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Research in Science, Technology,
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Optimized Rack and Pinion steering system with Steering Stops

incorporation over Rack-Casing Assembly for a BAJA SAE All terrain
Vehicle
Asad Khan1, Mayan Kansal1, Rahul Sindhu1, Vasu Bhardwaj1
1
Department of Mechanical and Automation Engineering
Maharaja Agrasen Institute of Technology, Guru Gobind Singh Indraprastha University
Rohini, PSP Area, Delhi 110086, INDIA.

Abstract: This study focuses on the design and optimization of Rack and Pinion steering system of a BAJA SAE
All-terrain vehicle. The major challenge in the design of a steering system is the weight reduction within the
limits of structural integrity of the design confining to the guidelines of BAJA SAE, which should easily run
through the harshest of conditions. Various parameters of the design of the steering system were analytically
calculated and decided upon. The basic design of the Rack and Pinion was made in SolidWorks. A number of
iterations were then carried out and analyzed in HyperWorks to finalize the design dimensions viz. Rack’s
diameter, teeth’s face width. Al 7075 was finalized as the material based on its superior hardness and strength
and being 1/3rd the density of Steel*. The weight reduction was then carried out based on the least stress
concentration which could further achieve a 15% weight reduction in the design. This study would also display
a new design for incorporation of steering stop in the rack and casing assembly itself.

Keywords: Baja SAE; Optimization; Rack and Pinion; Steering Stop; Weight Reduction.

I. Introduction
The prime objective of a steering system is to provide maximum directional control and easy manoeuvrability of
the vehicle in all types of terrains with optimum safety and minimum effort. In case of an ATV (All terrain
vehicles), the steering system must be designed according to the worst possible terrain conditions while carefully
considering parameters like weight, space, and structural rigidity. The use of Rack and pinion type steering
geometry in vehicles is very common because of its simplicity in design [6], good suitability with the front wheel
drive system, adaptability to vehicles without frames [5][7] and easy manufacturing.

In order to provide pure rolling to the road wheels and to reduce wear and tear of the tires, a steering linkage must
handle the vehicle so that it follows Ackermann principle (see Fig. 1). It states that during low speed cornering
when free from lateral inertia forces, the lines drawn from the centres of the wheels (axes) should intersect at the
centre of the bend (or the instantaneous centre) [4], i.e., point Oof Fig. 1. For a two-wheel steering vehicle, this
point must lie on the common axis of the rear wheels. Referring to Fig. 1, the relation between the inner wheel
angle δi, and the outer wheel angle δo, according to Ackermann principle, is given by,
1
δo = arctan w
cot δi +
l

Figure1. Ackermann Geometry

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II. Methodolgy
The designing process of the rack and pinion was taken in a systematic order so that various objectives of the
vehicular design must be attained with the utmost perfection. This was accomplished with the initial scrutiny of
previous designs and the various parameters it lacked and the limitations associated with them. The vehicle needs
to be designed within the guidelines of BAJA SAE rule book and the parameters be within defined [8].

Mathematical Weight
Design Designing of Final
Calculation of Material Reduction and Manufacturing
Approach Various Components
Steering Selection Optimization in Processes
Planning Components testing
Parameters Hyperworks

Our Objective for the vehicle’s steering system was to incorporate a steering Stop on the rack casing itself and
design the system according to the desired steering ratio with oversteer characteristics with optimum driver
comfort. This was to be achieved with a geometry that needed to be easy to assemble, having a low lock to lock
rotation and highly reduced weight.

Design Parameters and Calculations

The steering system calculations were done taking into consideration the desired dynamical characteristics of the
vehicle. A set of conditions best suitable for the design were first analyzed and then taken as the initial parameters
of the steering system of the vehicle.

