Analisis Comparativo Pruebas de Frenado

International Journal of Automotive Technology, Vol. 13, No. 5, pp. 735742 (2012)

DOI 10.1007/s122390120072x

Copyright 2012 KSAE/ 06605

pISSN 12299138/ eISSN 1976-3832

735

COMPARATIVE ANALYSIS OF VEHICLE BRAKE DATA IN THE

MINISTRY OF TRANSPORT TEST ON THE ROLLER BRAKE TESTER

AND ON FLAT GROUND

C. SENABRE*, E. VELASCO and S. VALERO

Miguel Hernndez University, Elche 03202, Spain

(Received 27 May 2010; Revised 5 January 2011; Accepted 23 December 2011)

ABSTRACTThis study performs a comparison between what occurs when braking on a Ministry of Transport (MOT) brake

tester and on flat ground. The tire pressure is changed, but the other parameters remain constant. The results from this research

and from the in-depth comparative study conducted by the mechanical engineering staff in the mechanical laboratory at the

Miguel Hernndez University in Elche have led to the following main conclusions: By varying the tire pressure, false results

can be obtained with the MOT brake tester, which means that, if the tires are inflated at a low pressure but the brakes are in

good condition, the vehicle will not pass the MOT. Conversely, if the brakes are in poor condition but the tire pressure is higher

than what is recommended by the manufacturer, a false pass is produced. This article shows that the MOT brake testing

equipment is often wrong and inexact, and the data and graphs presented prove that the tire pressure is a determining factor

when assessing the condition of brakes.

KEY WORDS : Braking, Ministry of transport (MOT), Roller brake tester, Roller bed, Tire pressure

1. INTRODUCTION

Currently, the International Motor Vehicle Inspection

Committee (CITA) states that the condition of brakes must

be checked at the Ministry of Transport (MOT) Test

Stations. The European Community Law (2002) in Law

no. 29 237, Article 14, states that the driver of the vehicle

must present the vehicle to the MOT Ministry of Transport

Test Station, with the right tire pressure. However, the

MOT procedure manual from Ministry of Industry,

Tourism and Trade of Spain (2006) does not mention the

tire inspection procedure at the stations. This paper

analyzes how the tire pressure and extra weight on the

vehicle can affect the longitudinal braking action and

sliding on a MOT brake tester, and this braking action is

compared with brake sliding on a flat road.

When a vehicle is taken to a MOT testing facility, the

brakes are tested on a roller bed to check the brake circuit.

Several questions on the efficiency of the MOT testing

facilities need to be answered:

Does the braking on a roller brake tester accurately

reproduce braking on flat ground?

To what extent does the tire pressure affect the

measurements taken on the rollers?

Is this test safe enough to assess the condition of the

brakes?

Is this brake test 100% effective?

The aim of the study is to calculate a vehicle's braking

capacity by measuring the slippage on a roller brake tester

at a MOT center, compare this slippage with similar

measurements taken on flat ground, and use these results to

assess the machines reliability to test brake systems.

This is the first time that a comparative analysis of the

longitudinal braking on a MOT roller brake tester and on

flat ground has been conducted.

The contributions from many authors on longitudinal

braking have been analyzed.

1.1. Background

The oldest model, Fiala (1954), was the first to ever

produce an iteration of the tire on the ground, although the

tire was not considered with dimensions. Bergman (1965)

conducted the first theoretical analysis of the drift during

braking. Meyer and Kummer (1962) published a study on

the transmission mechanisms of the forces between the

wheel and the ground. Nordeen and Cortese (1963a)

studied the relationship between the F side and the F drive

and braking. Nordeen and Cortese (1963b) published

studies on the characteristic forces and moments that are

involved in tire rolling. Frank and Hofferberth (1967)

studied the mechanical properties of tire technology and

the qualities of rubber. Bekker (1969) published the first

study on the interactions in terrain-vehicle systems.

