Abstract

The use of LS-DYNA in vehicle design development is currently confined largely to crashworthiness. However, the extensive capabilities of the solver have spin-off benefits in other areas. One of these is durability analysis. LS-DYNA can simulate events such as kerb-strikes with a level of realism not achievable using traditional linear analysis techniques. This paper demonstrates how the whole vehicle can be simulated, including tyres, suspension and body as well as the test track. The dynamic loading on the various components is automatically calculated as a result of driving the model vehicle over the test track surface, and stress distributions are predicted dynamically. The first potential advantage of this technique is that the loading on the vehicle can be quantified with confidence, owing to finite element tyre models. The second is that more realistic stress distributions can be calculated due to the inclusion of dynamic nonlinear effects. Thirdly, any permanent deformation and areas of plasticity can be quantified. In addition, by animating results, the analyst obtains an intuitive feel for the causes and effects of the loading that may help to identify and resolve durability problems.

The paper illustrates the LS-DYNA modelling techniques. The model presented has not been correlated to test and further work remains to be done to develop the simulation methods. However, the results demonstrate the potential benefits of using LS-DYNA to analyse this class of problem.

Introduction

Durability is one of the principal concerns in the design of vehicles. The term is used here to mean the vehicle's ability to survive the loading encountered during its life, from one-off abuse conditions such as driving over a kerb, to less severe loading that is repeated millions of times during the life of the vehicle such as accelerating and braking. Traditionally, durability performance has been achieved largely by test and development backed up by linear finite element analysis. However, with each new vehicle programme becoming more compressed than its predecessor, and having fewer prototypes, there is less and less opportunity to test. It is becoming essential for designs to be right first time, with testing taking place only as a confirmatory exercise at the end. Test failures at this stage can compromise the timing of the whole programme. Therefore the accuracy of the analytical techniques is becoming critical.

In this paper, we show that LS-DYNA is well suited to simulating vehicle on test track situations with more realism than can be obtained by the more traditional methods, because the test is modelled as it is performed in reality. The LS-DYNA modelling techniques have not been correlated to test and require some further development, but there is clearly potential for LS-DYNA to make an important contribution to durability analysis of vehicles.

Disadvantages of Traditional Durability Analysis

The three main steps in traditional durability analysis of vehicle structures are:

• Calculate loads to apply to the structure at each input point. This may be done with the aid of a dynamic calculation using a rigid body mechanisms package, often in combination with measured spindle force data. Loads are measured or calculated as time-histories. In other cases, loads may simply be peak tyre contact patch forces estimated using experience. The input point forces would then determined by static mechanisms analysis. The difficulty of making accurate prediction of the loads is recognised as being a key limitation of durability analysis.
• Perform linear static FE analysis to obtain stress distribution, often as a series of unit loadcases. A development of this technique is to use a dynamic modal model [2] to calculate the dynamic stress distribution.
• Combine loadcases according to input load calculation; often a fatigue life calculation is performed and linked to the load time histories to determine number of repeats to crack initiation.

The traditional multi-step approach to durability analysis has several inherent disadvantages, which together reduce the predictive ability of the calculations. This paper focuses on two aspects: determining the loads, and calculation of stresses. The final step, prediction of fatigue life from the stresses, is not covered here. The problems considered in this paper are:

• Difficulty in quantifying loads. For vehicle on test track situations, results are dependent on the quality of the tyre model. As will be shown in this paper, it is essential to include the flexibility of body and suspension components - rigid body calculations may be grossly inaccurate.
• Linear stress analysis techniques ignore yielding. The effects of local yielding on fatigue life at individual elements can be allowed for in a fatigue post-processor, but the change in stress distribution in other elements as a result of the yielding would not be accounted for.
• Linear stress analysis techniques ignore nonlinear geometry effects. For example, forces applied perpendicular to flat panels are assumed to be reacted entirely by local bending. In reality, as the panel bends, the change in geometry allows load to be carried in membrane tension. This effect can be highly significant at the top of a shock tower, for example. It is possible to run most of the commonly used linear codes with geometric and material nonlinearity included, but it then becomes impossible to superpose different loadcases in the normal manner, and many of the advantages of the traditional techniques are lost.
• Static stress analysis cannot account for dynamic effects: the various components of the vehicle respond dynamically to the input load time histories and hence the true stress distributions are poorly represented by static loadcases in which equilibrium must be assumed.
• Loads on different points of the vehicle body may be out-of-phase, i.e. may peak at different times. It is not possible to select one combination of loads that represents the worst-case loading condition, because different areas of the structure may reach their peak stresses at different times.

Because of these difficulties, it is unlikely that stress distributions used for durability analysis accurately reflect the real situation. Therefore, no matter how sophisticated the life calculation that forms the final step, results will always be circumspect.

In addition, it is often desirable to quantify the damage to a vehicle from the various "abuse" loadcases (for many of these, localised yielding is tolerated provided that the permanent deflections are within pre-set limits). It is not possible to calculate the permanent deformation using linear stress analysis techniques.

Objectives and Outline of the LS-DYNA Technique

Our aim in the work reported here was to overcome as many of the disadvantages of the traditional techniques as possible. Most of the errors occur because each stage of the analysis is to some extent removed from the real conditions of the test. We have therefore sought to remedy this by making the simulation as realistic as possible, and by doing the analysis in a single step. The approach was to model the whole vehicle driving on the test track, including suspension and tyres, using LS-DYNA. In theory, all of the disadvantages listed above are overcome by this modelling method. It should be possible to calculate the loads accurately for any road surface, using a finite element tyre together with a fully deformable model of the vehicle; all the dynamic and nonlinear effects are automatically included; because yielding is represented, permanent damage to the vehicle can be quantified. There is also the practical advantage of performing the whole calculation in a single analysis.

