Nowadays any scooter is equipped by a CVT transmission. Literally CVT stands for continuos variable transmission and in fact this kind of transmission offers the possibility to vary in a continuous and automatic way the transmission ratio.
Such a device is nothing more than a progressive gearbox able to develop a continuous range, and therefore infinite, of gear ratio between a minimum and a maximum, established at the design stage. The variation of the gear ratio in this case is thus not gradual but continuous. It is as if, time by time, we have two wheels which mesh between them , but the diameter of which varies continuously as a function of the transmission ratio required to overcome the external resistances that the vehicle encounters (slopes, variations in weight and so on).
So let’s see what a Scooter variator is: generally, a scooter variator consists of two pulleys and a belt of trapezoidal type.
Each pulley is made up of two plates with a conical profile, facing each other so as to constitute a throat on which it wraps the transmission belt. Of the two plates, one is fixed while the other is free to move axially. At each displacement of the scooter variator there is a variation of the diameter of the pulley, passing from the point of maximum approach (larger diameter) to the point of maximum distance (smaller diameter). To cause such a displacement in the scooter variator, there are rollers, which due to the centrifugal force, they run inside special guides formed on the scooter variator. The variation in the diameter of the drive pulley then generates the variation of the transmission ratio and then, the elongation or the shortening of the belt, which for this, acts on the driven pulley by moving the mobile plate which is kept pressed against the fixed one, thanks to the force exerted by an adjuster spring. By varying both the rollers acting on the plate of the drive pulley, and the stiffness of the spring that presses the plates of the driven pulley, you will understand how easy it is to change the behavior of the transmission.
The aim of the project is precisely the modeling and simulation of the transmission of a modern average engine capacity scooter to understand the actual operation and the role played by the various components that constitute it.
Not having found in the various sites of the sector, a 3Dcad-model of a CVT transmissions for scooter, the first step was to model the transmission from the beginning.In order not to make the discussion too tedious, I will not explain in detail how you model the various components making up the transmission but I will just list them by attaching their images. Among the various components will not be mentioned the belt, that it will be treated in more detail in the appendix.
The first step was to create the front fixed half-pulley and the scooter variator that are then keyed to the drive shaft.
The second step was instead to create the fixed half-pulley and the torque driver which are then keyed in the driven shaft. From the point of view of the simulation what is important are the angles of the inclination of the various pulleys and therefore the torque driver and the fixed half-pulley rear coincide from the geometrical point of view.
In addition to the basic components listed above, have been modeled the limit of the adjuster spring, the axle and a wheel (model downloaded from GrabCAD Site) required to be able to assign the low inertia of the entire vehicle.
Without going further into the discussion, once assembled the various components by imposing the proper constraints, we obtain the following configuration:
First, to the drive shaft is applied the following torque variable with trend similar to a real engine:
As seen in the section concerning the modeling were not modeled the rollers. This is because the actual opening of the scooter variator due to the centrifugal force exerted by the rollers is simulated by simply applying a force (acting on the scooter variator) that varies proportionally with the square of the angular speed of the drive shaft.
Thanks to the friction force that will be born between belt and pulleys, the belt drag in rotation the driven shaft. Then, the fundamental point is the definition of the belt and the adjuster spring that will serve to counter the opening of the driven pulley.
Once correctly defined the belt and the adjuster spring , were made different analyses to understand mainly, the influence of the inclination angle of the half-pulleys and the influence of the stiffness of the adjuster spring on the working of the transmission. The data obtained from analyses carried out with Virtual.Lab, were then processed using MATLAB, obtaining the following diagrams:
By varying the inclination angle of the half-pulleys it’s seen as is strongly influenced the gear shift:
As can be seen from the diagram, smaller is the inclination angle of the half-pulleys, steeper is the half-pulleys, more rapidly changes the transmission ratio. This means that the scooter will go from a short ratio to a long quickly . Is very clear that the angle of inclination of the pulleys plays an important role. In fact, if the variation of the gear ratio is too fast, would risk not fully exploit the torque delivered by the engine. It is as if ,riding a bicycle, we shift up too fast without waiting for the achievement of the appropriate speed, and in this way, to increase the speed of the bicycle, we should apply a torque bigger than what we would have applied if we have inserted a shorter gear.
