Finding the contribution of roll stiffness toward the front of the vehicle using Excel

https://drive.google.com/file/d/12gDwnCz4-JApIYwOGUXBdmRLbY_nGmHp/view?usp=sharing

Aim

To calculate the roll stiffness of anti roll bar and its contribution toward the front system of car

Software Used

Excel

Given Data

Flow of Calculation

Note : Before starting the calculation one must ensure the spring rates unit's should be in pounds per inch and the roll stiffness should be in Feet-Pounds per degree , make conversions at each step according to it .

• First find out the roll moment by lateral component and gravity component .h_arm is the torque arm length .

Lateral Component = Sprung mass * h_arm

Gravity Component = Sprung mass *h_arm *roll gradient *(pi/180)

• Roll gradient should be found out first to calculate gravity component roll stiffness .

Roll Gradient = (sprung mass *sprung mass roll moment )/((front roll stiffness +rear roll stiffness )-(sprung mass *sprung mass roll moment )*(pi/180))

• Sum the roll contribution from lateral and gravity components .

Total Roll Moment = Lateral Component roll + Gravity component roll

• Now calculate relative load transfer of sprung masse ( remember whole weight of the vehicle is assumed at the roll center so no corner masses will be used )

Load transfer due to elastic component = Total Roll moment / Track width

• Now our main aim is to first calculate the roll stiffness contributed by the tire and the wheel rate ( which is ultimatly the function of spring rate & motion ratio ) . We should keep in mind that we have to calculate of the stiffness of the front anti roll bar , so all our paramteres will be of front axle .

Roll stiffness by the tire = (Tire stiffness *((track width)^2/2 ))/(180/Pi )

Wheel Rate Contribution = (Wheel rate *((Track width)^2/2))/(180/Pi)

• Now we must know that what we are basically doing , since we got the stiffness from the tire and we know the total roll stiffness at the front ,

so we have to find the roll stiffness at wheel center level ( which is given by the sway bars attached to them ) ,

the theoretical formula will look like i.e. (1/stifffness at WC ) =(1/stiffness by the tire)-(1/total front roll stiffness )

Rewriting the formula ,

Front roll stiffness at WC = (Tire rate contribution to stiffness*Total front roll stiffness ) /| Tire rate contribution to stiffness - Total front roll stiffness|

• Now we will subtract the wheel rate contribution to the stiffness from the overall roll stiffness at WC

Front roll bar contribution = Total front roll stiffness at WC level - Wheel rate contribution

• Now we have to calculate the %tage of ARB contribution to stiffness

%tage of Auxiliary roll stiffness = (Front roll bar contribution /Total front roll stiffness at WC )*100

• Now , we will use a predefined formula to calculate the spring rate of ARB for 1 Wheel Jounce ,we just have to multiply the resultant stiffness with (Motion Ratio)^2, i.e.

ARB spring rate for 1 wheel jounce = stiffness*(MR)^2

• Now we will calculate for both the wheels at front , since they both can be jounce or reboud at the same moment when passing over a bump .

ARB Spring rate for 2 wheels = (ARB spring rate for 1 wheel jounce)*2

• Now we will calculate the resultant stiffness of the ARB using ARB spring rates

Front ARB stiffness = (Front ARB spring rate for 2 wheels *((Track Width)^2)/(180/Pi)

Observation and Calculation

Result

The stiffness of ARB comes out to be 1492.436331 feet pounds per degree & its contribution towards the front system roll stiffness of car is around 71% (approx).