Pfeifer Industries :: Power Transmission Applications

Power Transmission Fundamentals

Horsepower / Kilowatt

Horsepower / Kilowatt

Horsepower (HP):
Quantity one (1) HP is the rate of work required to raise 33,000 pounds one (1) foot in one (1) minute

Kilowatt (KW):
Quantity one (1) KW is the rate of work required to raise 11,163 kilograms 0.305 meter in one (1) minute

Note: It is important to realize that when you increase or decrease speed (RPM), horsepower also increases or decreases proportionately. HOWEVER, torque always remains constant.

Conversions:
HP =	4KW x 1.31
KW =	HP x 0.7457
ft-lb =	Nm x 0.737562
in-lb =	Nm x 8.85
Nm =	ft-lb x 1.356
Nm =	in-lb x 0.113
ft-lb/sec =	HP x 550

Torque

Torque

Torque:
The twisting or turning effort around a shaft tending to cause rotation. Torque is determined by multiplying the applied force by the distance from the point where force is applied to the shaft center. It is measured in terms of pounds, or ounces; acting on a lever arm, measured in terms of feet or inches (Metric = Newton Meters (Nm). This lever arm is connected to a shaft that can rotate.

Torque (ft-lb) = Force x Distance

Note: Torque can be present at zero (0) rpm, in which case the horsepower would be zero (0).

Full-Load Torque:
Full-load torque is the torque to produce the rated power at full speed of the motor.

Note: Ratios, whether by gears, belts, chain and sprockets or anything else, are usually thought of as speed reducers, or less often, as speed increasers. They should be thought of more in terms of what they do to torque. A speed reducer is a torque increaser and vice versa. The laws of physics dictate that a change of speed via a ratio, proportionally changes the torque, as a factor of the ratio. Disregarding the friction in the system, the torque is multiplied or divided as a factor of the ratio. Thus a 5:1 speed reduction ratio, multiplies the input torque five (5) times (a MECHANICAL ADVANTAGE) and 1:5 speed increasing ratio would reduce the torque 5 times (a MECHANICAL DISADVANTAGE).

Conversions:
HP =	KW x 1.341
KW =	HP x 0.7457
ft-lb =	Nm x 0.737562
in-lb =	Nm x 8.85
Nm =	ft-lb x 1.356
Nm =	in-lb x 0.113
ft-lb/sec =	HP x 550

Horsepower / RPM / Torque Relationship

Horsepower / RPM / Torque Relationship

Note: It is important to realize that when you increase or decrease speed (RPM), horsepower also increases or decreases proportionately. HOWEVER, torque always remains constant.

Note: Ratios, whether by gears, belts, chain and sprockets or anything else, are usually thought of as speed reducers, or less often, as speed increasers. They should be thought of more in terms of what they do to torque. A speed reducer is a torque increaser and vice versa. The laws of physics dictate that a change of speed via a ratio, proportionally changes the torque, as a factor of the ratio. Disregarding the friction in the system, the torque is multiplied or divided as a factor of the ratio. Thus a 5:1 speed reduction ratio, multiplies the input torque five (5) times (a MECHANICAL ADVANTAGE) and 1:5 speed increasing ratio would reduce the torque 5 times (a MECHANICAL DISADVANTAGE).

Circumference

One of the most common basic geometric figures used when designing a power transmission component (pulley, sprocket, gear, etc) is the circle. The circle is the geometrical shape on which the entire power transmission process is based. In simple terms circumference is defined as the distance around the edge of a circle.

An effortless method of obtaining this dimension is by measuring the exact length of string needed to go around the circle. To calculate a circle’s circumference, we must know that the ratio between the circumference and the diameter is a constant. This constant is named Pi Π. Its value is 3.14159……..

Calculating the circumference of a circle with a diameter of 1.27” you would get 4” (3.141159 x 1.27” = 4”). Again thinking of it as a piece of string needed to go around the outside edge of a circle that string would be 4” laid end to end.

Gear Ratios

Understanding the concept of a gear ratio is easy if you understand the concept of the circumference of a circle. Keep in mind that the circumference of a circle is equal to the diameter of the circle multiplied by Pi (Pi is equal to 3.14159...). Therefore, if you have a circle or a gear with a diameter of 1” inch, the circumference of that circle is 3.14159” inches.

Expanding on the concept of circumference, let’s say you have a circle whose diameter is 1.27”. The circumference of this circle would be 4” inches (3.141159 x 1.27” = 4”). Let's say that you have another circle whose diameter is 0.635” inches (1.27” inches / 2 = .0635”) with a circumference of 2” inches (3.141159 x .635” = 2”). You'll find that, because its diameter is half of the 1.27” inch circles, it has to complete two full rotations to cover the same 4” inch circumference. This explains why two gears, one half as big as the other, have a gear ratio of 2:1. The smaller gear has to rotate twice to cover the same distance covered when the larger gear rotates once.

This leads us into talking about ratios in terms of gears (gear ratios). Gear teeth are proportional to the circumference of the gear wheel (the bigger the wheel the more teeth it has). Gear ratios can also be expressed as the relationship between the circumferences of both wheels (where d is the diameter of the smaller input gear (driver) and D is the diameter of the larger output gear (driven)).

Counting the teeth calculates the exact gear ratio, regardless of any variations in the diameter measurement. As long as the gear teeth remain meshed, the counting of teeth and revolutions will remain perfect.

Pitch diameter measurements are useful for determining approximate gear ratios for non-gear linkages such as V-Belt pulleys and belts. Smooth belts can slip, so even if exact pulley diameters are known, the gear ratio may vary in operation, and may even depend on the load.

Note: V-Belt pulley ratios are calculated by dividing the pitch diameters

Timing belt pulleys coupled with timing belts have teeth that behave just like meshing gear teeth and exact counting of teeth and revolutions can be applied with these machines. Chain sprockets coupled with chains work exactly the same way.

In order to calculate gear ratios you just count the number of teeth in the two gears and divide.

Note: Typically you are dividing the larger driven (D) output gear (D) (larger # of teeth) divided by the smaller driver (d) input gear (smaller # of teeth).

So if the driven gear has 60 teeth and the driver gear has 20 teeth, the gear ratio when these two gears are connected together is 3:1 (60 teeth / 20 teeth = 3) a mechanical advantage.

Ratios, whether by gears, timing belt pulleys and belts, chain and sprockets or anything else, are usually thought of as speed reducers, or less often, as speed increasers. They should be thought of more in terms of what they do to torque. A speed reducer is a torque increaser and vice versa. The laws of physics dictate that a change of speed via a ratio, proportionally changes the torque, as a factor of the ratio. Disregarding the friction in the system, the torque is multiplied or divided as a factor of the ratio.

Thus a 3:1 speed reduction ratio, multiplies the input torque three (3) times (a MECHANICAL ADVANTAGE) and 1:3 speed increasing ratio would reduce the torque three (3) times (a MECHANICAL DISADVANTAGE).

Note: Ratios cannot be added or subtracted; only multiplied or divided.

The golden rule of gear ratios are they are the SAME no matter how you arrive at them. For example if you have a 50 tooth 8mm pitch timing belt pulley and a 25 tooth 8mm pitch timing belt pulley the ratio is 2:1 (50 tooth / 25 tooth = 2) and if you have a 100 tooth 8mm pitch timing belt pulley and a 50 tooth 8mm pitch timing belt pulley the ratio is 2:1 (100 tooth / 50 tooth = 2). These ratios are the same, clear and simple, “old math” or “new math” slide rule or calculator, it is still 2 to 1 (2:1).