齿轮系统倍周期分岔和混沌层次结构的研究

针对考虑间隙和时变啮合刚度的强非线性齿轮系统动力学模型,讨论了混乱带中倍周期分岔现象及混沌的层次结构问题。利用频谱分析法对周期运动和混沌运动进行判断,并对嵌于不同混乱带中的周期轨道进行区分。运用分频采样法求解强非线性齿轮系统主倍周期分岔序列与混沌带合并序列,以及混沌带中周期窗口和混沌窗口共存的层次结构问题。通过分析揭示了强非线性齿轮系统存在着复杂的分岔结构和普适规律,并为深入研究机械系统非线性动力学行为的性态提供参考。     

Global Dynamic Characteristic of Nonlinear Torsional Vibration System under Harmonically Excitation

Torsional vibration generally causes serious instability and damage problems in many rotating machinery parts. The global dynamic characteristic of nonlinear torsional vibration system with nonlinear rigidity and nonlinear friction force is investigated. On the basis of the generalized dissipation Lagrange's equation, the dynamics equation of nonlinear torsional vibration system is deduced. The bifurcation and chaotic motion in the system subjected to an external harmonic excitation is studied by theoretical analysis and numerical simulation. The stability of unperturbed system is analyzed by using the stability theory of equilibrium positions of Hamiltonian systems. The criterion of existence of chaos phenomena under a periodic perturbation is given by means of Melnikov's method. It is shown that the existence of homoclinic and heteroclinic orbits in the unperturbed system implies chaos arising from breaking of homoclinic or heteroclinic orbits under perturbation. The validity of the result is checked numerically. Periodic doubling bifurcation route to chaos, quasi-periodic route to chaos, intermittency route to chaos are found to occur due to the amplitude varying in some range. The evolution of system dynamic responses is demonstrated in detail by Poincare maps and bifurcation diagrams when the system undergoes a sequence of periodic doubling or quasi-periodic bifurcations to chaos. The conclusion can provide reference for deeply researching the dynamic behavior of mechanical drive systems.     

基于OGY方法的间隙非线性齿轮系统混沌控制

针对单级间隙非线性齿轮系统在部分参数区域发生的混沌运动,运用OGY(Ott-Grebogi-Yorke)控制原理以两种途径实现了混沌吸引子内部不稳定周期轨道的稳定化。考虑到经典OGY方法只适用于离散动力系统的局限性,根据系统运动方程及其变分形式,指出了将OGY控制算法直接应用于周期性连续时间系统的方法和步骤;对于系统方程未知的情形,根据系统轨线频闪数据时间序列,从中提取不稳定周期轨道及计算参数扰动所需的信息,实现了混沌控制。通过数值模拟比较了采用这两种途径的控制效果。     

质量慢变转子-滚动轴承系统的支承松动故障分析

根据转子动力学、非线性动力学及Hertz理论,建立了带有一端支座松动故障的滚动轴承—质量慢变转子系统的非线性动力学模型。通过数值积分和Poincare映射方法对其非线性动力学行为进行了数值仿真研究,给出了系统响应随转子转动频率变化的分岔图和一些典型的轴心轨迹图及Poincare截面图,分析了转动频率对转子系统动力学行为的影响。结论表明,转子系统在滚动轴承、支承松动和质量慢变的同时作用下具有复杂的动力学行为,转子系统的起始松动频率为0.6倍的固有频率,转子的周期运动均为多周期运动,转子圆盘和松动质量的运动特性均不稳定等。     

双杆摆机构中混沌现象的数值分析

采用数值分析方法对双杆摆机构的混沌运动现象进行了研究。通过时间历程图和相图法 ,Poincare截面法及最大 L yapunov指数分析法 ,分析出该动力系统由倍周期分岔进入混沌 ,并由此获得了产生混沌运动的一个参数条件 ,对该机构混沌的预测和控制具有指导意义。     

基于Taylor变换法的转子系统分岔与稳定性研究

对双盘转子系统的非线性动力学模型，引入求解非线性微分方程的Taylor变换法，分析转子振动系统动力学特性以及激振频率等参数对系统的影响，利用非线性动力学分析中的打靶法求该系统的周期解，并利用Floquet主导特征乘子判断不同周期轨道的失稳方式。结果表明，考虑非线性油膜力影响后，转子系统的运动状态随转速增加由周期至二倍周期再至周期再至拟周期，或者经周期运动直接至混沌运动．不平衡质量影响转子系统的分岔阈值和分岔类型，阻尼对分岔阈值和系统的运动稳定性有一定的影响。     

