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

following are the steps with formulas which are used for calculations

NOTE: unit converstions needs to be taken care before proceding to the calculation.

1. the roll moment by lateral component and gravity component.h_arm is the torque arm length.
   i) Lateral Component = sprung mass * h_arm
   ii) Gravity Component sprung mass *n_arm*roll gradient *(pi/180)
   
   
2. Roll gradient should be found out first to calculate gravity component roll stiffness.
   i) Roll Gradient = (sprung mass *sprung mass roll moment )/((front roll stiffness +rear roll stiffhess)- (Sprung mass *sprung mass roll moment )*(pi/180) )
   
   
3. Sum the roll contribution from lateral and gravity components.
   i) total Roll Moment Lateral Component roll + Gravity component roll
   
   
4. calculate relative load transfer of sprung mass (whole weight of the vehicle is assumed at the roll center so no corner masses will be used)
   i) Load transfer due to elastic component = Total Roll moment / Track width
   
   
5. first roll stiffness contributed by the tire is calculated and the then wheel rate.
   i) Roll stiffness by the tire = (Tire stiffness *(( track width) ^2/2 ))/(180/Pi)
   ii) Wheel Rate Contribution = (wheel rate ((Track width) ^2/2))/(180/Pi)
   
   
6. i) Front roll stiffness at WC = (Tire rate contribution to stiffness*Total front roll stiffness)/( tire rate contribution to stiffness - Total front roll stiffness)
   
   
7. we should subtract the wheel rate contribution to the stiffness from the overall roll stiffness at WC
   i) Front roll bar contribution = total front roll stiffness at WC level - wheel rate contribution
   
   
8. i) ARB Spring rate for 1 wheel jounce stiffness* (MR)^2
   ii) Kq(Lbs/in) = (500,000 x ((OD^4)- (ID^4)))/(0.4244 x (A^2)x B) + (0.2264 x (C^3))
   
   
9. Front anti-roll spring rate for roll = (Front anti-roll spring rate for one wheel jounce)/2
   
   
10. Front anti-roll bar stiffness = [(front anti-roll sprirng rate for roll)"(track width)" 2/2]"pi/180
    
    
11. Front roll bar contribution = (ftront roll stitfness at wheel centre)-(wheel rate contribution)
    
    
12. Auxiliary roll stiffness = [(front roll bar contribution)/front roll stiffness at wheel centre)]*100
    
    Result:
    The stiffness of ARB comes is 1492.43 ft-lb/deg & its contribution towards the front system roll stiftness of car is around 71%.

https://1drv.ms/x/c/f9c2fd74cf84750d/EaWXND1XCQ5GlbHyTqADOtwBhLqVMXRedvhlueGkS5QIZg?e=jCffJk