# Numerical Design Method for CVT Supported in Standard Variable Speed Rubber V-Belts
## 3 Methodology  
To compare and validate this proposed method, three types of test are performed: (a) a measurement and characterization of all the elements and components of a commercial CVT is elaborated. The values are used as parameters in the design using the equations presented. The capacity in torque, speed ratio, and others are compared with the manufacturers' specifications. This testing is carried out on the test bench. (b) Using this method, a design for a powertrain composed of a rubber V-belt CVT and a differential reducer is presented. (c) The behavior of the designed CVT operating in an electric vehicle is simulated running a stringent route. To validate the proposed numerical design method, a computer simulation tool is developed which sequentially addresses the different steps presented. This tool solves the iterations and equations using [PERSON]'s method. For the selection of the commercial elements, a database is created taking the greatest amount of specifications that can be obtained, and then introduced into the computer simulation tool. With this application, a programming object that uses the results of the design is developed, and it performs as such in a complete vehicle model that includes other remaining objects. For the method development, some aspects were found in the literature and others had to be validated. The test bench is a device in which data from the road and the vehicle as weight of the vehicle along the road, number of random or fixed stops, and the desired cruise speed are introduced. The vehicle or powertrain is tested in the device to obtain information about torques, speeds, currents, and energy consumption. Figure 16 shows the elements that make up the vehicle and the dynamometer that allows for the acquisition of real-time data from the powertrain. Its characteristics and components are 1. Commercial CVT: Polaris, USA, sportsman 500 primary drive clutch 1996-2011; Team, USA, tied driven secondary clutch 421896, Gates, USA, 19G4006E G-force CVT belt; 2. Galoce, China, GTS100 torque sensor (150 Nm); 3. Electric motor and controller HPEVS, USA, AC20 + Curtis instruments, USA, 1238E-7621; 4. Galoce, China, Torque sensor GTS-100 torque sensor (1000 Nm); 5. Flowfit, UK, Gearbox 40-97001-3.8 gear ratio 3.8; 6. DANA SPICER, USA, 520290T-3X differential D-max gear ratio 4.3; 7. 2 Brakes load capacity 1400 Nm; 8. Wheels 255/70R17.5. These are part of a kit with various motors, gearboxes and some own made CVTs. Due to the maximum size of vehicles available, the variation of rubber V-belt CVTs is given only from a width of 32 mm until the industrial or agricultural belts with a width of 100 mm. Using this test bench, a powertrain operated simulating different torques and angular speed. Data obtained and the inferences from these test were used in order to make considerations, which were converted into algorithms or equations providing robustness to the design method and the computer tool. The design process of the gear systems was not evaluated in this analysis. The following parameters can be measured on the test bench torque and speed at the input and output of the CVT shafts: angular and linear speed at the rollers where the wheels are located; brake pressure; brake temperature; motor temperature; and voltage and current of the energy system. This data are collected by a Delta, Taiwan, PLC (DVP28 SV211T) using digital and analog signals and then analyzed in real-time in LabVIEW SP1 2019. The test bench and the powertrain can be configured with the components list in Table 2.  
The route chosen to test the vehicle's CVT (in the simulation software) has a distance of 15.704 km; a range of slopes from 4\({}^{\circ}\) to 16\({}^{\circ}\); a maximum speed of 80 km/h and an average speed of approximately 27.8 km/h, and conditions of active and passive load of 5500 N without variation over the entire route. Some of this data were collected from a previous study for a public transport vehicle that circulates every day on this same route.