Influence of Material Parameters on the Contact Pressure Characteristics of a Multi-Disc Clutch

As an essential part of the transmission, the life of the clutch directly affects the stability of the transmission. In this paper, a finite element model and a thermodynamic numerical model of a multi-disc clutch are established to investigate the influence of material parameters on the contact pressure distribution. The pressure distribution index (PDI) is firstly proposed to evaluate the pressure difference among friction pairs. Moreover, the correctness of the numerical model is verified by the clutch static pressure experiment. The results show that increasing the elastic modulus and Poisson’s ratio of the backplate can effectively improve the uniformity of the contact pressure. However, the variations in material parameters of other clutch components can not easily smooth the pressure difference. Therefore, optimized material parameters for the clutch are proposed, where the maximum pressure and temperature differences are reduced by about 27.2% and 10.3%, respectively.


Introduction
The wet multi-disc clutch, determining the reliability and safety of the transmission, has always been pivotal in vehicle transmissions [1,2]. To extend transmission life, considerable efforts have been devoted to the failures of wet clutches, such as wear, buckling, cracks, etc. [3]. It should be noted that the friction material plays a substantial role in wear performance. Fei et al. [4] found that the friction components with high porosity could decrease the surface temperature, thus leading to the enhancement of wear resistance. Since Fe could enhance the strength and hardness of material, the wear rate decreased before increasing as the Fe content increased [5]. Yu et al. [6] investigated the wear mechanisms of copper-based and paper-based friction materials, indicating that the wear depth increased dramatically with the ambient temperature increase. Moreover, Zhao et al. [7] verified the dramatic influence of temperature on wear characteristics via pin-on-disc tests. Li et al. [8] and Zhao et al. [9] studied the thermal buckling phenomenon of clutches via sliding experiments and finite element analysis. They suggested that buckling occurred when temperature distribution was non-uniform in the radial direction. Yang et al. [10], Wu et al. [11] and Li et al. [12] investigated the clutch crack phenomenon, suggesting that cracks usually appeared near hotspots. Therefore, clutch stability is crucially affected by the temperature of friction components, and excessive temperature is a major reason for clutch failures.
Many numerical simulations and experimental demonstrations have been conducted in order to improve the clutch temperature distribution. Li et al. [13,14] established clutch heat transfer models, and revealed the influences of the density and specific heat capacity of the carbon fiber on the clutch temperature field. Reduced carbon fiber content led to an increase in porosity, which could discharge lubrication oil effectively, resulting in increase in porosity, which could discharge lubrication oil effectively, resulting in decreased surface temperature [4]. Yu et al. [15] investigated the temperature of a Cu-based clutch by proposing a thermodynamic model. Wang et al. [16] found that the friction material with the granulated carbon black had lower temperature compared to high-strength graphite. Marklund et al. [17] revealed that friction material permeability could affect clutch temperature distribution. Additionally, many factors can affect the material permeability, such as composition, temperature and operating conditions [18]. Ma et al. [19] proposed that the heat capacity of the metal matrix could also determine its temperature. The wear mechanism of Cu-based brake pads was investigated by Xiao et al. [20]. They found that some debris could be trapped between friction surfaces, then leading to a further increase in temperature. Therefore, almost every aspect of the friction materials has a significant influence on clutch temperature distribution.
In addition, the working conditions are also important in terms of temperature. Zhang et al. [21] found that increasing the working pressure, initial angular velocity and permeability of the friction discs could lead to a significant temperature increase. Mahmud et al. [22] and Kong et al. [23] investigated the clutch temperature fields with consideration for the grooves of friction discs. Zhao et al. [24] simulated clutch non-uniform contact, indicating that the surface temperature gradually increased as the contact ratio decreased. Many works illustrated that the temperature field was also directly determined by the friction materials.
However, these studies mainly focused on the failures and temperature transfer mechanism with a simplified single friction-pair model. The actual clutch structural characteristics significantly affect the contact pressure distribution difference, thus leading to uneven temperature distributions on friction components [25]. As shown in Figure 1, during the clutch engagement process, the piston together with friction components moves axially by hydraulic pressure, while the circlip in the groove of the cylinder liner restricts their axial movement; gaps between friction components are eliminated progressively, and then the sliding friction occurs. Such a circlip restraint form leads to a dramatic concentration of force in the clutch, resulting in the uneven distribution of contact pressure. Due to the limitations of the spatial arrangement of the transmission system, such a structure is widely used on heavy-duty vehicles. It is known that temperature and pressure fields have a positive correlation [26]. The influence of clutch structure on the contact pressure distribution has already been fully investigated [27,28]. However, the influence of material parameters is rarely investigated, and these possibilities remain to be explored. In this paper, a finite element model and a thermodynamic numerical model are developed with consideration for the actual structural characteristics of a multi-disc clutch. In this paper, a finite element model and a thermodynamic numerical model are developed with consideration for the actual structural characteristics of a multi-disc clutch. Static pressure experiments are conducted to verify the actual contact pressure distribution. Moreover, PDI is employed to evaluate the influence of different materials on the radial pressure distribution. Eventually, the optimized material characteristics and the corresponding temperature fields are obtained. This paper presents a wide range of possibilities for further optimizing the clutch pressure distribution characteristics by material parameters.

