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Technical Paper

Suspension Systems: Some New Analytical Formulas for Describing the Dynamic Behavior

The paper presents some new and unreferenced analytical formulae describing the dynamic behaviour of the suspension system of road or off-road vehicles. The quarter car model (2 degrees of freedom) is considered, the suspension can be either passive or active. Passive suspensions can be simplified as the spring-damper combination or the spring-damper combination with an additional in series spring (representing, e.g., the rubber bushing at the top of a McPherson strut or the rubber bushing at the end joints of the damper). The mathematical system is linear and the excitation is given by a random stationary and ergodic process. The standard deviations in analytical form are given referring to, respectively, the vehicle body acceleration, the relative displacement between sprung and unsprung mass, and the force at the ground. The so called invariant points of the frequency response functions are derived for both active and passive suspension.
Technical Paper

Vehicle Dynamics, Stability and Control

In the last years the number of electronic controllers of vehicle dynamics applied to chassis components has increased dramatically. They use lookup table of the primary order vehicle global parameters as yaw rate, lateral acceleration, steering angle, car velocity, that define the ideal behavior of the vehicle. They are usually based on PID controllers which compare the actual behavior of every measured real vehicle data to the desired behavior, from look up table. The controller attempts to keep the measured quantities the same as the tabled quantities by using ESP, TC (brakes and throttle), CDC (control shocks absorbers), EDIFF(active differential) and 4WS (rear wheels active toe). The performances of these controls are good but not perfect. The improvement can be achieved by replacement of the lookup tables with a fast vehicle model running in parallel to the real vehicle.
Technical Paper

Development of a Control Strategy for a Suspension System with an Active Variable Kinematics

Active and semi-active suspension systems are widely diffused into the automotive industry. Most of the proposed devices try to achieve a better compromise between handling and comfort requirements by replacing traditional springs, shock absorbers and antiroll bars with active or semi-active actuators allowing to change suspension stiffness and damping according to a suitable control strategy. An alternative way for controlling passenger car suspensions is proposed in this paper. Traditional passive springs and dampers are maintained, while the geometry of the suspension and thus its kinematics is actively varied. By changing the suspension geometry, spring and damper rates are in fact varied, this modifying the vertical load on the tire and/or the vehicle height from the ground.
Journal Article

Brake Based Torque Vectoring for Sport Vehicle Performance Improvement

The most common automotive drivelines transmit the engine torque to the driven axle through a differential. Semi-active versions of this device ([4], [5], [6]) have been recently conceived to improve vehicle handling at limit and under particular conditions; these differentials are based on the structural scheme of the passive one but they try to manipulate the vehicle dynamics by controlling the distribution of the driving torque on the wheels of the same axle thus generating a yaw moment. Unfortunately a semi-active differential is not able to perform a complete yaw control since the torque can only be transferred from the faster wheel to the slower one; on the other hand, active differentials ([11], [12], [13]) allow to generate the most appropriate yaw moment controlling both the amount of transferred torque and its direction.