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Technical Paper

Indirect Measurement of Tire Slip and Understeer/Oversteer

This paper presents a method for indirect measurement of tire slip angles from chassis acceleration, yaw rate, and steer angle measurements. The chassis is assumed to be rigid so that acceleration data can be integrated to estimate velocities of the front and rear of the vehicle, from which slip angles can be predicted. The difference in front and rear slip angles is indicative of vehicle oversteer/understeer. Understeer data can then be correlated with position on the track to better understand vehicle handling behavior, aiding the tuning process. The technique is presented, and shown to work well with simulated data, even when the data is corrupted with up to 20% noise. Therefore, the inversion process presented here is theoretically sound. However, when the technique is applied to measured data from race cars, it is shown to be inaccurate. One suspected problem is the difficulty of getting accurate yaw rate data.
Technical Paper

Derivation of the Three-Dimensional Installation Ratio for Dual A-Arm Suspensions

Conventional suspension analysis of three-dimensional suspensions typically use two-dimensional analyses. This is done by projecting suspension components onto two-dimensional planes and then performing a two-dimensional analysis in each of these orthogonal planes or neglecting motions in one of the planes entirely. This requires multiple iterations because changes in one plane require a checking of their effects on motion in the other orthogonal planes. In doing so, much of the insight and accuracy gained from a three-dimensional analysis can be lost. A three-dimensional kinematic analysis approach is presented and applied to a dual A-Arm suspension system. All motions are considered instantaneously about a screw axis instead of a point as used by the usual two-dimensional modeling approach. The model predicts deflections of suspension components in response to the three-dimensional forces present at the contact patch.
Journal Article

The Development of Terrain Pre-filtering Technique Based on Constraint Mode Tire Model

The vertical force generated from terrain-tire interaction has long been of interest for vehicle dynamic simulations and chassis development. To improve simulation efficiency while still providing reliable load prediction, a terrain pre-filtering technique using a constraint mode tire model is developed. The wheel is assumed to convey one quarter of the vehicle load constantly. At each location along the tire's path, the wheel center height is adjusted until the spindle load reaches the pre-designated load. The resultant vertical trajectory of the wheel center can be used as an equivalent terrain profile input to a simplified tire model. During iterative simulations, the filtered terrain profile, coupled with a simple point follower tire model is used to predict the spindle force. The same vehicle dynamic simulation system coupled with constraint mode tire model is built to generate reference forces.
Journal Article

Improved Model for Coupled Structural-Acoustic Modes of Tires

Experimental measurements of tire tread band vibration have provided direct evidence that higher order structural-acoustic modes exist in tires, not just the well-known fundamental acoustical mode. These modes display both circumferential and radial pressure variations within the tire's air cavity. The theory governing these modes has thus been investigated. A brief recapitulation of the previously-presented coupled structural-acoustical model based on a tensioned string approach will be given, and then an improved tire-acoustical model with a ring-like shape will be introduced. In the latter model, the effects of flexural and circumferential stiffness are considered. This improved model accounts for propagating in-plane vibration in addition to the essentially structure-borne flexural wave and the essentially airborne longitudinal wave accounted for in the previous model. The longitudinal structure-borne wave “cuts on” at the tire's circumferential ring frequency.