# Multi-Criteria Optimization of an Innovative Suspension System for Race Cars
## 1 Introduction
The suspension designed for a race car (rear wheel drive and front wheel steering) presented in [36] is designed from tubular components. The front axle suspension is designed from a quadrilateral mechanism with unequal arms that is linked to the chassis by ball joints. The spring and damper assembly is mounted in a quasi-horizontal position. The main disadvantage in this suspension system is the fact that it changes its dynamic behavior by changing the camber (\(\gamma\)) and caster (\(\beta\)) angles, presented in Figure 1, and wheel track during cornering. This resulted in non-linear behavior and required compensation of the steering wheel angles during cornering. At the same time, the constant change of caster angle during cornering resulted in a change of zero return (straight ahead) of the steering forces, and this induced variation in the required steering force. Based on the above analysis of the existing solutions, the suspension system found to be the most commonly used on a Formula Student single seater (for both the front and the rear wheels/axle) was based on four-bar guiding mechanism (also called SLA--short-long arm). Compared with the regular suspension systems used by passenger cars in which the spring and damper assembly is mounted vertical (usually between the upper suspension arm and the chassis, as shown in Figure 2a), in the case of the single-seater race cars, the spring and damper assembly was mounted horizontally (Figure 2b), and this would help  
Figure 1: Camber and caster angles. with force distribution and keep the chassis as low as possible. It is important to mention that both suspension systems presented in Figure 2 had a single degree of mobility (i.e., the wheel vertical travel--Y\({}_{\text{K}}\)). The suspension system shown in Figure 2b imposed the use of a pushrod and rocker assembly that transferred the vertical movement from the wheel to a horizontal movement to the spring and damper assembly. The rocker assembly was linked to the pushrod and the damper assembly. This allowed for the reduction of the force that the wheel transferred to the spring and damper assembly by changing the length of the rocker arms and angles, creating the opportunity to use a smaller spring and damper assembly. Such a solution could confer the following benefits: It could decrease the variation of the camber angle, it would need a small space to be fitted, and it could accommodate tuning for both road wheel toe angle and camber angle. On the other hand, as a main disadvantage, it is well known that the four-bar suspension mechanism has contradictory behavior regarding the wheel track and camber angle variations (decrease of one of these variations generates the increase of the other one). Starting from the classic four-bar suspension mechanism, a possible solution to avoid the above-mentioned issue is to transform the passive (pure mechanical) suspension into an active (controlled) one, and this could be achieved with the solution shown in Figure 3. In this regard, a linear actuator type assembly was disposed between the chassis and the suspension. In this way, a three-contour mechanism with two degrees of freedom (the wheel travel and the actuator movement--expansion or compression, by case) was obtained, which helped in minimizing the wheel track variation. Figure 3: Scheme of an active suspension system derivate from the four-bar mechanism. Figure 2: Sketch of the classic four-bar suspension system (**a**) and the configuration used on single-seater cars (**b**). Besides the wheel track variation reduction, the active system had the advantage that it could change its ride height according to the weight of the vehicle and the dynamic loads that appeared during braking, accelerating, and cornering. The active suspension system behavior was mainly based on the sensors that had to read the road ahead and prepare the damping and spring stiffness for the upcoming irregularities in the rolling surface so that the driver (and the passengers as well) would feel as little as possible in the cockpit [37, 38].