Contact Pressure Model
In order to study the transmission law of concentrated pressure, a semi-infinite solid cylindrical-coordinate system has been established, as shown in Figure 2. Static pressure experiments are conducted to verify the actual contact pressure distribution. Moreover, PDI is employed to evaluate the influence of different materials on the radial pressure distribution. Eventually, the optimized material characteristics and the corresponding temperature fields are obtained. This paper presents a wide range of possibilities for further optimizing the clutch pressure distribution characteristics by material parameters.

Contact Pressure Model
In order to study the transmission law of concentrated pressure, a semi-infinite solid cylindrical-coordinate system has been established, as shown in Figure 2. After applying a concentrated load at the coordinate point A(0, 0, c), the following equation can be obtained according to the force balance condition.
where Fj is the concentrated force, r is radial coordinate, and σz is pressure in the z-axis direction.
The relationship between the pressure distribution at any point B can be obtained from the Galliakin displacement function as [29] ( ) where Z is the Galliakin function and Δ is the Laplace operator.
When the concentrated pressure is applied at the point O (c = 0), the pressure distribution in each direction can be deduced as follows: After applying a concentrated load at the coordinate point A(0, 0, c), the following equation can be obtained according to the force balance condition.
where F j is the concentrated force, r is radial coordinate, and σ z is pressure in the z-axis direction.
The relationship between the pressure distribution at any point B can be obtained from the Galliakin displacement function as [29] where Z is the Galliakin function and ∆ is the Laplace operator. When the concentrated pressure is applied at the point O (c = 0), the pressure distribution in each direction can be deduced as follows: where v is Poisson's ratio, ξ = r 2 + z 2 .

Thermodynamic Numerical Model
As can be seen from Equation (3), the contact pressure remains the same in the circumferential direction. Thus, the heat transfer equation can be simplified as two-dimensional as follows: where ψ is the temperature and λ, c and ρ are the thermal conductivity, specific heat capacity and density of the friction material, respectively. The heat flux equation between the frictional pairs is: where n is the relative speed between the friction pairs. The friction coefficient is obtained from the pin disc experiment as [8]: where σ is the contact pressure and u is the friction linear velocity. The heat partition factor between the frictional pairs is expressed as [30]: where the subscripts s and f represent steel and friction discs, respectively.
The thermal boundary conditions for the friction pairs are as follows: where t presents the time, ψ 0 is the initial temperature, ψ e is the environmental temperature, and H is the thickness of the friction component. r in and r out are the inner and outer diameters, respectively; h in and h out are the convective heat transfer coefficients, respectively; q a and q b , and σ a and σ b are the heat fluxes and contact pressures at the two friction surfaces of the steel disc, respectively.

