弹性机构动力平衡的有效新方法

从改善弹性机构动力特性的角度研究了机构弹性动力平衡的本质问题。提出了附加弹性元件的新方法，有效地解决了弹性机构震动力、震动力矩、输入扭矩波动和运动副反力的平衡难题。首次推导出具有弹性元件的弹性连杆机构动力学方程，从理论上阐述了此平衡方法的有效性。仅用附加一根扭簧的简单方法实现了平面四杆机构的弹性动力平衡，效果明显。     

The effect of speed of balanced rotor on nonlinear vibrations associated with ball bearings

The paper deals with the structural dynamic response of rotor supported by ball bearings. The mathematical model takes into account the sources of nonlinearity such as Hertzian contact force, surface waviness, varying compliance and internal radial clearance resulting transition from no contact to contact state between rolling elements and races. In terms of the feature that the nonlinear bearing forces act on the system, a new reduction method and corresponding integration technique is used to increase the numerical stability and decrease computer time for system analysis. The effects of speed of balanced rotor in which ball bearings show periodic, quasi-periodic and chaotic behavior are analyzed. The results are presented in the form of time displacement responses, frequency spectra and Poincarè maps. It is implied from the frequency spectra that peak amplitude of vibrations appear at the varying compliance frequency.     

轴承间隙及柔性特征对机构动态误差的影响分析

为能够准确、有效地揭示轴承间隙与柔性特征对机构动态误差的影响规律,基于多体动力学理论与Hertz接触理论,提出一种计及轴承间隙与柔性特征影响的多体系统建模方法。该方法采用力约束替代运动约束,构建多体系统环境下的轴承精细化模型。基于该方法,可深入揭示轴承微观动力特性与多体系统宏观动态性能及运动精度之间的映射关系。在此基础上,以含深沟球轴承的曲柄滑块机构为仿真算例,分析轴承间隙与柔性特征对该机构运动位置与速度误差的影响规律。研究表明,轴承内外圈中心形成的相对偏心轨迹的变化特征是由多体系统动态环境下的轴承受载特性决定的;在轴承偏心影响下的机构运动位置与速度误差大小会随曲柄转角位置不同而变化。     

A novel nonlinear model of rotor/bearing/seal system and numerical analysis

A novel nonlinear model of rotor/bearing/seal system based on the Hamilton principle is proposed for steam turbine systems in power plants. The Musznyska model and unsteady bearing oil-film force model were applied to describe the nonlinear steam excitation force and oil-film force. The Runge-Kutta method was used to solve the motion equation of the rotor/seal/bearing system. The dynamic characteristics of the rotor/bearing/seal system were analyzed with bifurcation diagrams, time-history diagrams, trajectory diagrams, Poincare maps and frequency spectrums. The numerical analysis indicates that the seal force and the oil-film force influence the nonlinear dynamic characteristics of the rotor system. With the increase of rotation speed, the rotor system exhibits rich forms of periodic, double-periodic, multi-periodic, quasi-periodic and chaotic motion. The combined impact of steam excitation force and bearing oil-film force may cause a severe vibration which seriously affects the safety and stability of the rotor. The presented model provides a theoretic foundation for further research on the ultra-supercritical steam turbines.     

含柔性转子的齿轮-轴承系统动态特性分析

为了分析齿轮系统动力学中的全耦合振动,提出采用虚拟样机建模的方法,将柔性转子引入到啮合耦合系统中,考虑齿轮时变啮合刚度、齿侧间隙和轴承间隙的影响,建立齿轮-柔性转子-轴承系统虚拟样机模型,通过求解模型的动力学方程得到系统的非线性动力学响应。仿真结果表明:考虑柔性转子的耦合系统,啮合冲击峰值下降明显;转子柔性增加,齿轮低频扭转振动出现"拍"现象;高速轻载时啮合振动非线性特性增强;轴承间隙增大使啮合力振动幅值显著增大。     

Effect of rotational speed fluctuations on the dynamic behaviour of rolling element bearings with radial clearances

The behaviour of rolling element bearings is of major importance to the vast majority of rotating machines. Due to the varying assembly compliance and the internal clearance existing in the bearing in most cases, a highly non-linear behaviour of the rotor bearing system appears. Thus, a dynamic model of a horizontal rotor supported on ball bearings with radial internal clearance is considered, taking into account contact forces between the balls and the races, as well as the effect of varying compliance and of the internal radial clearance. However, since rotational speed fluctuations of various levels practically appear in all rotating equipment, their effect is now additionally considered. Their effect is examined in two characteristic rotor bearing cases. The analysis includes all the characteristic states of the dynamic behaviour of the rotor, such as periodic, unstable periodic and chaotic responses, using methods like frequency spectra, phase spaces, higher-order Poincare maps and Lyapunov exponents. All results presented show a dominant stabilization effect of the speed fluctuations with respect to the system behaviour. From the analysis performed, it is concluded that even a minimum fluctuation of the rotor speed may result in major changes of the system dynamics, indicating that speed fluctuations of the rotor are a governing parameter for the dynamic behaviour of the system.     

