A novel monitoring method of wet friction clutches based on the post-lockup torsional vibration signal

Mechanical Systems and Signal Processing 35 (2013) 345–368

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A novel monitoring method of wet friction clutches based on the post-lockup torsional vibration signal Agusmian Partogi Ompusunggu a,b,n, Jean-Michel Papy a, Steve Vandenplas a, Paul Sas b, Hendrik Van Brussel b a b

Flanders’ Mechatronics Technology Centre (FMTC), Celestijnenlaan 300D, 3001 Heverlee, Belgium Katholieke Universiteit Leuven, Department of Mechanical Engineering, Division PMA, Celestijnenlaan 300B, 3001 Heverlee, Belgium

a r t i c l e i n f o

abstract

Article history: Received 5 May 2011 Received in revised form 21 September 2012 Accepted 1 October 2012 Available online 2 November 2012

Wet friction clutches play a critical role in vehicles equipped with automatic transmissions, power shift transmissions and limited slip differentials. An unexpected failure occurring in these components can therefore lead to an unexpected total breakdown of the vehicle. This undesirable situation can put human safety at risk, possibly cause long-term vehicle down times, and result in high maintenance costs. In order to minimize the negative impacts caused by the unexpected breakdown, an optimal maintenance scheme driven by accurate condition monitoring and prognostics therefore needs to be developed and implemented for wet friction clutches. In this paper, the development of a condition monitoring system that can serve as a basis for health prognostics of wet friction clutches with a focus in heavy duty vehicle applications is presented. The developed method is based on monitoring the dominant modal parameters extracted from the torsional vibration response occurring in the post-lockup phase, i.e. just after the clutch is fully engaged. These modal parameters, namely the damped torsional natural frequency fd and the decay factor s, are computed based on the pre-filtered Hankel Total Least Squares (HTLS) method which has an excellent performance in estimating the parameters of transient signals with a relatively short duration. In order to experimentally validate the proposed monitoring method, accelerated life tests were carried out on five different paper-based wet friction clutches using a fully instrumented SAE#2 test setup. The dominant modal parameters extracted from the postlockup velocity signals are then plotted in function of the service life (duty cycle) of the tested clutches. All the plots exhibit distinct trends that can be associated with the progression of the clutch degradation. Therefore, the proposed quantities can be seen as relevant features that may enable us to monitor and assess the condition of wet friction clutches. Since velocity sensor(s) is typically available in a transmission, the proposed monitoring method allows for the practical implementation. & 2012 Elsevier Ltd. All rights reserved.

Keywords: Wet friction clutches Condition monitoring Prognosis Torsional vibration Exponential data fitting Hankel total least squares (HTLS)

1. Introduction 1.1. General aspect Wet friction clutches are mechanical components enabling the power transmission from an input to an output shaft, based on the friction occurring in lubricated contacting surfaces. The clutch is lubricated by an automatic transmission

n

Corresponding author at: Flanders’ Mechatronics Technology Centre (FMTC), Celestijnenlaan 300D, 3001 Heverlee, Belgium. Tel.: þ32 16 32 80 42. E-mail address: [email protected] (A.P. Ompusunggu).

0888-3270/$ - see front matter & 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.ymssp.2012.10.005

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fluid (ATF) having a function as a cooling lubricant cleaning the contacting surfaces and giving smoother performance and longer life. However, the presence of the ATF in the clutch reduces the coefficient of friction (COF). In applications where high power is necessary, the clutch is therefore designed with multiple friction and separator discs. This configuration is known as a multi-disc wet friction clutch as can be seen in Fig. 1, in which the friction discs are mounted to the hub by splines, and the separator discs are mounted to the drum by lugs. In addition, the input shaft is commonly connected to the drum-side, while the output shaft is connected to the hub-side. The friction disc is made of a steel-core-disc with friction material bonded on both sides and the separator disc is made of plain steel. An electro-mechanical-hydraulic actuator is commonly used to engage or disengage wet friction clutches. This actuator consists of some main components, such as a piston, a returning spring which is always under compression and a hydraulic group consisting of a control valve, an oil pump, etc. As can be seen in Fig. 1, the piston and the returning spring are assembled in the interior of a wet friction clutch. To engage the clutch, pressurized ATF that is controlled by the valve is applied through the actuation line in order to generate a force acting on the piston. When the applied pressure exceeds a certain value to overcome the resisting force arising from both spring force and friction force occurring between the piston and the interior part of the drum, the piston starts moving and eventually pushes both friction and separator discs toward each other. To disengage the clutch, the pressurized ATF is released such that the returning spring is allowed to push the piston back to its rest position. In general, the duty cycle of wet friction clutches can be classified into four consecutive phases: (1) fully disengaged, (2) filling, (3) engagement and (4) fully engaged phase. The illustration of a complete duty cycle is depicted in Fig. 2. In the fully disengaged phase (t o t f ), the returning spring holds the piston at its rest (re-tracked) position so that there is no direct contact between the friction and separator discs. This condition allows the friction and separator discs to rotate independently. In this initial phase, the relative rotational velocity, from now on called the sliding velocity, between the input and the output shaft is at high value. Afterwards, the actuator is activated at a given initial sliding velocity nrel, pushing the piston to move as quick as possible before making contact with the neighbor disc. The latter phase is called the filling phase which occurs between time instant tf and te. In the engagement phase (t e o t o t s ), the clutch is actuated by gradually increasing the ATF pressure such that gentle contacts between the friction and separator discs can be established. As a result, the transmitted friction torque increases gradually with the increasing ATF pressure. Because of the increasing friction torque, the sliding velocity gradually decreases until it reaches zero value. As sliding (rubbing) in the engagement phase constitutes an irreversible process, some portion of the transmitted energy is converted into heat which

Fig. 1. The configuration of a multi-disc wet friction clutch, (a) cross-sectional and (b) exploded view.

Fig. 2. A graphical illustration of a complete duty cycle of a wet friction clutch. Note that a.u. is the abbreviation of arbitrary unit.

