On the correlation between a 3D high-fidelity multi-body ...past.isma-isaac.be/downloads/isma2014/papers/isma2014_0671.pdf · concept design phase, leading to an improved initial

On the correlation between a 3D high-fidelity multi-body vehicle model and a 1D 15-DOFs vehicle concept model

2 Simulation Division – LMS, A Siemens Business Interleuvenlaan 68, 3001 Leuven, Belgium

Abstract The presented work focuses on the correlation between a 3D high-fidelity (hi-fi) multi-body vehicle model built within LMS Virtual.Lab Motion and a 1D vehicle concept model with 15 DOFs built within LMS Imagine.Lab AMESim for future real-time applications. The latter is a full vehicle concept model for longitudinal and lateral dynamics with only 15 DOFs that integrates several sub-systems (e.g. suspensions, steering system, tires, chassis), including also a more detailed modelling of the suspension system through kinematics look-up tables compared to other models proposed in literature. The correlation is based on a nominal parameterization of the 1D model in terms of masses, inertias, geometry, suspension parameters and kinematics, starting from the 3D multi-body model. The two vehicle models (3D detailed and 1D concept) are then compared through maneuvers for validation.

1 Introduction

Automotive suspensions have a primary role in the overall ride and handling performances of a passenger car. The main objectives of suspension systems consist in isolating the vehicle body from excitations due to road irregularities, providing good road holding performances, minimizing the rattle space and providing good handling performances [1,2]. Forces developed at the tires are transmitted through the suspensions into the chassis, whose characteristics strongly affect the dynamic response of the vehicle. In particular the main properties of the chassis are its mass and centre of gravity (CG) position, the bending and torsional stiffness, the wheel base and the wheel track. The importance of concept models in the automotive field is well known. Concept modelling techniques are widely used to evaluate the dynamic properties of suspension systems and their interaction with the chassis already at the very early stage of the design process of new vehicles, when detailed multibody models are not yet available [3]. This allows engineers to perform preliminary analysis and optimization studies in order to meet a set of performance and functional requirements. Concept models are used in this phase due to their low complexity (parametric approach) and computational efficiency as well as the possibility to investigate specific rather than global behaviours/performances. Suspension concept models mainly consist of very simplified models, which can be defined using only few physical data corresponding to the main design parameters of the suspension system. The influence of these parameters on the suspension performances can be easily and efficiently evaluated within the concept design phase, leading to an improved initial CAD model of the suspension assembly and enabling a fast convergence of the development cycle towards an optimal final chassis and suspension configuration.

S. Candreva1, D. Mundo1, M. Gubitosa2, A.Toso2

1 Department of Mechanical, Energy and Management Engineering, University of CalabriaPonte Pietro Bucci, 87036 Rende, Italye-mail: [email protected]