Effects of restitution coefficient and material characteristics on dynamic response of planar multi-body systems with revolute clearance joint

To study the effects of restitution coefficient and material parameters on the dynamic characteristics of planar multi-body systems with revolute clearance joints, a comprehensive methodology for clearance revolute joints in a planar multibody system is presented and analyzed. A new nonlinear contact force model, which accounts for the axial length of bearing and has a wide suitable range of impact situation, is presented to evaluate the contact force between journal and bearing. Furthermore, a modified Coulomb friction force model also presented to consider the effect of friction in clearance joint. Then, a typical journal-bearing model and a planar slider-crank mechanism has revolute clearance joint are used as examples. From the main numerical results under the different restitution coefficient and material parameters, it can be concluded that coefficient of restitution has significant effects on dynamic response of multi-body systems with revolute clearance joint. Additionally, materials of journal and bearing with smaller Young’s modulus will cause obvious delay on dynamic response of multi-body systems.     

含Alford力的非线性转子-滚动轴承系统动力分析

将非线性滚动轴承力模型与Alford力模型相结合,建立了转子系统的动力学模型,并研究了Alford力和非线性滚动轴承力共同作用下转子系统的非线性动力学特性。其中,将滚动轴承的实际接触角考虑进滚动轴承的模型中,并将改进后的滚动轴承模型与已有的结论作比较,达到了较好的一致性,说明用该模型来分析转子系统的动特性是可行的。继而针对角速度等因素对耦合系统动态响应的影响进行了仿真计算,给出了系统响应随转子角速度变化、滚动轴承间隙变化和转子偏心变化的分岔图,以及一些典型的Poincare截面映射图和功率谱图。数值仿真表明,在Alford力与滚动轴承力的共同作用下,系统呈现了复杂的动力学行为,产生了周期、拟周期和混沌等丰富的振动现象。     

Effect of Bearing Surroundings on the High-Speed Spindle-Bearing Compliance

This paper investigates the effect of bearing assembly tolerance on spindle-bearing compliance. In a high-speed spindle system, the bearing characteristics are influenced significantly by the initial assembly tolerances and the thermal deformation of the bearing surroundings. In the very early stage of spindle operation, spindle bearings could be under hazardous conditions owing to the rapid change of the internal pressure resulting from thermal deformation or centrifugal force-oriented deformation. The bearing’s internal clearance also may be changed by the operating conditions such as external load, rotational speed, and operating cycle time. To determine the initial tolerance and the optimal cooling regimen, a comprehensive dynamic modelling and analysis of a high-speed spindle system in terms of bearing pressure, bearing compliance, and heat generation is required with consideration of those effects. Moreover, in order to predict spindle characteristics in operation, all of these parameters should be monitored and recalculated in real-time. For this purpose, very simple and effective equations are suggested, representing the bearing stiffness in accordance with the thermal deformation. Most former bearing analyses were based on the Hertzian contact model, without considering the radial elastic defor-mation of the races. In this paper, analytical and experimental investigations of the bearing compliance are conducted with consideration of both the elastic deformation of the race and the thermal deformation of the housing in terms of the bearing stiffness. The experimental results show the effectiveness of the proposed equations, which are simple and useful for fast calculation of the bearing stiffness by dynamic simulation.     

滚动轴承支承下的不平衡转子系统非线性动力响应分析

建立了滚动轴承支承下的转子系统非线性动力学模型。在滚动轴承模型中,充分考虑了滚动轴承的间隙、滚动轴承的滚珠与滚道的非线性赫兹接触力及由滚动轴承支撑刚度变化而产生的VC（varying compliance）振动,在转子系统中考虑了由于转子质量偏心而产生的不平衡力。运用数值积分方法获取了系统的非线性动力响应,分析了转子旋转速度、滚动轴承间隙对系统动力响应的影响,并运用分叉图、相平面图、频谱图及Poincaré映射进行了系统分叉与混沌特征分析,发现了通往混沌的倍周期分叉、拟周期环面破裂和阵发性分叉途径。     

考虑接触特性的滚动轴承系统建模与仿真分析

根据Hertz接触理论和滚动轴承功能原理,以SKF6208深沟球轴承为参考,在ADAMS/View软件环境下设计建立了基于Impact函数的滚动轴承多体动力学仿真模型。通过实体接触条件下的轴承运转过程动态仿真分析,计算获得了滚珠与内圈、外圈及保持架之间的接触力动态分布规律。指出:轴承系统在启动瞬间(0~0.22 s)存在一定滑动,且接触力变化频率较大;进入滚动阶段(0.22~0.4 s)后,接触力变化频率减小,且呈周期性分布。仿真结果验证了滚动轴承的启动打滑现象,符合实际运行工况。为深入研究滚动轴承系统的接触机理及动态载荷提供了技术参考。     

