How Planetary Gearbox Works?

2025-06-04

I. Basic motion model of planetary gear train: coupling of rotation and revolution

The core of a planetary gearbox is the planetary gear train, whose motion characteristics adhere to a 'solar-system-like' mechanical principle: the central gear (sun gear) is positioned at the center of the system, while the planet gears revolve around the sun gear and roll along the inner wall of the ring gear (annulus). This compound motion includes two basic actions:

1. Self-rotation of planet gears

When the sun gear rotates clockwise, the tooth surface of the planet gear meshing with the sun gear experiences a tangential driving force. Due to the reverse-direction characteristic of gear meshing, this force causes the planet gear to rotate counterclockwise around its own axis.

2. Revolution of planet gears

During the meshing process with the internal teeth of the ring gear, the planet gears, while rotating on their own axes, revolve clockwise along the circumferential trajectory of the ring gear. The center of this revolution coincides with the axis of the sun gear.

 

The combined effect of these two motions causes the planet carrier (the component supporting the planet gear shafts) to develop a rotational motion synchronous with the revolution of the planet gears, thereby converting high-speed low-torque input into low-speed high-torque output.

 

II. Three elements of power transmission: fixed parts, input parts and output parts

The transmission characteristics of a planetary gear train are determined by the selection of the "fixed component," meaning any one of the three components—sun gear, ring gear, or planet carrier—can be fixed or serve as the input/output terminal. The three common working modes are as follows:

1. Fixed ring gear (most typical deceleration mode)

·Input: The sun gear (driving gear) rotates clockwise.

·Fixed parts: The ring gear (inner ring gear) is fixed.

·Output: The planet carrier (driving the output shaft) rotates clockwise.

·Motion transmission process:

·The sun gear drives the planet gear to rotate (counterclockwise), and at the same time, the planet gear is forced to revolve along the inner wall of the ring gear (clockwise) because the ring gear is fixed.

·The planet carrier rotates synchronously with the revolution of the planet gears at a lower speed than the sun gear.

· Transmission ratio calculation: Let the number of teeth of the sun gear be Zs, the number of teeth of the ring gear be Zr, the rotational speed of the planet carrier be nc, and the rotational speed of the sun gear be ns. According to the gear meshing speed relationship: (ns-nc)/(nr-nc)=-Zr/Zs. When the ring gear is fixed and nr = 0, the transmission ratio is simplified to: i=ns/nr=1+Zr/Zs

· For example, Zs=20, Zr=60, then i=4, the output speed is 1/4 of the input, and the torque is increased by 4 times (ignoring efficiency loss).

 

2. Sun gear fixed (speed increase mode)

·Input: The planet carrier rotates clockwise.

·Fixed part: The sun gear is stationary.

·Output: The ring gear rotates clockwise at a higher speed than the planet carrier

·Transmission ratio: i=ns/nr=1+Zr/Zs achieves speed increase at this time, but in actual applications, due to the large input inertia of the planet carrier, it is rarely used in speed increase scenarios.

 

3. Planet carrier fixed (differential mode)

·Input: The sun gear and ring gear rotate in conjunction (with directions being the same or opposite).

·Fixed part: The planet carrier is stationary.

·Output: No direct output, often used in scenarios where motion synthesis is required (such as automotive differentials).

 

III. Principle of transmission ratio superposition of multi-stage planetary gear train

The transmission ratio of a single-stage planetary reducer typically ranges from 3 to 10. If a larger transmission ratio (such as more than 100) is required, a multi-stage series connection is required. Take a two-stage planetary reducer as an example:

 

·First stage: sun gear Zs1 input, ring gear Zr1 fixed, planet carrier C1 output (speed).

·Second stage: planet carrier C1 of the first stage serves as the input for the sun gear Zs2 of the second stage, ring gear Zr2 is fixed, and the second-stage planet carrier C2 outputs.

·Total transmission ratio: iΣ=i1xi2=(1+Zr1/Zs1)x(1+Zr2/Zs2). The multi-stage design can achieve a large transmission ratio in a compact space through gear parameter optimization (such as unequal tooth difference, staggered meshing), and at the same time balance the load of each planetary gear through a load-sharing structure (such as a floating sun gear, a flexible planet carrier) to avoid single tooth overload.

 

IV. Principle support of key technical advantages

The high performance of planetary reducers comes from their unique motion transmission characteristics:

 

1. Power diversion effect: Multiple planetary gears (usually 3-6) are evenly distributed around the sun gear, decomposing the input torque into multiple parts, and transmitting them to the ring gear and the planet carrier through tooth surface contact. This multi-point meshing reduces the load-bearing pressure of a single gear, and the torque carrying capacity is 3-5 times higher than that of a single-stage cylindrical gear reducer at the same volume.

