MULTI BODY SYSTEMS INSIDE FEA FOR STRUCTURAL NONLINEARITY IN VEHICLE DYNAMICS SIMULATION

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1 EAEC2011_C15 MULTI BODY SYSTEMS INSIDE FEA FOR STRUCTURAL NONLINEARITY IN VEHICLE DYNAMICS SIMULATION Thomas Wissart* Bernard Voss Stephane Grosgeorge CAE Engineer SAMTECH Deutschland Tempowerkring,6 D Hamburg Automotive application coordinator SAMTECH LIEGE science park Rue des Chasseurs- Ardennais, 8 B-4031 Liège (Angleur) 1 Simulation Engineer SAMTECH Deutschland Oskar-Kalbfell-Platz 8 D Reutlingen thomas.wissart@samtech.com, Bernard.Voss@samtech.com stephane.grosgeorge@samtech.com Abstract: Multi Body System (MBS) is nowadays accepted as a reliable tool to develop new components for vehicles suspensions, steering or powertrain parts and to simulate the low frequencies of the response spectrum seen by the vehicle. The simulation of vehicle dynamics with MBS software includes rigid components, kinematical joints and possibly Super-Elements to represent an approximation of reality. Using rigid components in the model of a vehicle has been proven to be too conservative and not reliable enough since flexibility is an important contributor to vehicle dynamics and can consequently no longer be neglected. This is especially of critical importance when modelling the complex suspension/steering system where bushings are present to isolate the chassis from external disturbance. The presence of bushings leads to high non linearity. Classical MBS software do not have the capability to predict such structural non linearity. The use of super elements (SE) can sometimes be seen as a good alternative but show some important limitations such as the assumption of linearity and the validity for a limited frequency range. The SE are therefore not sufficient when contact (pothole or curb strike), prestresses due to assembling, friction (steering or suspension), nonlinear geometric behaviours (bushings) or complex interaction with control systems (ABS system on a bumpy road) are required. The need to reduce vehicles weight in order to minimize the fuel consumption also highlights the increasing importance of durability in today s car design process. This constraint adds to the already existing compromise of safety and comfort. For the modelling of durability problems, a higher level of accuracy for higher frequencies is required. This creates a need for an advanced solution procedure complementary with pre-existing methods. This new solution

2 must be able to take all these nonlinear phenomena into account, must be easy to use and capable to provide a reliable solution in a reasonable computational time. In this paper, the advantages of using the Motion in FEA simulation capabilities are demonstrated with relevant vehicle dynamics examples. The Motion in FEA approach is very accurate since it can describe all the non-linear effects present in the vehicle. As they are not limited to low frequencies or connection modes, results are more accurate. With respect to the engineering process efficiency, the Motion in FEA model also allows eliminating unnecessary iterations between local separate mechanical models. Keywords: Nonlinear FEA, MBS, flexible mechanism, Motion in FEA, vehicle dynamics 1. INTRODUCTION In the industry, CAE methods are being used extensively to predict the performances of a mechanical system such as motion or stress. CAE tools are also used to optimize the design of the systems based on previously validated results of simulations. The use of CAE aims at reducing building physical prototypes so that design cost and time-to-market can both be reduced. CAE techniques are very useful for efficient diagnosis and refinement engineering as the numerical methods enables estimating parameters that are sometimes not physically measurable or cost prohibitive to measure. The current simulation methodology nevertheless suffers some limitations in the case of vehicle dynamics. Indeed Multi Body System (MBS) is the standard for vehicle dynamics analysis and especially for kinematics, ride and handling simulation up to a certain frequency. To reach higher frequency, MBS models need to include flexibility. Currently this can only be done efficiently importing reduced linear Finite Elements (FE) [1] models called Super Elements [2]. This methodology is proven to be working and is currently used in most of the industry. Nevertheless it is clearly demonstrating a loss of time for the engineers who spend time transferring data from one platform to another instead of analysing the results of the simulation. This limits the advantages of the virtual prototyping against building physical prototypes as time is inefficiently lost in the design process transferring data. Therefore the need for increasing accuracy points towards coupling the two methodologies for systems undergoing global large displacements but also local nonlinear structural deformations, pre-stresses, material nonlinearity or contact-friction phenomena between flexible bodies. 2. CURRENT STATE OF THE ART 2.1. AUTOMOTIVE CONTEXT FOR SIMULATION In the automotive industry and especially for vehicle dynamics, engineers design vehicles and components with a certain number of requirements ranging from comfort to passive safety. In that matter, specific norms or load cases are defined for the vehicle to comply with. Nevertheless the vehicles must be lightweight, easy to manufacture, reduce energy consumption and meet emission targets. This means that vehicle manufacturers and tier suppliers are facing the 2

