Contact Stiffness Characteristics of Paper-Based Wet Clutch

8/8/2019 Contact Stiffness Characteristics of Paper-Based Wet Clutch

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Contact Stiffness Characteristics of a Paper-Based Wet Clutchat Different Degradation Levels

Agusmian P. Ompusunggu, Thierry Janssens, Farid Al-Bender, Paul Sas, Hendrik Van BrusselKatholieke Universiteit Leuven (KUL), Department of Mechanical Engineering, Division of PMA, Leuven, [email protected]

Steve VandenplasFlanders Mechatronics Technology Centre (FMTC), Leuven, Belgium

Summary

After clutch engagement in the post-lockup phase, the contact stiffness between friction materials and separators playsan important role in the dynamic behaviour of an Automatic Transmission (AT). The friction material deteriorates

progressively during the service-life of a clutch, thus affecting the contact stiffness. The deterioration therefore changesthe dynamic behaviour of the AT. In order to be able to predict the dynamic behaviour of the latter in the post-lockup

phase, the contact stiffness characteristics at different degradation levels must be investigated. Consequently, thischange in the dynamic behaviour can be used as a means to monitor clutch degradation. In this paper, both simpleelastic contact model of rough surfaces, and experimental-setup tests are presented. Three identical paper-based frictionmaterials with different degradation levels were used. Disc-on-disc experiments were performed on a newly developedrotational tribometer to simulate the representative post-lockup phase. In the experiments, those identical specimenswere immersed in a fresh Automatic Transmission Fluid (ATF). The experimental results qualitatively agree with the

presented model. In general, it can be concluded that, due to the friction material degradation, normal contact stiffnessexhibits an increasing trend; in contrast, tangential contact stiffness exhibits a decreasing trend.

1. Introduction

In recent years, the use of Automatic Transmissions(ATs) in automobiles has become increasingly popular,especially in the North American, and Asian markets. Incontrast to this fact, ATs are still not very popular inEuropean market; 80 % of drivers prefer to use aManual Transmission (MT) [1]. ATs are driver-friendly and easy to drive, and consequently the demandof AT remains high. Nevertheless, the energy efficiency

of ATs is 5 15 % less than that of MTs [2,3]. Inaddition, ATs are also widely used for heavy-dutycommercial and industrial vehicles and equipment.

In an AT, wet clutches are commonly used asmechanical elements transferring power from a driving

part (e.g. engine) to a driven part (e.g. wheel) through africtional mechanism. Wet here means that theclutches are immersed in an Automatic TransmissionFluid (ATF). The ATF has a function as a coolinglubricant fluid maintaining the surfaces clean and givingsmoother performance and longer life. A multi disc wetclutch is the most common configuration, whichconsists of several friction and separator discs, as shownin Figure 1. In general, the friction discs are mounted tothe input shaft by splines, and the separator discs are

mounted to the output shaft by lugs. The friction disc ismade of a steel disc with a friction material bonded on

both sides, and the separator disc is made of plain steel.Moreover, in wet clutch application, a hydraulicactuator is commonly used for engagement anddisengagement mechanism. The actuator consists of several main components, such as a hydraulic cylinder and a control valve.

Figure 1: Schematic of a Wet Clutch [4]

Because of a relatively high friction coefficient, stable

friction characteristics, and low cost; paper-basedfriction materials have been popularly used for clutchand brake applications since the late 1950s. This type of


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friction material is also called the high performance paper, which consists of various specific ingredientssuch as cellulose fibre, synthetic fibre, solid lubricant,and friction modifiers [5]. In general, the composition of a paper-based friction material is schematically shownin Figure 2.

Figure 2: General Composition of the Paper-BasedFriction Material (Reproduced from [5])

The main function inherent in wet clutches leads themto play a critical role in an AT. It is unavoidable that thewet clutches degrade while the AT is in operatingcondition. Since wet clutches are critical components, a

proper condition monitoring tool should therefore beapplied in order to avoid unpredictable failure. Manystudies on the investigation of tribological behaviour of friction materials due to degradation have beenintensively performed. In general, the studies show thatthe friction coefficient progressively decreases duringthe service-life [3,6,7], as can be seen in Figure 3. Thedecreasing trend remarkably enables us to forecast whena wet clutch will fail. However, in practice, the use of afriction coefficient to monitor wet clutches degradationis not easy to implement and cost expensive.