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Moreover, since the mechatronic content in current passenger cars is continuously increasing due to an extensive use of advanced driver assistance systems (ADAS), the current tendency in the automotive industry is to rely on the concept design phase also for early optimization and verification of the interaction between suspension, chassis and active control systems [4]. For this purpose, suspension and chassis concept models are provided with virtual sensors and actuators, simulating the hardware part of the ADAS, and used to test the control logics (e.g. ABS, ESP,…) implemented in the electronic control units (ECU) by means of both HIL and SIL simulations. Chassis and suspension models for the analysis of the vertical dynamics can be employed to assess the ability of the suspension to isolate the chassis from excitations due to road irregularities, its road holding performances and the required rattle space. These three basic functions are often conflicting with each other, thus requiring a careful optimization of the design parameters of the suspension, such as its stiffness and damping properties as well as the free length of the spring (suspension pre-load). The simplest model that can be used to characterize the vehicle vertical dynamics is the quarter car model [5]. The vertical displacements of the sprung and unsprung masses are the only two degrees of freedom considered in this model. Even if the 2 DOFs quarter car model is characterized by a very low complexity level, it can be used to assess the three basic suspension requirements previously described. The 4 DOFs half car model [1,6] is characterized by a sprung body of non-negligible longitudinal dimension, including inertia momentum along the pitch axis. The bounce and pitch movements of the chassis and the vertical displacements of the two unsprung masses are the 4 DOFs considered in this model. In order to analyse the ride behaviour of a passenger car equipped with independent suspensions, the 7 DOFs full-vehicle model is generally adopted [7]. The 7 DOFs retained in this model are the bounce, roll and pitch movements of the sprung mass and the vertical displacement of each of the four unsprung masses. For a preliminary analysis of the vehicle lateral behaviour during steady-state cornering, the so called bicycle model can be considered [5,8]. It is a simplified 2 DOFs model in which the two degrees of freedom retained are the yaw velocity and the chassis sideslip at the centre of gravity. This model is valid if the corner radius is considerably bigger than the vehicle wheel base and thus the difference in the steering angles between the outer and inner front wheels can be neglected. The suspension systems are not taken into account into this model, meaning that the suspension effects on cornering behaviour are not considered. The 2 DOFs bicycle model can be used for basic and preliminary performance analyses, such as the assessment of the understeer/oversteer properties of the vehicle. The 7 DOFs half car model in [9] can be used to assess the longitudinal dynamic behaviour of the vehicle. In this model kinematics look-up tables are used to relate spindle vertical displacement to its relative positioning and orientation with respect to the chassis, reproducing the five degrees of restraint (DOR) of the suspension’s linkage and uniquely determining the path of motion of the spindle with respect to the chassis [8]. The 15 DOFs full vehicle model in [9] can be used for handling analysis involving both the longitudinal and the lateral dynamics. It is composed by ten bodies, including also the steering rack. Also in this model each suspension is represented as a kinematic constraint imposing 5 DORs and the relative motion between spindle and chassis is modelled with a functional representation introduced by means of look-up tables. Compliance effects of the suspension (e.g. in the bushing connections of the links) can be also taken into account through proper elasto-kinematic look-up tables containing information about the axle compliance characteristics. The present work focuses the attention on this latter 1D vehicle concept model with 15 DOFs built in LMS Imagine.Lab AMESim, presenting its correlation with a 3D hi-fi multi-body vehicle model built in LMS Virtual.Lab Motion with the aim of future real-time applications. The correlation is based on a nominal parameterization of the 1D model in terms of masses, inertias, geometry, suspension parameters and kinematics extracted from the 3D multi-body model. The two vehicle models (3D detailed and 1D concept) are then compared through two open-loop maneuvers for validation. The results show a good agreement between the two models with only slight and in any case acceptable differences, considering the reduced complexity offered by the concept model. The rest of the paper is organized as follows. Section 2 presents the 15 DOFs full vehicle concept model available in LMS Imagine.Lab AMESim. Section 3 deals with suspensions kinematics characterization and nominal parameter extraction. Section 4 illustrates the correlation between the two models. Conclusions are given in Section 5.

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2 15 DOFs vehicle concept model in LMS Imagine.Lab AMESim

The 15 DOFs model shown in Figure 1 can be used for handling analysis involving both the longitudinal and the lateral dynamics. It is composed by ten bodies, which are the vehicle chassis, the 4 wheels, the 4 spindles and the steering rack. Each wheel is connected to the corresponding spindle by means of a revolute joint, while a prismatic joint along the lateral direction is used to restrict the relative motion of the steering rack body with respect to the chassis. As mentioned above, kinematics and compliances of each suspension are taken into account and modelled with a functional representation introduced by means of look-up tables.

Figure 1: 15 DOFs vehicle model for longitudinal dynamics [9].

As introduced in the previous section, the conceptual representation of the suspension system by means of kinematics and elasto-kinematics look-up tables is adopted in order to obtain reliable vehicle models even if characterized by a low complexity level. Kinematics and elasto-kinematics look-up tables have a key-role in the conceptual modelling of suspension systems [10,11]. Indeed, this can be easily understood by recognizing that two different suspension layout having the same component characteristics (i.e. equal tire properties, equal shock-absorber properties) may behave very differently in response to a given input. For example the response of a multilink suspension to a given road input can significantly differ from that of a MacPherson suspension mounting the same tire and shock-absorbers due to the different way how road loads are transmitted into the chassis via the suspension links. Another relevant factor, which is completely neglected in several concept models in literature (such as the quarter car), is the presence of the elastic bushings connections joining the suspension links to the chassis and to the knuckle. The global stiffness and damping properties of the suspension are greatly influenced by this elastic connections and this influence must be taken into account in order to reach a higher level of accuracy. The degrees of freedom retained in the considered vehicle concept model are the 6 DOFs of the chassis, the 4 relative vertical displacements of the spindles with respect to the body, the 4 rotations of the wheels around their spin axis and the lateral position of the steering rack with respect to the chassis. In order to extract the relative position and orientation of the spindle with respect to the chassis from the kinematic look-up tables, the relative vertical displacement of the opposite spindle must be also considered in addition to the relative vertical displacement of the current spindle. This is particularly important for solid axle suspensions, where the vertical motion of one wheel greatly influences the position and orientation of the opposite wheel on the same axle. Moreover, when the front spindles are considered, the lateral position of the steering rack must also be taken into account within the kinematics look-up tables to determine the influence of the steering system on the relative position and orientation of the front wheels with respect to the chassis. Due to compliance effects (e.g. in the bushing connections of the suspension’s links) the position and orientation of the spindle with respect to the vehicle body is also influenced by the loads acting on the wheel. This phenomenon is modelled by adding the elastic displacements and rotations of the spindle to the position and orientation computed by means of the kinematics look-up tables. In order to obtain the

