A survey on modeling and engagement control for automotive dry clutch

Mechatronics 55 (2018) 63–75

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Review

A survey on modeling and engagement control for automotive dry clutch Antonio Della Gatta a, Luigi Iannelli a, Mario Pisaturo b, Adolfo Senatore b,∗, Francesco Vasca a a b

Dipartimento di Ingegneria, Università del Sannio, Piazza Roma 21, Benevento 82100, Italy Dipartimento di Ingegneria Industriale, Università di Salerno, Via Giovanni Paolo II 132, Fisciano - Salerno 84084, Italy

a r t i c l e

i n f o

Keywords: Automotive control Automated manual transmission Dry clutch Engagement control Friction torque modeling

a b s t r a c t Single and dual dry clutches are widely used in automotive transmissions because of their reliability and efficiency paired with low fuel consumption and reduction of pollutant emissions. A prerequisite to attain these goals in automated manual transmissions is the adoption of a “good” clutch model and the design of a robust control strategy. Several papers have been dedicated to modeling and engagement control of dry clutches, both in mechanical and control engineering literature. The wide practical interest of the application and the maturity of the research field motivate the need for a state of the art analysis on the topic. This paper aims at exploring clutch transmissibility models and engagement control strategies proposed in the last decades. An overview of dry clutch torque modeling is proposed together with a discussion on the main factors which affect the torque transmission, such as temperature, sliding speed, contact pressure, wear. Then, the prevalent clutch actuator architectures and control strategies are analyzed by discussing pros, cons and open issues. The survey is concluded by suggesting some topics of interest for future research.

1. Introduction Automotive transmissions based on dry clutch architectures are widely used, so many solutions with different technologies have been proposed in these years [1]. Manual transmission is the most common transmission type, especially in the European market [2]. An evolution of this solution is the Automated Manual Transmission (AMT) which was introduced about thirty years ago for race cars and it is currently adopted for many different driveline architectures. The main difference between manual transmissions and AMTs is that the latter are equipped with an intelligent actuator which manages the shifting process. Thus, a conventional car can easily be converted into one with AMT by improving its performances. On the other hand, the main disadvantage of AMTs is the torque gap during gearshifts which reduces driving comfort and efficiency. A technological solution that mitigates this problem is the dry dual clutch transmission. Unlike the twin or multi-disc clutch in which there is only one input shaft connected to the clutch discs, the dual clutch is based on two separate dry clutches for odd and even gear sets and it can fundamentally be described as two separate AMTs with their respective clutches and contained within one housing. This is achieved through double coaxial shaft in which each shaft is clamped to one clutch disc. In order to familiarize with the structure of a dual dry clutch system one can consider the scheme in Fig. 1. The architecture of a single clutch transmission can be easily

deduced as a simplification of that with dual clutches since, at a certain level of abstraction, torque modeling and engagement control can be analyzed in a unified manner. The main advantages of dry clutch transmissions with respect to the other type of transmissions, including those with wet clutches, are: fuel savings, pollutant reduction, fast response coupled to high comfort, high efficiency and reliability, low production and maintenance costs. Unfortunately, dry clutches suffer for limited transmissible torque because of drawbacks related to durability, thermal capacity and stability of their characteristics [4]. Furthermore, in order to ensure the driving comfort, it is also necessary to eliminate or minimize the associated vibrations [5]. Such issues motivate the research interest in modeling and engagement controls for dry clutches which is demonstrated by the wide literature on these topics whose practical relevance is corroborated by the continuous development of transmissions in real cars. Time is mature for proposing a state of the art analysis on these topics, which is the main goal of this paper. The analysis is carried out in a systematic way by encompassing existing contributions in the literature about modeling of subparts in the clutch system mechanism, estimation of friction and transmitted torque also as regards the temperature effects, clutch engagement control strategies and corresponding validation routes. Some evaluations about the effectiveness of different approaches are proposed throughout the manuscript. The main aspects that characterize the behavior of the dry clutch will be highlighted, especially with reference to the phys-

∗

Corresponding author. E-mail addresses: [email protected] (A. Della Gatta), [email protected] (L. Iannelli), [email protected] (M. Pisaturo), [email protected] (A. Senatore), [email protected] (F. Vasca). https://doi.org/10.1016/j.mechatronics.2018.08.002 Received 27 December 2017; Received in revised form 22 June 2018; Accepted 13 August 2018 0957-4158/© 2018 Elsevier Ltd. All rights reserved.

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Fig. 1. A typical dual dry clutch scheme [3] - (1) crankshaft, (2) dual mass flywheel, (3) central plate, (4) support bearing, pressure plates of the first (5) and second (7) clutches, disc of the first (6) and second (8) clutches, engagement bearing of the first (9) and second (10) clutches, (11) tie rod, first (12) and second (13) transmission input shafts, lever spring of the first (14) and second (15) clutches.

ical quantities that influence its performance. In particular, it will be possible to observe that the advantages and performances of automated dry clutches, both in single and dual configurations, are strongly influenced by the clutch torque transmissibility model implemented in the control strategy. The main contribution of the paper is twofold. Firstly, we present in a unified way most relevant contributions related to automated dry clutches coming from different engineering fields, i.e. mechanical, electronic and control systems literatures. Secondly, we provide evaluations of pros and cons of different approaches for modeling the clutch subsystems with the perspective of the engagement control implementation. The paper is organized as follows: in Section 2 clutch torque frictional models along with deep analysis on main factors which affect torque transmission are proposed. A focus on thermal effects is reported in Section 3. Section 4 describes different actuators (electrohydraulic, electropneumatic and electromechanical) used in automotive applications. In Sections 5 and 6 clutch torque estimation and control strategies are debated, respectively. Conclusions of the overview and suggestions for future research are presented in Section 7.

2.1. Torque dependence on pressure distribution In a dry clutch, the frictional torque is closely related to the clamping load and sliding between clutch disc, flywheel and pressure plate. The friction force results from the normal force provided by the diaphragm spring which axially presses the disc pads against cushion spring reaction, Ffc . Finite Element (FE) and dedicated experiments can be carried out in order to determine the specific dependence of the contact pressure on the radial direction. In [6] it is demonstrated with experimental and FE results that the cushion spring acts mainly along the framed contact lines. The numerical results shown in Fig. 14 in [7] indicate a pressure distribution that varies almost linearly with the radial direction with maximum and minimum values at the outer and inner disc radii, respectively. A contact analysis on a three dimensional element model is proposed in [8] by taking into account the effects of the pressure and centrifugal force loads. The pressure distribution also largely influences progressive wearing of clutch facing, as well as noise of the actuation mechanism often caused by a misalignment between the pressure plate and the clutch disc. It has been proved that most of driveline vibration phenomena excited during clutch engagement maneuvers are partially or substantially due to fluctuations of the contact pressure [9]. Furthermore, recent efforts by automotive systems manufacturers are aiming at improving the clutch design to reduce the clutch actuating pressure as well as actuation losses [10]. The dependences of the contact pressure can be represented through a corresponding transmitted torque lumped model. For each pair of friction surfaces, a typical expression of the transmitted torque Tfc in a dry clutch can be written as

2. Dry clutch torque modeling An accurate transmissibility model is crucial to improve performances of automated dry clutches. Indeed, dry clutches exhibit significant torque capacity variations. Thus, the estimation of the clutch torque as a function of the actuation variable is essential for a precise clutch engagement control. The basic model of a single clutch consists of a static friction characteristic which relates the transmitted torque to the normal force, the slip speed, the actuation variable and the temperature. In the following we assume that the clutch engagement is controlled through the actuator position. In some cases, the torque characteristic is represented as a function of the actuator pressure, however the corresponding models can be derived from those presented below by assuming a static relation between the piston chamber pressure and the actuator position. Moreover, by collecting torque characteristics of single clutches, one can easily obtain transmissibility models of a dual clutch, as well.

