Project Report on Anti Roll Bar selection, Roll Gradient, Stiffness Analysis & Under steer budget sheet based on vehicle level compliance targets for a 4 Wheel sedan.

Project Report on Anti Roll Bar selection, Roll Gradient, Stiffness Analysis & Under steer budget sheet based on vehicle level compliance targets for a 4 Wheel sedan.

Suspension system is generally the tire air, springs & shock absorbers that absorbs the vehicle ex citations due to road profile irregularities. So designing the optimized suspension system is important to achieve good ride and handling. The processes that are involved in designing the suspension system are:

1. Selecting AppropriateVehicle Level Targets.
2. Selecting System Architecture.
3. Choosing location of hard points.
4. Analyzing loads in the suspension.
5. Estimating Spring Rate.
6. Estimating Shock Absorber Characteristics.
7. Selecting Materials based on load conditions cheap to manufacture.
8. Analysizing the entire system in dynamic condition analyze the results based on targets, either proceed or redesign the system to achieve the desired result.

Basically the Hard points are of two classifications:

1. Static- Toe,Camber,Caster,RCH,Mech Trail,Anti drive & squat,KPI,Scrub & Motion Ratio.
2. Kinematic - Bump Steer, Roll Steer, Tractive Force Steer, Brake force steer, Camber Gain in roll, Ackermann Change with STEERING ANGLE etc.

VEHICLE LEVEL TARGETS: (A broader picture helps in understanding and evaluating your Designed system)

Some of the Vehicle Level Targets Are:

1. Roll Stiffness.
2. Ride Frequencies.
3. Load transfer ( lateral & longitudinal).
4. Roll moment.
5. Under steer Gradient.
6. Jounce & Rebound.

Etc.

Given Data:

Vehicle Weights and Dimensions
Parameter	Units	Value
Total Weight	lb	2750
Weight Distribution	% front	60
Front axle unsprung mass	lb	187
Rear axle unsprung masss	lb	121
Wheelbase	in	98.42
CG Height	in	21.62
Track Width	in	58
Front RCH	in	0.497
Rear RCH	in	0.896

Drive/Brake Proportions
	Units	Value
Drive Ratio- Front	-	0.7
Brake Ratio-front	-	0.6
Throttle Acceleration	in/s^2	216
Spring
Parameter-Front	Units	Value
Motion Ratio	in/in	0.95
Spring Rate	lb/in	250
Parameter-Rear	-
Spring Rate	lb/in	300
Motion Ratio	in/in	0.8
Tires
Parameters	Units	Value
Loaded Radius	in	12.27
Vertical Stiffness	lb/in	1313

Anti-Roll Bar
Parameter-Front	Units	Value
Motion Ratio	in/in	0.64
Virtual Torque Arm (A)	in	8.9
Center Length(B)	in	32
Physical Torque Arm[C]	in	10.7
Parameter-Rear
Motion Ratio	in/in	0.75
Virtual Torque Arm (A)	in	8.51
Center Length(B)	in	32.28
Physical Torque Arm[C]	in	8.59
Extended Input - TIRES
Parameter	Front	Rear
Slip Angle (deg/g)	3.88	3.1
Camber (deg/g)	4.55	2.26
Lateral Force (N/g)	3753	2375
Aligning Torque (Nm/g)	139.8	50.8
Pneumatic Trail(m)	0.0372502	0.021389474

Normal Load	Cornering Stiffness	Camber Stiffness	Aligning Stiffness
lb	lb/deg	lb/deg	ft-lb/deg
500	167.23	8.37	9.27
1000	262.17	17.76	35.12
1500	301.75	25.3	57.26
2000	269.86	29.9	75.36

Vehicle Level Targets:

Target		Units		Value
Roll gradient		deg/g		3.50-3.80
Understeer gradient @tires		deg/g		Max possible
	Parameter		Max		Min
	Aux roll stiffness front (%)		60		25
	Aux roll stiffness rear (%)		20		0
	Roll steer front (%)		6.50		3
	Roll steer rear (%)		-4		-8
	Roll camber front (%)		90		80
	Roll camber rear (%)		65		50
	Lateral force compliance steer front (deg/kN)		0.05		0.008
	Lateral force compliance steer rear (deg/kN)		0.04		0.015
	Lateral force compliance camber front (deg/kN)		0.3		0.1
	Lateral force compliance camber rear (deg/kN)		0.4		0.15
	Aligning torque compliance steer front (deg/100 Nm)		0.4		0.2
	Aligning torque compliance steer rear (deg/100 Nm)		0.1		0.06

ADDITIONAL ASSUMPTIONS:

1. You will need to do this project in excel. Do not attempt to due it through pen and paper calculations. It will become very tedious. Remember this isan iterative process.
2. Assume that roll bar diameters are available only in increments of 0.25 mm.
3. Assume the roll bar to be solid (inner diameter = 0)
4. We want a 5% higher load transfer in the front to get understeer. So if you get x lb/g of load transfer in the front, add 5% of the total load transfer to
5. this number to get the desired front load transferA 5% deviation in all targets is allowed
6. Pay attention to signs when dealing with K&C parameters. Remember that with respect to understeer gradient calculations, a positive sign in the front denotes understeer and a positive sign in the rear denotes oversteer. It is vice versa for negative signsMake sure you use tire properties corresponding to the appropriate load conditions.
7. You are only allowed to tune the roll bar diameters and K&C parameters. Weights, dimensions and tire properties cannot be altered in any way