3 challenge of consistently maintaining high quality, minimizing vehicle weight within a certain cost. For the design of a new vehicle, a MBS model is built and the loads on a given component of a system are calculated. Secondly a FEA model of this component also needs to be created and the loads previously calculated are exported in an appropriated format and used as inputs for this FEA model (see Figure 1). For every iteration of the design, both MBS and FEA models need to be updated in parallel generally by two different teams. Eventually the fatigue life can be estimated thanks to dedicated programs. Figure 1: Classical simulation process This simulation process intervenes early in the design process but with different types of virtual models. - Concept phase: This phase is initiated before the first CAD model is even finished. It aims at defining the targets for the vehicle. During this first phase, a classical MBS model can be used to perform the simulations of the global vehicle and then estimate rough load cases for early design. - Detailed design: the CAD models are created and assembled into the vehicle body and other subsystems and finally the full vehicle. The objective of this second step is to perform fast design and iterate simulations based on the evolution of the design. - Fine tuning and optimisation: CAE tools are used to investigate the issues identified in testing. Both MBS and FEA tools are used generally involving loops between the different models. The MBS and FEA are therefore the main tools helping the mechanical designer to design vehicle and data have to be exchanged during the simulation process MBS/FEA CHAINING The creation of a reliable flexible MBS model for vehicle dynamics is a complex task involving both MBS and FEA. In order to introduce linear flexibility in a model, a model of a given part needs to be first created in FEA and then a Super Element model has to be generated. In a second step, this Super Element needs to be imported in the MBS model. For nonlinearity, the loads calculated with the MBS model are imported in the FEA code. 3

4 MBS simulation In the vehicle design process, the MBS model is first used during the concept phase. The front and rear suspension subsystems are created thanks to templates and then assembled to the vehicle body. Depending on the needs of the simulation, the powertrain model can also be imported or lumped models are used. Figure 2: MBS vehicle model from Imperia GP [3] Most of the time, only kinematic analysis is used early in the design of suspension geometry with compliant effects being considered later in the vehicle development. An update of the compliance of the suspension is provided once the vehicle has been measured on the K&C test rig. The correlation between rig measurements and simulation is performed for steady state conditions or low frequency. This limits the validity of the simulation results to low frequency. However, with the requirements to shorten development times and improve the end product, there is an increasing need to perform compliance simulations early in the design phase to obtain the optimum solution with minimal on-vehicle testing. For this reason it is necessary to include suspension compliance effects in simulation from the start of a project therefore involving the use of nonlinear FEA simulation FEA simulation FEA simulation is not directly used in vehicle dynamics but is used for structural analysis and then the results are imported to be used in MBS environment. For instance, the detailed dynamic compliance of a suspension can only be accurately described thanks to FEA. Indeed, for accurate predictions of medium frequencies or nonlinear deformations (geometrical or material), more detailed FEA models are required. However large models can limit the number of design iterations in a given time and even make optimisation impossible because of too important CPU time. Such circumstances result most of the time in simulation projects only confirming the design and measurement but not contributing to a better design before the test vehicle is built. A trade-off to FEA can be to use Super-Elements to take into account the flexibility. Super- Elements consist in reduced FEA models maintaining accuracy up to a certain frequency for linear analysis. In order to further reduce the development time, FEA model should be integrated early in the design process even through Super-Elements. The added value would be a better integration of the flexibility and consequently a better assessment of the durability. 4

5 2.3. MODELLING OF STRUCTURAL NONLINEARITY Even with the integration of Super-Elements, structural nonlinearity cannot be accurately simulated in MBS environment. It is clear that for medium frequency vehicle dynamics simulation can only be performed with nonlinear FEA software. Figure 3: MBS and FEA range of applications Indeed, the sources of local nonlinearity are numerous in vehicle dynamics: pre-stress, bushings, contacts, tyres One of the easiest ways to treat nonlinearity is to use semi empirical models such as the well-known Magic Formula developed by Pacejka [4] for the tyre models or spline curves for suspension stiffness. A similar methodology is applied to model bushings and dampers. Nevertheless, as the model is empirical and not physical uncertainties about the quality of the model are always present. A tuning of the model is also difficult as the model is not physical and rely consequently more on experience than on pure analytical techniques. These alternative methods provide therefore little or no direction on what is needed to solve. Furthermore, for higher nonlinearity and frequency, the uncertainty can become very important and have a non-negligible impact on the validity of the simulation results. This is typically the case for the modelling of phenomenon that cannot be handled by classical MBS package as it is lacking nonlinear FEA capabilities for local structural nonlinearity. This lack in the current MBS simulation software shows the need for a new solution procedure capable of simulating such phenomenon but also including the classical methodology. 3. NEW BOUNDARIES FOR VEHICLE DYNAMICS SIMULATION In this period of crisis, the automotive market requires that more efficient design methodologies are developed to launch in a shorter time innovative, satisfactory and low cost products meeting the needs of customers. This is the right time to rethink the current methodology of simulation and adopt innovative methodology to better optimise the vehicles of today and tomorrow INNOVATIVE METHODOLOGY: A UNIFIED NONLINEAR FEA/MBA APPROACH In the automotive industry, there is strong demand for reductions in the weight, cost, and development period of motor vehicles without sacrificing safety and quality. Simulation with 5