2. Error equalization mechanism: The revolution of the planetary gear averages the machining errors of each gear (such as pitch deviation) in the circumferential direction. With the high-precision gear grinding process (accuracy level ISO 4-6), the return clearance (the angular difference between input and output when no-load) can be controlled within 1-10 arc minutes to meet the requirements of precision positioning.

3. Axial load self-balancing: The axial forces generated by the helical planetary gears during meshing are offset by the symmetrically arranged planetary gear sets, without the need for additional thrust bearings, simplifying the structure and improving rigidity.

 

V. Motion simulation and force analysis under typical working conditions

Take the joint drive of industrial robots as an example. when the planetary gear is in the high-speed, light-load start-up stage:

 

·The sun gear rotates rapidly, and the rotation speed of the planetary gear is higher than the revolution speed. At this time, the meshing point between the planetary gear and the ring gear slides along the tooth surface, generating meshing impact. Impact noise can be reduced by tooth surface modification (such as drum teeth and helix angle optimization).

 

·After entering the stable load stage, the revolution speed of the planetary gear is synchronized with the output speed, the meshing point turns to pure rolling, and the contact stress is evenly distributed in the tooth width direction. With oil bath lubrication or grease lubrication, a life of 10,000 hours can be achieved.

 

VI. Principle Differences from Other Reducers

Compared with worm gear reducers (relying on worm-and-gear helical pair transmission) and cycloidal pinwheel reducers (utilizing meshing between cycloidal gears and pin teeth), the core advantages of planetary reducers are as follows:

·Pure gear meshing: Eliminates the sliding friction of worm gears, increasing efficiency by 20%-30%.

·Coaxial reducers: the input and output shafts are coaxial, and the space utilization rate is higher than that of parallel shaft reducers.

·Combinability: through modular design, multi-stage transmission and different installation methods (flange type, shaft extension type) can be easily realized.

 

VII. Conclusion

The working principle of the planetary gear is essentially to convert "high-speed rotation" into "low-speed high torque" through the compound motion of the planetary gear. Its core secret lies in the precise control of gear meshing motion -- from the single-stage differential principle to the multi-stage transmission ratio superposition, from the load diversion of material mechanics to the error averaging of precision manufacturing, every link reflects the wisdom of mechanical engineering. As industrial automation's requirements for precision, efficiency, and reliability continue to increase, the principle innovation of planetary reducers will continue to deepen in the fields of materials, lubrication, control algorithms, etc., becoming the "precision heart" that drives modern industry.

I. Basic motion model of planetary gear train: coupling of rotation and revolution

The core of a planetary gearbox is the planetary gear train, whose motion characteristics adhere to a 'solar-system-like' mechanical principle: the central gear (sun gear) is positioned at the center of the system, while the planet gears revolve around the sun gear and roll along the inner wall of the ring gear (annulus). This compound motion includes two basic actions:

1. Self-rotation of planet gears

When the sun gear rotates clockwise, the tooth surface of the planet gear meshing with the sun gear experiences a tangential driving force. Due to the reverse-direction characteristic of gear meshing, this force causes the planet gear to rotate counterclockwise around its own axis.

2. Revolution of planet gears

During the meshing process with the internal teeth of the ring gear, the planet gears, while rotating on their own axes, revolve clockwise along the circumferential trajectory of the ring gear. The center of this revolution coincides with the axis of the sun gear.

 

The combined effect of these two motions causes the planet carrier (the component supporting the planet gear shafts) to develop a rotational motion synchronous with the revolution of the planet gears, thereby converting high-speed low-torque input into low-speed high-torque output.

 

II. Three elements of power transmission: fixed parts, input parts and output parts

The transmission characteristics of a planetary gear train are determined by the selection of the "fixed component," meaning any one of the three components—sun gear, ring gear, or planet carrier—can be fixed or serve as the input/output terminal. The three common working modes are as follows:

1. Fixed ring gear (most typical deceleration mode)

·Input: The sun gear (driving gear) rotates clockwise.

·Fixed parts: The ring gear (inner ring gear) is fixed.

·Output: The planet carrier (driving the output shaft) rotates clockwise.

·Motion transmission process:

·The sun gear drives the planet gear to rotate (counterclockwise), and at the same time, the planet gear is forced to revolve along the inner wall of the ring gear (clockwise) because the ring gear is fixed.

·The planet carrier rotates synchronously with the revolution of the planet gears at a lower speed than the sun gear.

· Transmission ratio calculation: Let the number of teeth of the sun gear be Zs, the number of teeth of the ring gear be Zr, the rotational speed of the planet carrier be nc, and the rotational speed of the sun gear be ns. According to the gear meshing speed relationship: (ns-nc)/(nr-nc)=-Zr/Zs. When the ring gear is fixed and nr = 0, the transmission ratio is simplified to: i=ns/nr=1+Zr/Zs

· For example, Zs=20, Zr=60, then i=4, the output speed is 1/4 of the input, and the torque is increased by 4 times (ignoring efficiency loss).

