Finite element analysis and torsional rigidity

Once the CAD model has been created, one of the most important parts of the present project is the creation of a FE model of the chassis to work out the torsional stiffness and to carry out an iterative process of changing and adding tubes in order to increase the torsional stiffness of the car.

In the present work it is need a reliable and easy adaptable model, not too time consuming when meshing and solving and easy to change the configuration of the tubes in order to test the influences of the changes in the configuration and the effect of the aluminium plates with or without rivets. In order to do that and as described in

the bibliography different simplifications have to be made in the FE element model. The approach of creating a model with the polyhedral configuration has also been tested, but has been rejected due to the problems presented when meshing, the lack of adaptability and the too high consumption of time. In order to overcome the meshing difficulties, advanced meshing software has been tried to create a good importable mesh to import into ANSYS obtaining unsuccessful results and due to the other approach selected this approach has been abandoned. In futures works an approach of image-based meshing from the stl has to be tried in order to improve the automation of the simulations.

Instead of that and as mentioned before, the approach of exporting the lines and meshing the tubes with BEAM 188 elements, given the different sections and meshing the aluminium plates with SHELL181 elements, has been undertaken. Related to the quality of the mesh, by default, ANSYS uses a mesh density that provides accurate results for torsional stiffness and even for nonlinear material calculations. Increasing cross-section mesh size, does not imply larger computational cost if the associated material is linear (ANSYS Online Documentation).

The configuration options for exporting into ANSYS the lines obtained in the last section are shown in the Figure 16. It is very important, once the model has been imported, to check the dimensions of the model by checking the distance of two key points known and if necessary, to use the scale option to scale the model to the correct dimensions.

Figure 16. Exporting lines as IGES file configuration options.

The next step is to define the element type, the materials models and the different sections of the different tubes of the chassis. As mentioned above in the selected approach, BEAM188 elements for the tubes and SHELL181 elements for the plates will be used (Raju, 1998). One of the most important characteristics of ANSYS is the possibility of automation of the process of creating a model. Once the IGES file with the lines of the chassis has been imported a txt file with all the commands can be created. This can be useful when starting other models and when doing smooth changes. Figure 17 shows the lines imported into ANSYS.

Figure 17. Lines of the chassis exported into ANSYS

Once the element types have been defined, the next thing to do is to define the sections used with the beam element to model the frame sections of the chassis. This can be made using instructions to define the 5 section types, thus each smooth change could be made in a txt file and easily pasted in the command bar (see Appendices for the commands and sections defined).

The next thing to do is to set the real constraint for the SHELL181 elements to give the thickness of 1.5 mm to the aluminium plates and the material properties of the materials. In order to create the model of the standard chassis of the Ultima GTR, two materials models have been created, one is steel for the dia tube MIG welded frames and the second one NS4 aluminium alloy. In order to create the material models in ANSYS, the Poisson coefficient and Young module have been inserted. See the Appendix for more detailed specification of the materials used. The aluminium and steel used in the standard chassis have the following Young module and Poisson coefficient:

Table 2. Material properties

Once the parameters have been set, the next step to do is to model the aluminium plates, this can be made directly in ANSYS with the modelling options or in Solidworks and exported into ANSYS. The Aluminium plates have been modelled as areas (see Figure 18 )

Figure 18. Aluminium Plates

The plate at the bottom of the cock pit is welded and will be modelled in ANSYS as attached to the frames (see Figure 19).

Young´s modulus

(GPa)

Poisson

coefficient ν

Steel

205

0.29

Aluminium

70

0.33

Figure 19. Welded cockpit plate

The next step is to apply the boundary conditions and loads. The boundary conditions have to be set to model the mechanical trials for working out the torsional stiffness. The computer simulation has the advantage of the possibility of applying the loads in any direction but in real trials applying forces in any direction is not that easy. Following the instruction of the configuration of the trial from Milliken and Milliken (1995), the chassis will be constraint in 4 key points at the rear, deleting the 6 degree of freedom of each node and other constrain is set at the front acting as a hinge joint with the displacement in the three axles eliminated and just allowing the roll. Two forces have also been applied in different directions to twist the chassis in the x axle. It is preferred to set the loads and constraints to the key points as are geometrical entities, better than applying it to nodes that could be removed when remeshing. The two forces have been applied in the key points of the front-front suspension. These forces twist the chassis and this movement produces a variation in the z axle of the key points where forces are applied (Figure 20 and Figure 21). By measuring this displacement we can get the angle the chassis has been moved and relating it to the force applied we can easily work out the torsional stiffness of the chassis (see Figure 5).

