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

1. Roll moment (ft-lb/g):

Lateral Component = Sprung Mass * Sprung mass Roll moment Arm

Lateral Component = 7241.11 ft-lb/in

Gravity Component = Sprung Mass * Sprung mass Roll moment Arm * (π/180)

Gravity Component = 126.38 ft-lb/in

Total Roll Moment = Lateral Component + Gravity Component

Total Roll Moment = 7367.60 ft-lb/in

2. Roll Gradient (deg/g):

Roll Gradient = Lateral Component
/((Front Roll Stiffness + Rear Roll Stifness)-Gravity Componetns)

Roll Gradient = 3.18 deg/g

3. Load Transfer due to Roll or Elastic Component (lb/g):

Load Transfer due to Roll or Elastic Component = Total Roll moment / Trackwidth

Load Transfer due to Roll or Elastic Component = 1507.19 lb/g

4. Front roll stiffness (ft-lb/deg) at wheel center level:

Front Roll Stiffness at WC = (Tyre Contribution * Total Front Tyre Stiffness)
/ (Tyre Contribution - Total Front Tyre Stiffness)

Tyre Contribution = Tire Stiffness *( (Trackwidth²/2)*(π/180))

Tyre Contribution = 3753.53 ft-lb/deg

Front Roll Stiffness at WC = 1988.80 ft-lb/deg

5. Front anti-roll spring rate (lb/in) for one wheel jounce:

Anti-Roll Spring Rate (One Wheel Jounce) = ((500000*(OD⁴-ID⁴))

/((0.4422*A²*B)+(0.2264*C³)))*MR²

Anti-Roll Spring Rate (One Wheel Jounce) = 149.102 lb/in

6. Front anti-roll spring rate (lb/in) for roll:

Front anti-roll spring rate for roll = 0.5 * Anti-Roll Spring Rate (One Wheel Jounce)

Front anti-roll spring rate for roll = 74.55 lb/in

7. Front anti-roll bar stiffness (ft-lb/deg):

Front anti-roll bar stiffness = (Front Anti-roll spring rate for roll *

Trackwidth²)/(180/π)

Front anti-roll bar stiffness = 373.10 ft-lb/deg

8. Auxiliary roll stiffness (%):

Auxiliary roll stiffness (%) = (Front Roll bar Contribution / Total Front Roll Stiffness at WC)

*100

Front Roll bar Contribution = Total Front Roll Stiffness - Wheel rate Contribution

Wheel Rate Contribution = (Wheel Rate * Trackwidth²)/(180/π)

Wheel Rate = (Front Ride rate* Tyre Stiffness)/(Tyre Stiffness - Front ride Rate)

Wheel Rate = 230.77 lb/in

Wheel Rate Contribution = 577.47 ft-lb/deg

Front Roll bar Contribution = 1411.34 ft-lb/deg

Auxiliary roll stiffness (%) = 70.96 %

Google Drive Link for Excel Sheet:

https://docs.google.com/spreadsheets/d/1KfNe6gt2p7mELEmFIYdJBGKAr-SN1h12/edit?usp=sharing&ouid=102891323117469303946&rtpof=true&sd=true