Robustness analysis of bogie suspension components Pareto optimised values

Bogie suspension system of high speed trains can significantly affect vehicle performance. Multiobjective optimisation problems are often formulated and solved to find the Pareto optimised values of the suspension components and improve cost efficiency in railway operations from different perspectives. Uncertainties in the design parameters of suspension system can negatively influence the dynamics behaviour of railway vehicles. In this regard, robustness analysis of a bogie dynamics response with respect to uncertainties in the suspension design parameters is considered. A one-car railway vehicle model with 50 degrees of freedom and wear/comfort Pareto optimised values of bogie suspension components is chosen for the analysis. Longitudinal and lateral primary stiffnesses, longitudinal and vertical secondary stiffnesses, as well as yaw damping are considered as five design parameters. The effects of parameter uncertainties on wear, ride comfort, track shift force, stability, and risk of derailment are studied by varying the design parameters around their respective Pareto optimised values according to a lognormal distribution with different coefficient of variations (COVs). The robustness analysis is carried out based on the maximum entropy concept. The multiplicative dimensional reduction method is utilised to simplify the calculation of fractional moments and improve the computational efficiency. The results showed that the dynamics response of the vehicle with wear/comfort Pareto optimised values of bogie suspension is robust against uncertainties in the design parameters and the probability of failure is small for parameter uncertainties with COV up to 0.1.     

Heavy vehicle pitch dynamics and suspension tuning. Part I: unconnected suspension

The influence of suspension tuning of passenger cars on bounce and pitch ride performance has been explored in a number of studies, while only minimal efforts have been made for establishing similar rules for heavy vehicles. This study aims to explore pitch dynamics and suspension tunings of a two-axle heavy vehicle with unconnected suspension, which could also provide valuable information for heavy vehicles with coupled suspensions. Based on a generalised pitch-plane model of a two-axle heavy vehicle integrating either unconnected or coupled suspension, three dimensionless measures of suspension properties are defined and analysed—namely the pitch margin (PM), pitch stiffness ratio (PSR), and coupled pitch stiffness ratio (CPSR)—for different unconnected suspension tunings and load conditions. Dynamic responses of the vehicle with three different load conditions and five different tunings of the unconnected suspension are obtained under excitations arising from three different random road roughness conditions and a wide range of driving speeds, and braking manoeuvres. The responses are evaluated in terms of performance measures related to vertical and pitch ride, dynamic tyre load, suspension travel, and pitch-attitude control characteristics of the vehicle. Fundamental relationships between the vehicle responses and the proposed suspension measures (PM, PSR, and CPSR) are established, based on which some basic suspension tuning rules for heavy vehicles with unconnected suspensions are also proposed.     

Multi-objective optimization of quarter-car models with a passive or semi-active suspension system

A systematic methodology is applied in an effort to select optimum values for the suspension damping and stiffness parameters of two degrees of freedom quarter-car models, subjected to road excitation. First, models involving passive suspension dampers with constant or dual rate characteristics are considered. In addition, models with semi-active suspensions are also examined. Moreover, special emphasis is put in modeling possible temporary separations of the wheel from the ground. For all these models, appropriate methodologies are employed for capturing the motions of the vehicle resulting from passing with a constant horizontal speed over roads involving an isolated or a distributed geometric irregularity. The optimization process is based on three suitable performance criteria, related to ride comfort, suspension travel and road holding of the vehicle and yielding the most important suspension stiffness and damping parameters. As these criteria are conflicting, a suitable multi-objective optimization methodology is set up and applied. As a result, a series of diagrams with typical numerical results are presented and compared in both the corresponding objective spaces (in the form of classical Pareto fronts) and parameter spaces.     

