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T R I B O L O G I A 1/2017
p. 35–43
Majid Habeeb Faidh-Allah*
Numerical and Finite Element Contact Temperature
Analysis of Friction Material’s Type Effect
on a Thermal Transient Behavior of a Single-Disc
Dry Clutch
Analiza numeryczna i elementów skończonych temperatury
styku jako efektu rodzaju materiału trącego i jej wpływ
na zachowanie termiczne suchych sprzęgieł jednotarczowych
Key words: dry friction clutch, thermoelastic problem, Friction materials.
Abstract: The sliding period is considered a critical period in the lifetime of friction clutches, because most failures
occur during this period. High temperatures due to sliding velocity will appear on the contacting surfaces
of the friction clutch system (e.g., in single -disc clutch are pressure plate, clutch discs and flywheel). The
finite element technique has been developed to investigate the effect of the type of friction material (material
properties) on the transient thermoelastic behaviour of a single-disc dry clutch. Two types of friction materials
are used in this work: organic and sintered friction materials. Axisymmetric models are developed to simulate
a friction clutch system (single disc with two effective sides). The results represent the comparisons between
organic and sintered friction discs, behaviours during slipping periods in clutches.
Słowa kluczowe: suche sprzęgło tarciowe, termosprężystość, materiały tarciowe.
Streszczenie: Stan poślizgu tarciowego ze względu na występowanie największej ilości uszkodzeń jest krytycznym stanem
pracy sprzęgieł tarciowych. Wysoka temperatura pracy występująca na powierzchniach trących elementów
sprzęgieł spowodowana jest poślizgiem (np. w sprzęgłach jednotarczowych na klockach, tarczach i kole zamachowym). Metoda elementów skończonych została wykorzystana do zbadania wpływu rodzaju materiału
(właściwości materiału) na zagadnienie termosprężystości w suchych sprzęgłach tarciowych. W pracy wykorzystano dwa rodzaje materiałów tarciowych: organiczny i spiekany. Opracowano osiowosymetryczne modele symulujące sprzęgło tarciowe (pojedyncza tarcza z dwoma okładzinami). Wynikiem pracy jest porównanie
cyklów poślizgu pomiędzy dyskami wykonanymi z materiału organicznego oraz spiekanego.
Introduction
Automotive friction clutches are considered a crucial
part in the torque transmission system, and it is also
responsible for the performance of the vehicle. The
friction clutches are also used in a wide range of
different applications, i.e. industrial applications. The
engagement cycle of clutches consists of two stages.
The first stage occurs when the clutch starts to engage
and consequently a high amount of heat is generated in
this period due to sliding between contacting parts. On
the contrary, in the second stage, all contact elements
rotate together with the same speed of rotation. The
first period (slipping period) is considered the most
*
important period, because the most failures that occur on
the surfaces of the contacting parts take place precisely
during this period.
Pisaturo and Senatore [L. 1] studied the heat transfer
problem of the surfaces of friction clutches under sliding
condition. They studied the temperature field of a friction
clutch after repeated engagement, and they found that the
surface temperature increases dramatically and reach, in
some cases, the peak value (300°C). Furthermore, they
investigated the frictional behaviour of the friction clutches
at high temperatures (250–300°C). They found that the
temperatures affect the cushion spring load-deflection
characteristic and the subsequent transmitted clutch torque.
A control algorithm to calculate the heat flux during vehicle
Department of Mechanical Eng. /College of Engineering / University of Baghdad, Baghdad-Aljadria 47024, Iraq, e-mail:
[email protected].
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launch and up-shift manoeuvres was presented as well in
this work. They used the finite element method to compute
the temperature field during repeated engagement of
a clutch system. The results showed that only few repeated
engagements of a clutch lead the temperature to reach
values near the critical point of 300 °C.
Yang et al [L. 2] conducted the transient thermal
problem of a multi-disc friction clutch to study the
deformation due to the thermal effect and distribution
of contact pressure of the contact surfaces. They used
the finite volume method (FVM) and the finite element
method (FEM) to compute the temperature field and
the distribution of the contact pressure. The couplings
between temperature, displacement, and contact
pressure were investigated using Matlab. In the contact
analysis, a penalty method was used to find the contact
pressure distribution of the contacting parts of clutch
system. The results showed that the distributions of
the contact pressure on the surfaces that exist near the
pressure plate are more smooth than those which exist
near the opposite plate, and non-uniformity will increase
when the temperatures increases. Moreover, their
results showed that the maximum contact pressure will
decreases due to the effect of heat transfer by conduction
and convection that occurred between the parts of the
clutch system when the engagement period reach the
end.
