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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.

Typical vehicle dynamics simulations demand a trade-off between short computation times and accuracy. Many of the more simple models are based on the kinematic roll center and the more accurate models tend to be multi-body dynamics simulation programs. There is a need for a model that improves the accuracy of the kinematic roll center models while still maintaining short computation times. Such a model could be used track-side during races to guide race teams toward improved handling. The model presented in this paper removes many of the assumptions and limitations of the kinematic roll center model. The model accounts for three-dimensional forces present at the contact patch and predicts deflections of suspension components. The modeling approach is applied to a NASCAR Craftsman Truck to predict the effects of suspension design and tuning on steady-state understeer characteristics of the vehicle. Braking and acceleration forces can also be applied to the vehicle.

This paper presents the development and experimental verification of a steady-state, half-vehicle cornering model. The goal of this effort is to develop a model which retains the physical insight inherent to simple models, while providing a higher degree of accuracy. The Force-based roll center (FBRC) model is presented as an evolution of traditional kinematic roll center (KRC) modeling. The FBRC model replaces the suspension with moveable wheel-chassis instant center pairs, and incorporates tire force/slip models. The FBRC model iteratively solves for vehicle position and loading during a steady-state cornering maneuver. Experimental verification of the FBRC vehicle model shows modeling accuracy up to tire saturation limits, which is well beyond the 0.4 g accuracy limit of KRC models.

A dynamic simulation has been developed to predict the acceleration of a manual-transmission vehicle at wide-open throttle. A notable feature of the model is that tire slip is included, and the coefficient of friction varies with slip. This allows the simulation to start from zero vehicle speed and include the dynamics of gear shifting. The model was used in optimization studies for 3-speed, 4-speed, and 5-speed transmissions which indicated that fastest times, for the vehicle studied, are obtained when the mass center is as close to the drive axle as possible, and gear ratios are selected so that the engine speed brackets the horsepower peak. Also, optimal gear ratios deviate slightly from a geometric progression by closer spacing in higher gears and wider spacing in low gears, a common practice in gear box design.