Investigation on the thermodynamic characteristics of the deformed separate plate in a multi-disc clutch

Journal Pre-proofs Investigation on the thermodynamic characteristics of the deformed separate plate in a multi-disc clutch Liang Yu, Biao Ma, Man Chen, Heyan Li, Jikai Liu PII: DOI: Reference:

S1350-6307(19)31043-X https://doi.org/10.1016/j.engfailanal.2020.104385 EFA 104385

To appear in:

Engineering Failure Analysis

Received Date: Revised Date: Accepted Date:

20 July 2019 17 November 2019 10 January 2020

Please cite this article as: Yu, L., Ma, B., Chen, M., Li, H., Liu, J., Investigation on the thermodynamic characteristics of the deformed separate plate in a multi-disc clutch, Engineering Failure Analysis (2020), doi: https://doi.org/10.1016/j.engfailanal.2020.104385

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Investigation on the thermodynamic characteristics of the deformed separate plate in a multi-disc clutch Liang Yu1, Biao Ma1, Man Chen1 *, Heyan Li2, Jikai Liu3 1School

of Mechanical Engineering, Beijing Institute of Technology, Beijing, 100081, P. R. China

2College

of Urban Transportation and Logistics, Shenzhen Technology University, Shenzhen,

518118, P. R. China 3Institute

of Microelectronics of Chinese Academy of Sciences, Beijing, 100029, P. R. China

*Corresponding author: [email protected] (Man Chen)

Abstract This work is devoted to investigate the thermodynamic characteristics of the deformed separate plate in a multi-disc clutch. The thermodynamic model is proposed, and the contact ratio of mating surface is varied to imitate the deformed plate. Moreover, the experimental study is conducted on the clutch test bench; in order to induce the plate deformation more easily, the thermometric plate has experienced the circumferential elastic deformation before experiments. Before the elastic deformation of separate plate occurs, the surface temperature increases steadily and the friction torque increases slowly with the increase of coefficient of friction. When the temperature gradient in the circumferential direction reaches the critical value 2~3°C, the elastic deformation is excited. In the process of elastic deformation, the temperature growth rate in the contact zone increases dramatically, and the friction torque rises steeply. As for the variation of friction torque after the elastic deformation, it can be divided into three categories: increase smoothly, stable and decrease gradually. Moreover, at this stage, the smaller the contact ratio is, the higher the temperature in the contact zone is, and the greater the friction torque is. Meanwhile, with the decrease of the radial length and circumferential angle in the contact zone, the radial and circumferential temperature differences of the plate expand dramatically. The conclusions can be used as a theoretical basis for evaluating the real-time status of friction components and diagnosing the clutch failure. 1

Key words: multi-disc clutch, elastic deformation, friction torque, temperature

Nomenclature c

specific heat (J/(kg·°C))

v

linear velocity(m/s)

Ff

friction force (N)

z

coordinate in axial direction (m)

Fn

applied force (N)

Z

number of friction pairs

h

thickness (m)

λ

thermal conductivity (W/(m·°C))

Mfc friction torque (N·m)

ω

angular velocity (rad/s)

n

θ

coordinate in circumferential direction (°)

papp applied pressure (MPa)

α

central angle of each period (°)

p

contact pressure (MPa)

β

central angle of the contact zone (°)

q

heat flux ((J/(m2·s))

ρ

density (kg/m3)

r

coordinate in radial direction (m)

γ

heat partition factor

S

contact area (m2)

μ

coefficient of friction

t

time (s)

κ

convective transfer coefficient

T

temperature (°C)

η

contact ratio

number of contact zones

1. Introduction The multi-disc clutch, which plays a significant role in the power transmission, is one of the most important frictional components for an entire vehicle [1, 2]. The main task of the clutch is to engage and disengage the connection between the driving and driven parts in various transmissions. To achieve the smooth power transfer, the clutch is always under the slipping status, which inevitably generates a large amount of friction heat. Usually, the clutch slipping brings about the high surface temperature and the large temperature gradient, thus increasing the clutch wear and, in severe conditions, resulting in not only poor shifting quality but also eventual clutch failure [3, 4].

