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.     

Wear/comfort Pareto optimisation of bogie suspension

Pareto optimisation of bogie suspension components is considered for a 50 degrees of freedom railway vehicle model to reduce wheel/rail contact wear and improve passenger ride comfort. Several operational scenarios including tracks with different curve radii ranging from very small radii up to straight tracks are considered for the analysis. In each case, the maximum admissible speed is applied to the vehicle. Design parameters are categorised into two levels and the wear/comfort Pareto optimisation is accordingly accomplished in a multistep manner to improve the computational efficiency. The genetic algorithm (GA) is employed to perform the multi-objective optimisation. Two suspension system configurations are considered, a symmetric and an asymmetric in which the primary or secondary suspension elements on the right- and left-hand sides of the vehicle are not the same. It is shown that the vehicle performance on curves can be significantly improved using the asymmetric suspension configuration. The Pareto-optimised values of the design parameters achieved here guarantee wear reduction and comfort improvement for railway vehicles and can also be utilised in developing the reference vehicle models for design of bogie active suspension systems.     

Multiobjective optimisation of bogie suspension to boost speed on curves

To improve safety and maximum admissible speed on different operational scenarios, multiobjective optimisation of bogie suspension components of a one-car railway vehicle model is considered. The vehicle model has 50 degrees of freedom and is developed in multibody dynamics software SIMPACK. Track shift force, running stability, and risk of derailment are selected as safety objective functions. The improved maximum admissible speeds of the vehicle on curves are determined based on the track plane accelerations up to 1.5?m/s². To attenuate the number of design parameters for optimisation and improve the computational efficiency, a global sensitivity analysis is accomplished using the multiplicative dimensional reduction method (M-DRM). A multistep optimisation routine based on genetic algorithm (GA) and MATLAB/SIMPACK co-simulation is executed at three levels. The bogie conventional secondary and primary suspension components are chosen as the design parameters in the first two steps, respectively. In the last step semi-active suspension is in focus. The input electrical current to magnetorheological yaw dampers is optimised to guarantee an appropriate safety level. Semi-active controllers are also applied and the respective effects on bogie dynamics are explored. The safety Pareto optimised results are compared with those associated with in-service values. The global sensitivity analysis and multistep approach significantly reduced the number of design parameters and improved the computational efficiency of the optimisation. Furthermore, using the optimised values of design parameters give the possibility to run the vehicle up to 13% faster on curves while a satisfactory safety level is guaranteed. The results obtained can be used in Pareto optimisation and active bogie suspension design problems.     

Optimal selection of suspension parameters in large scale vehicle models

Optimum values are selected for the suspension damping and stiffness parameters of complex car models, subjected to road excitation, by applying suitable numerical methodologies. These models result from a detailed finite-element discretisation and possess a relatively large number of degrees of freedom. They also involve strongly nonlinear characteristics, due mostly to large rigid body rotation of some of their components and the properties of the connection elements. First, attention is focused on gaining some insight into the dynamics of the mechanical models examined, resulting when the vehicle passes over roads involving typical geometric profiles. Then, the emphasis is shifted to presenting results obtained by applying appropriate optimisation methodologies. For this purpose, three classes of design criteria are first set up, referring to passenger ride comfort, suspension travel and car road holding and yielding the most important suspension stiffness and damping parameters. Originally, the optimisation is performed by forming a composite cost function and employing a single-objective optimisation method. Since the design criteria are conflicting, a multi-objective optimisation methodology is also set up and applied subsequently.     

Hybrid modelling and damping collaborative optimisation of Five-suspensions for coupling driver-seat-cab system

For the complex structure and vibration characteristics of coupling driver-seat-cab system of trucks, there is no damping optimisation theory for its suspensions at present, which seriously restricts the improvement of vehicle ride comfort. Thus, in this paper, the seat suspension was regarded as ‘the fifth suspension’ of cab, the ‘Five-suspensions’ for this system was proposed. Based on this, using the mechanism modelling method, a 4 degree-of-freedom coupling driver-seat-cab system model was presented; then, by the tested cab suspensions excitation and seat acceleration response, its parameters identification mathematical model was established. Based on this, taking optimal ride comfort as target, its damping collaborative optimisation mathematical model was built. Combining the tested signals and a simulation model with the mathematical models of parameters identification and damping collaborative optimisation, a complete flow of hybrid modelling and damping collaborative optimisation of Five-suspensions was presented. With a practical example of seat and cab system, the damping parameters were optimised and validated by simulation and bench test. The results show that the model and method proposed are correct and reliable, providing a valuable reference for the design of seat suspension and cab suspensions.     

