Horsepower

Power can be expressed in foot-pounds per second, but is often
expressed in horsepower (HP). This unit was defined in the
18th century by James Watt. Watt sold steam engines and was
asked how many horses one steam engine would replace. He
had horses walk around a wheel that would lift a weight. He
found that each horse would average about 550 foot-pounds of
work per second. One horsepower is equivalent to 500 footpounds
per second or 33,000 foot-pounds per minute.

The following formula can be used to calculate horsepower
when torque (lb-ft) and speed (RPM) are known. It can be seen
from the formula that an increase of torque, speed, or both will
cause a corresponding increase in horsepower.

HP = T * RPM / 5250

Power

Power is the rate of doing work, or work divided by time.
In other words, power is the amount of work it takes to move
the package from one point to another point, divided by the
time.

power = force*distance / time

power = work / time

Work

Whenever a force of any kind causes motion, work is
accomplished. For example, work is accomplished when an
object on a conveyor is moved from one point to another.

Work is defined by the product of the net force (F) applied and
the distance (d) moved. If twice the force is applied, twice the
work is done. If an object moves twice the distance, twice the
work is done.

W = F x d

Friction

A large amount of force is applied to overcome the inertia of
the system at rest to start it moving. Because friction removes
energy from a mechanical system, a continual force must
be applied to keep an object in motion. The law of inertia is
still valid, however, since the force applied is needed only to
compensate for the energy lost.
Once the system is in motion, only the energy required to
compensate for various losses need be applied to keep it in
motion. In the previous illustration, for example: these losses
include:
• Friction within motor and driven equipment bearings
• Windage losses in the motor and driven equipment
• Friction between material on winder and rollers

Law of Inertia

Mechanical systems are subject to the law of inertia. The law
of inertia states that an object will tend to remain in its current
state of rest or motion unless acted upon by an external force.
This property of resistance to acceleration/deceleration is
referred to as the moment of inertia. The English system of
measurement is pound-feet squared (lb-ft2).
If we look at a continuous roll of paper, as it unwinds, we know
that when the roll is stopped, it would take a certain amount
of force to overcome the inertia of the roll to get it rolling. The
force required to overcome this inertia can come from a source
of energy such as a motor. Once rolling, the paper will continue
unwinding until another force acts on it to bring it to a stop.

Acceleration

An object can change speed. An increase in speed is called
acceleration. Acceleration occurs only when there is a change
in the force acting upon the object. An object can also change
from a higher to a lower speed. This is known as deceleration
(negative acceleration). A rotating object, for example, can
accelerate from 10 RPM to 20 RPM, or decelerate from 20
RPM to 10 RPM.

Angular (Rotational) Speed

The angular speed of a rotating object is a measurement of how
long it takes a given point on the object to make one complete
revolution from its starting point. Angular speed is generally
given in revolutions per minute (RPM). An object that makes ten
complete revolutions in one minute, for example, has a speed
of 10 RPM.