A Model Reduction Procedure for the Dynamic Analysis of Rail Vehicles Subjected to Linear Creep Forces

The set of differential equations governing the motion of an unrestrained coned wheelset travelling on a tangent section of track and acted upon by creep forces arising from the contact between wheel and rail are, in the terminology of numerical analysis, extremely "stiff". This stiffness can be attributed to the existence of two negative real eigenvalues in the solution of the eigenproblem associated with the linearized equations of motion. Compared with the two complex conjugate eigenvalues that complete this solution, the real eigenvalues have large magnitudes and necessitate that relatively. small timesteps be used in order to obtain an accurate numerical integration of the full set of equations of motion. However, by truncating the set of left and right eigenvectors to eliminate these real eigenvalues in a modal analysis of the wheelset, it was found that their contribution to the overall dynamic response is negligible. This same modal truncation approach was then applied to the sub-structured equations of motion for a simple rail vehicle system consisting of two wheelsets connected to a main body by linear springs and dampers. Essentially, the physical degrees of freedom for each wheelset substructure were replaced by a single complex coordinate obtained from the previous normal modes analysis. Using this model reduction procedure, accurate numerical results for the motion of the rail vehicle were generated several times faster than the results obtained by numerically integrating the full set of differential equations directly.     

斜拉桥拉索磁流变阻尼器减振技术研究

采用数值仿真和现场试验对磁流变阻尼器的减振性能进行了研究。数值仿真计算评估了磁流变阻尼器安装高度、外部激励、阻尼器输入电压等参数对拉索系统模态阻尼比的影响 ,结果表明磁流变阻尼器具有良好的阻尼可调特性 ,调节阻尼器的输入电压可以获得拉索系统的最佳模态阻尼比 ;现场试验表明 ,安装该阻尼器后 ,拉索系统的模态阻尼比提高 3～ 6倍 ,并存在一优化电压 ,在该电压下模态阻尼比达到最大 ;实际风雨振时的现场观测结果显示 ,磁流变阻尼器具有很好的减振效果 ;拉索磁流变阻尼器减振技术已在岳阳洞庭湖大桥全桥实施 ,解决了该桥的风雨振问题     

MR阻尼器对斜拉索减振控制的数值仿真

为控制斜拉索的大幅振动,在Hamilton原理基础上应用Galerkin法建立了斜拉索振动控制的计算模型。通过改进形函数,采用四阶五级RK算法对钱江三桥南岸154 m长的斜拉索进行了现场试验的数值仿真。磁流变(MR)阻尼器力学关系采用由室内试验结果回归的非线性滞回双粘性数学模型,系统等效阻尼比通过希尔伯特变换识别。分析表明:数值仿真对现场试验具有很好的指导作用,同时能进一步验证现场试验的结果。MR阻尼器作为被动控制器件时制振效果明显,与最优油阻尼器控制效果相当且控制的频域范围要比油阻尼器的广;当供电失效时也可满足斜拉索减振的要求。斜拉索的各阶共振峰频率在安装MR阻尼器后略微增大。MR阻尼器在施加一合适的电压时可以发挥最佳的制振效果。     

Determining damping characteristics of railway-overhead-wire system for finite-element analysis

In order to investigate the damping characteristics of railway-overhead-wire systems, we propose herein an approach based on the continuous wavelet transform (CWT) and two existing formulas concerning Rayleigh damping coefficients (RDCs). In the proposed process, the displacement histories of a real catenary are first obtained by using a set of noncontact photogrammetric devices, following which an exclusive catenary damping ratio related to the first dominant modal component in the catenary response is identified through a complex Morlet CWT. Thereafter, iterative finite-element analysis is conducted to find the optimal RDCs, which involves using two related formulas and the similarity between the catenary displacements obtained by simulation and experimentation. The results of our study demonstrate that this combined approach is constructive, especially for structures with closely spaced modes, such as catenaries. For the case studied herein, the catenary modal damping ratio at 1.19?Hz is approximately 1%, and the mass and stiffness proportional Rayleigh damping coefficients are approximately 0.02845 and 0.00274, respectively.     