(a) Buckling

(b) wear

(c) Carbonization

Fig. 1. Failures of the friction components

2

(d) Crack

The failure of friction components has long been of interest to the designers and manufacturers [5]. Fig. 1 depicts different forms of clutch failure, including thermal buckling [6], wear [7], carbonization [8] and crack [9], etc. The separate plates are often found to be permanently deformed into two different modes, namely the coning mode and the potato chip mode [10]. As shown in Fig. 1 (a), the separate plate underwent the conical plastic deformation. Zhao et al. [11] studied the thermal buckling mode at high orders via the finite element method. Cui et al. [12] investigated the combined effect of temperature variation and constraints on the deformation of friction components. As for the wear of friction components, Zhao et al. [13] investigated the friction and wear behaviors of Cu-based friction pairs in wet clutches under the high temperature conditions. An uncertainty quantification analysis was carried out to explore the nature of the wear process of paper-based friction materials [14]. Additionally, the linear equations were developed to mark the transition boundaries between wear regimes of the copper-based friction material according to the test data [15]. As shown in Fig. 1(c), the black band on the outer radius of disc was induced by the carbonization of the lubricating oil at high temperature. Yu et al. [16] found that the contact pressure was concentrated on the outer radius of friction components due to the circlip constraint; thus, the surface temperature in outer radius is much higher than that in the other radial directions. Xiong et al. [8] used the energy spectrum instrument to analyze the material composition of the black band. Moreover, the fracture mechanics method was proposed to conduct the thermal fatigue crack growth simulation of the railway brake disc [17]. Li et al. [18] investigated the behavior of crack propagation under different braking conditions, suggesting that the high braking energy could accelerate the crack propagation.

3

(a)

(b)

(c)

Fig. 2. Periodic deformation of the separate plates In addition to the thermal stress, mechanical loads can also cause the plate deformation. As shown in Fig. 2, these separate plates, obtained from the major overhaul of a heavyduty vehicle, have undergone the circumferential elastic or plastic deformation. The reason for this kind of failure has been discussed in our previous studies [19]. Such periodic bright spots are induced by the resistance torque, and the number of spots corresponds to the number of spline teeth. When the resistance torque transmitted by spline exceeds the critical value, the plate will suffer the elastic deformation in the circumferential direction, leading to the local contact of mating surface. Such coupled thermo-mechanical behaviors can give rise to so-called macroscopic hot spots. It is known that hot spots are high thermal gradients on the friction surfaces [20]. Baber et al. [21] explained the mechanism of hot spots, which was induced by the thermal instability. Zagrodzki and Truncone [22] investigated the generation of hot spots during the short-term engagement numerically and experimentally. Kumar et al. [23] studied the influence of metallic fillers in friction materials on the appearance of hot spots during the braking process. Moreover, the infrared camera was used to monitor the process of the formation of hot spots [24, 25], where a portion of the plate was exposed during the experiments. Unfortunately, this method can only be used for the theoretical research, and it is not practical to monitor the thermal status of clutches and brakes in a vehicle due to high costs or technical challenges involved. Likewise, when slight hot spots occur, the generated thermal stress can give rise to the elastic deformation of separate plate; while in moderate cases, the degradation of 4

friction material can be observed; in some extreme cases, the separate plate will suffer the plastic deformation. Hot spots and plate deformation are mutually reinforcing. Therefore, the appearance of hot spots basically means that the friction surface is in the local contact status. Zhao et al. [26] found that as the contact ratio of mating surface reduced, the temperature on the contact zone rose dramatically. Otherwise, the increase of contact ratio could contribute to the lower and more uniform temperature and pressure distributions on the friction surfaces [27]. The dynamic characteristics of a multi-disc clutch will also be varied significantly when the contact status of friction surfaces changes. Nevertheless, little research has been carried out to investigate the dynamic characteristics of the clutch when the plate deformation occurs. Therefore, there is no theoretical knowledge and engineering technique to identify whether the separate plate is deformed or not during the clutch engagement process. This paper is conducted to remedy this deficiency. Herein, this paper aims to investigate the thermodynamic characteristics of the clutch before and after the elastic deformation of separate plate. The detailed numerical model is developed, and the mating surface is modified to different contact ratios to imitate the deformed plate. Moreover, the experimental investigation is carried out; the plate that experienced the circumferential elastic deformation is selected as the thermometric plate. The conclusions are aimed to provide a theoretical basis for judging the real-time status of friction components in the on-line monitoring of clutch.

