EB2015-STQ-015

ESTIMATION OF BRAKE ENERGY POTENTIAL 1Grkić, Aleksandar

*;

1Muždeka, Slavko;

2Arsenić, Živan;

3Duboka, Čedomir

1Military Academy, Belgrade, Serbia;

2Faculty of Mechanical Engineering, Belgrade, Serbia;

3Belgrade, Serbia

KEYWORDS – brake energy potential, friction, wear rate, testing, simulation model

ABSTRACT

Braking is a complex stochastic and tribological process characterized by the significant

variation of input energy status of a specific tribo-mechanical system whereby energy of

motion of vehicle is irrevocably converted into heat and dissipated into the environment. At

road vehicles equipped with conventional friction brakes, braking is an extremely unfavorable

energy transformation process from energy consumption and recuperation point of view in

which energy is irretrievably lost. That is why the question might be raised whether there are

any possibilities to manage the brake energy consumption in friction brakes, i.e. would it be

possible to manage both work done by the brake and brake wear in order to maximize both

the efficiency and life of braking systems and what would be amount of energy that a given

brake will transform during its service life? In other words, the question is how big the energy

potential of a given brake would be and how to use and/or dissipate it in the best possible

manner with no risk to jeopardize achieving of high enough braking performance?

Brake performance evaluation is usually based upon realized deceleration, stopping distance,

brake torque and similarly, it does not comprise braking power/energy rate characterization.

However, brake performance realization basically depends on “what was available in the

brake” i.e. “generic” or initial energy potential/capacity of a given brake and “how this was

consumed” under given load conditions and the way brake was used during its service life.

Furthermore, acquiring the quantity of generic energy potential of the given brake one may

manage braking process in order to optimize interdependence between brake performance and

its service life i.e. wear. Most vehicles are nowadays already equipped with different sensors

(speed, application pressure, temperature) and that is why it might be feasible to measure

actual value of the brake energy potential in every moment in time of operation. That is how

individual brake influencing parameters can be managed simultaneously by means of an

appropriate algorithm so as to optimise requested brake performance with the projected brake

service life.

Brake energy potential is defined by its performance, service life and friction coefficient

stability. It tells us how many braking energy has to be spent before brake lining/pad is

reaching its physical wear limit. In order to assess it all influential factors are to be identified

and analyzed, and the procedure of doing so is demonstrated in the paper. With this aim,

numerous tests were carried out with samples of passenger car disk brakes under laboratory

conditions by means of single-ended full-scale inertia dynamometer. Afterwards, results of

these tests were used to establish an analytical model which enables us to estimate friction,

wear and work done by the brake for a given braking application and the whole service life.

Based on the results of experimental and theoretical studies that have been conducted energy

potential rate for the given brake may be assessed, and the applied procedure is described in

the paper. Finally, the idea for an algorithm of braking management based on the optimization

of brake potential is outlined.

INTRODUCTION

Braking of road vehicles where friction brakes are used is an irretrievable energy loss process.

By selecting brake’s design features, materials of which its components are manufactured,

and taking realised operating conditions into consideration for each individual brake amount

of friction power/energy that will be lost during its service life can be “allocated” to the given

brake. That is how brake will transform corresponding part of the vehicle motion energy into

heat which will consequently be dissipated to environment. While doing so, friction brake

will offer certain braking performance, like brake torque, deceleration, stopping distance, etc.

in order to enable requested vehicle’s speed reduction. However, during this process, sliding

elements of a brake are subject to certain amount of consumption (or wear). Physical quantity

which best describes and also “envelopes” all of the above mentioned brake characteristics is

sometimes known under the name „energy specific wear“, which represents the rate of brake

wear per unit brake friction power/energy spent [1-4].

