# Numerical Design Method for CVT Supported in Standard Variable Speed Rubber V-Belts
## 1 Introduction  
The implementation of continuously variable transmission (CVT) systems in transport vehicles has been growing during the last decades [1, 2] due to the inherent advantages of using this type of transmission [3]. CVTs offer the option of continuously varying their speed ratio over a wide range of angular speeds, allowing for an infinite number of ratios to be obtained [4, 5]. CVT transmissions in vehicles achieve lower values of polluting gases emissions [6, 7, 8], involve smaller parts, weigh less, and allow for better energy performance when compared to gearboxes [3, 9]. These systems allow engine operation to be sustained at maximum efficiency, which improves energy consumption and enhances driving comfort either in electric vehicles (EV), internal combustion engine (ICE) vehicles, and hybrid vehicles [10, 11]. Although CVTs have relatively low local efficiency compared to traditional vehicle transmissions [5], when operating in conjunction with an engine or motor, the system's overall efficiency increases, due to CVTs operating more frequently in the regions of higher engine/motor efficiency [10, 12, 13]. The following articles present a component-based approach to address the design of this type of transmission. A taxonomic description of the most sensitive research in the field of CVT design is presented below. Certain parameters such as clamping force, slip between pulleys, torque load, and many others must be considered when designing a CVT, because the interactions between them affects the operation, efficiency, and conceptualization of the system [5, 14, 15, 16]. The belt is the main component responsible for developing and interacting with the mentioned forces. Therefore, authors such as [PERSON] et al. in [4] described a formula to easily determine the axial forces present in a rubber V-belt CVT withassumptions such as a negligible slip angle in the driven pulley active area and a constant belt tension on the driver pulley with an accuracy of 5%. Furthermore, they found that when it is desired to maintain a constant speed, the driver pulley axial force has a linear behavior against the increased system torque load. In [17], the authors compare three analytical rubber V-belt models; the Kim-Kim model, the Dittrich model, and the Cammalleri model, where the most sensitive results indicate that the Kim-Kim model describes the CVT transmission working accurately based on the experimental data. Other researchers such as [PERSON] et al. [18] developed an analytical model of metal belts behavior, in order to specify the variations on belt tension that take place when operating CVT. The study also allows the method to determine the clamping force under certain conditions, and thus determine the required pressure to prevent slippage on the belt. The efficiency of the CVT systems depends on the required clamping force values and the belt slip. Regarding the latter, in research by [19; 20] the authors use metal V-belts and argue that the belt slip depends on the driven pulley capacity to transmit torque; considering a relation between torque, clamping force, the friction coefficient between the pulleys and the belt, and the speed ratio. In the operation of the metal belts CVT system, the metal belt passes through the idle sector of the pulley, a gap is generated between the members, generating a micro-slip and thus causing a loss in the torque transmission [14]. At low speed ratios this type of belt adds power transmission to the system, but at high ratios this capacity decreases [2]. Furthermore, the efficiency of a CVT decreases against high values of clamping force [21]. In chain CVT systems, the chain pins and the pulley plates are in contact. This interaction provides the power transmission from the driver pulley to the driven pulley. This leads to impacts when the chain pins and links pass in and out of the pulleys [2]. Although the belt is an important element in the design of the CVT, there are also other crucial elements that allow the change of the speed ratio and interaction with the belt.