Marklund et al [L. 3] developed a new model based
on a simple technique to measure the friction coefficient
under wet conditions then calculated the temperature
and torque transmit for a wet clutch that are working
under limited slip conditions. This model can be used to
investigate the torque behaviour of the wet clutches and
to find the optimal values of the design parameters that
improve the performance of a clutch system. Their model
takes into consideration the fluid dynamics, the contact
mechanics, and the temperature calculations in the fluid
film between the friction disc and the separator disc. The
calculations of the fluid dynamics use homogenized flow
factors to facilitate simulations of the flow on a coarser
grid and also contain the surface roughness effects. The
results showed that the temperature distribution in the
film of the sliding interface is approximately represented
as a polynomial of the second order. The results of their
model were validated with experimental work, and it
showed a good agreement between the measured and
the simulations.
Zhuo et al [L. 4] conducted a numerical analysis
to study the thermal buckling of annular rings using
a reduced Fourier method. They derived the stress
stiffness matrix from the geometric nonlinearity in the
Green strains with a predefined circumferential wave
number. Their results were validated with commercial
software, Abaqus, assuming that the model annular
ring is axisymmetric. They also found the solutions of
non-axisymmetric problems with multiple waves along
the circumference. The results showed that there exists
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a specific wave number for the buckling temperature
that reaches a minimum value.
Marklund et al [L. 5] studied the behaviour of wet
clutches under low speed and heavy-duty load. They
developed new models to estimate the torque transfer
under lubricated boundary conditions. Their models take
into consideration the effect of temperature, speed, and
nominal pressure on the behaviour of a wet clutch that is
working in boundary lubrication regime. The results of
the torque and the temperatures that were obtained from
the numerical work have acceptable agreement with the
experimental results.
Awrejcewicz and Grzelczyk [L. 6] built
a mathematical model that illustrated the processes
of the heat generated and how this heat generated
will affect the friction clutch system behaviour. They
assumed that the heat flux is an unequal distribution over
the contacting surfaces. They solved a set of algebraic
linear homogeneous and heterogeneous equations and
then simulated it using a numerical method. The results
of the torque and the temperatures that were obtained
from the numerical work have acceptable agreement
with experimental data.
Zhao et al [L. 7] investigated the stability issue
of the thermal buckling that occurred in automotive
clutches using the finite element method. Two- and
three-dimensional models were built using commercial
software ABAQUS. They found that the radial variation
of the temperature will significantly affect the critical
buckling temperature. They also obtained numerical
solutions assuming the variation of the temperature is
periodic with multiple waves along the circumference
direction. They concluded that the buckling can happen
in the case when the temperature is uniform in the
circumference, but it will be non-uniform in the radial
direction. The other important conclusion is that the
patterns of the radial temperature distribution strongly
affect the critical value of buckling load and the mode
shapes of the dominant buckling.
Chao et al [L. 8] proposed a new model of pressure
plate that have channels in the radial direction and holes
on the traditional pressure plates to increase the amount
of heat that transfers to the surrounding. The finite
element method was applied to achieve numerical work
in this analysis using commercial software Ansys. They
studied the boundary conditions such as environment
temperature, and the heat transfer coefficient for
convection of the friction and steel surfaces. They also
investigated the effect of design parameters such as
dimensions of the radial cooling channels, the diameter
of the holes that used for cooling on the temperature
field and deformation of the proposed model of pressure
plate. Based on the obtained results, they found that
the thermal behaviour of a new pressure plate model is
better than the classical one.
Pisaturo et al [L. 9] estimated the error due to the
neglect the effective spatial distribution of the heat
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generated in the dry friction clutches during a vehicle
launch manoeuvre. The finite element technique was
used to assess the effect of the spatial distribution of
the heat flux on the surface temperature. Axisymmetric
models were built to obtain the thermal behaviour of
a friction clutch system. Their analysis covered different
assumptions. The first one supposed that the heat flux
function of disc radius and the second one supposed the
heat flux is uniform over the contacting area. The results
showed that the surface temperature was increased very
quickly after a few repeated engagements.
Pica et al [L. 10] studied the thermal behaviour
of dry dual clutches in the case when the sliding speed
and the temperature were the function of the transmitted
torque. The results from their model showed how the
temperature affects the torque transmitted via clutch.
They used a driveline model to prove that the temperature
variation can determine the critical degradations of the
clutch engagement performances.