Therefore, brake energy potential as expressed in this paper, represents amount of energy

dissipated by brake until reaching full wearing-out of lining/pad i.e. until the physical limit of

available brake thickness was attained [5]. This factor can indeed be rated, in order to allow

different brakes to be compared between each other from the “spared” friction energy or

lining/pad thickness point of view. In addition to that, operation condition of each individual

brake might be used in such a way to represent optimisation criteria for brake energy potential

based on its instantaneous rate or actually available lining/pad thickness based on the need to

rationally consume energy. In the particular case presented here so called “Linear wear

hypothesis” [6-8] is applied for prediction of brake lining life. One should have in mind that

reaching certain energy specific wear rate by the given brake also means that a portion of the

its total brake energy potential was already spared, while the remaining part can be used to

predict remaining service life of this brake taking in consideration brake operation conditions

and related service loads.

However, brake energy potential should simultaneously enable characterization of the brake

performance behaviour which should primarily be expressed by means of the friction height

and stability, but also taking into consideration of brake reliability, which reflects the

achievement of designed performance in all operation conditions of braking system (including

fade and recovery etc.). These may be assessed by means of the developed mathematical

model which rely on usage of relevant experimental results, having in mind that both friction

“µ” and wear “w” of friction mechanisms can be related to a set of variables which depends

on the design of a given friction mechanism, properties of both friction material and rotor, and

other “inherent” characteristics which all can be represented by single quantities “Kµ” for

friction and “Kw” for wear as given bellow:

µ = µ (Kµ, p, v, θ) and w = w (Kw, p, v, θ) (1)

where application pressure “p” over the friction surface, brake sliding speed “v” and brake

interface temperature “θ” represent factors mostly depending on the brake load conditions

under certain usage pattern [1, 5, 8, for example].

MODELLING

Mathematical method for the Design of Experiments was the theoretical backgrounds for

modelling of friction and wear in the form of step function of the third degree as follows:

B B B Bt K p t v t t

(2)

and

w w w

B w B B Bw t K p t v t t

(3)

where:

αµ, αw, βµ , βw and γµ, γw are coefficients to be determined.

tB - braking time (time of duration of brake application).

Based on such models, work done by the brake can be modelled in the following way:

0

B

B

t

B B W B B B BW t K K p t v t t dt (4)

where:

WB – work done by the brake,

BWK - constant that depends on brake geometry, size of brake cylinder and wheel.

On the other hand, should this type of model be applicable in the above mentioned cases, it

seems one may assume that so called “energy specific wear” can also analytically be

presented in the following way:

0

w w w

B

B

B B Bwsp B t

W

B B B

p t v t tKw t

K Kp t t dt

(5)

Besides, the above given relation for friction, for example, can be rewritten in the following

logarithmic form:

ln ln ln ln lnK p v

(6)

to which the method of least squares can be applied in order to determine the constant k and

coefficients α, β, and γ. The whole problem is thus reduced to find solutions for a four

equation system with four unknown variables (k, α, β and γ) in the matrix form as follows:

2

2

2

ln ln ln ln ln ln ln ln ln

ln ln ln ln ln ln ln ln ln

ln ln ln ln ln ln ln ln ln

ln ln ln ln ln

p p v p K p p

p v v v K v v

p v K

p v N K

(7)

where “N” is the total number of experimental data.

The solution of this system of equations provides predicted value of friction for the given and

predetermined operating conditions (application pressure, interface temperature, and sliding

speed), during the entire braking cycle/application.

In the similar way a model for analytical representation of the brake wear, but also of the

brake friction power output, or work done by the brake, but also for “energy specific wear”

may be developed, but should be experimentally verified and validated.

EXPERIMENT

Having in mind that brake energy potential deals not only with the operation life of a brake

but also with the brake performance and reliability including friction stability, procedure to

assessing it is based on identification and analyses of all influencing factors as presented in

this paper. With this aim, numerous tests were carried out with passenger car disk brake

samples under laboratory test conditions by means of single-ended full-scale inertia

dynamometer. Results of these experiments were afterwards used to formulate relevant

mathematical model for estimation of both friction and wear but primarily for estimation of

work done by the brake for a given braking application, but also to confirm previously

established position with the respect to some specific issues like validation of Linear Wear

Hypothesis and tribo-mutations consideration.

