Design of Rear Wheel Steering System of an Experimental Electric Vehicle

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2019 International Conference on Electrical Drives & Power Electronics (EDPE)
The High Tatras, 24-26 Sept. 2019
978-1-7281-0389-1/19/$31.00 ©2019 IEEE
Design of Rear Wheel Steering System of an
Experimental Electric Vehicle
Lukáš Krčmář
Faculty of Mechatronics, Informatics
and Interdisciplinary Studies
Technical University of Liberec
Liberec, Czech Republic
lukas.krcmar@tul.cz
Josef Břoušek
Faculty of Mechanical Engineering,
Department of Vehicles and Engines
Technical University of Liberec
Liberec, Czech Republic
josef.brousek@tul.cz
Tomáš Petr
Faculty of Mechanical Engineering,
Department of Vehicles and Engines
Technical University of Liberec
Liberec, Czech Republic
tomas.petr@tul.cz
Abstract—The article deals with a topic of the rear wheel
steering of an experimental electric vehicle. Steering of the rear
wheel of a vehicle is no new topic, it was being solved ever since
the beginning of the vehicle manufacture. The main task of a
rear wheel steering is to improve the maneuverability of a
vehicle, especially at lower speeds of up to 50 km / h. This
solution has recently been seen primarily in vehicles of larger
car manufacturers which have higher wheelbase. This solution
is also appearing in sports cars, for their better
maneuverability in urban environments.
Keywords— Vehicle steering system, electric vehicle, four
wheel steering, control system, CAN bus
I. I
NTRODUCTION
(H
EADING
1)
The issue of an experimental electric vehicle bearing the
name eŠus is continuously being investigated at the
Technical University of Liberec. Several projects are
currently being solved using this experimental vehicle, one
of them being the rear wheel steering.
Manufacturers have been working since the beginning of
vehicle production on steering of the rear wheels as a way to
improve maneuverability of a vehicle. However, the rear
wheel steering has been mostly used for large machines that
would otherwise be difficult to maneuver. Due to sufficient
maneuverability of passenger cars the manufacturers have
begun to address this idea with the development of larger
vehicles. Rear-wheel steering have been slightly expanded to
passenger cars and some of the big car manufacturers have
already adapted this system for their larger cars in recent
years.
An initial impulse for the rear axle adjustment of an
experimental electric car was parking in the premises of labs
in which driving is considerably difficult even for a Škoda
Fabia-like vehicle with a hatchback body. A second impulse
came after completing and testing another experimental
vehicle, namely the experimental "Citigo" two-sided vehicle.
Specifically, these are two Škoda Citigo vehicles that had
their rears separated in the area of pillar B. These front
"halves" of the two vehicles were then joined together in a
single unit. The result is a vehicle that has two steerable
axles together with two engines. The idea of a vehicle with
two controllable axles could be tested on this concept.
Fig. 1. Experimental two-sided vehicle [1].
II. B
ASIC
I
SSUES OF
S
TEERING
Vehicle steering is used to guide a vehicle in the desired
direction. In order to prevent the wheel from slipping, a so-
called Ackermann steering condition must be met. All
wheels are rolled and no wheel slip occurs as this condition
is observed. Ackermann's steering condition is as follows:
"In order for all wheels to roll freely in the curved trajectory,
a normal of the center area of each wheel must pass through
one point - the common center of rotation” [2].
Ackermann's steering condition only applies if the planes
of rotation of wheels and the spindle pivots axle are
perpendicular to the road and at the same time if the object
with rigid wheel moves slowly along the track with a large
radius of rotation. This assumption is not entirely valid when
driving a real vehicle, the so-called directional deviations
occur in all wheels because of the elasticity of the tires and
the influence of centrifugal force. These deviations causes a
change in the position of the radius of rotation, which no
longer lies on the extended axis of the rear axle.
For four-wheel vehicles with front wheel drive, the
Ackermann steering condition is as follows [2]:
l
w
i
=−
δδ
cotcot
0
(1)