Stiffness and damping coefficients for journal bearing using the 3D transient flow calculation

The dynamic coefficients of journal bearing are necessary components in the analysis of linear stability and response of rotating dynamic systems. We propose a new method for the numerical identification of bearing support force coefficients in flexible rotor-bearing systems based on the 3D transient flow calculation. The CFD commercial software FLUENT is mainly used in this simulation, which employs a finite volume method for the discretization of the Navier-Stokes equations. To determine the dynamic coefficients, a new mesh movement approach is presented to update the volume mesh when the journal moves during the 3D transient flow calculation of a journal bearing. Existing dynamic mesh models provided by FLUENT are not suitable for the transient oil flow in journal bearings. Measurements and identification are performed on a test rotor supported on a pair of identical two-lobe fluid film bearings, and the results obtained from the CFD methods agree well with experimental results. The results indicate that the methods proposed in this paper can predict the dynamic coefficients of the journal bearing in a rotor-bearing system effectively, and provide a further tool for stability analysis.     

松动对碰摩转子-轴承系统非线性特性的影响研究

在同时考虑轴承油膜力和碰摩发生时转子与定子之间的相对滑动速度对非线性摩擦力的影响基础上,构造了含有松动和碰摩故障转子系统的动力学模型,对转子 轴承系统由松动和碰摩耦合故障导致的非线性动力学行为进行了数值仿真研究,发现该类系统在运行过程中存在周期运动、拟周期运动和混沌运动等丰富的非线性现象,研究结果为转子 轴承系统故障诊断、动态设计和安全运行提供了理论参考。     

Dynamic analysis of planar mechanical systems with clearance joints using a new nonlinear contact force model

We investigated the dynamic behavior of planar mechanical systems with clearance joints. First, the contact effect in clearance joint was studied using a new nonlinear contact force model, and the rationality of this model was verified by the results of numerical simulations, which are based on a journal and bearing contact model. Then, the dynamic characteristics of a planar slider-crank mechanism with clearance were analyzed based on the new nonlinear contact force model, and the friction effect of clearance joint was also considered using modified Coulomb friction model. Finally, the numerical results of the influence of clearance size on the acceleration of slider are presented, and compared with the published experimental results. The numerical and experimental results show that the new nonlinear contact force model presented in this paper is an effective method to predict the dynamic behavior of planar mechanical system with clearance joints, and appears to be suitable for a wide range of impact situations, especially with low coefficient of restitution.     

带有支座松动故障的离心泵叶轮转子分岔特性分析

将离心泵叶轮转子系统简化为中间带有刚性圆盘的柔性转子,在引入非线性横向流体激振力的条件下,建立带有支座松动故障的不平衡离心叶轮转子在非线性轴承油膜力作用下的振动模型,并推导系统的无量纲运动方程.运用数值积分法研究系统的分岔特性,分析横向流体激振力以及松动端轴承支座质量对该类离心泵叶轮转子系统非线性动力学特性的影响.     

椭圆轴承-转子系统失稳运动数值分析

滑动轴承油膜力是一种强非线性作用力,滑动轴承转子系统是一种典型的非线性动力系统,传统的线性方法无法计算系统失稳后的运动。文中给出用数值积分瞬态模拟对轴承－转子系统非线性振动进行计算分析的方法,并以椭圆滑动轴承－刚性转子系统为例,对系统失稳后的运动状态进行了计算和分析。     

机器人柔顺力控装置研究

机器人自动化抛光过程中,工具与工件间的接触力控制尤为重要.基于主动柔顺控制的原理,提出了面向工业机器人的柔顺力控装置及控制方法.进行了系统的结构设计和动力学建模,基于BP神经网络PID算法,设计了该柔顺力控装置的自适应控制策略.最后进行力控跟踪实验,实验结果表明,柔顺力控装置能够保证打磨过程中工件与工具之间的接触力恒定...     

Non-linear dynamics of a rigid,unloaded andunbalanced rotor on lubricated bearings

The dynamic behaviour and stability analysis of an unloaded rotoron cylindrical lubricated bearings subjected only to the actionof unbalance is presented. The ``short bearing model' has beenadopted to evaluate the hydrodynamic fluid film force. As theunbalance increases, the system shows the typical behaviour ofnon-linear mechanical systems as the non-linearity of the hydrodynamic force field becomes more important. Evaluating theapproximate circular and centred analytical expressions of thetrajectory, the frequency response curves of the amplitude ofthe synchronous orbit have been reported. The stability limitcurve of the synchronous response has been obtained by means ofthe Floquet theory. Several examples of journal trajectories,obtained through step-by-step integration of the motionequations, are reported to illustrate the dynamic behaviour ofthe system and to verify the validity of the stability limitcurve.