Experimental research was thoroughly planned and performed in laboratory under strictly

controlled test conditions. Single-ended full-scale inertia dynamometer PSK-20 earlier

developed and installed at the University of Belgrade, Faculty of Mechanical Engineering,

Serbia was used to perform all tests. Its outlook is shown in Fig.1. This “in-line” inertia

dynamometer can be applied for testing wide range of brake types and sizes intended for

application in cars and light duty vehicles, like vans, pick-ups etc. This dynamometer consists

of three basic groups of elements:

I. The propulsion group,

II. Six inertia flywheels enabling rotational mass inertia from 10 to 200 kgm2, and

III. Brake station, i.e. the part in which the brake under test is mounted.

A system of six flywheels (3) is mounted onto a common central shaft (4) to simulate the

mass of the test vehicle. Variable inertia is obtained by engaging the appropriate flywheels.

Requested inertia simulation is obtained by “trimming” enabled with the DC electric motor

(1), having continuous regulation of angular speed, to drive the flywheels with the help of a

special type clutch (2). Disc of the tested brake (8) is via flange (5) firmly attached to the shaft

(4), while brake caliper (9) is firmly connected to the test stand foundation (7) via fixed flange

(6). The control system enables strict controlling of brake operating conditions under test, and

namely brake application pressure, brake disc rotational speed, and brake sliding surface

temperature. However, the whole system is equipped with a PC-based automatic control and

data acquisition system.

Experiments were conducted following standardized brake tests developed at the Faculty of

Mechanical Engineering in Belgrade during last 40 years for brake and/or friction material

evaluation purposes, adjusted to the main purpose of the present research. The text test types

were realized:

Burnish test,

Cold brake performance tests,

Fade and recovery test,

Hot brake performance tests,

Specifically designed test programme adjusted to the analysis of tribo-mutation

phenomenon in the braking process, and

Wear tests.

Figure 1. Full-scale single-ended inertia brake dynamometer PSK-20

All these tests were designed to cope with the philosophy of mathematical modelling of

braking cycles in order to assess brake energy potential influential factors. Brake tests were

conducted with samples type “A” and type “B” brake pads from two manufacturers.

RESULTS AND EVALUATIONS

A large number of test results set forth in the frame of experimental research allows detailed

analysis of phenomena and processes during each braking application, as well as making

comparative analysis of a group of brake applications realized within the same or different

operating conditions. Analysis of the experimental results conducted afterwards allows

assessing the impact of certain influencing factors on brake energy potential.

Experimental studies were realized under strictly controlled laboratory conditions (initial test

condition for the brake load at every individual brake application). It means unchanged

conditions for the operating and service environment provided for the research with the

selected disk brake type, in order to secure the test repeatability. That is how brake energy

potential influencing factors were identified and studied by means of the brake application

pressure “p”, sliding speed at the friction surface expressed in the form of brake disk angular

speed “ω”, and interface temperature at the sliding surface “Θ”. Some of the most important

research results are presented bellow, having in mind that brake energy potential is a “generic

friction energy rate” provided by the given automotive brake for being “spared”, and therefore

transferred into heat and dissipated to environment during its whole service life.

Friction tests and modelling

Experimental and analytically expressed values for friction over time elapsing during brake

application are shown in Table 1, where the first column is for time of braking, second

column gives experimentally obtained values of friction coefficient, while third column shows

modelled (analytical) values for the friction coefficient.

134

p

p

Q

w

w

T

controlunit

25 6 78910

IIIIII

Table 1: Experimental and analytically expressed values for friction

Column four shows the deviation of calculated value of friction compared to experimentally

obtained values, while column five shows mean deviation of experimental value of brake

factor during the whole duration of the brake application, which in this case is 2,5%.

