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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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Sayel M. Fayyad, Mohannad O. Rawashdeh

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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.

References:

[1] H.R. Muhammad, G. Yimin, E.G. Sebastien,

and E. Ali, 2004, Modern Electric, Hybrid

Electric, And Fuel Cell Vehicles, CRC Press.

[2]A. T. van Zanten, “Bosch ESP systems: 5

years of experience,” in Proc. Automot. Dyn.

Stabil. Conf., Troy, MI, 2000, paper no. 2000-01-

1633.

[3] J. Farrelly and P. Wellstead, “Estimation of

vehicle lateral velocity,” in Proc. IEEE Int. Conf.

Contr. Appl., Dearborn, MI, 1996, pp. 552–557.

[4] Y. Fukada, “Slip-angle estimation for vehicle

stability control,” Vehicle Syst. Dyn., vol. 32, no.

4, pp. 375–388, 1999.

[5] P. J. TH. Venhovens and K. Naab, “Vehicle

dynamics estimation using Kalman filters,”

Vehicle Syst. Dyn., vol. 32, no. 2, pp. 171–184,

1999.

[6] A. Y. Ungoren, H. Peng, and H. E. Tseng, “A

study on lateral speed estimation methods,” Int.

J. Veh. Auton. Syst., vol. 2, no. 1/2, pp. 126–144,

2004.

[7] U. Kiencke and A. Daib, “Observation of

lateral vehicle dynamics,” Contr. Eng. Pract., vol.

5, no. 8, pp. 1145–1150, 1997.

[8] U. Kiencke and L. Nielsen, Automotive

Control Systems: For Engine, Driveline, and

Vehicle. Springer, 2000.

[9] M. Hiemer, A. von Vietinghoff, U. Kiencke,

and T. Matsunaga, “Determination of the vehicle

body slip angle with non-linear observer

strategies,” in Proc. SAE World Congress,

Detroit, MI, 2005, paper no. 2005-01-0400.

[10] A. von Vietinghoff, M. Hiemer, and U.

Kiencke, “Nonlinear observer design for lateral

vehicle dynamics,” in Proc. IFAC World

Congress, Prague, Czech Republic, 2005, pp.

988–993.

[11]A. von Vietinghoff, S. Olbrich, and U.

Kiencke, “Extended Kalman filter for vehicle

dynamics determination based on a nonlinear

model combining longitudinal and lateral

dynamics,” in Proc. SAE World Congress,

Detroit, MI, 2007, paper no. 2007-01-0834.

[12] A. Suissa, Z. Zomotor, and F. Böttiger,

“Method for determining variables characterizing

vehicle handling,” US Patent 5,557,520, 1994,

filed Jul. 29, 1994; issued Sep. 17, 1996.

[13] L. R. Ray, “Nonlinear tire force estimation

and road friction identification: Simulation and

experiments,” Automatica, vol. 33, no. 10, pp.

1819–1833, 1997.

[14] M. C. Best, T. J. Gordon, and P. J. Dixon,

“An extended adaptive Kalman filter for realtime

state estimation of vehicle handling dynamics,”

Vehicle Syst. Dyn., vol. 34, no. 1, pp. 57–75,

2000.

[15] H. Lee, “Reliability indexed sensor fusion

and its application to vehicle velocity

estimation,” J. Dyn. Syst. Meas. Contr., vol. 128,

no. 2, pp. 236–243, 2006.

[16] A. Hac and M. D. Simpson, “Estimation of

vehicle side slip angle and yaw rate,” in Proc.

SAE World Congress, Detroit, MI, 2000, paper

no. 2000-01-0696.

[17] W. Klier, A. Reim, and D. Stapel, “Robust

estimation of vehicle sideslip angle – an

approach w/o vehicle and tire models,” in Proc.

SAE World Congress, Detroit, MI, 2008, paper

no. 2008-01-0582.

[18] H. E. Tseng, “Dynamic estimation of road

bank angle,” Vehicle Syst. Dyn., vol. 36, no. 4,

pp. 307–328, 2001.

[19] C. Sentouh, Y. Sebsadji, S. Mammar, and

S. Glaser, “Road bank angle and faults

estimation using unknown input proportional-

integral observer,” in Proc. Eur. Contr. Conf.,

Kos, Greece, 2007, pp. 5131–5138.

[20] J. Ryu and J. C. Gerdes, “Integrating inertial

sensors with Global Positioning System (GPS)

for vehicle dynamics control,” J. Dyn. Syst.

Meas. Contr., vol. 126, no. 2, pp. 243–254, 2004.

[21] D. M. Bevly, J. C. Gerdes, and C. Wilson,

“The use of GPS based velocity measurements

WSEAS TRANSACTIONS on SYSTEMS and CONTROL

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for measurement of sideslip and wheel slip,”

Vehicle Syst. Dyn., vol. 38, no. 2, pp. 127–147,

2002.

[22] D. M. Bevly, “Global Positioning System

(GPS): A low-cost velocity sensor for correcting

inertial sensor errors on ground vehicles,” J. Dyn.

Syst. Meas. Contr., vol. 126, no. 2, pp. 255–264,

2004.

[23] D. M. Bevly, J. Ryu, and J. C. Gerdes,

“Integrating INS sensors with GPS

measurements for continuous estimation of

vehicle sideslip, roll, and tire cornering

stiffness,” IEEE Trans. Intell. Transport. Syst.,

vol. 7, no. 4, pp. 483–493, 2006.

[24] J. A. Farrell, Aided navigation: GPS with

high rate sensors. McGraw-Hill, 2008.

[25] J.Y. Wong, Theory of Ground Vehicles,

John Wiley & Sons, New York, 1978.

[26] Bosch, Automotive Handbook, by Robert

Bosch GmbH, Stuttgart, 2000.

[27] S. Mizutani, Car Electronics, Sankaido Co.,

Warrendale, PA, 1992.

[28] Chi Jin, Liang Shao, Cornelia Lex and Arno

Eichberger (2017). Vehicle Side Slip Angle

Observation with Road Friction Adaptation.

Conference Paper · July 2017.

https://www.researchgate.net/publication/315815

208

[29] Kanghyun Nam 1, Yoichi Hori 2 and

Choonyoung Lee (2014). Wheel Slip Control for

Improving Traction-Ability and Energy

Efficiency of a Personal Electric Vehicle.

Energies 2015, 8, 6820-6840

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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BY4.0)

This article is published under the terms of the

Creative Commons Attribution License 4.0

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WSEAS TRANSACTIONS on SYSTEMS and CONTROL

DOI: 10.37394/23203.2020.15.26

Sayel M. Fayyad, Mohannad O. Rawashdeh

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Volume 15, 2020