Multibody Vehicle Model Research Articles

A local degraded adhesion model for creep forces evaluation: An approximate approach to the tangential contact problem

The calculation of the creep forces has always been one of the fundamental goals for a wheel-rail contact model. At the same time, a wheel-rail contact model has necessarily to consider the phenomena related to degraded adhesion because they deeply affect both creepages and creep forces. Degraded adhesion is extensively observed at the wheel-rail interface. However, the development of an accurate and efficient adhesion model is quite a challenge due to the complexity of the system and the difficulty in collecting detailed experimental data.In this framework, the paper presents a local degraded adhesion model (based on local slidings/creepages and local pressures inside the contact area) able to provide a more accurate description of the contact phenomena characterizing the wheel-rail degraded adhesion with respect to analogous global models (involving global sliding/creepages and forces). The new model is able to consider important phenomena like the energy dissipated at the contact and the consequent surface cleaning effect leading to an adhesion recovery between wheel and rail. To reach this goal, the Kalker's FASTSIM algorithm has been properly extended and improved to include the previous phenomena.Furthermore, the new model allows the achievement of a good trade-off between accuracy and numerical efficiency. Thank to its efficiency, the model can be implemented inside general railway vehicle multibody models to perform large scale dynamical simulations.The model has been finally validated through experimental data coming from on-field tests and consisting of specific braking maneuvers under degraded adhesion conditions.

Implementation of a non-Hertzian contact model for railway dynamic application

The development of wheel–rail contact models is an active topic of railway research with the dual objective of improving the accuracy of multibody simulations and reducing its computational effort. This paper extends the online Hertzian contact model, proposed by Pombo et al. (Veh. Syst. Dyn. 45: 165–189, 2007) to propose a non-Hertzian contact model. The new methodology presented here includes the following steps: (i) search of the points of contact; (ii) identification of the undeformed distance function; (iii) evaluation of the contact patch; (iv) calculation of the normal and tangential contact forces; (v) application of the contact forces in the multibody vehicle model. Among several contact models available in the literature, this non-Hertzian contact approach uses the Kik–Piotrowski model for the normal contact force, while the tangential forces are obtained from the interpolation of the available Kalker Book of Tables for non-Hertzian (KBTNH) contact. With the purpose to demonstrate the proper implementation and selection of parameters that define this new model, several contact analysis and dynamic simulations are performed in which the wheel S1002 and the rail UIC50 are considered. First, the contact analyses that determine the contact condition of different wheel–rail interactions serve to assess the accuracy of the Hertzian and non-Hertzian models with respect to the software of reference CONTACT. Second, the Hertzian and non-Hertzian models are utilised to perform dynamic simulations of a wheelset, a bogie and a vehicle running in tangent and curved tracks. In short, this work provides, not only a complete description of the implementation of a non-Hertzian contact model in a multibody code, but also suggests for the proper selection of the parameters that promote better accuracy and optimal computational efficiency.

Improvement of both handling stability and ride comfort of a vehicle via coupled hydraulically interconnected suspension and electronic controlled air spring

The trade-off between handling stability and ride comfort is a disadvantage for the bus fitted with passive suspension due to its high center of gravity and heavy load. A novel suspension configuration with both hydraulically interconnected suspension and electronic controlled air spring is created to handle this conflicting requirement. The proposed whole vehicle system model has three subsystems: a 9-degree-of-freedom vehicle multi-body model, hydraulically interconnected suspension model, and electronic controlled air spring. The electronic controlled air spring comprises an air spring and an auxiliary air chamber, and its height can be adjusted by a fuzzy controller. Then, analytical work is performed to evaluate the handling stability and ride comfort of the vehicle with different suspension configurations under various maneuvers and suspension height modes. Finally, the vehicle on-road test is conducted to experimentally validate the proposed models. Both analytical and experimental results indicate that the vehicle fitted with hydraulically interconnected suspension and electronic controlled air spring can obtain high performance for both handling stability and ride comfort.