All these results are based upon experimentally obtained results in addition to which

appropriate solutions of the system of equations (3) should be added.

Figure 2. Graphical interpretation of experimental and calculated friction coefficient

Graphical interpretation of these results is shown in Figure 2, where blue line represents

experimental result of friction coefficient while red line corresponds to calculated values of

the same parameter. Furthermore, Figure 3. shows comparative review of theoretical and

predicted (calculated) values of friction for different initial speed, brake application pressure

and initial interface temperature.

The label on the top of the diagram indicates initial operating conditions for the braking

application in the format “p20,S20,Θ50”, which means application pressure of 20 bar, sliding

speed of 20 km/h and initial interface temperature of 50oC.

0 0 0 0

0,02 0,13029 0,17208 -0,04179

0,04 0,20327 0,1911 0,01217

0,06 0,24981 0,21114 0,03867

- - - -

- - - -

- - - -

18,34 0,23572 0,29758 -0,06186

18,36 0,17348 0,29764 -0,12416

18,38 0 0 0

μ e -μ theor [%]μ e -μ theor

2,5

t[s] μ e μ theor

0

0,05

0,1

0,15

0,2

0,25

0,3

0,35

0 5 10 15 20μe μtheor

0

0,05

0,1

0,15

0,2

0,25

0,3

0 1 2 3 4 5 6µe µtheo

p20, S20, Θ50

0

0,05

0,1

0,15

0,2

0,25

0,3

0,35

0,4

0,45

0,5

0 0,5 1 1,5 2 2,5 3 3,5μe μtheor

p60, S60, Θ100

Figure 3. Comparative review of theoretical and experimental values of the friction coefficient for different

values of speed at the start of braking, the brake application pressure and the surface temperature

From the plots above very good match can be seen between experimental and modelling

results for friction coefficient.

Brake Performance Tests

In order to analyse friction performance of brake pads used in this research four tests of so

called „Cold Performance Evaluation Tests“ were performed, with initial interface

temperature maintained at 100oC.

a) b)

Figure 4. Comparative review of cold performance mean friction coefficient values for fixed application pressure

of 60 bar and (a) 5 different initial sliding speed values, and (b) 5 different brake application pressure values

Analysis of the impact of (a) initial speed on the friction coefficient is carried out by

comparing the mean value of the friction coefficient per brake application for the fixed

application pressure value of 60 bar, with 5 different initial brake sliding speed values - 20,

40, 60, 80 and 100 km/h; while (b) the impact of application pressure analyses on the friction

coefficient tests was carried out comparing of mean values of friction coefficien per brake

application for fixed initial brake speed equivalent to 60 km/h vehicle speed but 5 different

application pressures - 20, 40, 60, 80 and 100 bar (Figure 4).

From Figure 5 bellow it is evident, for the same test results as shown in Figure 4 that the

mean value of the friction coefficient increases with increasing application pressure more

significantly compared to the increase in friction coefficient with increasing brake initial

speed.

0

0,05

0,1

0,15

0,2

0,25

0,3

0,35

0,4

0 0,5 1 1,5 2 2,5μe μtheor

p80, S60, Θ250

0

0,1

0,2

0,3

0,4

0,5

0,6

0 1 2 3 4 5 6μe μtheor

p50, S100, Θ400

0,15

0,2

0,25

0,3

0,35

0,4

0,45

1 2 3 4µ_S60_P20 µ_S60_P40 µ_S60_P60 µ_S60_P80 µ_S60_P100

a) b)

Figure 5 The trend of change in friction coefficient (a) while increasing sliding speed and (b) while increasing

brake application pressure

In order to analyse initial interface impact on mean value of the friction coefficient, four

braking tests were carried out with the same initial brake speeds and application pressure,

while initial interface temperatures in these tests were 50 ÷ 300oC in steps of 50

oC, as shown

in Figure 6.

