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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

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.
Technical Paper

A 2D Model for Tractor Tire-Soil Interaction: Evaluation of the Maximum Traction Force and Comparison with Experimental Results

The paper investigates the interaction between soil and tractor tires through a 2D numerical model. The tire is schematized as a rigid ring presenting a series of rigid tread bars on the external circumference. The outer profile of the tire is divided into a series of elements, each one able to exchange a normal and a tangential contact force with the ground. A 2D soil model was developed to compute the forces at the ground-tire interface: the normal force is determined on the basis of the compression of the soil generated by the sinking of the tire. The soil is modeled through a layer of springs characterized by two different stiffness for the loading (lower stiffness) and unloading (higher stiffness) condition. This scheme allows to introduce a memory effect on the soil which results stiffer and keeps a residual sinking after the passage of the tire. The normal contact force determines the maximum value of tangential force provided before the soil fails.
Technical Paper

Tempered Wire Fatigue Testing

A new bench for the rotating bending fatigue tests of tempered steel wires is presented. The new bench is used to check the spring wire just before it is finally winded to realize a spring. The bench is basically a four-point bending machine. There are two main differences with respect to current bending machines. The first one is that the focus is on semi-finished components (more than 1 meter long), rather than standard small-scale specimens. The second one is that there is a non-linear configuration of the tested component due to its length. The bench design has provided some unreferenced features that make the bench quite accurate and effective in producing quick fatigue assessments. A rotor-dynamic study has allowed to perform tests at 50 Hz. As a preliminary application, some fatigue bending tests of tempered steel wires are described and discussed.