Livingston and Brown (1969) compared the effects of

different types of brake pressure. Dugoff et al. (1971)*Corresponding author. e-mail: [email protected]

736 C. SENABRE, E. VELASCO and S. VALERO

developed the friction coefficient slip-speed expression of

the tread. Hays and Browne (1974) made a list of the

theory and data from the friction of rubber tires. They also

studied the physical properties of the drive wheel. Moore

(1975) conducted an extensive study on the relevant slip

and friction properties of the vehicle. Bernard et al. (1977)

published a study on the semi-empirical tire model used for

continuous slipping. Potts et al. (1977) studied the

vibrations that tires. Shearer (1977) analyzed the rolling of

the wheel and established methods to improve tires of the

wheels. Pacejka (2005) came up with mathematical models

that outlined the behavior of the steady drift and the

relationship between the rim and other parameters. Topkins

(1981) provided a massive collection of tire theory and

data. Sakai (1981) conducted in-depth theoretical and

experimental studies of advanced tire models and their

dynamic properties. Milliken and Rice (1983) published a

study about non-nimensionalizing tire data for vehicle

simulation. Sharp and El-Nashar (1986) conducted a

computer application-based mathematical model to

simulate rupture forces on the tires of wheels. Bakker et al.

(1989) devised a pseudo-experimental model, which is

called the Magic Formula model. Gim and Nikravesh

(1990), from the University of Arizona, conducted studies on

tire forces. Senabre et al. (2004) developed mathematical

models to simulate tire movement and interaction with the

surface (Mechanical Conference). Garca-Pozuelo et al.

(2009) studied improvements in the inspection procedure of

brake disc warping (Securitas Vialis).

2. TESTING METHODS

The vehicle used in this test was a Renault 21 model

Nevada that seats 7 and has a diesel engine. It has front disc

brakes with sliding clamps, uses DOT 4 brake fluid, and

uses a tandem brake pump. The rear wheels have drum

brakes.

The measurements were taken from 2 encoders fitted to

the roller brake tester, and the wheels of the vehicle and a

pressure sensor were attached to the vehicle's brake circuit.

These instruments were used to measure the pressure in

the hydraulic circuit after pressing the brake pedals and to

correlate the data to the speed of the wheels

The two tests conducted are described below:

2.1. Test 1

The braking is measured on the roller brake tester at a

MOT center by placing the vehicle on rollers that rotate at

5 km/h (see figure 2). All roller banks on the MOT brake

testers rotate at 5 km/h in all MOT stations in Spain. This

velocity is enough to obtain 100% wheel slip.

The vehicle tries to stop the wheel through braking. A

sensor in the hydraulic pipe placed on the front right wheel

is used to obtain data on the brake. The slip value was

measured using the angular velocity of the rollers and the

vehicle wheel data.

The emergency brake should not be on. The brake pedal

has to be pressed down until 100% slippage is obtained.

After 100% slippage and with a fully locked wheel, the tire

cannot transmit additional brake torque to the terrain or the

roller tester sensor, which means that the pressure in the

brake circuit after this point is ineffective.

The torque on the rotation axis of the rollers is measured

using a strain gauge. The pressure in the hydraulic brake

circuit on the right front wheel of the vehicle is also

measured using a sensor in the hydraulic pipe of the right

front wheel, as shown in figure 1. There is a pipe for the

brake of each wheel, and the pipe in the right front wheel is

no longer than 2 m; therefore, the position of the sensor on

the pipe does not affect the measurements because there are

no flow losses.

Measurements were taken from the 2 encoders attached

to the roller brake tester and the right front wheel of the

vehicle, and a pressure sensor is attached to the vehicle's

brake circuit. These instruments were used to measure the

pressure in the hydraulic circuit after pressing the brake

pedals and to correlate the data to the speed of the wheels.

The test data were recorded using an LMS Pimento

portable, multi-channel analyzer. This analyzer provides for

real-time monitoring of the process and data recording.

