Dynamic Simulation of Vehicle Suspension Systems for Durability Analysis

Transcription

1 Dynamic Simulation of Vehicle Suspension Systems for Durability Analysis Levesley, M.C. 1, Kember S.A. 2, Barton, D.C. 3, Brooks, P.C. 4, Querin, O.M 5 1,2,3,4,5 School of Mechanical Engineering, University of Leeds, Leeds LS 29 JT, UK Keywords: multi-body systems, full vehicle model, quarter vehicle model, vehicle suspension model, virtual prototype. Abstract. Optimisation for fatigue life is currently carried out manually, which is time consuming and may not achieve the best design. To shorten the design process, software for automated durability optimisation is being developed at the University of Leeds and is initially aimed at the automotive industry. A key aspect of the optimisation process is to obtain accurate load histories for the particular component to be optimised. If this is to be done early in the design process, before a rolling chassis prototype is available, then simulation must be relied upon to obtain these load histories. In the case of suspension components either a quarter vehicle model (QVM) or a full vehicle model (FVM) can be used as the basis for the multi-body system (MBS) simulation. This paper compares the suitability of the QVM and FVM for durability analysis. Results are presented for both a simplified vehicle suspension and for a more realistic suspension. Step inputs representing a kerb and a simplified pothole were applied to one wheel only. For the simplified suspension case, the local displacement of the body was less for the FVM than for the QVM. This indicates that the dynamic response at the other wheel stations contributes to the behaviour of the wheel station directly subjected to the step or pothole input. The study was repeated with a more realistic suspension model in the QVM and at one wheel station of the FVM, with similar results to the simplified suspension case. This study has shown that coupling exists between the four wheel stations of the FVM even when the suspension is independent. This coupling can affect the load histories applied to a particular suspension component, which may then affect its calculated durability. The strength of this coupling is such that the use of the QVM for durability analysis becomes questionable and the FVM should be used as the default. Introduction With increasing processing power and enhanced software capabilities, the advantages of virtual prototyping as a realistic alternative to physical prototyping are becoming increasingly apparent. In structural analysis the use of so called 'super' models as an alternative to physical dynamic testing is expected to become widespread in the near future. Unlike current practice, where appropriately sized finite element (FE) models are derived from the designer's CAD drawings, these super FE models will include all manufacturing detail and will effectively replace detail CAD drawings. It is predicted from current trends that the errors between super model results and physical tests data will be of the same order of magnitude as the natural variation between two nominally similar manufactured items. Future research challenge will be in accurately modelling the non-linear interfaces between these super model components in a large assembly. In multi-body system analysis, enhanced computational capability has resulted in the ability to model systems with larger numbers of rigid bodies, and to model the connection between these bodies with increasing sophistication, within reasonable computational constraints. In the automotive industry this is currently being used to build more representative vehicle models enhancing and some cases replacing physical testing [1-6] Building upon these advances, research at the University of Leeds is seeking to link results from MBS analysis to FE models with structural optimisation algorithms, to generate a method for

2 automating the design of light weight components with maximum fatigue life [7,8]. Currently, the focus of this research is on the automotive industry but clearly other sectors such at the aerospace industry would be a key beneficiary of this method. At the heart of the method is the assumption that accurate load histories can be predicted efficiently from MBS vehicle models when subjected to appropriate road inputs. Further, since the technique is currently being designed to remove the need for physical durability tests, the predicted load histories must be accurate for road inputs specifically intended to apply significant damage to a vehicle's components, such as large amplitude transient inputs generated by a pavé test track for example torsion bar 2- damper 3- upper arm 4- bump stop 5- lower arm 6- tie rod 7- hub Fig. 1 Vehicle Suspension Details 7 3 Spherical joint Spherical joint 5 2 Revolute joint Revolute 4 joint Rigid connection to 6 Bushing (Revolute joint) Vehicle body Bushing (Revolute joint) In a recent paper [9], a complex QVM of the suspension system shown in Fig. 1 was generated and driven over a virtual pavé test track in order to obtain load histories for the lower arm. Results from the MBS model were compared to experimental data. A sensitivity study showed that despite the use of a variety of tyre models and the inclusion of various bushes attached to the component of interest, simulation results did not correlate well with the experimental data. The paper concluded that one of the most likely causes for the discrepancy was the original assumption, that for the purposes of predicting the behaviour of the lower arm, the vehicle could be adequately represented by a QVM, suggesting that neglecting the pitch and roll degrees of freedom was not valid. Simplified Quarter Vehicle and Full Vehicle Models In order to test the validity of the well established assumptions made when reducing a model from a FVM to a QVM, a simple linear 2 degree of freedom (DoF) QVM and a linear 7 DoF FVM were built using the MBS code Visual Nastran as shown in Fig. 2a and 2b respectively. The models were built using data for a typical medium sized saloon passenger car [1], as given in Table 1. Fig. 2a 2 Degree of Freedom Quarter Vehicle Model Fig. 2b 7 Degree of Freedom Full Vehicle Model