Figure 3: Friction coefficient in function of the service-life (reproduced from [7])

The degradation occurring in a wet clutch is mainlycaused by both friction material and ATF degradation.The degradation mechanisms reported can occur due tomechanical degradation (adhesive wear) and thermal

degradation (carbonisation) [3,8]. In reality, anyhow, both degradation mechanisms always occur simultaneously, resulting in a well known phenomenon

which is called glazing. This degradation is reported todeteriorate the friction characteristics of wet clutches[6,7]. Several previous researchers experimentallyrevealed that the slope of the Stribeck curve ( curve), hereafter the slope of this curve called theStribeck slope, in mixed-lubricating regime becomes

more negative for degraded friction material than thatfor new friction material [9]. In contrast to the latter result, Li et al . [3] revealed that the degradation of friction material has less impact on changing theStribeck slope. Moreover, they also found that ATFdegradation has a far greater impact than frictionmaterial degradation on changing the Stribeck slope to

become more negative. When the Stribeck slope becomes more negative, it is known as the loss of anti-shudder.

As a result of the glazing phenomenon, the topographyof the contact surfaces changes. Previous studies [3,10]report that the surface roughness of a glazed paper-

based friction material is quantitatively lower than thatof a new material. Moreover, Gao and Barber [10] alsoreport that the surface topography of a paper-basedfriction material has a negative skewness, and becomesmore negative due to the glazing phenomenon. Anextension of the Greenwood-Williamson (GW) theorydeveloped by McCool [11] was used by the latter researchers to predict the real contact area, in order tostudy the contact characteristics of a wet clutch duringthe engagement phase. The increasing real contact areaduring the service-life of a wet-clutch was alsoanalytically calculated and experimentally validated byKimura and Otani [12], as can be seen in Figure 4.

Figure 4: Increasing real contact area in function of service-life (reproduced from [12])

Furthermore, it is also reported that due to the glazing phenomenon, the shear strength of paper-based frictionmaterials deteriorates. This deterioration is believed to

be caused by the degradation of the cellulose fibre and by pull-out of the cellulose fibre due to cyclic

compression and shear stress [13]. As a consequence,the mechanical and physical properties of the frictionmaterial change [14].


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Figure 5: Correlation between glazing and shear strength of friction material (reproduced from [13])

Several techniques have been proposed to characterisethe degradation of paper-based friction materials, such

as Pressure Differential Scanning Calorimetry (PDSC),and Attenuated Total Internal Reflectance AbsorbanceInfrared Spectroscopy (ATR IR) [15]. However, thesetechniques do not allow us to implement while the AT isstill in operating condition. In other words, the onlinemonitoring can not be implemented by using theseexisting techniques.

The authors believe that, the two aforementioned major factors caused by glazing phenomenon might lead to achange of the contact stiffness in the so-called pre-sliding regime which corresponds to the post-lockup

phase. Obviously, if this hypothesis holds, it impliesthat the dynamic behaviour of the AT also changes. Thischange in the dynamic behaviour can be used as ameans to monitor wet clutches degradation.

So far, investigations on contact stiffness characteristicsof a wet clutch in the post-lockup phase were notreported yet. Therefore, this study is more focused oninvestigating the effects of different degradation levelsof friction material on contact stiffness characteristics.Relevant models to predict the contact stiffness are alsodiscussed in this paper. Since the surface topographiesof the friction materials were not measured in this study,some relevant values given in the literatures weretherefore used for the model to qualitatively predict the

characteristics of the contact stiffness at differentdegradation levels. Furthermore, some experimentswere performed in order to experimentally validate theused models. The experimental results show aqualitative agreement with the model.

2. Contact Model of Rough Surfaces

2.1 Review of Elastic Contact

In practice, all engineering surfaces are rough. This paradigm has been long realized on microscopic scale[16]. Thus, contact only occurs at asperity summits withextremely small contact area compared to the nominalarea as illustrated in Figure 6. Deformation occurring at

contacting region can be elastic, plastic, or elastic- plastic depending on the nominal pressure, surfaceroughness, and material properties. Since the aim of thisstudy is to qualitatively predict the contact stiffnesscharacteristics at different degradation levels (not toaccurately predict the contact stiffness), therefore, the

contact occurring here is assumed to be elastic.

Figure 6: An illustration of contact mechanism

Before we further discuss the elastic contactcharacteristics of rough surfaces, it is important torevisit the Hertzian contact theory. According to thistheory, the contact radius a i, area Ai and load W i areusually expressed in function of the interference w as

2121 wa i = , (1)

w Ai = , (2)

2121

34

w E W i = (3)

where E is the combined Youngs modulus defined as1

2

22

1

21 11

+= E E

E (4)

E 1 and E 2, and 1 and 2 are respectively the Youngsmoduli and the Poissons ratios of contacting roughsurfaces 1 and 2.

A Greenwood-Williamson (GW) theory [16] has beenwidely used to model the contact characteristics of rough surfaces. In this theory, a rough surface isassumed as a stochastic process where the surface isregarded to have asperities with simple geometricalshapes and a probability distribution function. Allasperities are commonly treated as identicalhemispheres having uniform radii . This theoryoriginally assumes that the asperities height has aGaussian distribution f ( y) with zero mean given by

( )

=

2

2

2exp

2

1

y y f (5)

where is the standard deviation which is equivalent tothe surface roughness, and y is the height of an asperityrelative to the mean.


