1. Introduction

High rigidity and lightweight are important factors in every frame of racing cars, and the same can be said for the vehicles of Formula SAE. So the frame had been designed to meet a better balance between rigidity and lightweight.

To achieve this aim, the target value of the torsional rigidity of the frame was determined in the test run, and the conditions of analysis were also developed to be able to measure the compartment of the frame which concerns the actual driving conditions of the vehicle. Additionally focusing on the dynamic conditions of the vehicle, special devices for the frame were employed.

The following is the improvement of the frame of the 2008 year’s model from past models.

2. Frame design

2. 1 Analysis

The frame is a space frame structure made by steel pipes (STKM). To calculate the torsional rigidity of the frame, the “beam analysis tool” in the PTC Mechanica was used.

Fig.1 beam analysis - Sophia Racing Lines between points in the 3D space (shown in Fig.1) can be treated as steel tubes by this tool, and this has the advantage that analysis time becomes shorter than that of normal FEM analysis.

The effect of end compartments of the frame (for example, bulkhead) in the actual driving conditions of the vehicle are considered small.

So in the analysis, points of applying the loads were located on the centre of front wheels, and constraints were located on the centre of rear wheels to be able to measure the influence of the wheel base length and the compartment of the frame which concerns the actual driving conditions of the vehicle.

2. 2 Target value of torsional rigidity

2005 year’s model had high torsional rigidity of 967Nm/deg, but the weight of the frame was so heavy which was 36kg. By cutting off some frame members of the 2005 year’s model and repeating road tests, the minimum target value of the rigidity of the frame was estimated.

Finally, the target value was determined to 403Nm/deg. Rigidity and Weight of 2006 year’s model was finally designed to 562Nm/deg and 25kg, which is 9kg lighter than 2005 year’s model as shown in Fig.2.

Fig.2 Target value of torsional rigidity - Sophia Racing

2. 3 Improvement of structure

As shown on Fig.3, considering F-SAE regulations, for the front section, to ensure the strength of bell crank pivots, we decided to adopt push rod style which mounts bell cranks on front hoop bracing (these pipes are required to be 1.6mm thick by collision safety regulation) instead of pull rod style which mounts bell cranks on sub frames (these pipes are 1.25mm thick).

Fig.3 Improvement of structures - Sophia Racing

For the rear section, the truss structure and the downsizing of the frame improved the frame rigidity. Fig.4 shows the effect of this truss structure.

Fig.4 Distribution of Frame Rigidity - Sophia Racing

3. Additional mountings

3. 1 Steel plates in the frame joints

Steel plates were set in the frame joints, which improved the rigidity by passing loads effectively from one pipe to another. This effect was measured by static experiments. As you can see from the result is shown in Fig.5, the displacement of the frame members was reduced by 19 percent in the concerned areas.

Fig.5 Load vs. Displacement - Sophia Racing

3.2 Chassis damper

Focusing on the dynamic conditions of the vehicle, “Chassis Damper” (which is shown in Fig.6) was employed in the frame.

Fig.6 dampers mounting points- Sophia Racing

The damper is a mono-tube type damper with no orifice characteristics, and it’s damping force works even on extremely slow piston speed range and can attenuate the slight deformation of the vehicle body.

By examining the impulse response of the vehicle body and analysing the frame damping characteristics of the frame, the effects of the damper were evaluated.

Fig.7 shows the displacement of the damper when the vehicle was dropped from 50mm above the ground. As one can see from the graph, amplitude is suppressed by 30 percent, and it is obvious that the oscillations settled quickly.

Fig.7 Examination result of chassis dampers - Sophia Racing

Frame members can be regarded as spring elements when considered the deformation of chassis in driving.

Without the damper, the vehicle rigidity would need to be increased by 1.4 times to achieve the same effect (Fig.8).

Fig.8 Image of the spring model - Sophia Racing Damping this deformation contributes to high chassis performance. Therefore, two dampers were adopted between the frame members near the A-arm pivot points.

Its effect is so remarkable that any driver can feel the difference even in normal driving. Benefits of such a damper are shown under the high performance setting of the FSAE competition.

4. Conclusion

Finally, the torsional rigidity of 2008 year’s model was designed to 853Nm/deg, and the weight of 24kg (incl. steel plates). If the torsional rigidity of the frame is not enough, the change of load transfer by the alternation of suspension-setting is considered to be unclear.

So in the test run, load transfer amount were measured by suspension stroke sensor to evaluate whether the torsional rigidity of the frame was enough or not.

Fig.9 shows the amount of lateral load transfer according to roll rigidity distribution change. As one can see from the graph, load transfer amount according to roll rigidity distribution change fit in theoretical lines, which means that the frame has enough torsional rigidity.

Fig.9 Load transfer amount according to roll rigidity distribution change. (Dashed lines are theoretical, and plots are actual measurement amount.) - Sophia Racing

Therefore, the space frame design had achieved to meet the goal of being both rigid and lightweight.

References

Race Car Dynamics: William F. Milliken Doughos, L. Milliken, Society of Automotive Engineer, Inc.
Development of the Performance Damper: Seiji Sawai, Kouji Sakai, Katsuhiro Kondou, Masashiro Satou