Goal:

8. Select roll bar diameters to meet target roll gradient
9. Select kinematic and compliance parameters to meet target understeer gradient

Deliverables:

10. Roll bar outer diameters (front and rear) (inner diameter = 0) in mm
11. Primary and secondary roll stiffness at the wheel center in ft-lb/deg
12. Auxiliary roll stiffness (front and rear) percentage
13. Tire stiffness plots (stiffness vs load)
14. Understeer budget sheet
15. Contribution bar chart

The Following are the Process in which the project was done: (PROCESS FLOW)

Stage 1: ROLL

The first stage of this process is to calculate the Primary & Aux roll stiffness to meet the given target value and also calculate the ARB - Anti roll bar Diameters, as well as the parameters including spring rate, tire rate, wheel rate etc.

1. Ride Rate

Ride Rate is determined by a combination of two spring rates working in series; the Suspension Rate & the Tire Stiffness rate.Static deflection of the suspension determines its natural frequency. Static Deflection (SD) = Sprung Wt. / Ride Rate Ride frequency is the undamped natural frequency of the body in ride. The higher the frequency, the stiffer the ride.

1. Primary & Secondary Roll Rate

Roll stiffness is the resistance of the springs within the suspension against the body roll when a vehicle goes through a corner. Roll stiffness is developed by a roll resisting moment of the body (sprung mass) about the roll axis. The roll stiffness in a vehicle is equal to the combined roll stiffness of the front and rear suspension. Roll stiffness expressed in (torque) N-m/degree of roll.Example: If a vehicle had a roll stiffness of 100 N-m/deg of roll, it would take a torque of 100 N-m about the roll axis to move the body 1 degree.Roll stiffness of the complete vehicle is the sum of the separate roll stiffness rates of all vehicle suspensions.

2. Diameter of anti roll bar

A - Length of end perpendicular to B (torque arm - inches)

B - Length of center section (inches)

C - Length of end (inches)

D - Diameter bar (millimeters)

Stage 2: TIRE STIFFNESS

In this stage the stiffness properties under dynamic & loading changes static conditions to determine How the load reacts with the Force component, to analyze the Friction and slip between the the tire and the road. The following are calculated.

NORMAL LOAD v/s Cornering stiffness

Camber stiffness

Aligning Stiffness

Vehicle Weights and Dimensions
Parameter		Units	Value
Total Weight		lb	2750
Weight Distribution		% front	60
Front axle mass		lb	1650
Rear axle masss		lb	1100
Normal Load	Cornering Stiffness			Camber Stiffness		Aligning Stiffness
lb	lb/deg			lb/deg		ft-lb/deg
500	167.23			8.37		9.27
1000	262.17			17.76		35.12
1500	301.75			25.3		57.26
2000	269.86			29.9		75.36
Interpolated Data	Weight/Axle			Cornering Stiffness		Camber Stiffness	Aligning Stiffness
Front Static Load	825			228.94		14.47	26.07
Rear Static Load	550			176.72		9.31	11.86

Stage 3: UNDER STEER BUDGET SHEET

The Under steer Sheet is the great way to understand the Kinematics & Compliance of the suspension system. Depending upon the reaction of the components on the under steer the bushings and the hard point optimization can be done. The following parameters contribute to the overall indersteer budget.

1. Weight Distribution.
2. Rigid body Aligning Torque.
3. Roll Steer.
4. Roll Camber.
5. Lateral Force Compliance Steer.
6. Lateral Force Compliance Camber.
7. Tire Aligning Torque.

CALCULATED RESULTS:

Under-Steer Budget Sheet
Cornering Compliance Contributions	Cornering Compliance(deg/g)		Understeer Gradient	Contribution
	Front	Rear	Front -Rear(deg/g)	%
Weight Distribution	7.21	6.22	0.98	48.6
Rigid body Aligning Torque	0.4125	0.2369	0.18	8.7
Roll Steer	0.2470	-0.3040	0.55	27.2
Roll Camber	0.2162	0.1001	0.12	5.7
Lateral Force Compliance Steer	0.1877	0.0356	0.15	7.5
Lateral Force Compliance Camber	0.0593	0.0188	0.04	2.0
Aligning Torque Compliance Steer	0.0056	0.0003	0.01	0.3
Total			2.02	100.00

Inference:

The above graphs shows the contribution of various components towards the under steer budget. In this the WEIGHT DISTRIBUTION occupies a major role, since weight distribution is hard to optimize ( Tedious process). the roll gradient can be optimized with varying stiffness parameters & the most easy way to achieve the under steer is by making the Ksteering<Ksuspension, the compliance of the steering to be less than the suspension.

THE BELOW LINK GIVES THE ACCESS FOR REPORT & EXCEL SPREAD SHEET CALCULATION:

EXCEL SHEET:

https://drive.google.com/file/d/1tGrzNifp-VSSFKznS8HFec-P21alynXa/view?usp=sharing

REPORT:

https://drive.google.com/file/d/1P5ZpX3sHL6hFkcrkO-BuzdfOPM0DHo9s/view?usp=sharing