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Since the summation result of two Gaussiandistributions are also a Gaussian distribution. Thus, bythis property, it is reasonable to consider the contact of two rough surfaces as the contact between a smooth

plane and an equivalent rough surface as depicted inFigure 6. From this figure, it can be seen that, the

equivalent rough surface has a reference plane(Gaussian zero plane) which is the same as the mean plane of the equivalent rough surface. At this reference plane, the height asperity is set to be zero.

If two rough surfaces are pressed together by a normalload W such that both reference planes (smooth andGaussian zero plane) are separated by a distance d (seeFigure 6), then a contact occurs at any asperity summitwhose relative height to the Gaussian zero plane greater than d . In accordance with the GW theory, a probabilityof making contact at any contacting asperity summitwith height y is defined as

( ) ( )dy y f d yd

=> prob (6)

Let there are N asperity summits in total, the expectednumber of asperity summits in contact is

( )

=d

dy y f N n (7)

The real contact area is given by

( ) ( )dy y f d y N Ad

r

= (8)

and the total elastic normal load is

( ) ( )dy y f d y NE W d

23

21

34

= (9)

In the GW theory, the number of asperity summits isdefined as

n A N = (10)

where is asperity density, An is the nominal contactarea.

The distribution functions in Eqs. (5) (9), for the

convenience, are usually written in function of non-dimensional asperity height s, where the asperity height y is normalized by the surface roughness ( s = y/ ).Hence, the real contact area and the total normal loadcan be rewritten in function of normalized asperityheight distribution as

( )h F A A nr 1 = (11)

( )h F E AW n 34

232321 = (12)

where

( ) ( )( )

=h

n

n ds sh sh F

(13)

,( s) is the normalized asperity height distribution, and is the non-dimensional separation = d/ .

2.2 Contact of Rough Surfaces with WeibullAsperities Height Distributions

It is well known in statistics that the skewness of aGaussian distribution is zero. As was mentioned in the

previous section, it is reported that the surfacetopography of a paper-based friction material has anegative skewness, and therefore the latter distributionis not suitable to apply. Moreover, the reports show thata Weibull distribution is more suitable than a Gaussiandistribution to characterise the surface topography of a

paper-based friction material. In the present paper, theWeibull distribution is therefore used to qualitativelymodel the contact characteristics.

Although the summation of two Weibull distributions isnot a Weibull distribution, McCool [11] analyticallyshowed that it is still possible to extract an equivalentWeibull distribution from two different Weibulldistributions. The equivalent Weibull distribution hasthe same mean and variance as the sum of two latter distributions. Thus, by following the GW theory, thecontact of two rough surfaces with Weibull asperitiesheight distribution can be also considered as the contact

between a smooth surface and an equivalent roughsurface (GW McCool theory). The mean value of aWeibull distribution is always positive, as will be shownlater on. Therefore, as is depicted in Figure 6, theWeibull zero plane is definitely below of the Gaussianzero plane where the relative distance is z . Thus, thedistance between the smooth and the Weibull zero

planes is z d + .

In statistics, a Weibull distribution f W ( z ) can bemathematically expressed as follows

( )

=

z s s

s W W W W

(19)

sW is the non-dimensional asperity height relative to theWeibull zero plane, where the relative height z isnormalized by the surface roughness ( sW = z/ ).Furthermore, in accordance with the GW McCooltheory, hence, Eqs. (11) (13) can be rewritten as

( ) ,1 W nr h F A A = (20)

( ) ,34 232321

W n h F E AW = (21)

( ) ( ) ( )

=W h

W W W

n

W W W W

n ds sh sh F

, (22)

where W is the non-dimensional distance between thesmooth and the Weibull zero planes given by

( )212121

B B

Bh

z d hW

+=+=

(23)

2.3 Real Contact Area

Gao et al. [10,17] firstly implemented the Weibulldistribution to predict the real contact area of a paper-

based wet clutch during engagement phase. Based onEq.(20), they derived a mathematical expression of thereal contact area which can be expressed as follows

( ) ( )

++=

W W

W

n

r

hh

h A A

exp

,11111

(24)

where is a correction factor which is given in [10],and P(.,.) is the incomplete gamma function.

Meanwhile, the real contact area predicted by using aGaussian distribution can be expressed as follows [18]

+

= 1

2

erf

2

2

exp

21 2 hhh

A A

n

r

(25)

Comparisons of the real contact area using these twodistribution functions have been performed in [10]. Thecomparisons show significantly different characteristics

of the real contact area during the engagement phase.

2.4 Normal Contact Stiffness

After engagement, the film thickness of the ATFreaches the minimum value, and therefore, the thicknessof this film is reasonably negligible compared to theseparation of two reference planes. Hence, it can beassumed that the contact behaviour as close to theunlubricated contact condition (Hertzian contact).

