# Numerical Design Method for CVT Supported in Standard Variable Speed Rubber V-Belts
## 2 Numerical Continuously Variable Transmission (CVT) Design Method
### Driver Pulley Actuators
#### 2.10.1. Ramp and Weight System Design  
The method for achieving this centrifugal force, which is nevertheless changing and has a component in the axial direction, consists of placing three weights (\(m_{\mathit{ave}}\)) on the driver pulley with the possibility of them moving radially. When the pulley is rotated, the weights will experience a centrifugal force, then the weights will be displaced in a ramp that has a variable angle such that the axial component varies, as shown in Figure 10.  
Knowing the maximum and minimum values in the change zone (Figure 8) for angular speed, displacements, forces, and speed ratio, ranges are established and divided into \(n_{\mathit{ave}}\) range differentials. In order to obtain the result, each weight's radial displacement differential is associated with the required lateral force, a centrifugal force, an angular speed, a speed ratio, and the ramp angle is to be calculated. The location of the starting point for the first ramp differential is an input parameter in the iterative method. For each iteration, the previous differential points are connected to the beginning of the next one in order to generate continuity. The result is the ramp or profile of the actuator as shown in the example in Section 4. For the ramp's design, an iterative calculation process is initiated with \(i=1\) to \(i=n_{\mathit{ave}}\) using the Equations (28)-(38) for each iteration, and considering the following:  
* The speed range in which the CVT changes from ratio \(R_{\mathit{cvt\_max}}\) to \(R_{\mathit{cvt\_min}}\) and (grey zone in Figure 8) to the maximum engine/motor speed. * The centrifugal force \(F_{\mathit{cen\_i}}\) at each speed (Figure 8, red line). * The clamping force weights value (\(F_{\mathit{c\_i\_rev\_i}}\)) required at each speed (Figure 8, orange line). \(F_{\mathit{cd\_iw\_ini}}\) and \(F_{\mathit{cd\_iw\_end}}\) are the initial and final force range. * The radial displacement \(R_{\mathit{ave\_i}}\) of the weights at each speed. \(R_{\mathit{ave\_min}}\) and \(R_{\mathit{ave\_max}}\) are the maximum and minimum radius displacement. Figure 10: Diagram of axial force (\(F_{\mathit{cd\_we}}\)) derived from the centrifugal force due to the ramp. Figure 9: Centrifugal actuation system: (**a**) ramps and roller weights, (**b**) flyweight cam. The following step is to select a starting point (\(\hat{X}_{i}\), \(\hat{Y}_{ini}\)) in the flyweight profile. This point corresponds to the initial angle \(\beta_{ini}\) of the flyweight and the initial distance of the follower \(\sigma_{full\_ini}\). Figure 8 shows the ratio change sector in the grey area. Here, initial and final speeds between which the ratio change occurs is declared. Immediately associated with each speed is the change in lateral displacement for the moving face of the driver pulley. As in the design case of centrifugal weight and ramp actuator, ranges are also declared and divided into \(n_{ave}\) range differentials. The lateral displacement of the follower center \(\sigma_{lat}\) is declared as an independent variable and the centrifugal force is calculated using the center of gravity location data, the flyweight angle \(\beta_{i}\)-1, and the initial contact point of the flyweight and the follower (\(X_{cpo}\), \(Y_{cpo}\)). The differential's inclination \(\theta_{s}\) is calculated in the flyweight profile ramp using the centrifugal force (\(F_{cm}\)) and the required clamping force (\(F_{cl}\)). If the center of gravity is located at a different site, the unusable weight should be relocated to different places where it is ensured that the center of gravity is relocated to the initially chosen point (\(X_{cg}\), \(Y_{cg}\)). This implies that the mass (\(m_{len}\)) is constant. The starting point of the ramp profile differential is linked to the endpoint of the previous iteration. In each iteration the previous differential is connected to the new one in such way that the end of the first one will coincide with the starting point of the second one.