Gear Speed and Ratio:
When two or more gears are in a mesh, one will drive the other. As such, one of the gears will be referred to as a driving gear and the other a driven gear.
Definition of Drivier Gear:
This is the gear that transmits power, force or speed to the other gear.
Definition of Driven Gear:
This is the gear that receives the force, power or speed transmitted to it.
Definition of Driven Gear Ratio (GR)
Gear ratio is the relationship between two gears in which one gear has a larger speed than the other. For instance, gear A (driver gear) has 120 teeth and gear B (driven gear) has 40 teeth. The gear ratio will be 3:1, which means that there is an increase in speed. If the ratio is 1:3, it means there is a speed reduction of ratio 1:3.
Gear Ratio (GR) = \( \frac{Number \: of \:Teeth \:on\:Driver\: Gear}{Number\: of \:Teeth\: on \:Driven\:Gear} \\ = \frac{120}{40} \\ =\frac{3}{1} \\= \scriptsize 3\: :1 \)
Definition of Speed Ratio (SR)
Speed ratio is the ratio of the rotation per minute of the driven gear to the rotation per minute of the driver gear.
\(\scriptsize Speed \: Ratio = \normalsize \frac{Rotation \: per \:minute \:for\:Driven\: Gear (S_D)}{Rotation \: per \:minute \:for\:Driver\: Gear (S_d)}\)
Example:
The speed of a driver gear is 60 rev/min and that of a driven gear is 30 rev/min. What is the speed ratio of the gear system?
Solution:
Sd = 60rev/min
SD = 30rev/min
Spped Ratio (SR) = \( \frac{Rotation \: per \:minute \:for\:Driven\: Gear (S_D)}{Rotation \: per \:minute \:for\:Driver\: Gear (S_d)} \\ = \frac{30}{60} \\ = \scriptsize 1\: :2\)
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