Figure 6. Mean friction coefficient for different initial interface temperatures

It is obvious from this plot that different initial interface temperature have much stronger

impact on variation of friction than variation of initial sliding speed, but even much stronger

impact is demonstrated by increasing initial brake application pressure.

Wear tests

Brake wear for one brake application cannot be measured due to its small rate, while friction

energy output is easy to measure with the use of appropriate digital acquisition system.

Establishing the relation between wear rate and corresponding energy output for single brake

application is, therefore, possible only indirectly, based on the principle of accumulation. It is

always possible to aggregate these quantities so as to obtain accumulated (or aggregated)

wear and energy rate over a given number of brake applications (for one wear test block, for

example). After dividing these values with the number of application we can obtain

“calculated” values both for wear and energy output for one single brake application. Such an

operation is indeed possible (i.e. correct) only if strictly identical brake applications are in

question for each wear test block. Such an attempt is demonstrated in Figure 7.

0,25

0,27

0,29

0,31

0,33

0,35

0,37

S_20 S_40 S_60 S_80 S_100

Series1 Linear (Series1)

0,2

0,22

0,24

0,26

0,28

0,3

0,32

0,34

0,36

0,38

P_20 P_40 P_60 P_80 P_100

Series1 Log. (Series1)

0,2

0,25

0,3

0,35

0,4

0,45

1 2 3 450 100 150 200 250 300

Sample “A” Sample “B”

Figure 7. Linear wear per one application over work done by the brake per one application

One can see five lines in each of these plots – each line corresponds to results obtained in one

block of wear tests as explained above. In plots, these wear test blocks are designated with the

symbols “Ex 100“, „Ex 150“, etc. for wear test blocks with the initial interface temperature of

100oC, 150

oC, etc. respectively. Point „E1“ in the left plot represents result of test in the first

200 applications of the first wear test block. Respectively, points „E2“ and „E3“ represent

results of remaining two sections of the same block. By means of the least square method a

straight line can be drawn, crossing through origin of the plot coordinate system and all three

points „E1“, „E2“ and „E3“. That is how we will obtain line designated with symbol „An

100“, which stands for „Analytical form for wear over work done by the brake per one brake

application under 100oC initial brake temperature“. Similarly, all other lines in this plot can

be interpreted. That is how one can qualify and quantify the specific energy wear rate for a

given brake.

Brake Power

According to equation (4) model of brake power was obtained and results for two different

braking tests are shown in Figure 8, where calculation results for the brake output power

versus experimentally obtained results can be seen. Blue line represents experimental results,

while calculated values are shown in red color. From there one can see that calculated and

experimental results correspond very well to each other: deviations are within limits of 3÷5%.

Figure 8. Comparative review of calculated versus experimental values of the brake output power

Work Done by the Brake

Expressions (3) ÷ (5) give an analytical form of brake wear rate per brake application, work

done by the brake per brake application, as well as “energy specific wear”. In Table 2 results

0

0,001

0,002

0,003

0,004

0,005

0,006

0,007

0 0,1 0,2 0,3

Wea

r p

er o

ne

app

lica

tio

n[m

m]

Work done by the brake per one application [MJ]

An100

Ex100

An150

Ex150

An200

Ex200

An250

Ex250

An300

Ex300

E2E3E1 0

0,001

0,002

0,003

0,004

0,005

0,006

0,007

0 0,05 0,1 0,15 0,2 0,25 0,3Wea

r per

on

e ap

plica

tion

[m

m]

Work done by the brake per one application [MJ]

An100

Ex100

An150

Ex150

An200

Ex200

An250

Ex250

An300

Ex300

0

5000

10000

15000

20000

25000

30000

35000

40000

45000

50000

0 0,5 1 1,5 2 2,5 3 3,5

Pk1E(W) Pk1T(W)

p60, S60, Θ100

0

10000

20000

30000

40000

50000

60000

70000

80000

90000

100000

0 0,5 1 1,5 2 2,5 3 3,5 4Pk1E(W) Pk1T(W)

p80, S100, Θ100

of modelling from wear tests are summarized thus obtaining values for energy specific wear

(wsp), work done by the brake per single brake application (WB), total work done by the brake

(ΣWB), and the total number of brake applications (NΣ) for given test (or service) conditions.