To measure the revolutions of both the rollers and the

vehicle wheels, 2 OMRON encoders were used. One

encoder was the E6B2-CWZ6C model, and the other

encoder was the E6B2-CWZ1X model. One encoder was

attached to the right-hand roller of the roller brake tester (see

Figure 1. Position of the hydraulic sensor.

Figure 2. Hydraulic sensor in pipe to right front wheel.

COMPARATIVE ANALYSIS OF VEHICLE BRAKE DATA IN THE MINISTRY OF TRANSPORT TEST 737

figures 3 and 4), and the other encoder came in contact with

the front right-hand wheel of the vehicle (see figure 4). To

ensure that the rotation of the encoders was synchronized

with the rollers and the wheels, connectors were built as

shown in figures 3 and 4 such that a spring guarantees that

good contact is achieved.

The slip in test 1 was calculated from the data recorded

during the test using expression (Dixon, 1996):

(1)

where rvehicle wheel is the brake torque on the wheel / the brake

force on the roller.

The torque at the roller axis is measured using the MOT

sensor, which is a gauge that determines the torque on the

shaft.

The brake torque was calculated in the following

manner. The driver released the brake pedal until the

torque generated at the wheel was higher than the

pressure applied to the brake circuit such that the torque

produced a rotation of the wheel (see figure 5). A triggers

is used, it measure 0 volts when the wheel rotate and a

circuit with a 5 volts battery is open, in that point the

measurement of the pressure in the brake circuit is

measured to calibrate the pressure sensor.

2.2. Test 2

In this test, the vehicle runs on flat ground until it attains a

velocity of 40 km/h, which is required to obtain 100%

slippage. In the test 2, It is braked the vehicle until the car

slides by 100%. The same signals as in test 1 are recorded

for the brake test. Both sensors are used in the two tests to

make sure that the measurement has been acquired in the

same manner.

A fifth wheel, driven by the vehicle, has been attached to

measure the slippage (see figure 6). This is used as a

reference. The track is assumed to be completely flat, with

no changes in the adhesion coefficients of the route. A

spring was attached to the fifth wheel to ensure good

contact. The velocity of the car is 40 km/h, as this velocity

is required to obtain 100% wheel slippage.

The values of the coefficient of adherence () (Dixon,

1996), which are affected by several internal factors

associated with the wheel and the vehicle, by external

factors, and even by environmental conditions where there

is movement, appear to be constant.

The adhesion coefficient is 1 for test 1 and 1 for test 2

(Dixon, 1996). This coefficient from the tester value is the

factory-supplied value for the MOT testers.

Therefore, the only difference in the measurements is the

change in tire pressure in both tests.

In test 1 and in test 2, once the test data were recorded,

any data points that were not characteristic were filtered and

deleted so that better results and a suitable interpretation

could be obtained.

Slip 1speed of vehicle wheel

roller speed-------------------------------------------------------=

1rvehicle wheel* Wr of vehicle wheel

rroller* Wr of roller-----------------------------------------------------------=

rroller 0.1 m=

Figure 3. Test 1 roller brake tester at the MOT center.

Figure 4. Encoder attached to the roller brake tester.

Figure 5. Pressure relation in the brake circuit and brake

torque on the wheel.

Figure 6. Fifth wheel or the drive wheel.


Sick Stegmann DKS-40 encoders were used in this

test, and the encoder was attached to the fifth wheel of the

vehicle, the drive wheel (see figure 4), and the other

encoder was attached to the front right-side wheel of the

vehicle, which is the same as that in the previous test.

The slip was calculated from the data recorded during

tests by means of expression (Aparicio, 2001):

(2)

The slip can be calculated if the angular velocity is

calculated:

All of the slip data are obtained when the wheel is

locked, hence: wr of vehicle wheel = 0 and wr of fifth wheel >0, where re

fifth wheel is the fifth effective rolling radius and can be written

as re fifth wheel = Vvehicle / wr of fifth wheel, r e vehicle wheel is the wheel

effective rolling radius, and Vvehicle is the vehicle velocity.