For the unlubricated elastic contact, the normal contactstiffness of two asperities can be calculated bydifferentiating Eq. (3) with respect to the interference w

21212 w E dw

dW k ini == (26)

By extending Eq. (26) with the GW McCool theory,the total normal contact stiffness of two contactingrough surfaces K n can be thus expressed as follows

( ) ,2 212121 W W nn h F E A K = (27)From Eq. (21) and (27), the normal contact stiffness can

be also rewritten in function of the normal load as[19,20]

( )

,23

W W

r n h F W

K = (28)

where ( ) ,W W r h F is given by

( ) ( )( )

,,

,

23

21

W W

W W

W W

r h F

h F h F = (29)

From Eq. (28), it can be seen that the normal contactstiffness is linearly proportional to the applied normalload. In addition, the approximation of Eq. (29) is givenin the Appendix A.

2.5 Tangential Contact Stiffness

If two contacting hemispherical asperities are subjectedto a tangential force Q i, then micro-slip i will beobserved (see Figure 7). The relationship between themicro-slip and the tangential force was independentlystudied by Cattaneo and Mindlin [21] as follows

( )2321

3

4ii w E W Q

=(30)

where is a constant friction coefficient, and is thecombined elastic material constant defined as [19]

E G 4= (31)

with G is the combined shear modulus defined as1

2

2

1

1 22

+=GG

G (32)

G1 and G2 are the shear moduli of contacting roughsurfaces 1 and 2.


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Let the two contacting hemispherical asperities lie in aninfinitesimal annulus with radius r , and thickness r , asdepicted in Figure 7.

Figure 7: A schematic of contacting friction disc with aninfinitesimal annulus. The annulus is considered as anominally flat surface with area equal to 2 r. r

Since i = r i , thus, the relative torsion T i with respect tothe annulus centre C , which is required to generatemicro-slip is given by

( ) 232134

iiiiii r wr E Wr Qr T == (33)

By differentiating Eq. (33) with respect to angular displacement , one can show that the tangential contactstiffness of the annulus can be expressed as follows

( )( ) 21221

21221

8

2

r wr G

r wr E d dT

k i

t i

=

== (34)

Furthermore, by extending Eq. (34) with the GW McCool theory, the total tangential contact stiffness of the infinitesimal annulus K t , can be thus expressed as(the derivation is given in the Appendix B)

( ) r r r h F G K W W t += 3212121 ,16 (35)where r r = is a non-dimensional radius.

Finally, the total tangential contact stiffness K t of the

friction disc with inner radius Ri, and outer radius Ro can be computed by integrating the annulus from Ri to Ro

( )dr r h F r G K o

i

R

RW

W t += ,16 2132121 (36)

Note that, according to Eq. (36), the tangential contactstiffness is not only dependent on the normaldisplacement, but also on the tangential displacement.

For a relatively thin disc, the term ( ) ,21 r h F W W + in Eq.(36) can be considered to be independent of the non-dimensional radius. Hence, the latter equation can be

approximated as follows( ) ,8 2122121 mW W md t Rh F RG A K += (37)

where Ad , ( ) 2oim R R R += , io R R R = , and mm R R = are the nominal area, the mean radius, the thickness, andthe non-dimensional mean radius of the thin disc,respectively.

From Eq. (21) and (37), the tangential contact stiffness

can be rewritten in function of the normal load asfollows

( )( )

,,6

23

212

W

mW W

mt

h F

Rh F

E WGR

K +

= (38)

3. Analytical Simulation of Degradation Effects

In this section, analytical simulations based on themodels previously presented were carried out. Thesimulations are mainly intended to numericallyinvestigate the effect of the friction material degradation

levels on the contact stiffness characteristics in the post-lockup phase. There are several assumptions used in thesimulations as follows: the contact occurs between afriction disc and a separator disc, the ATF effect in thecontact is neglected, the geometry of the friction disc isthin without grooves, and the separator disc has asmooth surface.

The calculations of the normal and the tangentialcontact stiffnesses are respectively based on Eqs. (28)and (38). In the calculations, the geometrical parametersused are based on the dimension of the specimens usedin the experiment. This experiment is referred to SAE#2tests and will be briefly discussed in the experimentalsection. Moreover, several material parameters given inreference [10] are used, and the others are obtained frommeasurement. The parameters used in the calculationare listed in Table 1.