A co-simulation approach to the wheel–rail contact with flexible railway track

The standard approach to railway vehicle dynamic analysis includes running the vehicle multibody models in rigid railway tracks. The wheel–rail contact, independently of the rolling contact model used, is either handled online or via lookup tables. This traditional approach disregards the coupling effects between the railway vehicle dynamics and the railway track flexibility. In this work the assumption of rigidity of the railway track is relaxed and a finite element model of the complete track, i.e. rails, pads, sleepers, ballast and infrastructure, is used to represent the track geometry and flexibility. A rail–wheel contact model that evaluates the contact conditions and forces is used online. The dynamics of the railway vehicle is described using a multibody methodology while the track structure is described using a finite element approach. Due to the fact that not only the multibody and the finite element dynamic analysis use different integration algorithms but also because the vehicle and track models are simulated in different, codes a co-simulation procedure is proposed and demonstrated to address the coupled dynamics of the system. This approach allows us to analyze the vehicle dynamics in a flexible track with a general geometry modeled with finite elements, i.e. including curvature, cant, vertical slopes and irregularities, which is another novel contribution. The methodology proposed in this work is demonstrated in an application, in which the railway vehicle–track interaction shows the influence of the vehicle dynamics on the track dynamics and vice versa.

Low Speed Longitudinal Control Algorithms for Automated Vehicles in Simulation and Real Platforms

Advanced Driver Assistance Systems (ADAS) acting over throttle and brake are already available in level 2 automated vehicles. In order to increase the level of automation new systems need to be tested in an extensive set of complex scenarios, ensuring safety under all circumstances. Validation of these systems using real vehicles presents important drawbacks: the time needed to drive millions of kilometers, the risk associated with some situations, and the high cost involved. Simulation platforms emerge as a feasible solution. Therefore, robust and reliable virtual environments to test automated driving maneuvers and control techniques are needed. In that sense, this paper presents a use case where three longitudinal low speed control techniques are designed, tuned, and validated using an in-house simulation framework and later applied in a real vehicle. Control algorithms include a classical PID, an adaptive network fuzzy inference system (ANFIS), and a Model Predictive Control (MPC). The simulated dynamics are calculated using a multibody vehicle model. In addition, longitudinal actuators of a Renault Twizy are characterized through empirical tests. A comparative analysis of results between simulated and real platform shows the effectiveness of the proposed framework for designing and validating longitudinal controllers for real automated vehicles.

A combined numerical/experimental prediction method for urban railway vibration

Railway-induced ground vibrations can cause negative effects to people/structures located in urban areas. One of the main sources of these vibrations is from the large vehicle forces generated when train wheels impact local defects (e.g. switches/crossings). The sole use of traditional in-field transfer-mobility approaches is well suited for plain-line assessments, however is more challenging when discontinuities are present, due to the generation of large magnitude impact forces. This paper presents a hybrid experimental-numerical approach that can predict ground-borne vibration levels in the presence of a variety of railroad artefacts such as transition zones, switches, crossings and rail joints on existing networks. Firstly, the experimental procedure is described, which consists of multiple single source transfer mobilities to determine the transmission characteristics between rail and nearby structures. This is then coupled with a combined multibody vehicle and track numerical model, which is capable of simulating vibration generation in the presence of railway discontinuities. The resulting model is advantageous over alternative approaches because it can account for complex railway discontinuities, while at the same time incorporating the large uncertainties associated with different soil configurations. It is used to analyse a case study, where it is shown that vibration levels are strongly dependent on vehicle speed, defect type and defect size.

Estimation of Road Profile with Multibody Vehicle Model Considering Longitudinal Tire Force

Estimation of Road Profile with Multibody Vehicle Model Considering Longitudinal Tire Force

An efficient contact analysis method between the carbody and the railway structures using a multi body dynamics

In this study, we have constructed an efficient contact model to express the contact phenomenon between the vehicle and the railway structure during a huge earthquake. In this method, contact sensing points are set on a multi-body vehicle model and contact surfaces are defined on railway structures FEM models. The dynamic interaction force is calculated by the penalty method. In addition, we have incorporated the model into the numerical analytical program DIASTARS III that is able to express the railway vehicle behavior before and after derailment. Finally, to validate the proposed model, we have conducted a trial analysis that the carbody contacted with the structure after derailment during the earthquake.