永磁电涡流阻尼新技术及其在土木工程中的应用

针对永磁电涡流阻尼减振的理论与技术进展进行了综述，主要包括：永磁电涡流调谐质量减振器、大吨位的滚珠丝杠式轴向电涡流阻尼器等新型减振装置；板式电涡流阻尼及滚珠丝杠式电涡流阻尼器的性能仿真与设计方法；桥梁涡激共振、斜拉索振动控制的电涡流阻尼三元减振理论；以及基于电涡流阻尼力非线性特性的减震性能研究。介绍了湖南大学新建的大型阻尼器特性综合试验平台及主要功能，以及永磁电涡流阻尼技术的典型工程应用。最后指出了值得进一步研究的若干问题。     

Active Damping in Road Vehicle Suspension Systems

Low order, linearized dynamic models of road vehicle suspension systems are analyzed to provide insight into the benefits of suspensions incorporating generalized velocity feedback compared with conventional passive suspensions. Damping forces from passive dampers are supplemented by forces generated by an active element requiring a power supply. A simple criterion is developed which indicates whether or not the introduction of activedamping forces will result in significant benefit for pneumatic tired vehicles.

An extended active suspension concept involving a high-gain load leveler as well as active damping is analyzed. The realization of active or semi-active damping forces through electrical or hydraulic means is briefly discussed.     

Experimental Verification of Resistance Control, Semi-Active Damping

Electronically controlled vehicle suspensions offer substantial improvements in performance over conventional, passive suspensions but with the price of power, complexity, and actuating bandwidth. Low-bandwidth, semi-active damping addresses the problems of power and bandwidth by using low power modulation of controllable dampers at the frequency of the isolated mass. Resistance controlled, semi-active damping is experimentally verified to better sprung mass isolation while reducing suspension stroke, something that a passive system cannot do. It is also shown to compare reasonably well with computer simulation results. The experimental implementation is a 1/30 scale, two degree-of-freedom test bed that represents the standard quarter vehicle model.     

Identification of the technical state of suspension elements in railway systems

The running safety and passenger comfort levels in a vehicle are tightly related to the technical state of the suspension elements. The technical state of the suspension depends of the service life time as its components become old and wear out. In this paper, a study on the dynamic behaviour of a railway vehicle is established in relation to the damping elements in one of its suspension stages. An experimental measurement model is developed, obtaining a set of useful signals for the identification of the dynamic parameters of the vehicle and developing a test through the application of the operational modal analysis technique, using least-squares complex exponential method as a basis to validate the numerical model of the multi-body system. Then, the study focuses on developing numerical simulations for the identification of the technical state of the dampers by the registration of dynamic variables under commercial service conditions and on estimating the state of the suspension elements.     

基于工作模态法的动力总成刚体参数识别

介绍一种基于多参考点最小二乘频域法(一种工作模态法)的刚体参数识别方法。它适用于具有阻尼和非线性刚度支承的系统(如汽车动力总成),可在实车工作情况下对动力总成的模态参数和惯性参数进行识别。通过实验验证了该方法的有效性。     

A semi-active control suspension system for railway vehicles with magnetorheological fluid dampers

The high-speed train has achieved great progress in the last decades. It is one of the most important modes of transportation between cities. With the rapid development of the high-speed train, its safety issue is paid much more attention than ever before. To improve the stability of the vehicle with high speed, extra dampers (i.e. anti-hunting damper) are used in the traditional bogies with passive suspension system. However, the curving performance of the vehicle is undermined due to the extra lateral force generated by the dampers. The active suspension systems proposed in the last decades attempt to solve the vehicle steering issue. However, the active suspension systems need extra actuators driven by electrical power or hydraulic power. There are some implementation and even safety issues which are not easy to be overcome. In this paper, an innovative semi-active controlled lateral suspension system for railway vehicles is proposed. Four magnetorheological fluid dampers are fixed to the primary suspension system of each bogie. They are controlled by online controllers for enhancing the running stability on the straight track line on the one hand and further improving the curving performance by controlling the damper force on the other hand. Two control strategies are proposed in the light of the pure rolling concept. The effectiveness of the proposed strategies is demonstrated by SIMPACK and Matlab co-simulation for a full railway vehicle with two conventional bogies.     

