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.     

Semi-active H∞ control of high-speed railway vehicle suspension with magnetorheological dampers

In this paper, semi-active H∞ control with magnetorheological (MR) dampers for railway vehicle suspension systems to improve the lateral ride quality is investigated. The proposed semi-active controller is composed of a H∞ controller as the system controller and an adaptive neuro-fuzzy inference system (ANFIS) inverse MR damper model as the damper controller. First, a 17-degree-of-freedom model for a full-scale railway vehicle is developed and the random track irregularities are modelled. Then a modified Bouc–Wen model is built to characterise the forward dynamic characteristics of the MR damper and an inverse MR damper model is built with the ANFIS technique. Furthermore, a H∞ controller composed of a yaw motion controller and a rolling pendulum motion (lateral motion+roll motion) controller is established. By integrating the H∞ controller with the ANFIS inverse model, a semi-active H∞ controller for the railway vehicle is finally proposed. Simulation results indicate that the proposed semi-active suspension system possesses better attenuation ability for the vibrations of the car body than the passive suspension system.     

A model for vehicle–track random interactions on effects of crosswinds and track irregularities

A stochastic mathematical model is developed to evaluate the dynamic behaviours and statistical responses of vehicle–track systems when random system excitations including crosswinds and track irregularities are imposed. In this model, the railway vehicle is regarded as a multi-rigid-body system, the track system is modelled by finite element theory. These two systems are spatially coupled by the nonlinear wheel–rail contact forces and unsteady aerodynamic forces. The high efficiency and accuracy of this stochastic model are validated by comparing to the robust Monte-Carlo method. Numerical studies show that crosswinds have a great influence on the dynamic performance of vehicle–track systems, especially on transverse vibrations. When the railway vehicle initially runs into the wind field, it will experience a severe vibration stage, and then stepping into a relatively steady state where the fluctuating winds and track irregularities will play deterministic roles in the deviations of system responses. Moreover, it is found that track irregularities should be properly considered in the safety assessment of the vehicle even in strong crosswinds.     

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.     

Fundamentals of vehicle–track coupled dynamics

This paper presents a framework to investigate the dynamics of overall vehicle–track systems with emphasis on theoretical modelling, numerical simulation and experimental validation. A three-dimensional vehicle–track coupled dynamics model is developed in which a typical railway passenger vehicle is modelled as a 35-degree-of-freedom multi-body system. A traditional ballasted track is modelled as two parallel continuous beams supported by a discrete-elastic foundation of three layers with sleepers and ballasts included. The non-ballasted slab track is modelled as two parallel continuous beams supported by a series of elastic rectangle plates on a viscoelastic foundation. The vehicle subsystem and the track subsystem are coupled through a wheel–rail spatial coupling model that considers rail vibrations in vertical, lateral and torsional directions. Random track irregularities expressed by track spectra are considered as system excitations by means of a time–frequency transformation technique. A fast explicit integration method is applied to solve the large nonlinear equations of motion of the system in the time domain. A computer program named TTISIM is developed to predict the vertical and lateral dynamic responses of the vehicle–track coupled system. The theoretical model is validated by full-scale field experiments, including the speed-up test on the Beijing–Qinhuangdao line and the high-speed running test on the Qinhuangdao–Shenyang line. Differences in the dynamic responses analysed by the vehicle–track coupled dynamics and by the classical vehicle dynamics are ascertained in the case of vehicles passing through curved tracks.     

Semi-active control of tracked vehicle suspension incorporating magnetorheological dampers

In past years, the application of magnetorheological (MR) and electrorheological dampers in vehicle suspension has been widely studied, mainly for the purpose of vibration control. This paper presents theoretical study to identify an appropriate semi-active control method for MR-tracked vehicle suspension. Three representative control algorithms are simulated including the skyhook, hybrid and fuzzy-hybrid controllers. A seven degrees-of-freedom tracked vehicle suspension model incorporating MR dampers has been adopted for comparison between the performance of the three controllers. The model differential equations are derived based on Newton's second law of motion and the proposed control methods are developed. The performance of each control method under bump and sinusoidal road profiles for different vehicle speeds is simulated and compared with the performance of the conventional suspension system in time and frequency domains. The results show that the performance of tracked vehicle suspension with MR dampers is substantially improved. Moreover, the fuzzy-hybrid controller offers an excellent integrated performance in reducing the body accelerations as well as wheel bounce responses compared with the classical skyhook and hybrid controllers.     