Distribution of the Initial Contact Pressure
As shown in Figure 3, a 6-friction-pair clutch finite element model is established to investigate the influence of material parameters on the contact pressure of the friction pairs. The friction disc consists of a friction core and friction linings, and the latter are bonded on both sides of the former. The piston, backplate, steel disc and circlip are usually made of 65Mn steel in heavy-duty vehicles. The actual parameters commonly used for friction components are shown in Table 1. In addition, the contact pair between the backplate and the steel disc is defined as S C , and the others are labeled as S 1 , S 2 , . . . , S 6 . The steel discs are numbered 1, 2, 3, 4 from the piston side to the circlip side. In operation, the circlip is retained and the loading pressure is 100 kPa on the piston. The initial material and structural parameters used in the simulations are presented in Table 1. In order to reveal the influence of material parameters on the contact pressure distribution, the initial EM and PR of steel are set to 160 GPa and 0.29 in the following simulations.
bonded on both sides of the former. The piston, backplate, steel disc and circlip are usually made of 65Mn steel in heavy-duty vehicles. The actual parameters commonly used for friction components are shown in Table 1. In addition, the contact pair between the backplate and the steel disc is defined as SC, and the others are labeled as S1, S2, ..., S6. The steel discs are numbered 1, 2, 3, 4 from the piston side to the circlip side. In operation, the circlip is retained and the loading pressure is 100 kPa on the piston. The initial material and structural parameters used in the simulations are presented in Table 1. In order to reveal the influence of material parameters on the contact pressure distribution, the initial EM and PR of steel are set to 160 GPa and 0.29 in the following simulations.    Figure 4 shows the contact pressure distribution of each friction pair. According to the pressure clouds, it is known that the circlip leads to a progressive increase in the contact pressure along the radial direction. The radial pressure distribution is becoming smoother and smoother from S 6 to S 1 . Thus, except for S C , the most significant and smoothest radial contact pressure differences respectively appear in S 6 and S 1 , where the pressure differences respectively reach 272 kPa and 93 kPa. The maximum pressure is reduced from 361 kPa in S C to 162 kPa in S 1 , and the minimum pressure is increased from 32 kPa in S C to 69 kPa in S 1 .   Figure 4 shows the contact pressure distribution of each friction pair. According to the pressure clouds, it is known that the circlip leads to a progressive increase in the contact pressure along the radial direction. The radial pressure distribution is becoming smoother and smoother from S6 to S1. Thus, except for SC, the most significant and smoothest radial contact pressure differences respectively appear in S6 and S1, where the pressure differences respectively reach 272 kPa and 93 kPa. The maximum pressure is reduced from 361 kPa in SC to 162 kPa in S1, and the minimum pressure is increased from 32 kPa in SC to 69 kPa in S1.  Figure 5 shows the radial pressure distribution of the clutch friction pairs under initial material conditions. Due to the difference of radial pressure, it is divided into two parts, namely, the pressure smoothing area A and the pressure concentration area B. In area A, the pressure is less than 75 kPa with little fluctuation. In area B, pressure increases rapidly from 75 kPa to 350 kPa. The pressure distribution index (PDI), k1 and k2 (kPa/mm) are employed to evaluate the uniformity of the contact pressure in areas A and B, respec-  namely, the pressure smoothing area A and the pressure concentration area B. In area A, the pressure is less than 75 kPa with little fluctuation. In area B, pressure increases rapidly from 75 kPa to 350 kPa. The pressure distribution index (PDI), k 1 and k 2 (kPa/mm) are employed to evaluate the uniformity of the contact pressure in areas A and B, respectively. The PDI is derived from Equation (10) k (1,2)

Effect of Material Parameters on the Contact Pressure
In order to evaluate the influence of material parameters on the clutch pressure distribution, the elastic modulus (EM) and Poisson's ratio (PR) of the friction components are changed to simulate different materials.

Elastic Modulus
The EMs of the steel discs, backplate and circlip are set to three levels: 160 GPa, 210 GPa and 260 GPa, respectively. Similarly, the EM of friction linings is set to 1600 MPa, 2260 MPa and 2700 MPa. As shown in Figure 6, the variations in the EMs of the steel discs, friction linings and circlip have little effect on the radial pressure distribution. However, the variation in the backplate EM can significantly affect the radial pressure distribution.

Effect of Material Parameters on the Contact Pressure
In order to evaluate the influence of material parameters on the clutch pressure distribution, the elastic modulus (EM) and Poisson's ratio (PR) of the friction components are changed to simulate different materials.