2019 International Conference on Electrical Drives & Power Electronics (EDPE)
The High Tatras, 24-26 Sept. 2019
where δ
i
is the steer angle of inner wheel and δ
o
is the
steer angle of the outer wheel. The wheelbase of the front
and rear axles is expressed by the symbol l. W expresses the
track width (distance between the left and right center
wheels). The used symbols are shown on the steering vehicle
scheme in the Fig. 2.
The center of gravity of the steering vehicle will then lie
on a circle with a radius R:
δ
222
2
cotlaR +=
(2)
Where for δ applies:
2
cotcot
cot
0i
δδ
δ
+
=
(3)
Fig. 2. A front-wheel steering vehicle and steer angles of the inner and
outer wheels [2].
III. F
OUR
W
HEEL
S
TEERING
K
INEMATICS
Four-wheel steering or four-wheel drive is used to
achieve better maneuverability at high speed or to reduce the
radius of rotation at low speeds [2].
Rear wheel steering can be used in two ways:
• Positive steering
• Negative steering
The goal at low speeds is to provide better
maneuverability and reduce the turning radius of the vehicle,
which is achieved by turning the rear axle in the opposite
direction to the front axle. Turning the rear wheels by 1 °
corresponds to the front wheel steer of 15 °. This makes it
possible to reduce the steering radius by up to a quarter
compared to a vehicle with only a front wheel drive. This
way of steering the rear axle is shown in the Fig. 3.
At higher speeds, the rear wheels turn in the same
direction as the front wheels. This makes it possible to
increase vehicle stability at higher speeds and improve
maneuverability, for example, when moving from one lane to
another. This way of steering the rear axle is shown in Fig. 3.
The kinematic condition of positive resp. negative
steering is described by the following equation:
ror
ifof
r
f
ifof
ll
w
δδ
δ
δ
ω
δδ
cotcot
cotcot
cotcot −
−
⋅−=−
(4)
where
f
ω
and
r
ω
are front and rear track widths
of
δ
and
if
δ
are the angles of the front inner and outer wheels,
o
r
δ
and
i
r
δ
are the steer angles of the rear inner and outer
wheels and l is the wheelbase.
Fig. 3. A negative 4-wheel steering vehicle [2]
A car chassis concept is shown in the Fig. 4 together with
the Ackermann four wheel steering system. This model as
well as its test prototype originated in the scope of another
project that was investigated at the Technical University of
Liberec. Basic calculations and testing took place using this
virtual model and then on its test prototype under laboratory
conditions [3].
Fig. 4. Car chassis concept with Ackermann four wheel steering system
[4].

2019 International Conference on Electrical Drives & Power Electronics (EDPE)
The High Tatras, 24-26 Sept. 2019
IV. C
ALCUALTION OF THE
R
EAR
W
HEEL
S
TEERING
A
NGLE
In order to get the ideal steer shape of the rear wheels
()
v
r
δ
a sinus function was used:
()
()()
max
sin
rtpr
pvvv
δδ
⋅−=
(5)








⋅
−=
p
t
v
v
p4
2
(6)
°= 5
maxr
δ
(7)