Table 1: Geometrical and material parameters used in thecalculation of the normal and tangential contact stiffness

Inner diameter of friction material, d i (m) 0.1115Outer diameter of friction material, d o (m) 0.1173Asperity radius of friction material, ( m) 500Asperity density of friction material, (m-2) 3x10 7 Youngs modulus of friction material, E 1 (MPa ) 45

Poissons ratio of friction material, 1 0.2Shear modulus of friction material , G 1 (MPa ) 18.75Youngs modulus of separator, E 2 (GPa ) 203Poissons ratio of separator, 2 0.3Shear modulus of separator , G 2 (GPa ) 78Friction coefficient, 0.15

Three different degradation levels were considered inthe simulation, namely new, run-in, and glazedmaterials. The topographical parameters given in [10]corresponding to the degradation levels of frictionmaterial were used, as tabulated in Table 2. In the table,it can be seen that, the surface roughness of the frictionmaterial decreases and the skewness becomes morenegative as the degradation progresses further.


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Moreover, one can see in the figure that, in the givenrange of the static normal loads, the normal contactstiffness definitely increases as the friction materialdegradation progresses. The discrepancy between thenormal contact stiffness of the run-in material and theone of the new material is relatively large. However, as

the friction material degradation becomes more severe,the discrepancy between the normal contact stiffness of the glazed material and the one of the run-in material isnot quite large.

Figure 9: The simulation of degradation effects on thenormal contact stiffness

3.2

Simulation results of the tangential contactstiffness

Slightly different to the latter calculations, the non-dimensional distance W and the tangential displacement have to be firstly determined before calculating thetangential contact stiffness. The value of the tangentialdisplacement must be chosen in such a way that themicro-slip is observed. In the simulations, = 1x10 -5 radwas used.

The simulation results of the tangential contact stiffnessat different degradation levels and different staticnormal loads are given in Figure 10, and Figure 11. As

is predicted by Eq. (38), the tangential contact stiffnessdepicted in both figures increases with the increase of the static normal load. In addition, both figures showdifferent characteristics, especially at relatively highnormal load.

From Figure 10 it can be concluded that, at relativelylow normal loads, the tangential contact stiffness of therun-in material is lower than that of the new material.On the other hand, at relatively high normal loads, thetangential contact stiffness of the run-in material ishigher than that of the new material.

Figure 10: The simulation of degradation effects on thetangential contact stiffness, case # 1 ( Grun-in = Gnew ,Gglazed = 0.5 Gnew , run-in = 0.9 new , glazed = 0.85 new )

In contrast to the latter result, Figure 11 shows that thetangential contact stiffness of the run-in material islower than that of the new material in all given loadsrange. However, both latter figures show that thetangential contact stiffness of the glazed material isdefinitely lower than that of the new material.

Figure 11: The simulation of degradation effects on thetangential contact stiffness, case # 2 ( Grun-in = 0.8 Gnew ,Gglazed = 0.5 Gnew , run-in = 0.9 new , glazed = 0.85 new )

4. Experiment

Two different tests were performed in this study,namely a durability test, and contact stiffnessidentification. The durability test was performed on aSAE#2 test setup in order to accelerate the service-lifeof the friction materials, and the contact stiffness

identification was performed on a newly developedtribometer.


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4.1 Experimental Setups

4.1.1 Description of the SAE#2 TestThe description of the SAE#2 test setup is brieflydescribed in this paper. Basically, this test setup consistsof input and output electric motors (1 & 9), input and

output flywheels (3 & 7), and a wet clutch (4) asschematically depicted in Figure 12. Both flywheels areindependently driven by the electric motors. Moreover,

both motors are driven at the same speed, but inopposite direction. The input and output flywheelsvelocities are measured by optical encoders (2 & 8). Ata desired relative speed (~ 4000 rpm), both motors are

powered-off and the wet clutch is immediately closed by applying a pressurised oil controlled by a valve (5)onto the clutch. As the oil pressure increases, therelative speed decreases as can be seen in Figure 8.

13

47

92 8

5

6

Figure 12: A schematic of the SAE#2 test setup

4.1.2 Description of the TribometerThe tribometer used in this study as shown in Figure 13,consists of the following main components: (1) shaker (dynamic load), (2) shaker holder, (3) frame, (4) verticalguide ways, (5) cantilever, (6) static load with cantilever,(7) axial bearing, (8) Direct Drive motor, (9) ball spline

bearing, (10) shaft, (11) bellow coupling, (12) tubcontaining the two friction discs (and oil), (13)capacitive displacement sensors (3 off), (14) three ringdynamometers for force and torque measurement, (15)

base plate.

Figure 13: General overview of the tribometer

The main objective of the tribometer is to characterisethe friction, in dry and lubricated conditions, occurring

between friction and separator discs from an AT [22].However, by a small modification, the functionality of the tribometer can be extended for identifying thecontact stiffness characteristics. The static normal load

was applied by a pneumatic actuator added on top of theshaker. This additional configuration allows us to easilyidentify the contact stiffness at different static normalloads and angular positions.

To identify the contact stiffness, the friction torque,normal force, and the relative displacements in bothnormal and tangential directions should be measured asaccurately as possible. This is briefly discussed asfollows

The friction torque and normal force are measured by a6 DOF measuring table with 3 ring dynamometerscomprising strain gauges. The maximum normal force

and torque which can be applied to the measuring tableare respectively 1293 N and 15 Nm.