Table 2. Results of modelling from wear tests

Developed mathematical models for wear and for work done by the brake enable that the total

number of brake application during the same time period can be evaluated. After such a

relation was it is always possible to predict the rate of one of these three quantities on

condition other two are known, and that is in fact the bases for applying brake energy

potential rate for optimisation of brake wear intensity, but also for optimization of friction

energy consumption by the brake.

Figure 9 shows graphical display of energy specific wear (wsp), work done by the brake per

single brake application (WB), total work done by the brake (ΣWB), and the total number of

brake applications (NΣ) depending on the initial brake speed, brake application pressure of 60

bar and interface temperature of 100oC.

Figure 9. (a) Work done by the brake per brake application (WB) and total work done by the brake (ΣWB); (b) specific wear per brake application (wsp),

c) total number of brake applications (NΣ) versus initial brake speed

p v θ w sp W B N Σ Σ W B

[bar] [km/h] [oC] [mm/MJ] [MJ] [-] [MJ]

60 20 100 0,00265 0,016 285959 4521

60 40 100 0,00297 0,045 89199 4044

60 60 100 0,00284 0,084 50074 4267

60 80 100 0,00217 0,135 40874 5526

60 100 100 0,00365 0,2132 15637 3289

NΣ [-]

0,000

0,050

0,100

0,150

0,200

0,250

0

1000

2000

3000

4000

5000

6000

0 20 40 60 80 100 120

ΣWB [MJ] WB [MJ]

[MJ] [MJ]

Speed [km/h]

a)

0

0,0005

0,001

0,0015

0,002

0,0025

0,003

0,0035

0,004

0 20 40 60 80 100 120

Spec

ific

ener

y w

ear

rate

per

ap

pli

cati

on

(mm

/MJ)

Speed [km/h]

b)

0

50000

100000

150000

200000

250000

300000

350000

0 20 40 60 80 100 120

Speed [km/h]

NΣ

c)

Validation of LWH

Linear wear hypothesis [7, 8] is used here to demonstrate the impact of brake energy potential

on wear rate of respective brake. That is why the initial step in the present experimental

research was to validate the Linear Wear Hypothesis, which says that there must be a linear

relation between accumulated brake wear and related work done by the brake per one brake

application at determined brake temperature level taking also into consideration a number of

brake applications. With this goal, 5 blocks of wear tests have been composed of 3 times 200

“identical” brake applications each. In all these tests initial brake rotor speed and application

pressure were fixed at certain level, while initial interface temperature was 100oC in the first

group, 150oC in second, 200

oC in third, 250

oC in fourth and 300

oC in the fifth group of wear

tests, respectively. Brake pad wear was measured for the whole block. All the results are

presented in Figure 10, where “Ex 100” is symbol used for test results of the first group, “Ex

200” is for the second group of results, etc.

Symbol “An” is used to show estimated brake pad life which is calculated according to [6]

following the formula:

sisp

pW

W

wL 11

(7)

where: Lp - is the predicted lining/pad life (life expectancy), Σwisp - sum of measured specific

wear in each wear test, W1- total work done by the tested brake for all brake applications in all

laboratory tests, and Ws - work done by the brake per kilometre under defined usage

conditions (or on average). It is obvous that LWH in this way was fully validated. An average

work done by brake per kilometer of travelled road in defined as 27 kJ/km for sample ”A”. It

means brake lining life would be of about 54.000 km with the 90% probability, while for

sample “B”this value is significantly lower - about 25.000 km only.