2. Numerical model The clutch system consists of a series of separate plates and friction discs. Fig. 3 demonstrates the heat transfer process in a set of friction pair. The contact status of the friction components can be divided into two categories: the uniform contact status (UCS) and the intermittent contact status (ICS). If the separate plate is brand new, the mating surface of the disc and plate is in UCS; accordingly, the contact pressure is evenly distributed on the friction surface. However, if the separate plate has

5

experienced the elastic or plastic deformation, the mating surface is in ICS; thus, the contact pressure is concentrated on the contact zone [28].

Fig. 3. Schematic of the heat transfer model The heat conduction equation of the friction pair can be written as follows [29].

c

T 1   T  1   T    T    r       t r r  r  r 2     z  z 

(2)

As it is assumed that the friction power is completely converted into the friction heat, the total heat flux can be given as [30] q  r ,     r ,   p  r ,     r

(3)

The coefficient of friction (COF) obtained from the pin-on-disc tests, is dependent on the surface temperature, velocity and contact pressure [26].

  r ,  

  2.6 v r    5.16    0.4   ln T  r , +1  28.3 p r ,   0.87    23e







+0.08 e

0.005T  r , 



1 e

0.2 v r 



0.01ln  4v  r   1



e

0.005T  r , 

(4)

 1  0.005ln  28.3 p  r ,     0.015

According to the thermal properties of friction materials, the friction heat is conducted proportionally to the disc and plate. The heat partition factor can be expressed as [31]:



s  s cs s  s cs   f  f c f

(5)

where λ, ρ and c are the thermal conductivity, density and specific heat, respectively; the subscripts s and f represent the separate plate and friction disc, respectively. 6

Consequently, the heat fluxes of the plate and disc can be given as: qs  r ,      q  r ,  

(6)

q f  r ,    1     q  r ,  

(7)

2.1 Uniform contact When the mating surface is in UCS, the contact pressure will not change in the circumferential direction ( p   0 ) and the heat transfer model can be idealized as an axisymmetric model. Thus, Eq. (1) can be simplified as [32, 33]:

c

  2T 1 T  2T  T +  2 +  r r z 2  t  r

(8)

As shown in Fig. 3, taking the separate plate as an example, the initial and boundary conditions are as follows.



T  r , z, t    i T  r , z, t   Toil  , 0  z  h r r r

(9)

T  r , z, t    o T  r , z, t   Toil  , 0  z  h r r r

(10)



T  r , z, t   qs ,i  r ,  , t  , ri  r  ro z z 0

(11)



T  r , z, t   qs ,i 1  r ,  , t  , ri  r  ro z zh

(12)

i



o

T  r , z , t  |t 0  Toil

(13)

where ri and ro are the inner and outer radii, respectively. Toil is the temperature of lubricating oil. Finally, the friction torque in UCS can be given as

M fc   

rFf

dS  

ro 2 p S  rFn   rdrd    r 2 app drd r 0 i S S

S 2 papp  ro3  ri3  S

S

3



ro

ri

 dr

7

(14)

2.2 Intermittent contact Basically, the periodic bright spots in Fig. 2 are the contact zones in ICS. Fig. 4 presents the equivalent model of the plate with circumferential elastic deformation. There are n periods in the circumferential direction, and each period contains the contact zone (colored yellow) and the non-contact zone. Since the number of periods is the same as the number of spline teeth, the central angle α of each period is determined. In order to facilitate the mesh generation, it is assumed that the contact zone is fan-shaped. Thus, angle β is the central angle corresponding to the contact zone in one period. If the contact surface is in UCS, α=β; otherwise, α>β.