To generate a micro-slip in the tangential direction, aDirect Drive motor from Dynaserv YOKOGAWAPrecision is used. The motor has a built-in encoder which is used for the angular position measurement.The resolution of the encoder is 163840

pulses/revolution. The motor is actuated by a proportional-derivative (PD) position controller.

To generate a dynamic normal force, a Philips PR 9270shaker is used. The shaker can generate a force of 35.7 I eff [N], where I eff is the effective current in Ampere.

The shaker is driven in open loop and has a frequency bandwidth of 0 10000 Hz.

The resulting normal displacement is measured by the 3capacitive displacement sensors. This is done byaveraging the signals coming out of the capacitivesensors.

A CLP1103 dSPACE system is used for the dataacquisition. The friction torque measurement isconnected to the first three ADC channels with aresolution of 16 bit. The other channels have aresolution of 12 bit. The other ADC inputs contain threechannels for the normal force, three channels for thenormal displacement, one encoder connection and sixdigital I/O to reset the torque and the normal force(auto-zero). Two DAC channels are used for the controlinputs, one for the motor and one for the shaker.

4.2 Procedures of the Contact StiffnessIdentification

The applied normal loads used in the identification of the contact stiffness (normal and tangential) are chosenthe same as the static normal loads used in thesimulation. Moreover, the contact stiffness was alsoidentified at 8 different angular positions.

In the identification of the tangential contact stiffness, ata given static normal and angular position, the motor is

1

3

5

7

9

11

13

15

2

4

6

8

10

12

14


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actuated with a dynamic command signal. In order toavoid undesired effects, the tangential displacementmust be chosen in such a way that micro-slip isobserved, and also the excitation frequency should notaffect the dynamic behaviours of the tribometer. In thisstudy, the command signal applied to the motor is

sinusoidal with experimentally predefined amplitude of 4x10 -4 rad, and excitation frequency of 0.5 Hz.

In the normal contact stiffness identification, at a givenstatic normal load and angular position, the shaker isactuated with a dynamic command signal. The currentsignal applied to the shaker is also sinusoidal withamplitude of 0.25 Ampere with frequency of 0.5 Hz.This current amplitude is approximately ~9 N.

4.3 Specimens

Three identical paper-based specimens were used in thestudy. These specimens have 2 sets of 9 parallel grooveswhich are perpendicular to each other , as can be seen inFigure 14. One specimen is totally new, and the othersare degraded. Since, the degraded ones have beenexposed to respectively 10,100 and 20,000 duty cycles,they can be considered as glazed materials. These twodegraded materials, namely Glazed 1 and Glazed 2, areobtained from the durability tests on the SAE#2 testsetup. While, the run-in material was obtained byrunning the new specimen on the tribometer for ~5hours with applied normal load of ~1200 N andrelatively constant sliding speed of ~2.5 rad/s which isequivalent to 500 actual duty cycles in the SAE#2 tests.

Prior to the contact stiffness identification on thetribometer, some preparations for the specimens arerequired. The friction lining in one side of thespecimens must be completely removed, and then thespecimens are machined such that the inner diameter isnot less than 0.11 m, in order to be able to mount themon the tribometer. Afterwards, the surface withoutfriction lining of each specimen is glued on a dedicateddisc holder which is specially designed for thetribometer. The nominal (apparent) contact area of eachspecimen after preparation, as depicted in Figure 15, isapproximately 1x10 -3 m2.

Figure 14: The specimens used before preparation

Figure 15: The specimens used after preparation

5. Results and Discussion

Some typical results obtained from the experiments aregiven in Figure 16, and Figure 17, and show a relativelylinear behaviour with a small hysteresis loop, especiallyfor the tangential contact stiffness. A simple linear regression method is therefore used here to identify thecontact stiffnesses by calculating the mean slope of thehysteresis curves.

Figure 16: A representative hysteresis curve of thenormal load vs the normal displacement (applied staticnormal load ~1000 N)

Figure 17: A representative hysteresis curve of thetorque vs the angular displacement (applied staticnormal load ~1000 N)

New Glazed 1 Glazed 2

New Glazed 1 Glazed 2


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The resulting normal and tangential contact stiffness for different normal loads and different degradation levelsare given in Figure 18 and Figure 19. As was previouslyexpected from the simulations, in general, the normaland tangential contact stiffnesses increase with anincreasing static normal load. This can be explained by

the fact that, the separation between two contactingsurfaces decreases with an increasing normal load.Consequently, the real contact area and the number of asperities in contact also increase.