⋅
−=
p
t
v
v
p4
2
(8)
where
]
1
[−
⋅hkmv
is the speed of the vehicle,
]
1
[−
⋅hkm
p
v
is the transient rate of change of positive steering to negative
steering and
t
p
is the harmonizing variable adjusting the
cut-off performance of the process.
maxr
δ
indicates the
maximum steer angle of the rear axle. Dependency of the
rear wheels rotation
()
r
v
r
δδ
,
to the speed and the rotation
of front wheels:
()
()
max
,
f
f
rfr
vv
δ
δ
δδδ
⋅=
(9)
, where is the angle of rotation of the front wheels and
is the maximum angle of rotation of the front wheels.
Fig. 5. Dependance of the rotation angle of the rear wheel to the speed –
graph of maximum rotation of the rear wheels.
V. C
ONCEPT OF THE
E
XPERIMENTAL
E
LECTRIC
V
EHICLE
R
EAR
W
HEEL
S
TEERING
The principles described in the previous chapter were
used in the rear axle design for the experimental electric
vehicle Ešus. In order to calculate the necessary engine
power used for rotation, an approximate speed of steering
wheel rotation by the driver was experimentally determined.
The necessary torque is the highest for the stationary vehicle,
hence the simplest method of determining the necessary
torque by the torque wrench. The required motor power is
determined by a simple calculation. Due to the use of worm
gears and its static efficiency, it is necessary to oversize the
required power.
1
57,122
−
⋅=⋅⋅= sradf
πω
(10)
NmM 15=
(11)
WWMP 290189 →=⋅=
ω
(12)
Fig. 6. Engine and gearbox for the rear steering [5].
Another issue is the steering itself. There are motor
converters from the manufacturer Sevcon, which
communicate via CAN bus, installed in the experimental
electric car. The sub-unit also communicates via CAN bus.
This bus was a clear choice for the use in steering
communication. As a basis for testing, a platform based on
the Arduino DUE development prototype was used together
with a voltage level converter for the CAN bus.
By testing, it was found that the prototype based on the
Arduino DUE is more than fast enough to control not only
rear wheel steering. The functional prototype now operates
with this prototype.
The experimental electric car uses a 120 V battery. Most
rear wheel steering electronics, such as the rotation angle
sensors, require lower voltage as their power supply. The
converter itself has a nominal voltage of 48 V. This voltage
is achieved by a step-down DC - DC converter. With regards
to safety it is necessary to supply the power to the steering
electronics even in case of a primary 120 V vehicle battery
failure [7]. That is why a backup battery is installed together
with the DC - DC converter.

2019 International Conference on Electrical Drives & Power Electronics (EDPE)
The High Tatras, 24-26 Sept. 2019
Fig. 7. Design model of the experimental electric vehicle [6].
Electric car
battery
120 V
DC / DC
Inverter
120 V -> 48 V
Batt ery
pack 48 V
with BMS
Motor
Driver
BLDC
motor with
gearbox
Angle
senzor
Tie rod
Steering
angle
sensor
Control
unit
Motor
drive
controller
CAN bus
Fig. 8. Basic block diagram for the rear steering of the experimental
electric vehicle.
VI. CONCLUSIONS
The rear wheel vehicle steering is a highly discussed
topic now in the time of the development of autonomously
steering vehicles. For non-autonomous vehicles, it will
improve driving performance, especially in lower-speed
driving in the "urban jungle" [8]. Until recently, this
management system has been known to luxury vehicle
brands that use this system at high speeds to increase vehicle
stability [9] or for heavier vehicles, such as buses. Driving
properties have been tested, for example, in the underground
garages of the Technical University in Liberec, where the
rear wheel steering in the narrow corners proved to be most
efficient.
Vehicles with an autonomous steering system can use
rear steering in a large number of cases. At the corresponding
angle of rotation of the front and rear axles, the vehicle
achieves the so-called "crab movement" as the vehicle drives
to the side. Otherwise, with the same angles of rotation but
opposite axle rotation, it is possible to rotate the vehicle "on
the spot" with a very low rotation radius.
In the scope of prototype testing, the rear axle system is
installed and fully functional in an experimental electric car.
A
CKNOWLEDGMENT
The result was obtained through the financial support of
the Ministry of Education, Youth and Sports of the Czech
Republic and the European Union (European Structural and
Investment Funds - Operational Programme Research,
Development and Education) in the frames of the project
“Modular platform for autonomous chassis of specialized
electric vehicles for freight and equipment transportation”,
Reg. No. CZ.02.1.01/0.0/0.0/16_025/0007293.
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