High fidelity quasi steady-state aerodynamic model effects on race vehicle performance predictions using multi-body simulation

ABSTRACTWe described in this paper the development of a high fidelity vehicle aerodynamic model to fit wind tunnel test data over a wide range of vehicle orientations. We also present a comparison between the effects of this proposed model and a conventional quasi steady-state aerodynamic model on race vehicle simulation results. This is done by implementing both of these models independently in multi-body quasi steady-state simulations to determine the effects of the high fidelity aerodynamic model on race vehicle performance metrics. The quasi steady state vehicle simulation is developed with a multi-body NASCAR Truck vehicle model, and simulations are conducted for three different types of NASCAR race tracks, a short track, a one and a half mile intermediate track, and a higher speed, two mile intermediate race track. For each track simulation, the effects of the aerodynamic model on handling, maximum corner speed, and drive force metrics are analysed. The accuracy of the high-fidelity model is shown to reduce the aerodynamic model error relative to the conventional aerodynamic model, and the increased accuracy of the high fidelity aerodynamic model is found to have realisable effects on the performance metric predictions on the intermediate tracks resulting from the quasi steady-state simulation.

Optimisation of driver actions in RWD race car including tyre thermodynamics

ABSTRACTThe paper presents an innovative method for a lap time minimisation by using genetic algorithms for a multi objective optimisation of a race driver–vehicle model. The decision variables consist of 16 parameters responsible for actions of a professional driver (e.g. time traces for brake, accelerator and steering wheel) on a race track part with RH corner. Purpose-built, high fidelity, multibody vehicle model (called ‘miMa’) is described by 30 generalised coordinates and 440 parameters, crucial in motorsport. Focus is put on modelling of the tyre tread thermodynamics and its influence on race vehicle dynamics. Numerical example considers a Rear Wheel Drive BMW E36 prepared for track day events. In order to improve the section lap time (by 5%) and corner exit velocity (by 4%) a few different driving strategies are found depending on thermal conditions of semi-slick tyres. The process of the race driver adaptation to initially cold or hot tyres is explained.

Dynamic response of high speed vehicles and sustaining curved bridges under conditions of resonance

This paper examines the dynamic response of vehicle(s) moving at high speeds and the sustaining horizontally curved (simple, continuous or multi-unit) bridges, when each subsystem is set into resonance. The bridge is simulated by finite elements and each vehicle as a multibody system. The coupling contact forces, between the vehicle and the bridge, are derived by adopting a rigid contact assumption. Key feature of the present study is the simulation of the three-dimensional (3D) dynamics of a vehicle running over a horizontally curved path. This simulation allows the examination of deformation modes of the 3D multibody vehicle model (e.g. related to lateral-rolling and yawing degrees of freedom) for the first time. In all cases, the numerical results agree well with pertinent analytical solutions. From the parametric study, the followings are observed: (1) The impact factors show the same pattern for the vertical and the radial directions. (2) The suspension damping can alleviate the resonance response of the car body even when the vehicle’s resonance condition is met. (3) The feedback effect of the bridge’s resonance to the vehicle response is large, but the vehicle’s resonance effect on the bridge response is quite small, especially along the vertical direction. (4) No resonance of the middle span of the continuous bridge occurs for the second mode in the vertical and the radial directions. (5) The increase in the number of spans results in both smaller displacement and lower impact factor.

An efficient methodology for simulating roll dynamics of a tank vehicle coupled with transient fluid slosh

An efficient methodology is proposed for simulation of roll dynamics of a tank vehicle system coupled with transient hydrodynamic forces due to fluid slosh. The transient fluid slosh in a horizontal cylindrical tank is analytically modeled considering simultaneous lateral, vertical and roll excitations assuming potential flows and a linearized free-surface boundary condition. For this purpose, the fluid domain in the Cartesian coordinate system is transformed to the bipolar coordinates, where the Laplace equation could be solved using separation of variables. The resulting hydrodynamic pressure, free-surface elevation and slosh force and roll moment are formulated in the tank-fixed coordinate system. The transient fluid slosh model is subsequently integrated to a dynamic roll plane model of a tank vehicle combination to investigate the effect of transient liquid slosh on the roll stability of the vehicle during steady-turning as well as path-change maneuvers. The analyses are performed for different fluid fill heights considering both variable and constant cargo load conditions. The results suggest that the roll stability of tank vehicles can be efficiently analyzed using the coupled linear slosh and multi-body vehicle models with significantly lower computational effort than the methods employing computational fluid dynamic fluid slosh models.