A structural articulation method for assessing railway bridges subject to dynamic impact loading from track irregularities

This paper discusses the importance of track irregularities in railway bridge design, and presents a new technique for calculating the dynamic impact load induced by such irregularities: the structural articulation method. The properties of the combined bridge-suspension system are coupled through global mass, stiffness, and damping matrices. Under the proposed method, the true suspension system over a particular point on the bridge girder at time t is divided into equivalent suspension systems attributed to adjacent finite-element nodes of the bridge. The time-dependent effects of a moving mass are thereby included in the equation of motion.     

Influence of uneven rail irregularities on the dynamic response of the railway track using a three-dimensional model of the vehicle–track system

A mathematical model of the vehicle–track interaction is developed to investigate the coupled behaviour of vehicle–track system, in the presence of uneven irregularities at left/right rails. The railway vehicle is simplified as a 3D multi-rigid-body model, and the track is treated as the two parallel beams on a layered discrete support system. Besides the car-body, the bogies and the wheel sets, the sleepers are assumed to have roll degree of freedom, in order to simulate the in-plane rotation of the components. The wheel–rail interface is treated using a nonlinear Hertzian contact model, coupling the mathematical equations of the vehicle–track systems. The dynamic interaction of the entire system is numerically studied in time domain, employing Newmark's integration method. The track irregularity spectra of both the left/right rails are taken into account, as the inputs of dynamic excitations. The dynamic responses of the track system induced by such irregularities are obtained, particularly in terms of the vertical (bounce) and roll displacements. The numerical model of the present research is validated using several benchmark models reported in the literature, for both the smooth and unsmooth track conditions. Four sample profiles of the measured rail irregularities are considered as the case studies of excitation sources, examining their influences on the dynamic behaviour of the coupled system. The results of numerical simulations demonstrate that the motion of track system is significantly influenced by the presence of uneven irregularities in left/right rails. Dynamic response of the sleepers in the roll direction becomes more sensitive to the rail irregularities, as the unevenness severity of the parallel profiles (quantitative difference between left and right rail spectra) is increased. The severe geometric deformation of the track in the bounce–pitch–roll directions is mainly related to such profile unevenness (cross-level) in left/right rails.     

H8 Control Performance of a Full-Vehicle Suspension Featuring Magnetorheological Dampers

Summary This paper presents an investigation of the feedback control performance of a full-vehicle suspension system featuring magnetorheological (MR) dampers. A cylindrical MR damper is designed and manufactured by incorporating a Bingham model of aMR fluid which is commercially available. After evaluating the field-dependent damping characteristics of the MR damper, a full-vehicle suspension system installed with 4 independent MR dampers is constructed and its governing equations of motion which include vertical, pitch and roll motions are derived. A H 8 controller which has inherent robustness against system uncertainties is formulated by treating the sprung mass of the vehicle as uncertain parameter. This is accomplished by adopting the loop shaping design procedure. For the demonstration of a practical feasibility, control performance characteristics for vibration suppression of the proposed MR suspension system are evaluated under various road conditions through the hardware-in-the-loop simulation (HILS) methodology.     

H8 Control Performance of a Full-Vehicle Suspension Featuring Magnetorheological Dampers

Summary This paper presents an investigation of the feedback control performance of a full-vehicle suspension system featuring magnetorheological (MR) dampers. A cylindrical MR damper is designed and manufactured by incorporating a Bingham model of aMR fluid which is commercially available. After evaluating the field-dependent damping characteristics of the MR damper, a full-vehicle suspension system installed with 4 independent MR dampers is constructed and its governing equations of motion which include vertical, pitch and roll motions are derived. A H 8 controller which has inherent robustness against system uncertainties is formulated by treating the sprung mass of the vehicle as uncertain parameter. This is accomplished by adopting the loop shaping design procedure. For the demonstration of a practical feasibility, control performance characteristics for vibration suppression of the proposed MR suspension system are evaluated under various road conditions through the hardware-in-the-loop simulation (HILS) methodology.     

