Final Project

The link for the excel sheet is here:

https://docs.google.com/spreadsheets/d/1JRQZ51l0fjZnCX-xvqcndQIWBSBy4NVfxNkYnr2N3Tk/edit?usp=sharing

The roll bar diameter selection is done first and then the understeer budget is taken out.

The deliverables are highlighted in green color in the excel sheet.

- The vehicle parameter like the sprung mass, un sprung mass, sprung mass distances from the front and rear.

- They are used to calculate the wheel rates and the roll moments

the gravity and the roll component of the Roll moments are calculated using

M_phi = Ms*harm/12 (1 + rollgrad(PI/180)).

then K_phi, the roll stiffness is calculated by M_phi/rollgrad. , The rollgrad is chosen to be 3.8 later can be changed.

then total lateral load transfer is calculated LLT_t = Mt * hs/t , hs-c.g of vehicle, t-track width.

LLT_f = LLT_t(front wt dist% + 5% )/100

LLT_r = LLT_t(1- front wt dist%)/100

Then the Load transfer due to the unsprung and the sprung mass on each axle is calculated

LLT_fu = Wfu*Rf/t , Rf - front tire loaded radius

LLT_fs = Wfs*Z_RCHf/t , Z_RCHf - front roll center height.

similarly done for the rear axle.

total Roll stiffness on each axle is then calculated by using

K_phi_f_total = (LLT_f - LLT_fu - LLT_fs)*t/(rollgrad*12) slly for the rear axle

Then the tire and the wheel rate contribution for the roll stiffness is calculated for both axles.

K_phi_ftire = ((Kft*12)*(t/12)^2)/2 * PI/180 Kft- front tire stiffness

K_phi_fw = ((Kwf*12)*(t/12)^2)/2 * PI/180 kwf - wheel rate of front = kfs*(M.R)^2 , kfs-front spring stiffness.

Then the tire contribution to the roll stiffness is isolated to get the Wheel center stiffness.

K_phi_fwc = (K_phi_tire*K_phi_f_total)/(K_phi_tire - K_phi_f_total)

then the roll stiffness due to ARB is calculated

K_phi_farb = (K_phi_fwc - K_phi_fw)*12 (in-lb/deg)

Roll rate of the ARB

K_farb = (K_phi_farb)/(M.R^2 * t^2) * PI/180

OD = (K_farb * ((0.4422*A^2*B) + (0.2264*C^3)) / 500000)^0.25 * 25.4

Then the OD of the ARB is calculated.

UNDERSTEER BUDGET SHEET

First the load on the front and the rear axle is calculated, then the cornering stiffness, camber stiffness and the aligning torque stiffness are calculated at that normal loads by using Interpolation method.

The understeer gradient under different influence

1. Weight dist = W/C_alpha , C_alpha - cornering stiffness.

2. Aligning torque = ( Aligning torque )/ (wheel base * C_alpha)

3. Roll steer = roll steer stiffness coeff * rollgrad

4. Roll steer camber change = roll camber stiffness coeff * rollgrad * tire camber stiff/ tire cornering stiff

5. Lat. force compliance steer = LFCS coeff * tire Lat. force

6. Lat. force compliance camber = LFCC coeff * tire Lat. force * tire camber stiff/ tire cornering stiff

7. Alignig torque compliance steer = ATCS * aligning torque

These values are changed accordingly.

Parameter	Units	Front	Rear
Roll steer stiffness %	%	6.5	-4
Roll camber stiffness %	%	90	65
Lat force compliance steer	deg/kN	0.05	0.04
Lat force compliance camber	deg/kN	0.3	0.4
Aligning torque compliance steer	deg/100Nm	0.4	0.1

UNDERSTEER BUDGET SHEET
	Front	Rear	Net	Percentage
Weight distribution	5.647145796	4.072776819	1.574368976	54.34295469
Aligning torque	0.1913970105	-0.07523926806	0.2666362786	9.203562458
Roll steer	0.2418	-0.1488	0.3906	13.48245451
Roll camber	0.3057147062	0.1725006998	0.1332140064	4.598186844
Lateral force compliance steer	0.18765	0.095	0.09265	3.198027163
Lateral force compliance camber	1.028088972	0.6777322779	0.3503566938	12.09336453
Aligning torque compliance steer	0.2861230329	0.1968503937	0.0892726392	3.081449812
Total			2.897098594	100