Fig. 4. Equivalent model in ICS Since the heat conduction process is the same for each period, the heat conduction equation can be simplified for one period as follows [34].

c

T 1   T  1   T    T    r       , 0      t r r  r  r 2     z  z 

(15)

The contact ratio can be expressed as [27]:

=

nS abcd S  abcd nS ABCD S ABCD

(16)

Thus, the contact pressure in one period can be given as:  papp  nS ABCD papp  ,   p  r ,     nS abcd  0, 8

 Contact zone   Non-contact zone 

(17)

As shown in Fig.4, AD and BC represent the insulated boundaries. Accordingly, the additional boundary conditions are as follows.





T  r ,  , t   0, ri  r  ro，0  z  h    0, AD

(18)



T  r ,  , t   0, ri  r  ro，0  z  h    , BC

(19)



T  r , z, t  z z  0, S

(20)

T  r , z, t  z z  0, S

 qs ,i  r ,  , t  , ra  r  rb abcd

 0, ri  r  ra , rb  r  ro

(21)

ABCD  S abcd

Finally, the friction torque in ICS can be given as

M fc  n 

ro

ri

2 n 0



r  2

papp



drd 

n  papp  ro3  ri3  3

ro

2 n 0

  ri

drd

(22)

3. Experimental procedure 3.1 Experimental apparatus The experimental study is conducted to investigate the thermodynamic performances of a multi-disc clutch before and after the plate deformation. As shown in Fig. 5, the test bench mainly consists of three parts: the driveline, the hydraulic system and the measurement and control system, respectively. The driveline rotates the clutch to produce relative rotation between the plates and discs. The hydraulic system provides the clutch with the lubricating oil and, more importantly, engages and disengages the clutch. Through the measurement and control system, the clutch temperature and friction torque can be obtained. In experiments, the driven part of test bench is fixed by the brake, thus the clutch temperature can be measured by the thermocouples conveniently.

9

Fig. 5. Schematic of the clutch test bench 3.2 Experimental method As shown in Fig. 6, the clutch pack used in the simulation and experiment is a fourfriction-pair system. The friction discs and separate plates are arranged alternately along the clutch driving shaft. The plate and friction core are made of 65 Mn steel; the friction lining is typically made of the copper-based powder metallurgy material. The thermophysical parameters of the friction components are listed in Table 1.

Fig. 6. Diagram of clutch installation Table 1 Overview of the thermophysical parameters Parameters

Separate plate

Friction disc

Thermal conductivity(W/(m·°C))

45.90

9.30

10

Density(kg/m3)

7800

5500

Specific heat(J/ (kg·°C))

487

460

Inner radius(mm)

86

86

Outer radius(mm)

125

125

As shown in Fig. 7, the thermometric plate has experienced the circumferential elastic deformation before experiments. This arrangement can increase the probability of the elastic deformation of thermometric plate during the slipping process, thus the variations of surface temperature and friction torque before and after the plate deformation can be more easily observed. The thermometric plate is close to the back plate to avoid the plastic deformation. In this way, the thermometric plate has only one friction surface to produce the heat flux, and there is a dramatic heat diffusion on the other friction surface. Besides, there are five thermometer holes equally spaced between two key teeth, where three holes are placed in the medial radius and the other two are respectively placed in the outer and inner radii. It should be noted that the rest plates and discs are brand new.

Fig. 7. Schematic of the temperature measurement Before the experiments, a run-in test is carried out to ensure all equipment and sensors are properly installed and operate well. The experimental conditions are listed in Table 2. If the plate temperature is high enough, the lubricating oil will evaporate and produce lampblack. When the lampblack is observed, the experiment stops immediately to prevent the plastic deformation of the thermometric plate. Thus, the slipping time of each experimental case is also listed in Table 2. 11

Table 2 Experimental conditions Cases

1

2

3

4

Applied pressure(MPa)

0.12

0.14

0.14

0.16

Rotating speed(rpm)

300

150

300

150

Slipping time(s)