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consequently results in an increase of the ATF temperature. The time instant when the sliding velocity reaches zero value for the first time is called the lockup time ts. After this time instant, the clutch enters the fully engaged phase (t 4t s ) wherein the sliding velocity remains around zero value. 1.2. Motivation and objective Wet friction clutches have become widely used in automotive applications, such as in vehicles equipped with automatic transmissions, power shift transmissions and limited slip differentials. Moreover, the clutch plays a critical role; an unexpected failure occurring in this component can therefore lead to total breakdown of the vehicle. This can put human safety at risk, possibly cause long-term vehicle down times, and result in high maintenance costs. In order to minimize the negative impacts caused by an unexpected breakdown, an optimal maintenance scheme driven by accurate condition monitoring and prognostics therefore needs to be implemented for wet friction clutches. Here, condition monitoring aims at assessing the condition of a wet friction clutch based on monitoring relevant feature(s), while prognostics aims at predicting the remaining useful life (RUL) of a wet friction clutch based on forecasting the time needed by monitored feature(s) to reach the threshold (hazard zone). A relevant feature can be defined as a parameter that effectively delivers useful information about the failure mode and level. In general, the evolution of (a combination of) relevant features can be associated with the progression of a target failure. Although wet friction clutches are critical components, to our knowledge, very little attention has been paid in the area of condition monitoring and prognostics research for these particular components. This paper aims at the development of a condition monitoring method (tool) that can provide a basis for the development of a prognostics method of wet friction clutches with a focus in heavy duty (off-road) vehicle applications, e.g. tractors, harvesters, etc. The development is motivated by the physical phenomena of degradation occurring in wet friction clutches. To succeed in the development of a condition monitoring method, relevant features to be monitored have to be determined and a strategy to extract them must be established. The coefficient of friction (COF) has been used for many years as a relevant feature for monitoring the condition of wet friction clutches [1–4]. However, the use of the COF for clutch monitoring is not easily implementable in real-life applications, because of the fact that at least two physical quantities are required to compute it, namely (i) the transmitted torque and (ii) the applied normal (axial) load, which are commonly difficult to measure in real transmissions. A torque sensor used to measure the transmitted torque is typically not available in transmissions. As the applied normal load can be approximated from the applied pressure which is usually measured, this approach however may lead to inaccurate normal load estimation. In addition, several methods have been proposed in the literature for assessing and quantifying the degradation level of wet friction clutches, e.g. pressure differential scanning calorimetry (PDSC) and attenuated total internal reflectance infrared (ATR-IR) spectroscopy [5]. Nevertheless, these methods are not practically implementable while clutch is under operation, owing to the fact that the friction discs have to be taken out from the clutch pack and then prepared for assessing the degradation level. In other words, an online condition monitoring system cannot be realized by using these two existing methods. It is reported that the main failure mode occurring in wet friction clutches is caused by the friction material degradation [6–8]. This failure mode frequently occurs in transmissions of heavy duty vehicles because the energy applied to the clutch is relatively high. As the friction material degradation progresses, two major phenomena can be observed: (i) the surface topography changes [9,10], resulting in an increase of the real contact area [9,11,12] and (ii) the mechanical and physical properties change [13,14,2]. These two phenomena strongly affect the contact stiffness characteristics of the clutch, as revealed in our previous study [15]. The study shows that the torsional (tangential) contact stiffness at a given normal load, measured in the fully engaged phase (hereafter called the post-lockup phase), at a constant room temperature, changes in function of degradation level. In addition, the study also shows that the contact stiffness is normal-load dependent where the contact stiffness typically increases with increasing normal load. Besides normal-load dependent, the contact stiffness might also be influenced by the contact temperature which needs to be further investigated. Furthermore, as degradation progresses, the contact damping may also change because of the two aforementioned phenomena. In the tribology domain, the post-lockup phase corresponds to the presliding friction regime, where the friction force (torque) seems to be relative displacement dependent and not sliding (relative) velocity dependent. In general, the nature of the presliding friction force (torque) Mfric exhibits a hysteretic behavior with a non-local memory property, where the friction is also dependent on the history of the motion [16]. The typical presliding friction exhibiting a hysteresis is illustrated in Fig. 3 (the non-local memory property is not shown here). The figure clearly depicts that the slope of the hysteresis curve, which corresponds to the torsional contact stiffness, decreases with increasing relative displacement y. In other words, the increasing relative displacement y has a weakening effect on the tangential contact stiffness (softening spring). Since the clutch’s torsional contact stiffness and damping change as the degradation progresses, as a consequence, the post-lockup torsional mode dynamic behavior of a driveline containing wet friction clutch(es) also changes during the service life. This hypothesis has been proven in our recent study [17], through modeling, simulation and experimental validation, where the change of the clutch torsional contact stiffness is reflected by the change of the post-lockup torsional mode dynamic behavior, namely the damped natural frequency fd and the decay factor s. Obviously, this hypothesis holds true if the properties of other surrounding components in the driveline remain constant (which is in general the case). Therefore, a condition monitoring method of wet friction clutches can be developed based on monitoring the change of the

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Fig. 3. Graphical illustration of a hysteretic friction torque Mfric under imposed sinusoidal relative-motion y with amplitude of A. The hysteresis curve is determined by the ‘‘virgin curve’’, where the former curve is a transformed version (i.e. applying the Masing rules) of the latter curve [16].

Fig. 4. Typical TFR of a measured post-lockup torsional vibration signal (torque signal) after applying the Morlet wavelet transform. Note that the postlockup torque signal yp is scaled by dividing the signal with its standard deviation. The threshold of the TFR is set to 20% meaning that only components with magnitude higher than 20% of the maximum magnitude are depicted. The arrows indicate time-variant components of the signal.

post-lockup dynamic behavior of the driveline, expressed by the modal parameters. This suggests that the modal parameters extracted from the post-lockup torsional vibration signal can be regarded as alternative features for condition monitoring of wet friction clutches. Compared to the COF, the use of modal parameters as features for clutch monitoring is more applicable and challenging in terms of the implementation, because a single sensor, e.g. a velocity sensor, which is typically available in a transmission, can be employed for this aim. Experimental data obtained from laboratory tests on SAE#2 test setups [18–20], e.g. see Fig. 11 and from field tests on actual transmissions [21] show that the torsional vibration occurring in the post-lockup phase, i.e. just after the clutch is fully engaged, exhibits a strong transient response with relatively short duration. The post-lockup transient vibration is actually the shuffle mode, which is well excited by the clutch locking event. In this particular phase, the pressure applied to a wet friction clutch can still vary, e.g. see Fig. 2. As a result, the contact stiffness in the post-lockup phase changes in time. The driveline, wherein a wet friction clutch is installed, thus possibly becomes a non-linear time-variant system, as revealed in the time frequency representations (TFRs) of the measured post-lockup signals [20,22]. A representative TFR of a post-lockup torsional vibration signal (torque signal) measured on an SAE#2 test setup is shown in Fig. 4. It can be seen in the TFR that the instantaneous frequencies of the two components, indicated by the arrows, increase with time. As previously discussed, these two particular components may result from the combination of both hysteretic and time-variant contact stiffness. Wang et al. [23] report that the instantaneous frequency of the transient response of a nonlinear mechanical system with a softening spring, which is qualitatively similar to the hysteresis exhibited by the presliding friction shown in Fig. 3, increases with time due to the amplitude decay. However, the TFR shows that the frequency of a dominant component at low vibration mode is relatively constant. This is remarkable because the dominant component of such a signal can be approximated with a linear time-invariant system identification techniques. To be able to monitor the clutch condition based on the monitoring parameters of the dominant component of such a signal, an appropriate method is obviously necessary. Since a frequency-domain based identification technique may result in large uncertainties on the estimation of modal parameters when it is applied to such a short transient signal [24], only a time-domain based identification is therefore considered in this study. In the time-domain identification technique, parameter identification from the aforementioned signal constitutes an exponential data fitting problem. This is normally

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solved either using a non-linear least squares minimization or using a state-space method. The first one is an iterative method with possibly many local minima, so that the convergence is not guaranteed; in contrast, the second one is a noniterative method. Although the second method may be suboptimal, it nevertheless has a unique solution. There exist several non-iterative time-domain methods commonly used for estimating the operational modal parameters of transient vibration responses, such as the Ibrahim time domain method and its variants [25,26]. However, these methods may not be accurate and robust to noise, since signal and noise are not well separated. As a consideration, a time-domain identification method, called the Hankel total least squares (HTLS) method [27,28] is implemented in this study because of its robustness and accuracy for estimating the parameters of such a signal. The remainder of the paper is organized as follows. In Section 2, a short consideration on the feasibility of the developed clutch monitoring method is presented. The development of the monitoring method comprising the signal pre-processing and feature extraction technique is discussed in Section 3. To experimentally validate the developed condition monitoring method, accelerated life tests (ALTs) were carried out on different wet friction clutches using a fully instrumented SAE#2 test setup. The experimental aspects comprising the test setup and procedure are discussed in Section 4. Results obtained by employing the developed method on the experimental data are further presented and discussed in Section 5. Some recommendations for practical implementation of the developed method are presented in Section 6. Finally, some conclusions drawn from the study are given in Section 7 which can be taken up for further investigation.

2. Theoretical background It has been stated in the introduction that the clutch monitoring method presented in this paper is based on monitoring the change of the post-lockup torsional dynamics of a driveline. Since the torsional dynamics of a driveline are not only influenced by clutch characteristics, but also by surrounding components, it is therefore necessary to understand how sensitive the proposed method in monitoring and quantifying the progression of clutch degradation, which is embodied by the progressive change of its torsional contact stiffness and eventually reflected by the change of the post-lockup torsional dynamics, such that the practical implementation for a given driveline can be succeeded. Moreover, a profound understanding can also aid in defining a new design criterion for a driveline, in which the proposed monitoring method is considered to be integrated and implemented. In the post-lockup phase, a driveline can be modeled (neglecting the clutch inertia) by a two-degree-of-freedom (2-DOF) system [29] with two predominant inertias: (1) input inertia Ji and (2) output inertia Jo, where the input shaft torsional stiffness ki, the clutch torsional contact stiffness kc and the output shaft torsional stiffness ko are connected in series, as can be seen in Fig. 5. Here, the damping is omitted and the non-linear clutch torsional contact stiffness is linearized (assuming small relative motion) in order to simplify the analysis. Despite oversimplification, the model is adequate in approximating the sensitivity of the proposed method to observe the change (due to degradation) of the clutch torsional contact stiffness embodied in the change of the post-lockup torsional dynamics of the driveline. For a 2-DOF (linearized) system as depicted in Fig. 5, one can easily show that the undamped natural frequency on (in rad/s) of the second (flexible) mode is given by sffiffiffiffiffiffiffi keq ð1Þ on ¼ J eq where keq and Jeq respectively denote the equivalent torsional stiffness and equivalent inertia of the driveline which are expressed as follows: keq ¼

ki kc ko , ki ko þ ki kc þko kc

ð2Þ

Jeq ¼

Ji Jo : Ji þ Jo

ð3Þ

The total derivative (small change) of the natural frequency don with respect to the changes of all the influencing parameters is mathematically expressed as follows: don ¼

@ on @on dkeq þ dJ eq : @keq @J eq

ð4Þ

Fig. 5. Simplified model of a driveline in the post-lockup phase.

