2008-01-0253

Improvement of an LS-DYNA Fuel Delivery Module (FDM) Crash Simulation

Michael Brusoe and Zlatko PenzarContinental

Chris RiedelLawrence Technological University

Copyright © 2008 SAE International

ABSTRACT

This paper proposes and evaluates improvements to a crash simulation of a fuel delivery module in a fuel tank. The simulations were performed in ANSYS/LS-DYNA. Deviations between the original simulation and test data were studied and reasons for the deviations hypothesized. These reasons stemmed from some of the simplifying assumptions of the model. Improvements consisted of incorporating plasticity and strain rate effects into the material models. Performance criteria were also directly incorporated into the material models such that non-performing portions of the model could be deactivated during the simulation. Finally, solid-fluid interactions were added into the simulation to include the momentum transfer from fuel to the fuel delivery module. It was previously thought that effects of a crash would be most severe on the module when the fuel tank was empty and the module was full with fuel. This was challenged because momentum transfer from fuel to the modules exterior was thought to be significant when the tank is half full. The new simulation demonstrates a half full tank is indeed the worst case.

INTRODUCTION

In the development of fuel delivery modules (FDM), simulation is commonly employed to have assurance the final product going into testing will pass, thereby reducing design iterations and cost, improving time to market, and producing a more robust product.

An original ANSYS/LS-DYNA simulation of a fuel delivery module was concerned with assessing the ability to meet two requirements. First, in order to satisfy FMVSS 301, the plastic flange must have been designed in such a way as to fracture in an intended area away form the flange outer surface. This outer surface then, is not breached in the event of a high speed impact. This has the effect of not allowing fuel to escape the flange causing a safety issue. Figure 1

shows one such design. There is sharp step in the interface where the strut is press fit into the polymer flange as pointed out in the figure. This creates an intentional separation area away from any external surfaces.

Figure 1. FDM in the tank environment with strut boss area pointed out.

The second requirement is customer driven and does not allow any damage to the FDM in a low speed impact. This means the struts cannot separate from the flange at the intended area for high speed separation. Also, a permanent bend in the strut rods was not allowed. Some tuning in this area was required such that the rod was not so stiff that too much energy was transferred to the strut boss causing premature separation, and the rods were sufficiently strong such that plastic deformation of the rods did not occur. Also if necessary, some appropriate adaptation of the tank bottom shape in the vicinity of the FDM-to-tank bottom

contact could be made. An example of this is the introduction of tank bottom bumps around the FDM reservoir, preventing its excessive lateral movement and thus extreme bending of struts. Figure 2 shows such bumps.

In a previous simulation, predicting where a separation would occur was done with success. Experimental data was well correlated with simulations and FDMs could be sent into FMVSS 301 testing with confidence of passage. However, correlation between experiment and simulation for the second requirement was not as successful. For a customer prescribed low speed impact, strut separation was seen as was plastic deformation of the strut rods where simulation did not predict this. This required implementation of countermeasures and retesting which increased development costs.

The intent of this work was to demonstrate feasibility of an improved simulation and to qualitatively show better correlation with physical experiment. Quantitative correlation is not intended at this point and as a result, the models were kept as simple as possible.

THE ORIGINAL SIMULATION

Figure 2 depicts the original model which consisted of a polymer flange with steel struts press fit into bosses at the base of the flange.

A - Strut

B - Flange

C - Reservoir

D - Spring elements

E - Tank shell

F - Retaining bumpsE

A

B

E

C

D

F

Figure 2. Original FDM model

The struts then were connected via a sliding interface into a reservoir which contained masses to simulate internal components. A section of the top and bottom of the fuel tank were modeled such that the flange was firmly attached to the top and the reservoir rested against the bottom as can also be seen in figure 2. Spring elements between the flange and reservoir were

used to apply a pressing force to the reservoir towards the tank bottom that held it in position on the bottom simulating actual pre-stressed springs in the physical assembly. Bumps in the tank bottom meant to restrain the reservoir against side loading were also modeled.

