Steady State Cornering

Steady-State Cornering Cornering behavior is important mode of handling. Handling is responsiveness of a vehicle to drivwer input, or ease of control. Driver vehicle is a closed loop system, but for characterization open loop behavior is used. Most common measure used in open loop is Understeer Gradient (a measure of performance under steady state condition as well as quasi-steady-state condition). Low Speed turning (Parking Lot) Tire need not develop lateral forces and will roll with no slip angle and turn as shown in fig.

High Speed Cornering (ENTRY OF Lateral Acceleration) To counteract LA tries must develop lateral forces, and slip angles will be present on each wheel. Tire Cornering Forces angle b/w direction of heading and direction of travel is slip angle (α). Lateral Forces Fy is called cornering forces when camber angle is zero. At low values (,5o) the relation b/w Fy and α is linear Fy = Cα α, Cα is cornering stiffness.

For vehicle to continue moving in intended direction, sum of forces in lateral direction from tires must be equal to mass times centripetal acceleration. ∑ Fy = Fyf + Fyr = MV2/R (sum of lateral (cornering) forces at front and rear axle).

For Moment Equilibrium (equating moment from front and rear) Fyfb - Fyrc = 0 ; Fyf = Fyrc/b. We get Fyr = Mb/L (V2/R); Mb/L portion of vehicle weight carried on rear axle = Wr/g. It tells the lateral forces developed at the rear axle must be Wr/g time’s lateral acceleration. Similarly Fyf = Wf/g (V2/R). Also from initial equation

In understeer vehicle understeer level is quantified by a parameter known as the characteristic speed. It is the speed at which the steer angle required to negotiate any turn is twice the Ackerman angle. In oversteer case,a critical speed will occur above which the vehicle will be unstable.