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In practice, the inertia of the system at a given operational condition (certain configuration) is typically constant (dJ eq ¼ 0), so that the last term in Eq. (4) becomes zero, and this equation can thus be reduced to d on ¼

@on dkeq dkc : @keq dkc

ð5Þ

By a simple calculus operation, one can easily prove that the change of the natural frequency don with respect to the change of the clutch torsional stiffness dkc is given by the following equation: d on 1 ¼ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi : dkc 2 kc J eq ½1 þ r i þ r o 3

ð6Þ

where ri and ro respectively denote the ratio of the clutch torsional contact stiffness with respect to the input and output shaft torsional stiffness, which can be expressed as: ðr i ¼ kc =ki Þ and ðr o ¼ kc =ko Þ. For a large change, Eq. (6) can be written into the following equation:

Don ¼ Hmethod Dkc ,

ð7Þ

with Hmethod denoting the sensitivity of the proposed condition monitoring method to observe the change of the clutch torsional contact stiffness Dkc based on the change of the natural frequency Don , which takes a form of the term in the right-hand side of Eq. (6). For given clutch torsional contact stiffness kc and equivalent inertia Jeq, one can deduce from Eq. (6) that the proposed condition monitoring method possesses a higher sensitivity when the two ratios ri and ro are smaller. By imposing 2 kc J eq ¼ 1 kg m4 =s2 , the effect of the two ratios ri and ro on the sensitivity of the proposed monitoring method Hmethod can be seen in Fig. 6. The figure clearly shows that the sensitivity drastically drops with an increase of the two ratios ri and ro. Based on this observation, the readers should be cautious that the proposed method would not be sensitive enough to detect the change of the clutch contact stiffness if both ratios are too large. Thus, the two ratios can be seen as factors that limit the performance of the proposed monitoring method. As will be discussed in Section 4, both stiffness ratios (ri and ro) of the driveline used in this study (SAE#2 test setup) are less than 0.4. This suggests that the proposed method would be sensitive to detect the change of the clutch contact stiffness. In addition to this, it has also been confirmed by our industrial partner that the maximum stiffness ratio in heavy duty transmissions is 2. Because the sensitivity of the proposed method for this particular stiffness ratio (r i ¼ r o ¼ 2) is relatively high, see Fig. 6, the clutch monitoring method presented in this paper is suitable for heavy duty vehicle applications. By knowing that the clutch torsional contact stiffness kc is influenced by the state of the clutch friction material (degradation level) z, contact pressure p and possibly contact temperature T, for convenience, the clutch contact stiffness can be formally defined as kc ¼ f ðz,p,TÞ:

ð8Þ

Thus, the total derivative of kc in function of all relevant variables z, p and T can be formulated as follows: dkc ¼

@f ðz,p,TÞ @f ðz,p,TÞ @f ðz,p,TÞ dz þ dp þ dT: @z @p @T

ð9Þ

For a large change, Eq. (9) can be rewritten as follows:

Dkc ¼

@f ðz,p,TÞ @f ðz,p,TÞ @f ðz,p,TÞ Dz þ Dp þ DT: @z @p @T |fflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflffl}

ð10Þ

of interest

As we are more interested in monitoring the change of the clutch contact stiffness caused by the degradation, the last two terms in Eq. (10) therefore need to be minimized in order to improve the accuracy of the proposed condition

2

Fig. 6. Sensitivity of the proposed condition monitoring method Hmethod, by imposing kc J eq ¼ 1 kg m4 =s2 , in function of the two stiffness ratios ri and ro.

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monitoring method. In other words, the first term in the equation must be maximized. To this end, both contact pressure variation Dp and temperature variation DT in the post-lockup phase must be as small as possible, viz. Dp-0 and DT-0. If these two conditions can be fulfilled, one can easily show that (by substituting Eq. (10) into Eq. (7)) the change of the natural frequency Don can be directly associated with the change of the clutch degradation level Dz. 3. Methodology A strategy to extract the dominant torsional natural frequency and the corresponding damping (the relevant features) for condition monitoring of wet friction clutches developed in this study is discussed in this section. The strategy is based on the HTLS method as schematically shown in Fig. 7. This scheme shows that there are in general two steps to be completed, viz. (i) the signal pre-processing step and (ii) feature extraction step which are discussed in the following subsections. The pre-processing step mainly aims at detecting and segmenting the post-lockup torsional vibration signal while the feature extraction step aims at quantifying modal parameters of the dominant torsional mode. 3.1. Signal pre-processing Prior to detecting the post-lockup torsional vibration signal, the lockup time instant ts has first to be determined. To this end, the sliding velocity signal nrel is utilized to detect the time instant when the sliding velocity reaches zero for the first time, t s ¼ minf8t 2 R þ : nrel ðtÞ ¼ 0g. This time instant is then used as a reference time to segment a post-lockup torsional vibration yp(t) from a raw torsional vibration y(t). As pointed out by the dashed line in Fig. 7, the velocity signal can also be used as a source of raw torsional vibration. However, this approach can be implemented as long as the velocity sensors installed on both input and output shafts have sufficient resolution to appropriately record the torsional vibration response occurring in the driveline. The use of only one input signal leads to an affordable implementation without involving additional sensors. Alternatively, if the existing velocity sensors cannot provide useful information about the post-lockup torsional vibration response due to insufficient resolution, other potential sensors (if possible to install); e.g. high resolution optical encoder, torque or Ferraris sensor; can be used for this purpose. Fig. 8 illustrates the procedure to capture the post-lockup signal by employing both sliding velocity signal nrel(t) and raw torsional vibration signal y(t). Suppose that the post-lockup signal at a given duty cycle yp(t) is captured with a predetermined time record length tR from the raw torsional vibration signal y(t). Then let us keep tR to be the same for all

Fig. 7. Flow chart of the signal processing and feature extraction.

Fig. 8. An illustration to capture the post-lockup signal. The upper and lower figure respectively denote a raw torsional vibration signal y, which can be e.g. velocity signal or torque signal, and a sliding velocity signal nrel.

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duty cycles. For the sake of consistency, the signal of interest is always captured at the same reference time instant, i.e. ts. Hence, the post-lockup signal yp(t) that is captured from a raw torsional vibration y(t) with a pre-determined tR is yp ðtÞ ¼ yðt s ot r t s þ tR Þ. Furthermore, the post-lockup signal yp(t) that has been captured may contain a drift component. This particular component results in a certain trend in the signal. Prior to the parameter estimation, the trend must be discarded from the captured post-lockup signal yp(t) in order to achieve accurate estimation. The detrending operation on the post-lockup signal yp(t) can be realized according to following equation: y p ðtÞ ¼ yp ðtÞbðtÞ,

ð11Þ

where bðtÞ denotes a model function of the drift component and y p ðtÞ denotes the detrended post-lockup signal (after removing the signal trend). In general, a polynomial function can be employed to model the drift component of such a signal.

3.2. HTLS based feature extraction Since the HTLS method is only valid for signals with constant parameters, the time-variant components of the postlockup signal, as depicted in Fig. 4, therefore need to be filtered out prior to the quantification of parameters of interest. In order to realize this, a band pass filtering technique can be applied to the signal, where the cut-off frequencies of the filter are selected such that the time-variant components can be removed. In this study, the filtering process is integrated with the HTLS method, which is called the pre-filtered HTLS method [30], as will be discussed in the subsequent paragraphs. To apply the latter method, one should have a priori knowledge about the frequency band of interest. This knowledge can be gained based on the dynamic analysis of the driveline under investigation. Alternatively, the frequency band can be roughly estimated from the measured post-lockup signal after the pre-processing step based on the following procedure.