𝑇𝑓 𝑐 (𝐹𝑓 𝑐 , 𝜔𝑓 𝑐 ) = 2 𝑅𝜇 (𝐹𝑓 𝑐 , 𝜔𝑓 𝑐 ) 𝐹𝑓 𝑐

(1)

where R𝜇 is the so called equivalent friction radius [11], that takes into account the friction phenomena and the specific geometry, 𝜔𝑓 𝑐 = 𝜔𝑓 − 𝜔𝑐 is the slip speed, 𝜔f is the flywheel speed, 𝜔c is the clutch disc speed, and the factor 2 is due to the number of friction surfaces. Experimental results on clutch material pads proved clear influence of the contact pressure on the friction coefficient [12]. In particular, the higher the contact pressure, the higher the friction coefficient with 64

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a nearly linear relationship. Under the hypothesis of uniform pressure distribution along the angular direction and an uniform wear of pads during contacts [13], the equivalent radius can be written as a function of the slip speed as follows 𝑅𝜇 (𝜔𝑓 𝑐 ) =

𝑅

2 1 𝜇(𝜌𝜔𝑓 𝑐 )𝜌 𝑑𝜌 𝑅2 − 𝑅1 ∫𝑅1

(2)

where R1 and R2 are the inner and outer radii of the pads, 𝜌 is the radius variable, and 𝜇(𝜌𝜔fc ) is the friction function that depends on the tangential velocity 𝜌𝜔fc [14]. 2.2. Friction dependence on the slip speed In the literature the friction function 𝜇(𝜌𝜔fc ) has been modeled through different approaches. In the following, by referring to typical clutch engagement maneuvers, it is assumed for simplicity that the slip speed is always positive as well as the friction function is defined as non-negative. An anti-symmetric behavior is usually assumed for negative speeds. Automotive engineers have measured sudden decrease of the transmitted torque in the last stage of the engagement process with an influence on the duration of the maneuver [15]. This effect is due to the dependence of the friction on the slip speed. A classical model is the Coulomb friction that corresponds to a constant dynamic friction coefficient, i.e., 𝜇(𝜌𝜔𝑓 𝑐 ) = 𝜇𝑑 . It is well known that the static friction coefficient 𝜇 s (also called breakaway friction coefficient) is larger than the dynamic one. At zero speed the friction behavior has a discontinuity given by 𝜇𝑠 − 𝜇0 , i.e., 𝜇(0+ ) = 𝜇0 different from 𝜇 s . For instance, in the case of the Coulomb friction one has 𝜇0 = 𝜇𝑑 . In other models the friction varies with the slip speed, tending to a constant value, say 𝜇 d , for large speeds. In [16] a regularization of such behavior has been proposed with the following continuous friction function ( ) 𝜌𝜔𝑓 𝑐 𝛼2 𝜇(𝜌𝜔𝑓 𝑐 ) = 𝜇𝑑 + (𝜇0 − 𝜇𝑑 ) exp − (3) 𝛼1

Fig. 2. Equivalent friction radius R𝜇 versus slip speed 𝜔fc substituting into (2) a constant friction function 𝜇d (○ cyan line), the friction function (3) (△ black curve), (4) with 𝛼3 = 1 (◊ blue curve) and 𝛼3 = 1∕3 ( + magenta curve), (5) ( × red line), (6) (□ green curve) respectively. The parameters are: 𝜇𝑠 = 0.30, 𝜇0 = 0.15, 𝜇𝑑 = 0.24, 𝑅1 = 74 mm, 𝑅2 = 108 mm, 1∕𝛼1 = 1.5 s/m, 𝛼4 = 3 10−3 s/rad, 𝛼5 = 2 10−2 s/rad, 𝛼6 = 0.3 s/rad. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

By observing Fig. 2, the linear and square-marked characteristics seem to be not representative of a realistic qualitative behavior. The other friction characteristic models are adherent to the real clutch behavior, provided that their corresponding parameters are identified accordingly. Experimental results performed in [12,15] highlighted that the friction dependency on the sliding speed can be approximated by the monotonically increasing functions reported in Fig. 2, whereas parameters identification plays a crucial role.

where the so-called Stribeck velocity 𝛼 1 determines the decay rate of the sliding friction coefficient with the sliding velocity of the friction surfaces. The parameter 𝛼 1 depends on the material properties and on the surface finish. The parameter 𝛼 2 determines the shape of the curve [17]. In [15], by interpolating experimental data, the following friction function has been suggested ( ) 𝜌𝜔𝑓 𝑐 𝛼3 𝜇(𝜌𝜔𝑓 𝑐 ) = 𝜇0 + (𝜇𝑑 − 𝜇0 ) tanh , (4) 𝛼1

2.3. Torque dependence on actuation variable and wear The force Ffc in (1) is a direct input for the transmitted torque model. In real applications this force is determined by a specific actuator (see Section 4). In particular, it can be considered as a function of the throwout bearing position xto , see Fig. 1 in [14] and Fig. 5 in [22]. Then the dry clutch transmissibility characteristic (1) can be rewritten as

with 𝛼3 = 1∕3. In [14] an expression similar to (4) is considered with 𝛼3 = 1. The positive parameter 𝛼 1 in (4) plays the role of the Stribeck velocity in (3). Other authors consider a friction function dependent only on the slip speed and not on the sliding velocity, i.e., 𝜇(𝜌𝜔𝑓 𝑐 ) = 𝜇(𝜔𝑓 𝑐 ). A linear dependence can be expressed as { } ( ) (5) 𝜇 𝜔fc = max 𝜇𝑠 − 𝛼4 𝜔fc , 𝜇𝑑

𝑇𝑓 𝑐 (𝑥𝑡𝑜 , 𝜔𝑓 𝑐 ) = 2 𝑅𝜇 (𝜔𝑓 𝑐 )𝐹𝑓 𝑐 (𝑥𝑡𝑜 )