The aim of this analysis is to develop a new
mathematical model that able to test different kinds of
friction material especially the new one. In this work, the
thermoelastic problem of dry friction clutches has been
solved using two kinds of friction material (organic and
sintered). The results are presented with the full details
of the temperature distribution, contact pressure, and the
heat generated during the slipping period.
Thermoelastic problem in Friction
Clutches
The main parts of a typical friction clutch system (single
disc) include a pressure plate, clutch disc, and a flywheel
as shown in Fig. 1. The working process of a friction
clutch consists of three stages (Fig. 2): the first stage
(disengaged) is when the engine is working but there is
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Fig. 2. The stages of lifecycle of a friction clutch system
Rys. 2. Etapy pracy sprzęgła
no torque transmitted to the driven shaft because of the
friction clutch disconnect; the second stage (engaging
phase / slipping period) is when the main elements of
clutch system will press together (flywheel, clutch disc
and pressure plate) and the torque will start to transfer
to the driven shaft; and, the last stage (engaged) is when
all elements of clutch system rotate together and there
is no slipping between the contacting elements. The
most critical phase is the second one (slipping period),
because of in this phase, a huge amount of heat will
generate due to the high kinetic energy that absorbed by
the clutch system. In order to obtain a successful design,
one should calculate the highest working temperature
during this phase.
Figure 3 illustrates the common failures that
occurred in the surfaces of friction clutches [L. 11]. It
can be seen that the most problems occur due to the high
temperatures that appeared during the slipping period.
Fig. 1. The elements of a single-disc friction clutch
Rys. 1. Elementy sprzęgła jednotarczowego
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a)
b)
Fig. 4. Mathematical model for the (a) contact and (b)
thermal problem for two bodies in contact
Rys. 4. Model matematyczny styku (a) oraz kierunek przepływu się ciepła dla dwóch stykających się powierzchni (b)
contact, the surfaces are assumed to be in an adiabatic
state (separated) as follows:
=
q= 0= qn1 q=
if P 0
n2 ,
Fig. 3. Typical types of failures that occur in the friction
material surfaces
Rys. 3. Typowe rodzaje uszkodzeń występujących na powierzchniach trących
Problem Statement
The thermoelastic problem can be solved in friction
clutches using two different models. The first model
(contact model) will be used to compute the contact
pressure of the contacting parts of a clutch system, while
the second model will be used to find the temperature
distribution of a clutch system.
The boundary conditions for two bodies (1 and 2)
when pressed together (contact problem) can be written
as follows [Fig. 4(a)]:
w1 = w2 ,
if
P>0
(1)
w1 ≤ w2 ,
if
P=0,
(2)
where P and w are the contact pressure between the
contacting bodies. The thermal boundary conditions for
two bodies (1 and 2) when they are contact together and
there is heat flux at the interface is shown in Fig. 4(b).
There are two anonymous variables, qn1 and qn2, that
appear on the surfaces of contact. In order to describe
the heat conduction problem, two added conditions
are needed on every interface of contact. The energy
balance and continuity in the temperature conditions are
assumed on every interface as follows:
T1 = T2 ,
if P > 0
q = µ P ω r = − ∑ qn = − (qn1 + qn 2 ),
(3)
if P > 0 , (4)
where μ is the coefficients of friction and ω is the angular
sliding velocity. In the case when the bodies are not in
(5)
In this work, the sliding angular velocity is assumed
to be decreases linearly with time as in the following
equation:
t
ω (t ) = ωo (1 − ), 0 ≤ t ≤ ts .
(6)
ts
The magnitude of the contact pressure P that is
needed to find the heat generated due to friction [Equation
(4)] can be obtained when one finds the solution of the
contact problem that occurs in the friction clutch system.
In order to find the solution of the thermoelastic
problem of a friction clutch, one should solve the coupling
problem (structural and thermal) instantaneously at each
time step during the slipping period. In order to find the
values of the contact pressure p(r,t), the temperature
distribution T(r,z,t) is given. Then, Hook’s law can be
used to solve the equation, including the thermal strain
relations as follows:
εij =
(1 + ν )
E
ν

σij −  σmm + αT  δij
E

(7)
when the equilibrium equation is
∂σij
∂x j
=0.
(8)
The transient heat conduction problem needs to
be solve, and then the new temperature distribution
T (r , z , t + δt ) can be estimated as follows:
∇ 2T =
1 ∂T
k ∂t
(9)
Finite element Formulation
In this section, the procedure of the numerical analysis
using finite element method will be explained. The
following equation can be used to find the solution of the
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39
transient thermal problem of axisymmetric model based
on Galerkin’s method [L. 12].