22

29

11.9

21

4. Results and discussion 4.1 Simulation results It should be highlighted that the operating condition in the simulation corresponds to the experimental case 1 as listed in Table 2. As shown in Fig. 8(c), the applied pressure first increases linearly and reaches a peak value of 0.12MPa at 6s, and then keeps constant. The rotating speed is constant at 300rpm, and the slipping time is predefined as 22s. Moreover, the contact ratio of the plate near the back plate is changed to imitate the deformed plate, and the other two plates are in good contact conditions. Corresponding to the spline teeth, there are 18 periods in the circumferential direction of the plate, thus angle α is kept at 20°. Table 3 demonstrates the geometric parameters of the contact zone in one period, and 4 different contact ratios are considered in ICS.

Table 3 Geometric parameters of the contact zone in one period Contact condition Uniform

Intermittent

Radii(ri/ro)

Central Angle(β)

Contact ratio(η)

85/125

20

1.000

87/123

18

0.810

90/120

18

0.675

90/120

15

0.563

95/115

15

0.375

Since the thermal and dynamic models are coupled together, the finite difference method is selected to solve such a complex thermodynamic model, which is simpler and more suitable than the finite element method to study the temperature and friction torque simultaneously in a multi-disc clutch [16, 35]. The MATLAB code is used to solve the surface temperature and friction torque in order iteratively. Additionally, the time step is 0.005s, and the program ends automatically when the simulation time reaches the preset value. The axisymmetric four-node elements are employed in the 2D 12

heat transfer model. To be more exact, there are 390 elements and 440 nodes for plate, 117 elements and 160 nodes for friction lining, 273 elements and 320 nodes for friction core, respectively. Likewise, the axisymmetric eight-node elements are used in the 3D heat transfer model. In one period, there are 7800 elements and 9240 nodes per plate, 2340 elements and 3360 nodes per friction lining, and 5460 elements and 6270 nodes per friction core, respectively.

(a) Surface temperature

(b) Temperature in radial direction

(c) Friction torque and applied pressure Fig. 8. Simulation results in UCS In UCS, the surface temperature at the end of slipping time is shown in Fig. 8(a), where the circumferential temperature difference equals zero. Fig. 8(b) demonstrates the temperature variations in the radial directions and, clearly, the radial temperature difference gradually expands with time. In the radial direction, the temperature increases linearly, and the highest temperature finally reaches 112.1°C. As depicted in Fig. 8(c), since the friction torque is proportional to the applied pressure, the friction 13

torque increases linearly at first. Subsequently, the increased surface temperature contributes to the rise of COF, thus the friction torque increases slowly after the applied pressure is stable.

(a) η=0.810

(b) η=0.675

(c) η=0.563

14

(d) η=0.375 Fig. 9. Temperature variations of the separate plate in ICS Fig. 9 presents the temperature variations with regard to different contact ratios. The hot spots gradually show up as the contact ratio decreases, indicating that the decline of contact ratio brings about the increase of contact pressure and surface temperature in the contact zone. The maximum temperatures in such four conditions are 120.6°C, 124.7°C, 130.4°C and 140.1°C, respectively. Since the temperature in the contact zone is much higher than that in the non-contact zone, there are obvious temperature gradients in the radial and circumferential directions of the separate plate. To be more specific, the radial temperature in ICS increases parabolically, and the circumferential temperature varies sinusoidally. As the contact ratio decreases, the temperature differences in radial and circumferential directions expand significantly. The maximum radial temperature difference in UCS is 24.4°C. However, the maximum radial temperature differences in ICS are 29.5°C, 35.9°C, 38.4°C and 52.4°C, respectively; the corresponding radial contact lengths are 36mm, 30mm, 30mm and 20mm, respectively. Consequently, the larger the radial contact length is, the smaller the radial temperature difference is. In addition, the maximum circumferential temperature differences are 3.1°C, 4.2°C, 6.7°C and 9.8°C, respectively; the angles in each contact zone are 18°, 18°, 15° and 15°, respectively. Accordingly, the larger the contact angle is, the smaller the circumferential temperature difference is. 15