(7)

where R𝜇 (𝜔fc ) can be given by (2). The normal force can be expressed in terms of the normalized effective displacement of the actuator position defined by { } 𝑥𝑡𝑜 − 𝑥𝑐𝑛𝑡 𝑡𝑜 𝜉𝑡𝑜 (𝑥𝑡𝑜 ) = sat10 , (8) 𝑐𝑛𝑡 𝑥𝑐𝑙𝑠 𝑡𝑜 − 𝑥𝑡𝑜

where 𝛼 4 is a positive parameter that determines the linear rate of variation of the friction which saturates when the constant dynamic friction is reached [18]. The combination of exponential and linear dependencies can be modeled by the following friction function [19] ( ) ( ) ( ) 𝜇 𝜔fc = 𝜇𝑑 + 𝜇0 − 𝜇𝑑 + 𝛼5 𝜔fc exp −𝛼6 𝜔fc , (6)

where sat10 {⋅} is the saturation function between 0 and 1, 𝑥𝑐𝑛𝑡 𝑡𝑜 , called kiss point or incipient sliding point, is the actuator position when the clutch disc comes into contact with the flywheel on one side and with the pressure plate on the other, 𝑥𝑐𝑙𝑠 𝑡𝑜 is the actuator position when the clutch is completely closed. The actuator variable 𝜉 to can be statically related to the cushion spring load-deflection by assuming rigidity of the corresponding leverage mechanism [14]. A proportional relationship between the actuator position and the transmitted torque can be described by

where the radial dependence in (3) has been eliminated and the coefficient 𝛼 weights the new linear relation on the slip speed. The different friction radii obtained through the friction functions are shown in Fig. 2. In [20] a customized pin-on-disc setup has been proposed for the experimental characterization of static and dynamic friction behaviors for various sliding sample pairs. The test bench described in [21] is dedicated to establish the friction coefficient model on the basis of the sliding speed, the pressure and the surface temperature of clutch plates.

𝐹𝑓 𝑐 (𝑥𝑡𝑜 ) = 𝐹̄ 𝜉𝑡𝑜 (𝑥𝑡𝑜 ) where 𝐹̄ is the diaphragm spring load and 0 ≤ 𝜉 to ≤ 1, see [23]. 65

(9)

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3. Thermal effects on torque transmission The main goal of a dry clutch system is to transmit the engine torque to the gearbox and consequently to the wheels. So, to ensure an efficient torque transmission it is desirable that the clutch lining has a high friction coefficient which remains constant over a wide range of temperatures. Unfortunately, the clutch torque transmissibility is highly influenced by the temperature rise due to the heat generation caused by frictional losses [36]. The tribological contact under sliding condition in the clutch facing surfaces during the engagement maneuver is strongly affected by heat transfer occurring in the system. The frictional forces acting on the contact surfaces produce mechanical energy losses converted in heat with ensuing temperature increase. The magnitude of temperature rise depends on the thermal properties of the clutch facings [37–39]. In the literature specific experiments were carried out in order to characterize the behavior of the friction coefficient when temperature and contact pressure vary. For instance, in [40,41] it has been experimentally verified that at high temperatures (more than 200° C) a significant variation of the friction coefficient occurs when varying the contact pressure. Moreover, above a certain critical temperature, namely 250–300 °C, the friction pads start having permanent damage [42]. In automotive applications, it is not unusual to attain such temperatures especially when the system is undergone to repeated clutch engagements. Even below these critical values the temperature increase determines major modifications of the clutch transmissibility. Thermal behavior in a clutch system is a complex phenomenon and the temperature distribution on the friction pads is typically not uniform. Due to the intrinsic difficulty to perform experimental tests in order to assess the temperature field in a dry clutch during the slipping phase, the FE approach is widely used to appraise the interface temperature [39]. In this section, assumptions and exploitations of clutch FE and lumped thermal models are discussed.

Fig. 3. Cushion spring force Ffc versus throwout bearing position xto . The parameters are: 𝑥𝑐𝑛𝑡 = 4.02 mm, 𝑥𝑐𝑙𝑠 = 7.78 mm, 𝐹̄ = 4.540 kN, 𝛽1 = 𝑡𝑜 𝑡𝑜 26.1195𝑒 − 3 kN, 𝛽2 = −1.3046 kN, 𝛽3 = 5.8185 kN. The star-marked points represent experimental data derived from [24].

In [15] specific experiments have been carried out in order to determine the dependence of the force Ffc on xto through the cushion spring deflection. In particular, it is noted that the dependence of the diaphragm spring compression on the throwout bearing position can be modeled with a saturated linear function, and the following expression was identified from experimental data: ( )2 ( )3 𝐹𝑓 𝑐 (𝑥𝑡𝑜 ) = 𝛽1 𝜉𝑡𝑜 (𝑥𝑡𝑜 ) + 𝛽2 𝜉𝑡𝑜 (𝑥𝑡𝑜 ) + 𝛽3 𝜉𝑡𝑜 (𝑥𝑡𝑜 ) .

(10) 3.1. FE Models for temperature distribution analysis

The model (10) can be also interpreted as a polynomial approximation for [ ] √ ( )2 𝐹𝑓 𝑐 (𝑥𝑡𝑜 ) = 𝐹̄ 1 − 1 − 𝜉𝑡𝑜 (𝑥𝑡𝑜 ) (11)

Specific assumptions must be introduced in order to construct suitable FE models. In particular, by considering the axial symmetry of the system, a 2D-model can be considered in numerical simulations instead of a more complex and, sometime worthless, 3D-model. In addition, it is possible to assume that at each contact pair the thermal flux consists of half of the total heat generated during the clutch engagement. Under such hypotheses a thermal symmetry condition, i.e. zero heat flux, can be imposed on the plane where the clutch disc is in contact with the flat spring, see Fig. 15 in [39]. Moreover, it can be assumed that the heat flows in one direction, perpendicular to the contact surfaces. Finally, due to the typical time durations and temperatures of engagement maneuvers, the radiant phenomenon can be neglected. As analyzed in the previous section, in particular by recalling how (2) has been obtained, two further hypotheses used to build up FE models are uniform pressure and uniform wear. In fact, as highlighted in [43–46] the temperature field is strongly affected by the contact pressure distribution.

which is the expression investigated in [18]. Fig. 3 shows the different dependencies of Ffc on xto for some typical values of an automotive dry clutch. The nonlinear functions all agree on the convexity of the dependence. The clutch torque is also influenced by wear [25]. Wear increases 𝑥𝑐𝑙𝑠 𝑡𝑜 which corresponds to a larger pressure plate force when the clutch is closed, thus better preventing unlocking [14]. The wear effect increases the clutch clearance due to the reduction of the friction plate thickness [26] and, at the same time, influences the friction coefficient behavior [20]. Consequently, the wear also affects the energy dissipation in the clutch system as highlighted in [27,28]. Another important issue to be considered is the contaminants impact on the frictional behavior. To this aim, in [29] the authors proposed a friction model which takes into account degraded adhesion conditions. Experimental results showed as wear debris drastically reduce the friction coefficient while increase the wear rate [30]. To solve this issue, many solutions have been proposed to compensate the facing wear by means of wear adjusting system, so that there is no relevant change in the clutch characteristic even after thousands of shifting maneuvers. The main idea is to arrange a self-adjuster mechanism between the pressure plate and the cover which can compensate the thickness variations due to wear [31–35]. In [4] authors performed specific experiments in order to achieve clutch wear model and characterize the influence of the wear compensation mechanism on the clutch characteristics. Their model predicts the friction plate wear based on the dissipated energy and on the clutch temperature. In [6] an FE analysis has been proposed to predict facing wear as a function of the contact pressure.