Elastic Modulus
The EMs of the steel discs, backplate and circlip are set to three levels: 160 GPa, 210 GPa and 260 GPa, respectively. Similarly, the EM of friction linings is set to 1600 MPa, 2260 MPa and 2700 MPa. As shown in Figure 6, the variations in the EMs of the steel discs, friction linings and circlip have little effect on the radial pressure distribution. However, the variation in the backplate EM can significantly affect the radial pressure distribution.
With the backplate EM increases, the pressure in the radial area between 115 mm and 125 mm is reduced significantly. To be exact, the maximum pressure is reduced from 361 kPa to 300 kPa in S C , whereas the contact pressure in S 1 is only reduced by 4 kPa. Thus, from S C to S 1 , the maximum pressure reduction rate slowly decreases.
Apart from S C , variations in material parameters have the most notable effect at S 6 , and the largest pressure difference also appears at S 6 . Figure 7 illustrates that the changes in backplate EM contribute to the slight pressure decrease in area A. As the backplate EM is increasing, the PDI k 1 are 0.46, 0.45 and 0.46, respectively. However, increasing the backplate EM can substantially smooth the pressure distribution in area B, where the k 2 are 14.56, 12.45 and 11.07, respectively.

Elastic Modulus
The EMs of the steel discs, backplate and circlip are set to three levels: 160 GPa, 210 GPa and 260 GPa, respectively. Similarly, the EM of friction linings is set to 1600 MPa, 2260 MPa and 2700 MPa. As shown in Figure 6, the variations in the EMs of the steel discs, friction linings and circlip have little effect on the radial pressure distribution. However, the variation in the backplate EM can significantly affect the radial pressure distribution.  With the backplate EM increases, the pressure in the radial area between 115 mm and 125 mm is reduced significantly. To be exact, the maximum pressure is reduced from 361 kPa to 300 kPa in SC, whereas the contact pressure in S1 is only reduced by 4 kPa. Thus, from SC to S1, the maximum pressure reduction rate slowly decreases.
Apart from SC, variations in material parameters have the most notable effect at S6, and the largest pressure difference also appears at S6. Figure 7 illustrates that the changes in backplate EM contribute to the slight pressure decrease in area A. As the backplate EM is increasing, the PDI k1 are 0.46, 0.45 and 0.46, respectively. However, increasing the backplate EM can substantially smooth the pressure distribution in area B, where the k2 are 14.56, 12.45 and 11.07, respectively.

Poisson's Ratio
The PRs of the steel discs, backplate and circlip are respectively set to 0.09, 0.19 and 0.29, and the PRs of the friction linings are 0.19, 0.29 and 0.39. Figure 8c,d illustrate that the changes in the PRs of the circlip and the friction linings have a slight influence on the contact pressure variation. As shown in Figure 8a, varying the PR of the steel discs produces only a weak effect on the pressure values at the inner and outer diameter. As shown in Figure 8b, with the drop in the backplate PR, the pressures in the inner and outer diameter increase radically, by 256 kPa and 214 kPa in SC, respectively, while from 95 mm to 115 mm in radial position, the pressure becomes lower and lower.

