Design of Steering Geometry for FSAE Car

Design of Steering Geometry for FSAE Car

Abstract:

Iniyavan P

Student, Department of Mechanical Engineering, Thiagarajar college of engineering, Madurai, Tamil Nadu, India

Fig 1: Geometrical parameters

Steering is an important part of an automobile. It helps to change the directions of the automobile and also helps in the straight lines stability of the vehicle. This report focuses on mathematical modelling and design of a rack and pinion steering mechanism of a formula student vehicle. We have developed a set of mathematical equations that governs the complete design of steering and later prepared the CAD model. By solving these equations, we can get different steering geometry parameters by fixing some variables according to restriction and considering optimum steering geometry with respect to steering effort and percentage Ackerman.

1. INTRODUCTION:

   Steering mechanism is designed in a way that it meets the Ackerman principle i.e. in order for a vehicle to perform a pure turning, the I-centre of all the wheels should meet at one single point. We have achieved this condition using rack-and pinion gear box in our project. The pinion gear is rotated when the steering wheel is rotated. The output shaft from the steering wheel and the input shaft to the pinon gear are connected by a universal coupling. The rotational motion of the pinion gear causes the rack to move transversally which in turn pushes the tie- rod and the tie-rod helps the wheels to turn by pushing the steering arm.

2. STEERING GEOMETRY MODEL:

   The image below shows the steering geometry and the value of it s important parameters. Our motive is to design Ackermann steering Geometry, so that the inner wheel turning angle more than the outer wheel. By this sketching this diagram in Solid works we can compute outer wheel turning angle and Turning radius using Measuring tool in Solid works.

   Where:

   W = Track width

   B = distance between left and right knuckles L = Wheel base of the vehicle

   do = outer wheel angle di = inner wheel angle

   Using the basic laws of trigonometry we arrive at the following equation:

   cot 0 + cot = /

   This is the Ackerman condition for a two-wheeled steering. When Ackerman condition is satisfied in a steering mechanism the vehicle takes a turn. The inner wheel needs to be turned more than the outer wheel in order for the condition to be satisfied.

   PARAMETERS	VALUES
   Wheel Base(L)	1600.2mm or 63inch
   Front track width(W)	1200mm
   Rear track width(w)	1150mm
   Left knuckle steering point to Right knuckle steering point(B)	1040mm
   Ackermann angle()	18 degrees
   Inner wheel turning angle()	40 degrees
   Outer wheel turning angle(1)	29.75 degree
   Tie rod length(y)	317.51 mm
   Ackerman arm length(x)	90mm
   Distance between front axis and rack axis(d)	100mm
   Length of rack(z)	350mm
   Steering Ratio	4:1

   Table 1: Parametric values of Geometry

3. RACK TRAVEL() AND CALCULATION

   Rack Travel is defined as the distance the rack travel for the full turning of a tyre on one side (left or right). The mathematical equation to calculate rack travel() is given by:

   ) +

   = sin( + ) ( [ 2 (

   2

   cos( + ))2]0.5

   By using this equation, the calculated rack travel()

   = 44.49mm

   Fig 2: Steering geometry 2-D sketch

4. PINION CALCULATION

   Now the rack travel for 1 degree turn of tyre() is given by,

   = / (1)

   Now our steering ratio is 4:1 so, for 1 degree turn of tyre we need 4 degrees rotation in steering wheel. So, the rack travel for 1 degree turn of tyre() can be calculated by using,

   = . (2)

   Where;

   = 4° ()

   180

   r = radius of pinion

   By equating the equations (1) and (2);

   r = 15.94mm

   r 16mm

   Diameter of pinion(D) = 2r

   D = 32mm

   Now by referring the Gear terminology and Nomenclature, for pinion diameter 32mm and steering ratio of 4:1, Module(M) is decided.

   M = 2mm

   No of teeth on pinion (TP) =

   TP = 16 teeth

   Addendum = 1M = 2mm Dedendum = 1.2 M = 2.4mm Working Depth = 2M = 4mm Total Depth = 2.2 M = 4.4mm

   Clearance = Total Depth Working Depth

   = 4.4 4

   Clearance = 0.4mm (between rack and pinion) Thickness of the Teeth = (sin 90°/)

   Thickness of the teeth = 2mm

   Circular pitch = *M

   Circular pitch = 6.28mm

   No of teeth on rack = TR =

   TR = 14.1687 14mm

   For manufacturing feasibility TR = 16 teeth Actual total length of rack (LR) = TR * *M LR = 100.48 mm

   Steering Effort Calculation:

   Total weight of car = 260kg

   Weight distribution = 51.4% in front and 48.5% in rear

   Weight on front two wheels(front)= 0.514(260)

   = 133.64 kg for two wheels

   P = 66.82 kg for one wheel or 655.50 N

   Resistance Force (RF) =

   = 0.6 * 655.50

   RF = 393.3 N

   Resistance Torque on tyre (RT) =

   where Sr = scrub radius = 50mm

   = 393.3 * 50

   RT = 19665 N-mm

   To calculate the force to be applied on the Ackermann arm(F) by the rod

   F =

   where i = horizontal distance of Ackermann arm=8.59mm

   F = 229.758mm

   Required torque at steering wheel (T) is:

   T= ()

   2

   T = 3676.128 N-mm

   Required steering effort (Se) =

   where R = radius of steering wheel = 125mm (Assumed)

   Fig 3: Isometric view of steering wheel

   = 3676.128/ 125

   Se = 29.409 N (In stationary condition)

   Table 2: Final values of Steering system

   PARAMETERS	VALUES
   Rack travel for full left or right turn	44.49mm
   Pinion diameter	32mm
   Module	2mm
   No. of. Teeth on pinion	16 teeth
   Clearance between rack and pinion	0.4mm
   Thickness of the teeth	2mm
   Circular pitch of pinion	6.28mm
   Axial pitch of rack	6.28mm
   No. of. Teeth on rack	16 teeth
   Length of rack (Actual)	100.48mm
   Steering Effort	29.409 N (stationary condition)

   Fig 3: Font view of Steering wheel

   Fig 4: Exploded view

5. REFERENCES

1. Race Car Vehicle Dynamics William F. Milliken & Douglas L. Milliken [ISBN: 978-1560915263]

2. Tune to Win Carroll Smith [ISBN: 978-0879380717]

3. V B Bhandari, Design of Machine Elements, Third edition, McGraw Hill Education, India, 2010.

4. McRae, John and Potter, James Jackson, "Design Considerations of an FSAE Steering System" (2019). Mechanical Engineering and Materials Science Independent Study. 94. https://openscholarship.wustl.edu/mems500/94.

5. R. Rajamani, Vehicle Dynamics and Control, 2nd ed., New York, NY: Springer, 2012. [Online]. Available: https://link.springer.com/book/10.1007/978-1-4614-1433-9

6. R. Rajamani, Vehicle Dynamics and Control, 2nd ed., New York, NY: Springer, 2012. [Online]. Available: https://link.springer.com/book/10.1007/978-1-4614-1433-9