The material model for the flange polymer was bilinear isotropic hardening plasticity. This model was intended to capture the plastic response of the polymer. Parameters for the model were experimentally determined. Steel in the struts were modeled with a simple linear elastic material. The reservoir was shell modeled and the material defined a rigid. The rigid material model greatly reduced the computational resources required for the simulation by reducing the numbers of degrees of freedom for the entire shell to six located at its center of mass. The tank top and bottom was modeled with a linear elastic material model. Loads were applied to each node of the tank top and bottom in the form of prescribed time dependent displacements. These were interpolated from a system level (entire vehicle) simulation performed at the OEM. As the particular tank studied behaved almost like a rigid body in OEMs investigations, an additional version of tank loading was attempted by loading the tank as a rigid body, exposed to time-dependent accelerations as measured close to the tank flange opening in OEMs crash tests. Both of these tank loading treatments resulted in similar results concerning the FDM.

There were several reasons theorized for the simulations’ deviation from experiment relative to the second requirement. First, it is clear that with a purely elastic material for the struts, no plastic response is possible. Upon seeing plastic deformation in the struts during experiment, it was deemed desirable to include a plastic response. It was also suspected that strain rate effects may be significant. An additional observation was the fact that when strut separation did occur, it occurred by the strut slipping out of its press fit in the simulation. In experiment a fracture occurs in the strut boss on the flange. Finally, fluid effects were not considered in the original simulation. Having a fuel tank mostly empty and the reservoir full would have the effect of increasing its apparent mass making inertial loading more severe. (There is a pump in the reservoir that draws fuel from the tank and keeps it full). An additional fluid consideration is the slosh wave. If the tank is about half full, fluid on the other side of the reservoir has room to move out of the way. A slosh wave can hit most of the side area of the reservoir transferring considerable momentum to the reservoir. This momentum transfer direction is approximately the same as the primary inertia force on the solid bodies in the tank, caused by impact accelerations. Therefore, this effect increases the effective load on the FDM. The case where the tank is mostly full was thought to be a best case in that the reservoir's motion would be impeded by the viscosity and inertia of the fluid.

AN IMPROVED SIMULATION

MATERIAL MODELS

To account for plasticity in the steel strut rods, a bi-linear isotropic hardening plasticity model was chosen. This model is generally suited for large deformation. The Bauschinger effect is not included and upon yielding, yielding in the reverse direction occurs at twice the original applied stress. Additionally, strain rate effects were considered using the Cowper and Symonds model. In this model, the yield stress is scaled by:

P

C

/1

1

+

ε&

Here, ε& is the strain rate and C and P are parameters. For the model, typical values of C and P were taken as 40.4 s-1 and 5 respectively for steel from the literature [1].

From the original simulation, the bi-linear isotropic plasticity model was fairly successful for modeling the polymer flange. However, new data was acquired which accounted for strain rate effects. LS-DYNA has a material model in which one can import individual stress vs. strain curves for each strain rate. This is the piecewise linear plasticity model. Additionally, it is well known that polymer material properties can be very dependent upon temperature. This being the case, three separate material models were created to include -40°C, 23°C, and 65°C. However, in this work, only 23°C was considered. To capture separation of the strut boss from the flange under sufficient loading conditions, a failure criterion was added to the material model which deactivated elements from the simulation once maximum principal strain reached 20%. With this, a fracture initiation and the tendency of its propagation could be simulated.

FLUID MODELING

To model the effects of fluid, a complete tank was constructed in which to contain the fluid. The tank for this vehicle had an approximate shape of a rectangular prism. Being the intent of this work was to qualitatively show an improvement with physical correlation, not quantitatively validate a design, a very simple rectangular prism was taken for the tank geometry, with global dimensions equal to those of the real tank. The tank was shell meshed and given elastic material properties.