Sample “A” Sample “B”

Figure 10. Number of braking application as function of work done by the brake

Tribomutation Analyses

Tribomutations [10, 11] represent the portion of changes of friction and wear rate in friction

mechanisms induced by inter-related influences between each-other of main influencing

factors. An analyses of tribo-mutation effects within the scope of the present research is based

on the number of tests already explained within the brake performance section. The analysis

of available test results demonstrate the class of dissipation of output data like friction

coefficient, brake torque and work done by the brake – see Figure 11.

0

0,05

0,1

0,15

0,2

0,25

0,3

0,35

0 10000 20000 30000 40000 50000 60000Work

done b

y t

he b

rake p

er

one

appli

cati

on [

MJ]

Number of brake appliction [-]

Ex 100

Ex 150

Ex 200

Ex 250

Ex 300

An

0

0,05

0,1

0,15

0,2

0,25

0,3

0,35

0 5000 10000 15000 20000 25000 30000

Work

done b

y t

he b

rake p

er

one

appli

cati

on [

MJ]

Number of brake appliction [-]

Ex 100

Ex 150

Ex 200

Ex 250

Ex 300

An

a) b)

Figure 11. a) Mean friction coefficient per brake application, b) work done by the brake per brake application

Figure 11 shows test results for mean friction coefficient per brake application (a) and work

done by the brake per brake application (b) for the same brake applications. It is obvious that

no similarities between behavioral characteristics of these two quantities may be seen.

Therefore, it is evident there must exist some additional or side influences being the cause of

that, while [10, 11] explain such situations by means of tribo-mutation phenomenon. It is of

particular interest to point out that results shown in Figure 7are from an identical brake

application, repeated six times. In this case, application pressure was 60 bar, initial brake

speed (expressed by means of the initial vehicle speed) was 60 km/h, while initial interface

temperature was 100oC. In the case other temperature values were applied differences in the

behavior of friction compared to bevahiour of work done by the brake will be even more

significant, as shown earlier in [10, 11].

BRAKING PROCESS MANAGEMENT FOR OPTIMAL BRAKE ENERGY POTENTIAL

Friction energy loss in automotive friction brakes is an inherent loss firmly related to wear of

friction brake components and in particular friction linings or pads. In the first approximation,

while performing friction linings and/or pads are losing their thickness. This change in

thickness is explicitly related to friction energy loss. Therefore it is right to say that a new

brake lining or pad initially has not only certain thickness, but also posses certain friction

energy potential. During operation of brake, the remaining portion of this energy potential

will decrease proportionally to increased lining/pad wear, or proportionally to its thickness

decrease.

It has been shown in the first part of the paper that this brake energy potential depends on

many influencing factors, as well as the process of friction and wear by which it is generated

and spared at the same time. Consumption of friction energy during braking is inevitable and

indeed irreversible in friction brakes. The famous contradiction that all brake engineers are

always facing is how to increase brake performance (meaning to increase friction as high as

possible while keeping it as stable as possible) by instantaneously decreasing brake wear?

That is in fact the starting point for the present research – we are looking to an answer to the

question how to keep consumption of friction brake energy as small as possible keeping

simultaneously brake wear as small as possible but without compromising in any way brake

performance and reliability characteristics? Brake management would be our answer to this

dilemma!

After having explained in previous sections of this paper many aspects of the brake energy

potential characteristics it is evident that the problem we are facing with can be best described

by the plot presented in Figure 12, where three-dimensional coordinate system was used to

interrelate brake performance, brake wear and brake reliability with brake energy potential.