Probabilistic assessment of railway vehicle-curved track systems considering track random irregularities

The randomness of track irregularities directly leads to the random vibration of the vehicle–track systems. To assess the dynamic performance of a railway system in more comprehensive and practical ways, a framework for probabilistic assessment of vehicle-curved track systems is developed by effectively integrating a vehicle–track coupled model (VTCM), a track irregularity probabilistic model (TIPM) with a probability density evolution method (PDEM). In VTCM, the railway vehicle and the curved track are coupled by the nonlinear wheel–rail interaction forces, and through TIPM, the ergodic properties of random track irregularities on amplitudes, wavelengths and probabilities can be properly considered in the dynamic calculations. Lastly, PDEM, a newly developed method for solving probabilistic transmissions between stochastic excitations and deterministic dynamic responses, is introduced to this probabilistic assessment model. Numerical examples validate the correctness and practicability of the proposed models. In this paper, the results of probabilistic assessment are presented to illustrate the dynamic behaviours of a high-speed railway vehicle subject to curved tracks with various radii, and to demonstrate the importance of considering the actual status of wheel–rail contacts and curve negotiation effects in vehicle-curved track interactions.     

Effect of vehicle vibration environment of high-speed train on dynamic performance of axle box bearing

In this study, we developed a comprehensive three-dimensional vehicle–track coupled dynamics model considering the traction drive system and axle box bearing. In this model, dynamic interactions between the axle box bearing and other components, such as the wheelset and bogie frame, are considered based on a detailed analysis of the structural properties and working mechanism of the axle box bearing. A few complicated dynamic excitations, such as the time-varying mesh stiffness of gears, time-varying stiffness of bearing, bearing gaps and track irregularities, are considered. Then, the dynamic responses of the vehicle–track system are demonstrated via numerical simulations based on the established dynamics model. The results indicate that the traction drive system and track irregularities can significantly influence the dynamic interactions of the axle box bearing. The necessity of considering the excitation caused by gear meshing and track irregularities when assessing the dynamic performance of the axle box bearing is demonstrated.     

Construction of a stochastic model of track geometry irregularities and validation through experimental measurements of dynamic loading

This paper describes the construction of a stochastic model of urban railway track geometry irregularities, based on experimental data. The considered irregularities are track gauge, superelevation, horizontal and vertical curvatures. They are modelled as random fields whose statistical properties are extracted from a large set of on-track measurements of the geometry of an urban railway network. About 300–1000 terms are used in the Karhunen–Loève/Polynomial Chaos expansions to represent the random fields with appropriate accuracy. The construction of the random fields is then validated by comparing on-track measurements of the contact forces and numerical dynamics simulations for different operational conditions (train velocity and car load) and horizontal layouts (alignment, curve). The dynamics simulations are performed both with and without randomly generated geometrical irregularities for the track. The power spectrum densities obtained from the dynamics simulations with the model of geometrical irregularities compare extremely well with those obtained from the experimental contact forces. Without irregularities, the spectrum is 10–50?dB too low.     

Ride Quality and Dynamics of Rail Vehicle Models for Microcomputers

This paper describes mathematical and computer models for ride quality and dynamics of rail vehicles developed for running on personal computers. The purpose of the computer simulations is for prediction of ride quality in order to study the dynamic stability of the system and the effect of track quality and irregularities on ride quality.

In deriving the equations of motion for dynamic stability, the tangential forces acting on the contact areas between the wheels and rails are of fundamental importance in railway vehicles dynamics and are included in the analysis [1]. These forces are due to the creep phenomenon between the wheel and the rail on which it is rolling. Track irregularities are defined in terms of four components consisting of gauge, cross level, alignment and vertical surface profile [2]. Relation of allowable track irregularities versus speed is given by the FRA Track Safety Standards. Analytical representation of track irregularities should include both PSD (Power Spectral Density) for CWR (Continuous Welded Rail) as well as discrete inputs from track joints.

In this paper, the rail vehicle suspension analysis and dynamics mathematical and computer models are described. The computer models are written in Fortran 77 and designed to run on personal computer. The paper also discusses programming considerations that must be taken into account when programming for microcomputers under DOS (IBM's Disk Operating System) and MS or RM Fortran Compilers. Most of the considerations are however, valid in general with respect to engineering software development and programming for microcomputers.