Railway vehicle performance optimisation using virtual homologation

Unlike regular automotive vehicles, which are designed to travel in different types of roads, railway vehicles travel mostly in the same route during their life cycle. To accept the operation of a railway vehicle in a particular network, a homologation process is required according to local standard regulations. In Europe, the standards EN 14363 and UIC 518, which are used for railway vehicle acceptance, require on-track tests and/or numerical simulations. An important advantage of using virtual homologation is the reduction of the high costs associated with on-track tests by studying the railway vehicle performance in different operation conditions. This work proposes a methodology for the improvement of railway vehicle design with the objective of its operation in selected railway tracks by using optimisation. The analyses required for the vehicle improvement are performed under control of the optimisation method global and local optimisation using direct search. To quantify the performance of the vehicle, a new objective function is proposed, which includes: a Dynamic Performance Index, defined as a weighted sum of the indices obtained from the virtual homologation process; the non-compensated acceleration, which is related to the operational velocity; and a penalty associated with cases where the vehicle presents an unacceptable dynamic behaviour according to the standards. Thus, the optimisation process intends not only to improve the quality of the vehicle in terms of running safety and ride quality, but also to increase the vehicle availability via the reduction of the time for a journey while ensuring its operational acceptance under the standards. The design variables include the suspension characteristics and the operational velocity of the vehicle, which are allowed to vary in an acceptable range of variation. The results of the optimisation lead to a global minimum of the objective function in which the suspensions characteristics of the vehicle are optimal for the track, the maximum operational velocity is increased while the safety and ride quality measures of the vehicle, as defined by homologation standards, are either maintained in acceptable values or improved.     

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.     

Active yaw damper for the improvement of railway vehicle stability and curving performances: simulations and experimental results

To further increase passenger train comfort and handling performances, a mechatronic approach to the design of railway vehicles is necessary. In fact, active systems on board a railway vehicle allow to push design barriers beyond those encountered with just passive systems. The article deals with the development of an electro-mechanical actuator to improve the running behaviour of a railway vehicle, both in straight track and curve. The main components of the active system are a brushless motor and a mechanical transmission, used to apply a longitudinal force between the carbody and the bogie of the vehicle. The actuator is operated in force control. Different control strategies were developed for straight track running, where the aim is to increase the vehicle critical speed, and for curve negotiation, where the goal is to reduce the maximum values of track shift forces. A mathematical model of the railway vehicle incorporating the active control device has been developed and used to optimise control strategies and hardware set-up of the active device and to estimate the increase in operating performances with respect to a conventional passive vehicle. The active control device has then been mounted on an ETR470 railway vehicle, and its performances have been evaluated during in-line tests in both straight and curved tracks.     

Active yaw damper for the improvement of railway vehicle stability and curving performances: simulations and experimental results

To further increase passenger train comfort and handling performances, a mechatronic approach to the design of railway vehicles is necessary. In fact, active systems on board a railway vehicle allow to push design barriers beyond those encountered with just passive systems. The article deals with the development of an electro-mechanical actuator to improve the running behaviour of a railway vehicle, both in straight track and curve. The main components of the active system are a brushless motor and a mechanical transmission, used to apply a longitudinal force between the carbody and the bogie of the vehicle. The actuator is operated in force control. Different control strategies were developed for straight track running, where the aim is to increase the vehicle critical speed, and for curve negotiation, where the goal is to reduce the maximum values of track shift forces. A mathematical model of the railway vehicle incorporating the active control device has been developed and used to optimise control strategies and hardware set-up of the active device and to estimate the increase in operating performances with respect to a conventional passive vehicle. The active control device has then been mounted on an ETR470 railway vehicle, and its performances have been evaluated during in-line tests in both straight and curved tracks.     

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.     

Conceptual design of high-speed semi-low-floor bogie for train-tram

Train-tram railway vehicles implement the connection between urban tramlines and the surrounding railway network. Train-tram railway vehicles, which use existing infrastructure, can help to avoid large investments in new railways or tramlines and make interchanges between city center and surrounding cities unnecessary. However, present train-tram rail vehicle cannot carry out the integration of operating by means of high speed in intercity railways with operating on small radius of curvature in inner city tramlines. This paper aims to develop a new model for solid wheelsets train-tram railway vehicles, which will not only pass the curve of 25mR radius of curvature traveling on inner city tramlines with the speed of 18 km/h, but also can travel on straight railway with 200 km/h high speed between intercity. In this paper, a new train-tram model, including five car-body and five motor bogies with ten traction motors, is addressed. Expect as a real rail vehicle testing, this study prefer virtual simulation, which is an effective way to show the rail vehicle performance, such as ride stability, ride comfort and ride safety, by means of evaluating the dynamic characteristics of rail vehicle. Moreover, Design of Experiment (DOE) method is used to optimize solid wheelsets bogie system on improving passenger comfort, safety and stability of train-tram. Parameters of components of bogie system are tuned to minimize the derailment coefficient and the ride comfort index. The results shows that the best comfort index for passenger and minimum derailment coefficient are found. The results also show that this optimized new train-tram model is reliable and practical enough to be applied on real rail vehicle design.     