Fig. 10. Variations of the friction torque in ICS As shown in Fig. 10, the friction torque increases with the decreasing contact ratio. As the contact ratio decreases, the friction torques are respectively 150.8N·m, 160.4N·m, 171.8N·m and 205.7N·m at the end of slipping time. In a conclusion, when the separate plate suffers the elastic deformation, not only the circumferential and radial temperature differences will expand, but also the friction torque will increase dramatically. 4.2 Experimental results Fig. 11 shows the variations of the friction torque and surface temperature in four experimental cases. The variations of friction torque can be divided into three stages. At the stage Ⅰ, the friction torque increases rapidly with the increase of applied pressure; after the applied pressure reaches the preset value, the friction torque increases slowly, which is consistent with the variation of friction torque as shown in Fig. 8(c). It should be noted that the simulation condition is consistent with the experimental case 1. As shown in Figs. 8(c) and 11(a), at the time instant t1, the friction torques in the simulation and experiment are respectively129.2N·m and 126.6N·m; moreover, in both cases, the temperatures in the different radial directions are (55.87°C, 62.87°C, 68.11°C) and (51.81°C, 61.17°C , 67.45°C), respectively. The maximum relative error between the simulation and experimental results is 7.8%. Therefore, the numerical model has been verified by the experimental results, which can correctly and effectively evaluate

16

the clutch thermodynamic performance before the plate deformation. Consequently, the thermometric plate is in a good condition without elastic deformation at stage Ⅰ. However, a torque jump occurs at stage Ⅱ, where the friction torques in such four cases increase by 43.6N·m, 40.9N·m, 39.7N·m and 39.2N·m, respectively. Since the experimental conditions have not changed, the torque jump indicates that the contact status of mating surface has changed, which will result in the uncomfortable sensation to drivers. Accordingly, the stage Ⅱ is a transitional stage where the contact status of mating surface changes from UCS to ICS.

(a)

Case 1

(b) Case 2

17

(c) Case 3

(d) Case 4 Fig. 11. Experimental results of the friction torque and surface temperature As shown in Fig.11(a), the friction torque is 186.3N·m at the end of stage Ⅲ. Since the real contact area and position of thermometric plate are uncertain in experiments, we can only verify the plate deformation by expanding the range of contact ratio in the simulation. As shown in Fig. 10, when the contact ratio drops from 0.810 to 0.375, the friction torque rises from 150.8N·m to 205.7N·m at the end of slipping time, a range that covers the experimental torque 186.3N·m. Thus, thermometric plate has suffered the elastic deformation, and the mating surface is in ICS. At the stage Ⅲ, the variation of friction torque is different under different applied pressures. To be more specific, the friction torque increases smoothly at 0.12MPa as shown in Fig. 11(a); the friction torque remains stable at 0.14MPa as shown in Fig. 11(b) and 11(c); however, when the applied pressure increases to 0.16MPa, the friction torque decreases gradually as shown in Fig. 11(d). These phenomena can be interpreted as 18

follows. The increase of applied pressure can contribute to the increase of the local contact pressure. When the local contact pressure is appropriate, it can contribute to the increase in COF; however, if the local contact pressure is high enough, it brings about the degradation of friction material, then resulting in the decrease in COF [13, 36]. As for the clutch temperature variations in such four cases, the temperature growth rate of B increases dramatically after the time instant td, followed by A1, A2 and A3, while the growth rate of C changes slightly. The sudden increase of temperature growth rate is related to the change of the contact status of mating surface; the zone where the temperature growth rate increases is the contact zone. The temperature turning point td is in the stage Ⅱ, thus the thermometric plate is deformed at stage Ⅱ. In addition, ΔT is the circumferential temperature difference in the medial radius. The temperature difference increases gradually during the slipping period. With the increase of circumferential temperature difference, the thermal stress increases gradually and finally results in the elastic deformation [6]. To be more accurate, the circumferential temperature differences in four experimental conditions are respectively 2.17°C, 3.23°C, 2.08°C and 2.70°C at the time instant td. It suggests that the critical temperature difference of circumferential elastic deformation is around 2~3°C. After the stage Ⅱ, the circumferential temperature difference increases significantly; at the end of slipping time, they have increased to 5.81°C, 5.20°C, 4.40°C and 4.55°C, respectively.

