient. With the finite element analysis （FEA）, the influences of flexibility and fitting status on the stress and elastic deflection of internal ring gear are predicted. The simulation reveals that the principal stress and deflection increase with the decrease of rim thickness of internal ring gear. Moreover, larger spring stiffness helps to reduce the stress and deflection of internal ring gear. Therefore, the flexibility of internal ring gear must be considered during the design of high-speed planetary gear transmissions.     

非解析径向轴承支承转子系统非线性动力特性分析

Nomenclaturex,y,x ·, y·-displacement and velocity of rotor-x,-y,x-·,-y·-displacement and velocity of rotor , di mension less¨x,¨y-acceleration of rotor¨-x,¨-y-acceleration of rotor ,di mensionlessω-rotating speed of rotor-ω-rotating speed of rotor ,di mensionlessx,y,z-Cartesian coordinates-x,-y,-z-Cartesian coordinates ,di mensionless2m-mass of rotorg-acceleration of gravityG-weight of rotor ,di mensionlesse=e2x e2y-mass eccentricity of rotorex,ey-mass eccentricity of rotor in thexan…     

A 2.5D finite element approach for predicting ground vibrations generated by vertical track irregularities

Dynamic responses of track structure and wave propagation in nearby ground vibration become significant when train operates on high speeds. A train-track-ground dynamic interaction analysis model based on the 2.5D finite element method is developed for the prediction of ground vibrations due to vertical track irregularities. The one-quarter car model is used to represent the train as lumped masses connected by springs. The embankment and the underlying ground are modeled by the 2.5D finite element approach to improve the computation efficiency. The Fourier transform is applied in the direction of train’s movement to express the wave motion with a wave-number. The one-quarter car model is coupled into the global stiffness matrix describing the track-ground dynamic system with the displacement compatibility condition at the wheel-rail interface, including the irregularities on the track surface. Dynamic responses of the track and ground due to train’s moving loads are obtained in the wave-number domain by solving the governing equation, using a conventional finite element procedure. The amplitude and wavelength are identified as two major parameters describing track irregularities. The irregularity amplitude has a direct impact on the vertical response for low-speed trains, both for short wavelength and long wavelength irregularities. Track irregularity with shorter wavelength can generate stronger track vibration both for low-speed and high-speed cases. For low-speed case, vibrations induced by track irregularities dominate far field responses. For high-speed case, the wavelength of track irregularities has very little effect on ground vibration at distances far from track center, and train’s wheel axle weights becomes dominant.     

行星齿轮系统的频响特性测试试验研究

以2K-H行星齿轮传动系统为研究对象,给出固有频率的计算结果。在此基础上,研究了该系统的频响特性试验,包括试验台的布置及其试验方案的设计;测得系统的频率响应函数和固有频率,并将试验结果与理论计算结果进行了对比分析。     

Nonlinear dynamic analysis of a rotor/bearing/seal system

In this study a new dynamic model of a rotor system is established based on the Hamilton principle and the finite element method (FEM). We analyze the dynamic behavior of the rotor system with the coupled effects of the nonlinear oil film force, the nonlinear seal force, and the mass eccentricity of the disk. The equations of the motion are solved effectively using the fourth order Runge-Kutta method in MATLAB. The dynamic behavior of the system is illustrated by bifurcation diagrams, largest Lyapunov exponents, phase trajectory diagrams, and Poincaré maps. The numerical results show that the rotational speed of the rotor, the pressure drop in the seal, the seal length, the seal clearance, and the mass eccentricity of the disk are the key parameters that significantly affect the dynamic characteristics of the rotor system. The motion of the rotor system exhibits complex types of periodic, quasi-periodic, double-periodic, multi-periodic, and chaotic vibrations. This analysis can be used to guide the design of seal parameters and to diagnose the vibration of rotor/bearing/seal systems.     

弯扭耦合振动模型在齿轮传动系统振动分析中的应用

根据齿轮动力学原理，在武钢调车用内燃机车中间齿轮箱全传动系统两种动力学模型（即扭转、横向振动模型）的基础上建立弯扭耦合振动模型。     

刚柔耦合条件下的差速器齿轮机构力学研究

为了获取差速器齿轮机构在多体动力学条件下的受力情况,以某款轿车使用的差速器为研究对象,利用三维绘图软件UG建立该差速器结构模型,并导入到ADAMS软件中,根据齿轮接触理论,添加合适的约束与载荷,建立齿轮机构刚体模型。在多体系统动力学理论的指导下,在ADAMS软件中建立行星齿轮的柔性体模型,从而得到差速器传动机构的刚柔耦合模型,并进行直线行驶和转向两种工况下的力学仿真分析。分析结果表明:在两种工况下行星齿轮与半轴齿轮接触位置的最大应力分别为377.15MPa和849.11MPa,均小于材料的许用应力;同时也得到了实际工作中行星齿轮应力最大的10个热点。这为后期齿轮的优化设计提供了一定的技术支持。     

Parametrically excited oscillation of stay cable and its control in cable-stayed bridges

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非线性双圆盘转子-密封系统的数值分析

研究目的：求斛双圆盘转了-密封系统的非线性振动特性和运动响应 创新要点：采用有限元法（FEM）和拉格朗目方程求解双圆盘转子-密封系统,进而为研究多级转了系统的非线性振动问题提供有效方法。研究方法：基于有限元法（FEM）和拉格朗目方程。同时利用四阶龙格-库塔法求解系统动特性运动响应情况,利用风岔图、时间历程图、轴心轨迹图、庞加莱映射和幅值谱等分析图研究双圆盘转子-密封系统的非线性振动特性。重要结论：随着转速的增大,双圆盘转子-密封系统呈现丰富的非线性运动形式,包括周期性运动、多周期运动,准周期运动以及混沌运动。在右端圆盘不平衡质量小于34kg、密封间隙范围为0.376mm-0.54mm、密封长度大于0.13m或者密封压差高于0.104MPa的情况下均有利于提高双圆盘转子-密封系统的稳定性。