Notes on Continuously Variable Transmissions

Continuously Variable Transmissions are transmissions that provide an uninterrupted range of speed ratios, unlike a normal transmission that provides only a few discrete ratios.

Frictional Type

The most common type of CVT is the frictional type, in which two bodies are brought into contact at points of varying distance from their axes of rotation, and allowing friction to transfer motion from one body to the other. Sometimes there is a third intermediary body, usually a wheel or belt.

The simplest CVT seems to be the "disk and wheel" design, in which a wheel rides upon the surface of a rotating disk; the wheel may be slid along it's splined axle to contact the disk at different distances from it's center. The speed ratio of such a design is simply the radius of the wheel divided by the distance from the contact point to the center of the disk.

Friction plays an important part in frictional CVT designs - the maximum torque transmissible by such a design is:

Tmax = Cf × FN × Ro

where To is the torque output, Cf is the coefficient of friction between the wheel and the disk, FN is the force pushing the wheel into the disk (normal force), and Ro is the radius of the output wheel or disk. The coefficient of friction depends on the materials used; rubber on steel is typically around 0.8 to 0.9.

Power is lost in two ways: deformation of the components; and differential slip. Deformation of the components, the larger factor of the two, is caused by high normal forces, and can be minimized by using very hard materials that do not deform much, and materials with a very high coefficient of friction. Differential slip is caused by a large contact area between the rotating components; in this example, the "footprint" of the wheel riding on the disk. The edge of the footprint closest to the axis of rotation of the disk will roll along a smaller radius than the edge furthest from the axis of rotation, causing further distortion of the wheel and the edges of the footprint to slip. Differential slip is minimized by using a hard wheel that produces a small contact area.

Very similar to the "disk and wheel" is the "cone and wheel" design, in which the disk is replaced by a cone. There is little advantage to using a cone instead of a flat disk, except to decrease the differential slip of the contact surface by minimizing the difference in the radius traveled by the inner and outer edges of the contact area. Other designs have used different shapes, but the principle remains the same.

More advanced designs used three bodies instead of two. There are two advantages to using three bodies: an increase in speed ratio range; and a simpler design. However, the range of speed ratios usually crosses unity - for example, it might range from 1:5 to 5:1 - making necessary a secondary gear sets, often a planetary set.

Almost all such designs are based on toroidal contact surfaces, an exception being the "dual cone" design, which only affords the former advantage.

The simplest toroidal CVT involves two coaxial disks bearing annular groves of a semi-circular cross section on their facing surfaces. The spacing of the disks is such that the centers of the cross sections coincide. Two or more (in patent-speak, "a plurality of") idler wheels, of a radius equal to the radius of the cross sections of the grooves, are placed between the disks such that their axes are perpendicular to, and cross, the axes of the disks.

In the image, the speed ratio is varied by rotating the wheels in opposite directions about the vertical axis (dashed arrows). When the wheels are in contact with the drive disk near the center, they must perforce contact the driven disk near the rim, resulting in a reduction in speed and an increase in torque. When they touch the drive disk near the rim, the opposite occurs. This type of transmission has the advantage that the wheels are not required to slide on a splined shaft, resulting in a simpler, stronger design.

This type of transmission was patented in the U.S. by Adiel Y. Dodge in 1935, patent number 2,164,504 (AlternaTIFF viewer required).

Just as the disk CVT evolved into the cone CVT, the toroidal CVT has evolved toward a cone-shape as well. The result is a much more compact transmission. This type is peculiar in that the speed ratio may be controlled by directly rotating the wheels, or by moving them slightly up or down, causing them to rotate and change the speed ratio on their own. This type of transmission is used in the Nissan Micra, Toyota Prius, and Audi A4.

Variable diameter pulleys are a variation in the theme. Two 20° cones face each other, with a v-belt riding between them. The distance from the center that the v-belt contacts the cones is determined by the distance between them; the further apart they are, the lower the belt rides and the smaller the pitch radius. The wider the belt is, the larger the range of available radii, so the usual 4L/A series belt is not often used in this way. Often special belts, or even chains with special contact pads on the links, are used.

Variable diameter pulleys must always come in pairs, with one increasing in radius as the other decreases, to keep the belt tight. Usually one is driven with a cam or lever, while the other is simply kept tight by a spring. Variable diameter pulleys have been used in a myriad of applications, from power tools to snowmobiles, even automobiles.

Variable diameter friction gears are very similar, only with the belt replaced by a wheel with friction surfaces along the sides of its circumference. The two wheels are moved together or apart to control the speed ratio, with the proper distance between the cones being maintained by a spring.

Electrical Type

It could easily be argued that a generator powering a motor through some kind of electronic speed control would constitute a continously variable transmission. Electrical transmissions have the advantage of great flexibility in layout, as the generator can be located at any distance or orientation with the motor. Furthermore, any excess power generated can be stored in batteries, and drawn upon when high loads are experienced. However, they are heavy and inefficient. A typical generator or motor is only 75% to 80% efficient, so compounding two results in an efficiency of only 56% to 64%. This limits their use to situations where other types of transmissions cannot be used.

Diesel locomotives and some ships use such drive trains, and more recently, "hybrid" gas-electric cars.

Hydraulic Type

A hydraulic CVT is a hydraulic pump driving a hydraulic motor, at least one of which has a variable displacement. If, for example, the pump has a variable displacement, the increasing the displacement will obviously increase the speed of the motor. If the motor has a variable displacement, then the situation is reversed; increasing the displacement will decrease the speed at which it turns, as the volume produced by the pump remains constant. Decreasing the displacement of the motor will likewise increase its speed.

This kind of transmission is used in the Honda Rubicon ATV. It consists of a hydraulic swash plate pump driving a swash plate hydraulic motor. The motor is variable displacement, achieved by controlling the angle of the swash plate.

Other Types

There must be a million ways to accomplish a continuously variable speed ratio, and many very creative minds have been at work developing new ones.

One especially unique example combines a planetary gear set with a gyroscope. The input power is divided between a planetary gear set and a gyroscope. The planetary gear set in turn divides the power between the gyroscope frame, forcing the gyroscope to precess, and the output shaft. As the gyroscope resists precession according to it's speed, at low gyroscope speeds, much of the power simply spins the gyroscope frame. However, the gyrosocope frame is arranged such that to precess, it must accelerate the gryoscope; as a result, the energy sent to the gyroscope is stored, rather than lost. This device, invented by Chris B. Hewatt, received patent 6,327,922 on November 10, 1999.

Another creative example uses a thick, flat, flexible belt running between two wheels. By pulling the belt tight against one wheel, the belt effectively increases it's radius, resulting in a change in speed ratio. Pulling the belt against the other wheel reverses the effect.