(a) LLW type

(b) LW type

Fig.12. Static pressure distribution of the deformed plate 19

After the experiments, the thermometric plate has undergone the plastic deformation. Due to the deformation deflection of the plate is small, it is difficult to show it in pictures. Thus, the pressure test papers (Prescale) with different ranges (LLW and LW) are used to depict the static contact pressure of the deformed plate. The static pressure is applied through the press, and the applied value is 1MPa. As shown in Fig. 12(a), the red zone representing the high contact pressure area is the contact zone. In order to better observe the distribution of contact pressure, the range of Prescale is enlarged as shown in Fig. 12(b). The green and white zones are alternately distributed in the circumferential direction, where the green zone is the real contact zone. Thus, the contact pressure of the deformed plate presents a periodic distribution in the circumferential direction, and the number of periods corresponds to the number of key teeth. Indubitably, if the friction torque and temperature growth rate increase suddenly during the clutch engagement process, the friction component will suffer the elastic deformation. The appropriate elastic deformation can not only heat up the clutch rapidly to increase COF, but also provide a large friction torque to engage the clutch quickly. However, if the contact ratio is too small, it does not simply bring about the ablation and wear of the friction components, but causes the clutch hot judder and reduces the comfort of the passengers [37, 38]. That’s why the grooved friction components are widely used in the automobile industry, but matching a suitable contact ratio for the clutch has been a lasting challenge for designers and manufacturers [39, 40]. If the plate with elastic deformation is not detected in time, it is likely to evolve into the plastic deformation as the number of engagement increases. Once the plate is plastically deformed, it will be subjected to a considerable thermal load. Thus, not only the thermal environment and dynamic response of the clutch will become worse, but also the wear and degradation of friction material will be accelerated. Meanwhile, the deformed plate may break at any time, leading to the complete failure of clutch. Therefore, the conclusions can be provided as a theoretical basis for judging the real-time status of 20

friction components in the clutch on-line monitoring as well as the fault diagnosis of clutch failure.

5. Conclusion The thermodynamic differences of a multi-disc clutch before and after the elastic deformation of the separate plate were presented numerically and experimentally. In order to imitate the deformed plate, the mating surface was artificially modified into different contact ratios. Moreover, in order to induce the plate deformation more easily, the plate which had undergone the circumferential elastic deformation was taken as the thermometric plate. The main conclusions were summarized as follows. 1.

If both the friction torque and temperature growth rate increase suddenly, the separate plate is experiencing the elastic deformation definitely. Moreover, the critical circumferential temperature gradient for the elastic deformation of the plate is 2~3°C. The conclusion can be used as a theoretical basis to evaluate the realtime status of friction components.

2.

After the elastic deformation, the smaller the contact ratio of mating surface is, the higher the local temperature is, and the greater the friction torque is. Additionally, the smaller the radial length (circumferential angle) in the contact zone is, the greater the radial (circumferential) temperature difference is.

3.

After the elastic deformation, the variation of friction torque, which is dependent on the contact pressure in the contact zone, can be divided into three categories: increase smoothly, stable and decrease gradually.

Acknowledgements This work was supported by the National Natural Science Foundation of China (Grant NO. 51775045 and NO. 51975047), and the basic product innovation research project of the Ministry of Industry and Information Technology of China (JCCPCX201705). Besides, the authors would like to thank the China Scholarship Council for supporting the lead author during his research leave at Canada.

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Highlights 1.

The thermodynamic differences of a multi-disc clutch before and after the elastic deformation of the separate plate are presented numerically and experimentally.

2.

In the process of the plate elastic deformation, the friction torque and temperature growth rate increase suddenly.

3.

The critical circumferential temperature difference for the plate elastic deformation is 2~3°C.

4.

After the plate elastic deformation, the variation of friction torque can be divided into three categories: increase smoothly, stable and decrease gradually.

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