Stability of Low-Friction Surface Sliding of Nanocrystals with Rectangular Symmetry and Application to W on NaF(001)

We investigate the stability of low-friction sliding of nanocrystal with rectangular atomic arrangement on rectangular lattices, for which analytical results can be obtained. We find that several incommensurate periodic orbits exist and are stable against thermal fluctuations and other perturbations. As incommensurate orientations lead to low corrugation, and therefore low friction, such incommensurate periodic orbits are interesting for the study of nanotribology. The analytical results compare very well with simulations of W nanocrystals on NaF(001). The geometry and high typical corrugation of substrates with square lattices increase the robustness when compared to typical hexagonal lattices, such as graphite.     

Second Order,Elastico-Viscous Lubricants in Dynamically Loaded Bearings

The hydrodynamic theory of lubrication for dynamically loaded journal bearings is extended to elastico-viscous lubricants. The Rivlin-Ericksen equation is assumed for the lubricant, with the second-order terms representing cross-stresses and stress relaxation.

The orbits of the journal center deviating from its static equilibrium position were calculated for constant and periodic load conditions.

A considerable improvement, compared with the Newtonian solution, is obtained. This is evident from the diminished eccentricity of the orbits and the faster damping of disturbances.     

同源信息融合的空间领域诊断分析与应用

通过分析一个截面上两通道信息融合后所得椭圆的大小、方向及相位角,对转子两个截面四通道的同源数据进行融合,得出两个截面上各自的中心轨迹,而且此轨迹图形的中心位移的复数向量并不都是具有相同的幅角,但这两空间曲线旋转一周的时间是相同的.由此得出转子轴线空间振动图形.     

吴消元法在转子动力学研究中的应用

以转子一轴承系统中短轴承的转子涡动，具有非线性支撑的柔性Jeffcott转子模型的周期响应为研究对象，对吴消元法在转子动力学研究中的应用作了初步探索。将吴消元法的特征列思想和Maple软件的符号计算机功能相结合，实现了对短轴承涡动参数的解析计算及对柔性Jeffcott转子模型周期响应的解析分析，在此基础上对Jeffcott转子的动态特性作了进一步的分析。     

Static and dynamic pull-in instability of multi-walled carbon nanotube probes by He’s iteration perturbation method

A continuum model is utilized to extract the nonlinear governing equation for Carbon nanotube (CNT) probes near graphite sheets. The van der Waals (vdW) intermolecular force and electrostatic actuation are included in the equation of motion. Static and dynamic pull-in behavior of the system is investigated in this paper. To this end, a new asymptotic procedure is presented to predict the pull-in instability of electrically actuated CNTs by employing an analytic approach namely He’s iteration perturbation method (IPM). The effects of basic non-dimensional parameters such as initial amplitude, intermolecular force, geometrical parameter and actuation voltage on the pull-in instability as well as the fundamental frequency are studied. The obtained results from numerical simulations by employing three mode assumptions verify the strength of the analytical procedure. The qualitative analysis of the system dynamics shows that the equilibrium points of the autonomous system include stable center points and unstable saddle nodes. The phase portraits of the carbon nanotube actuator exhibit periodic and homoclinic orbits.     

含时变啮合刚度的间隙非线性齿轮系统的混沌控制

基于含时变啮合刚度和间隙非线性单级齿轮系统的动力学模型,分析了系统响应的动态特性。针对系统在部分参数区域发生的混沌运动,运用OGY控制原理,以混沌吸引子内部不稳定周期轨道为目标,通过对系统的外激励参数实施连续的小扰动,使系统的轨道始终落在未加扰动的鞍点轨道的稳定流形上,从而实现了系统运动的稳定化。     

带闭链六自由度工业机器人动力学解析模型

提出了一种建立带闭链工业机器人动力学解析模型的方法。将闭链的某一非主动关节的运动副拆开，其运动关系用约束方程来代替，从而形成带有附加约束的等效开链系统，然后基于Kane动力学方程，导出了显式形式的动力学方程。推导解析模型时将部分变量处理为符号量，其余变量处理为数字量，获得了动力学各模型矩阵元素的数字一符号表达式，并给出一计算实例。     

Microtopographic analysis of turned surfaces by model-based scatterometry

Turned surface profiles can be divided into a periodic and a random component. The periodic component is a function of the tool shape and the feed rate. The random component is caused by machine vibrations. To monitor the turning process, the periodic component is the essential global microtopographic feature which reacts sensitively to tool wear and tool scars. A measuring method evaluating the periodic component of turned surfaces is developed based upon the model-based scatterometry. Using an optimized scattering geometry, the model-based scatterometry leads to an intensified mapping of the microtopographic surface features in the angular distribution of scattered light. The profile parameters measured with the introduced scattering technique agree well with the values obtained by stylus measurements. Hence, in the range of precision engineering (R_a≤1.5 μm) the mean profile of the dominant periodic component can be measured optically without scanning and without resorting to comparator standards.     

