This project aim is simulating the behavior of “Edyson CVT”, a continuously variable transmission which uses only mechanical elements. “Edyson CVT” is a patent protected technology, created by “Pavilcu Edyson” and its “Bitraptor” property.
More information is available at the inventor website.
CVT is a gearbox that allows variations in the transmission ratio without any discontinuity in the rotation; the transmission ratio choice is theoretically boundless as it can assume any value included between the superior and the inferior limits given by the mechanism elements shape.
Actually there are many kind of commercial continuously variable transmissions, but “Edyson CVT” is a new original type of them because it uses only mechanical elements like toothed gears and sprockets even if it does not belong to the epicycloidal CVT group.
This work purposes are:
- To verify how the CVT works;
- To analyze the transmission ratio for a fixed configuration of the CVT;
- To verify if “Edyson CVT” is an omocinetic mechanism. A mechanism is omocinetic if the output velocity is constant with a given constant input velocity;
- To find the CVT efficiency measuring the power losses in the power transmission;
- To identify the CVT power fluxes and forces during the power transmission.
In the first figure the single mechanism is represented and the next figure illustrates a more complex system that is composed by two single mechanisms; the second solution is adopted to extend the boundaries of the transmission ratio reached by a single mechanism.
The input torque is applied on the shaft with number 1; this shaft is joined with the base 13 by means of a simple bearing and it’s integral with the principal gear which is fixed on the other side of the shaft.
The principal gear transmits the rotation to the pinions satellites 5; this other gears are dovetailed on lateral shafts that can rotate around the principal shaft axis by means of supports, indicated with number 6. Between this gears and the shafts are dovetailed free wheel mechanisms; this systems can prevent the rotation of the gears in one direction and allow the rotation in the opposite direction.
The end of the satellites shafts 8 are inserted in pockets of the disk 7; in this way the shafts can move only in the radial direction of the disk.
The output shaft, attached to the disk 7, is supported by the slide 10. The slide can translate on the horizontal direction, changing output shaft axis offset respect to input shaft axis. The user can easily move the slide continuously during CVT working, modifying the revolution multiplier operating. For a null slide displacement the output and input shafts result aligned while for a positive slide displacement the input-output shafts offset is greater than zero.
The extension to the description of the double mechanism geometry can be done similarly.
When an entering torque is applied to the input shaft the principal gear rotates because it’s dovetailed to this shaft. There are two possible types of motion for the system:
- If the input shaft rotates in the direction that brings in rotation the pinion satellites in the way permitted by the free wheel mechanisms, the satellites shafts rotate only about their axes and in this way the disk, and the output shaft, do not rotate.
- If the input shaft rotates in the other direction, at least one of the four pinions satellites at time is pushed to rotate around the direction locked by the free wheel mechanism but this rotation is impeded. Because the main sprocket rotates and at least one satellite gear is locked, the satellite shaft of the locked gears rotates around input shaft axis; during this movement the principal gear applies to the lateral wheels both a radial force and a tangential force respect to gears primitive circumference. The radial force is absorbed by the support and the tangential force allows the power transmission since it puts in rotation the disk, which is welded to the output shaft.
For transmitting power in continuous way at least one pinion satellite at time is locked. In the CVT configuration where the output shaft is aligned to the input shaft, all four lateral wheels are locked and transmit torque from input to output shaft. If there is input-output shafts offset, only one satellite at time transmits torque and power to the disk.
System with one pinion satellite locked:
The transmission ratio varies with the slide displacement and so with the input-output shafts offset. The “Edyson CVT” is a multiplier gearbox, so the rotational velocity of the output shaft is bigger or at least equal than the rotational velocity of the input shaft; contrariwise the output torque is always less or equal than the input torque.
The modelling problem
The multibody virtual model of “Edyson CVT” is been developed using LMS Virtual.Lab software. Simulations made on this virtual model permit to analyze the gearbox working.
The modelling purpose was to recreate all product features resumed in previous paragraphs. We chose to represent an external spur gears based CVT, thought for operating with torque of about 100÷150 Nm.
For more details about the modelling see section “The modelling problem”.
Proof of concept
For demonstrating the right working of “Edyson CVT” some simulations have been done on the virtual model. First of all these simulations have proofed that the gearbox works only if the input shaft rotates in one sense and not in the other; in this particular case the CVT works only with counterclockwise input torques.