Table 1. Design Parameters

Mass of the vehicle 140kg
Mass with driver 200kg
Wheel base 55inches
Track width 52inches
Turning Radius 1.75 m
Lock to lock Angle 180 degrees
Radius of Steering Wheel 5 inches
Displacement of Rack 90mm

The Inner wheel angle and outer wheel angle were first calculated using a number of iterations of the
fixedparameters, for 100% Ackerman Geometry using,

l
δi = arctan (1)
R1+w/2
Similarly,
l
δo = arctan (2)
R1−w/2

Figure 2. Track width VS Inner angle

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Asad et al.., American International Journal of Research in Science, Technology, Engineering & Mathematics,26(1), March-May 2019, pp.
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Figure 3. Track width VS Outer angle

The angles along with the parameters were then tested and validated on the steering geometry based on the
optimum strength and alignment of the various Suspension points using LOTUS Shark. A 68% Ackerman
geometry was used which could work efficiently based upon the overall dynamics of the vehicle.

Rack and pinion design calculation

Initially, the Steering Ratio was analyzed based upon the optimum driver comfort and steering effort. The Pinion
radius was then designed using the best suitable steering ratio for a BAJA ATV. Consequently, the module was
calculated for the pinion and the Torque acting over the pinion was analyzed.

Displacement of Rack = Radius of Pinion * Ø

Displacement of rack (l) = πZØm / 360◦ (3)

Where, Z = no. of teeth on the pinion

Ø = angle of rotation of pinion
m = module

Steering ratio
The Steering Ratio is defined as the ratio of steering wheel rotation angle to steer angle at the road wheels.
Steering ratio = degrees of steering wheel turned / degrees of driving wheels turned
=90 / 52
=1.73 : 1

Steering Characteristics (oversteer, understeer)

Under Steer Gradient, K=Wf/Cf – Wr/Cr (4)
= (90/56346-110/56346)
= -0.02033 deg/g
i.e. Oversteer Condition

In this case, the lateral acceleration at the Centre of Gravity causes the slip angle on the rear wheel to increase
than the front wheels. The outward drift at the rear of the vehicle turns the front wheel inward, thus diminishing
the radius of turn.

Steering effort
Steering effort is the effort to be made by the driver in turning the steering wheel. This can be calculated in either
static condition i.e. when the vehicle is stationary and in dynamic conditions. Steering effort is maximum when
the vehicle is stationary.
Vehicle weight was designed so as to distribute the weight in the ratio of 55:45 rear to front.
Weight on the front tires, Wf = 0.45 * 200= 90 kg
Weight on the rear tires, Wr = 0.55 * 200 = 110 kg
Corner mass front = 45kg
Corner mass rear = 55kg

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Steering Force Calculations

Force of friction (on one wheel) = µ x g x corner mass (5)
= 0.8 x 9.81 x 45
= 353.16 N

Input torque from ground (on one wheel) = force of friction x lateral distance between contact patch and kingpin
centre
= 353.16 x .12831
= 45.31 Nm

This torque will be equal to the lateral push from the tie rod.
Torque due to lateral push from tie rod = force on tie rod x longitudinal distance between outer tie rod end and
front axle
= force on tie rod (ft) x 0.0945m
ft =479.47N

Total force on rack = 479.47x 2 = 958 ~1000N

Radius of pinion = 28.1mm= .0281 m
Torque on pinion = 1000 x .0281 =28.1 Nm
Torque on steering wheel = Torque on pinion = 28.1 Nm
Radius of steering wheel = 5 inch = 0.127 m
Force applied by the driver to steer the wheels = torque on steering wheel/radius of steering wheel
= 28.1/.127
= 221.26 N

Material selection
To design a lightweight steering system without compromising its strength and integrity various material
properties were studied and components were designed according to their optimum use. Material selection was
carried out by Ashby Method.

For the Rack and Pinion Al 7075 was finalized due to its low weight, suitable tensile and shear strength and
hardness. It was also concluded that EN 24 can be utilized for Tie Rods due to their superior bending strength,
and stiffness.

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Asad et al.., American International Journal of Research in Science, Technology, Engineering & Mathematics,26(1), March-May 2019, pp.
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Table 2 Properties of Al 7075 Table 3 Properties of EN 24

S.No Properties Values S.No Properties Values

1. Density 2700 kg/m3 1. Density 7850 kg/m3

2. Young’s 72 GPa 2. Young’s 205 GPa

Modulus Modulus
3. Ultimate 590 MPa 3. Ultimate 1110 MPa
Tensile Tensile
Strength Strength

Design, Analysis and Optimization

Taking into account the Numerical Results and the parameters, the CAD model of the steering geometry was
designed on SolidWorks and its Finite Element Analysis was carried out on HyperWorks. The Suspension and
Steering geometry was analyzed over LOTUS Shark.