The value of wvehicle wheel/wfifth wheel are multiplied by the

fraction re vehicle wheel / re fifth wheel , which is considered to be

constant to simplify the calculation.

The vehicle velocity is determined with a Wilcoxon

784A accelerometer that is placed inside the car, as shown

in figure 7.

The velocity is obtained by integrating the acceleration

values acquired from the accelerometers, located on the

floor by the rear seats of the vehicle, which is the center of

gravity of the vehicle.

Additionally, 2 more accelerometers were installed to

make sure there is no vertical (z axis) or horizontal (y

axis) acceleration.

3. RESULTS

A tire with pressure that is too low overheats, the surface

does not wear uniformly so more fuel is consumed. The tire

is less durable, becomes more sensitive to impact and has a

lower resistance to stress and strain, which means it might

become irreparably damaged. At a pressure lower than 1

bar, the tire may even come loose from the rim. This did

not happen in this study because a pressure of 1 bar or

greater was used. The tires have been inflated to have

pressures of 1, 1.5 and 2 bar. These three values clearly

show how events occur, although the range was increased in

later studies.

The measurements of the brake pressure on the vehicle

and the slippage in the braking wheel were obtained for

both tests.

A comparative analysis was conducted on the braking

and slip measurements for the same test performed with

different tire pressures to examine how the test evolved.

The braking and slippage data were also compared for both

tests at the same tire pressure to investigate if there are any

differences in the braking measurements between the roller

tester and flat ground.

3.1. Comparison of the Braking-slip Ratio Data at Various

Tire Pressures for Both Tests

3.1.1. Results and discussion from test 1

When the brake pedal is pressed down, the pressure values

in the circuit and the corresponding slippage that is obtained

in test 1 for different tire pressures are shown below.

The measurements produced from the pressure sensors

versus time are as shown in figure. 8:

From the data obtained, only the measurements taken up

to the maximum slippage are considered, which corresponds

to 100% wheel slip.

Once the measurements have been processed, which


seep of fifth wheel-------------------------------------------------------=


speed of fifth wheel--------------------------------------------------------- ==

1re vehicle wheel* Wr of vehicle wheel

re fifth wheel* Wr of fifth wheel--------------------------------------------------------------=

Figure 7. Accelerometer installed inside the vehicle.

Figure 8. Pressure measurements in the brake circuit of the

vehicle versus time on the MOT roller brake tester and on

flat ground with 1-1.5-2 bar of wheel pressure.

Figure 9. Start and end points of the measurements.


means removing anomalies, such as sensor or wire

disconnection, the useful part of the measurement is

obtained. All data files have a clear start and end point (see

figure 9). The starting point has to be the last point with 0

pressure in the brake circuit, and the last point is the

maximum slip value. If the measurements begin with a

torque value greater than 0 the file is removed, and if the

measurement finishes without a maximum and constant

slip value, the file is deleted.

A summary for test 1 was obtained for each tire pressure

value and is shown in figure 10.

As seen in the graph in figure 10, when the tire pressure

increases, the braking pressure required for the braking

system to be able to stop the vehicle on the MOT roller

tester increases as well, and there is some delay in the slip

increase. This means that when the tire pressure is too low,

the maximum slip value can be obtained with less pressure

on the vehicles brake circuit.

3.1.2. Results and discussion from test 2

This test shows that there are smaller differences in the

brake curves in relation to the slippage at various tire

pressures compared with the MOT test 1, as shown in

figure. 11.

The maximum pressure applied in the brake circuit to

stop a vehicle moving on flat ground is observed to decrease

by 6.09% from 128.62 to 121.24 bar as the tire pressure

increases from 1 to 2 bar, as shown in the maximum values

in figure 11. This, however, is not as significant as the

48.1% increase in the maximum value of the pressure in the

brake circuit in test 1, which increased from 45.07 to 86.83

bar and was enough to obtain 100% slippage as the tire

pressure increased from 1 to 2 bar (see figure 9).