3.2. Geometry and materials Numerical FE methods allow one to take into account nonlinear behaviors from a geometrical point of view, to select different materials, and to analyze the corresponding time-spatial distributions [47]. In [48,49] the authors analyzed the effects of groove pattern and size on the temperature field and thermal energy. The influence of torque variations and pressure plate thickness on the surface temperature distribution have been also investigated [50]. In [51] different geometrical configurations (full disc, four and eight friction surfaces) and different lining materials (SiC, Si3 N4 and Al2 O3 ) for clutch disc have been analyzed by using the Ansys software. The results therein highlight that the 66

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temperature difference between a full disc and a disc with eight friction surfaces is about 48°C, i.e. a decrease of 37%. In fact, the higher is the number of friction surfaces the higher is the cooling effect of the grooves. Furthermore, also the lining material has a strong influence on clutch disc thermal response. Indeed, the alumina Al2 O3 has shown better thermal behavior in relation to the two other materials. 3.3. Effects on cushion spring load-deflection The torque transmitted by a dry clutch is directly influenced by the cushion spring load-deflection. Indeed, at high temperatures there is an axial thermal expansion of the clutch components which produces a reduction of the total actuator stroke and consequently an increase of the clutch normal force for a given actuator position [26,52–54]. FE analyses have been used also to investigate the temperature effects on the cushion spring load-deflection behavior, so as shown in [24] where a numerical thermal model has been validated with experimental results. The temperature affects the cushion spring characteristic in two ways: firstly, the thermal load induces a thermal expansion that results in an axial size increase and consequently in a change of the kiss point. Secondly, by increasing the temperature, the material stiffness changes and this results in local modifications of the load-deflection characteristic slope. These two effects together lead to model uncertainties during the engagement phase. Indeed, the kiss point changes and if this issue is not taken into account the transmission control unit could lead to a wrong position of the throwout bearing and the actual transmitted torque will be different from the expected one. In order to cope with such issues, a calibration phase is adopted to estimate the kiss point as the value of the actuator position such that a nonzero torque is transmitted by the clutch. This calibration is performed on-vehicle and at specific operating conditions, e.g. at key-on. In order to reduce the sensitivity of this estimation to uncertainties and measurement errors, the estimated kiss point is adapted by using a filtering approach.

Fig. 4. Torque map (12): Tfc versus the throwout position xto and the slip speed 𝜔fc for different temperatures 𝜃 c .

spring force. Therefore the temperature-dependent torque model can be written as 𝑇𝑓 𝑐 (𝑥𝑡𝑜 , 𝜔𝑓 𝑐 , 𝜃𝑐 ) = 2𝑅𝜇 (𝜔𝑓 𝑐 , 𝜃𝑐 )𝐹𝑓 𝑐 (𝑥𝑡𝑜 , 𝜃𝑐 )

(12)

where 𝜃 c is a scalar variable representing an equivalent clutch temperature. A typical approach for considering the temperature effects on the equivalent radius consists of including the temperature dependence on the dynamic friction, say 𝜇 d (𝜃 c ). For this function suitable low order polynomials are used to approximate the corresponding experimental data [15,59,61,62]. In [63] the experiments were carried out by considering different values of the normal force and, for fixed normal force and slip speed, an expression similar to (12) was used to compute the dependence of the friction on the temperature. The expression (12) highlights the temperature dependence of the cushion spring force, see [24,54,64]. By considering the friction models presented above, the temperature effects on the cushion spring force can be modeled by generalizing (8) with

3.4. Contact pressure and slip speed Simultaneous influence of temperature, slip speed and contact pressure on the friction coefficient have been taken into account in [37] where the authors proposed an original experimental friction map, see Fig. 2 in that paper, which confirms the high variability of the frictional response observed over a broad range of operating conditions. This behavior is also mentioned in [42] and discussed by using experimental data in [15]. FE analyses have been proposed to simulate the frictional behavior between contact surfaces in order to obtain the temperature and contact pressure distributions on the friction surfaces in single disc [55] and multi-disc clutches [56,57]. In [58] a coupled thermal-mechanical FE analysis has been carried out to study the interaction between the contact pressure distribution and the thermal field during a clutch engagement by taking into account surfaces roughness. Also in this case the authors underline that the contact pressure is affected by the thermal level. Moreover, it is shown that the maximum contact pressure of a rough surface is higher than a flat surface.

{ 𝜉𝑡𝑜 (𝑥𝑡𝑜 , 𝜃𝑐 ) = sat10

𝑥𝑡𝑜 − 𝑥𝑐𝑛𝑡 𝑡𝑜 (𝜃𝑐 )

𝑐𝑛𝑡 𝑥𝑐𝑙𝑠 𝑡𝑜 (𝜃𝑐 ) − 𝑥𝑡𝑜 (𝜃𝑐 )

} ,

(13)

𝑐𝑙𝑠 where 𝑥𝑐𝑛𝑡 𝑡𝑜 (𝜃𝑐 ) and 𝑥𝑡𝑜 (𝜃𝑐 ) can be represented with suitable polynomial functions approximating corresponding experimental data. Temperature effects on the kiss point position 𝑥𝑐𝑛𝑡 𝑡𝑜 (𝜃𝑐 ) are discussed in [15] (see Fig. 6 therein) where experimental results of three partial clutch engagements at different temperatures are analyzed. It is clearly deduced that the transmitted clutch torque is highly influenced by the temperature also for the same throwout bearing maneuvers. The map (12) is shown in Fig. 4 for different temperatures and in Fig. 5 for different slip speeds. For the calculation of the equivalent radius it has been considered (2) with (6) and 𝜇 d (𝜃 c ) given by a second order interpolating function. The values of Ffc (xto , 𝜃 c ) are calculated by substituting (13) into (10). A similar behavior have been showed through experimental results on a heavy duty truck equipped with a single-plate dry clutch [65]. Figs. 2, 7, and 8 therein demonstrate the variation of the transmitted torque due to thermal effects. That variation can be modeled in terms of a thermal dependence of the throwout bearing position.

