Lateral load transfer and Anti-roll bar characteristics determination

AIM: Calculate the following parameters:

(i) Roll moment (ft-lb/g)

(ii) Roll gradient (deg/g)

(iii) Load transfer due to roll or elastic component (lb/g)

(iv) Front roll stiffness (ft-lb/deg) at wheel center level (Hint: isolate the tire contribution)

(v) Front anti-roll spring rate (lb/in) for one wheel jounce

(vi) Front anti-roll spring rate (lb/in) for roll

(vii) Front anti-roll bar stiffness (ft-lb/deg)

(viii) Auxiliary roll stiffness (%)

GIVEN DATA:

SOLUTION:

Formulae:

Roll moment (ft-lb/g) = Sprung mass * Sprung mass roll moment arm * `frac[pi][180]`

Roll gradient (deg/g) = Sprung mass * Sprung mass roll moment arm / [Front roll stiffness + Rear roll stiffness - Sprung mass x Sprung mass roll moment arm * `frac[pi][180]`]

Load transfer due to roll or elastic component (lb/g) = Roll moment / Track width

Front roll stiffness (ft-lb/deg) at wheel center level = Tire rate contribution * Total front roll stiffness / (Tire rate contribution - Total front roll stiffness)

Tire rate contribution = [Tire stiffness * Track width^2 / 2] / `frac[180][pi]`

Front anti-roll spring rate (lb/in) for one wheel jounce = `frac[500000 (OD^4 - ID^4) . MR^2][0.4422A^2B + 0.2264C^3]` ... (MR = Motion Ratio)

Front anti-roll spring rate (lb/in) for roll = 2 * Front anti-roll spring rate for one wheel jounce

Front anti-roll bar stiffness (ft-lb/deg) = [Front anti-roll spring rate for roll * Track width^2 / 2] / `frac[180][pi]`

Auxiliary roll stiffness (%) = (Front roll bar contribution / Front roll stiffness at wheel center level) * 100

Front roll bar contribution = Front roll stiffness at wheel center level - Wheel rate contribution

Wheel rate contribution = [Wheel rate * Track width^2 / 2] / `frac[180][pi]`

Parameter	Value	Unit
Roll moment	7643.824911	ft-lb/g
Roll gradient	3.184927046	deg/g
Load transfer due to roll or elastic component	1563.687333	lb/g
Front roll stiffness at wheel center level	1988.662965	ft-lb/deg
Front anti-roll spring rate for one wheel jounce	149.1027242	lb/in
Front anti-roll spring rate for roll	298.2054484	lb/in
Front anti-roll bar stiffness	1492.629844	ft-lb/deg
Auxiliary roll stiffness	70.95821756	%

Excel Output:

Excel Link: https://docs.google.com/spreadsheets/d/16H0vFLRVZE6hZGracqvnVRO5Z-JE5ifWgaDnP96rvUc/edit#gid=0