∂T 
 + [ K (T ) ]{T } = {R} ,
 ∂t 
[C (T )] 
(10)
where C(T), K(T) and {R} are the matrix of heat
capacity, the matrix of heat conductivity and the vector
of thermal force. The differential equation (10) can be
solved using the direct integration method. Assuming
that temperature {T}t occurs at time t and {T}t+∆t occurs
at t+∆t, then the solution can be written as follows:


dT 
 dT 
 +β  
 ∆t , (11)
 dt t
 dt t + ∆t 
{T }t + ∆t = {T }t + (1 − β ) 

where β is the factor that used to find the accuracy of
the integration and the stability of the scheme, and the
range of the values of this factor is between 0.5 and 1.
The implicit equation can be obtained by substituting
Equation (11) into Equation (10)
( C (T ) + β ∆t  K (T ) ){T }t + ∆t =
= ( C (T )  − (1 − β )  K (T )  ∆t ) {T }t +
(12)
+ (1 − β ) ∆t {R}t + β ∆t {R}t + ∆t
The equation that is used to find the solution of the
contact problem can be written as follows:
Ku=F
(13)
where K, F and u are the matrix of stiffness of the
complete model, the force vector that applied to the
model and the displacement vector of nodes. Owing to
the initial strain that occurs in the system, the formulas
of the stiffness matrix K and the force vector F are
K =2π
∫∫ B
A
F =2π
T
D Br dr dz
T
∫∫ B D εor dr dz
(14)
Fig. 5. Flowchart of solving thermoelastic problem in dry
friction clutch using finite element method
Rys. 5. Przyjęty schemat postępowania przy rozwiązywaniu
zagadnienia termosprężystości dla sprzęgła tarciowego wykorzystujący metodę elementów skończonych
Table 1. The properties of materials
Tabela 1. Właściwości materiałów
Friction materials
(15)
A
The integrations of Equations (14 and 15) should
be calculated for the complete surface area A where the
tractions exist. Figure 5 demonstrates the flowchart
of the processes that are used to find the solution of
the thermoelastic problem using the finite element
method. Tables 1 and 2 list the properties of materials,
the dimensions, and the operational factors of a clutch
system that were used in this analysis. The axisymmetric
finite element models that were used to solve the
thermoelastic problem in a dry friction clutch system are
shown in Fig. 6.
Material properties
Steel
(Flywheel,
pressure plate
Organic Sintered
&
axial cushion)
Coefficient of friction, μ
0.3
0.3
0.3
Young’s modulus, E [GPa]
0.2
1
200
Poisson’s ratio, ν
0.3
0.25
0.25
Density, ρ [kg/m3]
1800
4500
7800
Specific heat, c [J/kg K]
1000
500
532
Conductivity, K [W/mK ]
0.65
20
54
30
12
12
Thermal expansion,
α [10-6 K-1]
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Table 2. The dimensions of a clutch system and
operational factors
Tabela 2. Wymiary sprzęgła oraz jego cechy
Dimensions / operational factors
Values
Inner radius of clutch disc, [m]
0.06
Outer radius of clutch disc, [m]
0.085
Thickness of friction layer in clutch disc, [m]
0.00275
Thickness of axial cushion, [m]
0.00135
Inner radius of the pressure plate, [m]
0.0580
Outer radius of the pressure plate, [m]
0.0920
Thickness of pressure plate, [m]
0.00965
Inner radius of the flywheel, [m]
0.0485
Outer radius of the flywheel, [m]
0.0975
Thickness of flywheel, [m]
0.0195
Applied pressure, pa [MPa]
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(a) Contact model
0.1
Heat transfer coefficient, h [W/m K]
40
No. of friction surfaces, n
2
Time of slipping, t [s]
0.4
2
Numerical Analysis
In this work, a typical friction clutch (single plate with
two effective sides of contact) that consists of pressure
plate, clutch disc, and a flywheel, using two kinds of
friction materials (organic and sintered) during the
slipping period was studied. The results covered the
thermal and structural behaviours of a friction clutch
system when it starts to engage.
Figures 7–9 show the distribution of the contact
pressure with a dimensionless radius of clutch on the
pressure plate side at different time intervals (t = 0.12,
0.24 and 0.4s). The results showed that the values of the
contact pressure will increase with time for both kinds
of friction materials. During the entire slipping period,
the contact pressure values that are obtained when using
organic friction material are higher than those obtained
using sintered friction material. The peaks of the contact
pressure occurred in the position that is located between
the inner and mean disc radii of organic clutch disc,
while for sintered clutch disc occurred at inner disc
radius. Owing to the increase in the thermal deformation
that occurred in the contact elements of friction clutch
(pressure plate, clutch disc, and flywheel), the contact
area will be decreased with slipping time for both cases.
