4. Aerodynamics
5.4 Analysis of the Chassis
5.4.1 Finite Element Analysis (FEA)
Finite Elements Analysis, with background from Korsunsky’s ‘B1 Finite Elements Note’s [23], is the most widely used computational method for simulating the behaviour of a mechanical system, and has been used in analysis of static responses of the chassis. The method involves dividing a domain up into a finite number of smaller more manageable sub-domains known as finite elements. Each finite element has its own boundary conditions, and the method effectively equilibrates every finite element to predict the overall response of the whole mechanical system.
This enables the stresses and strains of any geometry to be calculated, however complicated. This is done by using shape functions, most commonly in the form of mapped triangles, due to its very simple geometry. A mesh of triangular elements is created, where the size of the triangles, or alternatively the density of triangles can be defined based on how accurate the calculation is needed to be – a finer mesh uses smaller elements and leads to more accurate results but takes more time to compute.
5.4.2 Impact Testing the Chassis
Before analysing the chassis model, the properties of the material need to be calculated and entered into Solidworks. This was done by defining the shell feature, where the material can be divided up with each layer treated as a unidirectional lamina, where the position, thickness and orientation can be specified. This was done for stacking of orientations [0˚/45˚/90˚/135˚]s
throughout the laminate with each layer 0.5 mm thick. The properties of the lamina to be used have all been calculated using the theory outlined in a previous chapter for a composite material of high modulus carbon fibre to epoxy resin unidirectional plies of volume fraction 50% and the results are shown in Table 5.6, using equations 5.1, 5.2, 5.3, 5.4, 5.7 and 5.10.
and Packaging
Table 5.6 Properties to be entered for simulating the analysis
E1 E2 G12
12
t
c
196 GPa 5 GPa 5 GPa 0.3 1300 MPa 1070 MPa 1630 kg/m3 The analysis tests were simulated on Solidworks using the built in FEA software.
Side Impact Test
The Side Impact Test [24] consists of a load of 7 kN applied to the side impact zone which is specified as the vertical impact zone between the upper surface of the floor and 350 mm above the ground in the direction of the driver, where the maximum allowable deflection cannot exceed 25 mm and there cannot be failure anywhere in the structure, with a failure considering all modes including tensile, compressive, shear or buckling.
Figure 5.14 Description of side impact zone for a monocoque [25]
This Side Impact Test was simulated by the fixing the geometry about where the suspension would be attached to the chassis on the same side as the applied load. Then multiple 7 kN forces were applied to the side of the cockpit. The results are shown in Figure 5.15, with the resultant
deflection, showing the maximum deflection of 4.4 mm with the maximum von Mises stress of 136 MPa occurring at the corners of the cockpit opening, not exceeding the yield stress of the material of around 800 MPa. The Side Impact Test is passed comfortably as it is only required to survive a single applied load, rather than multiple loads distributed evenly over the impact zone of 7.5 kN.
and Packaging
Figure 5.15 Results of the Side Impact Test 5.4.3 Torsion Test
The torsion test isn’t a test specified in the FSAE Rules, but it is very much of interest as high torsional rigidity is thought of as the primary function of high performance chassis. This was also carried out in Solidworks by trying to recreate the effects of cornering on the vehicle. This fixed the geometry to the rear of the vehicle, and then a torque was created on the front of the vehicle by applying two equal and opposite directional forces of 5 kN to opposing sides of the front of the car at a distance of .223 m from the centre of rotation. The diagram showing the resultant displacement of this process is shown in Figure 5.16, where it can be seen that the maximum deflection is 5.1 mm, at a distance of 1.2 m from where the geometry is fixed.
and Packaging
Figure 5.16 Resultant Displacement of the Torsion Test
TorsionalRigidity Torque
AngularDisplacement
2
5
.223 tan
15.10310
31.2
9153Nm/ deg
This is a very good torsional rigidity, satisfying the priority of high chassis stiffness for the design.
5.4.4 Rollover stability test
Rollover stability is specified in Article 6: T6.7 of the FSAE Rules, specifying that the track of the car along with the centre of gravity of the car must combine to provide adequate rollover stability, which is tested on a tilt table. The vehicle must not roll when tilted at an angle of 60˚ to the horizontal, with the tallest driver in the normal driving position. This test involves the calculation of the position of the centre of mass of the full vehicle. A value for this was calculated through superposing the result from Solidworks of the overall chassis with all the components, with additional calculations to take account for the centre of mass of a driver of 77 kg in normal driving position. For a human, this is positioned just above the hipbone, so at the upper part of the circumference of the circle representing the hips in the 95th percentile template. The position of the centre of mass in relation to the z-direction is irrelevant due to the orientation of the tilt table, so it is
and Packaging
only of interest to see where it is in the x-y plane. This point must be inside the centre of rotation, defined as the contact point between the outer surface of the tyre and the ground. The coordinates for the centre of mass of the vehicle are (-17, 284), with the origin positioned on the car centreline level with the floor of the vehicle. When the vehicle is tilted at 60˚, this is not beyond the rotation pivot, or alternatively, angled at over 90˚ to the ground about the centre of rotation, shown by lying right of the horizontal line.
Figure 5.17 Rollover stability test: vehicle tilted at 60˚ to the horizontal