Retraction: A New Approach for Testing Engagement Characteristics of Clutch (J. Phys.: Conf. Ser. 1885 022027)

It has come to the attention of IOP Publishing that this article should not have reached publication because the paper contains a number of fundamental errors in the initial data, calculation, and conclusion which has led to the findings being unreliable. Consequently, this paper has been retracted by IOP Publishing. The authors agree to this retraction. Retraction published: 15 September 2021


Introduction
In developed countries and regions of automobile industry, the market share of automatic transmission is between 80% and 90% [1]. The friction behaviour of clutch strongly influences the dynamic characteristics of the entire machine. The wear and friction curve determines the service life of the clutch [2][3][4][5]. The SAE #2 test bench is the most commonly used to evaluate the friction characteristics of clutch engagement [6][7]. However, this kind of equipment belongs to large mechatronics products whose cost is expensive, manufacturing is complicated and cumbersome. In addition, the test results can only be used to verify the product performance, but can not guide product design in the early stage. As the factors mentioned above, the application of the tribology is restricted seriously in the field of engineering design. Thus, the numerical simulation method can agree well with the test results, and has great research value, which can shorten development cycles and save design cost greatly.
The clutch engagement is a fairly complicated process, which is mainly affected by such as the engagement pressure, the surface roughness of the friction plates, the friction material permeability, which are considered as major factors to establish the process model [8][9][10].
In 1970 and 1971, Wu [11][12] studied the squeezed oil film characteristics of the porous annular disk and the rotating porous annular disk respectively. Ting et al [13] modeled the engagement process of clutch with a rough and porous surface in 1975 and applied the porous elastic theory to study the boundary friction. In 1977, EI-Sherbiny and Newcomb [14] studied the engagement process of clutch with the grooves and the non-porous friction plates by adopting the finite element method, and concluded that the groove pattern had an eventful influence on the engagement process of clutch. Zagrodzki [15] studied thermodynamic phenomena during clutch engagement in 1985, and applied the finite difference method to the axisymmetric temperature field problem [16] in 1990. In 1994, Natsumeda and Miyoshi [17] carried out numerical calculation on the clutch engagement process based on the mean Reynolds equation proposed by Patir-Cheng [18]. In 1995, Berge [19][20] further studied the mathematical model of the clutch engagement process with a grooved rough surface by using the  [14] studied the clutch engagement process whose surface roughness is nonnormally distributed in 2002. Iqbal et al [22] conducted dynamically modeling and analysis on the engagement process of clutch in 2014. In 2015, Zhang Jiayuan [23] used the finite element analysis software to simulate and analyze the temperature field and stress field in the engagement process of the clutch. In 2018, Wang Yongli et al [18] studied the temperature change of friction surface of clutch by using finite element method. At present, the finite difference method or the finite element method based on the average Reynolds equation is relatively mature aimed at the basic theoretical researches on the engagement characteristics of the clutch, which can fundamentally reflect the essence of the engagement process [22]. In this paper, a method based on the finite element is used to simulate the dynamic friction characteristics of the engagement process of clutch.

Mechanism Analysis of the Engagement Process of Clutch
The clutch is submerged in an automatic transmission fluid(ATF) which acts as a lubricant and a coolant. The flywheel rotates through the bearing to drive the friction disc. The friction plates and the corresponding to steel plates are pressed against each other by means of an axial hydraulic piston to transmit a certain torque.
The schematic view of the clutch bench test rig is shown Figure 1. A set rotational speed is provided by the motor. At a certain moment (under pre-set rotational speed), the motor is powered off and the clutch begin to engage (the pressure on the axial piston is control by the computer). The out torque is measured by a torque transducer. The rotational speed of the fly wheel is measured by a magneto-resistive speed sensor. All measured signals are amplified, digitized and stored on a computer. the motor speed and the engagement pressure are controlled by this computer. Figure 1 The schematic view of the clutch bench test rig

The Mathematical Model for the Engagement Process of Clutch
From the analysis in the previous section, the engagement of the clutch can be seen as the fluid extrusion effect and the contact problem of rough surface. According to the mechanism of friction torque under the actions of pressure and rotation speed, the fluid dynamics model and rough contact model of clutch engagement are established, which can be used to calculate change rate of oil film, pressure distribution of oil film, viscous torque, rough contact torque and total clutch torque.
In view of the fluid dynamic pressure effect in the engagement for the circular dual steel plates friction, we propose a mathematical model based on the mean Reynolds equation in the cylindrical coordinates, which is improved by adopting dimensionless parameters.
In the model, some major factors are considered, such as the viscosity of lubricating oil, the angular velocity, the rotation radius and the fluid contact area. Since the derivation process is too complicated, a new simplified model of the friction torque in the fluid friction is shown in equation (1).  (1) where  , fs  and f  refer to equation (2), (3) and (4) respectively.
The viscous torque scaling parameter: where o r , i r is outer radius and inner radius of the friction plates respectively.

The Simulation and Test of the Clutch Engagement
In this section, the simulation and bench test are completed to verify model proposed, which is under the same conditions. For the convenience of illustration, we compare output torque curves with the experiment data from the SAE #2. Main input parameters in simulation shown in Table 1

The Simulation Result
The viscous torque simulation result based on formula (1) can be seen from Figure 2(a) that, when the engagement pressures are 350kPa, 300kPa, 250kPa and 200kPa, the viscous torques peak value are 69.3Nm, 66Nm, 59.4Nm and 53.9Nm, and the corresponding time are 0.12s, 0.16s, 0.19s and 0.21s, respectively. It can be implied, the larger the engagement pressure，the earlier the response time of viscous torques will appear, and the larger the viscous torque.
The rough contact torque simulation result based on formula (5) can be seen from Figure 2(b) that, when the engagement pressures are 350kPa, 300kPa, 250kPa and 200kPa, the occurrence times of rough contact torques are 0.1s, 0.115s, 0.135s and 0.162s respectively, and the change of the corresponding curve is getting slower and slower. It can be inferred, the larger the engagement pressure, the earlier the response time of the rough contact torque.
The total output torque simulation result based on formula (9) can be seen from Figure 2(c) that, when the engagement pressures are 350kPa, 300kPa, 250kPa and 200kPa, the engagement times of clutch are 0,70s, 0.78s, 0.91s and 1.06s, and the torque peak value at the lockup are 226.6Nm, 208Nm, 181.5Nm, 167.2Nm, respectively. In fact, Figure 2(c) is a superposition of Figure 2(a) and Figure 2(b). It can be inferred, the larger the engagement pressure is, the total torque will increase and the shorten the engagement time will be in terms of the whole engagement process. Furthermore, the torque peak at the lockup increases significantly, that is, the larger the engagement pressure, the severer the impact of the gear shifting.

Conclusions
In light of the simulation and experiment in the previous section, the method proposed in this paper can analyze quantitatively the dynamic engagement characteristics in each stage, which is in good agreement with the test results of SAE #2 bench . By adjusting the input parameters such as pressure supplied, viscosity of ATF, initial film thickness, the desired torque output curve can be found. Contrary to the SAE #2 bench test, the simulation method not only can save design time and material consumption, but it can reduce greatly labor intensity, which contributes to guiding product design in the early stage. However, in digital simulation, it is not convenient to obtain the input parameters such as the lubricating oil viscosity, the oil film thickness, the friction plate roughness and the friction plate permeability. Future work will thus be devoted to build the measurement system of physical properties for the simulation model.