Multi-objective optimization of quarter-car models with a passive or semi-active suspension system

A systematic methodology is applied in an effort to select optimum values for the suspension damping and stiffness parameters of two degrees of freedom quarter-car models, subjected to road excitation. First, models involving passive suspension dampers with constant or dual rate characteristics are considered. In addition, models with semi-active suspensions are also examined. Moreover, special emphasis is put in modeling possible temporary separations of the wheel from the ground. For all these models, appropriate methodologies are employed for capturing the motions of the vehicle resulting from passing with a constant horizontal speed over roads involving an isolated or a distributed geometric irregularity. The optimization process is based on three suitable performance criteria, related to ride comfort, suspension travel and road holding of the vehicle and yielding the most important suspension stiffness and damping parameters. As these criteria are conflicting, a suitable multi-objective optimization methodology is set up and applied. As a result, a series of diagrams with typical numerical results are presented and compared in both the corresponding objective spaces (in the form of classical Pareto fronts) and parameter spaces.     

Smoothing dry friction damping by dither generated in rolling contact of wheel and rail and its influence on ride dynamics of freight wagons

Friction dampers of mechanical systems are frequently exposed to medium-frequency (M-F) dither generated in the surrounding environment. A dithered system of technical importance is the railway freight wagon with friction dampers in the primary suspension developing two-dimensional friction, where dither is generated by the rolling contact of wheel and rail. This paper presents some results of the investigation of the influence of dither on dry friction damping. This influence has been studied experimentally and theoretically, and the parameters of dither influencing dry friction damping have been indicated. An experimental set-up has been designed that allows investigating friction damping in the presence of dither. The experiments have shown that friction damping in the presence of the M-F dither behaves like viscous damping. This means that dither smoothes dry friction as far as damping is concerned. To investigate this phenomenon theoretically, a rheological model of dry friction has been proposed that is applicable to one- and two-dimensional friction. In the latter case, the model takes into account friction anisotropy. According to performed numerical simulations of freight wagon motion, with dither supplied to the model through measured vertical accelerations of axle boxes, smoothing dry friction by dither strongly influences ride dynamics of the wagon with friction dampers in the primary suspension. Smoothing dry friction by dither should be accounted for in numerical simulations of motion of vehicles with friction dampers in the primary suspension by employing a proper model of the two-dimensional friction and application of realistic dither generated by rolling contact.     

The influence of suspension components friction on race car vertical dynamics

This work analyses the effect of friction in suspension components on a race car vertical dynamics. It is a matter of fact that race cars aim at maximising their performance, focusing the attention mostly on aerodynamics and suspension tuning: suspension vertical and rolling stiffness and damping are parameters to be taken into account for an optimal setup. Furthermore, friction in suspension components must not be ignored. After a test session carried out with a F4 on a Four Poster rig, friction was detected on the front suspension. The real data gathered allow the validation of an analytical model with friction, confirming that its influence is relevant for low frequency values closed to the car pitch natural frequency. Finally, some setup proposals are presented to describe what should be done on actual race cars in order to correct vehicle behaviour when friction occurs.     

Roll and pitch independently tuned interconnected suspension: modelling and dynamic analysis

In this paper, a roll and pitch independently tuned hydraulically interconnected passive suspension is presented. Due to decoupling of vibration modes and the improved lateral and longitudinal stability, the stiffness of individual suspension spring can be reduced for improving ride comfort and road grip. A generalised 14 degree-of-freedom nonlinear vehicle model with anti-roll bars is established to investigate the vehicle ride and handling dynamic responses. The nonlinear fluidic model of the hydraulically interconnected suspension is developed and integrated with the full vehicle model to investigate the anti-roll and anti-pitch characteristics. Time domain analysis of the vehicle model with the proposed suspension is conducted under different road excitations and steering/braking manoeuvres. The dynamic responses are compared with conventional suspensions to demonstrate the potential of enhanced ride and handling performance. The results illustrate the model-decoupling property of the hydraulically interconnected system. The anti-roll and anti-pitch performance could be tuned independently by the interconnected systems. With the improved anti-roll and anti-pitch characteristics, the bounce stiffness and ride damping can be optimised for better ride comfort and tyre grip.     

