Multibody Vehicle Research Articles

Real-Time Modeling of Vehicle’s Longitudinal-Vertical Dynamics in ADAS Applications

The selection of an appropriate method for modeling vehicle dynamics heavily depends on the application. Due to the absence of human intervention, the demand for an accurate and real-time model of vehicle dynamics for intelligent control increases for autonomous vehicles. This paper develops a multibody vehicle model for longitudinal-vertical dynamics applicable to advanced driver assistance (ADAS) applications. The dynamic properties of the chassis, suspension, and tires are considered and modeled, which results in accurate vehicle dynamics and states. Unlike the vehicle dynamics models built into commercial software packages, such as ADAMS and CarSim, the proposed nonlinear dynamics model poses the equations of motion using a subset of relative coordinates. Therefore, the real-time simulation is conducted to improve riding performance and transportation safety. First, a vehicle system is modeled using a semi-recursive multibody dynamics formulation, and the vehicle kinematics and dynamics are accurately calculated using the system tree-topology. Second, a fork-arm removal technique based on the rod-removal technique is proposed to reduce the number of bodies, relative coordinates, and equations constrained by loop-closure. This increase the computational efficiency even further. Third, the dynamic simulations of the vehicle are performed on bumpy and sloping roads. The accuracy and efficiency of the numerical results are compared to the reference data. The comparative results demonstrate that the proposed vehicle model is effective. This efficient model can be utilized for the intelligent control of vehicle ADAS applications, such as forward collision avoidance, adaptive cruise control, and platooning.

Phase plane analysis applied to non-explicit multibody vehicle models

A new methodology for constructing stability maps (phase-plane analysis) is presented and validated for application to complex multibody vehicle models implemented in Multibody Dynamics simulation software (Adams®). Traditional methodologies are developed to be applied to explicit mathematical models. Given the complexity of some special multibody systems, particularly in vehicle dynamics, simplifications are needed to apply this stability analysis technique. The main limitation when using simplified models is the need to neglect components which could have a significant influence on the dynamic behavior of the system and therefore on its stability. In the proposed methodology it is not necessary to have access to explicit mathematical models of multibody systems. Thus, the stability map of a vehicle model can be constructed by considering highly nonlinear dynamic elements, such as tires and silent-blocks components, modeled using the nonlinear finite element technique.

Design and safety analysis of a 11-Waggon consist for transporting rails

ABSTRACT A special case study of a rail transport consist comprised of 11 wagons on three-piece bogies was carried out using advanced multi-body vehicle simulations to evaluate if the safety and stability of the wagons would be compromised by loading 39 continuous welded rails on the wagon decks. Each rail was 139 m long and laterally fastened to the wagon decks. The wagon model components, including a car body, two bolsters, 4 sideframes and 4 wheelsets, were connected by non-linear spring and damping elements. A non-linear coupler was used to connect the adjacent wagon models. A twist simulation for a single wagon model was conducted and the results were compared with experimental data for validation. The lateral stability analysis found that the lowest critical hunting speed was 90 km/h for the empty wagon model, which satisfies the current operational speed range from 0 to 70 km/h. Safety simulations were conducted on the curved track geometry modelled from the actual track alignment and included FRA Class 4 track irregularities. The safety simulation results indicated that the 11-wagon consist performed within the maximum safety criteria limits as stipulated in the AS7509:2017 standard.

An efficient prediction model for vibrations induced by underground railway traffic and experimental validation

This study proposes an efficient prediction model for the vibration generated by underground railways. The proposed model is based on an analytical approach for a tunnel in a horizontally multi-layered half-space, showing the advantage of high computational efficiency and accuracy. Three alternative modelling strategies regarding hypotheses about the cross-section behavior of the slab and the connection condition between the slab and tunnel are introduced. A multi-body vehicle model is subsequently coupled with the track-tunnel-ground system in the moving frame of reference to determine the train-induced vibration. The predicted vibrations on the track, tunnel, and ground surface induced by the passage of trains are compared with the measured vibrations from an underground railway line in London from the literature. The predicted results for the double-beam track model with uniform support and the continuum track model exhibit a good agreement with the site measurements. The cross-section deformation of the track can be ignored and has little influence on the responses of the tunnel and ground. However, the assumption of the one-line connection between the slab and tunnel results in an overestimation of the track vibration, up to 20 dB, and an underestimation of the tunnel and ground vibration, up to 10 dB.