Poisson's Ratio
The PRs of the steel discs, backplate and circlip are respectively set to 0.09, 0.19 and 0.29, and the PRs of the friction linings are 0.19, 0.29 and 0.39. Figure 8c,d illustrate that the changes in the PRs of the circlip and the friction linings have a slight influence on the contact pressure variation. As shown in Figure 8a, varying the PR of the steel discs produces only a weak effect on the pressure values at the inner and outer diameter. As shown in Figure 8b, with the drop in the backplate PR, the pressures in the inner and outer diameter increase radically, by 256 kPa and 214 kPa in S C , respectively, while from 95 mm to 115 mm in radial position, the pressure becomes lower and lower. As shown in Figure 9, when the backplate PR is 0.09, the S6 pressure decreases from 575 kPa to 8 kPa in area A; however, the pressure increases from 8 to 288 kPa in area B. As the PR increases, the PDI k1 are respectively −7.03, −3.04 and 0.46, while k2 are 22.51, 18.59 and 14.56. Therefore, the pressure distribution in S6 becomes more uneven with the increase in the backplate PR. Similarly, when the PR of steel discs changes to 0.09 and 0.19, the k1 values in S6 are respectively 2.04 and 1.61, and the k2 values are 11.63 and 13.15. It can be seen that the pressure distribution becomes smoother with the decrease in the PR of steel discs. The effect of material parameters of steel discs on the contact pressure is weaker than that of the backplate. As shown in Figure 9, when the backplate PR is 0.09, the S 6 pressure decreases from 575 kPa to 8 kPa in area A; however, the pressure increases from 8 to 288 kPa in area B. As the PR increases, the PDI k 1 are respectively −7.03, −3.04 and 0.46, while k 2 are 22.51, 18.59 and 14.56. Therefore, the pressure distribution in S 6 becomes more uneven with the increase in the backplate PR. As shown in Figure 9, when the backplate PR is 0.09, the S6 pressure decreases from 575 kPa to 8 kPa in area A; however, the pressure increases from 8 to 288 kPa in area B. As the PR increases, the PDI k1 are respectively −7.03, −3.04 and 0.46, while k2 are 22.51, 18.59 and 14.56. Therefore, the pressure distribution in S6 becomes more uneven with the increase in the backplate PR. Similarly, when the PR of steel discs changes to 0.09 and 0.19, the k1 values in S6 are respectively 2.04 and 1.61, and the k2 values are 11.63 and 13.15. It can be seen that the pressure distribution becomes smoother with the decrease in the PR of steel discs. The effect of material parameters of steel discs on the contact pressure is weaker than that of the backplate. Similarly, when the PR of steel discs changes to 0.09 and 0.19, the k 1 values in S 6 are respectively 2.04 and 1.61, and the k 2 values are 11.63 and 13.15. It can be seen that the pressure distribution becomes smoother with the decrease in the PR of steel discs. The effect of material parameters of steel discs on the contact pressure is weaker than that of the backplate.

Optimization of Material Parameters
As the radial pressure difference of steel disc 4 is the greatest among these steel discs, it has the shortest service life [28]. Consequently, S 6 is selected to evaluate the influence of material parameters on pressure difference, as shown in Table 2 via PDI. The smaller the k 3 is, the smaller the radial pressure difference is. Increasing EM and PR of the backplate and reducing PR of the steel discs can reduce the radial pressure difference of S 6 . The optimum operating conditions are achieved when the EM and PR of the backplate are 260 GPa and 0.29, and those of the steel discs are 160 GPa and 0.09. As shown in Figure 10, under the optimized working conditions, the radial pressure differences of S 6 and S 1 are reduced to 198 kPa and 63 kPa, respectively. The maximum pressure is reduced by 74 kPa, about 27.2%. The k 1 of S 6 changes from 0.46 to 2.58, and k 2 is reduced from 14.56 to 8.48, contributing to a significant improvement in radial pressure distribution.

Optimization of Material Parameters
As the radial pressure difference of steel disc 4 is the greatest among these steel it has the shortest service life [28]. Consequently, S6 is selected to evaluate the influe material parameters on pressure difference, as shown in Table 2 via PDI. The smaller the k3 is, the smaller the radial pressure difference is. Increasing EM PR of the backplate and reducing PR of the steel discs can reduce the radial pressur ference of S6. The optimum operating conditions are achieved when the EM and PR backplate are 260 GPa and 0.29, and those of the steel discs are 160 GPa and 0.09. As s in Figure 10, under the optimized working conditions, the radial pressure differen S6 and S1 are reduced to 198 kPa and 63 kPa, respectively. The maximum pressure duced by 74 kPa, about 27.2%. The k1 of S6 changes from 0.46 to 2.58, and k2 is red from 14.56 to 8.48, contributing to a significant improvement in radial pressure dis tion.