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elastic displacements and rotations of the spindle, the loads acting on the wheel must be inserted into the above mentioned elasto-kinematic look-up tables. Kinematic parameters of interest are wheelbase variation x, track variation y, camber angle ε, toe angle δ and self-rotating angle η. Those parameters have to be defined as function of current spindle vertical displacement z and opposite spindle vertical displacement zopp for the rear axle, while the steering rack displacement YN has to be included for the front axle. Figure 2 shows a schematic representation of those kinematics parameters.

Figure 2: Kinematics parameters of the suspension systems.

3 Suspensions kinematics characterization and nominal parameter extraction

In Figure 3 the multi-body model used as reference model is shown. It is a BMW rear driven vehicle model with 132 DOFs, equipped with MacPherson suspension at front and multilink suspension at rear. The tire model adopted is TNO Magic Formula.

Figure 3: 3D hi-fi multi-body vehicle in LMS Virtual.Lab Motion.

In this work only the kinematics characterization of the suspensions is described (and taken into account) while compliances effects are neglected. This is because the values found for the compliance matrices to be implemented in the concept model were very low and thus not influencing the final results of the


simulations run to compare the concept model with the 3D model. Moreover, it heavily affected the computational time. In order to extract the kinematics relations between spindles and chassis, kinematics tests are run on the multi-body model. The vehicle body is clamped and only wheels and steering rack are able to move, in order to reproduce real K&C tests [12]. For the front axle, rack displacement and current spindle displacement are considered as input signals, neglecting the opposite spindle movement (that is zero). This is to simplify the kinematics look-up tables associated to the front suspension. In any case, it is justified by the fact that the suspension is of the independent type. The procedure implies to move the spindle up and down (complete stroke) for each rack position, meanwhile extracting the kinematics parameters x, y, ε, δ and η. Figure 4-a shows the signals used for the characterization of the front suspension. For the rear axle, current and opposite spindles displacements are considered. No simplification is made in this case although possible due to independent suspensions. Current spindle is moved up and down for each position of the opposite spindle to extract kinematics parameters. The tests are executed very slowly to avoid unwanted dynamics in the kinematics measurement. Figure 4-b shows the signals used for the characterization of the rear suspension. Both figures axes are normalised because of data confidentiality.

Figure 4: Signals for kinematics characterization of a) front suspension and b) rear suspension.

After the kinematics test is done, five look-up tables for each spindle are obtained. Figure 5 shows two examples of the kinematics tables extracted: track variation y as function of spindle vertical displacement z and steering rack movement YN for the front left suspension and camber angle ε as function of current and opposite spindle vertical displacements z and zopp. Figures axes are again normalised because of data confidentiality.

Figure 5: Example of kinematics tables: a) track variation at front left suspension and b) camber angle at

rear right suspension.


On top of the kinematics tables derived with the above described procedure, several other parameters have to be extracted from the multi-body model of the vehicle. In Figure 6 a schematic representation of the 15 DOFs vehicle concept model in LMS Imagine.Lab AMESim is shown. With reference to this model, hereafter the description of the model with the required parameters follows. The model is mainly composed by five parts:

1. chassis submodel: it contains mass and inertia properties of sprung, unsprung and rack bodies, the geometrical parameterization of the vehicle, such as CG position, spindles position and rack position, and the look-up tables for the kinematics relations between spindles and chassis. All the parameters are taken directly from the model in LMS Virtual.Lab Motion.