Design of passive vehicle suspensions for maximal least damping ratio

This paper studies the use of the least damping ratio among system poles as a performance metric in passive vehicle suspensions. Methods are developed which allow optimal solutions to be computed in terms of non-dimensional quantities in a quarter-car vehicle model. Solutions are provided in graphical form for convenient use across vehicle types. Three suspension arrangements are studied: the standard suspension involving a parallel spring and damper and two further suspension arrangements involving an inerter. The key parameters for the optimal solutions are the ratios of unsprung mass to sprung mass and suspension static stiffness to tyre vertical stiffness. A discussion is provided of performance trends in terms of the key parameters. A comparison is made with the optimisation of ride comfort and tyre grip metrics for various vehicle types.     

Parameters optimisation of a vehicle suspension system using a particle swarm optimisation algorithm

The purpose of this paper is to determine the lumped suspension parameters that minimise a multi-objective function in a vehicle model under different standard PSD road profiles. This optimisation tries to meet the rms vertical acceleration weighted limits for human sensitivity curves from ISO 2631 [ISO-2631: guide for evaluation of human exposure to whole-body vibration. Europe; 1997] at the driver's seat, the road holding capability and the suspension working space. The vehicle is modelled in the frequency domain using eight degrees of freedom under a random road profile. The particle swarm optimisation and sequential quadratic programming algorithms are used to obtain the suspension optimal parameters in different road profile and vehicle velocity conditions. A sensitivity analysis is performed using the obtained results and, in Class G road profile, the seat damping has the major influence on the minimisation of the multi-objective function. The influence of vehicle parameters in vibration attenuation is analysed and it is concluded that the front suspension stiffness should be less stiff than the rear ones when the driver's seat relative position is located forward the centre of gravity of the car body. Graphs and tables for the behaviour of suspension parameters related to road classes, used algorithms and velocities are presented to illustrate the results. In Class A road profile it was possible to find optimal parameters within the boundaries of the design variables that resulted in acceptable values for the comfort, road holding and suspension working space.     

An efficient recursive least square-based condition monitoring approach for a rail vehicle suspension system

A model-based condition monitoring strategy for the railway vehicle suspension is proposed in this paper. This approach is based on recursive least square (RLS) algorithm focusing on the deterministic ‘input–output’ model. RLS has Kalman filtering feature and is able to identify the unknown parameters from a noisy dynamic system by memorising the correlation properties of variables. The identification of suspension parameter is achieved by machine learning of the relationship between excitation and response in a vehicle dynamic system. A fault detection method for the vertical primary suspension is illustrated as an instance of this condition monitoring scheme. Simulation results from the rail vehicle dynamics software ‘ADTreS’ are utilised as ‘virtual measurements’ considering a trailer car of Italian ETR500 high-speed train. The field test data from an E464 locomotive are also employed to validate the feasibility of this strategy for the real application. Results of the parameter identification performed indicate that estimated suspension parameters are consistent or approximate with the reference values. These results provide the supporting evidence that this fault diagnosis technique is capable of paving the way for the future vehicle condition monitoring system.     

离散元法的沥青路面车-路动力学响应分析

为了分析车辆荷载作用下沥青路面结构的细观状态力学响应，建立了二自由度1/4车辆模型与多层路基路面耦合离散元模型，通过各结构层单轴压缩应力-应变试验与相同工况试验数据比较，经迭代运算得到路面离散元模型各结构层细观参数，应用试验得到的沥青路面细观参数建立多层路基路面模型，在离散元模型的上表面设定一定不平度，在一定速度作用下，1/4车辆模型在路基路面离散元模型上表面匀速移动，从而求解车辆动荷载作用下沥青路面各结构位移、应力等细观受力状态。进而改变1/4车辆模型的车体悬架刚度、悬架阻尼系数、轮胎刚度，轮胎阻尼系数，从而获得在改变车辆参数作用下沥青路面内部的应力变化规律。研究结果表明：基于离散元理论不但可以求得沥青路面在车-路相互作用下各层的应力与变形，而且还可以求得沥青路面各结构层颗粒流的变化趋势，在车辆移动荷载作用下，随着路基路面深度增加，各结构层颗粒流竖直方向动态位移与应力响应依次减少，其中上基层颗粒流动位移比上面层颗粒流动位移减少25%，下面层颗粒流竖向应力约为上面层颗粒流竖向应力的50%，水平方向上颗粒流既有压应力又有拉应力，变化比较复杂，上面层颗粒流水平方向主要承受压应力，其余结构层主要承受拉应力；增加轮胎与悬架刚度系数对模型颗粒流水平方向拉应力影响较大，增加轮胎与悬架阻尼系数对垂直方向颗粒流压应力与水平方向拉应力影响较小。     