盘式制动器制动尖叫的有限元分析与试验

建立了产生制动尖叫的钳盘式制动器各主要零件的有限元模型,并通过集成构建了制动器总成的接触摩擦耦合有限元模型,计算了制动器振动系统的复特征值分布和模态,分析了可能产生制动尖叫的不稳定模态,并与制动噪声台架试验统计结果进行了对比,结果表明所建模型能够较好地预测出制动器发生制动尖叫的倾向;分析了各零件的振动模态对产生制动尖叫不稳定模态的贡献大小,揭示出有尖叫倾向的不稳定模态是由子结构未耦合时的多阶振动模态叠加而成;分析讨论了摩擦因数、摩擦片结构及其背板阻尼对制动尖叫的影响,为控制制动尖叫提供了途径。     

重型商用车驾驶室白车身的模态分析与实验研究

建立了某国产重型商用车驾驶室白车身的有限元模型并进行计算模态分析.同时采用多输入多输出方法对实际白车身结构进行模态实验并经处理得到实验模态.应用模念相关分析理论计算了计算模态与实验模态之间的振型相关度.结果表明:二者具有很高的相关性,有限元模态分析能够足够精确地确定实际结构的整体动力学特性.     

Effect of System Nonlinearities on Locomotive Bogie Hunting Stability

This paper presents the effect of system parameters on hunting of a rail vehicle with nonlinear yaw dampers and wheel-rail interface. This study is intended to complement earlier studies by True et al. where they investigated the effect of nonlinearities stemming from creep-creep force saturation and wheel/rail contact forces. The rail vehicle is represented by a two-axle truck (bogie) that includes the dynamics of the wheelsets and the truck frame. The numerical simulation results show that yaw damping can have a mixed effect on the hunting critical speed. In some ranges, increasing damping can actually lower the critical speed, unlike the results commonly obtained from a linear model. Flange contact nonlinearities can also have a significant effect on the hunting behavior. Large lateral stiffness of the rail can increase lateral force to vertical force (L/V) ratio during hunting. Increasing the gauge clearance, however, can have an opposite effect. The effect of a variety of other parameters, such as the primary suspension yaw and lateral stiffness, primary suspension lateral damping, wheelset mass, and truck frame mass, are summarized in a table.     

Modelling and validation of electromechanical shock absorbers

Electromechanical vehicle suspension systems represent a promising substitute to conventional hydraulic solutions. However, the design of electromechanical devices that are able to supply high damping forces without exceeding geometric dimension and mass constraints is a difficult task. All these challenges meet in off-road vehicle suspension systems, where the power density of the dampers is a crucial parameter. In this context, the present paper outlines a particular shock absorber configuration where a suitable electric machine and a transmission mechanism are utilised to meet off-road vehicle requirements. A dynamic model is used to represent the device. Subsequently, experimental tests are performed on an actual prototype to verify the functionality of the damper and validate the proposed model.     

An investigation into the effect of suspension configurations on the performance of tracked vehicles traversing bump terrains

This is a theoretical investigation into the effect of various suspension configurations on a tracked vehicle performance over bump terrains. The model developed is validated using published experimental data of the modal characteristics of the vehicle. The desired performance is based on ride comfort via the mixed objective function (MOF), which combines the crest factor of bounce acceleration, bounce displacement, angular acceleration, and pitch angle. The optimisation process involves evaluating the MOF for different numbers and locations of dampers and under different rigid bump road conditions and speeds. The system responses of the selected suspension configurations in the time and frequency domains are compared against the undamped suspension. The results show that the suspension configurations have a significant effect on the vehicle mobility over bump road profiles. For a five-road–wheel half model of a tracked vehicle, the maximum number of dampers to use for ride comfort over these road bumps is three with the dampers located at wheel positions 1, 2 and 5. This confirms the current practice for many tracked vehicles with 10 road wheels. However, it is further shown that the suspension fitted with two dampers at the extreme road wheels offer the best performance over various rigid bump terrains.     

Active Suspension Control to Improve Vehicle Ride and Handling

In practice most active vehicle suspension work can be traced to two sources, Lotus' modal control and Karnopp's skyhook damper. A model is developed which allows comparison of different active suspension control algorithms. The Lotus modal control algorithm is reviewed, and compared with Karnopp's skyhook damper. It is shown that a tight inner closed loop allows the Lotus algorithm to achieve the inertial damping described by Kamopp for a single comer or quarter car. It is suggested that to achieve simultaneously high inertial damping and good disturbance rejection an inner force loop is desirable. A vehicle control scheme is presented which combines the Lotus modal decomposition with Karnopp's skyhook damper, allowing nearly optimal ride and simultaneously permitting modification of vehicle handling properties.     

