## 1 Introduction  
Dry clutch is one of the important parts of automotive transmission systems. Meanwhile, the pressure plate is one of the main components of a dry clutch. When a clutch is in operation, the torque from the engines is transmitted by the sliding of the pressure plate against the friction plate. The frictional heat introduced by the relative motion increases the temperature of the pressure plate, which normally increases the thermal stress and deformation of pressure plate, sometimes resulting in the failure of the clutch [1,2]. As the deformation of the pressure plate, especially the concave deformation of the pressure plate used for heavy duty, has an obvious relationship with the clutch slipping, it is often required that the maximum concave deformation of the pressure plate be below some specific threshold value in the clutch applications.  
[PERSON] [3] obtained the tendency relationship between the deformation of the pressure plate and the temperature during the slip period of the clutch engagement, and observed that the friction surface of pressure plate appears in \"drum\" type (internal convex) when heating and in \"dish\" type (internal concave) when cooling. [PERSON] and [PERSON] [4] et al. used the finite element method to simulate the drum type thermal deformation under the starting condition of the pressure plate. [PERSON] [5] et al. simulated the temperature field and the axial (drum) deformation of the friction surface of a heated pressure plate. Through the finite element method, [PERSON] [6] and others also obtained the \"drum-shaped\" thermal deformation of the pressure plate in the clutch engagement process.  
A two-dimensional axisymmetric model was established by [PERSON] et al., and the distribution of temperature field during the 10-times process of clutch pressure plate engagement was analyzed under the two assumptions of uniform pressure distribution and linear pressure distribution [7]; the temperature field distributions of the pressure plate under three different contact areas--100%, 75%, and 50%--between the pressure plate and the friction plate were also analyzed and compared [8]. [PERSON] et al. [9] used the thermomechanical coupling method to analyze the radial temperature distribution of the friction surface of the pressure plate under different slipping speeds. Also, [PERSON] et al. [10] performed the thermal analysis on the flywheel clutch disc, and pointed out that the deformation of pressure plate approximately increases along the radial direction. [PERSON] and [PERSON] [11,12] conducted numerical simulation of temperature field and thermal stress field under different loading conditions. [PERSON] and others [13] discussed the effect of thermal parameters and structural parameters on the temperature field and deformation field of pressure plate using the response surface method, and proposed a new structure of the pressure plate. [PERSON] and others [14] provided evidence that the concave deformation of pressure plate is not induced by the thermal buckling mechanism through thermal buckling simulation.  
It can be seen that there are few researches on the concave deformation of the pressure plate, and its mechanism is not clear yet. In this paper, a simplified model of the assembly of the pressure plate is developed, and the evolution of the deformation of the pressure plate during frictional heating and cooling is simulated by thermal mechanical coupling. The distributions of stress in the radial and axial directions of the pressure plate during these processes are obtained and the internal concave deformation is analyzed. The equivalent von Mises stress of pressure plate is compared with the results without internal concave deformation. The characteristics of the stress distribution of the pressure plate are obtained, and the critical distribution of stress causing the concave deformation of the press plate is discussed.