基于舒适性和轮胎动载的车辆悬架参数优化

为了改善汽车行驶的舒适性并减小轮胎对路面的动载，以某载货汽车为研究对象，建立了多目标优化模型，并采用统一目标函数法对车辆悬架参数进行优化。优化结果表明：优化后悬架刚度减小而阻尼增大，且前悬架参数变化较小，后悬架参数变化较大；相比于优化前，车身垂直方向加速度均方根值减小了20％，前轮动栽均方根值减小了40％，后轮变化更显著，减小了49％；采用多目标优化设计方法不仅可提高车辆自身的舒适性，而且可减小轮胎对路面的动载。     

油气弹簧非线性特性对车辆平顺性的影响分析

推导并建立了某工程车辆油气弹簧的非线性刚度和阻尼特性的数学模型，并将其导入到车辆模型中。根据汽车悬架质量分配特点．将汽车简化为两自由度的舣质量振动系统，对此两自由度模型的车轮加速度、车身加速度和悬架动行程进行了仿真从仿真结果可以看出，非线性油气弹簧能很好地衰减由路面传递来的振动。分析了刚度和阻尼的变化对车辆平顺性的影响。     

Sensitivity analysis to assess the influence of the inertial properties of railway vehicle bodies on the vehicle's dynamic behaviour

A sensitivity analysis has been performed to assess the influence of the inertial properties of railway vehicles on their dynamic behaviour. To do this, 216 dynamic simulations were performed modifying, one at a time, the masses, moments of inertia and heights of the centre of gravity of the carbody, the bogie and the wheelset. Three values were assigned to each parameter, corresponding to the percentiles 10, 50 and 90 of a data set stored in a database of railway vehicles. After processing the results of these simulations, the analysed parameters were sorted by increasing influence. It was also found which of these parameters could be estimated with a lesser degree of accuracy for future simulations without appreciably affecting the simulation results. In general terms, it was concluded that the most sensitive inertial properties are the mass and the vertical moment of inertia, and the least sensitive ones the longitudinal and lateral moments of inertia.     

Roll- and pitch-plane coupled hydro-pneumatic suspension

Passive fluidically coupled suspensions have been considered to offer a promising alternative solution to the challenging design of a vehicle suspension system. A theoretical foundation, however, has not been established for fluidically coupled suspension to facilitate its broad applications to various vehicles. The first part of this study investigates the fundamental issues related to feasibility and properties of the passive, full-vehicle interconnected, hydro-pneumatic suspension configurations using both analytical and simulation techniques. Layouts of various interconnected suspension configurations are illustrated based on two novel hydro-pneumatic suspension strut designs, both of which provide a compact design with a considerably large effective working area. A simplified measure, vehicle property index, is proposed to permit a preliminary evaluation of different interconnected suspension configurations using qualitative scaling of the bounce-, roll-, pitch- and warp-mode stiffness properties. Analytical formulations for the properties of unconnected and three selected X-coupled suspension configurations are derived, and simulation results are obtained to illustrate their relative stiffness and damping properties in the bounce, roll, pitch and warp modes. The superior design flexibility feature of the interconnected hydro-pneumatic suspension is also discussed through sensitivity analysis of a design parameter, namely the annular piston area of the strut. The results demonstrate that a full-vehicle interconnected hydro-pneumatic suspension could provide enhanced roll- and pitch-mode stiffness and damping, while retaining the soft bounce- and warp-mode properties. Such an interconnected suspension thus offers considerable potential in realising enhanced decoupling among the different suspension modes.     