6 CAE is one of the important means for achieving these conflicting objectives. In this race for weight saving, most of the efforts focused on material technology in the last few years [13]. A better physical description of the dynamic phenomenon would also help better optimise the components of a vehicle avoiding over dimensioning. This opens the door to a new approach benefiting from the synergy between Mechanical Engineering (initial domain of MBS software) and Stress Analysis (initial domain of FEA software), enabling higher nonlinearity and frequencies [5] & [6]. Figure 4: Modeling hierachy The new methodology will extend the capability of mechanical engineering to stress analysis and also extend the capability of stress analysis to mechanical engineering. Indeed, mechanical engineers will now have access to local detailed nonlinear structural models and stress engineers will have access to exact boundary conditions coming naturally from the global vehicle model prepared by mechanical engineers APPLICATIONS AND EXAMPLES A list of examples showing the need of combined MBS and FEA approach in vehicle dynamics is presented in the following sections Suspension compliance prediction Suspension compliance results from the application of the tyre forces at the contact patch. They lead to deformation of the suspension. Suspension compliance is known to affect both handling and comfort for many years. Predicting and optimising the suspension compliance is a very complex task as forces and moments are applied in the tyre contact patch. On top of that, the requirements are most of the time contradictory for ride (soft) and handling (stiff). The differences between test rig and simulation reveal the importance and necessity of using nonlinear FE model (even just using deformable beam elements) to include the component flexibility in vehicle chassis/suspension dynamic analysis. 6

7 camber vs wheel displacement camber vs lateral force Figure 2: Compliance with meshed parts Theoretically kinematics and compliance should not be assessed separately from one another as the attachments points of the suspension affect with a first order effect the motion of the suspension but also with a second order effect the flexibility. In Current MBS simulation, the hysteresis cannot be accurately modelled because it results from complex 3D contact/friction with elastomer parts, pre-stresses and non-linear material interactions that cannot be modelled in MBS tools Curved centreline spring in McPherson strut Undesired lateral force inevitably exists in a MacPherson suspension system leading to friction in the damper tube because of bending moment. This bending moment has a consequence on the ride performance but also leads to an excessive wear of the damper tube (see figure 7). Tilted spring Side load spring Figure 7: McPherson sketch To minimize or even eliminate this problem, one possible solution requires tilting the coil spring with regards to the damper. This solution is nevertheless not always feasible because of packaging reason. Another solution not conflicting with the packaging is the substitution of the conventional coil spring with a new side load spring with curved centreline (see Figure 7) sometimes called side-load spring. With an appropriate design of the curvature such a spring can therefore generate a side load when compressed or elongated. The side-load spring itself but also the integration of the side-load spring in the suspension system needs to be optimised all together as the position of the attachments points are of critical importance. Indeed for a curve centreline spring, the force is no longer in the axis of the spring but can have transverse components and also moment components. It is clear that alternatives methods can be used. Nevertheless it will not give accurate results. Optimisation will not be robust as based on simulation results lacking 7

