求解齿轮系统非线性动力学微分方程的多尺度方法

首先建立了描述齿轮系统扭转振动的动力学分析模型,并推导出综合考虑时变啮合刚度、齿侧间隙、动态传递误差等非线性因素的齿轮系统非线性动力学的统一微分方程。介绍了用于求解齿轮系统非线性动力学微分方程的多尺度方法的原理,并推导了频率响应方程。利用多尺度方法获得的近似解析解与直接进行数值积分所获得的精确解吻合得较好,表明多尺度方法是求解复杂非线性微分方程最有效的方法之一。     

Dynamic load sharing behavior of transverse-torsional coupled planetary gear train with multiple clearances

A new nonlinear transverse-torsional coupled model with backlash and bearing clearance was proposed for planetary gear set. Meanwhile, sun gear and planet's eccentricity errors, static transmission error, and time-varying meshing stiffness were taken into consideration. The differential governing equations of motion were solved by employing variable step-size Rung-Kutta numerical integration method. The behavior of dynamic load sharing characteristics affected by the system parameters including input rate, sun gear's supporting stiffness and eccentricity error, planet's eccentricity error, sun gear's bearing clearance, backlashes of sun-planet and planet-ring meshes were investigated qualitatively and systematically. Some theoretical results are summarized at last which extend the current understanding of the dynamic load sharing behavior of planet gear train, enrich the related literature and provide references for the design of planetary gear train.     

Effect of Tooth Profile Modification on Vibration of Power Split Gear Transmission System

Based on Newton''s second law, the bend-torsion-shaft coupling nonlinear dynamic model and equations of power split gear transmission system are established. According to the principle of tooth profile modification, the tooth profile modification is considered as time-varying gear backlash function acting along the line of action. Then the dynamic functions are solved by using Runge-Kutta numerical method. After analyzing the effect of tooth profile modification quantity(TPMQ) and relative tooth profile modification length(TPML) to the nonlinear dynamic characteristics of power split gear transmission, the following conclusions are drawn: ①The TPMQ of a certain stage transmission affects the vibration of its own stage more significantly than the other stage, and the coupling effect between two stages can be ignored usually in the modification design; ②If the first stage TPMLs are less than 0.3, the influence of the first stage TPMLs to the first stage transmission vibration is much more greatly than the influence of the second stage TPMLs to the first stage transmission vibration, or else both the first and second stage TPMLs affect the first stage transmission vibration largely. The same is true for the second stage TPMLs, and the cutoff value is 0.2; ③The TPMQ affects the vibration of power split gear transmission system more principally than the TPML, and should be top-priority in the modification design.     

起落架磁流变减振系统的特性分析研究

大型飞机的安全研究,起落架是保障飞机起飞与降落安全的关键部件,该文根据起落架的减振系统对其进行动力学特性分析。由于磁流变阻尼力的出现,导致了起落架磁流变减振系统成为了非线性系统,为了研究系统特性,通过对其非线性部分线性化,构造出起落架磁流变减振系统的动力学数学模型,分析不同阻尼比下机身位移、机身加速度、起落架位移和起落架动载荷的频率响应,并对跑道的随机路面激励时域特性分析,这对起落架磁流变减振系统结构设计和减振系统优化控制具有重要意义。     

负载与支承刚度对面齿轮传动系统动态特性的影响分析

为研究负载及支承刚度变化时对面齿轮传动系统动态特性的影响,建立了包含支承、齿侧间隙、时变啮合刚度、综合传动误差、阻尼和负载激励等参数的系统弯-扭耦合动力学模型,并使用PNF（Poincaré-Newton-Floquet）方法进行求解。计算结果表明,在不同的负载及支承刚度条件下,系统会出现简谐响应、次谐响应、拟周期响应及混沌响应4类稳态响应。增加负载及支承刚度能有效降低系统的动载荷,而增大支承刚度还可以减小面齿轮支承在方向与方向上的振动位移幅值差距。     

风电齿轮箱齿轮传动系统非线性因素影响分析

针对风力发电机齿轮箱在实际风场中工况复杂的问题,采用集中质量参数法建立了风电齿轮箱传动系统高速级齿轮滚动轴承耦合动力学模型,考虑了传动系统的综合啮合刚度、误差激励、齿面侧隙和轴承径向刚度等非线性影响因素,对1.5 MW风力机齿轮箱传动系统的非线性动力学模型进行了仿真计算分析.采用Runge-Kutta法对模型进行求解得到传动系统的时域波形和幅频响应.结果表明:较小齿面侧隙会使系统出现较大振动响应,随着齿面侧隙增大,系统振动位移减小,会导致系统从周期走向混沌响应;轴承游隙的存在使系统产生混沌响应,呈现出非周期的特征.     