To model the fluid, the mesh less technique Smoothed Particle Hydrodynamics was chosen. This has been incorporated into LS-DYNA in recent years and has shown to have some advantages over finite elements for modeling fluids. Large distortions which would cause numerical issues with a Lagrangian finite element mesh are well tolerated. Also, computational cost can be

reduced compared to an Eulerian mesh because the entire problem domain does not have to be discretized, only the fluid. It is also easy to track the fluid interface through time. Liu and Liu provide an excellent description of the theoretical background and applications of the technique in their book "Smoothed Particle Hydrodynamics a Meshfree Particle Method" [2]. In the application here, the field equations were represented as an integral form with a smoothing function and then converted to sums. In this way, a particle in influenced by its neighbors. The smoothing function used was the cubic B-spline which is commonly used as it has good properties of regularity. This is all done internally in LS-DYNA. To demonstrate the applicability, advantages, and drawbacks of the technique, Castelletti, et al. performed a comparison to Lagrangian, Eulerian, and ALE techniques in two papers directed at examining a helicopter fuel tank impact with the ground and a hail impact on the nacelle of a turbofan engine [3, 4].

Figure 3 below shows a typical model construction. A rectangular, shelled tank is attached to the original top and bottom interface containing the restraining bumps. The FDM model is contained in this interface as before. The SPH fluid is contained in the tank and is at a predefined fill level. A convenient aspect of using an SPH fluid is the coupling with the tank and bump shells and also the reservoir shells is easy to accomplish with simple fluid geometry. Since shells have no physical thickness (only thickness mathematically assigned in the formulation), they fit neatly between SPH particles. The fluid then was initially a rectangular slab. Once motion starts, the particles are prevented from penetrating the shells by a penalty coupling algorithm. If a finite element mesh were used for the fluid with the Langrangian treatment, the fluid would have to be carefully meshed around the shells.

Figure 3. FDM in tank with SPH fluid

The material model selected for the fluid was the null material available in LS-DYNA. This model is well suited for fluids because deviatoric stresses are not

calculated. An equation of state is used to relate density to pressure from which stresses are calculated. Optionally, viscosity effects can be calculated from the deviatoric strain rate.

The equation of state used for the improved simulation was the linear polynomial equation of state given as:

( )ECCCCCCCP 2654

33

2210 µµµµµ ++++++=

Where

10

−=ρρ

µ

Here P, E, ρ , and 0ρ are pressure, initial energy per unit reference specific volume, density and reference density respectively. C0 – C6 are constants [5]. This equation of state is linear in internal energy. For the application here, C1 was set to the bulk modulus of the fluid which was 2300 MPa. Setting the remaining constants to zero gave a simple elastic fluid. Perhaps a more direct approach might have been to simply use the elastic fluid material model in LS-DYNA in place of the null material and equation of state. However, the approach used here allows for greater possibilities later. For example, the equation of state can be manipulated to give the gamma law ideal gas equation to represent the headspace in the tank, or even fitted to physical test data.

Coupling between the SPH fluid and the finite element solids was accomplished with penalty based contacts. In this treatment, a restoration force is created when an SPH particle penetrates a finite element defined as contact. This restoration force is proportional to contact stiffness and penetration depth and so can be viewed as placing a spring between the penetrating particle and contact surface.

SIMULATION SPECIFICS

For the new simulation, the original model and mesh from the old simulation was used. The new components were built around the old and attached as appropriate. The new tank shell was coarsely meshed with 25mm spacing between the nodes. This was because stresses, strains, and relative displacements of the tank itself were not of interest in this study. The new tank shell was attached to the old top and bottom using tied nodes to surface contact. In this way, motion from the original model was transferred to the new tank. An initial velocity was applied to all components in the first few milliseconds of the simulation. Then, motion with the subsequent deceleration applied to the original tank top and bottom. The other components interacted by means of their associated contacts. The SPH particles had an initial spacing of 15mm, consistent with a previous test case.

For efficient simulation, the mesh had to be kept very regular. There was a fine balance between having a mesh fine enough for clear resolution and coarse enough for reasonable execution times. Typically, the mesh size in areas of interest was on the order of a millimeter. With this, the execution time was predicted to be on the order of 700 hours by the software. To reduce this time, mass scaling was incorporated. This had the effect of increasing the maximum time step of the some of the elements with the smallest time step in the simulation by increasing their apparent mass density. Since the maximum time step of the simulation is the time step of the element with minimum time step, the simulation time can be significantly reduced. In this simulation, the 700 hours was reduced to 70 hours with a mass gain of nine percent.