8 accuracy. Consequently tuning will be needed on the physical prototype. With such a spring, it is therefore mandatory to use a combined nonlinear FEA/MBS approach to have an accurate numerical simulation. Otherwise data exchanges between the MBS and FEA software will be needed and the fine tuning will be time inefficient and maybe even not converging Interaction between coil spring and rubber insulator As seen in the previous section, the friction in the suspension has a direct impact on ride comfort and alternatives need to be found to classical suspension design to optimise the comfort. Again for the particular case of the McPherson suspension, the sitting of the spring on the rubber insulator is therefore of critical importance with regard to comfort and low frequency vibration. There are different sources of nonlinearity in the McPherson suspension taking into account the rubber insulator: large strain of the elastomer, large displacements of the coil spring contact between the spring and the elastomer and possibly between the coils. Thanks to the hybrid nonlinear FEA/MBS approach it is possible to estimate the contact pressure in the rubber insulator. This helps indicating the high contact pressure location and can therefore help optimising the shape of the rubber insulator for better noise and vibration insulation. The results obtained underline the importance of integrating the rubber insulator into the suspension subsystem for the optimisation of the MacPherson suspension. This problem can only be solved by the synergy of a MBS and a nonlinear program because of large nonlinearity Torsion beam and leafspring suspension Torsion beam and leafspring suspensions are widely used for rear suspension on front wheel drive passenger vehicle with small to medium size. Their main advantages of these suspension geometries are the simplicity and the small number of components offering maximum space usage combined with a low manufacturing cost. Despite the simplicity, the accurate simulation requires nonlinear FEA as the torsion beam and leafspring can undergo significant nonlinear displacement for specific manoeuvres. Contact adds damping for the leafspring suspension which cannot be modelled with MBS software. The nonlinear deformation is further exaggerated for manoeuvres like braking on a pothole for one wheel as large rotation take place in the beam section. Classical flexible MBS software can only support linear structural compliance valid only for small deflections. For large structural deflections, nonlinear structural compliance must be represented for accurate results using a nonlinear FEA tool. With a combined nonlinear FEA/MBS approach, a better prediction of the toe and camber compliance under longitudinal and lateral load will be possible. Otherwise only a linear compliance value will be computed. For small lateral acceleration manoeuvre, this is acceptable as the force generated by the tyre is small but in the case of heavy cornering or heavy braking manoeuvres nonlinear deformations occur and the assumption of linear compliance is no longer valid. 8

9 Tyre The tyre is the component of the vehicle having the most important influence on vehicle dynamics. The modelling of rubber tyres involves many nonlinear phenomenon: geometric material, contact... Several commercial tyre models have been developed in order to extend the modelling capabilities for tyre simulation [3] & [9]. All these models are said to be valid up to at least 100Hz which is far beyond the capabilities of rigid MBS software (see Figure 10). Figure 3: Tyre models validity Consequently the capabilities of the advanced tyre models are often limited by the capabilities of the MBS software. Classical MBS software are not able to simulate high enough frequency and need to be complemented by flexible components such as FEA or even nonlinear FEA. For some specific applications, the commercial tyres models are not accurate enough and a full nonlinear FEA tyre model is mandatory. For such simulation, hybrid nonlinear FEA/MBS approach is mandatory Other applications The differential is an important component of the powertrain influencing not only the handling and stability of the car but also its performance. A limited slip differential called C Torsen from JTEKT TORSEN is an example where a coupled approach nonlinear FEA/MBS is needed [10]. Figure 4: Type C Torsen differential This central differential is in charge of transferring the input torque from engine to the front and rear axles of a four-wheel drive vehicle. The Torsen (Torque Sensing) differential works like a 9

10 conventional differential but can lock up if a torque imbalance occurs. The type C Torsen differential includes gears, satellite-planetary systems with helix angle and several trust washers. According to the considered mode, the elements of the differential move axially and a friction is generated between some parts. For instance, when one axle tries to speed up, the axial force produced by the helical mesh leads to contact between the circular face of the gear and a trust washer. The friction encounters tends to slow down the rotation speed of the gear. 4. CONCLUSION The competiting environment in the automotive market requires now to integrate early in the design the interaction between the parts and systems. For vehicle dynamics, this interaction between the different elements of a vehicle can only be done through a monolithic nonlinear FEA approach embedding MBS when local structural nonlinear phenomena occur. SAMCEF Mecano enables modelling a wide range of problems in vehicle dynamics in one single environment. However this method can also be used for classical MBS or FEA analyses, with the big advantage that the same simulation tool can be used from early pre-design activities (mechanism synthesis, kinematics, load estimation) to detailed stress analysis. The Finite Element approach complemented with MBS developed in SAMCEF Mecano allows extending the field of dynamics simulations to medium frequency range and to systems involving higher level of nonlinearity. 5. REFERENCES [1] O.C. Zienkiewicz, The finite element method, 3rd ed, McGraw-Hill, New York, [2] Craig R., Bampton M.: "Coupling of substructures for dynamic analyses", AIAA Journal, 6, [3] Green Propulsion: [4] H. B. Pacejka, Tyre and Vehicle Dynamics 2nd ed, Butterworth-Heinemann Ltd [5] [6] M. Géradin, A. Cardona: "Flexible multi-body dynamics: a finite element approach", John Willey & Sons, [7] SAMCEF: "Système d Analyse des Milieux Continus par Eléments Finis", [8] B. Voss, F. Cugnon, Ph. Prétot, D. Granville, M. Bruyneel, Advances in vehicle dynamics simulation with SAMCEF Mecano, 15th International Conference on Vehicle Dynamics, SIA, Lyon, September 23-24, 2009 [9] [10] G. Virlez, O. Brüls, N. Poulet, P. Duysinx, Multibody Dynamics Analysis of Differentials in Vehicle Drivetrains, The 1st Joint International Conference on Multibody System Dynamics 10