Also the stiffness of the adjuster spring plays a fundamental role and strongly influences the transmission ratio. This you can see by looking at the following two diagrams (Figure 9 and Figure 10):
As you can see from the graph we see that parity of the force exerted by the rollers, more rigid the adjuster spring is, more slowly the transmission ratio grows; not only that but also if the spring is too stiff we could not achieve the desired final gear ratio . If this happens, the scooter would never reach the desired final speed because, it is as if it remained always in gear “short”.
The spring does not have the sole purpose of countering the opening of the driven pulleys, but it also serves to get the right friction force between the belt and pulleys to transmit the motion. Anyway good rule is to use the contrast spring softer possible that is able to transmit the motion. A spring excessively rigid in fact not only causes the effects mentioned above but also absorb power from the engine to be compressed, thus obtaining a power to the wheel less than that which could be achieved by appropriately calibrating the transmission. It is clear however that the choice of the adjuster spring is closely linked to the choice of the weight of the rollers and so the calibration of a transmission is anything but a simple thing.
NOTE: As it can be seen in figure 9 (but also in the other figures) there are initially a small oscillation of the transmission ratio. This is due to the fact that the belt is not tensioned correctly at the beginning. To resolve this issue it should know the real modulus of elasticity of the belt and the initial static tension that arises when attaching the belt, on which we unfortunately don’t have data available.
From the considerations made, it is clear that parity of the force exerted by the rollers, more rigid the adjuster spring is , less you open the driven pulley and this can be seen from the graph below (figure 10).
In conclusion was also performed an analysis to see how the transmission ratio varies in function of the engine torque requested by the pilot with the throttle.
From the graph (Figure 11) it is seen how, at the same time, more we turn the throttle, and therefore more is the torque required to the engine, higher is the transmission ratio reached.
The project provides a clear view of the functioning of a CVT transmission for scooters, showing the importance that certain components have on the working. From the analysis performed with Virtual.Lab it is understood that, established the configuration of the transmission (angles and diameters of the pulleys), to get the correct calibration of the transmission, able to exploit the full power delivered by the engine, you have to find the right compromise between the weight of the rollers and the stiffness of the adjuster spring; so the two things are not independent of one another.
The most complicated part was undoubtedly the definition of the belt also because on this topic the online help offers very little explanation. This is why in the appendix will explain in more detail how you define the belt, in the hope that it will be helpful to someone.
Definition of the belt
Before defining the belt, is necessary to define the pulleys. In reality the two pulleys (driving and driven) are both composed of two half-pulleys, one fixed and the other which can slide axially along the two shafts to allow belt to move radially, and so change the gear ratio.
To define the body pulley click on:
INSERT -> POWERTRAIN SYSTEMS -> STATE EQUATION PULLEY
At this point you will see the following window (Figure 12):
Under the voice attachments we have to insert the two bodies that constitute the pulley. In our case, in fact, the pulley is constituted by two half-pulleys, one fixed and the other that can slide axially.
At this point we need to define the various geometric parameters that define the pulley and which are explained very well in the online help and then I will not elaborate further.
Once you have defined the two pulleys, being careful to number them correctly (see “Pulley Number” in the online help), it goes to the definition of the belt itself.
First, the belt is an analytical belt and therefore no body will have to be modeled.
To define the belt you have to click on:
INSERT -> POWERTRAIN SYSTEMS -> STATE EQUATION BELT
This opens the following window (Figure 13):
Firstly, for the correct working of the belt is necessary to define the mysterious “base body”. Being the belt an analytical entity, there is no “body” to represent it. With “base body”, Virtual.Lab means the reference frame in which the belt is defined, making sure that the XY plane is the working plane of the belt as shown in the figure 13.
Once the “base Body” is defined shall we specify the pulleys over which the belt runs. Next step is the definition of the various parameters that are well explained in the online help . Not all parameters must be entered: very important are the mass, the elastic modulus, the damping coefficient, the inertia and the cross-area of belt. We have also added the parameter named “Length” that indicates the length of the belt under static conditions. The help states that the program automatically calculates the length, and this is absolutely true, but we preferred to define an initial length to better control the elongation at which the belt was subject and then adjust the elastic modulus (physical data not available to us).
- it is important to define the proper working plane of the belt
- it is important to correctly numbering the pulleys on which the belt runs (in a clockwise direction starting from the drive pulley).