As was investigated in [10,17], due to high negativeskewness, the real contact area of the glazed materials ishigher than that of the new and the run-in materials. Asa result, at a given static normal load, the glazedmaterials have more contact zones compared to the newand run-in materials. Therefore, the normal contactstiffness of the glazed material is higher than that of theothers, as has been seen in Figure 18. This figure showsthat, the normal contact stiffness increase, with theincrease of degradation levels. Moreover, this figurealso shows that the glazed friction materials have higher normal contact stiffness than the new and run-inmaterials.

Figure 18: The experimental normal contact stiffness atdifferent degradation levels

In contrast to the latter results, the tangential contactstiffness shows opposite characteristics; the tangentialcontact stiffness decreases with increasing thedegradation level which confirms the simulation results.

However, at low static normal load (~200 N) thetangential contact stiffness of the new and run-inmaterial is lower than that of the glazed material. It isobvious that, at low static normal load, the separation

between the two contacting surfaces is relatively large.However, due to the high negative skewness and lowroughness of the glazed material, the separation of theglazed material is much smaller than that of the run-inand the new material. Therefore, at the low staticnormal load, the film fluid formed in between of the two

contacting surfaces is not really dominant for the glazedmaterial, which is in contrast to the run-in and the new

material where the film fluid formed plays a dominantrole.

Figure 19: The experimental tangential contact stiffnessat different degradation levels

6. Conclusions

Stochastic models of the normal and tangential contactstiffness using the GW McCool theory have been

presented in this paper. The models show a qualitativeagreement with the experimental results. As the materialdegradation level progress, both tangential and normalcontact stiffnesses deviate from the initial values (atnew material). The normal contact stiffness shows anincreasing trend; in contrast, the tangential contactstiffness shows a decreasing trend. Remarkably, theaforementioned trends enable us to develop a conditionmonitoring strategy on wet clutches. This can be done

by a means to monitor the contact stiffness based ondynamic behaviours.

Acknowledgment

Financial support by Flanders MechatronicsTechnology Centre (FMTC) is gratefully acknowledged.Part of this research is also funded by the IWT, theInstitute for the Promotion of Innovation by Science andTechnology in Flanders, Belgium, grant SB-53043. Theauthors also wish to thank Dr. M. Versteyhe and K.Callier of DanaSpicer Off Highway Belgium (SOHB)for providing the experimental supports.

References

[1]. http://en.wikipedia.org/wiki/Automatic_transmission

[2]. http://en.wikipedia.org/wiki/Manual_transmission

[3]. S. Li, M.T. Devlin, S.H. Tersigni, T-C. Jao, K.Yatsunami, and T.M. Cameron.: Fundamentals of Anti-Shudder Durability: Part I Clutch Plate


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[5]. K. Ito, K.A. Barker, M. Kubota, and S. Yoshida.:Designing Paper Type Wet Friction Material for High Strength and Durability. SAE TechnicalPaper Series (1998), No. 982034, 1 7

[6]. J. Fei, H-J. Li, L-H. Qi, Y-W. Fu, and X-T. Li.:Carbon-Fiber Reinforced Paper-Based FrictionMaterial: Study on Friction Stability as a Functionof Operating Variables. ASME Journal of Tribology, 130 (2008), 041605-1 041605-6

[7]. W. Ost, P. De Baets, and J. Degrieck.: TheTribological behaviour of paper friction plates for wet clutch Application Investigated on SAE#II and

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[8].

Y. Yang, P.S. Twadell, Y-F. Chen, and R.C. Lam.:Theoretical and Experimental Studies on theThermal Degradation of Wet Friction Materials.SAE Technical Paper Series, No. 970978 (1997),175 183

[9]. H. Gao, G.C. Barber, and H. Chu.: FrictionCharacteristics of a Paper-Based Friction Material.International Journal of Automotive Technology, 4(2002) 4, 171 176

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and Numerical Comparison. STLE Tribo. Trans.,(1997),40, 539 548[19]. R. Buczkowski, and M. Kleiber.: A Stochastic

model of Rough Surfaces for Finite ElementContact Analysis. Comput. Methods Appl. Mech.Engrg., 169 (1999), 43 59

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[23]. http://en.wikipedia.org/wiki/Taylor_series


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Appendix A

From Eq. (19), the normalized Weibull distribution can be rewritten as

( )

=

W W W W s s

s exp1

(A1)

where =

Since the contact occurs if and only if sW > W , or for theconvenience it may also be written as W /sW < 1, then

( ) ,21 W W h F can be computed as follows

( ) ( ) ( )

( ) W h

W W W

W W

h

W W W W W W W

ds s sh

s

ds sh sh F

W

W

=

=

21

21

21

21

1

,

(A2)

as W /sW < 1, the term in the brackets of Eq. (A2) can beexpanded using an infinite Taylor series as follows [23]

( )( )

n

W

W

nn

W

W

sh

nnn

sh

=

=

4!12!2

1

11

2

21

(A3)

Substituting Eq. (A3) into Eq. (A2) results in

( ) ( )( ) ( )