3.5. Temperature-dependent lumped models The use of parameter distributed models for temperature estimation requires a high computational effort which is often not compatible with the currently available commercial control units. On the other hand, the temperature influence on the torque characteristic cannot be disregarded and must be accurately taken into account into the model [59,60]. Lumped models which approximate the temperature spatial distribution can be a valuable solution for the control design. The torque lumped model (7) can be generalized by including the temperature dependencies on the equivalent radius and on the cushion

3.6. Dynamic thermal models In order to estimate the temperature(s) of a clutch system, dynamic models with different levels of complexity have been proposed in liter67

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A representative thermal model can be obtained by introducing the following assumptions [15,68]: uniform temperature distribution inside the clutch housing; all slipping energy is converted to frictional heat; when the clutch is engaged there is an equal thermal exchange between the clutch disc and the left and right pressure plates; when the clutch is open it happens only convective heat exchange with the room air; when the clutch is closed it happens only conductive heat exchange; the conductive heat exchange between the clutch disc and the cushion spring is always existing; the clutch and pressure plate/flywheel temperatures are the same. Other assumptions can further simplify the derivation of a heat exchange model [69]. In particular, the heat absorbed by the clutch friction can be neglected if the thermal capacity of the friction lining is much lower than that of the pressure plate and flywheel. Furthermore, the pressure plate and flywheel are usually not affected by radial thermal conductivity, i.e. uniform temperature distribution on the friction disc can be assumed. A model which could represent a good compromise between simplicity, which is required for possible implementation in real control units, and capability to capture the thermal behavior of the clutch, can be written under the above stated assumptions by introducing the equivalent thermal capacitances for the two clutches, say C1 and C2 , and for the central disc or “body”, say Cb . The resulting model is [15,59,70]

Fig. 5. Torque map (12): Tfc versus the throwout position xto and the temperature 𝜃 c for different slip speeds 𝜔fc .

ature. In [66] a seven states thermal model that includes temperatures of bell housing air, skin, ambient, engine coolant and transmission oil has been suggested. A lower order model can be obtained by considering five temperatures as state variables, i.e. those of the two pressure plates, the two clutch discs and the central plate, and by assuming the air temperature in the housing to be an external input [15]. In that model, the temperature of the clutch disc was assumed equal to the averaged value of the two friction facings temperatures. In [65,67] it has been used a model with three thermal state variables for capturing the dynamic behavior in an heavy-duty truck dry clutch at slipping conditions. The engine heat can be also taken into account for the determination of the clutch dynamic thermal response [61]. Here below we discuss a simple dynamic thermal model which can be a guideline for catching the major phenomena influencing the clutch control. This model can be easily adapted in order to obtain the other models presented in the literature. Moreover, this class of models allows one to analyze the thermal dynamics in a dual dry clutch as a simple generalization of that for a single clutch.

𝐶1 𝜃̇ 𝑐1 =𝛾1 𝛿1 (𝜃𝑏 − 𝜃𝑐1 ) + 𝛾2 (1 − 𝛿1 )(𝜃ℎ − 𝜃𝑐1 )+ + 𝛾3 𝑇𝑓 𝑐1 𝜔𝑓 𝑐1

(14a)

𝐶2 𝜃̇ 𝑐2 =𝛾1 𝛿2 (𝜃𝑏 − 𝜃𝑐2 ) + 𝛾2 (1 − 𝛿2 )(𝜃ℎ − 𝜃𝑐2 )+ + 𝛾3 𝑇𝑓 𝑐2 𝜔𝑓 𝑐2

(14b)

𝐶𝑏 𝜃̇ 𝑏 = − 𝛾1 𝛿1 (𝜃𝑏 − 𝜃𝑐1 ) − 𝛾1 𝛿2 (𝜃𝑏 − 𝜃𝑐2 )+ + 𝛾2 (2 − 𝛿1 − 𝛿2 )(𝜃ℎ − 𝜃𝑏 )+ + 𝛾3 (𝑇𝑓 𝑐1 𝜔𝑓 𝑐1 + 𝑇𝑓 𝑐2 𝜔𝑓 𝑐2 ),

(14c)

where 𝜃 represent the different temperatures: 𝜃 b for the pressure-plate and flywheel, 𝜃 c1 and 𝜃 c2 for the two clutches, 𝜃 h for the room air. The logic variables 𝛿 1 and 𝛿 2 represent the state of the corresponding clutches with 𝛿1 = 1 (𝛿2 = 1) if the first (second) clutch is not open.

Fig. 6. Electromechanical actuator for dry dual clutches and its components [81] - (1) base plate, (2) spindle, (3) traverse, (4) nut ball screw, (5) rollers, (6) engagement lever, (7) return spring, (8) servo motor. 68

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Fig. 7. Clutch control scheme.

The temperature of the room air is an input of the system and it is assumed to be directly measurable. The constants 𝛾 1 , 𝛾 2 and 𝛾 3 can be obtained experimentally or through dedicated FE simulations. The model can be simply adapted for the case of a single clutch by considering only (14a) and (14c) with 𝛿2 = 1, 𝜃𝑐2 = 𝜃𝑏 and 𝜔𝑓 𝑐2 = 0. A dynamic thermal model can be used to obtain an on-board estimation of the clutch temperature in order to adapt the torque transmission characteristic accordingly. In particular, the model ((14)) can be further simplified by observing that the body temperature 𝜃 b has no direct influence on the clutch torque and it might be measurable. Moreover, it is possible to neglect the conductive and convective heat transfers during the slip phase.

unexpected higher (or lower) clutch torque producing jerks, overheating or even engine halt. That is amplified in dual clutch transmissions where the gear shifting process sees one clutch (on-coming clutch) to be engaged, while another (off-going clutch) needs to be disengaged. Thus, a precise coordination of the on-coming clutch and the off-going clutch is critical, which otherwise will cause undesirable torque interruption and oscillations [85,86]. In order to overcome the latter drawback, in the last decades numerous control strategies have been suggested to improve management of clutch actuators. Some authors proposed to use a position sensor in order to have a direct measure of the throwout bearing position [87–90]. Others proposed to adopt a pressure sensor because for both electrohydraulic and electropneumatic actuators it is possible to control the throwout bearing position by controlling the piston chamber pressure [85,89,91,92]. Instead in [93] authors presented a mechatronic add-on system which can be used to implement a force trajectory without replacing the traditional diaphragm spring. The main disadvantages of those approaches are due to the complexity and feasibility to integrate position and/or pressure sensors into a clutch assembly. Thus, a further approach for overcoming such difficulties is to replace sensors by nonlinear observers [75,85,91,94,95]. Unfortunately, the nonlinearities listed above require an appropriate mathematical modeling to implement a good observer and consequently to obtain acceptable control performance. Definitely, the main challenge of current development of clutch actuators is represented by high accuracy and quick response. From this point of view the undergoing research is still of wide interest.