单级齿轮系统拍击特性研究

用数值仿真法和映射法研究了齿轮系统的拍击振动特性。通过研究每一次碰撞之间的映射关系、每一拍击周期之间的映射关系,得出的结论是:激励幅值的大小是影响系统拍击性能的一个重要因素;当激励幅值增大时,齿轮碰撞速度也增大,在一定条件下,将发生齿背碰撞;当激励幅值变化时,齿轮系统的初始脱齿状态也将发生变化,由此导致系统产生1周期、2周期、多周期甚至准周期拍击振动;转速波动的二次谐波分量对系统拍击性能的影响与基频分量的影响基本相同,因此,忽略二次谐波将导致较大的误差。用周期性拍击过程之间的映射关系研究齿轮系统的拍击特性,会带来很大的方便。     

动态油膜―柔性转子系统混沌运动的控制

借助最优控制混沌动力特性的方法,仅通过最优过程中的可调小参数的瞬态干扰反馈。将非稳态非线性油膜力作用下的不平衡转子系统出现的混沌运动,引导到嵌入在混沌吸引子内无数不稳定周期轨中预期的一个轨,并使之稳定。数值结果表明动态油膜—转子系统中的混沌运动也是可以有效控制的。     

斜齿轮柔性转子轴承系统非线性动力学分析

考虑齿侧间隙、轴承径向间隙、齿轮不平衡力,使用有限元法建立质量矩阵、刚度矩阵、阻尼矩阵并组装成整体参数矩阵,建立了适用于斜齿轮柔性转子滚动轴承系统的非线性动力学模型。采用Runge-Kutta法求解,并分析系统的动力学行为。研究了转速、转轴刚度、不平衡力对斜齿轮系统非线性动力学行为的影响规律。结果表明：随着转速的变化,系统将经历周期、拟周期、混沌等多种运动状态;随着转轴刚度的减小,混沌运动的区间减小,振幅大小发生改变;不平衡力增大后,系统混沌区间增大,混沌运动的区间也发生改变。     

松动-裂纹耦合故障转子系统的非线性动力学行为研究

以现代非线性动力学和转子动力学理论为基础。分析了带有一端轴承支座松动和裂纹耦合故障的弹性转子系统的复杂非线性现象。针对非线性转子一轴承系统的具体特点，采用短轴承油膜力模型。应用Runge—Kutta法数值模拟得到的系统在某些参数域中的分岔图、Poincare映射和频谱图等反映了系统的运动状态，并分析了该耦合转子系统的故障特征，研究结果对该类转子-轴承系统的故障诊断和预防提供一定的参考。     

The continuous Poincare-like cell mapping method and its application to nonlinear dynamics analysis of a bearing–rotor system

Based on the idea of continuous cell mapping, an improved Poincare-like cell mapping method is developed. This method can be used for global analysis of nonlinear dynamic systems without missing the periodic solutions and the domains of attraction. A bearing–rotor system is analyzed by using this method, and the influences of initial conditions on transient movement are discussed in detail.     

基于连接组合体方法的关节机器人动力学参数辨识

为获得不受负载影响的机器人动力学参数的独立值,采用连接组合体方法辨识机器人动力学参数,即辨识时按照一定的方式及次序锁定其他关节,每次仅让某几个关节运动,从而辨识出全部参数的独立值。编写了机器人动力学参数辨识程序,对某确定工业机器人进行了动力学参数辨识计算。结果表明：该方法能够获得独立的机器人动力学参数;绝大多数参数能够获得理想的辨识精度;受噪声影响,部分参数辨识结果与理想值差距较大,原因在于这些参数对力矩的贡献很小,在噪声存在的情况下,其信息被淹没;基于辨识结果的力矩计算结果与机器人控制理想力矩具有很高的吻合度,验证了该方法的正确性。