Factors Affect Slipping of Automobiles

Abstract

This paper presents an analysis of the slipping phenomenon in automobiles; the parameters affect the slipping of automobiles are discussed. An analytical equation is constructed to relate all factors that affect the slipping ratio. Some relations are predicted to show the factors affect the slipping in automobiles. It is found that the parameters affect slipping can be summarized as the radius of curvature of the curve, angle of the curve (slope), RPM of the tire, the radius of the tire in addition to the nature of the road. It is found that: as the normal acceleration increases the slipping ratio decreases, as the RPM of the tire increase the slipping ratio increases, and as the radius of the tire increases the slipping percent increases. It is obvious that as the path slope (tan θ) increases the slipping value decreases. It is noticed that: as the radius of curvature increase the slipping % decrease which is logic since the slipping on the straight dry path is nearly close to zero. Also, it is noticed that: as the tire radius decreases the slipping % increases.

Full text

Factors Affect Slipping of Automobiles
SAYEL M. FAYYAD AND MOHANNAD O. RAWASHDEH
Department of Mechanical Engineering, Faculty of Engineering Technology,
P.O. Box 15008, Al-Balqa Applied University
Amman, JORDAN
Abstract: -This paper presents analysis for the slipping phenomenon in automobiles; the parameters
affects slipping of automobiles are discussed. An analytical equation is constructed to relate all factors
affect slipping ratio. Some relations are predicted to show the factors affect the slipping in automobiles.
It is found that the parameters affect slipping can be summarized as: radius of curvature of the curve,
angle of the curve (slope), RPM of the tire, radius of the tire in addition to the nature of the road. It is
found that: as the normal acceleration increases the slipping ratio decreases, as the RPM of the tire
increase the slipping ratio increases and as the radius of the tire increases the slipping percent increases. It
is obvious that as the path slope (tan θ) increases the slipping value decreases. It is noticed that: as the
radius of curvature increase the slipping % decrease which is logic, since the slipping on straight dry path
is nearly close to zero. Also it is noticed that: as the tire radius decreases the slipping % increases.
Key-Words: - Slipping, Normal Acceleration, Radius of Curvature, Tires, Velocity, and Automobiles
Dynamic
Received: March 26, 2020. Revised: May 21, 2020. Accepted: June 1, 2020. Published: June 5, 2020
1 Introduction
In automobiles there are many control
systems that can assist the driver to keep away
from accidents and their danger, or restrict the
damage in the case of accidents. Such systems in
new vehicles normally have an anti-lock braking
system (ABS), which prevents the wheels from
locking during difficult braking, and
they frequently have an
electronic stability manage system (ESC) or it is
able to be named ( in present paper) as slip-
preventer system ( SPS) which stabilizes the
lateral motion of the vehicle to save
you skidding.
Collisions caution and avoidance, rollover
prevention, crosswind stabilizers
and preparation for
an impending accident through adjusting seat
positions and seat belts are additional examples
of manage structures for car safety.
To obtain this records, modern day motors are
equipped with various sensors.
For a typical car with an ESC
system, essential measurements encompass the g
uidance wheel angle, wheel angular velocities,
lateral acceleration, and the rate of
rotation around the vertical body-
constant axis, referred to as the yaw rate.
Under typical conditions, when the auto is
pushed appropriately without risk of losing road
grasp, the car sideslip demeanor is little, not
surpassing ±2 degrees for the regular driver [1].
In addition, for a given pace in ordinary driving
circumstances, the directing attributes indicate
tight association among the direction wheel edge,
yaw rate, horizontal increasing speed, and
vehicle sideslip mentality. During slipping a
lateral force affects the dynamics of the car, this
force is proportional to the slipping angle. There
is a relation between lateral forces and slipping
angle which depends on the radius of curvature.
During slipping a sidelong power or force
influences the elements of the vehicle, this force
is relative to the slipping point. And also there is
a connection between sidelong powers and
slipping edge which relies upon the span of the
curvature.
1.1 Road-Tire Friction
At the point when the driver turns the
controlling wheel to make a customary turn, the
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tires on the front hub of the vehicle become
skewed with the bearing of movement, and we
get a tire-slip edge. The tire-slip point is
thoughtfully like the vehicle sideslip edge, then
again, actually the pertinent edge of reference is
related with a solitary tire as opposed to the
vehicle body. Specifically, the tire-slip edge is
characterized as the point between the speed
vector at the focal point of the haggle direction of
the tire. This definition is outlined for the front
left wheel in Figure 1, where α1 signifies the tire-
slip point. A nonzero tire-slip edge infers a
relative contrast in speed between the street
surface and the tire, in the parallel course of the