4. Clutch actuators The clutch actuator is the linkage between the transmission control unit and the clutch assembly. Thus, its operation accounts for critical issues and drastically affects the clutch performance. Actuators for clutch control and gear speed selection are paired with efficient control modules to cope with high performances requirements of modern automated transmissions. The current trends show continuous technical effort toward cost and complexity reduction, time stability, durability. The lever actuator for both dry and wet clutch systems is an architecture which offers benefits with regard to efficiency and costs [71]. In recent years different actuation systems have been developed to automate clutches: electrohydraulic [72,73], electropneumatic [74,75] or electromechanical [76–78] systems. Both electrohydraulic and electropneumatic actuators are relatively complex systems because they need pump, tank, filter, pipeline and valves. In detail, electrohydraulic actuators are usually employed in cars, whereas electropneumatic actuators are widely used in commercial vehicles [74], as pressurised air is already available for a number of truck services, even though this feature makes harder the modelling task due to the air compressibility [79]. Their working principle is similar to electrohydraulic actuators but in this case the compressed energy of the gas is used as a source of the force transmission. Conversely, an electromechanical actuator involves an electrical motor as power source and one worm gear, screw nut or ball screw as speed reduction mechanism [80]. They have been introduced into the market more recently to replace electrohydraulic systems. Fig. 6 describes the main components of an electromechanical actuator for dry dual clutches [81]. The main advantages of the electromechanical actuation solutions include easier integration into transmission system [82] and potentially better total efficiency due to low losses in electrical motors [76,83]. The actuator control task is designed as a position control problem or a force control problem according to the clutch architecture, passively closed or actively closed, respectively. Indeed, in dry clutches the transmitted torque is a nonlinear function of the throwout bearing displacement, which is driven by the clutch actuator [80]. Furthermore, dry clutch systems are also affected by other nonlinear effects such as friction coefficient uncertainty, thermal dynamics hysteresis, and wear [79,84]. So, also a small error in the throwout bearing position could result in an

5. Transmitted torque estimation The accuracy of the clutch torque control is highly influenced by torque transmission characteristic variations. This has been clearly shown not only for conventional cars but also for dry dual clutches [15] and heavy duty trucks [65,96]. Due to the difficulties of an on-board torque measurement, a torque estimator is usually adopted [97] and the engagement controller is adjusted accordingly. In real vehicles, it is difficult to measure the torque on a rotating axle using direct torque measurement, such as with wireless torque sensors, and also expensive. Thus, the use of such sensors in practice is not common. Using available sensors existing in the vehicle is much more feasible by way of the so-called “sensor fusion” approach, which can include the use of measured velocity through wheel, transmission and engine speed sensors [98]. The analysis performed by control designers in automotive industry could provide useful elements about the controller burdening for estimation task. A prerequisite for the design of a torque observer is a proper driveline model. A typical model of a transmission equipped with a single dry clutch can be obtained by considering kinematics and dynamics of the different driveline elements [99]. By introducing the rigidity assumptions for the mainshaft, the following second order dynamic model can 69

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be written 𝐽𝑓 𝜔̇ 𝑓 = −𝑏𝑓 𝜔𝑓 + 𝑇𝑒 (𝜔𝑓 ) − 𝑇𝑓 𝑐 (𝑥𝑡0 , 𝜔𝑓 𝑐 )

(15a)

𝐽𝑐 (𝑟)𝜔̇ 𝑐 = −𝑏𝑐 𝜔𝑐 + 𝑇𝑓 𝑐 (𝑥𝑡0 , 𝜔𝑓 𝑐 ) − 𝑇𝐿 (𝜔𝑐 , 𝑟)

(15b)

a state which includes the unknown clutch torque, similarly to the idea expressed by (18b). An alternative approach which does not exploit the dynamic driveline model consists of estimating the transmitted torque by adapting the parameters of the static model Tfc (xto , 𝜔fc ) expressed by (7) or by using similar quasi steady-state characteristics. Recursive least square techniques have been used for this purpose: in [113] the friction coefficient is estimated under different operating conditions; in [114,115] three parameters of an exponential-like torque characteristic are estimated. In [116] the kiss point 𝑥𝑐𝑛𝑡 𝑡𝑜 is estimated online by exploiting the input shaft speed delay time and the maximum crankshaft acceleration.

where Jf is the flywheel inertia, Jc is the equivalent vehicle inertia evaluated at the clutch, bf and bc are the damping coefficients, r is the gear ratio, Te is the engine torque, TL is the load torque. For the sake of simplicity the temperature dependence in ((15)) has been omitted. Analogous procedures can be applied in order to obtain a driveline model for the case of dry dual clutches [100]. A corresponding model can be written as

6. Engagement controls

𝐽𝑓 𝜔̇ 𝑓 = − 𝑏𝑓 𝜔𝑓 + 𝑇𝑒 (𝜔𝑓 ) − 𝑇𝑓 𝑐1 (𝑥𝑡𝑜1 , 𝜔𝑓 𝑐1 ) − 𝑇𝑓 𝑐2 (𝑥𝑡𝑜2 , 𝜔𝑓 𝑐2 )

The engagement maneuver for a dry clutch is a challenging control problem. In this section, classical and modern clutch control techniques are analyzed by discussing pros and cons of the different strategies.

(16a)

𝐽𝑐 (𝑟1 , 𝑟2 )𝜔̇ 𝑐 = − 𝑏𝑐 𝜔𝑐 + 𝑟1 𝑇𝑓 𝑐1 (𝑥𝑡𝑜1 , 𝜔𝑓 𝑐1 ) + 𝑟2 𝑇𝑓 𝑐2 (𝑥𝑡𝑜2 , 𝜔𝑓 𝑐2 ) − 𝑇𝐿 (𝜔𝑐 , 𝑟1 , 𝑟2 )

6.1. A control scheme for clutch engagement

(16b)

The engagement control of a dry clutch must be designed by taking into account several, sometimes conflicting, objectives. First of all, the clutch should engage as fast as possible, compatibly with the actuator time response. A fast engagement determines high slip speeds with high friction torques and then high friction losses Indeed, the power dissipated during the engagement results from the product of the transmitted torque and slip speed. Moreover, a fast engagement is usually in contrast with a smooth maneuver and a comfort performance corresponding to the so-called no-lurch conditions is a small acceleration diriveline discontinuity at the lock-up [117]. The engagement control should be designed such that undesired driveline oscillations are avoided in all operating conditions [118,119]. In particular, self-excited vibrations during the engagements could be also due to the slope of the friction coefficient vs. the slip speed [120,121]. The engagement control can be viewed for each dry clutch as a tracking problem with two reference speeds. A quite general control scheme of a dry clutch is shown in Fig. 7. The clutch and engine reference speeds can be assigned through some heuristics or designed by using optimization strategies, for single [122] and dual [123] clutches. The reference speeds profiles should be designed in order to prevent undesirable effects, such as those due to the system nonlinearities [124]. Soft computing techniques seem to be quite interesting for generating reference signals representing the driver intentions. A fuzzy estimator has been presented in the earlier work [125] and artificial neural networks have been shown to be useful for reconstructing the rapid modifications of the driver intentions which influence the clutch engagements [126–128]. The speed controller elaborates the speed errors and generates the reference torque to be transmitted, say 𝑇𝑓𝑟𝑒𝑓 and the reference engine 𝑐

where 𝜔𝑓 𝑐1 = 𝜔𝑓 − 𝑟1 𝜔𝑐 , 𝜔𝑓 𝑐2 = 𝜔𝑓 − 𝑟2 𝜔𝑐 , r1 , r2 are the gear ratios and Tfc1 , Tfc2 are the torques transmitted by the two clutches, respectively, see [101]. Control-oriented dynamic models of more involved driveline architectures can be obtained by using similar arguments [102]. Higher order models could be useful for numerical analysis purposes but are usually too complex to be implemented adopted in a practical digital controller currently available in the automotive industry. The basic idea for torque observers exploits the driveline dynamic model [14,103]. From ((15)) one can write 𝑇̂𝑓 𝑐 = −𝐽𝑓 𝜔̂̇ 𝑓 − 𝑏𝑓 𝜔𝑓 + 𝑇𝑒 (𝜔𝑓 )