The principal limitation is CPU time. At present it is not practical to simulate events longer than 1-10 seconds, depending on the degree of detail in the vehicle model. As faster computers become available, longer events will be simulated with more of the vehicle modelled as finite elements.

Suspension Abuse Load Model

An example is shown in Figure 1. A small hatchback vehicle weighing 997kg is driven over a 100mm kerb at 13.4m/s (30mph). At this speed some localised yielding might be tolerated but the vehicle should remain driveable.

Suspension components are modelled with shell elements with elastoplastic material properties, mounted to the body and to each other using spring elements that represent the compliance of the bushes and/or bolts. These have individually determined force-deflection characteristics that mimic those of the real components. The tyre model consists of orthotropic shell elements with internal pressure determined by a control volume. This paper presents work in progress, and at present most of the vehicle body is modelled as rigid, with deformable elements only at the front shock towers. However, the results suggest that body flexibility is significant in determining loads and stresses even in the suspension; it is our intention to include at least a proportion of the body as deformable elements at a later date.

The model statistics are:

• 34284 shell elements
• 396 beam elements
• 108 discrete elements
• Simulation time 0.2 sec
• CPU time 59069 sec (16.4 hours) on a single processor of a Cray J916

RESULTS

Figure 1 shows the vehicle model driving over the kerb. The development of stresses in the front suspension components is illustrated in Figure 2.

Quantifying the loading

The force generated at the top of the spring/damper is shown in Figure 3. The peak force (9.79kN) is equivalent to 3.26g times the front corner weight of the vehicle. Estimates for the loading in this type of event (used for design purposes when no other information is available) would typically be around 3g. Given the extreme deformation of the tyre (Figure 4), it is doubtful whether the look-up table method of calculating tyre forces used by rigid body mechanisms programs would be sufficiently accurate for this situation. The facilities available in LS-DYNA for modelling tyres with finite elements confer a very significant advantage over traditional methods, because of the ability to predict loads.

Out-of-phase loading

Force histories at selected points are shown in Figure 5. The results show some evidence of out-of-phase loading: the forces on the body via the subframe peak at around 120ms, while the force through the shock tower peaks at 128ms. A static analysis of the body in which all peak loads were applied simultaneously would be incorrect. However, the loads on the subframe in this analysis are in phase with each other, all peaking at close to 120ms.

Note also that the longitudinal (X) force on the tyre has a lower and earlier peak that the spindle - the dynamic response of the lower control arm amplifies the loading into the suspension.

Effect of flexibility of suspension and body

To test the effect of the flexibility of the suspension, the LS-DYNA model was rerun with the main member of the front subframe made rigid. The model is otherwise identical to the baseline analysis. Forces at selected points are compared with the baseline analysis in Table 1 below.

Table 1 - Peak Forces for Deformable vs Rigid Subframe Models

	Peak force, deformable subframe	Peak force, rigid subframe (% difference)
Subframe to body, front bolt, X	3.96kN	3.06kN (-23%)
Subframe to body, rear bolt, X	6.59kN	9.81kN (+49%)
Subframe to body, front bolt, Y	2.47kN	1.52kN (-38%)
Subframe to body, rear bolt, Y	12.15kN	1.41kN (-88%)
Wheel spindle, X	11.40kN	13.23kN (+16%)

Subframe flexibility affects the load distribution into the body dramatically. If the suspension members were assumed rigid when determining the loads, any subsequent durability calculation would be grossly inaccurate. It is likely that body flexibility would have a similarly significant effect. The Y-force on the rear bolt is of particular interest. It arises from bending of the main subframe member - as the bolts are offset behind the member, they force the subframe to strain axially as it bends (Figure 6). This effect is not shown with the rigid subframe. The lack of body flexibility in the model exaggerates the difference between the two cases, but the conclusion is clear - assumption of rigid suspension components would lead to gross underprediction of the lateral loads on the body at the rear bolt. Consequently, a durability problem in the vehicle body might be missed.

Ability to predict permanent deformation

Permanent deformations in the shock tower are shown in Figure 7. After the event, the maximum deformation of the shock tower is 1.1mm. If linear stress analysis methods were used, the permanent deformation could not be estimated - the only tool at the analyst's disposal would be a "gut feel" interpretation of the stresses, possibly leading to over-conservative design.

CONCLUSIONS

It is now possible to model certain durability tests as they are carried out in practice, using LS-DYNA. The analysis techniques presented in this paper are most usefully applied in extreme load conditions where nonlinear behaviour and consequent errors in the more traditional techniques are most significant, or where the loads generated by tyre deformation are not easily quantified. These cases also have the advantage of relatively short event times.

The potential advantages are:

• Ability to predict the loads on the structure including those due to tyre response
• Ability to predict the amount of permanent deformation
• More accurate stress predictions because fewer unrealistic assumptions are made.
• The whole event can be modelled in a single analysis
• By animating results, the analyst obtains an intuitive feel for the causes and effects of the loading - this in itself may allow rapid identification and resolution of durability problems.

The models have not been correlated to test. The magnitudes of the stresses and forces quoted should therefore be treated with caution; however, the models clearly demonstrate some important principles and we believe the techniques presented could be developed to form the basis of an accurate predictive method for calculating stresses for durability analysis.

References

1. Hallquist, J.O., LS-DYNA 940 manual, LSTC, 1997
2. Huang L, Agrawal H & Kurudiyara P, Dynamic Durability Analysis of Automotive Structures, SAE, 1998
3. Sturt R and Shah B, Tyre Modelling in LS-DYNA, 4th LS-DYNA Japan Users Conference, 1997