3.2. Comparison of the Results from Both Tests

When comparing the pressure curves in the brake circuit

for both tests and the slippage for various tire pressures, the

graphs in figs. 11, 12 and 13 show a clear and distinct

difference in the pressure required in the brake circuit to

stop the vehicle.

As shown in figure 12, the % difference of the maximum

value of the pressure in the brake circuit between both tests

for a tire pressure of 1 bar is 65% if 100% slippage is to be

obtained. This difference decreases to 40.64% when the

tire pressure is 1.5 bar (see figure 11), and it drops to

28.38% when the tire pressure is 2 bar (see figure 14).

Figure 10. Pressure in the brake circuit for the slippage in

test 1 at various tire pressures.

Figure 11. Pressure in the brake circuit for slippage in test 2

at various tire pressures.

Figure 12. Comparison of the pressure in the brake circuit

versus slippage when the vehicle is on the roller tester and

on flat ground at a tire pressure of 1 bar.


versus the slippage of the vehicle on the roller tester and on

flat ground at a tire pressure of 1.5 bar.


Although figure 14 shows a reduction in the difference

in braking pressure between both tests, a roller brake tester

does not reproduce braking on flat ground.

3.3. Comparison of the Braking Data for Both Tests

According to the tests conducted, the pressure in the brake

circuit required to stop the wheel for the test on flat ground

decreases as the tire pressure increases. Therefore, at tire

pressures lower than 2 bar, a higher pressure is required in

the brake circuit to stop the vehicle. This should be avoided

so that less energy is consumed and the vehicle can be

stopped in time.

However, this result does not correspond to what occurs

on the roller brake tester. As observed in fig. 15, the

maximum pressure applied to the brake circuit to obtain

maximum slippage (and the vehicle leaves the tester, as a

result) increased as the tire pressure increased, and

therefore, a greater hydraulic pressure in the brake circuit

has to be applied in the case of higher tire pressure for the

vehicle to leave the tester.

One of the possible reasons why this tendency is

observed at the peak braking values in the MOT is that the

tire deforms on the rollers, and at higher tire pressures, it

deforms less, resulting in less contact area between the tire

and roller. This means that with a smaller frictional area, a

greater force is required with the rollers before the vehicle

can leave the tester.

In contrast, the braking force required to stop the vehicle

on flat ground, regardless of the tire pressure, is always

greater than the force required on the roller tester. This is

due to the fact that, when a moving vehicle is stopped, the

forward inertial motion must be counteracted, and this does

not occur on the roller brake tester.

Quantitatively, if the tire pressure is 2 bar, the pressure

sensor in the roller brake tester sensor captures a 28%

difference in the measurements from the test on flat

ground, and this increases to 65% if the tire pressure drops

to 1 bar.

The minimum brake efficiency required to pass the

MOT test is 48-50% for vehicles without ABS. Our vehicle

does not have ABS. This is pursuant to Directive 96/96

CEE (EC) and the MOT vehicle inspection manual.

The efficiency is:

where E is the efficiency, F is the sum of the braking forces

from all the wheels, M.M.A is the maximum permissible

vehicle mass in kg (1350 kg), and g is the acceleration due

to gravity.

If there is a pressure of 1 bar in the brake circuit, 13.87 N

of force is available to brake each wheel (see figure 5).

Therefore, 121.24 bar (maximum brake value) in the

brake circuit is equal to 1681.5 Nm, and this value over 4

wheels is 6726 N.

If the pressure of the brakes is equal in the 4 wheels, the

efficiency is:

E= 6726 N/(1140 kg*10 m/s2)= 59%

Therefore, this vehicle should pass the MOT test

because its brakes are in good condition, and this vehicle

should pass the test with pressure of 2 bar or less in the

tires.