3.2.1. Frequency band estimation Let Fðf Þ be the power spectrum of the detrended post-lockup signal y p ðtÞ. The central frequency f0, which is a rough estimate of the frequency of interest (the dominant mode), is obtained from the spectrum Fðf Þ as follows: f 0 ¼ arg max 9Fðf Þ9: þ

ð12Þ

f 2R

 Once the central frequency f0 has been identified, the frequency band f band ¼ f l upper bound fu, can be estimated based on the following definitions: f l ¼ maxff o f 0 9f 2 R þ :

F0 ðf Þ ¼ 0 4 F00 ðf Þ 40g,

f u ¼ minff 4f 0 9f 2 R þ :

F0 ðf Þ ¼ 0 4 F00 ðf Þ 4 0g,

 f u , consisting of the lower bound fl and

ð13Þ

where the primes denote derivatives with respect to the frequency f. The procedure to estimate the frequency band of interest of the post-lockup signal is visualized in Fig. 9. In this study, the power spectrum Fðf Þ is computed based on the Welch’s method [31] which reduces the variance of the spectrum. The method consists of dividing the time waveform signal into (possibly overlapping) segments, computing a modified periodogram of each segment, and then averaging the power spectral density (PSD) estimates.

3.2.2. Pre-filtered HTLS method After the frequency band fband has been determined, the pre-filtered HTLS method can be applied to the detrended postlockup signal y p ðtÞ for quantifying the signal parameters of interest. The pre-filtered HTLS is a variant of the HTLS method, in which the pre-filtering process is integrated with the parameter estimation in a more elegant and compact way. In this section, the HTLS method is first reviewed briefly and then the pre-filtered variant is introduced and discussed.

Fig. 9. Visualization of the frequency band estimation. The f0 denotes a rough estimation of the central frequency.

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3.3. A brief review of the HTLS method In principle, the HTLS method assumes that a uniformly sampled signal yn , n ¼ 0,1, . . . ,N1 can be modeled as a sum of K exponentially damped sinusoids, with K denoting the model order yn ¼

K X

ck exp½sk nT s þ jð2pf k nT s Þ þ en ¼

k¼1

K X

ck znk þ en ,

ð14Þ

k¼1

pffiffiffiffiffiffiffi where j ¼ 1, ck is the kth complex amplitude, sk is the kth decay factor, fk is the kth damped natural frequency, Ts is the constant sampling period, zk ¼ exp½ðsk þj2pf k ÞT s  is the kth signal pole and en is the noise. The signal parameters ck , sk and fk can then be computed based on the following algorithm: Given that N uniformly sampled data yn ,n ¼ 0,1, . . . ,N1, and a model-order K, the data samples yn s are mapped into an L  M Hankel matrix Y as follows: 2 3 y0 y1 y2 . . . yM1 6 y y2 y3 ... yM 7 6 1 7 6 7 y y3 y4 . . . yM þ 1 7, Y ¼6 ð15Þ 6 2 7 6 ^ 7 ^ ^ ^ ^ 5 4 yL1 yL yL þ 1 . . . yN1 with L 4K,M 4 K and Lþ M1 ¼ N. It is recommended that the Hankel matrix Y should be chosen as square as possible in order to achieve the best accuracy [28]. In practice, one can choose the value of M between d2N=5e and d2N=3e, where de denotes a ceiling operator. Step 1: Compute a truncated singular value decomposition (SVD) of Y: Y¼ U

R V HMK :

LK KK

ð16Þ

Step 2: Compute the total least squares (TLS) [32] solution Z U or Z V of the inconsistent and over-determined shiftinvariant equation of either matrix U or V: U m  U k ZU V m  V k ZH V:

ð17Þ

The up (down) arrow on the U and V matrices means deleting the top (bottom) row. The superscript H on the above-mentioned matrices denotes Hermitian conjugate. Eigenvalue decomposition (EVD) on either the matrix Z U or Z V leads us to compute the estimates signal poles zk. Once the signal poles zk are obtained, the signal parameters of sk and fk can then be estimated. Step 3: Compute the complex amplitude ck by solving a set of over-determined equation in Least Squares (LS) sense: 9 8 2 3 1 1 1 ... 1 y0 > 8 9 > > c1 > > > > 1 1 1 7> > 6 z1 > > > z2 z3 ... zK 7> y1 > > > > > 6 1 = = < < c 6 2 7 2 2 2 2 6 z1 z2 z3 ... zK 7 y2 : ð18Þ ¼ 6 7> ^ > > > > > > 6 ^ 7> > ^ ^ ^ ^ > ; > > : > 4 5> > > > > cK ; :y zN1 zN1 . . . zN1 zN1 N1 K 1 2 3

For further explanation, the HTLS method is fully given in [27,28]. 3.4. Pre-filtered HTLS Since the use of an Infinite Impulse Response (IIR) filter can possibly distort the signal by the introduction of artifact components due to the poles of the IIR filter, as reported in [33], only a finite impulse response (FIR) filter is therefore considered in this study. It is well known that a linear filtering process in the time-domain, e.g. an FIR filtering process constitutes a convolution between an input signal and the impulse response function of the filter. For an FIR filter, the convolution operation can be simplified by means of a matrix multiplication a filter matrix H 2 Cpp with an input signal vector y 2 Cp1 , such that yf ¼ Hy 2 Cp1 corresponds to the filtered signal vector. If the input and the filtered signals are row vectors instead of column vectors, the filtering process becomes yTf ¼ yT H T 2 C1p . Let h^ n be the impulse response function of an FIR filter having length of q. h^ n is then windowed by a window function wn in order to avoid the Gibbs phenomenon due to signal truncation. Furthermore, to eliminate the end effect owing to the filtering process, the windowed impulse response of the FIR filter hn ¼ h^ n wn is mapped into a Toeplitz matrix H FIR 2 Cpp

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with zero-padding as follows [30]: 2 ht ... 6 ^ 6 6 6 hq 6 6 & H FIR ¼ 6 0 6 6 ^ & 6 6 ^ 4 0 ...

h1

0

^

&

...

...

&

^

h1

&

^

^

&

hq &

&

^ ^

0

hq

...

...

0

3

^ 7 7 7 ^ 7 7 0 7 7: 7 h1 7 7 ^ 7 5 ht

ð19Þ

l

m where t ¼ q þ2 1 . Recall that the impulse response of an FIR filter represents a set of the filter coefficients. To construct the Toeplitz matrix as expressed in Eq. (19), an FIR filter has first to be designed. Here, its design is based on the window design method [34], where the window function used in this study is the Kaiser window with the parameter b ¼ 5:658 as recommended in [35]. A Matlab toolbox is used in the study for the FIR filter design. The resulting algorithm of the pre-filtered HTLS method is summarized as follows: Given that N uniformly sampled data yn ,n ¼ 0,1, . . . ,N1, are mapped into L  M Hankel matrix Y as in Eq. (15), a model-order K and a windowed impulse response of a band-pass FIR filter (hn ,n ¼ 1,2, . . . ,q) encompassing the frequency range of interest. Step 1: Construct an FIR filter matrix H ¼ H FIR as in Eq. (19), where H 2 Cpp . For the filtering via right (respectively left) multiplication p ¼M and H r ¼ H T (respectively p ¼L and H l ¼ H) are taken. Step 2: Pre-filter the Hankel matrix Y by matrix multiplication: Y~ ¼ YHr

ðalternatively

Y~ ¼ H l YÞ:

ð20Þ

Step 3: Apply the HTLS algorithm described above to matrix Y~ in order to obtain the signal parameters of ck , sk and fk. 4. Experiment Service-life data of wet friction clutches are required for validation of the developed condition monitoring method. In order to obtain the clutch service life data in a reasonable period of time, the concept of an accelerated life test (ALT) is applied in this study. This can be realized by means of applying high energy levels to a tested wet friction clutch with large flywheel inertia and high initial sliding velocity. A fully instrumented SAE#2 test setup designed and built by the industrial partner, Dana Spicer Off Highway Belgium, was made available for this purpose. Notice that the test setup was made such that it can closely replicate the clutch degradation in a real vehicle. The test setup and the ALT procedure are discussed in the forthcoming subsections. 4.1. SAE#2 test setup The SAE#2 test setup used in the experiments, as depicted in Fig. 10, basically consists of three main systems, namely: driveline, control and measurement system. The driveline comprises several components: an AC motor for driving the input shaft (1), an input velocity sensor (2), an input flywheel (3), a clutch pack (4), a torque sensor (5), output flywheel (6), an output velocity sensor (7), an AC motor for driving output shaft (8), a hydraulic system (11–20) and a heat exchanger (21) for cooling the outlet ATF. An integrated control and measurement system (22) is used for controlling the ATF pressure (both for lubrication and actuation) to the clutch and for the initial velocity of both input and output flywheels as well as for measuring all relevant dynamic signals. It should be mentioned here that both velocity sensors are Hall-effect encoders sensing gear with the teeth number of 51. This means that, the resolution of the velocity sensors is 51 pulses per revolution. 4.2. Test specification To experimentally validate the developed condition monitoring method for wet friction clutches in various condition and configuration, a test scenario was designed for this purpose. The general specification of the test scenario is given in Table 1. Five experiments were conducted in this study wherein a different clutch pack was used for each experiment. The energy applied to each clutch pack in the first four tests is set to a relatively high level; while the energy applied to the last test is set to a lower level, see Table 2. In terms of design, all the used clutch packs are identical, only the friction material is different for each clutch pack, see Table 2. Lining materials of the friction discs used in all the tests are paper-based type while the materials of all the separator discs are steel. It should be noted that all the used friction discs, separator discs and ATF are commercial ones which can be found in the market. In all the tests, the inlet temperature and flow of the ATF were kept constant, see Table 1. Additionally, one can see in the table that the inertia of the input flywheel (drum-side) is lower than that of the output flywheel (hub-side).

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Fig. 10. The SAE#2 test setup used in the study, (a) photograph and (b) scheme, courtesy of Dana Spicer Off Highway Belgium. Table 1 Overview of the test specification. Number of clutch packs to be tested Number of friction discs in the clutch assembly Inner diameter of friction disc (di) [mm] Outer diameter of friction disc (do) [mm] ATF Lubrication flow [liter/min] Inlet temperature of ATF [1C] Output flywheel inertia [kg m2] Input flywheel inertia [kg m2] Sampling frequency [kHz]

5 8 115 160 John Deere J20C 18 85 3.99 3.38 1

Table 2 Detailed test specification. Clutch pack

1 2 3 4 5

Friction disc

Dynax Raybestos I Raybestos II Wellman Raybestos III

Separator disc

Miba Miba Miba Miba Miba

Tyzack Tyzack Tyzack Tyzack Tyzack

Initial sliding velocity (rpm) Run-in test

ALT

2600 2600 2600 2600 1930

3950 3950 3950 3950 2950

4.3. Test procedure Before an ALT is carried out to a wet friction clutch, a run-in test (lower energy level) is first conducted for 100 duty cycles in order to stabilize the contact surface. The run-in test procedure is in principle the same as the ALT procedure,

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but the initial sliding velocity of the run-in tests is lower than that of the ALTs. Fig. 11 illustrates a duty cycle of the ALT that is carried out as follows. Initially, while both input flywheel (drum-side) and output flywheel (hub-side) are rotating at pre-defined respective speeds in opposite direction, the two motors are powered-off and the pressurized ATF is simultaneously applied to a clutch pack at time instant tf. The pressurized oil thus actuates the clutch piston, pushing the friction and separator discs towards each other. This occurs during the filling phase between the time instant tf and te. While the applied pressure is increasing, contact is gradually established between the separator and friction discs which results in an increase of the transmitted torque on the one hand and a decrease of the sliding velocity on the other hand. Finally, the clutch is completely engaged when the sliding velocity reaches zero at the lockup time instant ts. As the inertia and the respective initial speed of the output flywheel (hub-side) are higher than those of the input flywheel, after ts, both flywheels rotate together in the same direction as the output flywheel (see Fig. 11). In order to prepare for the forthcoming duty cycle, both driving motors are braked at the time instant tb, such that the driveline can stand still for a while. The ALT procedure discussed above is continuously repeated until a given total number of duty cycles is attained. For the sake of time efficiency in measurement, all the ALTs are performed for 10,000 duty cycles. Moreover, when testing the clutch pack is sprayed by the ATF due to the centrifugal force effect, which represents the actual operation. The ATF is continuously filtered, such that it is reasonable to assume that the used ATF has not degraded during all the tests.

5. Results and discussion Fig. 12 shows the photographs of friction and separator discs of a wet friction clutch after 10,000 duty cycles, taken from the first clutch pack. It can be seen that the surface of the friction discs has become smooth and glossy, see Fig. 12. Nevertheless, it is evident that the separator discs are still in good condition. The change of the color (darkening, see Fig. 13) and the surface topography (flattening, see Fig. 14) of the friction discs is known as a result of the glazing phenomenon that is believed to be caused by a combination of wear and thermal degradation [9]. The experimental results obtained from all the tests are presented and discussed in this section. The representative measured signals obtained from the run-in tests and ALTs are depicted in Fig. 15. The left panel shows the applied pressure signal p in bar, the middle panel shows the transmitted torque signal M in Nm and the right panel shows the sliding velocity signal nrel in rpm. As can be seen in the figure, the pressure profile applied in the run-in test is different from the ALT. To summarize the measured signals of the run-in tests and ALTs, only values of the signals at the time instant when the transmitted torque reaches the maximum value tm are presented, as listed in Table 3. In addition, it should be mentioned that all the listed values in the table are obtained from the first measurement of the run-in tests and the ALTs.

Fig. 11. A representative duty cycle of the clutches. Note that the transmitted torque drops to zero after the lockup time instant ts because there is no external load applied during the test.

Fig. 12. Friction and separator discs after 10,000 duty cycles, courtesy of Dana Spicer Off Highway Belgium.

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Fig. 13. Representative optical images before and after the test captured using a Zeiss microscope. (a) The photograph of the fresh friction material and (b) the photograph of the degraded friction material after 10,000 duty cycles.

Fig. 14. Representative surface profiles before and after the test measured using a Taylor Hobson Talysurf profilometer. (a) The surface profile of the fresh friction material and (b) the surface profile of the degraded friction material after 10,000 duty cycles. Notice that Z denotes the displacement of the profilometer stylus in z-axis (perpendicular to the surface), X denotes the displacement of the profilometer stylus in x-axis (along the sliding direction) and fðZÞ denotes the probability distribution function of the surface profile.

Fig. 15. Representative measured signals obtained from the run-in tests and ALTs. (a) Applied pressure signal, (b) torque signal and (c) sliding velocity signal. The gray dashed lines denote the signals measured in the run-in test and the black solid lines denote the signals measured in the ALT.

Without loss of generality, energy density that is defined as the transmitted energy per unit of total contact area is introduced here for comparing the degradation rate of the tested clutches with different test conditions. The transmitted energy Ecycle at a given duty cycle is computed as follows: Z ts M orel dt, ð21Þ Ecycle ¼ te

where M denotes the transmitted torque and orel ¼ ð2pnrel =60Þ denotes the sliding velocity in rad/s. Hence, the energy density E cycle transmitted by a wet friction clutch at a given duty cycle can be computed as follows: E cycle ¼

Ecycle , N f Af

ð22Þ

where Nf is the number of friction faces and Af is the apparent contact area between friction disc and separator disc. By applying Eqs. (21) and (22) to the measured torque and sliding velocity, the energy density of each test can be computed as presented in Table 4. As was expected from the design of experiments (see the tests specification), it can be clearly seen from the table that the energy density E cycle applied to the fifth clutch pack is lower than (approximately half of) that of other clutch packs. This section is structured as follows. First, the COFs of all the tested clutches are computed and their characteristics during the clutch service life are evaluated and discussed. The features proposed in this paper, i.e. the dominant modal

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Table 3 Summary of the measured signals. Note that pm and Mm respectively correspond the pressure and torque measured at time instant tm. Clutch pack

Run-in test

1 2 3 4 5

ALT

pm (bar)

Mm (Nm)

pm (bar)

Mm (Nm)

5.1 7.4 7.1 7.1 6.7

426.8 678.8 685.0 713.2 662.4

8.6 8.8 8.8 9.0 8.8

881.1 950.9 1019.0 934.8 1034.0

Table 4 The calculated energy density E cycle obtained from the run-in tests and the ALTs. Test