Figure 4. Steering Geometry Design

Figure 5. Suspension analysis on LOTUS Shark

Stress concentrations over the rack and pinion were analyzed for different compressive and shear loads. The
overall deformation was also analyzed over the rack due to the various loads acting over the vehicle.
A number of iterations were carried out and a highly optimized Rack and Pinion were designed by eliminating
material from around the neutral axis and regions of low stress concentrations. A circular cutout was made along
the length of the circular Rack without compromising the required strength of the member.

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Figure 6. Stress analysis over pinion

Figure 7. Stress analysis over rack

Steering Stop
Steering stops are used in vehicles so as to limit the turning of wheels after a certain limit. They are designed to
prevent the steering system to turn to a point where they resist turning back to thus straining the geometry. In
commercial power steering systems, the vehicle uses software stops, limit switches and valves to maintain the
steering angle.
A locking mechanism to limit the steering angles from lock to lock was designed for the vehicle. This was designed
taking into consideration to be lightweight and employable over the BAJA SAE vehicle providing safe and better
driving conditions for the driver.
Due to the extreme stresses generated over the tie rods and steering linkages at sharp turns, and to avoid major
failure of the vehicle, steering stop was incorporated over the rack casing assembly in the vehicle. The steering
stop would also allow the vehicle to avoid excessive Oversteer and in turn avoid rollover of the vehicle.
The design was then further scrutinized and tested through computational analysis and then validated through
experimental testing of the vehicle.

Fig 5. Stress analysis over the rack casing assembly

III. Conclusions
The main objective of the study was to design an efficient steering mechanism with the incorporation of steering
stop having minimum weight. Rack and pinion steering systems promise the most efficient system for a BAJA
SAE vehicle. It was concluded that
 Lightweight vehicle reduces inertia losses and ensures a faster response of the steering system.
 Aluminum being one of the lightest metals provides the necessary strength and hardness and thus

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Asad et al.., American International Journal of Research in Science, Technology, Engineering & Mathematics,26(1), March-May 2019, pp.
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offers a great potential to be used as the material for manufacturing rack and pinion.
 A steering stop incorporated over the rack casing provides the necessary stopping mechanism without
compromising the safety and effectiveness.
 The steering stop design ensures safe loads over the steering linkages.

IV. References
[1] Thomas D. Gillespie; Fundamental of Vehicle Dynamics; ISBN: 978-1- 56091-199-9; February 1992
[2] John C. Dixon; Suspension analysis and computation geometry; ISBN: 978-0-470-51021-6; October 2009
[3] William F. Milliken, Douglas L. Milliken; Race Car Vehicle Dynamics; 1994
[4] A. Rahmani Hanzaki, P.V.M. Rao, S.K. Saha; Kinematic and sensitivity analysis and optimization of planar rack-and-pinion
steering linkages; Mechanism and Machine Theory 44(1): 42-56; August 2008
[5] Upendra S. Gupta, Sumit Chandak, Devashish Dixit; Design & Manufacturing of All Terrain Vehicle (ATV)- Selection,
Modification, Static & Dynamic Analysis of ATV Vehicle; International Journal of Engineering Trends and Technology (IJETT),
V20(3),131-138; ISSN:2231-5381; Feb 2015
[6] Dr. S. Neelakrishnan, Kowshik T, Krishnakumar G, Bharathi Mohan M P; Analysis and Improvement of the Steering
Characteristics of an ATV; Int. Journal of Engineering Research and Application; ISSN: 2248-9622, Vol. 7, Issue 5, ( Part -4);
May 2017
[7] Dr. V.K. Saini, Sunil Kumar, Amit Kumar Shakya, Harshit Mishra; Design Methodology of Steering System for All-Terrain
Vehicles; International Research Journal of Engineering and Technology; ISSN: 2395 -0056, Volume: 04, Issue: 05; May 2017
[8] BAJA SAE rule book 2019. Retrieved from https://bajasaeindia.org/pdf/BAJA-SAEINDIA-Rulebook-2019-Rev.00.pdf; 1 August,
2018

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