However for 2 bar of wheel pressure, the maximum

value in the brake circuit is 86.83 bar for test 1, and for 4

wheels, the brake torque is 4817.3 N.

E = 4817.3 N/1140 kg*10 m/s2= 42.2%

Therefore, this vehicle will not pass the test 1 with 2 bar

of tire pressure or less.

If the tendency of the maximum bar in the brake circuit

for test 1 (figure 12) is captured by the following:

EF

M.M.A.g---------------------100=

EF

M.M.A.g---------------------100=


versus slippage of the vehicle on the roller tester and on

flat ground at a tire pressure of 2 bar.Figure 15. Relation of the maximum pressure in the brake

circuit for different tire pressures when the vehicle is

running on the MOT roller tester and on flat ground.


y = 41.78x+8.81,

where x is wheel pressure, the maximum brake value for

2.5 bar of wheel pressure can be predicted.

Hence, the efficiency for 2.5 bar of tire pressure will be:

E = 107*13.87*4 N/1140 kg*10 m/s2 = 52.4% > 48%

The car will pass test 1 with 2.5 bar of wheel pressure

because the efficiency is greater than 48%.

Our conclusion is that the car will pass test 1 only with a

wheel pressure 2.5 bar or more, and it will fail the MOT

test with a wheel pressure lower than 2.5 bar even if the

brake system is in good condition.

4. DISCUSSION AND CONCLUSIONS

This study was conducted after ensuring that the measurement

control was the same in both tests. Indeed, large differences in

the pressures in the vehicle brake circuit were required to

stop the vehicle before obtaining 100% wheel slip. The

maximum pressure applied in the brake circuit to stop the

vehicle movement on flat ground was observed to decrease

by 6.09% from 128.62 to 121.24 bar as the tire pressure

increased from 1 to 2 bar (see figure 7). However, this is

not as significant as the 48.1% increase in the maximum

value of pressure in the brake circuit, from 45.07 to 86.83

bar, in test 1 to obtain 100% wheel slippage, as the tire

pressure increased from 1 to 2 bar (see figure 6). Therefore,

there is an adverse tendency in tracking the pressure

measurements in the brake circuit related to the wheel slip

for the 1 and 2 bar tire pressures in both tests.

On flat ground, less braking force was required to stop the

vehicle as the tire pressure increased, and the opposite was

observed with regard to the roller test when tire pressure

increased. The braking force was required to increase as

well, i.e., the pressure in the brake circuit has to be increased

to obtain 100% slippage. This means that, as the tire pressure

increases, the roller brake tester captures the measurements

that are closer to those of the flat ground test.

In summary, a low tire pressure on the MOT roller brake

tester produces values in the brake pressure circuit that may

vary up to 65% from the real braking force required on flat

ground.

The difference in the measurements between the two

tests may be due to the following:

(1) There is a visible difference between the processes

compared: in test 2 (on flat ground), the brake circuit

pressure required to stop the vehicle was measured,

and (on the roller tester) in test 1, the pressure required

to eject the vehicle from the roller tester was also

obtained.

(2) On flat ground (test 2), the forward motion inertia has to

be counteracted, which is not observed on the roller

tester.

(3) The contact zone between the tire and the MOT roller

test track decreases as the tire pressure increases;

therefore, a larger area of friction with the rollers will

involve a greater braking force.

(4) The contact zone between the tire and the flat ground is

230 mm2 and the contact zone between the tire and the

roller is 48.04 mm2 for a wheel pressure of 2 bar. This

difference affects the maximum value of the pressure in

the brake circuit because less contact means that 100%

slippage with a lower pressure in the brake circuit can

be obtained (see figures 16 and 17).

(5) According to the measurements taken when the vehicle

is stationary, the contact surface between the tire and

the roller, at any tire pressure, is always less than the

contact area of the wheel on flat ground.

(6) The velocity could be a reason why there is a difference

between the brake measurements in the two experiments.

