Velocity Frequency Analysis for a Transverse Half-Car Model With Third Damper Using Bond Graph Approach

Abstract

We present a bond graph analysis of a three-damper suspension system in a transverse half-car model. This is compared against the conventional two-damper system used in most commercial and racing vehicles. The transverse third damper system pioneered by the Koenigsegg Triplex suspension system is an innovative design said to improve straight-line tire contact during single-sided disturbance and help mitigate the adverse effects of squat and dive, while not inhibiting the function of the anti-roll bar’s lateral load transfer in cornering capability. No published literature exists exploring a transverse half-car model with effects of a third damper. We focused specifically on mathematical modeling of energy element relationships exploring vehicle dynamics frequency response behavior compared between transverse half-car models with and without the third damper. Calculated transfer functions explore first-order time derivative relationships of wheel-mass velocity to the harmonic input velocity of the road surface. The mathematical model demonstrated some ranges of resonance within typical driving and racing frequencies. Implementing the model to a Formula SAE race car, we explored the effects of manipulating spring stiffness, anti-roll bar stiffness, damping ratio, and mass in both two- and three-damper systems. Ultimately, it was observed that the addition of the third damper resulted in objective improvements in vehicle dynamics, shown by a reduction in amplitude ratio of both the left and right wheels compared to a conventional system. Interestingly, the left wheel (input side) experienced a greater reduction in amplitude ratio when it was hypothesized that the right wheel would be more affected.