2. steering subsystem: it is a simplified representation of the complex steering system of the multi-body model, using only a stiff torsional spring and pinion-rack ratio extracted from LMS Virtual.Lab Motion.

3. front suspension subsystem: it is a simplified representation of the front suspension system of the vehicle, with bump and rebound elements, spring and damper components. The value of each parameter comes directly from LMS Virtual.Lab Motion.

4. rear suspension subsystem: similar to the front suspension subsystem. 5. tires subsystem: it is a simplified representation of tires behaviour. From top to bottom (and

marked in red in Figure 6), the first block takes into account the kinematics relations between the wheel centre and the tire-road contact point, the second one models tire belt and implements equations for camber and slip angles, the third one implements Pacejka tire equations in order to compute contact forces and to take into account the effects of the coupling between lateral and longitudinal forces. The last two blocks are road friction and weather (sub-)models. Tire subsystem uses the same parameters used by the TNO tire model adopted in the BMW vehicle model in LMS Virtual.Lab Motion.

Figure 6: 15 DOFs vehicle concept model plant in LMS Imagine.Lab AMESim.


Each of the five subsystems has been tested individually before assembling the whole model, in order to check the quality of the nominal parameterization. For instance, the kinematics test applied to the multi-body model in LMS Virtual.Lab Motion has been reproduced in the case of the 15 DOFs concept model in LMS Imagine.Lab AMESim to see whether the same results are obtained or not. Also in this case the body of the vehicle is clamped while spindles and steering rack are moved accordingly to the same signals used in the previous test (Figure 4). The comparison between the results obtained in the two different simulation environments is shown for two kinematics parameters in Figure 7. As an example, front left track variation and rear right toe angle during the test are shown. As usual, axes are normalised for data confidentiality. From figures a perfect match between curves can be appreciated.

Figure 7: Comparison between kinematics test in LMS Virtual.Lab Motion and LMS Imagine.Lab

AMESim. a) Front left track variation (current spindle and rack displacement as input) and b) rear right toe angle (current and opposite spindles displacements as input) during the test.

Other test examples to make a first check of the nominal parameterization quality are showed in normalised plots of Figure 8. In particular, comparisons between hi-fi multi-body model and concept model refer to chassis CG height from ground and front left suspension spring displacement in static condition (monitored for 50 s), and front left suspension spring displacement and rear left suspension spring force during the kinematics test. Also in this case a good match can be appreciated with some deviation only in the CG height.

Figure 8: Comparison between LMS Virtual.Lab Motion and LMS Imagine.Lab AMESim models. a) Chassis CG height from ground and b) front left suspension spring displacement in static condition. c)


Front left suspension spring displacement and d) rear left suspension spring force during the kinematics test.

4 Comparison through maneuvers

This section illustrates correlation results by comparison of the two models through different maneuvers. In particular, two open-loop maneuvers are considered in this study. The first one consists in the vehicle moving along a straight line while the second one is a step steer maneuver.

4.1 Straight line maneuver

This maneuver was used especially to check the capability of the parameterized vehicle to move along a straight line when a steering input of zero is provided. In this way it is possible to check the timeliness of the kinematics characterization of the suspensions. Indeed, if strange behaviour or exaggerated lateral drift occur it is quite possible that there is something wrong with the kinematics look-up tables. This maneuver is also appropriate to check the longitudinal load transfer (i.e. vertical forces on the tires) during acceleration phases. Figure 9 shows the driving torque provided at rear wheels of both models. The torque curve slowly reaches the value of 250 Nm after 30 s and then it is constant for 20 s.

Figure 9: Driving torque at rear wheels.

Figure 10 shows the comparison between the hi-fi multi-body model in LMS Virtual.Lab Motion and the 15 DOFs concept model in LMS Imagine.Lab AMESim with respect to the longitudinal and lateral position of the chassis CG.

Figure 10: Comparison between hi-fi multi-body model in LMS Virtual.Lab Motion and the 15 DOFs

concept model in LMS Imagine.Lab AMESim. a) CG longitudinal position and b) CG lateral position in the straight line maneuver.


From the figures, a good match can be observed. The two vehicle models travel the same distance and exhibit almost the same lateral drift during the 50 s maneuver. Biggest differences occur at the end of the simulation, when higher velocities (about 45 m/s) and thus instabilities are reached, accordingly with the previous torque curve. For this reason, it can be considered as a good result. In Figure 11 the comparison in terms of the vertical forces at the four tires is illustrated. Also in this case the correlation is quite good, with the concept model following in the right way the multi-body model.

