Steering System Design Calculation

Please read last 3 blogs as these blogs have theoretical analysis, Design review, DFMEA of brake and steering system. Without previous blogs understanding, below calculation is  worthless. 

Steering Calculations

Load on Front Axle Wfront = 3762 N (See Table - Brake Design 5 at the end of this blog)

Load on Rear Axle Wrear= 1584

Wheel Base L = 2700mm = 2.7 m

Assumption:

Formula Ford Worst Corner Track Radios = 200 m

Formula Ford Worst Corner Track Angle = 150 Degree

Cornering Stiffness Front Cfront= 1250 N/Degree

Cornering Stiffness Rear Crear= 600 N/ Degree

Acker Man Angle = Wheel Base / Track Radios = 2.7/200 = 0.0135 Radian = 0.773 Degree

Under Steer Gradient K = {(Wfront/Cfront) – (Wrear / Crear)} = {(3762/1250) – (1584 / 600)}

                                        = 0.3696N/ (N/Degree)

Characteristic Critical Speed = [{gL(57.3)/K}^0.5] = [{9.81*2.7*(57.3)/0.3696}^0.5]= 64m/s=230Km/h

As per Powertrain Designer Feedback roughly 250 Km/hour is maximum vehicle speed; so if worst corner on Formula Ford race track has radios of 200m then driver can maintain speed up to 230Km/h however it is ideal condition without real life factors (check primary assumption at beginning). 

Steering Ratio & Variable Rack Calculation
Steering Ration	1 to 1	1.25 to 1	1.5 to 1
	1	1.25	1.5
Lock To Lock Turn	1.4	1.4	1.4
Steering Wheel can turn	252	252	252
Front Wheel can turn	252	201.6	168
Conclusion	Vehicle Topple /Roll Over	Quick  Turn	Smooth Turn
Driver’s Input	Steering Wheel Turn	Wheel Turn	Rack Tooth Spacing
Steering at Centre /Middle	1.25 Deg	1 Deg	1.25 Unit
Steering Near Full Lock	1 Deg	1  Deg	1 Unit

Rack Gear will be designed such that smooth steer near central position and quick steer near corner.

Lock to Lock Turn Calculation:

Average Steering Ration	(Near Centre Steering Ration + Near Full Lock Steering Ratio )/2
	(1.25 + 1) /2 = 1.125
	1.125	1.125	1.125
Lock To Lock Turn	0.8	0.9	1
Steering Wheel can turn Max	144	162	180
Front Wheel can turn Maximum	128.0	144.0	160
Conclusion	Choose from above as per worst track angle

Conclusion:- 

According to race track requirement Steering design can be fixed by keeping Steering Lock to Lock=1.4 turn with Average Steering Ratio of 1.125.  

Challenge:- Vehicle can topple / roll over at sharp corner. To avoid this driver can reduce speed. Or at early design stage Chassis Designer can reduce height of centre of gravity.

Next is design verification process for brake and steering. DVP is sequential process; however performance/ durability failure at latter stage can compel us to repeat the DVP testing from beginning for subsystem or whole vehicle. So Front Loading concept is very popular in industry: - high resources are allocated at early stage of DVP for DFMEA and simulation. Manufacturing starts only after successful child part+ Subsystem+ Vehicle Simulation result.     

Please read next slide to know how testing of steering and brake is done in industries. 

Brake Design 5 Table for reference ( It is explained in previous 3 blogs, here only for reference)

Brake Design Iterations	D1	D2	D3	D4	D5	1V*	Design Review
Pedal Level Ratio	5	4	5	5	5	5	If Master Cylinder dia is increased, driver needs to apply more force to stop vehicle.
Master Cylinder Diameter mm	10	20	10	10	10	10
Front/rear caliper piston diameter mm	45	40	45	45	45	45
Mean effective radius of front braking disc mm	230	230	220	200	250	230	For bigger Disc, Driver needs to apply lesser force.
Mean effective radius of rear braking disc mm	220	220	220	200	250	220
Vehicle Parameters
Height of Centre of Gravity mm	350	350	350	350	350	300	*Vehicle COG, Wheel Base and Front Axle Location is changed for study.
Wheel Base Length mm	2700	2700	2700	2700	2700	2800
Front Axle to Centre of Gravity Distance mm	1900	1900	1900	1900	1900	2100
Driver effort to generate Actual Braking Force equivalent to vehicle weight (N)
To generate Normalized Actual Front Braking force equal to 1g	60	375	60	70	53	50	D5: At 1g driver need to apply only 53N to stop front wheel and 70N to stop rear wheel.
To generate Normalized Actual Rear Braking force equal to 1g	75	325	75	90	70	75
Performance of Vehicle ( Different Driving Condition)
Maximum wheel unlocked deceleration ( Stable Design up to)	1 g	1 g	1.2 g	1.3 g	1.2 g	1.5g	Design 4 is most stable up to 1.3g line.
Optimal Front Force 0 at this deceleration (g) (X Intersection)	-2.28	-2.28	-2.28	-2.28	-2.28	-2.33	For further Improvement COG must be lowered, Wheel base need to be increased and COG shifted to rear wheel.
Optimal Rear Force 0 at this deceleration  (g) (Y Intersection)	5.42	5.42	5.42	5.42	5.42	7
Max deceleration during rear circuit failure with µ 0.8 Dry	0.25	0.25	0.25	0.27	0.27	0.2
Max deceleration  before front wheel  lock with µ 0.3 Wet	0.2	0.2	0.2	0.2	0.2	0.18