How to calculate the reduction ratio of a planetary gearbox?

Planetary gearbox, also known as planetary gearbox or planetary gear reducer. In the reducer family, planetary reducers are widely used in transmission systems such as automotive transmissions, smart homes, communication devices, robots, mechanical equipment, and industrial automation due to their small size, high transmission efficiency, wide reduction range, and high precision. The reduction range of planetary gear reducers is wide. When selecting technical parameters, it is necessary to calculate the reduction ratio in order to choose a reducer with a reasonable reduction ratio.

The calculation formula for planetary reduction gearbox is influenced by factors such as transmission ratio calculation, gearbox efficiency, the relationship between power and speed torque, current, and efficiency.

One Calculation formula for reduction ratio:

Formula: n1/n2=i

1. Definition calculation method: Reduction ratio=input speed ÷ output speed, the ratio of the connected input speed to the output speed. If the input speed is 1500r/min and the output speed is 25r/min, then the reduction ratio is i=60:1

2. Calculation method for gear system: Reduction ratio=number of teeth on the driven gear ÷ number of teeth on the driving gear (if it is a multi-stage gear reduction, then multiply the number of teeth on the driven gear of all meshing pairs ÷ number of teeth on the driving gear, and then multiply the results obtained).

II Transmission ratio calculation formula:

Planetary gearbox: First stage: i=(number of internal gear teeth/number of sun gear teeth)+1

Multi level: i=i1 * i2 * i3

III Calculation formula for gearbox efficiency:

Planetary gearbox: Stage: η=0.9 * 0.9 * (Normal ST28P \ ST32P \ ST36P \ ST42P are calculated according to this)

56% (ST16P \ ST22P low efficiency calculated based on this, technical department needs to improve)

Multi level: η=η 1 * 0.9, where n is the series

Advantages of planetary gear transmission

1. Compact structure, small volume, and light weight

Planetary transmission has the transmission characteristics of planetary motion and power splitting, which is why there is an internal gear pair. It can fully utilize the large load-bearing capacity of the internal gear and the full capacity of the internal gear ring, making the reduction gearbox compact in structure, small in outer dimensions, and light in weight. Generally, when the transmission power and transmission ratio are the same, the volume and weight of the planetary gear reduction motor are about 1/2 to 1/6 of those of ordinary gear transmission

2. Large transmission ratio, capable of synthesizing and decomposing motion

There are many types of planetary transmissions, such as involute planetary transmission, cycloidal pinwheel planetary transmission, harmonic planetary transmission, and movable tooth planetary transmission, which generally have the characteristic of large transmission ratio. When used for transmitting motion, its maximum transmission ratio can reach tens or hundreds of thousands, and as a power transmission, its maximum transmission ratio can reach tens or hundreds. The planetary transmission using differential motors can achieve the synthesis of two movements and the decomposition of one action. In some cases, selecting the appropriate type of planetary gear reduction motor can achieve various complex movements with variable speeds.

3. High efficiency and minimal power loss

Planetary transmission uses several planetary gears evenly distributed between the inner and outer center wheels, which can balance the inertial forces acting on the center wheel and planetary carrier bearings. Adopting this symmetrical structure is beneficial for improving the efficiency of the transmission system. The optimized transmission design can achieve an efficiency of 0.97-0.99 for planetary gear reduction motors.

4. Transmission balance, strong resistance to impact and vibration

By using multiple planetary gears evenly distributed between two central gears, and using a load sharing device to maintain uniform load distribution and power distribution between each planetary gear, not only can the inertial forces of each planetary gear and the rotating arm be balanced, but also the stability and resistance to impact and vibration of the planetary gear reduction motor are significantly improved.