齿轮动力互研法的振动机理的研究

齿轮动力互研法利用齿轮在啮合过程中的齿面动态力来达到研齿的目的。因此，齿面动态力的变化规律是影响研齿精主工的重要因素。本文从非线性振动的理论出发，分析了研齿系统的振动机理，并对齿面动态力做了定量的分析。     

变双曲圆弧齿线圆柱齿轮非线性振动特性分析

为得到变双曲圆弧齿线圆柱齿轮（CHATT）工作时的振动规律,以便设计出运行平稳可靠、传动高效的齿轮,对其非线性振动特性展开研究。通过齿轮副承载接触分析,计算啮合线上轮齿的时变啮合刚度和轴向误差激励,并依据啮合冲击计算模型得到啮入冲击激励。基于集中参数理论建立CHATT的12自由度的弯扭轴多因素耦合振动模型,再依据牛顿第二定律建立包含上述三种内部激励的振动微分方程组。采用变步长四阶Runge-Kutta法对量纲一化后的方程组求解,对比主动轮和从动轮各自垂直、扭转和轴向上的振动特性数值解,结果表明：主动轮和从动轮的振动规律始终保持一致,竖直和扭转方向上作拟周期运动,轴向振动处于稳态响应的近混沌状态。进一步研究齿线半径、负载转矩和输入转速等三个参数变化对系统振动特性的影响规律,分析结果表明：轴向振动从多周期运动向近混沌运动演变,其振动的规律性更容易受到上述三个参数变化的影响。变双曲圆弧齿线圆柱齿轮振动模型的建立、求解和参数影响分析为后续的动态设计、预测不同参数下的振动响应趋势以及降噪提供一定的理论依据。     

Theoretical and experimental study on non-linear vibration characteristic of gear transmission system

In order to investigate the vibration of gear transmission system with clearance, a vibratory test-bed of the gear transmission system was designed. The non-linear dynamic model of the system was presented, with consideration of the effects of nonlinear dynamic gear mesh excitation, flexible rotors and bearings. Integration method was used to investigate the non-linear dynamic response of the system. The results imply that when the mesh frequency is near the natural frequency of gear pair, it is the first primary resonance, the bifurcation appears, and the vibration becomes to be chaotic motion rapidly. When the speed is close to the natural frequency of the first-order bending vibration, it is the second primary resonance, the periodic motion changes to chaos by period doubling bifurcation. The vibratory measurement of test-bed of the gear transmission system was performed. Accelerometers were employed to measure the high frequency vibration. Experimental results show that the vibration acceleration of the gear transmission system includes mesh frequency and sideband. The numerical calculation results of low speed can be validated by experimental results basically. It means that the presented non-linear dynamic model of the gear transmission system is right.     

二维非线性动力系统的截断近似求解

通过对二维非线性动力系统的截断近似，使得二维非线性动力系统由一组方程来表达。本文用一个特例解出方程组，说明了二维线性动力系统向圆映象的转换，并且表明了这种方法的有效性。     

基于多项式的等高齿锥齿轮时变啮合刚度建模

针对某型雷达装置的等高齿锥齿轮在啮合时的时变啮合刚度,提出一种多项式函数展开的时变啮合刚度新模型。通过转速、负载扭矩、阻尼因子系数分析,构建了多项式函数展开的时变啮合刚度模型,建立了等高齿锥齿轮的非线性动力学方程。将本文建立的时变啮合刚度模型与传统的多阶简谐波叠加形式的时变啮合刚度模型以及综合刚度参考数据模型进行分析对比,发现在小阻尼、重载工况下这种多项式形式的时变啮合刚度模型能更贴近于时变啮合刚度的实际特性,该模型为齿轮传动的减振、降噪、平稳传动等方面的动力学研究打下基础。     

销齿轮传动的动态设计

文章采用微分几何的方法建立了销齿轮齿形的曲线方程,设计了销齿轮传动的动态设计软件。使用动态设计软件可以进行销齿轮传动的啮合模拟和动态设计,确定销齿轮的齿顶圆直径、啮合传动的重叠系数以及其他结构参数,为销齿轮三维建模提供了有效的图形数据。     

Dynamic response of large increased pressure wind tunnel rotor-gear coupling system with parallel misalignment

To study the misalignment of gear coupling, this paper analyzed the distortion of the tooth of gear coupling on the base of gear coupling ＇ s motion under parallel misalignment, and derived the specific expression of additive radial force, which produced by the rotor＇ torque. The motion differential equations of the large in- creased pressure wind tunnel rotor-gear coupling system were derived by the finite element method. Newmark integral method was applied to calculate the dynamic response of the system with parallel misalignment. The nu- merical results show that： under the effect of additive radial force, the static misalignment can arouse 2X frequency component lateral vibration; the dynamic misalignment can arouse2X,4X,6X multiple frequency components lateral vibration. The 2X frequency component is obvious. The additive radial force of the gear coupling can arouse lateral vibration with even multiple frequency components.     