Computer graphics is a powerful tool for visualization of the resulting solutions such as the display of the characteristic roots for the eigenvalues solution on a root locus plot and representation of acceleration levels versus the “Reduced Comfort Boundary” limits defined by the International Standards Organization” (ISO 2631-1985). In this paper some examples of these resulting outputs are presented and their significance discussed.     

Theoretical and experimental excitation force spectra for railway-induced ground vibration: vehicle–track–soil interaction,irregularities and soil measurements

Excitation force spectra are necessary for a realistic prediction of railway-induced ground vibration. The excitation forces cause the ground vibration and they are themselves a result of irregularities passed by the train. The methods of the related analyses – the wavenumber integration for the wave propagation in homogeneous or layered soils, the combined finite-element boundary-element method for the vehicle–track–soil interaction – have already been presented and are the base for the advanced topic of this contribution. This contribution determines excitation force spectra of railway traffic by two completely different methods. The forward analysis starts with vehicle, track and soil irregularities, which are taken from literature and axle-box measurements, calculates the vehicle–track interaction and gets theoretical force spectra as the result. The second method is a backward analysis from the measured ground vibration of railway traffic. A calculated or measured transfer function of the soil is used to determine the excitation force spectrum of the train. A number of measurements of different soils and different trains with different speeds are analysed in that way. Forward and backward analysis yield the same approximate force spectra with values around 1 kN for each axle and third of octave.     

Performance of spade-less wheeled military vehicles with passive and semi-active suspensions during mortar firing

Many armies are replacing heavy slow tracked vehicles with their lighter wheeled counterparts for their high mobility and better shoot and scoot capabilities. These features make the vehicle hard to track and target in counter-battery fire. However, when firing high calibre guns, spades are needed to connect the vehicle chassis to the ground, so as to transmit parts of the large firing force directly to the ground. Use of spades hinders the vehicle mobility, while elimination of them paves the way for having quicker and more mobile wheeled vehicles. In this article, vibration response of a spade-less High Mobility Multi-purpose Wheeled Vehicle with a mounted mortar is studied and controlled using stock passive, optimised passive, and optimised semi-active dampers as primary suspensions. The spade-less vehicle with optimised passive and semi-active dampers has a better response in heave, pitch, and fore-aft motions and can fire with better accuracy compared to a spade-less vehicle with stock passive dampers. Simulation results indicate that the spades can be removed from wheeled military vehicles if the precautions are taken for the tyres.     

The effect of worn profile on wear progress of rail vehicle steel wheels over curved tracks

Dynamic performance, safety and maintenance costs of railway vehicles strongly depend on wheelset dynamics and particularly on the design of wheelset profile. This paper considers the effect of worn wheel profile on vehicle dynamics and the trend of wear in the wheels as a result of the vehicle movements. ADAMS/RAIL is used to build a multi-body system model of the vehicle. The track model is also configured as an elastic body. Measured new and worn wheel profiles are used to provide boundary conditions for the wheel/rail contacts. The fleet velocity profile taken during its normal braking is also used for the simulation. Wear numbers are calculated for different sets of wheels and the results compared with each other. Outcome of this research can be used for modifying dynamic performance of the vehicle, improving its suspension elements and increasing ride quality. It can also be further processed to reach to a modified wheel profile suitable for the fleet/track combination and for improved maintenance of the wheels. A major advantage of the computer models in this paper is the insertion of the wheel surface properties into the boundary conditions for dynamic modelling of the fleet. This is performed by regularly measuring the worn wheel profiles during their service life and by the calculation of the wear rate for individual wheels.     

Optimal Performance of Variable Component Suspensions

Most vehicle suspension systems use fixed passive components that offer a compromise in performance between sprung mass isolation, suspension travel, and tireroad contact force. Recently, systems with discretely adjustable dampers and air springs been added to production vehicles. Active and semi-active damping concepts for vehicle suspensions have also been studied theoretically and with physical prototypes. This paper examines the optimal performance comparisons of variable component suspensions, including active damping and full-state feedback, for “quartercar” heave models. Two and three dimensional optimizations are computed using performance indicators to find the component parameters (control gains) that provide “optimal” performance for statistically described roadway inputs. The effects of performance weighting and feedback configuration are examined. Active damping is shown to be mainly important for vehicle isolation. A passive vehicle suspension can control suspension travel and tire contact force nearly as well as a full state feedback control strategy.