3 Model Inputs Parameter Symbol 2 DoF 7 DoF QVM Data FVM Data Effective body mass (kg) M b Front wheel mass (kg) M wf 4.5 Rear wheel mass (kg) M wr Distance from CG to front axle (m) l Distance from CG to rear axle (m) l Half track width W w.74 Front suspension stiffness (kn/m) k sf 17 Rear suspension stiffness (kn/m) k sr Front tyre stiffness (kn/m) k tf 192 Rear tyre stiffness (kn/m) k tf Front damping coefficient (kns/m) c sf 1.5 Rear damping coefficient (kns/m) c sr Pitch inertia (kgm 2 ) I bp 1222 Roll inertia (kgm 2 ) I br 38 Table 1: Vehicle Data for the 2DoF QVM and 7 DoF FVM Both models were subjected to a step input of amplitude 12mm to simulate a kerb strike and to an input representing a pothole. The pothole was of depth 5mm, length 6mm and was traversed at a forward speed of 1m/s. To make the pothole input more representative the falling and rising edges were shaped as shown in Fig. 3 to take account of the rolling radius of a typical tyre Fig. 3 Pothole Profile Traversed at 1m/s For the 7 DoF model these inputs were applied to the rear right hand side wheel station only, which induces significant roll and pitch motion. Results for the step input are given in Fig. 4a and 4b which show the displacement of the unsprung mass (wheel hub) and sprung mass (vehicle body) respectively (Note that for clarity in Fig. 4a, only data for the rear right hand side wheel is included for the FVM, while in Fig. 4b body displacements are included at all 4 corners to indicate the degree of pitch and roll present in the response) From Fig. 4a and 4b it can be seen that while the displacement history for the unsprung mass of the QVM compares well with the rear right hand corner FVM data, the same is not true for the sprung mass, due to the effects of pitch and roll of the vehicle body. For the sprung mass, comparison between the rear right hand corner displacement of the FVM and the QVM prediction reveals two

4 key differences, the first is that the displacement is lower for the FVM and the second is the FVM response appears more heavily damped than the QVM response. 2 2 rear right front right front left rear left QVM Fig. 4a Unsprung Mass Response to a Step Input Fig. 4b Sprung Mass Response to a Step Input Fig. 5a and 5b show results from the pothole input for the unsprung mass (wheel hub) and sprung mass (vehicle body) respectively. Trends seen for the step input are also apparent in this data. For the unsprung mass, the displacement histories for the QVM are now almost identical to those from the FVM. For the sprung mass comparison between the rear right hand corner of the FVM and the QVM show that in general the FVM exhibits lower displacements that appear more heavily damped. 4 1 rear right front right front left rear left QVM -6-2 Fig. 5a Unsprung Mass Response to a Pothole Input Fig. 5b Sprung Mass Response to a Pothole Input Differences between the FVM and the QVM are smaller than those seen in the previous example. The main reason for this is the length of the pothole and the vehicle speed chosen for this particular example. With the particular pothole and speed parameters selected, the duration of the input is only.6 seconds as can be seen in Fig. 3 and hence compared to the dynamic characteristics of the sprung mass the input approximates to an impulse. Within the time period over which the pothole input lasts, the sprung mass only has time to descend by approximately one quarter of the pothole depth. In general sprung mass displacements and hence also differences between the models are much lower than those seen for the step input.