A Screw-Axis Approach to the Stability of Two-Wheeled Vehicles

The stability of two-wheeled vehicles is predominantly characterized by the well-known weave and wobble vibration modes, which have been extensively investigated in the literature, mainly in terms of their frequencies and damping ratios. In this work the focus is towards their mode shapes, which are investigated using the screw-axis (also called Mozzi-axis), instead of the classic compass diagrams, for a better understanding of their three-dimensional patterns. The analysis is then carried out using the velocity centres for a characterization from the top, rear and side view of the vehicle. The multibody vehicle model employed for the numerical analysis is built in Adams. The dataset resembles that of a 250cc sport motorcycle, and has been derived from laboratory tests. The stability analysis is carried out in the frequency domain. It is found that, depending on the selected plane for the projection of the three-dimensional vibration motion, the trajectories of the velocity centres of the weave and wobble can cross either aft or fore the centre of mass, which has been associated to the under- and over-steering behaviour in the literature.

Numerical and experimental investigation of the wheel/rail interaction and dynamics for a high-speed gauge-changeable railway vehicle

For a high-speed rail vehicle with gauge-changeable wheelsets, wheel/rail interactions and vehicle dynamics were numerically and experimentally studied within 600 km/h. Matching among four treads, three rail profiles, two gauges, and two rail cants are analysed by examining the wheelset conicity, contact points distribution, and stress. It shows that the conicities of the S1002 and LMA become smaller than the permitted minimum when rail cant 1/20 is used instead of 1/40 when matching with any of the three rail profiles. The conicity of S1002 decreases by up to 95% while that of LMA drops by about 30%. Whereas the RUS and LMB10 are compatible with two cants. Worn treads are more sensitive to the rail cant than new ones. Wheelback distance error leads to a conicity change, especially for worn profiles. A multi-body vehicle system dynamics analysis indicates that a 0.6 mm wheel-axle clearance leads to running instability at low speeds, but will not have an obvious effect on running safety and ride comfort. The vehicle dynamics behaviour on the standard- and broad-gauge tracks shows a slight difference. This has been validated through lab tests performed on a full-scale roller rig.

The Effect of Vehicle and Road Conditions on Rollover of Commercial Heavy Vehicles during Cornering: A Simulation Approach

Heavy vehicles make up a relatively small percentage of traffic volume on Malaysian roads compared to other vehicle types. However, heavy vehicles have been reported to be involved in 30,000–40,000 accidents yearly and caused significantly more fatalities. Rollover accidents may also incur cargo damages and cause environmental or human disasters for vehicles that carry hazardous cargos if these contents are spilled. Thus, in this paper, a comprehensive study was conducted to investigate the effects of vehicle and road conditions on rollover of commercial heavy vehicles during cornering at curved road sections. Vehicle conditions include the heavy vehicle class (based on the axle number and vehicle type), speed and gross vehicle weight, while road conditions include the cornering radius and coefficient of friction values. In order to reduce the risks involved in usage of actual heavy vehicles in crash experiments, a simulation approach using a multi-body vehicle dynamic software was applied in this study, where the verified virtual heavy vehicle model was simulated and the output results were extracted and analyzed. The results showed that a maximum of 40% and a minimum of 23% from the total number of simulations resulted in an unsafe condition (indicated as failed) during the simulations. From the unsafe conditions, two types of rollover accidents could be identified, which were un-tripped and tripped rollovers. The heavy vehicle speed was also found to have a strong correlation to the lateral acceleration (to cause a rollover), followed by gross vehicle weight, coefficient of friction and cornering radius, respectively.

Performance of leaf spring suspended axles in model approaches of different complexities

Axles with leaf spring suspension systems are still a popular choice in many commercial vehicles. However, leaf springs are not in perfect conformity to standard multibody vehicle models because they combine guidance and suspension in one single element. Combining standard multibody vehicle models with sophisticated finite element leaf spring models results in rather complex and computing time-consuming solutions. Purely kinematic models, defined by lookup tables or the design kinematics approach, cover only some but not all features of the leaf spring suspension. As shown here, the five-link model, which incorporates a quasi-static solution of the leaf spring compliance, provides a very practical model. It is comparatively lean and provides results of sufficient accuracy in the whole application range.

