Calculation formula of gear-rack transmission ratio

Transmission ratio = number of teeth of driven wheel/number of teeth of driving wheel = speed of driving wheel/speed of driven wheel.

i=z2/z 1=n 1/n2

Transmission ratio is the ratio of angular velocities of two rotating members in a mechanism, also called speed ratio. The transmission ratio of component a and component b is I =ωA/ωB = Na/Nb, where ωA and ωB are the angular velocities (radian per second) of components a and b respectively; Na and nb are the rotational speeds (rpm) of components A and B, respectively.

When the angular velocity in the formula is instantaneous, the obtained transmission ratio is instantaneous. When the angular velocity in the formula is averaged, the obtained transmission ratio is the average transmission ratio. Theoretically, for most gear drives with correct involute profile, the instantaneous transmission ratio is constant; For chain drive and friction wheel drive, the instantaneous transmission ratio changes. For meshing transmission, the transmission ratio can be expressed by the number of teeth Za and Zb of a and b wheels, and I = zb/za; For friction transmission, the transmission ratio can be expressed by the diameters Da and Db of a wheel and b wheel, and i=Db/Da.

The distribution of transmission ratio of multi-stage reducer directly affects the bearing capacity and service life of reducer, and also affects its volume, weight and lubrication. The transmission ratio is generally allocated according to the following principles: to make the bearing capacity of all levels of transmission roughly equal; Make the reducer smaller in size and mass; Make the peripheral speed of gears at all levels smaller; When oil bath lubrication is used, the oil immersion depth of the big gears of each gear pair is relatively small.

The low-speed gear directly affects the size and weight of the reducer, reducing the transmission ratio of the low-speed gear, that is, reducing the size and weight of the low-speed gear and the machine body containing it. Increasing the transmission ratio of high-speed gears means increasing the size of high-speed gears and reducing the size difference between high-speed gears and low-speed gears, which is beneficial to oil bath lubrication of all gears; At the same time, after the size of high-speed pinion is reduced, the peripheral speed of high-speed and subsequent gears is reduced, which is beneficial to reduce noise and vibration and improve transmission stability. Therefore, it is reasonable that the final transmission ratio is small under the condition of meeting the strength.

Transmission ratio = working torque ÷9550÷ motor power × motor power input revolutions ÷ working coefficient.

Transmission ratio = the rotational speed of the driving wheel divided by the rotational speed of the driven wheel = the reciprocal of the diameter ratio of their indexing circles. That is, i=n 1/n2=D2/D 1.

I=n 1/n2=z2/z 1 (gear)