Problem set 3 -week 3 challenge: Anti-roll bar optimization

1. Roll Moment: calculates the total moment acting on the vehicle due to body roll. The π/180\pi/180π/180 converts degrees to radians.

Roll moment = (sprung mass)*(sprung mass roll moment arm length)*pi/180

2. Roll Gradient: Determines how much the vehicle rolls per unit lateral acceleration (g-forces). A lower value means better handling.

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 (Elastic Load Transfer): calculates how much load shifts from one side of the vehicle to the other due to roll, affecting grip and stability.

Load transfer due to roll or elastic component = (Roll moment)/(track width)

4. Tire Rate Contribution: Determines how much the tires contribute to the vehicle’s overall roll stiffness.

Tire rate contribution = [(tire stiffness)*(track width)^2/2]*pi/180

5. Front Roll Stiffness at Wheel Centre: Accounts for the interaction between tire stiffness and the suspension’s roll stiffness at the wheel centre.

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: calculates the stiffness of the anti-roll bar when one wheel moves up (jounce).

7. Front Anti-Roll Spring Rate for Roll: Since roll affects both wheels, the anti-roll bar rate for roll is half the single-wheel rate.

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

8. Front Anti-Roll Bar Stiffness: determines how much the anti-roll bar contributes to roll stiffness, reducing body roll.

Front anti-roll bar stiffness = [(front anti-roll spring rate for roll)*(track width)^2/2]*pi/180

9. Wheel Rate Contribution: calculates the suspension’s contribution to roll stiffness based on the wheel rate.

Wheel rate contribution = [(wheel rate)*(track width)^2/2]*pi/180

10. Front Roll Bar Contribution: Determines how much of the roll stiffness is due to the anti-roll bar versus the suspension.

Front Roll Bar Contribution=Front Roll Stiffness at Wheel Center−Wheel Rate Contribution

11. Auxiliary Roll Stiffness: Expresses the percentage of roll stiffness contributed by the anti-roll bar. A higher value means the anti-roll bar plays a bigger role in controlling body roll.

Auxiliary roll stiffness = [(front roll bar contribution)/front roll stiffness at wheel centre)]*100

Parameter	Units	Value
Roll moment	ft-lb/deg	7643.758
Roll gradient	deg/g	3.185
Load transfer due to roll or elastic component	lb/g	1563.674
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	74.551
Front anti-roll bar stiffness	ft-lb/deg	1492.436
Auxiliary roll stiffness	%	70.964

auxiliary roll stiffness = 70%, it means:

• 70% of the total roll stiffness is provided by the anti-roll bar.
• 30% comes from the suspension springs and tires.

To optimize roll stiffness:

1. Increase the front anti-roll bar stiffness – This reduces roll but may affect ride comfort.
2. Increase tire stiffness – Helps with better roll resistance.
3. Adjust the front-to-rear roll stiffness ratio – A balanced ratio improves handling dynamics.
4. Reduce the roll moment arm – Lowering the CG reduces body roll naturally.

excel file:

https://docs.google.com/spreadsheets/d/1xUd51cAFU36jwZjLbsebz5utuBtowE6p/edit?usp=drive_link&ouid=106354191505670406233&rtpof=true&sd=true