Figure 11: Comparison between hi-fi multi-body model in LMS Virtual.Lab Motion and the 15 DOFs concept model in LMS Imagine.Lab AMESim. a) Vertical force at front left (FL); b) Vertical force at

front right (FR); c) Vertical force at rear left (RL); d) Vertical force at rear right (RR).

The concept model behaves quite well in this maneuver, accordingly to the hi-fi one. Moreover, the CPU time required for the simulation of the concept model was about 14.86 s against the 122 s for the multi-body model, remarking the computational effciency of concept modelling techniques.

4.2 Step steer maneuver

This maneuver was used to further compare the two models and check their correlation, considering also the lateral dynamics. Figure 12 shows driving torque and steering angle input signals used for this maneuver. The torque curve slowly reaches the value of 75 Nm after 30 s and then it is constant for 20 s. The steering angle is zero for 30 s and then reaches linearly a value around 30° in 10 s. It stays then constant for the last 10 s. So, this means that the vehicle will go straight for 30 s, approaching a curve of fixed radius after the steering angle reaches its final value. The maximum speed reached in this case is about 14 m/s.


Figure 12: a) Driving torque at rear wheels and b) steering wheel angle.

Figure 13 shows the comparison between the hi-fi multi-body model in LMS Virtual.Lab Motion and the 15 DOFs concept model in LMS Imagine.Lab AMESim with respect to the longitudinal and lateral position of the chassis CG.


concept model in LMS Imagine.Lab AMESim. a) CG longitudinal position, b) CG lateral position in the step steer maneuver.

Also in this case a good match between the two models can be appreciated, since only a slight oversteering of the concept model can be seen in the last part of the maneuver. Other comparisons are presented in next figures as examples. Figure 14 is related to chassis CG orientation while Figure 15 shows the comparison of longitudinal tire forces at front wheels and lateral forces at rear wheels. Also in this case a good match can be appreciated with only slight differences, which are in any case acceptable, considering the reduced complexity offered by the concept model: 14 s of CPU time against the 79 s required by the hi-fi multi-body model.


Figure 14: Comparison between hi-fi multi-body model in LMS Virtual.Lab Motion and the 15 DOFs concept model in LMS Imagine.Lab AMESim. a) CG roll, b) CG pitch and c) CG yaw in the step steer

maneuver.



concept model in LMS Imagine.Lab AMESim. Longitudinal force at a) front left (FL) and b) front right (FR); Lateral force at c) rear left (RL) and d) rear right (RR).

5 Conclusions

The presented work focused the attention on the correlation between a 1D vehicle concept model with 15 DOFs built in LMS Imagine.Lab AMESim and a 3D hi-fi multi-body vehicle model built in LMS Virtual.Lab Motion. The aim of this work is to check the accuracy of a concept model for future real-time applications. The correlation is based on a nominal parameterization of the 1D model in terms of masses, inertias, geometry, suspension parameters and kinematics characterization derived from the 3D multi-body model. The two vehicle models (3D detailed and 1D concept) have been compared through two different open-loop maneuvers for validation. In the first one, the vehicle is moving along a straight line while the second one consists in a step steer maneuver. The results showed a good agreement between the two models, been the observed differences acceptable, while the reduced complexity and CPU time offered by the concept model are relevant. Future work will consider further investigation of compliance tables and effect especially in high speed maneuvers. An interesting next step would be a comparison between the two models also through closed-loop maneuvers, comparing control signals such as the torque at driven wheels and the steering wheel angle.


Acknowledgements

We gratefully acknowledge the European Commission for their support of the Marie Curie IAPP project 285808 “INTERACTIVE” (“Innovative Concept Modelling Techniques for Multi-Attribute Optimization of Active Vehicles”) with contract number 285808; see http://www.fp7interactive.eu. Furthermore, we kindly acknowledge IWT Vlaanderen for their support of the ongoing research project “Model Driven Physical Systems Operation - MODRIO”, which is part of the ITEA2 project 11004 “MODRIO”.

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On the correlation between a 3D high-fidelity multi-body ...past.isma-isaac.be/downloads/isma2014/papers/isma2014_0671.pdf · concept design phase, leading to an improved initial