# Numerical Design Method for CVT Supported in Standard Variable Speed Rubber V-Belts
## 1 Introduction
The CVTs speed ratio actuation and control are given by a variety of mechanisms present on the pulleys. The actuators design has been an important matter discussed by different authors. [PERSON] [22] presents a model to design the mechanical actuators for the driver and driven pulleys, being the actuators, respectively, a centrifugal roller and a helical torque cam with a compression torsion spring. The model presented allows calculation of the torque required by the system to be kept as close as possible to that provided by the engine/motor, thus increasing efficiency. The latter mechanisms are usually installed in low-powered vehicles. Complementing the above, different authors present models, designs and control strategies of these systems that allow pulleys to be operated with higher power systems, such as electric [23; 24], hydraulic; electro-hydraulic [25; 26], and electro-mechanical actuators [27]. These systems are approached from the control of the speed ratio change, and thus guarantee better performance and efficiency [28; 29]. When analyzing the drive system, literature provides evidence that an electric motor delivers 100% of the torque when operated from rest while the efficiency curves present different topologies and values over 80% providing a better dynamic control capacity [30]. [PERSON] et al. [31] define which characteristics, such as speed range and energy efficiency, are factors influenced by system dynamics and architecture, so the selection of the drive system requires specific emphasis on both variables. Additionally, [PERSON] et al. [5] discuss in their research, that the powertrain design specifications are more straightforward for an EV compared to an ICE. The complexity of a design method for CVT lies in factors such as component selection (belt, kind of actuators, pulleys, and engine/motor), interaction with other systems, and design parameters optimization. Different authors present several models and designs of CVT systems. [PERSON] et al. [32], present the powertrain design for hybrid vehicles, implementing and analyzing the best kind of CVT for each vehicle. Herein, fuel consumption is considered as the main design objective, where the proposed solution has an average error of less than 1.6%. However, they do mention that it is difficult to find an optimal overall design solution due to the interdependence of design options regarding topology of the drive train and its implications. [PERSON] and [PERSON] [33], propose an integrated design method of an electromechanically actuated CVT and its control system, minimizing CVT mass up to 46.2%; tracking error, control effort up to 62%; and minimizing the distance between centers. However, they do not consider factors such as efficiency and control of belt slippage. The authors also mention that a vehicle powertrain is a complex dynamic system due to the mathematical complexity of its designs. Despite these proposals, some equations and approaches are complex and do not explicitly apply at a basic design level, and the methods do not address the design of the CVT from each of its components in a practical manner. Therefore, this research aims to introduce a numerical CVT design method for ICEs and EVs considering each component, using mechanical centrifugal actuators and standard rubber V-bells. The method is validated on simulations under real operation conditions. The numerical design method is presented in Section 2. The methodology developed to evaluate the veracity of the method is explained in Section 3. The example analysis and discussion are shown in Section 4. Finally, Section 5 presents the conclusions.