Asymptotic tracking position control with active oscillation damping of a multibody Mars vehicle using two artificial augmentation approaches

The Valles Marineris Explorer Cooperative Swarm navigation, Mission and Control research project aims to explore the Valles Marineris canyon system on Mars with, among others, multibody rotary-wing unmanned aerial vehicles (UAVs) comprising of a hexrotor system and a helium-filled balloon being attached to it by means of a rope. In this paper, we develop a high-fidelity closed-loop control system in MATLAB® and Simulink™ to present the application of an adequate flight controller guaranteeing (1) asymptotic tracking position control of the multibody flight system, (2) suppression of the balloon’s swinging motion in forward flight case, and (3) stabilization of the rope angle around its equilibrium for steady-state conditions. Applying feedback linearization for the outer loop and analytical backstepping for the inner loop of a nonlinear cascaded control design model of the hexrotor system, we propose an extension of the baseline flight controller by two artificial augmentation approaches to cope with the balloon dynamics. Basically, by utilizing oscillation damping feedbacks of the uncertain plant which are applied as additional commands to either the inner or the outer loop’s reference model. Simulation results are presented for an eight-shaped flight maneuver at the bottom of Valles Marineris proving that the augmentation units increase the flight controller capabilities to suppress modeling errors artificially—without changing the baseline control laws. The augmentation units actively damp the balloon motion in the forward flight case for non-steady-state conditions to counteract the rope oscillations and finally stabilize the rope angle around its equilibrium, so that the Mars vehicle is able to reach a steady-state in position when its extraterrestrial mission profile is successfully completed.

Experimental-Numerical Study of Indexation of Scenic Road Vertical Alignment in China

The vertical alignment design method of road in scenic spots does not evolve enough along the vehicle’s rapid variation. Values of the maximum longitudinal slope (MLS) and longest slope length (LSL) applicable to scenic roads used by the environmental-friendly vehicle (EFV) are not provided. To compensate for this shortage, a multibody vehicle dynamic model in uphill traving is built, providing the static equilibrium state and dynamic balancing process of a typical vehicle. MLS and LSL values in scenic roads are obtained based on this model through numerical simulation, considering typical EFV, maximum velocity loss (MVL), and ideal velocity loss (IVL). Field experiments for verifying the results are also carried out in Huashan Mountain, Cuihua Mountain National Park, and Taiping Forest Park, using two EFV types. MLS and LSL values in scenic roads applicable to EFV obtained in this research vary from 7.8% to 10.2% and 200 to 955 m, respectively, and both are larger than the corresponding values in current criteria. According to verification results, relative errors of climbing velocity vary from 0.0104 to 0.0205, showing the dynamic model’s accuracy and further proving the practicality of MLS and LSL values obtained. The results obtained in this research lay a foundation for establishing the scenic-road vertical alignment design method.

A roll frequency design method for underframe equipment of a high-speed railway vehicle for elastic vibration reduction

Field measurements of the elastic vibration of a car body (CB) and its coupling with the underframe equipment vibration were carried out for a high-speed railway vehicle, it was found that there was a significant increase of CB elastic vibration when passing a particular location and the equipment absorbed little of the CB vertical elastic vibration. In order to reduce the CB elastic vibration, the suspension parameters of the underframe equipment in the roll direction were optimized. A simplified vehicle model including the roll motion of the CB and the underframe equipment was built for theoretical study, in which the modal displacement of the CB floor corresponding to the CB diamond mode was extracted from finite-element analysis. Based on the frequency response analysis, the frequency range in which the elastic vibration was magnified was obtained. By increasing the roll moment of inertia of the equipment and decreasing lateral distance between the suspension points, the roll frequency of the underframe equipment was decreased and the CB vibration was reduced. To verify the analysis, a three-dimensional multi-body dynamic railway vehicle system was established in SIMPACK. The optimized parameters were validated and shown to be effective for absorbing the CB diamond-mode elastic vibration.

A Comparison of Trajectory Planning and Control Frameworks for Cooperative Autonomous Driving

Abstract This work considers the cooperative trajectory-planning problem along a double lane change scenario for autonomous driving. In this paper, we develop two frameworks to solve this problem based on distributed model predictive control (MPC). The first approach solves a single nonlinear MPC problem. The general idea is to introduce a collision cost function in the optimization problem at the planning task to achieve a smooth and bounded collision function, and thus to prevent the need to implement tight hard constraints. The second method uses a hierarchical scheme with two main units: a trajectory-planning layer based on mixed-integer quadratic program (MIQP) computes an on-line collision-free trajectory using simplified motion dynamics, and a tracking controller unit to follow the trajectory from the higher level using the nonlinear vehicle model. Connected and automated vehicles (CAVs) sharing their planned trajectories lay the foundation of the cooperative behavior. In the tests and evaluation of the proposed methodologies, matlab-carsim cosimulation is utilized. carsim provides the high-fidelity model for the multibody vehicle dynamics. matlab-carsim conjoint simulation experiments compare both approaches for a cooperative double lane change maneuver of two vehicles moving along a one-way three-lane road with obstacles.