1 2 3 4 5

E cycle  106 (J/m2) Run-in test

ALT

0.170 0.478 0.475 0.475 0.256

1.068 1.068 1.068 1.068 0.584

parameters, are then extracted from the measured post-lockup torsional vibration signals (velocity and torque signals). Finally, the proposed features are compared with the COF which can be considered here as a reference feature. 5.1. COF characteristic during the service life of the tested clutches As previously stated in Section 1, the COF has been used for many years to evaluate the condition of wet friction clutches. In this study, the COF is employed as a reference feature in order to evaluate and justify the correlation of the proposed features with respect to the progression of the clutch degradation. At a given duty cycle, the instantaneous COF mðtÞ of a wet friction clutch can be computed according to the following equation [19]:

mðtÞ ¼

3 Mðr 2o r 2i Þ , 2Nf F a ðr 3o r 3i Þ

ð23Þ

where ro is the outer radius of friction disc, ri is the inner radius of friction disc, Nf is the number of friction faces, and Fa is the axial force applied to the clutch. The applied force can be estimated based on the applied pressure p and the force of the returning spring Fs, i.e. F a  pAp F s , with Ap denoting the area of the piston. With given spring force and friction disc geometry, by applying Eq. (23) to the experimental data (the measured torque and pressure signals) the instantaneous COFs of all the clutch packs can be computed. The spring force is determined here based on the deformation of the returning spring, when the piston and all the discs make contact, with respect to its rest position. Figs. 16–20 depict the plots of the instantaneous COF mðtÞ obtained from all the tests. It should be noted here that all the instantaneous COFs are plotted with respect to the lockup time instant ts (nrel ¼ 0) with a pre-defined time record length of tl . In order to quantify the global characteristic of the COF of a wet friction clutch, the mean COF mm as proposed in [19] can be applied for this purpose. For one duty cycle, this quantity is defined as follows: Z ts 1 mm ¼ mðtÞ dt, ð24Þ ðt s t e Þ te where mðtÞ denotes the instantaneous COF. For a convenience, the mm can be normalized according to the following equation:

dm^ m ¼

mm mim , mim

ð25Þ

with dm^ m denoting the normalized mean COF and mim denoting the mean COF measured from the first duty cycle. Since the instantaneous COF evolves as the clutch degradation proceeds, this consequently gives the same effect to the mean COF. Fig. 21 shows the evolution of the mean COF mm and the normalized mean COF dm^ m obtained from the run-in tests and ALTs. As can be seen in the figure, the mean COFs show gradually increasing trends during the run-in tests; in contrast, the mean COFs in general exhibit decreasing trends during the ALTs. During a run-in test, the surface topography of a friction material may change (flattening) drastically leading to a drastic increase of the real contact area [12].

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Fig. 16. Instantaneous COFs obtained from the run-in test (left) and ALT (right) of the clutch pack#1.

Fig. 17. Instantaneous COFs obtained from the run-in test (left) and ALT (right) of the clutch pack#2.

Fig. 18. Instantaneous COFs obtained from the run-in test (left) and ALT (right) of the clutch pack#3.

Fig. 19. Instantaneous COFs obtained from the run-in test (left) and ALT (right) of the clutch pack#4.

Fig. 20. Instantaneous COFs obtained from the run-in test (left) and ALT (right) of the clutch pack#5.

Suppose that the friction material has sufficient resiliency and porosity such that the ATF is able to squeeze out when all the discs are approaching. In this desired situation, the asperity (direct) interaction between the two contacting surfaces plays a dominant role in determining the clutch friction characteristics. As the real contact area increases during the run-in tests,

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Fig. 21. Evolution of the mean COF mm and the normalized one dm^ m obtained from the run-in tests (left) and ALTs (right). Note that the resulting curves are obtained after applying the second-order Savitzky–Golay filtering technique [36].

the asperity interaction becomes more pronounced which consequently results in a higher COF (see the left panels of Fig. 21). Different from the run-in tests, the dropping COFs observed in the ALTs can be explained as follows. As the degradation progresses, the surface of the friction material becomes smoother and debris particles are possibly entrapped on the surface pores of the friction material. In addition, the deposition of ATF products may also blockade the surface pores of the friction material. This complex phenomenon is well known as a glazing process [3]. As a result of the glazing phenomenon, the ability of the ATF to escape from the approaching contact surfaces decreases. In this situation, the ATF stays between the contacting surfaces which hampers the occurrence of surface-to-surface contact corresponding to the boundary lubrication regime, thus decreasing the COFs. In addition, the mechanical properties of the friction material change, e.g. reduction of the shear strength [2], which has an additional effect on the COFs reduction. By considering that the ATF has not significantly degraded during the tests (which is the case in this study), the progressive change of the COFs implies that all the tested friction materials have degraded to a certain extent. The level of friction material degradation is not only dependent on the amount of input energy, but also the design, e.g. material durability. As can be seen in Fig. 21, the effect of the used friction material on the COF evolution can be observed. Despite the same energy level, the mean COF reduction of the fourth clutch pack with the Wellman friction material is less than that of the first three clutch packs. It can be seen that the mean COF reduction after 10,000 cycles of this particular friction material is approximately half of the others conducted at the same energy level (Dynax, Raybestos I and Raybestos II, see Table 2). Accordingly, it can be concluded that the used Wellman product is more durable than the other friction materials tested in the study. In addition, the effect of energy level can also be observed from the data. As expected, the lower the energy level the smaller the COF change will be. 5.2. Implementation of the developed condition monitoring tool For practical purposes, the velocity signal measured on either the input shaft (drum-side) or the output shaft (hub-side) of a transmission can be employed to extract the proposed features, i.e. the dominant modal parameters. In this study, the velocity signal measured on the input shaft nd is utilized for this purpose. However, one may also use the velocity signal measured on the output shaft nh for this purpose. Based on the experimental data obtained in this study, the features extracted from the velocity signal measured either on the input or output shaft show qualitatively similar trends. Additionally, the torque signal M is also utilized in this study to extract the proposed features to compare with the ones extracted from the velocity signals. Note that estimation of the dominant modal parameters from both velocity and torque signals can be different since both sensors are located at different positions, see Fig. 10. Prior to the estimation of the dominant component, the torsional vibration signal captured in the post-lockup phase has first to be segmented in accordance with Eq. (8). For this purpose, the post-lockup time instant ts and the time record length tR are required. The post-lockup time instant ts is obtained by employing the technique as discussed in Section 3 to the measured sliding velocity signal nrel, while tR is pre-determined based on the observation of the behavior of the postlockup signals. The time record lengths for the run-in tests and ALTs are set to value of 0.2 s, respectively. As can be seen in Figs. 22–31 that the post-lockup velocity and torque signals are already damped out after this pre-determined time record length. In the figures, the upper panels represent the time waveform post-lockup signals recorded in the first cycle, while the lower panels represent the time waveform post-lockup signals recorded in the last cycle. By employing Eq. (11), the segmented post-lockup signals are then detrended with a first-order polynomial function in order to discard the drift

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Fig. 22. Time waveform post-lockup velocity signals (drum-side) obtained from the run-in tests (left) and ALTs (right) of the clutch pack#1.

Fig. 23. Time waveform post-lockup velocity signals (drum-side) obtained from the run-in tests (left) and ALTs (right) of the clutch pack#2.