Finite-element model calibration of a railway vehicle based on experimental modal parameters

This article describes the experimental calibration of a three-dimensional numerical model of an Alfa Pendular train vehicle based on modal parameters. The dynamic tests of the carbody and bogie of the vehicle allowed the determination of the frequencies and modal configurations of 13 vibration modes, by applying the data-driven stochastic subspace identification method. In addition, a dynamic characterisation test of the passenger-seat system was also conducted. The calibration of the model was performed using a submodelling/multistep approach involving two phases, the first one focused on the calibration of the model of the bogie under test conditions and the second one focused on the calibration of the complete model of the vehicle. The calibration was performed through an iterative method based on a genetic algorithm and allowed to obtain optimal values of 17 parameters of the numerical model. For the pairing of the vibration modes, real and complex, a recent technique was used based on the calculation of the modal strain energy. The stability of a significant number of parameters considering different initial populations demonstrated the robustness of the algorithm. The comparison of experimental and numerical responses before and after calibration revealed significant improvements in the numerical model and a very good correlation between the responses obtained with the calibrated model and the experimental responses.     

Semi-active suspension systems for railway vehicles using magnetorheological dampers. Part II: simulation and analysis

In this paper, the semi-active suspension system for railway vehicles based on the controlled (MR) fluid dampers is investigated, and compared with the passive on and passive off suspension systems. The lateral, yaw, and roll accelerations of the car body, trucks, and wheelsets of a full-scale railway vehicle integrated with four MR dampers in the secondary suspension systems, which are in the closed and open loops respectively, are simulated under the random and periodical track irregularities using the established governing equations of the railway vehicle and the modelled track irregularities in Part I of this paper. The simulation results indicate that (1) the semi-active controlled MR damper-based suspension system for railway vehicles is effective and beneficial as compared with the passive on and passive off modes, and (2) while the car body accelerations of the railway vehicle integrated with semi-active controlled MR dampers can be significantly reduced relative to the passive on and passive off ones, the accelerations of the trucks and wheelsets could be increased to some extent. However, the increase in the accelerations of the trucks and wheelsets is insignificant.     

黏滞惯性质量阻尼器对斜拉索减振效果的数值分析

随着斜拉桥跨度的增大,斜拉索长度也越长,会同时存在发生风雨激振和涡激共振的可能性。风雨激振参与模态主要为低阶,涡激共振参与模态为高阶,这给斜拉索减振阻尼器的设计带来了新的挑战。采用数值方法,研究了黏滞惯性质量阻尼器（Viscous Inertial Mass Damper,VIMD）的斜拉索减振效果。首先,将斜拉索简化为张紧弦,建立了斜拉索-VIMD系统的运动微分方程,采用有限差分方法对方程进行数值求解。然后,以苏通大桥A30号斜拉索为工程背景,研究了各参数对该系统模态阻尼比的影响。最后,研究了阻尼器支架刚度对斜拉索-VIMD系统减振效果的影响,并将数值解与近似解析解进行对比。研究结果表明：在传统的黏滞阻尼器中并联惯性质量单元,可显著提高斜拉索的模态阻尼比,非常有利于减振;斜拉索-VIMD系统各阶模态的量纲为1的阻尼比曲线不重合,这与传统的斜拉索-VD（Viscous Damper）系统不同;斜拉索-VIMD系统的模态阻尼比随支架刚度的减小而急剧减小。     

Permanent Magnet Linear Motors Used as Variable Mechanical Dampers for Vehicle Suspensions

Linear electrodynamic motors consisting of coils of copper wire interacting with magnetic fields produced by permanent magnets can be used to construct mechanical dampers with a damping coefficient which can be rapidly varied by changing the external resistance connected to the coil. Limitations to the use of these variable dampers arise due to the coil's own resistance and mass and the practically achievable magnetic field. A moving coil system is first analyzed and then modifications to the basic results when a moving magnet design is used are given. The results indicate that for the oscillation freauencies tvoicallv encountered in road vehicle suspensions, electrodynamic variable shock absorbers are feasible. A novel coreless design appropriate for use with high energy permanent magnets is proposed which would significantly reduce the weight of the units.