Test Rig
The test rig (Nantong YG132-40), as shown in Figure 11, was employed to veri clutch contact pressure distribution. More precisely, it was connected with the cont via a hydraulic circuit. The clutch pack was placed on the commodity shelf accord the simulation. Fuji pressure test paper was used to measure the contact pressure d bution in the experiment. The paper type was LW, with a pressure range from 2.5 M 10 MPa. In addition, the FPD8010E analysis software was used to obtain the actual sure values from the pressure test paper. Meanwhile, to highlight the effect of ma parameters, 304# steel and aluminum alloys were used in the following tests. The EM

Test Rig
The test rig (Nantong YG132-40), as shown in Figure 11, was employed to verify the clutch contact pressure distribution. More precisely, it was connected with the controller via a hydraulic circuit. The clutch pack was placed on the commodity shelf according to the simulation. Fuji pressure test paper was used to measure the contact pressure distribution in the experiment. The paper type was LW, with a pressure range from 2.5 MPa to 10 MPa. In addition, the FPD8010E analysis software was used to obtain the actual pressure values from the pressure test paper. Meanwhile, to highlight the effect of material parameters, 304# steel and aluminum alloys were used in the following tests. The EM and PR of aluminum alloy and 304# steel were 68.9 GPa and 194.02 GPa, and 0.33 and 0.3, respectively, and the piston pressure was set to 6 MPa. PR of aluminum alloy and 304# steel were 68.9 GPa and 194.02 GPa, and 0.33 and 0.3, respectively, and the piston pressure was set to 6 MPa. Figure 11. Test rig and samples.

Test Results and Discussion
Numerous repeated experiments were conducted and the corresponding results were highly consistent. Due to the fact that the pressure values remained unchanged in circumferential directions, a 60° sector area was chosen for analysis. Figure 12a shows the pressure of SC, S6 and S1 in the LW paper for the initial material parameters; the values were extracted as shown in Figure 12b. Taking the area where pressure is greater than 2.5 MPa as the concentration area, the area widths of S6, S4 and S1 were 11.5 mm, 14 mm and 18 mm, respectively. Due to the limitations of the test paper range, the maximum values could not be accurately reflected. Nevertheless, the expansion of the concentration area could also prove that the pressure distribution in S1 was far smoother than that in S6. According to the circlip restriction, the large concentrated force exacerbated the radial pressure difference on all friction surfaces. Moreover, the radial pressure difference was also obvious even at S1. Such a problem seriously affects the service life of the clutch. The material of the backplate was replaced with the 304# steel and aluminum alloy. Since the PRs of 304# steel and aluminum alloy are almost the same, Figure 13a illustrates that the concentration area expands as the EM increases. As shown in Figure 13b, the concentration areas of 304# steel and aluminum alloy were 11.5 mm and 9.5 mm, respectively.

Test Results and Discussion
Numerous repeated experiments were conducted and the corresponding results were highly consistent. Due to the fact that the pressure values remained unchanged in circumferential directions, a 60 • sector area was chosen for analysis. Figure 12a shows the pressure of S C , S 6 and S 1 in the LW paper for the initial material parameters; the values were extracted as shown in Figure 12b. Taking the area where pressure is greater than 2.5 MPa as the concentration area, the area widths of S 6 , S 4 and S 1 were 11.5 mm, 14 mm and 18 mm, respectively. Due to the limitations of the test paper range, the maximum values could not be accurately reflected. Nevertheless, the expansion of the concentration area could also prove that the pressure distribution in S 1 was far smoother than that in S 6 . According to the circlip restriction, the large concentrated force exacerbated the radial pressure difference on all friction surfaces. Moreover, the radial pressure difference was also obvious even at S 1 . Such a problem seriously affects the service life of the clutch. PR of aluminum alloy and 304# steel were 68.9 GPa and 194.02 GPa, and 0.33 and 0.3, respectively, and the piston pressure was set to 6 MPa. Figure 11. Test rig and samples.

