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"Gear Ratio Concepts" When troubleshooting,
maintaining, or designing a gear drive
system, it is necessary to understand the
concept of gear ratios. A simple gear
train consisting of two spur gears is
shown here. Notice how one gear turns
slower than the other. Also notice that
there is a different number of teeth on
each of the gears. There is a
relationship of the ratios of the output
gears and the input gears number of
teeth, circumference, diameter, radii,
torque, and velocity. The pinion gear has
a 1-inch diameter and the output gear
has a 5-inch diameter. Pi can be
considered a constant because the
diameter ratio 5 inches to 1 inch
equals 5:1 which equals the
circumference ratio, 15.7
inches to 3.14 inches,
which equals 5:1. The diameters
and the circumferences of these two
gears have the same relationships. The
linear lengths illustrate the
relationship between the distances
traveled as the gears rotate one
revolution.
The ratio of the diameters of the output
gear to the input gear is 5:1.
The ratio of the circumferences of
the output gear to the input gear is
5:1. The distance traveled by the
smaller gear during one revolution is
less than the distance traveled by the
larger gear. The same number of teeth
have made contact, but there are more
teeth on the larger gear because of its
larger circumference. When the larger
output gear rotates one revolution, the
smaller pinion gear will rotate five
revolutions. This gives an angular
displacement ratio of 5:1. The
pinion is driven by a motor at 100
revolutions in one minute. The output
gear will rotate 20 revolutions
during that same minute. Remember that
the ratio of the diameters and the ratio
of the number of teeth are the same
ratio.
Note that the ratio of the diameters and
the ratio of the revolutions per minute
are also the same ratio, 100 RPM to 20
RPM equals 5:1. Note the velocity
ratio is inverse that of the diameter
ratio or the number of teeth ratio. Since
the ratio of the number of teeth and the
ratio of the diameters are the same, you
can use either ratio to find the unknown
velocity.
What is the Output RPM of the gear train
shown if the input is driven at 1750 RPM.
To find a velocity of a gear, set up a
basic linear equation, cross multiply,
and divide. Set up your formula as
follows:
Input RPM / Output RPM equals Output
Diameter / Input Diameter. 1750 * 1
equals Output RPM * 5. Solve for the
Output Gear RPM: 1750 / 5 equals
350 RPM.
Remember, you can use either the ratio of
the diameters, or the ratio of the number
of teeth, since they are the same, to find
an unknown velocity. Cross multiply: 1750
* 8 which equals Output RPM * 40. Solve
for the Output Gear RPM 14,000 / 40
equals 350 RPM.
Congratulations! You have completed this
learning activity on "Gear Ratio Concepts".
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