tire.
Figure 1: Vehicle velocity, yaw rate, vehicle
sideslip angle, tire-slip angle, and road-tire
friction forces [1].
Numerous articles talked about this issue,
Huemer et al. (2001a); Liu et al. (2000) and
Huemer et al. (2001b) related slipping in tires to
frictional conduct of elastic, where a
phenomenological contact law for elastic track
hinders on day off cement is introduced for use
in a naturally visible model. The coefficient of
grating relies upon ordinary weight, sliding speed
and temperature. The grinding coefficient itself is
just an element of typical weight and sliding
speed. Temperature impacts are joined utilizing
the WLF change, i.e., if the present temperature
is unique in relation to the reference temperature,
a proportionate new sliding speed for the
reference temperature is determined. This
examination has been proceeded by Hofstetter et
al. (2003), where a thermo-mechanical coupling
has been presented. Vitality dissemination during
sliding is changed over into warmth and this
warmth motion causes a temperature ascent of
the elastic and street. In (Hofstetter et al., 2006)
likewise re-enactments of scraped area of the
track square are included. Dorsch et al. (2002)
determined a phenomenological erosion law
utilizing information acquired from probes the
LAT100. The displaying and estimation of the
transient moving contact of tires on street tracks
is the subject of a huge multidisciplinary
investigate venture (FOR492) at the University
of Hannover. One of the undertakings centres on
computational homogenization techniques, to
build up a contact law at a naturally visible level,
in light of consequences for a tiny level. Nam et
al. (2015) talked about a powerful wheel slip
control framework dependent on a sliding mode
controller is proposed for improving footing
capacity and diminishing vitality utilization
during unexpected quickening for an individual
electric vehicle. Sliding mode control strategies
have been utilized generally in the advancement
of a vigorous wheel slip controller of customary
inner ignition motor vehicles because of their
application viability in nonlinear frameworks and
heartiness against model vulnerabilities and
unsettling influences. A down to earth slip
control framework which exploits the highlights
of electric engines is proposed and a calculation
for vehicle speed estimation is additionally
presented. The vehicle speed estimator was
planned dependent on rotational wheel elements,
quantifiable engine torque, and wheel speed just
as rule-based rationale. The recreations and tests
were completed utilizing both Car-Sim
programming and a trial electric vehicle
furnished with in-wheel-engines. Through field
tests, footing execution and viability as far as
vitality sparing were completely confirmed.
Similar analyses with varieties of control factors
demonstrated the adequacy and common sense of
the proposed control structure. Jin et al. (2017)
tended to the eyewitness structure issue for
evaluating the side-slip edge and the obscure
street contact coefficient, in view of estimated
signals from sensors normal to present day
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arrangement creation autos. We plan state and
parameter estimation as a non-curved
improvement issue. By intertwining discrete time
arrangement of the improvement and consistent
combination of sensor information, our plan
takes into consideration adequate time for finding
the worldwide optima around through a lattice
search. Thusly, in spite of the non-raised
advancement we are confronting, our perception
conspire can run progressively. We show some
alluring properties of the proposed plot
concerning the security and intermingling of
estimation mistake. One preferred position of our
eyewitness is that for the ostensible model the
estimation mistake doesn't develop in any event,
when the framework needs discernibleness.
Reproduction shows that the proposed spectator
gives exact estimation in testing situations where
the vehicle executes outrageous moves and
estimated signals are undermined by clamour.
1.2 Mathematical Modelling of Slipping
- Equation of motion of vehicle movement When
the car moves along any road it may concern the
following forces shown in figure 2.
Figure 2: Free body diagram of the automobile
moving up some hill of angle α [1].
By applying Newton's second law, the equation
of motion of the car:
)()(
gwrrrftrtfv
FFFFFF
dt
dV
M (1)
1.3 Curvilinear Motion of the Car
Any particle moves in a curve of radius ρ applied
to a kind of force called normal force, such force
effects on the particle and causes what is called
slipping. The slipping percent depends on many
factors like (depending on [1]):The velocity of
the car, V, the rolling of the free rolling tire, r,
angular speed of the tire, w, the nature of the
road: dry, wet, snow, rainy….etc. The tire slip
can be defined as:
%100)1(%100)1(  r
r
rw
V
s
e
(2)
Where V: is the velocity of the automobile
during traction(m/s), r: is the effective radius of
the tire (m), w: is the angular speed of tire
(rad/s). But from dynamics it is known for any
particle moves in a curve of radius (ρ) it exposes
to two kinds of acceleration: tangential at, and
normal an, such that:
a
t
=dV/dt,
a
n
=V
2
/ρ (3)
The normal component of the acceleration is
responsible for causing slipping, and velocity in
equation (2) can be substituted as:

n
aV  (4)
This yields to
%100)1(


r
a
s
n
 (5)
Also the radius of curvature of any curve can be
written as:
)(
))(1(
)(
32
xy
xy
x




(6)
Substitute equation (5) in (4) to get
%100)
)tan1(
1(
43
yr
a
s
l
n





(7)
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Equation (7) describes the slip ratio as a function
of normal acceleration tangential acceleration
which is considered here as constant, also
slipping ratio is a function of the effective radius
of the tire and angular speed of the tire.
The error in calculating the tire slip using
equation (7) is calculated by differentiating s
with respect to r or θ such that:
error
l
n
error
r
yr
ya
s
2
43
)(
*)tan1(






(8)
While the error with respect to θ can be given as
error
l
n
error
yr
a
s



*sec
)tan1(
75.0
41




(9)
2 Results and Discussion
It can be noticed that as the normal acceleration
increases the slipping ratio decreases. Figure 3
shows the relation between slip percent and
normal acceleration of the car during curve-linear
motion of the car.
Figure 3: Slip percent and normal acceleration
Case II. The relation between the slipping
percent and angular velocity of the tire. Figure 4
shows the relation between the slipping ratio and
the angular speed of the tire.
Figure 4: Slipping ratio and the angular speed of
the tire.
Case III. The relation between the slipping ratio
and the effective rolling radius of the tire.
Figure 5 shows the relation between the slipping
ratios as a function of radius of the tire. The
results shows that as the radius of the tire
increases the slipping percent increases.
Figure 5: Relation between the slipping ratios as
a function of radius of the tire.
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Case IV. The effect of the path slope on the
slipping ratio.
Figure 6 shows the effect of the road slope (tan
θ) on the slipping percent. It is obvious that as
the path slope (tan θ) increases the slipping value
decreases.
Figure 6: Slipping percent as a function with
slope of the road.
Case V. The relation between the slipping ratio
and the radius of the curvature of the path.
Figure 7 shows the relation between the slipping
percent and the radius of curvature of the path. It
can be noticed that as the radius of curvature
increase the slipping % decrease which is logic
the slipping on straight dry path is nearly close to
zero.
Figure 7: The relation between the slipping
percent and the radius of curvature of the path.
Case VI. The relation between the slipping
percent and the rate of decreasing of the radius of
the tire (Δr) with time. Figure 8 shows the
relation between the slipping percent and the tire
corrosion. It can be noticed that as the tire radius
decreases (more corrosion) the slipping increase.
Figure 8: Relation between the slipping percent
and the tire corrosion.
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3 Conclusions
It is found that as the normal acceleration
increases the slipping ratio decreases. Also as
the RPM of the tire increase the slipping ratio
increases. It can be noticed that as the radius of
the tire increases the slipping percent increases.
It is obvious that as the path slope (tan θ)
increases the slipping value decreases. Also it
can be noticed that as the radius of curvature
increase the slipping % decrease which is logic
the slipping on straight dry path is nearly close to
zero. It can be noticed that as the tire radius
decreases (more wear) the slipping increase.
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Contribution of individual authors
to the creation of a scientific article
(ghostwriting policy)
-Sayel M. Fayyad derived the mathematical
model in its final state and carried out the
simulation and the optimization. Also writing up
the article with sharing with the second author.
-Mohannad O. Rawashdeh preparing data from
real cases and apply the final derived equations
on them to extract the results and conclusions.
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