Test Results and Discussion
Numerous repeated experiments were conducted and the corresponding results were highly consistent. Due to the fact that the pressure values remained unchanged in circumferential directions, a 60° sector area was chosen for analysis. Figure 12a shows the pressure of SC, S6 and S1 in the LW paper for the initial material parameters; the values were extracted as shown in Figure 12b. Taking the area where pressure is greater than 2.5 MPa as the concentration area, the area widths of S6, S4 and S1 were 11.5 mm, 14 mm and 18 mm, respectively. Due to the limitations of the test paper range, the maximum values could not be accurately reflected. Nevertheless, the expansion of the concentration area could also prove that the pressure distribution in S1 was far smoother than that in S6. According to the circlip restriction, the large concentrated force exacerbated the radial pressure difference on all friction surfaces. Moreover, the radial pressure difference was also obvious even at S1. Such a problem seriously affects the service life of the clutch. The material of the backplate was replaced with the 304# steel and aluminum alloy. Since the PRs of 304# steel and aluminum alloy are almost the same, Figure 13a illustrates that the concentration area expands as the EM increases. As shown in Figure 13b, the concentration areas of 304# steel and aluminum alloy were 11.5 mm and 9.5 mm, respectively. The material of the backplate was replaced with the 304# steel and aluminum alloy. Since the PRs of 304# steel and aluminum alloy are almost the same, Figure 13a illustrates that the concentration area expands as the EM increases. As shown in Figure 13b, the concentration areas of 304# steel and aluminum alloy were 11.5 mm and 9.5 mm, respectively. As was found, the pressure increased more evenly in 304# steel. Increasing the backplate EM could significantly reduce the difference in pressure distribution. The result was in great agreement with the simulation. Since the friction did not occur on the backplate, many factors, such as wear, did not need to be considered in the selection of the backplate materials; additionally, changes in backplate materials had little influence on the clutch structure. This indicates that materials with high hardness can be used for the backplate, e.g., ceramic materials, composite materials, or new materials in the near future.
Materials 2021, 14, x FOR PEER REVIEW 12 of 15 As was found, the pressure increased more evenly in 304# steel. Increasing the backplate EM could significantly reduce the difference in pressure distribution. The result was in great agreement with the simulation. Since the friction did not occur on the backplate, many factors, such as wear, did not need to be considered in the selection of the backplate materials; additionally, changes in backplate materials had little influence on the clutch structure. This indicates that materials with high hardness can be used for the backplate, e.g., ceramic materials, composite materials, or new materials in the near future.  Figure 14a shows the pressure distribution of S6 on LW test paper with different circlip materials. As the material parameters of the circlip changed, the pressure curve was almost identical and the pressure distribution remained unchanged. Therefore, changes in the circlip material did not affect the clutch pressure distribution, which is consistent with the simulation results. From the simulations and experiments above, changes in the backplate material have a much greater effect on the clutch pressure difference than any other components' materials. When loading the piston pressure, the circlip restriction leads to a dramatic concentration of pressure, which causes the deformation of the backplate. The increases in EM and PR can reduce the deformation, thus contributing to a smoother pressure transfer to the friction pairs. Since the backplate directly contacts with the circlip, the inhomogeneity of the concentrated force on the backplate is greater than that on the steel and friction discs. Thus, changing the material parameters of the backplate is the most efficient approach.  Figure 14a shows the pressure distribution of S 6 on LW test paper with different circlip materials. As the material parameters of the circlip changed, the pressure curve was almost identical and the pressure distribution remained unchanged. Therefore, changes in the circlip material did not affect the clutch pressure distribution, which is consistent with the simulation results. As was found, the pressure increased more evenly in 304# steel. Increasing the backplate EM could significantly reduce the difference in pressure distribution. The result was in great agreement with the simulation. Since the friction did not occur on the backplate, many factors, such as wear, did not need to be considered in the selection of the backplate materials; additionally, changes in backplate materials had little influence on the clutch structure. This indicates that materials with high hardness can be used for the backplate, e.g., ceramic materials, composite materials, or new materials in the near future.  Figure 14a shows the pressure distribution of S6 on LW test paper with different circlip materials. As the material parameters of the circlip changed, the pressure curve was almost identical and the pressure distribution remained unchanged. Therefore, changes in the circlip material did not affect the clutch pressure distribution, which is consistent with the simulation results. From the simulations and experiments above, changes in the backplate material have a much greater effect on the clutch pressure difference than any other components' materials. When loading the piston pressure, the circlip restriction leads to a dramatic concentration of pressure, which causes the deformation of the backplate. The increases in EM and PR can reduce the deformation, thus contributing to a smoother pressure transfer to the friction pairs. Since the backplate directly contacts with the circlip, the inhomogeneity of the concentrated force on the backplate is greater than that on the steel and friction discs. Thus, changing the material parameters of the backplate is the most efficient approach. From the simulations and experiments above, changes in the backplate material have a much greater effect on the clutch pressure difference than any other components' materials. When loading the piston pressure, the circlip restriction leads to a dramatic concentration of pressure, which causes the deformation of the backplate. The increases in EM and PR can reduce the deformation, thus contributing to a smoother pressure transfer to the friction pairs. Since the backplate directly contacts with the circlip, the inhomogeneity of the concentrated force on the backplate is greater than that on the steel and friction discs. Thus, changing the material parameters of the backplate is the most efficient approach.