マルチボディ車両モデルを用いた並列計算によるリアルタイム解析

マルチボディ車両モデルを用いた並列計算によるリアルタイム解析

A hierarchical integrated chassis control strategy based on wheel force feedback

The motivation to investigate a novel integrated chassis control (ICC) strategy emerges from recent advances in on-board force transducers. This study proposes a novel hierarchical framework adopting feedback control on tyre force level, and an on-target high level control algorithm including Force Reference Generator and allocation strategy to supervise front steering and braking subsystems. In the proposed method, force reference is generated regarding linear vehicle behaviour and guaranteed to be achievable, bounded by tyre grip limit. Allocation strategy tracks force reference and penalises undesired vehicle body motion, capturing significantly faster dynamics. In order to address the non-linearities and uncertainties of the vehicle model, a modified model reference adaptive control (MRAC) scheme is used, which both stabilises the lateral dynamics and maintains maximum lateral performance. The proposed method is validated and evaluated on a multi-body vehicle model simulation.

Hydrodynamics study of a BCF mode bioinspired robotic-fish underwater vehicle using Lighthill’s slender body model

This paper investigates the hydrodynamic characteristics of the rectilinear motion of a robotic fish underwater vehicle. This 2-joint, 3-link multibody vehicle model is biologically inspired by a body caudal fin carangiform fish propulsion mechanism. Navier–Stokes equations are used to compute the unsteady flow fields generated due to the interaction between the vehicle and the surrounding incompressible and Newtonian fluid (water) environment. The NACA 0014 airfoil aerodynamic profile has been designed to boost the swimming efficiency by reducing drag as the vehicle undergoes an undulatory/oscillatory motion. Using the Lighthill slender body model, a traveling wave mathematical function is defined to undulate the robotic fish posterior (caudal) region while the motion tracking is carried out by dynamic meshing technique. The results obtained show that though the net lift force approaches to zero, the net thrust or negative drag coefficient maintains a finite value dependent on kinematic parameters like tail beat frequency (TBF) and amplitude span (AS) at a given propulsive wavelength and the forward velocity of the vehicle. The results reveal the effects of TBF and AS on the coefficient of drag friction and the thrust force. Drag coefficients obtained from the simulations are compared and validated with the experimental results. The hydrodynamic results are found to be similar to the kinematic study results and suggest that TBF and AS play the most effective roles in the bioinspired propulsion technique. Relation of these parameters with propelling thrust force and forward velocity is also in conjunction over a given range of TBF and AS values.

Railway ground vibrations induced by wheel and rail singular defects

Railway local irregularities are a growing source of ground-borne vibration and can cause negative environmental impacts, particularly in urban areas. Therefore, this paper analyses the effect of railway track singular defects (discontinuities) on ground vibration generation and propagation. A vehicle/track/soil numerical railway model is presented, capable of accurately predicting vibration levels. The prediction model is composed of a multibody vehicle model, a flexible track model and a finite/infinite element soil model. Firstly, analysis is undertaken to assess the ability of wheel/rail contact models to accurately simulate the force generation at the wheel/rail contact, in the presence of a singular defect. It is found that, although linear contact models are sufficient for modelling ground vibration on smooth tracks, when singular defects are present higher accuracy wheel/rail models are required. Furthermore, it is found that the variation in wheel/rail force during the singular defect contact depends on the track flexibility, and thus requires a fully coupled vehicle/track/foundation model. Next, a parametric study of ground vibrations generated by singular rail and wheel defects is undertaken. Six shapes of discontinuity are modelled, representing various defect types such as transition zones, switches, crossings, rail joints and wheel flats. The vehicle is modelled as an AM96 train set and it is found that ground vibration levels are highly sensitive to defect height, length and shape.