( )( )

( )( ) ( )

=

=

=

=

1

221

2

21

12

2121

4!12

!2

4!12!2

1,

n h

W W W n

W n

nW

hW W W W

W

h

W W

n

W

W

nnW W

W

ds s snnhn

ds s s

ds s sh

nnn

sh F

W

W

(A4)

let

1u s s

u W W =

= (A5)

thus

W W ds sdu

1

= (A6)

Substituting Eqs. (A1), (A5), and (A6) into Eq. (A4)results in

( ) ( )( )

( ) ( )( )

( ) ( )( )

( ) ( )( )

( ) ( )( )

( ) ( )

( ) ( )( )

=

=

=

=

W

W

W

W

hn

n

nn

nnW

h

n h

nn

nnW

h

W W

duuu

duuunn

hn

duuuduuu

duuunn

hn

duuuh F

0

221

1 0

2212

221

0

21

0

2121

1

2212

221

212121

exp

exp4!12

!2

expexp

exp4!12

!2

exp,

(A7)

For the convenience, Eq. (A7) can be rewritten as

( ) ( )( )

( )Wn

nn

nnW W

W W F

nnhn

F h F 211

2

2210

2121

21 4!12

!2,

=

= (A8)

where

+

+=

W W h F

,

21

121

1021 , (A9)

and

1 ,

,2

211

221

121

+

+= nhnn F W Wn

(A10)

In similar way, ( )W W h F 23 can be computed as follows

( ) ( ) ( )

( ) W h

W W W

W W

h

W W W W W W W

ds s sh

s

ds sh sh F

=

=

23

23

23

23

1

,

(A11)

Again, by using Taylor series expansion and by the helpof Eq. (A3), the term in the brackets of Eq. (A11) can bewritten as

( )( )

( )( )

( )( )

1

12

12

12

23

4!12!2

4!12!2

1

1

4!12!2

1

1

+

=

=

=

+

=

=

n

W

W

nn

n

W

W

nn

W

W

W

W

n

W

W

nn

W

W

sh

nnn

sh

nnn

sh

sh

sh

nnn

sh

(A12)

One can show that, the Eq. (A12) can be simplified asn

W

W

nn

W

W

W

W

sh

sh

sh

+

=

=

23

1

12

23

(A13)

where

( )( )( )

( )( ) nnn nn

nnn

n4!12

!24!132

!22212

= (A14)


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14

Substituting Eq. (A13) into Eq. (A11) results in

( ) ( ) ( )( ) ( )

=

+

=

2

223

21

2323

2

3,

n h

W W W n

W n

W n

h

W W W W W

h

W W W W W W

W

W W

ds s sh

ds s sh

ds s sh F

(A15)

and again, substituting Eqs. (A1), (A5), and (A6) intoEq. (A15), one can show that

( )( )

( )

( ) ( )

( )

=

+

=

2

223223

2121

232323

)exp(

)exp(2

3

)exp(,

nh

nnnW n

h

W

h

W W

W

W

W

duuuh

duuuh

duuuh F

(A16)

as the same procedure in Eq. (A7), hence, Eq. (A16) can be reformulated as follows

( ) ( ) Wnn

nnW n

W W W W

W F h F h

F h F 232

223123

210

2323

23

2

3,

=

+= (A17)

where

+

+=

W W h F

,

23

123

1023 (A18)

+

+=

W W h F

,

21

121

1123 (A19)

2 ,

,2

231

223

123

+

+= nhnn F W Wn

(A20)

Figure A1: The applied normal load ( W ) as a functionof the non-dimensional distance ( W )

Appendix B

The interference w as depicted in Figure 6 can be alsowritten as

( ) z d z w += (B1)

From Eq. (32), for the convenience, the tangentialcontact stiffness of two contacting hemisphericalasperities, can be rewritten as

( )[ ] 212218 r z d z r Gk it

++= (B2)

According to the GW McCool theory, the expectedtangential contact stiffness of the infinitesimal annulusis

( )dz z f kt N K W z d

it

+

= (B3)

Substituting Eq. (B2) into Eq. (B3) results in

( )[ ] ( )dz z f r z d z r NG K W z d

t ++=

+

212218 (B4)

by a definition

( ) ( ) W W W W ds sdz z f = (B5)

and by normalizing the term in the brackets of Eq. (B4) by , one can show that this equation can also be writtenas

( )( )

( )

( )[ ] ( ) W W W h

W W

W W W

z d

t

ds sr h sr NG

ds sr z d z

r NG K

W

+

+=

++=

2122121

2122121

8

8

(B6)

Finally, from Eq. (10) and (22), the latter equation can be rewritten as

( ) r r r h F G K W W t += 3212121 ,16 (B7)where ( ) ,21 r h F W W + is calculated by using Eq. (A8).

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Contact Stiffness Characteristics of Paper-Based Wet Clutch