0

0,05

0,1

0,15

0,2

0,25

0,3

0,35

0,4

0,45

0 1 2 3 4 5 6

μ

brake cycle

71000

72000

73000

74000

75000

76000

77000

78000

79000

1 2 3 4 5 6

Wdbb [J]

brake cycle

Figure 12. Brake Energy Potential Factor

In this plot one can see two triangular slices (EPI and EPII) representing brake energy

potential and its “position” with respect to each of axles, which means should we know

requested (needed or wanted) level of brake performance, wear and reliability characteristics

we will also know what would be an appropriate brake energy potential rate. On condition we

can vary these influences, and not only that we can do that but this is happening all the time

due to stochastic nature of these parameters, we can see whether or not it would be possible to

manage the rate of brake energy potential.

Figure 13. Block diagram for adaptive management of braking process

This is what one can see in Figure 13, where a block diagram for adaptive management of

braking process with the above explained task to manage brake energy potential in order to

reach satisfactory rate of it, whether being as low as possible or being “optimized” with

respect to brake wear, but also to brake performance and reliability.

Performance

Wear

Reliability

0

2

3

4

5

1

23

45

12

34

5

EPI

EPII

1

model of friction model of wear

model of work done by the brake

SENSORS- application preasure- speed- temperature

B R A K E

pp

Brake Energy Potential

model of brake power

CONCLUSION

Energy potential of friction brakes represents an aggregate, summarised or cumulative index

of all brake characteristics in terms of performance, reliability and service life. In order to

assess brake energy potential rate it is necessary to identify and quantify all influential factors.

It can be estimated in an appropriate and acceptable way only if based on projected or needed

brake life but also taking into consideration achieved brake performance and reliability.

Despite this, it is more important the degree of their impacts to the brake energy potential.

The brake energy potential can be best described by the plot, where three-dimensional

coordinate system was used to interrelate brake performance, brake wear and brake reliability

with brake energy potential. Triangular surface as shown represents the value of brake energy

potential.

The value of the brake energy potential varies during the brake pad life but having knowledge

about its value at any time provides the ability to manage the process of braking at the level of

braking cycle. This will allow the rational utilization of the available energy potential along

achievement of projected performance in all operating conditions.

REFERENCES

[1] Duboka Č, Arsenić. Ž., Friction and wear of brake linings with regard to the Bedding

procedure, FISITA 86, Belgrade 1986.

[2] Jahangiria M., Hashempourb M., Razavizadehb H., Rezaieb H., A new method to

investigate the sliding wear behaviour of materials based on energy dissipation: W–25 wt%

Cu composite, Wear 274– 275, 2012, 175– 182.

[3] Ramalhoa A., Miranda J. C., The relationship between wear and dissipated energy in

sliding systems, Wear 260, 2006, 361–367.

[4] Uetz H., Fоhl J., Wear as an energy transformation process, Wear, 49, 1978, 253 – 264

[5] Duboka Č., Brake Energy Potential Factor, “Zastava Journal” No. 37(2004)29-37 (in

Serbian), Kragujevac, 2004

[6] Duboka Č., Todorović J., Linear wear hypothesis for the prediction of brake pad lining

life, IMechE Paper C15/83, Braking of Road Vehicle, 1983.

[7] Todorović J., Duboka Č., Arsenić Ž., Operational life expectancy of rubbing elements in

automotive brakes, Tribology international, Vol. No. 7. pp 423-432, 1995.

[8] Arsenić Ž., Duboka Č., Todorović J., Prediction of brake pad life - Further development of

LWH, SAE Technical paper series, 860631, 1986.

[9] Arsenić Ž., Investigating possibilities of predicting the functional characteristics of brake

friction materials for motor vehicles, PhD thesis, University of Belgrade, 1986.

[10] Duboka Č., Arsenić Ž., Milosavljević M., Tribo-mutations in tribo-mechanical systems,

Intl. Conf. on Tribology “Balkantrib '96”, Thessaloniki, 1996.

[11] Duboka Č., von Glasner E.–C., Todorović J., Arsenić Ž., Identification of tribo-mutation

effects in road vehicle brakes, I World Tribology Congress, London, 1997.