How to calculate the gear transmission ratio of the motor

The calculation of gear transmission ratio is based on the tooth ratio of the gear. The transmission ratio (i) is defined as the ratio of the number of teeth (z1) of the driving gear (usually connected to the motor) to the number of teeth (z2) of the driven gear (usually connected to the load), expressed by the formula:
\[i=\ frac {z1z2} \]

This means that if the driving gear has more teeth (z1), it will rotate less times to complete one rotation of the driven gear. This is a deceleration drive because the output speed has decreased, but the output torque has increased because the motor must provide more force to overcome the friction and load caused by deceleration.

For example, if the driving gear in a gearbox has 3 teeth and the driven gear has 1 tooth, then the transmission ratio is: \ [i=\ frac {31}=3 \]

This means that the driving gear rotates 3 turns, and the driven gear only rotates 1 turn.
If it is necessary to calculate the transmission ratio based on a known speed ratio, the speed of the motor and driven wheel can be first determined, and then the following formula can be used: \ [i=\ frac {n1n2} \]

Among them:
-N1 is the speed of the motor (usually measured in revolutions per minute, RPM stands for RPM.
-N2 is the rotational speed of the driven wheel (also expressed in RPM).

It should be noted that the transmission ratio not only depends on the number of teeth in the gear, but may also be influenced by other factors, such as the addition of other gears or transmission mechanisms. In a multi-stage gear transmission system, the total transmission ratio is the product of the transmission ratios at each level.