5 Detailed Quarter Vehicle and Full Vehicle Models of a Multi-Purpose Vehicle As previously stated, the primary aim of the MBS model in this application, is to provide load histories for dynamically loaded components to allow subsequent structural optimisation. To demonstrate this application, the optimisation of a lower arm of the suspension arm from a multi purpose vehicle (MPV) was chosen as an appropriate case study (note this is a different vehicle from that used in the previous section and due to commercial sensitivity, the exact make and model of the vehicle can not be given). Clearly, in order to provide load histories for the lower arm a detailed MBS model of the suspension is required, rather than the simple QVM or FVM models presented in the previous section. To develop this more representative model the following steps were performed, noting that all parameter values given below including weight distribution etc. where derived directly from the MPV designer's data and CAD drawings. A three-dimensional solid model of the rigid components of the suspension system was created using CAD software. The CAD models were then imported to the Visual Nastran MBS software environment. The mass and inertia properties calculated from the CAD data and shown in Table 2 were assigned to the corresponding elements of the imported model. Element Mass Centroidal inertia (kg.m 2 ) (kg) I xx I yy I zz Hub Lower arm Upper arm Tie rod Table 2: The Mass and Inertia Properties of the Rigid Suspension Components The joints between the suspension components and the vehicle body were then modelled using the Visual Nastran MBS software tools at the front right hand corner of the vehicle. For the QVM, a rigid element of mass equal to half of the unladen front axle load, 535 kg, was added to represent the vehicle body and this element was constrained to move vertically. For the FVM, a rigid element of mass equal to the total unladen mass was added and this element was constrained to move in vertical, pitch and roll degrees of freedom. It was supported at the other 3 corners by simple mass-spring-damper representations of the suspension with the parameter values shown in Table 3. Parameter Symbol FVM Data Wheel mass (kg) M w 42 Suspension stiffness (kn/m) k s 32.5 Tyre stiffness (kn/m) k t 2 Suspension damping coefficient (kns/m) C s.5 Tyre damping coefficient (kns/m) C t.1 Table 3: Additional Suspension Component Parameters A torsion spring-damper element was used to represent the torsion bar which is located between the upper arm and the vehicle body. An initial torsion angle of 28 was set to account for the initial twisting of the bar. The torsion rate k tor of this element was calculated using Eq. 1 in which d is the bar diameter, L is the bar length and G is the shear modulus of the bar material. 4.d.G ktor = π = Nm/deg. (1) 32.L Spring-damper elements were used to represent the bump stop and the damper. A suspension bushing can be modelled as either a revolute joint with non-linear compliance, a revolute joint with linear compliance or as a revolute joint with no compliance. Blundell [11]

6 showed that there is little difference between the results obtained using the three modelling strategies. In this study, suspension bushings were modelled as revolute joints with no compliance. The rubber component that lies between the end of the tie rod and the vehicle body was modelled using four linear spring elements. The stiffness of each spring was assumed to be 1 N/mm. A vertical spring-damper element was added to simulate a point contact tyre model. A stiffness rate of 239 N/mm and damping rate of.1 Ns/mm were assigned to this element. A static analysis was first performed to bring the elements within the models to their respective equilibrium positions. A step input was then applied in order to simulate a kerb strike. The more detailed QVM and FVMs developed in Visual Nastran can be seen in Fig. 6a and 6b respectively (Note that in Fig. 6b the other three corners are supported on simple mass/spring/damper elements similar to those shown in Fig. 2b). Fig. 6a Detailed Quarter Vehicle Model Fig. 6b Detailed Full Vehicle Model Initially a step of amplitude 12mm was applied to both the QVM and the FVM. Results for the unsprung and sprung mass can be seen in Fig. 7a and 7b respectively. For the QVM, both figures show a very lightly damped responses. Careful examination of the data revealed that for this level of input, the lower arm impacts upon the bump stops, causing a non-linear response and creating a system which is generally stiffer and less well damped than may otherwise have been expected. From the figures it is again seen that amplitudes for the FVM are lower than for the QVM particularly for the sprung mass. Careful examination of the data revealed that these lower amplitudes in the FVM reduced the occurrence of impacts with the bump stops. Displacement Fig. 7a Unsprung Mass Response to a 12mm Step Input Displacement Fig. 7b Sprung Mass Response to a 12mm Step Input QVM Front right Front left Rear right Rear left