Therefore, the brake efficiency has been demonstrated to

depend on the condition of the brakes and on the tire

pressure during inspection on a roller brake tester. As

mentioned before, the car would pass test 1 only with a tire

pressure of 2.5 bar or more, and the car would fail the

MOT test with a tire pressure lower than 2.5 bar, even if the

brake system was in good condition.

Consequently, the suitability of a roller brake tester to

determine whether a vehicles brakes are in good condition

Figure 16. Print on flat ground.

Figure 17. Print on the MOT brake tester.


is debatable.

REFERENCES

Aparicio, F. and Vera, C. (2001). Teora de los Vehculos

Automviles. Seccin de Publicaciones de la E.T.S. Madrid.

Bakker, E. and Pacejka, H. B. and Lidner, L. (1989). A new

tire model with an application in vehicle dynamics

studies. Autotechnologies, Proc. SAE Paper No. 890087,

8395.

Bekker, M. G. (1969). Introduction to Terrain-vehicle

Systems. The University of Michigan Press. Ann Arbor.

Michigan.

Bergman, W. (1965). The basic nature of vehicle

understeer-oversteer. SAE Paper No. 650085.

Bernard, J. E., Segel, L. and Wild, R. E. (1977). Tire shear

force generation during combined steering and braking

maneuvers. SAE Paper No. 770852.

Dugoff, H. and Segel, L. and Ervin, R. D. (1971).

Measurement of vehicle response in severe braking an

steering maneuvers. SAE Paper No. 710080.

Dixon, J. C. (1996). Tires, Suspension and Handling. 2nd

Edn. Society of Automotive Engineers, Inc. London.

Fiala, E. (1954). Lateral forces at the rolling pneumatic tire.

Seitenkraefte am Rollenden Luftreifen. Wien Technische

Hochschule, 31.

Frank, F. and Hofferberth, W. (1967). Mechanics of the

pneumatic tire. Rubber Chemistry and Technology 40, 1,

271322.

Garcia-Pozuelo, D., Gauchia, A., Boada, B. L. and Diaz, V.

(2009). Improvements in the Inspection Procedure of

Brake Disc Warping. Securitas Vialis. 8389.

Gim, G. and Nikravesh, P. E. (1990). An analytical model

of pneumatic tires for vehicle dynamic simulations. Part

1: Pure slips. Int. J. Vehicle Design, 11, 589618.

Hays, D. F. and Browne, A. L. (1974). The Physics of Tire

Traction. Plenum. New York.

Livingston, B. I. and Brown, J. E. JR. (1969). Physics of

the slipping wheel. I. Force and torque calculations for

various pressure distributions. Rubber Chemistry and

Technology 42, 4, 10141026.

Meyer, W. E. and Kummer, H. W. (1962). Mechanism of

force transmission between tire and road. Society of

Automotive Engineers, SAE Technical Paper 490A.

Milliken, W. F. JR. and Rice, R. S. (1983). Moment

method. I. Mech. E Conf. Road Vehicle Handling, Paper

C113/83.

Ministry of Industry, Tourism and Trade of Spain (2006).

Station Inspection Procedures Manual. No. 29237.

Ministry of Industry, Tourism and Trade of Spain,

Madrid, 7081.

Moore, D. F. (1975). The Friction of Pneumatic Tires.

Elsevier.

Nordeen, D. L. and Cortese, A. D. (1963a). Small

differences in tire properties, large differences in vehicle

handling. General Motors Corporation, Warren, Mich.

SAE J. 71, 7, 8390.

Nordeen, D. L. and Cortese, A. D. (1963b). Force and

moment characteristics of rolling tires. General Motors

Corporation, Warren, Mick, Report No. SAE 713A, 13.

Pacejka, H. B. (2005). Tire and Vehicle Dynamics. SAE.

USA.

Potts, G. R., Bell, C. A., Charek, L. T. and Roy, T. K.