 

2. Sun gear fixed (speed increase mode)

·Input: The planet carrier rotates clockwise.

·Fixed part: The sun gear is stationary.

·Output: The ring gear rotates clockwise at a higher speed than the planet carrier

·Transmission ratio: i=ns/nr=1+Zr/Zs achieves speed increase at this time, but in actual applications, due to the large input inertia of the planet carrier, it is rarely used in speed increase scenarios.

 

3. Planet carrier fixed (differential mode)

·Input: The sun gear and ring gear rotate in conjunction (with directions being the same or opposite).

·Fixed part: The planet carrier is stationary.

·Output: No direct output, often used in scenarios where motion synthesis is required (such as automotive differentials).

 

III. Principle of transmission ratio superposition of multi-stage planetary gear train

The transmission ratio of a single-stage planetary reducer typically ranges from 3 to 10. If a larger transmission ratio (such as more than 100) is required, a multi-stage series connection is required. Take a two-stage planetary reducer as an example:

 

·First stage: sun gear Zs1 input, ring gear Zr1 fixed, planet carrier C1 output (speed).

·Second stage: planet carrier C1 of the first stage serves as the input for the sun gear Zs2 of the second stage, ring gear Zr2 is fixed, and the second-stage planet carrier C2 outputs.

·Total transmission ratio: iΣ=i1xi2=(1+Zr1/Zs1)x(1+Zr2/Zs2). The multi-stage design can achieve a large transmission ratio in a compact space through gear parameter optimization (such as unequal tooth difference, staggered meshing), and at the same time balance the load of each planetary gear through a load-sharing structure (such as a floating sun gear, a flexible planet carrier) to avoid single tooth overload.

 

IV. Principle support of key technical advantages

The high performance of planetary reducers comes from their unique motion transmission characteristics:

 

1. Power diversion effect: Multiple planetary gears (usually 3-6) are evenly distributed around the sun gear, decomposing the input torque into multiple parts, and transmitting them to the ring gear and the planet carrier through tooth surface contact. This multi-point meshing reduces the load-bearing pressure of a single gear, and the torque carrying capacity is 3-5 times higher than that of a single-stage cylindrical gear reducer at the same volume.

2. Error equalization mechanism: The revolution of the planetary gear averages the machining errors of each gear (such as pitch deviation) in the circumferential direction. With the high-precision gear grinding process (accuracy level ISO 4-6), the return clearance (the angular difference between input and output when no-load) can be controlled within 1-10 arc minutes to meet the requirements of precision positioning.

3. Axial load self-balancing: The axial forces generated by the helical planetary gears during meshing are offset by the symmetrically arranged planetary gear sets, without the need for additional thrust bearings, simplifying the structure and improving rigidity.

 

V. Motion simulation and force analysis under typical working conditions

Take the joint drive of industrial robots as an example. when the planetary gear is in the high-speed, light-load start-up stage:

 

·The sun gear rotates rapidly, and the rotation speed of the planetary gear is higher than the revolution speed. At this time, the meshing point between the planetary gear and the ring gear slides along the tooth surface, generating meshing impact. Impact noise can be reduced by tooth surface modification (such as drum teeth and helix angle optimization).

 

·After entering the stable load stage, the revolution speed of the planetary gear is synchronized with the output speed, the meshing point turns to pure rolling, and the contact stress is evenly distributed in the tooth width direction. With oil bath lubrication or grease lubrication, a life of 10,000 hours can be achieved.

 

VI. Principle Differences from Other Reducers

Compared with worm gear reducers (relying on worm-and-gear helical pair transmission) and cycloidal pinwheel reducers (utilizing meshing between cycloidal gears and pin teeth), the core advantages of planetary reducers are as follows:

·Pure gear meshing: Eliminates the sliding friction of worm gears, increasing efficiency by 20%-30%.

·Coaxial reducers: the input and output shafts are coaxial, and the space utilization rate is higher than that of parallel shaft reducers.

·Combinability: through modular design, multi-stage transmission and different installation methods (flange type, shaft extension type) can be easily realized.

 

VII. Conclusion

The working principle of the planetary gear is essentially to convert "high-speed rotation" into "low-speed high torque" through the compound motion of the planetary gear. Its core secret lies in the precise control of gear meshing motion -- from the single-stage differential principle to the multi-stage transmission ratio superposition, from the load diversion of material mechanics to the error averaging of precision manufacturing, every link reflects the wisdom of mechanical engineering. As industrial automation's requirements for precision, efficiency, and reliability continue to increase, the principle innovation of planetary reducers will continue to deepen in the fields of materials, lubrication, control algorithms, etc., becoming the "precision heart" that drives modern industry.