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Physical Testing of the Chassis
The chassis supplied by Luego was tested on a torsion rig to determine its torsional stiffness. The suspension planned for the chassis is of the coil-spring over damper variety. This implies all loads will be applied through these mounting points. The coil-over mounts were therefore used for the constraints and load. An object always has six equations of equilibrium, three force equations and three moment equations. In order to achieve a statically determinate system, six forces must then be applied. As can be seen in Fig.24 this was accomplished by restraining three of the coil over suspension mounts of the chassis and applying a load to the free suspension mount. If more than six restraints are employed the structure becomes statically indeterminate making the chassis appear stiffer than it is. The deflection was measured along the length of the chassis on both sides with dial test indicators and the global torsional stiffness calculated as described in chapter 4.
Fig. 24 Many torsion figures claimed by manufacturers for vehicles are arrived at while using torsion rigs with seven or more restraints causing the over constraint as described above, i.e. the chassis is fully restrained on both rear corners and at one front corner. Fig. 25 shows the left rear restraint. The restraint is mounted to the chassis suspension mounting points with ball joints to prevent any moments being applied. The gaps between the ball joints and the suspension mounts are filled with spacers to prevent movement.
Fig.25
The load was measured with a Horseshoe Dynamometer as shown in Fig. 26 and applied with a turnbuckle. The chassis was preloaded with the turnbuckle before any load and deflection measurements were taken to take up any slack in the rig.
Fig. 26
Fig. 27 shows the deflection measurement points on the chassis.
Fig. 27 Dial Test Indicator measurement positions
1 – Front left suspension mount 2 – Front right suspension mount 3 – Left footwell bulkhead 4 – Right footwell bulkhead 5 – Left mid-passenger compartment 6 – Right mid-passenger compartment 7 – Left rear suspension mount 8 – Right rear suspension mount
From the measurements the Global torsional stiffness K = 1330 Nm/Deg FE Modelling Description and Validation of Baseline Model
FE Model
To begin the Finite Element analysis a model of the chassis must be created. This was achieved using the universities Patran/Nastran FE modeller/solver software. It was decided to create a line model of the prototype chassis. This type of model is not a dimensionally or geometrically perfect copy of the prototype but a simple representation of it. This was chosen to facilitate relatively simple modification of the baseline model for the improvement study. The results are not intended to be 100% accurate but are intended to give an indication of the stiffness achievable and the effects each of the modifications has. Patran/Nastran
The finite element analysis software used is the Patran/Nastran geometric and solver package developed by MSC [Ref. 6]. Patran is the geometric section where a line model representative of the chassis is created. The geometry (cross sectional area A; 2nd moment of inertia Ix, Iy; torsion constant J), element type, load cases and application regions, material properties (Young’s modulus E; shear modulus G; Poisson’s ratio m; density kg/m3) and basic analysis are selected and created. The Nastran solver can then be employed for the full analysis of the structure. The output file is then read back into Patran for viewing the results. The geometry is modelled in 3D with point-to-point lines representing the beams and tubes and their intersections. Surfaces are also created in this way with either points or lines representing surface vertices or edges. The element type can then be selected and a mesh applied to all beams and surfaces. The element types selected were the Beam element for all beams and tubes, and the shell element for all surfaces. Bar element
The RBAR element is a beam element that supports tension, compression, torsion, bending and shear in two perpendicular planes. It connects two nodes and provides stiffness to all six degrees of freedom in each end. Its gravity axis, elastic axis and its shear centre are all coincident [Ref. 6].
Shell element
The shell element chosen for modelling surfaces and panels was the QUAD4 element. This is a 2-dimensional shell element that can represent in-plane bending and transverse shear behaviour. This means it only has five degrees of freedom at the nodes, the rotational degree of freedom perpendicular to the element is unconnected and must be given an artificial stiffness. This is performed in Patran by setting the K6ROT – parameter to a greater than zero value [Ref. 6]. Model correction
A number of models were created, as the stiffness value necessary was not being obtained. Upon analysis of these models, it was found that some of the geometry of the engine bay was incorrect. This was modified but the stiffness value was still not in the region of the physical test result further analysis of the model was required. After thorough examination of the model, it was discovered that the main engine bay top rails were not connected to the front suspension box. With this corrected the model achieved a stiffness value of 1352.33 Nm/deg.
The model should not be expected to give completely accurate results when comparing with a torsion test of the real chassis, as certain simplifications may be influential: - Offset connection of two tubes, leading to local bending is not included in the model. - Varying material thickness due to welds, etc. has not been taken into consideration. - A finite element model assumes that joints are infinitely stiff, which is incorrect. - The suspension mounts are approximate to the actual shape and exact location. These factors should lead to the model being slightly stiffer than the test result as has been found with this model.
Fig. 28
Table 2
This model [Fig. 28] represents the prototype chassis as supplied by Luego for physical testing. All modifications were made to this model to ensure as accurate a stiffness value as possible. The areas highlighted in green are mild steel panels. The engine plates, gearbox plates, roll bar plates and rear side plates are all 3mm thick with the remaining floor panels and footwells 1.6mm thick.
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7.4 Final Validation of Baseline Model
The mass of the model is higher than the physical chassis due to a number of factors. The modelling software does not take into account that material is removed from each beam where it joins another, i.e. at every joint the software assumes that the material from each beam is present so for a joint with four connecting beams there will be material from each beam at the same point. The software also extends the material of angled beams past their end-points on the chassis. As previously mentioned the model is also not an exact geometrical copy. This material will add up to give the excess mass. These phenomena can be seen in Fig. 29 below.