Analytical models correlation for vehicle dynamic handling properties (original) (raw)

2011, Journal of the Brazilian Society of Mechanical Sciences and Engineering

Analytical models to evaluate vehicle dynamic handling properties are extremely interesting to the project engineer, as these can provide a deeper understanding of the underlying physical phenomena being studied. It brings more simplicity to the overall solution at the same time, making them very good choices for tasks involving large amounts of calculation iterations, like numerical optimization processes. This paper studies in detail the roll gradient, understeer gradient and steering sensitivity vehicle dynamics metrics, starting with analytical solutions available in the literature for these metrics and evaluating how the results from these simplified models compare against real vehicle measurements and more detailed multibody simulation models. Enhancements for these available analytical formulations are being proposed for the cases where the initial results do not present satisfactory correlation with measured values, obtaining improved analytical solutions capable of reproducing real vehicle results with good accuracy. Nomenclature a L = lateral acceleration, m/s 2 b / c = distance between CG and front/rear axle, m F yf , F yr = front and rear centrifugal force per axle, N H r = effective roll arm, m H CG = CG height to the ground, m H rf , H rr , H rcg = vehicle roll center height at front axle, rear axle and CG position, m K = understeer gradient, rad/( m/s 2 ) K bf , K br = front and rear roll stiffness due to stabilizer bars, (Nm)/rad K fyf , K fyr = front and rear wheel steer angle stiffness with respect to tire lateral force, rad/N K mzf , K mzr = front and rear wheel steer angle stiffness with respect to tire align torque, rad/(Nm) K roll = roll gradient, rad/( m/s 2 ) K s = steering sensitivity, ( m/s 2 )/rad K sf , K sr = front and rear wheel roll stiffness due to springs, (Nm)/rad K T = vehicle's total roll stiffness, (Nm)/rad K tirf , K tirr = front and rear wheel roll stiffness due to tires, (Nm)/rad L = wheelbase, m M = vehicle mass, Kg M ext,zf , M ext,zr = front and rear tire align torque, Nm r dir = steering ratio, dimensionless V f , V r = front and rear tire velocity vector, m/s T roll = roll moment, Nm Greek Symbols α f , α r = front and rear tire slip angle, rad δ = front wheel steer angle, rad θ = vehicle roll angle, rad C αf , C αr = front and rear tire cornering stiffness, N/rad