# Analytical-Numerical Model for Temperature Prediction of a Serpentine Belt Drive System
## 1 Introduction  
The serpentine belt drive system is used in a variety of applications, especially in the auto industry (Figure 1). In this system, power is transmitted from a driver (DR) pulley to several driven (DN) pulleys through the belt. The advantages of this system are that is economical, efficient, and compact and has a good overload protection. However, an increasing number of pulleys used in high torque/speed power transmission systems are being fabricating using fiber-reinforced polymers (FRPs), resulting in an increased risk of thermal deterioration [1]. The heat from the torque/speed loss accumulates inside these components owing to the low thermal conductivity of the FRPs, which can damage the material and reduce its life expectancy [2]. To avoid thermal destruction inside the belt drive and improve the thermal fatigue life of pulley materials, a novel thermal model is required that can promptly predict the temperature distributions of the belt drives under different load cases. Moreover, this model must be independent of the component geometries because a belt drive consists of an arbitrary belt layout with many types of pulleys. Considering this aspect, this paper proposes a model to determine the temperature distribution of the belt drives. The proposed approach, similar to any general thermal analysis model, consists of two major substeps: determining the heat generation within the system, and analyzing the heat transfer among the components. The heat generation of the belt drive system is strongly related to the power loss during the operation because the power loss is converted to heat and dissipated into the environment through the surfaces of the components. Several well-developed theories and experimental research are available, focusing on the power loss of belt drive systems to improve the system efficiency. The most prevalent theory for flat and V-belt drive systems groups the losses into five main contributions: belt bending, belt radial compression, belt tension, belt shear, and belt-pulley slip [3]. The first four types of power losses occur because of the belt hysteresis, whereas the last type of power loss can be attributed to the belt frictional slippage against the pulley outer radius (OD) surfaces. [PERSON] [4] expanded this theory to a poly-V belt transmission, which involves the combination of flat and V-belts. [PERSON] [5,6] focused on the power losses owing to the belt hysteresis caused by the dynamic bending, stretching, shear, flank and radial compression of the belt rubber, and they further considered other losses such as the bearing loss [7] in the belt transmission. Another theory classified the power losses into three types: frictional sliding, belt longitudinal and lateral material hysteresis, and frictional losses owing to the engagement/disengagement of the belt at the entrance and exit from the pulleys [8]. However, another existing study indicated that the slip loss between the belt and pulley is the main cause of power loss in belt drive transmissions [9]. Furthermore, the power loss is influenced by several factors, one of which is the belt pressure on the pulley. Some authors reported on an analytical model [10] for the friction damping of round clamp band joints, which can be used to predict the energy dissipation caused by the friction contact between the joint components. The belt pressure on the pulley also leads to a change in the axial force of the pulley, and some experiments indicated that this force influences the power transmission efficiency, although this influence is not significant [11]. In addition, [PERSON] and [PERSON] [12] developed a dynamic model to predict the transmission ratio time response under different conditions of the drive pulley axial force, load torque, and engine RPM.