component. A first-order polynomial function is chosen in this study because it is adequate (based on observation to the measured signals) to model the drift component of the post-lockup signals. Since there is only one component in the frequency band of interest, i.e. the dominant component, the model order K necessary to estimate the parameters of the dominant component using the pre-filtered HTLS algorithm is 2 (K ¼2). The number of columns M to construct the Hankel matrix is set equal to d0:57  Ne (M ¼ d0:57  Ne), where N is the length of the discrete post-lockup signal. Moreover, the band pass filter is designed with length of q which is set to be the same as M (q¼M). By applying the pre-filtered HTLS algorithm with given input parameters of K, M and q to the captured postlockup signals, the dominant component of the post-lockup signals can thus be estimated. The plots of the post-lockup velocity and torque signals and the estimated dominant components are depicted in Figs. 22–31. As can be seen in the figures, the lockup time instant ts, which is the reference time instant of the post-lockup signal, is set to zero. It is worthwhile to emphasize here that the developed method only estimates the parameters of the dominant component of the post-lockup signal. Thus, the fitted signals or the estimated ones (black lines) as shown in the figures are referred to the dominant component. One may can see in Figs. 27–31 that the measured post-lockup torque signals (gray dashed lines) exhibit a deadzone-line effect which can be speculated due to the backlash present between the teeth of the separator discs and the lugs of the drum, see Fig. 1. Figs. 32–35 show the evolution of the dominant modal parameters fd and s (proposed features) and the normalized ones, which are extracted from the post-lockup velocity and torque signals. The upper and lower panels in the figures respectively depict the non- and normalized features. In similar way to the normalized mean COF (see Eq. (25)), the proposed features fd and s can be normalized which take the following forms:

df^ d ¼

d^s ¼

i

f d f d i fd

,

ð26Þ

ssi , si

ð27Þ

where df^ d and d^s respectively denote the normalized damped natural frequency and normalized decay factor, while f d and si respectively denote the damped natural frequency and decay factor measured in the first cycle. It is important to note that all the curves in Figs. 32–35 are the smoothed ones which are obtained after applying the second-order Savitzky-Golay filtering technique [36]. In general, one can see that (by comparing Figs. 32 and 33) the trends of fd extracted from the velocity and torque signals are qualitatively identical. In addition, one can notice that the trends of the decay factor s extracted from the velocity signals in the run-in tests are rather different from the trends of the decay factor s extracted from the torque signals. Regarding the decay factor, the change of this parameter with respect to the progression of clutch degradation is more pronounced when it is extracted from the velocity signal. One possible explanation is due to the location of the velocity sensor which is close to the anti-node (more sensitive) of the lowest torsional mode (flexible one) which is the mode of interest. As the i

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Fig. 24. Time waveform post-lockup velocity signals (drum-side) obtained from the run-in tests (left) and ALTs (right) of the clutch pack#3.

Fig. 25. Time waveform post-lockup velocity signals (drum-side) obtained from the run-in tests (left) and ALTs (right) of the clutch pack#4.

Fig. 26. Time waveform post-lockup velocity signals (drum-side) obtained from the run-in tests (left) and ALTs (right) of the clutch pack#5.

Fig. 27. Time waveform post-lockup torque signals obtained from the run-in tests (left) and ALTs (right) of the clutch pack#1.

properties of the other components in the driveline remain the same, it is reasonable to conclude that the progressive changes of fd and s are caused by the clutch degradation. One can see in Figs. 32 and 33 that the damped torsional natural frequency fd, in general, shows decreasing trends in the run-in tests. In this particular tests, all the clutches are still in good condition and far from the end of their life. As previously stated, the increasing mm in the run-in tests is believed to be caused by the increasing real contact area. In contrast, fd exhibits a decreasing trend, for which one possible reason is that thermal degradation perhaps (predominantly) takes place during this period, deteriorating the mechanical properties of the friction material (i.e. shear strength reduction, see [2]). Reduction of the shear strength is speculated to decrease the torsional contact stiffness which is reflected by a dropping fd. Moreover, the decreasing trend also seems to appear in the early stage of the ALTs.

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Fig. 28. Time waveform post-lockup torque signals obtained from the run-in tests (left) and ALTs (right) of the clutch pack#2.

Fig. 29. Time waveform post-lockup torque signals obtained from the run-in tests (left) and ALTs (right) of the clutch pack#3.

Fig. 30. Time waveform post-lockup torque signals obtained from the run-in tests (left) and ALTs (right) of the clutch pack#4.

Fig. 31. Time waveform post-lockup torque signals obtained from the run-in tests (left) and ALTs (right) of the clutch pack#5.

In the further stage, adhesive wear may predominantly take place resulting in an increase of the contact stiffness. As can be particularly seen in Figs. 32 and 33, (see tests 1, 2 and 3), fd increases dramatically after the first  3500 duty cycles. This drastic increase perhaps indicates that the tested clutches approach the end of their life. Despite the same energy level with the first three tests, fd extracted from the fourth test shows a gradual decrease which indicates that the friction material tested in the fourth test is perhaps still in a good condition. Such a finding is correlated with the progressive change of the mean COF mm , see Fig. 21, which leads to the same conclusion that the friction material used in the fourth test (Wellman) is more durable than the other friction materials tested with the same energy level (Dynax, Raybestos I and II). Furthermore, one can observe the effect of the energy level on the evolution of the fd and s after a certain number of cycles, where it is evident that the lower the energy level is, the smaller the change of the parameters will be, which is consistent with the evolution of the mean COF mm .

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Fig. 32. Evolution of the dominant damped natural frequency fd and the normalized one df^ d extracted from the post-lockup velocity signals measured in the run-in tests (left) and in the ALTs (right).

Fig. 33. Evolution of the dominant damped natural frequency fd and the normalized one df^ d extracted from the post-lockup torque signals measured in the run-in tests (left) and in the ALTs (right).

Fig. 34. Evolution of the dominant decay factor s and the normalized one d^s extracted from the post-lockup velocity signals measured in the run-in tests (left) and in the ALTs (right).

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Fig. 35. Evolution of the dominant decay factor s and the normalized one d^s extracted from the post-lockup torque signals measured in the run-in tests (left) and in the ALTs (right).

As stated previously, the torsional contact stiffness typically increases with an increase of the contact pressure (normal load) [15]. Although the post-lockup contact pressure in the ALTs is higher than that in the run-in tests (see Table 3), it is evident in Figs. 32 and 33 that fd extracted from the first few ALT cycles is lower than fd extracted from the run-in tests. This implies that the equivalent torsional contact stiffness of the clutch in the first few cycles of the ALTs (with higher contact pressure) is lower than that of the run-in tests (with lower contact pressure). Such findings seem to be a contradiction with the experimental evidence in [15] where the contact stiffness increases with the applied pressure. However, this may suggest to speculate that besides the pressure (normal load) dependency, another factor affecting the clutch torsional contact stiffness may be present. By comparing the evolution of the damped natural frequency fd obtained from the run-in tests and the first cycle of the ALTs, see Figs. 32 and 33, one may notice that fd seems to be dependent on the initial sliding velocity. From the figures, it is evident that the higher the initial sliding velocity is, the lower the torsional natural frequency will be and vice versa. This can be possibly explained as follows. At a given pressure profile, the engagement duration of a wet friction clutch run at higher initial sliding velocity is longer than that run at lower sliding velocity and vice versa, see Fig. 15(c). Owing to the increasing applied pressure, the maximum transmitted torque (occurring just before the lockup time instant is attained) of the clutch run at high initial sliding velocity is higher than that run at low initial sliding velocity, see Fig. 15(b). Because there is no external load applied on the driveline, the transmitted torque drops from its maximum to zero and then oscillates around zero in the post-lockup phase. Consequently, it is reasonable to speculate that the post-lockup relative displacement (i.e. the relative motion between friction and separator discs) of the clutch which is run at high initial sliding is larger than that run at low initial sliding velocity. As previously stated in Section 1.2, the tangential (torsional) contact stiffness exhibits a strong relative-displacement dependency where the tangential contact stiffness decreases with an increasing relative displacement, and vice versa. Because the torsional contact stiffness at large relative displacement is lower than that at small relative displacement (at a given pressure), the torsional natural frequency fd of a wet friction clutch run at high initial sliding velocity is therefore lower than that of the clutch run at low initial sliding velocity.