7 Since one of the main aims of this paper is ascertain the validity of the QVM against a comparable FVM, the previous test was repeated for a lower amplitude step input. This was done to eliminate the non-linear effects seen in the previous example, which clearly affected the QVM more than the FVM. Results for the unsprung and sprung mass can be seen in Fig. 8a and 8b respectively. Both responses now show no evidence of impact from the bump stops. From the figures it is still evident that amplitudes for the FVM are lower than for the QVM Displacement Displacement QVM Front right Front left Rear right Rear left Fig. 8a Unsprung Mass Response to a 3mm Step Input Fig. 8b Sprung Mass Response to a 3mm Step Input Discussion In the application suggested in this paper, the ultimate aim of the MBS model is to predict load histories that can be used in subsequent analysis and optimisation of a particular system component. These load histories arise from a number of sources but ultimately they rely upon the MBS model being capable of accurately predicting displacements and hence also velocity and acceleration time histories for the component of interest. In the case study selected to demonstrate this application, the component of interest is a lower suspension arm. This is a component that connects the unsprung and sprung masses and hence it is vital that the model can predict both unsprung and sprung responses with a degree of accuracy. In addition, a component of this nature may well in general carry loads from the damper, the suspension stiffness and from any bump stops, as well as its own inertial loads. It is thus vital that not only displacement but also velocity and acceleration amplitudes are accurately predicted. Due to the nature of the application presented here, the model must be accurate when subjected to the type of inputs that would be used to input significant damage to the component under virtual test, which implies large amplitude transient events such as steps and pot holes. For the variety of test cases presented above, two consistent trends have been noted when comparing data from the QVM with the FVM. Firstly, the QVM significantly overestimates the displacements resulting from either a step or pothole input. This is particularly noted in the sprung mass displacement responses but is also present to a lesser extent in the unsprung mass displacement responses. Secondly the responses seen from the FVM appear to be more heavily damped than those from the QVM, with settle times being shorter and attenuation of successive vibration peaks being greater. In the more detailed MBS models investigated, the generally larger displacements predicted by the QVM resulted in the lower arm impacting upon the bump stops when subjected to a step input of 12mm. With lower predicted displacements from the FVM, these impacts were much reduced. If the QVM were being used to calculate the load histories of the lower arm, as is the case in this

8 application, then these impacts would generate significantly higher predicted load histories than the FVM. Thus, due to the non-linear nature of the models, differences in predicted amplitudes of vibration could cause disproportionately large differences in the predicted load histories, thus exaggerating any differences between the model output. Conclusions Quarter vehicle and full vehicle models of two different vehicles and of varying levels of complexity have been compared using inputs likely to be encountered in a typical virtual durability test. In all cases the QVM was found to overestimate displacements both for the unsprung and sprung mass when compared to the FVM. Though differences were small for the unsprung mass they were significantly larger for the sprung mass. For the more detailed models examined, which included a non-linearity in the form of a bump stop, the differences in predicted displacements for the sprung mass between the QVM and FVM were further exaggerated under some input conditions. When analysing the response of any components attached to the vehicle body, such as the suspension arm, it is thus vital that the vehicle body is modelled appropriately. In these cases, neglecting pitch and roll degrees of freedom of the vehicle body is not necessarily valid and the full vehicle model should be used as a default. However it is not necessary to model the suspension at all three corners in great detail if components at just one corner are under investigation. References [1] F. A. Conle, C. W. Mousseau: Using Vehicle Dynamics Simulations and Finite Element Results to Generate Fatigue Life Contours for Chassis Components, International Journal of Fatigue, 13 (3) (1991), pp [2] M. Chaika, C. Riedel, Chin Anton: Correlation between Simulations and Experimental Data for Military Vehicle Applications, SAE Technical Paper Series, No (1995). [3] S. Medepalli, R. Rao: Prediction of Road Loads for Fatigue Design- Sensitivity Study, International Journal of Vehicle Design, 23 (1-2) (2), pp [4] T. J. Stadterman, W. Connon, K. K. Choi, J. S. Freeman, A. L. Peltz: Dynamic Modelling & Durability Analysis from the Ground Up, Proceedings of test technology symposium, Baltimore, USA, 1-2,5 (21). [5] M. D. Letherwood, D. D. Gunter: Ground Vehicle Modeling and Simulation of Military Vehicles Using High Performance Computing, Parallel Computing, 27 (21), pp [6] W.B. Ferry, P.R.Frise, G.T.Andrews, M.A.Malik: Combining Virtual Simulation and Physical Vehicle Test Data to Optimize Durability Testing, Fatigue & Fracture of Engineering Materials & Structures, Vol. 25 (22), pp [7] M. Haiba, D.C. Barton, P.C. Brooks, M.C.Levesley: Review of Life Assessment Techniques Applied to Dynamically Loaded Automotive Components, Computers and Structures, Vol. 8 Issues 5-6 (22), pp [8] M. Haiba, D.C. Barton, P.C. Brooks, M.C.Levesley: The Development of an Optimisation Algorithm Based on Fatigue Life, International Journal of Fatigue, Volume 25(23), pp [9] M. Haiba, D.C. Barton, P.C. Brooks, M.C.Levesley: Using a quarter-vehicle multi-body model to estimate the service loads of a suspension arm for durability calculations, Proceedings of the IMechE, Part K, Journal of Multi-body Dynamics (23) Ref :K242. [1] D.A. Crolla, G.Frith, D. Horton, An Introduction to Vehicle Dynamics, School of Mechanical Engineering, University of Leeds, 1991 [11] M. V. Blundell: The Influence of Rubber Bush Compliance on Vehicle Suspension Movement, Materials & Design, 19 (1998), pp