The highest magnitude of contact pressure is 0.36Mpa at
t = 0.4 s when an organic clutch disc is used.
The variations of the surface temperature with disc
radius on the pressure plate surface for different times
are presented in Figures 10 and 11. It is obvious that
the maximum values of temperature corresponding
to the organic clutch disc are higher than are those of
(b) Transient thermal model
Fig. 6. Finite element models for friction clutch system
Rys. 6. Modele elementów skończonych sprzęgła tarciowego
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Fig. 7. The distribution of contact pressure at t = 0.12 s
Rys. 7. Rozkład nacisku powierzchniowego dla t = 0,12 s
Fig. 8. The distribution of contact pressure at t = 0.24 s
Rys. 8. Rozkład nacisku powierzchniowego dla t = 0,24 s
41
Fig. 10.
The distribution of surface temperature at
t = 0.24 s
Rys. 10. Rozkład temperatury na powierzchni dla t = 0,24 s
Fig. 11. The distribution of surface temperature at t = 0.4 s
Rys. 11. Rozkład temperatury na powierzchni dla t = 0,4 s
Fig. 9. The distribution of contact pressure at t = 0.4 s
Rys. 9. Rozkład nacisku powierzchniowego dla t = 0,4 s
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sintered clutch disc. It can also be distinguished that the
behaviours of each kind of friction material is different
during the entire slipping time. The values of surface
temperatures of the organic clutch disc increase from
the inner disc radius to the peak values near the point
that is located between the inner and mean disc radii
and then decreases to the minimum values at the outer
disc radius. On the other hand, for a sintered clutch disc,
the maximum values of surface temperature occurred
at the inner disc radius and then the values of surface
temperatures are decreased to the minimum values at the
outer disc radius.
Figures 12 and 13 illustrate the variation of the
heat flux at the pressure plate side with the radius of
clutch disc at different times during the slipping. It can
be observed that the heat flux is semi-uniform over the
contact area for both kinds of friction materials at the
beginning of engagement (t = 0.04s), because the contact
pressure is still semi-uniform over the contact area at
the same time. In the other words, the thermoelastic
phenomenon has no effect at this time (values of thermal
deformations are very small).
The heat generated is from the function of slipping
speed; therefore, at the beginning of the slipping time, the
maximum amount of heat generated will occur, but later
it can noticed that the behaviour of the heat generated is
changed, and the heat generated is focused one specific
area of the entire contact area. The reason for these
results is the change that occurred in the distributions
of contact pressure, where the contact pressure will be
focused on some specific area of the nominal contact
area that leads to the increase in the magnitude of the
heat generated on this specific area.
Figure 14 exhibits the variation of maximum
surface temperature with an initial angular velocity of
300 rad/s using organic and sintered clutch discs. It is
clear from the figure that the values of the temperature
increased dramatically at the beginning of slipping
to the peak values that occurred approximately at the
middle of the slipping phase. Finally, the temperature
decreases to the final values at the end of the slipping
phase. The highest temperature values are 335K and 331
K corresponding to the organic clutch disc and sintered
clutch disc, respectively. It is obvious that the values of
temperature that appeared on the organic clutch disc are
greater than those that appeared on the sintered clutch
disc during the whole slipping stage.
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Fig. 12. The distribution of the heat flux at t = 0.04 s
Rys. 12. Rozkład przepływu ciepła dla t = 0,04 s
Fig. 13. The distribution of the heat flux at t = 0.12 s
Rys. 13. Rozkład przepływu ciepła dla t = 0,12 s
Conclusions
In this work, new mathematical models have been
developed to find the solution to the transient thermoelastic
problem of the dry friction clutches during the slipping
period. The analysis examined the thermal and structural
behaviours of the friction clutch system using two kinds
of friction materials (organic and sintered). The results
Fig. 14.The maximum surface temperature evolution with
time
Rys. 14.Przebieg maksymalnej temperatury powierzchni
w funkcji czasu
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showed that the thermal behaviour of a friction clutch
was improved when a sintered friction material was used
instead of organic friction material. The reduction of the
maximum temperature was found to be approximately
11% when organic friction material was replaced by
sintered material. It can also be concluded that the
43
maximum surface temperature occurred approximately
during the middle of the slipping period for both cases.
This analysis is considered the basis for subsequent
research to investigate the effect of design parameters on
the thermal stresses and stability of dry friction clutch
systems.
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