# Integrated Thermal and Dynamic Analysis of Dry Automotive Clutch Linings
## 1 Introduction
The heat generated in the contact due to slipping leads to the development of undesired thermal stresses during the clutch engagement as kinetic energy converts into thermal energy. The generated heat is conducted away from the clutch interface by some constituents of the lining material (e.g., copper), which can be depleted with repetitive engagement and wear, thus altering the frictional characteristics which may increase the propensity to judder. This has been investigated as hot judder by some authors. For example, in the study of [PERSON] and [PERSON] [17] the temperature distribution in the friction disc, flywheel and pressure plate was calculated using thermo-elastic finite difference method in order to investigate the effect of contact area on temperature rise. They predicted temperatures of 100-120 \({}^{\circ}\)C for a single engagement and 280-300 \({}^{\circ}\)C for multiple engagements that included sliding times of up to 2 s. The model developed by [PERSON] [18] predicted the bulk and surface temperatures in good agreement with experimental data. A finite element analysis (FEA) thermal model developed by [PERSON] et al. [19] was applied to the case of ceramic clutches, showing good correlation with measurements. Unlike the work of [PERSON] and [PERSON] [17], the model included heat partitioning so that equal contact temperatures would be achieved on both frictional surfaces. [PERSON] et al. [20] also studied the thermal behavior of clutch systems, using a simple linear thermal model to predict the temperature rise in the clutch disc. Their model was based on conservation of energy applied to the friction disc and neglecting the other components of the clutch assembly such as the flywheel and the pressure plate. Their model produced results faster, from a computational viewpoint, when compared with FEA. The accuracy of their model and the predicted results are, however, unclear as no validation data were provided. Recently, [PERSON] et al. [21] developed a clutch thermal network model and used a heat partition method to determine the temperature of clutch interfaces with repeated engagements. They also showed that depletion of heat conducting elements in the friction lining material (e.g., copper) affects its frictional characteristics and affects the judder. [PERSON] and [PERSON] [22] also investigated the manner that high operational temperatures (250-300 \({}^{\circ}\)C) influence the dry automotive clutches. An FEA model was created to predict the temperature field during different maneuvers. Their FEA model predicted high temperature rises, up to 30-35 \({}^{\circ}\)C per clutch actuation. This resulted in final temperatures of up to 160-180 \({}^{\circ}\)C after a mere five consecutive engagements. These high temperatures reached can be mainly attributed to rather prolonged engagement times of 2.7 to 3.5 s.  
This paper presents a multi-degree of freedom torsional dynamic model of a rear wheel drive light truck powertrain system, integrated with an analytical thermal model of the clutch system. The dynamic model incorporates the interfacial frictional characteristics of the clutch lining material, measured through the use of a pin-on-disc tribometry. A non-linear clamp load and torque fluctuations due to engine order vibrations are also included. The clutch thermal model is based on the principle of conservation of energy, incorporating all the major components of the clutch assembly (i.e., friction disc, flywheel and pressure plate). The combination of these models is accomplished by coupling the angular velocities calculated from the dynamic model which are used as input parameters into the analytical thermal model.