Vehicle Dynamics - Anti-roll bar optimization
AIM: To calculate required parameters for Anti-roll bar optimization
OBJECTIVES:
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
(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:
Front Ride Rate: 200 lb/in
Rear Ride Rate: 250 lb/in
SOLUTION:
An excel sheet is used to calculate all the parameters.
PROCEDURE:
Formulae used-
1. Roll moment = (sprung mass)*(sprung mass roll moment arm length)*pi/180
2. Roll gradient = (sprung mass)*(sprung mass roll moment arm length)/[(front roll stiffness + rear roll stiffness) - (Sprung mass)*(sprung mass roll moment arm length)*pi/180]
3. Load transfer due to roll or elastic component = (Roll moment)/(track width)
4. Tire rate contribution = [(tire stiffness)*(track width)^2/2]*pi/180
5. Front roll stiffness at wheel centre level = (Tire rate contribution)*(Total front roll stiffness)/[(Tire rate contribution) - (Total front roll stiffness)]
6. Front anti-roll spring rate for one wheel jounce = `(500000(OD^4 - ID^4)*MR^2)/(0.4422A^2B+ 0.2264C^3)`
7. Front anti-roll spring rate for roll = (Front anti-roll spring rate for one wheel jounce)/2
8. Front anti-roll bar stiffness = [(front anti-roll spring rate for roll)*(track width)^2/2]*pi/180
9. Wheel rate contribution = [(wheel rate)*(track width)^2/2]*pi/180
10. Front roll bar contribution = (front roll stiffness at wheel centre)-(wheel rate contribution)
11. Auxiliary roll stiffness = [(front roll bar contribution)/front roll stiffness at wheel centre)]*100
| FINAL DELIVERABLES | ||
| Parameter | Units | Value |
| Roll moment | ft-lb/deg | 7643.767 |
| Roll gradient | deg/g | 3.185 |
| Load transfer due to roll or elastic component | lb/g | 1563.676 |
| Front roll stiffness at WC | ft-lb/deg | 1988.800 |
| Front anti-roll spring rate for one wheel jounce | lb/in | 149.103 |
| Front anti-roll spring rate for roll | lb/in | 74.552 |
| Front anti-roll bar stiffness | ft-lb/deg | 373.110 |
| Auxiliary roll stiffness | % | 70.964 |
Excel sheet (snapshot):
(drive link for the excel sheet: https://drive.google.com/file/d/1RnvYFGctExcTbIsMQZZGjwv1-_C9jMXd/view?usp=sharing )