(1977). Tire vibrations. Tire Science and Technology 5,

4, 202225.

Sakai, H. (1981). Theoretical and experimental studies on

the dynamic properties of tires, Parts 13. Int. J. Vehicle

Desing, 2, 13.

Senabre, C. and Velasco, E. and Sanchez, M. (2004). Study

of mathematical models to simulate Tire movement and

interaction with the surface. Proc. 7th Mechanical Conf.,

Leon, 129132.

Sharp, R. S. and El-Nashar, M. A. (1986) A generally

applicable digital computer based mathematical model

for the generation of shear forces by pneumatic tires.

Leeds University, England. Vehicle System Dynamics 15,

4, 187209.

Shearer, G. R. (1977). The rolling wheel the development

of the pneumatic tire. Proc. I. Mech. E. (A.D.) 191, 11/

77, 7587.

Tompkins, E. (1981). The History of the Pneumatic Tire.

Eastland Press. Dunlop.

/ColorImageDict > /JPEG2000ColorACSImageDict > /JPEG2000ColorImageDict > /AntiAliasGrayImages false /DownsampleGrayImages true /GrayImageDownsampleType /Bicubic /GrayImageResolution 150 /GrayImageDepth 8 /GrayImageDownsampleThreshold 1.33333 /EncodeGrayImages true /GrayImageFilter /FlateEncode /AutoFilterGrayImages false /GrayImageAutoFilterStrategy /JPEG /GrayACSImageDict > /GrayImageDict > /JPEG2000GrayACSImageDict > /JPEG2000GrayImageDict > /AntiAliasMonoImages false /DownsampleMonoImages true /MonoImageDownsampleType /Bicubic /MonoImageResolution 150 /MonoImageDepth -1 /MonoImageDownsampleThreshold 1.33333 /EncodeMonoImages true /MonoImageFilter /CCITTFaxEncode /MonoImageDict > /AllowPSXObjects false /PDFX1aCheck false /PDFX3Check false /PDFXCompliantPDFOnly false /PDFXNoTrimBoxError true /PDFXTrimBoxToMediaBoxOffset [ 0.00000 0.00000 0.00000 0.00000 ] /PDFXSetBleedBoxToMediaBox true /PDFXBleedBoxToTrimBoxOffset [ 0.00000 0.00000 0.00000 0.00000 ] /PDFXOutputIntentProfile (None) /PDFXOutputCondition () /PDFXRegistryName () /PDFXTrapped /False

/DetectCurves 0.000000 /EmbedOpenType false /ParseICCProfilesInComments true /PreserveDICMYKValues true /PreserveFlatness true /CropColorImages true /ColorImageMinResolution 290 /ColorImageMinResolutionPolicy /Warning /ColorImageMinDownsampleDepth 1 /CropGrayImages true /GrayImageMinResolution 290 /GrayImageMinResolutionPolicy /Warning /GrayImageMinDownsampleDepth 2 /CropMonoImages true /MonoImageMinResolution 800 /MonoImageMinResolutionPolicy /Warning /CheckCompliance [ /None ] /PDFXOutputConditionIdentifier () /Description > /Namespace [ (Adobe) (Common) (1.0) ] /OtherNamespaces [ > /FormElements false /GenerateStructure false /IncludeBookmarks false /IncludeHyperlinks false /IncludeInteractive false /IncludeLayers false /IncludeProfiles false /MultimediaHandling /UseObjectSettings /Namespace [ (Adobe) (CreativeSuite) (2.0) ] /PDFXOutputIntentProfileSelector /DocumentCMYK /PreserveEditing true /UntaggedCMYKHandling /LeaveUntagged /UntaggedRGBHandling /UseDocumentProfile /UseDocumentBleed false >> ]>> setdistillerparams> setpagedevice

Analisis Comparativo Pruebas de Frenado

Documents

Transcript of Analisis Comparativo Pruebas de Frenado