Building a novel dynamics rollover model for critical instability state analysis of articulated multibody vehicles

Articulated wheel loaders in construction industry have poor lateral stability and high rate of accident due to their multibody structure and uneven working fields. In order to realise early rollover warning and active control, it is necessary to explore the mechanism of instability and the change rules of dynamics parameters. This paper proposes a novel dynamics rollover model with 6 degrees of freedom (DOF) for modelling the instability process of an articulated wheel loader. The proposed rollover model is compared with a virtual prototype and a 1:5 scale-down physical prototype under four typical working conditions to verify its reliability, and its accuracy is investigated via a rotation motion under a constant steering angle under the critical state of rollover. Finally, the dynamics rollover model is used to investigate the influence of different kinematic parameters on lateral stability of an articulated wheel loader with steady-state margin angle (SSMA) as stability index.

A robust non-iterative algorithm for multi-body dynamics and vehicle–structure interaction analysis

ABSTRACT This paper presents a novel, non-iterative, general formulation for the transient analysis of interacting elastodynamic systems in contact that may exhibit relative motion with respect to each other. The overall system consists of a collection of individual structures (subsystems). Each of the structure is solved at first independently of the others assuming no interactive contact forces exist. The solution of the overall system is obtained by enforcing compatibility of displacements and dynamic force equilibrium at the interface boundaries using dynamic ‘mortar elements’. The proposed method obtains the solution in a time marching fashion without the need for iterations. The proposed coupling algorithm is versatile and is designed to accommodate different numerical time integration schemes and different mathematical model solving techniques. The proposed method is computationally advantageous to the substructure methods reported in the literature, which usually use the iterative procedure. It is also computationally efficient to the methods using the monolithic approach, since smaller systems are solved at a time and there is no need to update structural matrices at every time step. The proposed method is verified through comparisons with results reported in the literature. The verification examples demonstrate the accuracy and the computational efficiency of the proposed algorithm.

Research on Cab Vibration Control Based on Parameter Hierarchical Interaction Model

The vibration level of a cab affects the passenger’s ride comfort and safety significantly. It is of great importance to control the vibration level of cabs under various driving conditions. The associated vibration transfer paths of cabs are studied by using a hierarchical analysis method of a parameter index. The multiobjective design analysis is carried out by using the multiparameter joint optimisation design. Further, the optimal control of the cab vibration level is obtained from a full-condition simulation environment. Additionally, a multibody vehicle model is established. The simulation analysis under multiple working conditions is conducted. The optimal parameter distribution of the cab mounting structure was established by analysing the influence of the design parameters and experimental verification. This greatly improves the comfort of the cab.

Grousers Effect in Tracked Vehicle Multibody Dynamics with Deformable Terrain Contact Model

In this work, a multibody model of a small size farming tracked vehicle is shown. Detailed models of each track were coupled with the rigid body model of the vehicle. To describe the interaction between the track and the ground in case of deformable soil, custom defined forces were applied on each link of the track model. Their definition derived from deformable soil mechanics equations implemented with a specifically designed routine within the multibody code. According to the proposed model, it is assumed that the main terrain deformation is concentrated around the vehicle tracks elements. The custom defined forces included also the effects of the track grousers which strongly affect the traction availability for the vehicle. A passive soil failure model was considered to describe the terrain behaviour subjected to the grousers action. A so developed model in a multibody code can investigate vehicle performance and limit operating conditions related to the vehicle and soil characteristics. In this work, particular attention was focused on the results in terms of traction force, slip and sinkage on different types of terrain. Tests performed in the multibody environment show how the proposed model is able to obtain tractive performance similar to equivalent analytical solutions and how the grousers improve the availability of tractive force for certain type of soil characteristics.