An Efficient Minimum-Time Trajectory Generation Strategy for Two-Track Car Vehicles

In this paper, we propose a novel approach to compute minimum-time trajectories for a two-track car model, including tires and (quasi-static) longitudinal and lateral load transfer. Given the car model and a planar track, including lane boundaries, our goal is to find a trajectory of the car minimizing the traveling time subject to steering and tire limits. Moreover, we enforce normal force constraints to avoid wheel liftoff. Based on a projection operator nonlinear optimal control technique, we propose a minimum-time trajectory generation strategy to compute the fastest car trajectory. Numerical computations are presented on two testing scenarios, a 90° turn and a real testing track. The computations allow us to both demonstrate the efficiency and accuracy of the proposed approach and highlight important features of the minimum-time trajectories. Finally, we integrate our strategy into a commercial vehicle dynamics software, thus computing minimum-time trajectories for a complex multibody vehicle model. The matching between the predicted trajectory and the one of the commercial toolbox further highlights the effectiveness of the proposed methodology.

Validation of a Real-Time Multibody Model for an X-by-Wire Vehicle Prototype Through Field Testing

This research focuses on the experimental validation of a real-time vehicle multibody (MB) model whose bodies are considered rigid. For this purpose, a vehicle prototype has been built and automated in order to repeat reference maneuvers. Numerous sensors on the prototype gather the most relevant magnitudes of the vehicle motion. Two low speed maneuvers involving the longitudinal and lateral vehicle dynamics have been repeated multiple times in a test area. Then, a real-time MB model of the vehicle prototype has been self-developed as well as a simulation environment that includes a true graphical environment, a true road profile, and collision detection. Subsystems like brakes and tires have also been modeled. Both test maneuvers have been simulated with the MB model in the simulation environment using inputs measured experimentally. Selected simulation variables have been compared to their experimental counterparts provided with a confidence interval (IC) that characterizes the field testing (FT) process errors. The results of the comparisons show good correlation between simulation predictions and experimental data, thus allowing to extract useful guidelines to build accurate real-time vehicle MB models. In this way, the present work aims to contribute to the scarce literature on vehicle complete validation studies.

Improvement in the dynamic responses of the semiempirical vehicle model using the Maxwell force model for the suspension forces

A multi-body vehicle model is more accurate than a lumped-mass model; however, it usually requires a cumbersome process to obtain accurate data for compliant elements such as bushings. To avoid this complex process associated with bushings or kinematic linkages, a semiempirical vehicle model was developed by switching the suspension characteristics to measured kinematic and compliance data. In a semiempirical vehicle model, it is assumed that the inertia effects in the suspension subsystem are ignored by replacing components of the suspension system with massless links. Although this semiempirical vehicle model is simple, it sometimes degrades the accuracy in the dynamic responses compared with those of the multi-body vehicle model. Thus, it is necessary to include the dynamic characteristics of the suspension in an semiempirical vehicle model to increase its accuracy. In this paper, a new technique is proposed that considers the dynamic effect of the suspension system in an semiempirical vehicle model by using the Maxwell force model. By comparing the vertical acceleration with that obtained by the proposed method, the dynamic responses with the semiempirical vehicle model become much closer to those of the multi-body vehicle model. The results show that the force with respect to the suspension’s motion has a strong effect on the dynamic responses, and this relationship becomes important to improve the accuracy of the semiempirical vehicle model.

Robust cascaded automatic cruise control of electric vehicles

SummaryThis article focuses on automatic cruise control for electrically driven vehicles. The objective is to track a given vehicle‐velocity profile. For this type of application, the so‐called wheel slip plays a key role, as it is a measure for the force transmitted from the wheel to the road. Conventional wheel‐ slip controllers are usually activated if the absolute value of the slip exceeds pre‐assumed thresholds. Furthermore, it is distinguished between a braking and acceleration maneuver using separately designed and implemented controllers. In contrast, the proposed concept requires neither an activation strategy for the slip controller nor a distinction between braking and acceleration. The cascaded control structure is based upon adaptive‐gains super twisting sliding‐mode algorithm, and the friction force estimator is realized as a second‐order sliding‐mode observer with constant gains. The effectiveness and robustness of the proposed concept are demonstrated in numerical simulations using a complex multibody vehicle model. Copyright © 2015 John Wiley & Sons, Ltd.