3765. Mass Properties and Automotive Directional Stability

Paper

Abstract

The quantification of automotive directional stability may be expressed through various stability metrics, but perhaps the most basic of these automotive stability metrics is the “Understeer Gradient” (Kus). The Understeer Gradient (in degrees or radians per unit gravity) appears extremely uncomplicated when viewed in its most common formulation. Kus =[ Wf / gCsf – Wr / gCsr ]
This metric appears to depend only on the front and rear axle weight loads (Wf, Wr), and on the front and rear axle cornering stiffnesses (Csf, Csr). However, those last quantities vary with lateral acceleration, and the nature of that variation is dependent upon many other parameters of which some of the most basic are: Total Weight, Sprung Weight, Unsprung Weight, Forward Unsprung Weight, Rear Unsprung Weight, Total Weight LCG, Sprung Weight LCG, Total Weight VCG, Sprung Weight VCG, Track, Front Track, Rear Track, Roll Stiffness, Front Roll Stiffness, Rear Roll Stiffness, Roll Axis Height, Front Roll Center Height, and Rear Roll Center Height. Note that exactly half of these automotive directional stability parameters as listed herein are mass properties.
The purpose of this paper is to explore, through a skidpad simulation, the relative sensitivity of automotive directional stability (as quantified through the Understeer Gradient) to variation in each of the noted vehicle parameters, with special emphasis on the mass property parameters.
The simulation is constructed in a spreadsheet format from the relevant basic automotive dynamics equations; the normal and lateral loads on the tires are determined as the lateral acceleration is increased incrementally by a small amount (thereby maintaining a “quasi-static” or “steady-state” condition). The normal loads are used for the calculation of the lateral traction force potentials at each tire, with the required (centripetal) lateral traction forces apportioned accordingly. From those required (actual) lateral tire forces the corresponding tire cornering stiffnesses are determined; this determination is based upon a tire model developed through a regression analysis of tire test data.
This construction of a fairly comprehensive lateral acceleration simulation from basic automotive dynamic relationships, instead of depending upon commercial automotive software such as “CarSim” (vehicle model) and Pacjeka “Magic Formula” (tire model), constitutes a unique aspect of this paper; this return to basics hopefully provides a clearer view and understanding of the results than would be the case otherwise. Even more unique is this paper’s emphasis on, and exploration of, the role specific mass property parameters play in determining automotive directional stability.