Ride comfort of high-speed trains travelling over railway bridges

The ride comfort of high-speed trains passing over railway bridges is studied in this paper. A parametric study is carried out using a time domain model. The effects of some design parameters are investigated such as damping and stiffness of the suspension system and also ballast stiffness. The influence of the track irregularity and train speed on two comfort indicators, namely Sperling's comfort index and the maximum acceleration level are also studied. Two types of railway bridges, a simple girder and an elastically supported bridge are considered.

Timoshenko beam theory is used for modelling the rail and bridge and two layers of parallel damped springs in conjunction with a layer of mass are used to model the rail-pads, sleepers and ballast. A randomly irregular vertical track profile is modelled, characterized by its power spectral density (PSD). The ‘roughness’ is generated for three classes of tracks. Nonlinear Hertz theory is used for modelling the wheel-rail contact. The influences of some nonlinear parameters in a carriage-track-bridge system, such as the load-stiffening characteristics of the rail-pad and the ballast and that of rubber elements in the primary and secondary suspension systems, on the comfort indicators are also studied. Based on Galerkin's method of solution, a new analytical approach is developed for the combination between the rigid and flexural mode shapes, which could be used not only for elastically supported bridges but also other beam-type structures.     

Pareto optimisation of railway bogie suspension damping to enhance safety and comfort

This paper presents the optimisation of damping characteristics in bogie suspensions using a multi-objective optimisation methodology. The damping is investigated and optimised in terms of the resulting performances of a railway vehicle with respect to safety, comfort and wear considerations. A complete multi-body system model describing the railway vehicle dynamics is implemented in commercial software Gensys and used in the optimisation. In complementary optimisation analyses, a reduced and linearised model describing the bogie system dynamics is also utilised. Pareto fronts with respect to safety, comfort and wear objectives are obtained, showing the trade-off behaviour between the objectives. Such trade-off curves are of importance, especially in the design of damping functional components. The results demonstrate that the developed methodology can successfully be used for multi-objective investigations of a railway vehicle within models of different levels of complexity. By introducing optimised passive damping elements in the bogie suspensions, both safety and comfort are improved. In particular, it is noted that the use of optimised passive damping elements can allow for higher train speeds. Finally, adaptive strategies for switching damping parameters with respect to different ride conditions are outlined and discussed.     

铰接式自卸车橡胶弹簧悬架系统试验研究

采用模拟随机输入路面谱激励室内台架试验的方法,对装有新型橡胶弹簧悬架系统的某型号铰接式自卸车进行台架试验研究,以评价橡胶弹簧悬架系统的减振性能和整车行驶平顺性。试验结果表明由于橡胶弹簧悬架系统某些参数匹配不合理导致该车行驶平顺性很不理想,通过优化悬架及座椅的刚度和阻尼参数,可提高整车行驶平顺性,并给出了座椅弹簧的优化结果。     

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.     

Ride dynamic evaluations and design optimisation of a torsio-elastic off-road vehicle suspension

The ride dynamic characteristics of a novel torsio-elastic suspension for off-road vehicle applications are investigated through field measurements and simulations. A prototype suspension was realised and integrated within the rear axle of a forestry skidder for field evaluations. Field measurements were performed on forestry terrains at a constant forward speed of 5 km/h under the loaded and unloaded conditions, and the ride responses were acquired in terms of accelerations along the vertical, lateral, roll, longitudinal and pitch axes. The measurements were also performed on a conventional skidder to investigate the relative ride performance potentials of the proposed suspension. The results revealed that the proposed suspension could yield significant reductions in magnitudes of transmitted vibration to the operator seat. Compared with the unsuspended vehicle, the prototype suspended vehicle resulted in nearly 35%, 43% and 57% reductions in the frequency-weighted rms accelerations along the x-, y- and z-axis, respectively. A 13-degree-of-freedom ride dynamic model of the vehicle with rear-axle torsio-elastic suspension was subsequently derived and validated in order to study the sensitivity of the ride responses to suspension parameters. Optimal suspension parameters were identified using the Pareto technique based on the genetic algorithm to obtain minimal un-weighted and frequency-weighted rms acceleration responses. The optimal solutions resulted in further reduction in the pitch acceleration in the order of 20%, while the reductions in roll and vertical accelerations ranged from 3.5 to 6%.