(17a)

( ) ̂̇ 𝑐 + 𝑏𝑐 𝜔𝑐 + 𝑇𝐿 𝜔𝑐 , 𝑟 𝑇̂fc = 𝐽𝑐 (𝑟)𝜔

(17b)

where hats indicate the estimated variables. This type of simple observer suffers from noise and uncertainties in the accelerations and torques estimations [104,105] and parameters identification [106]. Indeed, the Eq. (17a) is typically used when the engine speed is constant so that the torque transmitted by the clutch can be computed by the engine torque without making any derivative. In general, the torque estimators based on the inversion of the dynamic model do not provide the required robustness features. A typical solution for getting better performance consists of an observer based on the engine speed error together with a constant model for the transmitted torque, see among others [107]. The dynamic model of this type of observers can be expressed as 𝐽𝑓 𝜔̂̇ 𝑓 = −𝑏𝑓 𝜔̂ 𝑓 + 𝑇𝑒 (𝜔𝑓 ) − 𝑇̂𝑓 𝑐 + 𝓁1 (𝜔𝑓 − 𝜔̂ 𝑓 ) 𝑇̂̇ 𝑓 𝑐 = 𝓁2 (𝜔𝑓 − 𝜔̂ 𝑓 )

(18a)

torque 𝑇𝑒𝑟𝑒𝑓 . The clutch torque controller provides the required reference signal for the throughout position, which is implemented through a controlled clutch actuator. The actuator position corresponds to the torque transmitted by the clutch. An engine torque controller completes the scheme. In addition, one could also consider a further control loop on the clutch torque error, by using a transmitted torque estimator such as that described by ((18)). Therefore, the observer allows a feedback action on the clutch torque. On the other hand, since the engine control system is faster than the clutch control system, the clutch torque observer considers directly the engine torque reference rather than the measured engine torque. If the internal loop constituted by the torque observer is not considered, the clutch torque controller just performs a feedforward action through the inversion of the clutch torque characteristic model. This block represents an irreplaceable element of any dry clutch control scheme because it relates the torque control variable with the actuation variable. This motivates the importance of considering wear

(18b)

where 𝓁 1 and 𝓁 2 are the observer gains to be designed. A Kalman filter with a model structure analogous to (19) is discussed in [108]. Kalman filtering techniques are also used in [109] for the training phase of a neural network which provides an online torque estimation by considering also the actuator dynamics. The actuator model is analyzed in [110] with a different perspective. In particular, the torque estimation is obtained by considering a disturbance observer based on the actuator dynamics and the transmitted torque is determined from the reaction load on the actuator. A similar idea based on the estimation of the load torque is used in [111] where a sliding mode observer is proposed. Observers have been also proposed for transmissions with dry dual clutches. A good overview of the results on that topic can be found in the recent paper [98]. Fuzzy techniques are adopted in [112] by estimating 70

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and temperature effects in the adaptation of the torque transmissibility characteristic [70]. A similar scheme can be used to represent most control strategies in the case of dual clutches too [129,130]. For such topologies it is important the combination and coordination of the controllers during the torque and inertia phases [131] and the clutch-to-clutch shift [132]. More in general the control strategy must discriminate and regulate the transitions among different logic phases of a clutch engagement process: engaged, slipping-opening, synchronization, go-to-slipping and slipping-closing [133,134]. In the following we consider the most critical phase of the slipping-closing conditions.

In addition to modeled uncertainties and nonlinearities of the dry clutch system, there are other disturbances that occur in the clutch engagement and disengagement phases, due mainly to the aforementioned phenomena of wear and heat generation. These disturbances involve variations in the friction function and the kiss point. Therefore, the control system will have to take into account these effects to compensate them. Unfortunately, this type of phenomena cannot be easily modeled. As an alternative to model-based strategies, or in combination with it, sliding model controllers have been investigated. A possible approach consists of choosing the sliding surface for the actuator position tracking [163], which can be also done by combining the actuator controller with a feedforward compensation on the clutch normal force [164]. Sliding techniques are also adopted in order to track suitable speeds reference signals which optimize the clutch engagement process [165,166]. The typical robustness property of the sliding control can be exploited in order to compensate for the nonlinear behavior of the clutch friction torque especially at low slip speeds [167]. In fact, sliding techniques have been used also for the estimation of the transmitted torque [161,168] and actuator position corresponding to the kiss points [169].

6.2. Control strategies The speed controller of the block scheme in Fig. 7 implements the tracking of the reference speeds. The speed controller is multivariable in the sense that cross-coupling of the feedback loops on the two speeds must be carefully handled. A possible solution consists of implementing a decoupling strategy. In this case, a classical engine speed controller generates as output the difference between the reference engine torque and the reference clutch torque, see ((15)). Then, the reference engine torque can be obtained by adding the clutch torque which is provided by the loop with a standard controller on the clutch speed [117]. This type of strategy can also include adaptations which allow comfort improvements [135]. An alternative approach for the multivariable speed controller design could be the use of model-based optimal control techniques. As firstly presented and analyzed in [136,137] where the minimization of a quadratic function dependent on the slip speed and normal force is considered. This controller can be also combined with a clutch observer [138–140], engagement comfort performance [141] and model parameters identification procedure [142]. The optimization problem and the corresponding controller design can be similarly formulated in terms of Lyapunov techniques [143,144]. The robust control techniques based on quantitative feedback theory [145] and H∞ control [146,147] represent a proper solution when frequency domain effects due to disturbances and/or parameters uncertainties are of primary importance for the engagement. The main difficulties in solving the problem of control with modelbased approaches are related to the constraints on the engagement process, such as finite-time duration and torques limitations, together with the hybrid nature of the driveline model which changes its structure after the clutch lock-up [148]. Those features suggest the interest for formulating the problems by using the model predictive control (MPC) approach as firstly proposed in [149] where the hybrid nature of the control solution was investigated. In [150] the authors compared the MPC performance with those achievable with a piecewise linear-quadratic controller designed by using a piecewise quadratic Lyapunov function. The MPC is able to explicitly take into account the problem constraints [151] and to reject disturbances, such as vehicle mass and road grade [152]. The good performance of MPC have been verified also experimentally [153,154]. On the other hand, the robustness of the MPC is paid with a large computational burden which might be prohibitive for commercial automotive control units. Therefore suitable strategies for reducing the computational costs and for supporting the model uncertainties, for instance by compensating for the clutch wear [155] or an adaptation to different road conditions [156], should be applied. The application of optimization strategies for dual clutches is more complicated because of the required coordination and optimal torques allocation [157] to be generated through the two clutches actuators [158,159]. A specific application of the optimal control theory to the case of dual dry clutches has been proposed in [160] by interpreting the performance index in terms of friction work, shock intensity and engine torque. That approach has been combined with a torque observer in [161] while a different approach, based on H∞ and on the optimization of torque and inertia phases in dry dual clutch, is presented in [162].

