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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

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

Design and Construction of a Test Rig for Assessing Tyre Characteristics at Rollover

The paper presents a new test rig (named RuotaVia) composed basically by a drum (2,6 m diameter), providing a running contact surface for vehicle wheels. A number of measurements on either full vehicles or vehicle sub-systems (single suspension system or single tyre) can be performed. Tire characteristics influencing rollover can be assessed. The steady-state maximum loads are as follows: Radial: 100kN, tangential: 100kN, lateral (axial with respect to the drum): 100kN. The superstructure carrying a measuring hub can excite the wheel under test up to 20 Hz in lateral and vertical directions. The steer angle range is ± 25 deg, the camber range is ± 80 deg. The minimum eigenfrequency of the drum is higher than 90 Hz and its maximum tangential speed is 440 km/h.
Journal Article

Indoor/Outdoor Testing of a Passenger Car Suspension for Vibration and Harshness Analysis

This paper presents a validation method for indoor testing of a passenger car suspension. A study was done to design a supporting modular structure with comparable inertances with respect to a vehicle's actual suspension and body connection points. For the indoor test, the rear axle is positioned on a rotating drum. The suspension system is excited as the wheel passes over cleats fixed on the drum and transient wheel motions are recorded. The indoor test rig outputs (i.e., wheel and chassis accelerations) were compared with experimental data measured on an actual vehicle running at different speeds on the same set of cleats along a flat road. The comparison results validate the indoor testing method. The forces and moments acting at each suspension and chassis connection point were measured with a set of patented six-axis load cells. The forces, moments, wheel and subframe accelerations were measured up to 120 Hz.
Technical Paper

Tire ply-steer, conicity and rolling resistance - analytical formulas for accurate assessment of vehicle performance during straight running

During straight-ahead running, the longitudinal axis of road vehicles - notably cars - is not parallel to road axis and sometimes a slight steering pull can be felt by the driver. This occurrence is general and is due both to road cross slope (road banking) and to tire characteristics, particularly ply-steer and conicity. In order to describe such a phenomenon, the paper introduces a new and relatively simple analytical model. Despite the linearity of the model, the solution provided is exact, since straight-ahead motion occurs with small angles and both the elastokinematics of suspension system and tire characteristics can be modelled by linearized equations. The validation of the analytical expressions is performed by using an MSC ADAMS full model of a car. By means of the new analytical formulae, the relationship between the tire ply-steer/conicity and the rolling resistance of the vehicle in studied.
Journal Article

Test Rig for Characterization of Automotive Suspension Systems

A test rig (named RuotaVia) is presented for the in-door testing of road vehicle suspension systems. It is basically a drum (ϕ 2.6 m) providing a running surface for testing the dynamic performance of a single tire or suspension system (corner). The suspension system is instrumented for the measurement of the forces and the moments acting at each joint connecting the suspension to the car body. A new 6 axis load cell was designed and manufactured for this purpose. The accelerations in various locations of the system (wheel carrier, suspension arms, …) and the wheel centre displacements in the longitudinal and vertical directions are monitored. The effect of the dynamic interaction between the test rig and the suspension system is discussed in the paper. The direct measurement of the forces and moments at the suspension-chassis joints is still an effective way for understanding the vibration and harshness (VH) suspension performances.
Journal Article

A Method for Vibration and Harshness Analysis Based on Indoor Testing of Automotive Suspension Systems

The paper presents a method for the indoor testing of road vehicle suspension systems. A suspension is positioned on a rotating drum which is located in the Laboratory for the Safety of Transport at Politecnico di Milano. Special six-axis load cells have been designed and used for measuring the forces/moments acting at each suspension-chassis joints. The forces/moments, wheel accelerations, displacements are measured up to 100 Hz. Two different types of test can be performed. The tire/wheel unbalance effect on the suspension system behavior (Vibration and Harshness, VH) has been analyzed by testing the suspension system from zero to the vehicle maximum speed on a flat surface and by monitoring the forces transmitted to the chassis. In the second kind of test, the suspension system has been excited as the wheel passes over different cleats fixed on the drum.
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.