6. Recommendation for the practical implementation As has been discussed in Section 2, the proposed method works based on the assumption that the properties of the other surrounding components in a driveline remain constant during the clutch service life. In many actual cases, this assumption is reasonable where the properties of the other components, such as the shaft stiffness and the driveline inertia at a certain configuration (e.g. at the first gear), are normally constant. Furthermore, as suggested in Section 2, a high accuracy of the proposed method can be achieved by reducing the pressure and temperature variations in the post-lockup phase, see Eq. (10). In practice, the pressure variation can be minimized by designing a proper pressure control strategy and an appropriate pressure profile. However, in practice it is not straightforward to control the temperature variation. To enable the proposed method to be implemented in real-life applications and in order to achieve an accurate monitoring, a testing mode can be designed for this purpose, wherein the aforementioned prerequisites can be fulfilled. Thus, all the relevant signals for clutch monitoring purpose are only measured and collected in this testing mode. More precisely, one may reserve an operational condition as a testing mode, for example when a vehicle runs on a flat road at the first gear in order to guarantee the driveline inertia and the external load are always the same and the outlet ATF temperature, read out by

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a typically available temperature sensor, is at a certain range, e.g. 95–100 1C in order to guarantee the temperature variation is minimum. The sensitivity of the proposed method in monitoring the change of the clutch contact stiffness is strongly determined by the two stiffness ratios ri and ro, as previously discussed in Section 2. It is shown in Fig. 6 that the lower the two ratios, the more sensitive the proposed method will be for monitoring the change of the clutch contact stiffness. If both ratios are too large, the proposed method would not be appropriate to be used for clutch monitoring, that can be seen as the limitation of the proposed method. For heavy duty transmissions, it has been confirmed (by our industrial partner) that the stiffness ratios are typically less than 2, revealing that the proposed method is sufficiently sensitive to monitor the change of the clutch contact stiffness due to the friction material degradation. This confirmation suggests that the proposed clutch monitoring method seems to be readily applicable for heavy duty transmissions. In terms of feature extraction, it has been demonstrated in this paper that the proposed features (fd and s) extracted from the post-lockup rotational velocity signal are qualitatively correlated to the ones extracted from the torque signals. This suggests that a velocity sensor, which is typically available in a transmission, is suitable to be used for the practical implementation of the proposed monitoring method. Since the accuracy of the features estimation of the proposed method is highly determined by the quality of the velocity signal, it is therefore important to know the minimum requirement for the used velocity sensor. For a rotary encoder (e.g. Hall-effect sensor), which is widely used in automotive applications to measure a rotational velocity, the quality of the measurement signal is well known to be determined by the resolution of the encoder given a certain measurement system (e.g. hardware and algorithm). So, quantification of the appropriate resolution of an encoder that would be used for the implementation of the proposed monitoring method is a very important aspect. A practical approach to determine the required resolution for an encoder in the context of clutch monitoring is discussed below. As described in [37], the instantaneous rotational velocity n (in rpm) measured using an encoder is expressible as n¼

60f c , Np Nc

ð28Þ

where fc denotes the clock frequency, Np denotes the resolution of the encoder and Nc denotes the number of clock units in a pulse generated by the encoder. In addition to this, the measurement error of the rotational velocity can be expressed as

Dn ¼

n2 Np , 60f c

ð29Þ

with Dn denoting the measurement error. For a given clock frequency, the formula reveals that the error Dn quadratically increases with the nominal shaft velocity n and linearly increases with the encoder resolution Np. In order to achieve a certain measurement error, the formula suggests that a higher resolution encoder is required for lower shaft rotational velocity, while a lower resolution encoder is required for higher nominal velocity. It is important to state here that the resolution of the encoders used in this study, i.e. 51 pulses per revolution (ppr), are sufficient to capture the post-lockup torsional vibration signals (just after the clutch is fully engaged) as can be seen in Figs. 22–26, where the nominal velocity measured is about 400 rpm. In practice, the nominal velocity when a clutch is fully engaged is typically higher than 400 rpm. Hence, encoders with the resolution of 51 ppr are not necessarily required to capture the post-lockup torsional vibration with a higher nominal velocity. Suppose that the shaft nominal velocity when a clutch is fully engaged in the testing mode (e.g. first gear) is about 1000 rpm. Moreover, let us assume that the amplitude of the torsional vibration is about 5 rpm as can be seen in Figs. 22–26. In order to preserve the signal quality, the absolute measurement error should not exceed to a certain value, say 0.5 rpm, i.e. Dns r 0:5 rpm. Given the typical clock frequency of 1 MHz, one can then use Eq. (29) to estimate the required resolution for an encoder, that is 30 ppr. To illustrate whether an encoder with the resolution of 30 ppr based on the estimation above is sufficient for clutch monitoring purpose, a signal that represents an encoder signal measured in the post-lockup phase is simulated. It is assumed that the shaft nominal velocity is 1000 rpm that is superposed by a transient vibration signal with the decay factor s of 6.28 rad/s and the damped torsional natural frequency fd of 10 Hz. Based on Eq. (28), the instantaneous rotational velocity can then be retrieved from the encoder signal which is plotted in Fig. 36. As can be clearly seen in the figure, the encoder with the resolution of 30 ppr is sufficient to capture the torsional vibration signal (black line) for this nominal velocity (i.e.1000 rpm). Furthermore, in order to demonstrate the performance of the pre-filtered HTLS method in estimating the parameters (s and fd) of the simulated signal, the estimated parameters are used to reconstruct the signal (gray line) which is plotted in the figure. It reveals that the relative errors of the frequency and the decay factor estimations are 0.02% and 0.7%, respectively. 7. Conclusion and future work The coefficient of friction (COF) has been used for many years in laboratory scale for assessing the condition of wet friction clutches. However, the use of this quantity as a relevant feature for condition monitoring of wet friction clutches is not easily implementable in real life applications since at least two sensors are required, i.e. a force sensor and a torque sensor, which are normally difficult to install in a transmission (not available in actual transmissions). Therefore a condition monitoring method which is practically implementable for wet friction clutches remains a challenging issue.

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367

Fig. 36. Comparison between the velocity signal retrieved from the simulated encoder signal (the encoder resolution is 30 ppr) and the velocity signal estimated using the pre-filtered HTLS method.

A novel monitoring method of wet friction clutches with a focus in heavy duty vehicle applications has been developed in this paper. The developed method is based on monitoring the change of the dominant modal parameters in the postlockup phase, which are proposed as features. It has been demonstrated that the proposed features can be extracted from the post-lockup velocity signal, where the velocity signal measured on the input shaft (drum-side) is used in this study. Since velocity sensors are typically available in a transmission, this may allow us to implement the developed method in real-life applications. In terms of velocity sensors to be used, it has been shown that encoders with the resolution of 30 pulse per revolution seem to be sufficient for the implementation. The Hankel total least squares (HTLS) technique that has an excellent performance in identifying the parameters of transient signals with a relatively short duration is used to estimate the post-lockup dominant modal parameters. Prior to applying the HTLS method, the post-lockup torsional vibration signal has to be filtered in order to discard the nonstationary component in the signal, which are speculated to be resulting from the non-linearity of the contact stiffness and varying applied pressure. The developed monitoring method has been experimentally validated on accelerated clutch’s life data obtained from accelerated life tests (ALTs) carried out on five clutch packs with different friction materials using a fully instrumented SAE#2 test setup. The mean COF that represents the global friction characteristic of a wet friction clutch, is employed here as a reference feature for evaluating and assessing the actual condition of the tested clutches. As expected, this reference feature shows a progressive change during the service life of the tested clutches, which indicates the progression of degradation. The dominant modal parameters (proposed features) are then extracted from the post-lockup torsional vibration, based on the developed method. As similarly exhibited by the mean COF, these proposed features also exhibit clear trends during the service life of the tested clutches. These trends can indeed be associated with the progression of the clutch degradation. Since the proposed features are able to show the progression of the clutch degradation, they can therefore be considered as relevant ones that may enable us to monitor and assess the condition of wet friction clutches. So far, the developed method has been validated under a controlled environment, where (1) the driveline configuration is fixed (inertia is constant), (2) the inlet temperature of the used ATF is controlled at constant value, (3) the applied pressure variation is relatively small and (4) the external load is absent. However, the developed monitoring method is still implementable in practice by means of collecting all the relevant signals for the monitoring purpose in a testing mode, wherein the prerequisites can be fulfilled. In order to extend the developed method in more generic situations, where all relevant signals can be measured at any condition, the effects of the operational parameters on the post-lockup torsional vibration response therefore need to be further investigated. Profound understanding the effects of the operational parameters on the post-lockup torsional dynamics may allow us to minimize the variations on the proposed features, such that an accurate monitoring system can be achieved. Furthermore, a prognostics model based on the evolution of the proposed features also needs to be derived for the remaining useful life (RUL) prediction.

Acknowledgment This work was carried out by the first author during his doctoral research at the Department of Mechanical Engineering of Katholieke Universiteit Leuven (KU Leuven). The financial support from Flanders’ Mechatronics Technology Center (FMTC) Belgium is gratefully acknowledged. All the authors wish to thank Dr. Mark Versteyhe of Dana Spicer Off Highway Belgium for the experimental support. Valuable comments of Prof. Farid Al-Bender on this study are also acknowledged. References [1] K. Matsuo, S. Saeki, Study on the Change of Friction Characteristics with Use in the Wet Clutch of Automatic Transmission, SAE Technical Paper 972928, 1997, pp. 93–98.

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