Next the CVT is analyzed as a revolution multiplier showing that it works as expected by description: the user can choose a certain slide displacement, and can vary it continuously to reach the desired mean transmission ratio. But it is possible to observe that the transmission ratio does not rest constant even if the slide displacement does not vary. In conclusion if a constant rotational velocity or a constant input torque is imposed to the input shaft, the same entity related to the output shaft is not constant even for a constant displacement of the slide and so the mechanism is not omocinetic. Furthermore oscillations rise when the slide displacement increases and consequently for the lowest transmission ratio the rotational velocity of the output shaft has the highest variations.
The next link is to a YouTube video that demonstrates the behavior of the CVT when a constant input torque of 100 Nm is applied and then the slide displacement increases from null value to a maximum value of 25 mm.
For further information see “Proof of concept”.
The revolution multiplier transmission ratio is defined as:
It is calculated analytically developing the formulas explained in the section “Analytical cinematic model”. It’s useful to summarize the principal results obtained in this paragraph; for more information visit the previous link.
The theoretical transmission ratio is: Where: with Rm pitch radius of the principal gear, Rl pitch radius of the satellite gears, Ts is the input-output shafts offset, δ output shaft angle with respect to horizontal direction, Δ the angle which describes lateral gear position with reference to input shaft axis and with respect to horizontal direction. Because there is a small angular sliding of the free wheel mechanism in the sense ideally forbidden, considering this effect through the sliding coefficient SL, the transmission ratio becomes: with: where ωl, ωs, ωc are the rotational velocities taken in a direction parallel to shafts axis; ωl is the rotational velocity of the lateral shaft, ωs is the rotational velocity of the support and ωc is the rotational velocity of the output shaft.
In the section “Transmission ratio” numerical results of different cases with increasing input-output shafts offset are compared in terms of velocity ratio. The numerical trends are then compared with the analytical ones.
The analytic results fit quite well the numerical ones, but there is a relevant difference in the first output shaft angles, where the reference pinion satellite is being locked. In fact, in the initial locking wheel transitory, the unilateral bearing has a wide sliding in the forbidden verse which bring to power losses and to an unwanted maximum point of the transmission ratio. Then the bearing is locking gradually.
The differences between numerical and analytical model increases for increased slide displacements; this is due to greater angular velocity oscillations of the lateral shafts in the rotations about their axis and about disk axis.
Interpolating analytical and numerical results obtained for a discrete number of input-output shafts offsets, a correlations between the slide displacement and the mean transmission ratio is been found.
Most of mechanical losses recorded in virtual model simulations derive from unilateral bearings working. Mostly they are caused by small relative rotations of their rings in the sense ideally impeded by the device. These rotations happen when bearing should lock lateral shaft when it transmits power from the principal gear to the disk and the output shaft. During this phase lateral shaft is subjected to high torque, so even if its relative velocity rotation is small, the power loss is not negligible.
Giving constant TIN = 100 Nm, C = 3 m2 Kg/(rad s) and a fixed slide position with 20 mm of shafts offset, one can obtain the results reported in the image below in term of η. Efficiency trends are all qualitatively similar varying TIN and C for not null shafts offsets.
Steepest efficiency drops, which repeat 4 times in an output shaft revolution, are due to transitory period between the unlocking of one lateral shaft in the rotation about its axis and the locking of the next. In fact unilateral bearing needs some time, when loaded, to pass from free to locked configuration. In this phase it is loaded by increasing torque but its locking is progressive and this brings to a maximum in power losses; these losses decrease when the relative angular sliding reduces gradually.
Aligning input and output shafts, the revolution multiplier assumes velocity ratio τ = 1. In this case transmission working is effectively stationary in all its parts, no locking processes of unilateral bearings occur during the CVT operating so efficiency returns its maximum mean value.
For details see the “Efficiency analysis” section.
Entering power is transferred to input shaft, passes through gears transmission and exits from output shaft reduced by a mechanical efficiency. Output torque (Tout =c ωout) can also be thought as the input torque reduced by transmission ratio and the mechanical efficiency of the gearbox: The mechanical system is a revolution multiplier so the transmission ratio τ ≤ 1 and Tout is smaller at increasing output shaft offset.