用静态传递误差法进行高速双圆弧齿轮的振动分析

在微机上建立并求解了双圆弧齿轮的单自由度非线性力学模型和动力学方程；编制了计算轮齿动载和动载系数的计算机程序，并将静态传递误差引入齿轮振动微分方程求解中；可为今后进一步进行高速双圆弧齿轮的动态优化设计打下了基础。     

一类具有纯非线性耗散的广义Kdv方程和Kp方程的行波解

通过运用动力系统分支理论,对两个具有纯非线性耗散的广义Kdv和Kp方程变式进行研究,获得了系统在各种参数条件下可能存在的孤立行波解、不可数无穷多光滑周期行波解和不光滑行波解,并就不同参数条件给出了上述解存在的充分条件.     

旋转刀盘母面成形的弧齿线圆柱齿轮数学建模

将空间啮合理论用于齿轮的齿面数学方程推导,建立了可用于理论分析的采用旋转刀盘为成形母面的弧齿线圆柱齿轮齿面数学方程.通过观察分析齿轮加工中刀盘与齿胚的运动关系,将弧齿线圆柱齿轮齿面分割为3个主要构成曲面,建立了加工过程中的动态与静态坐标系,依据曲面包络理论建立工作曲面的曲面数学方程,根据坐标转换关系建立了齿底和齿根曲面方程;在此基础上建立齿面方程.输出齿面的点云数据,通过逆向工程拟合取得可用于编辑裁剪的齿轮曲面,再根据曲面之间的关系裁剪曲面,最终生成齿轮3D模型实体.此方法建立了精确的弧齿线圆柱齿轮3D模型,并且与采用模拟加工方法生成的模型一致,为精确地进行有限元分析提供了基础;而由此方法获得的曲面方程可用于对弧齿线圆柱齿轮的理论分析.     

XFY718液压仿形铣床的动态分析

本文对XFY718液压仿形铣床的轮廓仿形系统进行动态分析,采用功率键合图建立起交系数的非线性状态方程,用计算机仿真方法了解其动态特性,为进一步的参数优比设计奠定基础。     

车辆多级行星传动系统强迫扭转振动与动载特性

针对某车辆行星传动系统,以发动机动态转矩为激励,采用集中参数法建立纯扭转强迫振动模型,利用拉格朗日方程建立系统微分方程并进行求解。分析了各部件在同一档位的振幅特性,得出不同部件的振动特点。研究了不同档位下行星排的振动,得出行星排在空载与受载时扭振的差异。最后对行星排啮合力波动量和动载荷系数进行计算,为行星传动系统设计和动态分析提供了依据。     

含齿面分形啮合刚度的齿轮传动系统动力学

为研究考虑齿面分形特性的时变啮合刚度对齿轮-轴承系统的影响,用分形理论描述齿轮轮廓,采用Weber-Banaschek公式计算和分析不同分形维数D对齿轮时变啮合刚度的影响,将不同分形维数D下的刚度代入计及滑动轴承非线性油膜力、综合传递误差及齿侧间隙等因素的齿轮-轴承系统中,分析不同分形维数D下的刚度对系统动力学特性的影响.采用Runge-Kutta法求解系统动力学微分方程,得到系统响应的相图、Poincaré截面图、时域图、分岔图以及三维频谱图等.结果表明:随着分形维数D的增大,时变啮合刚度波动降低,系统趋于更加稳定的周期运动;相比含随机扰动的刚度,齿轮-轴承系统对于考虑齿面分形特性的齿轮啮合刚度的变化更加敏感,更能表现因齿廓变化导致的系统响应的变化;随着阻尼比的增大,系统会趋于相对稳定的单周期运动.     

中心传动磨机减速机齿轮传动系统动力学模型分析和研究

本文以中心传动磨机减速机斜齿轮传动系统即一多质量多自由度系统为对象，建立了同时考虑扭转振动和横向振动以及弯扭耦合效应的动力学模型和动力学方程，对比分析了三种模型下高速级和低速级齿轮的动载系数和振动强度，结果表明考虑了弯扭耦合效应的动力学模型能更全面地反映磨机减速机齿轮传动系统的动态特性，为进一步分析磨机减速机齿轮的失效打下理论基础。