6.3. Numerical co-design AMT models with single and dual dry clutch have been widely used as numerical co-design tools for clutch design [61,170] and fault diagnosis purposes [171–173]. Those models have been implemented within the typical numerical environments dedicated to the simulation of dynamic systems. Matlab/Simulink is used in most cases but also other tools such as Adams [108] and Modelica [174] have been chosen. The usefulness of numerical co-design techniques is particularly evident in hardware-in-the-loop (HIL) platforms, which allow to test the transmission controls in early stages of their development and also to reduce the time and costs of calibration. Extensive HIL testing and embedded platforms are a crucial aid to attain trade-off equilibrium between accuracy and computational time [151]. In [175] the HIL environment is used for rapid prototyping of an energy-efficient and smooth clutch engagement and to verify the possibility to generate the optimal clutch and engine torque control inputs by means of dynamic programming. The rapid prototyping HIL platform presented in [176] provides a tool for testing transmission control units when the transmitted torque model is linearly dependent on the clutch position determined by the actuator. HIL setups for dry dual clutches are used in [177,178], where transmission control units are validated during functional tests and failure recovery procedures, and in [161] for the validation of sliding mode torque observers. The analysis proposed in [179,180] concentrates on the effects of (multiple) friction elements in changing the structure of the driveline models. The hybrid nature of the AMT model introduces several difficulties for the HIL numerical integration which must satisfy the strict real-time constraints. 7. Conclusion and future research Engagement control of the automotive dry clutch plays a key role for the satisfaction of comfort and performances objectives in automated manual transmissions. The combination of different elements determine the overall behavior: friction torque transmission, thermal effects, wear, actuator technology, control strategy. Different levels of deepening about clutch torque assessment are often perceivable by going through the overview: simpler models could be sometimes preferred to more complex ones, to provide real time torque estimation in on-board environment, even though delivering lower accuracy. The analysis also encompasses how classical control, optimal control and adaptive techniques have found a challenging field of application over last years. Optimal control techniques are effective for obtaining a good quality of the dry clutch engagement and rejecting disturbances. 71

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On the other hand, their implementation requires a high computational cost often not compatible with commercial automotive control units. This favors simpler not model-based techniques in which, in addition to speed control, the control of the torque transmitted by the clutch is implemented through a torque estimator. Further research efforts in the direction of accurate transmitted torque estimators, including the temperature effects, could be useful. New add-on technological solutions which allow direct or indirect torque and temperature measurements could improve the engagement performances and robustness. The temperature distribution on the friction pads motivates further studies on the appropriate thermal variables to take into account for an effective clutch control. The development of more detailed dry clutch models will maintain its importance for the inclusion in hardware-in-the-loop platforms which represent an indispensable paradigm for the design and the verification of automotive components and controls. The general overview presented in this paper can be especially useful to developers of next generation of vehicles, in particular for hybrid architectures, as current forecast about automated dry clutches market is expected to gain traction in all countries where higher fuel economy and ease of driving on congested roads continue to influence buying decisions.

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Antonio Della Gatta is working as PhD student in Automatic Control at University of Sannio in Benevento on the theme “Dry dual clutch modeling and control”. His research focuses on classical control strategies, optimal control, adaptive, sliding, fuzzy and neural network techniques about automated manual transmissions in single and dual clutch architectures. Luigi Iannelli was born in Benevento, Italy, in 1975. He got the “Laurea” degree in computer engineering from the University of Sannio in Benevento in 1999 and the PhD in information engineering from University of Napoli Federico II in 2003. In 2002, he was visiting student at the Royal Institute of Technology (KTH), in Stockholm, and in 2003 guest researcher (responsible of the Automatic Control Project course) working with Prof. Karl Johansson. Since December 2004 he has been working with the University of Sannio in Benevento, Italy, firstly as assistant professor and then (May 2016) as associate professor of automatic control.

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Mario Pisaturo was born in Salerno, Italy, in 1984. He received the M.Sc. and Ph.D. degrees in mechanical engineering from the University of Salerno, Fisciano Salerno, Italy, in 2010 and 2014, respectively. He is currently a Research Fellow at Department of Industrial Engineering, Salerno University. His main research topic is the theoretical/experimental analysis of dry clutches for automotive with regard to automated manual transmissions. He develops research on clutch engagement control with focus on frictional behavior influence of slip speed, load and thermal field at facings interface.

of Applied Mechanics of the Technische Universitat Berlin with a grant from DAAD. He served as reviewer for several journals on the topics of System dynamics, Mechatronics, Tribology. Francesco Vasca was born in 1967 in Giugliano (Napoli, Italy) and currently he is Full Professor of Automatic Control at the University of Sannio (Benevento, Italy). In 1995 he received the Ph.D. in Automatic Control from the University of Napoli Federico II. In 1995 he has been appointed as Assistant Professor at the Department of Engineering of the University of Sannio (Benevento, Italy), where he has been Associate Professor of Automatic Control since 2000. In 2014 he received the Italian national qualifications for Full Professor position in Automatic Control and in Power Systems. In 2015 he has been appointed as Full Professor at the University of Sannio. Since 1995 he developed his research and teaching activities at the Department of Engineering of the University of Sannio, where he taught courses on Automatic Control and Switched Systems. He has been tutor for more than 100 master degree theses. From 2005 till 2010 he has been President for the master degree curriculum in Automatic Control. In 2004–2013 he has been a member of the Board for the Ph.D degree in Information Engineering.

Adolfo Senatore received the M.Sc. degree in Mechanical Engineering from the University of Salerno, Salerno, Italy, in 1998, and the Ph.D. degree in tribology from the University of Pisa, Pisa, Italy, in 2002. He is associate professor of Mechanics for Machine Systems with the Department of Industrial Engineering, University of Salerno, while he has been serving as teacher of Mechanical Vibrations and Mechatronics. More than 180 scientific papers in the following areas document his scientific work: frictional modeling and model-based control in automotive transmissions, lubrication in internal combustion engines and journal bearings, effects of nanoparticles as friction reducer additives, vibration measurement methods. During 2012, he visited as Guest Professor the Department

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