Robust design of a passive linear quarter car suspension system using a multi-objective evolutionary algorithm and analytical robustness indexes

This paper deals with the robust design of a passive vehicle suspension system. A robust design methodology based on a multi-objective evolutionary algorithm (MOEA) is used to handle the trade-off between the considered conflicting performance requirements under uncertainty and feasibility constraints. A constrained multi-objective optimisation problem is formulated and the notion of Pareto-optimality is used to increase the quality of the candidate design solutions obtained at each generation by the MOEA. To save computation time, a simplified physical model (quarter car) is considered and the optimisation is performed in the frequency domain, using relevant transmissibilities of the system. The robustness is directly investigated by means of analytical robustness indexes. Time-consuming a posteriori methods, like designs of experiments or Monte Carlo analysis, are therefore avoided. A set of non-dominated solutions is obtained. Thus the designer not only selects a special design, in accordance with the wanted vehicle configuration, but also includes the robustness of each performance requirement in his final decision.     

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.     

Active lateral secondary suspension with H ∞ control to improve ride comfort: simulations on a full-scale model

In this study, a full-scale rail vehicle model is used to investigate how lateral ride comfort is influenced by implementing the H _∞ and sky-hook damping control strategies. Simulations show that significant ride comfort improvements can be achieved on straight track with both control strategies compared with a passive system. In curves, it is beneficial to add a carbody centring Hold-Off Device (HOD) to reduce large spring deflections and hence to minimise the risk of bumpstop contact. In curve transitions, the relative lateral displacement between carbody and bogie is reduced by the concept of H _∞ control in combination with the HOD. However, the corresponding concept with sky-hook damping degrades the effect of the carbody centring function. Moreover, it is shown that lateral and yaw mode separation is a way to further improve the performance of the studied control strategies.     

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.     

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.     

Hierarchical optimisation on scissor seat suspension characteristic and structure

Scissor seat suspension has been applied widely to attenuate the cab vibrations of commercial vehicles, while its design generally needs a trade-off between the seat acceleration and suspension travel, which creates a typical optimisation issue. A complexity for this issue is that the optimal dynamics parameters are not easy to approach solutions fast and unequivocally. Hence, the hierarchical optimisation on scissor seat suspension characteristic and structure is proposed, providing a top-down methodology with the globally optimal and fast convergent solutions to compromise these design contradictions. In details, a characteristic-oriented non-parametric dynamics model of the scissor seat suspension is formulated firstly via databases, describing its vertical dynamics accurately. Then, the ideal vertical stiffness-damping characteristic is cascaded via the characteristic-oriented model, and the structure parameters are optimised in accordance with a structure-oriented multi-body dynamics model of the scissor seat suspension. Eventually, the seat effective amplitude transmissibility factor, suspension travel and the CPU time for solving are evaluated. The results show the seat suspension performance and convergent speed of the globally optimal solutions are improved well. Hence, the proposed hierarchical optimisation methodology regarding characteristic and structure of the scissor seat suspension is promising for its virtual development.     

An approach for the validation of railway vehicle models based on on-track measurements

This paper proposes an approach for the validation of railway vehicle models based on on-track measurements. The validation of simulation models has gained importance with the introduction of new applications of multi-body simulation in railway vehicle dynamics as the assessment of track geometry defects, the investigation of derailments and the analysis of gauging. These applications are not only interested in qualitative predictions of the vehicle behaviour but also in precise quantitative results of the safety and comfort relevant vehicle responses. The validation process aims at guaranteeing that the simulation model represents the dynamic behaviour of the real vehicle with a sufficient good precision. A misfit function is defined which quantifies the distance between the simulated and the measured vehicle response allowing to evaluate different models at different running conditions. The obtained modelling errors are compared to the measurement uncertainty estimated for one vehicle using repeatability analysis.     

Optimisation of lateral car dynamics taking into account parameter uncertainties

Simulation studies on an active all-wheel-steering car show that disturbance of vehicle parameters have high influence on lateral car dynamics. This motivates the need of robust design against such parameter uncertainties. A specific parametrisation is established combining deterministic, velocity-dependent steering control parameters with partly uncertain, velocity-independent vehicle parameters for simultaneous use in a numerical optimisation process. Model-based objectives are formulated and summarised in a multi-objective optimisation problem where especially the lateral steady-state behaviour is improved by an adaption strategy based on measurable uncertainties. The normally distributed uncertainties are generated by optimal Latin hypercube sampling and a response surface based strategy helps to cut down time consuming model evaluations which offers the possibility to use a genetic optimisation algorithm. Optimisation results are discussed in different criterion spaces and the achieved improvements confirm the validity of the proposed procedure.