Problem set 3 -week 3 challenge: Anti-roll bar optimization
The above-required calculations were carried out in Excel with given input data.
Necessary unit conversions were made from inches to feet and millimetres to inches.
The following formulae were used: -
1. roll moment lateral component = sprung_mass * h_arm
2. roll gradient = (sprung_mass * h_arm)/ ((front_roll_stiffness + rear_roll_stiffness) - sprung_mass * h_arm(pi/180))
3. roll_moment_gravity_component = sprung_mass*h_arm*roll_gradient*(pi/180)
4. total roll moment = roll moment lateral component + roll moment gravity component.
Next, we determine the tire and wheel rate contribution to rolling stiffness,
5. tire contribution to roll stiffness = tire_rate*(track_width^2)/(180/pi)
6. wheel rate contribution to roll stiffness = wheel_rate*(track_width^2)/(180/pi)
Now we determine the front roll stiffness at wheel centre level,
7. front roll stiffness at WC level = (tire contribution * front roll stiffness)/(tire contribution - front roll stiffness)
With all the above values, the ARB parameters can now=ow be calculated.
8. rollbar contribution to roll stiffness = front roll stiffness - wheel rate contribution
9. % auxiliary roll stiffness = (front_rollbar_contribution/ front_roll_stiffness_at WC)*100
10. antiroll spring rate (one wheel jounce) = (500000*(OD^4-ID^4)/(0.4422*A^2*B + 0.2264*C^3))*MR^2
11. anti roll spring rate for roll = 0.5 * anti_roll_spring_rate(one wheel jounce)
12. anti rollbar stiffness = anti rollbar spring rate for roll *(track_width^2)/(180/pi)
The google drive link is posted below: -