Temperature Field Comparison
To investigate the clutch temperature field under the optimized conditions, the clutch was operated under long-time slipping conditions: piston pressure 0.1 MPa, ambient temperature 40 • C, relative speed 300 r/min and slipping time 5 s. The contact pressure distribution in Figure 5 was used as the initial pressure in the temperature simulation.
As shown in Figure 15, the temperature at the outer diameter was much greater than that at the inner diameter. The temperatures of steel disc 1 and steel disc 4 were crucially lower than any other friction pairs. This was because no friction motion occurs on the backplate side and the piston side. Therefore, steel disc 3 had the largest radial temperature difference of 79.4 • C and a maximum temperature of 135.3 • C.

Temperature Field Comparison
To investigate the clutch temperature field under the optimized conditions, the clutch was operated under long-time slipping conditions: piston pressure 0.1 MPa, ambient temperature 40 °C, relative speed 300 r/min and slipping time 5 s. The contact pressure distribution in Figure 5 was used as the initial pressure in the temperature simulation.
As shown in Figure 15, the temperature at the outer diameter was much greater than that at the inner diameter. The temperatures of steel disc 1 and steel disc 4 were crucially lower than any other friction pairs. This was because no friction motion occurs on the backplate side and the piston side. Therefore, steel disc 3 had the largest radial temperature difference of 79.4°C and a maximum temperature of 135.3 °C. As shown in Figure 16, there was a significant temperature drop in the optimized condition. Similarly, steel disc 3 had the largest radial temperature difference of 64.5 °C and a maximum steel disc temperature of 121.3 °C, roughly a 10.3% reduction. After changing the material parameters of the backplate and steel discs, the clutch pressure was more evenly distributed. Since the heat flow density has a positive relationship with the contact pressure, the temperature distribution was much more uniform with the increasing uniformity of contact pressure.  As shown in Figure 16, there was a significant temperature drop in the optimized condition. Similarly, steel disc 3 had the largest radial temperature difference of 64.5 • C and a maximum steel disc temperature of 121.3 • C, roughly a 10.3% reduction. After changing the material parameters of the backplate and steel discs, the clutch pressure was more evenly distributed. Since the heat flow density has a positive relationship with the contact pressure, the temperature distribution was much more uniform with the increasing uniformity of contact pressure.

Temperature Field Comparison
To investigate the clutch temperature field under the optimized conditions, the clutch was operated under long-time slipping conditions: piston pressure 0.1 MPa, ambient temperature 40 °C, relative speed 300 r/min and slipping time 5 s. The contact pressure distribution in Figure 5 was used as the initial pressure in the temperature simulation.
As shown in Figure 15, the temperature at the outer diameter was much greater than that at the inner diameter. The temperatures of steel disc 1 and steel disc 4 were crucially lower than any other friction pairs. This was because no friction motion occurs on the backplate side and the piston side. Therefore, steel disc 3 had the largest radial temperature difference of 79.4°C and a maximum temperature of 135.3 °C. As shown in Figure 16, there was a significant temperature drop in the optimized condition. Similarly, steel disc 3 had the largest radial temperature difference of 64.5 °C and a maximum steel disc temperature of 121.3 °C, roughly a 10.3% reduction. After changing the material parameters of the backplate and steel discs, the clutch pressure was more evenly distributed. Since the heat flow density has a positive relationship with the contact pressure, the temperature distribution was much more uniform with the increasing uniformity of contact pressure.