Figure 20. Constraints at the rear

Figure 21. Loads and constraint at the front

The torque applied is the product of the force applied at one key point and the distance from the point of application to the centerline of the car. The deflection is taken to be angle formed from the center of the car to the position of the deflected

corner. In order to work out the torsional stiffness we take the average of the right and left deflections so we are generating a more accurate estimate of the total angular deflection of the chassis of the Ultima GTR (Riley, 2002).

Though this trial is easy to be done in FE software as Ansys this configuration is difficult to reproduce in a laboratory as it is quite difficult to apply a vertical load counter to the direction of gravity. Instead of that in many torsional stiffness trials a known weight is hanged on the corner of the chassis to allow it to pivot about a roller. This method can be seen in the Figure 22.

Figure 22. Configuration of the trials usually applied in a lab (Riley, 2002)

In the present work and due the facility of setting the loads in the direction required the approach of setting one force in each corner has been carried out.

Once the geometrical configuration of the model, the constraints and the loads have been set the next step is to mesh the model. It is important to explain here a bit the approach followed to model the rivets. As said before the FE model made in the present work aims to be reliable and easy adaptable, not too time consuming when meshing and solving and easy to change the configuration of the tubes in order to test the influences of the changes in the configuration and the effect of the aluminium plates with or without rivets. In order to achieve that a simplification when modelling

the rivets has to be carried out, otherwise if we would like to create a more realistic model of the rivets we should made a model based on the polyhedral representation of the CAD of the chassis, but this would lead to a high time consuming and not easy to adapt model that is not what we are aiming in the present project. Future works should compare the results with the two different approaches and characterize the influence of the simplifications made.

In order to model the rivets, nodes can be located every 30 mm both in the plates and in the tubes. This can be made by giving the manual size of the entities with the command LESIZE and AESIZE and setting the element edge length to 30mm. Once the manual size has been given it is time to mesh the model. It is important to be careful when selecting the elements types, the materials models, the real constant and the section numbers as any mistake will lead to confusing results.

Figure 23 shows the model meshed with the aluminium plates with the ESHAPE command (ANSYS Online Documentation) activated to display the elements with shapes of the section defined.

Once the model is meshed it is time to model the rivets, this has been made in the present project by coupling degrees of freedom of the nodes representing the rivets in the lines and in the plates. The coupling option of ANSYS is very useful when modeling forming pins, hinges, universal, and slider joints between two coincident nodes. This option force two or more degrees of freedom (DOFs) to take on the same unknown value forcing the nodes in the frames and in the aluminium plates of the model to behave as rigid bodies. A set of coupled DOFs contains a prime DOF, and one or more other DOFs. Coupling will cause only the prime DOF to be retained in the analysis' matrix equations, and will cause all the other DOFs in a coupled set to be eliminated. The value calculated for the prime DOF will then be assigned to all the other DOFs in a coupled set (Figure 24).

Figure 24. Model of the rivets

In the present job, the rivets of the two plates of the cock pit have been modeled and at the front, one plate has been modeled as a riveted plate and at the opposite corner the other one has been modeled as a plate attached to the tube by all his nodes, in

order to compare the difference of modeling the plate transmitting the forces just by points situated every 30 mm (with rivets) and simply attached to the tube (without modeling rivets) as a completely attached part (Figure 25).

Figure 25. Rivets in the plates of the left side of the chassis

One very important thing to do is to verify the connectivity of the different elements. One of the causes that lead to a very confusing results is when two adjacent elements are not joint together because of two key points situated in the same position have not been merged correctly or inaccuracies when modelling the lines and the joint points in the CAD software. This is an important step to be done. As looking for non connected frame in the model could be quite tiring due to the high amount of nodes and elements a simple program called grow up will be written and used to show that all the elements are connected. This program select all the elements attached to a selected node and select the nodes of the selected elements

and replot the new entities selected. Figure 26 shows verification steps of the mesh connectivity.

Figure 26. Mesh and verification

Once the connectivity of the elements has been verified it is time to solve the model by using the current LS solver. After about 4 minutes the solution is done and we can check the results in the general post processer.