SIMULATION RESULTS

Simulation results were typically favorable. Many of the limitations imposed by the assumptions of the original model were overcome and the results were, from a qualitative standpoint, much better.

Figure 4 below shows an FDM in a tank without fluid 100ms after a low speed impact. There is considerable plastic deformation in the strut rods. Most likely, there is some tuning of the material properties necessary as this was a first attempt. Fully annealed properties were used for the steel which is probably too soft.

Figure 4. FDM in an empty tank

Figure 5 below shows an FDM filled 25% with fluid 100ms after low speed impact. Here, plastic deformation in the strut rods is seen, but more toward the middle of the rod. The reservoir was restrained by the tank bumps and inertial forces in combination with the momentum transferred from the fluid created a bending action, somewhat resembling a simply supported beam loaded in the middle.

Figure 5. FDM in a 25% filled tank

Figure 6 below has an FDM in a half filled tank 100ms after low speed impact. In this case, the bending is much more pronounced. Additionally, one of the polymer strut bosses has fractured in its intended separation path. This is more clearly visible in figure 7. This type of fracture is consistent with experiment which gives added confidence that the failure criterion set forth in the material model has functioned properly.

Figure 6. FDM in a half filled tank

Figure 7. Detail view of boss fracture

Figure 8 below shows an FDM in a full tank 100ms after low speed impact. In this case, there is no plastic deformation of the strut rod or damage to the polymer flange boss. This is because the movement of the reservoir was impeded by the viscosity and inertia of the fluid.

Figure 8. FDM in a full tank

Figure 9 below shows an FDM in a half filled tank during a high speed impact. Here, considerable plastic deformation of the strut rods is seen. Also, both polymer strut bosses have separated. Separation in this manner is consistent with experiment.

Figure 9. FDM in a half full tank after high speed impact

CONCLUSION

The results of the improved simulation were encouraging. Phenomena seen in physical experiment have been qualitatively realized. In particular, it was demonstrated that a half full tank produced a slosh wave that resulted in the most severe damage to the FDM. Additionally, a new means to simulate solid fluid interactions in the fuel tank environment has been acquired. Although, more work is required to fully evaluate the method and develop a quantitative simulation. The method was easy to apply and produced good qualitative results.

The next logical step to carry this work forward will be to model an actual fuel tank. Automotive fuel tanks are much more complex than rectangular prisms. The shape is such that it can be packaged easily in an automobile and associated tank components can be packaged in and around the tank. Additionally, baffles

are typically used to reduce the effects of slosh waves. As the slosh wave is a major contribution to the effects on the FDM, an accurate baffle system should be modeled in the simulation. Once the above has been accomplished, the material properties and parameters in the model can be tuned to represent actual physical experiment. These results can then be used to create new simulations and make predictions.

ACKNOWLEDGEMENT

We appreciated the engaged and helpful suggestions by Dr Uli Stelzmann of CADFEM GmbH, our German support for ANSYS/LS-DYNA.

REFERENCES

1. Weijia W., Thomson R.,”A Study of the Interaction Between a Guardrail Post and Soil During Quasi-static and Dynamic Loading”, International Journal of Impact Engineering 34 (2007) 883-898.

2. Liu G.R., Liu M.B., “Smoothed Particle Hydrodynamics a Meshfree Particle Method”, World Scientific Publishing Co. Pte. Ltd., 2003.

3. Castelletti L., et. al., “Fluid-structure Interaction of Water Filled Tanks During the Impact with the Ground”, International Journal of Impact Engineering 31 (2005) 235-254.

4. Castelletti L., et. al., “A Survey of Numerical Models for Hail Impact Analysis Using Explicit Finite Element Codes”, International Journal of Impact Engineering 31 (2005) 929-944.

5. Hallquist J.O., “LS-DYNA Theory Manual”, Livermore Software Technology Corporation, 2006