Parallelized Multiscale Off-Road Vehicle Mobility Simulation Algorithm and Full-Scale Vehicle Validation

Abstract In this work, a scalable parallel computing scheme for the hierarchical multiscale off-road vehicle mobility simulation capability is developed with the hybrid message passing interface (MPI)/OpenMP framework, and it is validated against full-scale vehicle test data. While the hierarchical multiscale modeling approach has been introduced to high-fidelity off-road mobility simulations to eliminate limitations of existing single-scale deformable terrain models, computational complexities associated with the large dimensionality of multibody vehicle equations, involving nonlinear finite element tires and multiscale terrain models, need to be addressed for use in full-scale vehicle mobility predictions. To this end, a co-simulation framework for the multiscale off-road vehicle mobility model is proposed by exploiting the moving soil patch technique. This allows for systematically extracting four moving soil patches for four tires in a vehicle model from the deformable terrain domain, and time integrations of the four tire–soil subsystems are performed concurrently to enable computational speedup. Furthermore, an automated updating scheme for multiscale moving soil patches for a full vehicle model is developed, considering the multipass effect in various vehicle maneuvering scenarios. To demonstrate the off-road mobility prediction capability using the proposed parallelized multiscale vehicle–terrain interaction simulation algorithm, full-scale vehicle validation is presented for the vehicle drawbar pull as well as variable grade hill climb tests on soft soil.

Coupled dynamic analysis of low and medium speed maglev vehicle-bridge interaction using SIMPACK

The low- and medium-speed maglev vehicle generally operates on elevated bridges with a levitation gap of only 8--10 mm, which makes it very sensitive to the vehicle--bridge coupled vibration. To conduct the corresponding modeling and simulation with common dynamics tools, an equivalent processing of the levitation system is required. Using the dynamics software SIMPACK, this paper first introduces the methods of building the multi-body vehicle system, levitation control system and the elastic bridge, respectively, in the SIMPACK railway module, levitation control module and SIMBEAM elastomer module, thus providing a modeling idea for the simulation of the active levitation and operation of low- and medium-speed maglev vehicles through multi-span bridges. It then goes on to simulate and analyze the coupled vibration of a 160 km/h low- and medium-speed maglev vehicle passing through 25 m + 25 m double-span continuous bridges. The research results show that the modeling method introduced in this paper can simulate the low- and medium-speed maglev vehicle--bridge coupled vibration phenomenon, which can be affected significantly by the low-order frequency of the elastic bridge, and can also be intensified under the bridge end impact when the vehicle enters and leaves the bridge. As the running speed of the vehicle increases and the dynamic force increases, the vertical vibration amplitudes of the elastic bridge mid-span, the car body as well as the levitation frame approximate a linear fitting with the vehicle speed. The variation amplitudes of the levitation gap and of the electromagnet current approximate a quadratic fitting with the vehicle speed.

Vibro-Acoustic Response in Vehicle Interior and Exterior Using Multibody Dynamic Systems Due to Cleat Impacts

This paper presents the structural vibration and acoustic radiation of a multibody vehicle system in interior and exterior under cleat impact excitations. The entire structure model, which consists of a hyper-elastic tire, a 17-inch lightweight wheel, a rotatable hub, a high-strength knuckle, a control arm and a spring-damper suspension, is a quarter vehicle to simulate transient response when passing through a cleat. The normal acceleration of a vibrating structure surface is applied as an acoustic noise source. A structural-acoustic coupling is employed to consider the interactive effects of the coupled system. The influence of the structure-borne noise can be confirmed by the frequency-correlation analysis between vibration acceleration and acoustic pressure. A sound pressure level (SPL) for near-field radiation is calculated by the finite element method (FEM). In addition, acoustic characteristics such as sound intensity in the passenger cabin are calculated through the boundary element method (BEM). The cleat impact experiment in a hemi-anechoic chamber is presented and validated in detail.

Validation of a Real-Time Capable Multibody Vehicle Dynamics Formulation for Automotive Testing Frameworks Based on Simulation

The growing functionalities implemented on vehicles have increased the importance of simulation in the design process. This complexity is mainly driven by the introduction of electrified powertrains, Advanced Driver Assistance Systems (ADAS) and Automated Driving Systems (ADS). Additionally, the automotive industry must reduce development times and cost, while keeping flexible development capabilities and fulfilling demanding regulation standards for safety-critical systems. Existing testing frameworks based on simulation implement typically analytical models to ensure real-time performance, and provide limited flexibility to perform Hardware in the Loop (HiL) setup based tests. In this work a vehicle modelling approach which guarantees high accuracy and real-time capabilities is proposed. Moreover, the proposed approach is validated firstly with real vehicle data, demonstrating that it can fairly reproduce the behaviour of the vehicle tested; and secondly, in a HiL setup to demonstrate the real-time execution capabilities of the approach.