The Belts, Pulleys and Gears calculator contains equations related to speeds, diameters and RPMs in systems of belts, pulleys and gears. two pulley system
The Belt and Pulley Calculator has equations to calculate lengths, speeds and RPMs of pulleys and belts. The equations include the following:
A belt and pulley system is characterized by two or more pulleys in common to a belt. This allows for mechanical power, torque, and speed to be transmitted across axles. If the pulleys are of differing diameters, a mechanical advantage is realized. pulley transfer
A belt drive is analogous to that of a chain drive, however a belt sheave may be smooth (devoid of discrete interlocking members as would be found on a chain sprocket, spur gear, or timing belt) so that the mechanical advantage is approximately given by the ratio of the pitch diameter of the sheaves only, not fixed exactly by the ratio of teeth as with gears and sprockets.
A pulley is a simple machine that uses grooved wheels and a rope to raise, lower or move a load. A pulley can also be used to simply change the direction of the force you are using when lifting a load.
It is easier to lift the load as the effort you put in is less than the load. By linking lots of pulleys together to form a system you can apply the force over a much longer distance (of rope attached to the load). There are many examples of pulleys being used in everyday life. For example, everyday window blinds, elevators, wells, flag posts, raising and lowering weights in the gym amongst many other examples.
In the case of a drum-style pulley, without a groove or flanges, the pulley often is slightly convex to keep the flat belt centered. It is sometimes referred to as a crowned pulley. Though once widely used on factory line shafts, this type of pulley is still found driving the rotating brush in upright vacuum cleaners, in belt sanders and bandsaws. Agricultural tractors built up to the early 1950s generally had a belt pulley for a flat belt (which is what Belt Pulley magazine was named after). It has been replaced by other mechanisms with more flexibility in methods of use, such as power take-off and hydraulics.
Just as the diameters of gears (and, correspondingly, their number of teeth) determine a gear ratio and thus the speed increases or reductions and the mechanical advantage that they can deliver, the diameters of pulleys determine those same factors. Cone pulleys and step pulleys (which operate on the same principle, although the names tend to be applied to flat belt versions and V belt versions, respectively) are a way to provide multiple drive ratios in a belt-and-pulley system that can be shifted as needed, just as a transmission provides this function with a gear train that can be shifted. V belt step pulleys are the most common way that drill presses deliver a range of spindle speeds.
Mechanical Advantage is defined as the ratio of the output force (Load) to the input force (Effort applied).
Mechanical Advantage = Load / Effort applied
where : Load - Weight of the object. It's measured in Newtons (N).
Effort - The force that you put in. It's measured in Newtons (N).
The Ideal Mechanical Advantage is the mechanical advantage in an ideal, frictionless world.
It equals the input distance divided by output distance.
Velocity Ratio is defined as the distance travelled by the effort to the distance travelled by the load.
Velocity Ratio = Distance moved by the effort / Distance moved by the Load
where : Load (Output Distance) - The distance that the object moves up. It's measured in Metres (m).
Effort (Input Distance) - The distance that you move the rope. It's measured in Metres (m).
Efficiency is defined as the ratio of work output to work input. It's also a measure of how well a machine or device uses energy.
Efficiency = Work Output / Work Input or Mechanical Advantage / Velocity Ratio χ 100 or (Effort χ Effort Distance) / (Load χ Load Distance) χ 100%
However, no pulley will be 100% efficient because not only will there be friction in the axles but the pulleys themselves have weight (friction in the bearings) and also need energy to be lifted.
Systems of gears work in a similar fashion to pulleys and belts, two gear system except there is no belt and the gears are inter-meshed with the teeth of one gear turning the teeth of a second gear. In this case, the RPM are a function of the number of teeth on the gear. The relationship between the gears is expressed as follows:
`RPM_1 * Teeth_1 = RMP_2 * Teeth_2`
Where:
The assumption is compatible teeth in the two gears.
Gears differ from a wheel and axle in that the output gear rotates in the opposite direction of the input gear. The gear ratio is the ratio of output turns to input turns.
Gear Ratio = Output Turns / Input Turns or Input Teeth / Output Teeth
The Mechanical Advantage of a gear system is the ratio of the torques.
Mechanical Advantage = Output Teeth / Input Teeth
N/B:- The Mechanical Advantage is the inverse of the Gear Ratio.