# A New Multi-Physics Coupled Method for the Temperature Field of Dry Clutch Assembly
## 1 Introduction  
Heavy-duty commercial vehicles undergo harsh operating conditions, such as high engagement frequencies, high temperatures, and high energy. Under harsh conditions, clutch slippage, burning, initial judder, and incomplete disengagement issues arise [1; 2; 3; 4], which reduce the dry clutch's torque transmission capacity and lifespan. Under the harsh conditions, a significant amount of heat is generated due to the frequent sliding friction between the friction pairs of the dry clutch. Moreover, the thermal deformation is greatly increased at high temperatures, which results in more friction heat being generated. Consequently, the sliding friction, friction-generated heat, thermal deformation, and uneven contact of the dry clutch assembly are tightly coupled [5; 6]. Since the coupling mechanism and the temperature field of the clutch are crucial for clutch design and reliability analysis, a large amount of research has paid attention to the temperature field of the clutch. [PERSON] et al. [7] used the thermo-mechanical coupling method to analyze the radial temperature distribution of the friction surface of the pressure plate under different slipping speeds. Also, [PERSON] et al. [8] performed the thermal analysis on the flywheel and clutch disc and pointed out that the deformation of the pressure plate approximately increases along the radial direction. [PERSON] et al. [9] analyzed and discussed the friction behaviorof friction discs at temperatures above 250 \({}^{\circ}\)C to 300 \({}^{\circ}\)C under three typical starting conditions. They found that factors such as contact pressure, rotational speed, and the initial temperature of the clutch affect the temperature distribution, and at high temperatures, the surface temperature distribution of the friction material is non-uniform, exhibiting hot spots. Regarding non-uniform heat distribution, [PERSON] et al. [10] found that the surface temperature distribution of the friction discs is non-uniform, and the thermal conductivity has a significant impact on temperature distribution. The operating conditions of the clutch and the thermal properties of the materials also influence the temperature distribution in the friction discs. [PERSON] et al. [11] investigated temperature distribution issues in continuously variable transmission clutches and found that the central temperature distribution of the clutch is sensitive to changes in parameters such as pressure, contact time, thermal conductivity, and heat capacity. [PERSON] et al. [12], through the exploration of temperature field distribution patterns under different clutch operating conditions, discovered that the convective heat transfer coefficients and thermal conductivity of the friction discs have a significant impact on the clutch temperature field.  
Previous research shows that although the temperature fields of the clutch pressure plate and driven plate have been studied in depth, the temperature field of the clutch assembly has not been studied comprehensively, mainly due to the complexity involved. In the meantime, most studies only investigate the temperature field for a relatively short time range of several seconds. In fact, this bidirectional coupling in the clutch assembly often lasts more than 30 s in some extreme conditions. The temperature distribution of the clutch assembly under the long-term scale time range remains unclear enough, either. An effective approach to studying the coupling field of the clutch assembly over a long-term time scale is needed for clutch performance design under harsh conditions.  
In this study, a new approach with high precision and a long time scale for modeling the temperature field of the dry clutch assembly is proposed. The temperature distribution of the \(\Phi\)430 dry clutch assembly under continuous engagement and disengagement operation conditions is conducted using this approach, and the model accuracy is validated by the rig test.