Input power makes in rotation the principal gear, which is connected to other 4 lateral wheels that can revolute about themselves and about the input shaft. When output shaft is offset by input shaft, for the presence of unilateral bearings, only one wheel is locked at time to rotate rigidly (ideally) with its support around the principal shaft axis transmitting power to the disk and the output shaft. Meanwhile the other 3 wheels freely rotate around their axis and moves around the principal shaft driven by disk rotation (induced by locked wheel). The nearest to output shaft axis wheel is the one which transmits power to disk. Ideally in one output shaft revolution, every wheel transmit power for an angle of 90°, that is from -45° to +45° respect to input-output shafts interaxis direction. In reality a little transitory period exists from the total power transmission through one wheel to the next one. In this period 2 wheels transmit a partial portion of the input torque, as one can see from numerical results below, obtained setting a constant input torque of 100 Nm. Every different color line shows the value of the torque transmitted from the principal gear to a lateral gear with time (1 revolution of output shaft in about 0.284 sec).
Idealizing a stationary behavior, ignoring mechanical losses and considering only the locked wheel, an “Analytical dynamic model” was developed for explaining how torques and forces are transferred from input shaft to output shaft.
Power flow analysis
In the numerical model simulations, resistance torque is set proportional to angular velocity of output shaft through a damping coefficient: Tout = C ωout.
Because of this constraint between output torque and output velocity, setting a constant entering torque, input shaft velocity results variable in time; for the same reason setting a constant velocity of the input shaft, entering torque to move it results variable. In fact, as shown in section “Transmission ratio”, velocity ratio τ is not constant during an output shaft revolution. So, for example, fixing a constant input torque and a constant shafts offset, resistance torque Tout =Tin τ η varies with time because η but especially τ varies in time. In the same way ωout varies and so ωin.
Typical trends of gearbox efficiency with entering power, absorbed by input shaft loaded by a constant torque, Pin = Tin ωin and output power, released by output shaft to external damper, Pout = Tout ωout = C ωout2 are reported in the image below. These plots are obtained setting a constant Tin = 100 Nm, C = 3 m2 Kg/(rad s), and a shafts offset of 10 mm. The maximum power transfer develops when Tout (and so ωout and ωin ) has is maximum , when locked wheel is farthest from disk axis. In these moments η has its minimum values for the locking wheel transitory.
In the section “Power flow analysis” it is reported how torques, velocities, power exchange and efficiency vary in the CVT changing its working conditions. In particular comparisons are made varying the transmission ratio (modifying the input-output shafts offset), the input torque and the resistant torque (modifying the damping coefficient at the output shaft).
In the “Double mechanism” section, it is analyzed a more complex system that contains two single mechanisms joined properly to have the output shaft of the first mechanism welded with the input shaft of the second one. The aim of this type of solution is broadening the range of transmission ratios reachable with a fixed maximum displacement of the slide and so permitting a wider range of possible transmission ratios maintaining the same global dimensions.
The numerical model analysis permits to show advantages and disadvantages of this solution. With same slide displacements, double mechanism reaches transmission ratio values τ2 lower than τ1 typical for single mechanism. Numerical results demonstrate the theoretical relationship: So fixing the maximum input-output shafts offset, the double mechanism CVT covers a wider velocity ratio range. However, for the higher number of mechanical losses sources, the double mechanism has lower efficiency than the single mechanism, even at the same transmission ratio.
In this “Edyson CVT” analysis we have created a multibody virtual model of the gearbox for simulating the revolution multiplier working. The virtual model is been verified comparing numerical results with the analytical ones obtained by a cinematic model and by a dynamic model.
It is been demonstrated that CVT effectively works as expected: the user can choose a certain slide displacement, and can vary it continuously to reach the desired mean transmission ratio. But it is possible to observe that the transmission ratio does not rest constant even if the slide displacement does not vary: the mechanism is not omocinetic.
Then a correlation (both numerical and analytical) is been found between the gearbox configuration and the transmission ratio. Transmission ratio mean value decreases with increasing input-output shafts offset and so with higher slide displacement. Transmission ratio oscillations amplitude in an output shaft rotation are wider for increasing offsets.
“Edyson CVT” behavior is unstationary, so calculated efficiency vary in an output shaft revolution. The drops recorded in its trend are caused mainly by unilateral bearing relative sliding in the ideally impeded rotational sense during the locking phase of every pinion satellite. Efficiency decreases for low transmission ratios.
The dynamic analysis has showed that only one pinion satellite at time transmits power from the input shaft to the disk. In this phase the unilateral bearing prevents the pinion free rotation.
The “Edyson CVT” based on a double mechanism is also been modeled and analyzed. Double mechanism reaches wider velocity ratio ranges losing something in terms of efficiency.