Planetary Gear Transmission: Design And Calculation

Publish Time: 2025-11-06 Origin: Site

Planetary Gear Transmission is a type of gear drive with compact structure, high transmission ratio and large load-carrying capacity. Its core feature is that the axis of the gear can rotate to form "planetary motion", hence the name.

1. Basic Structure and Types

1.1 Core Components

Sun Gear: The central gear of the planetary gear system.
Planet Gear: Gears rotating around the sun gear (usually 3-6 pieces).
Ring Gear: An annular gear with internal teeth on the outer edge.
Planet Carrier: A rotating component that supports the planet gears.

1.2 Main Types

NGW Type: Most commonly used, including sun gear, planet gear and ring gear.
NW Type: Double planet gear structure.
WW Type: Double internal meshing structure.
NGWN Type: Compound planetary transmission.

2. Determination of Gear Teeth Number

The number of teeth of each gear must meet four key conditions:

2.1 Transmission Ratio Condition

It should realize the given transmission ratio requirement as much as possible. The basic formula for the transmission ratio of the planetary gear train is: (n_1 + a cdot n_3 - (1 + a)n_H = 0), where (a = z_3/z_1), (z_1) is the number of teeth of the sun gear, and (z_3) is the number of teeth of the ring gear.

2.2 Concentricity Condition

Ensure the rotating shaft of the planet carrier coincides with the axis of the sun gear. For standard gears, the formula is (z_1 + z_2 = z_3 - z_2) (simplified), meaning the number of teeth of the sun gear and the ring gear should both be odd or even.

2.3 Assembly Condition

Multiple planet gears must be evenly distributed around the sun gear. If k planet gears are needed, the sum of the number of teeth of the sun gear and the ring gear should be divisible by k (i.e., (z_1 + z_3) is divisible by k).

2.4 Adjacency Condition

Prevent interference between adjacent planet gears. For standard gears, the center distance between adjacent planet gears must be greater than the addendum circle diameter of the planet gears.

3. Load Sharing of Planetary Gear Trains

3.1 Key Issue

Manufacturing errors, installation errors and force deformation can lead to uneven load distribution among planet gears.

3.2 Load Sharing Devices

Floating Basic Component Device: Use single-tooth or double-tooth couplings. Floating one or two basic components (sun gear, ring gear or planet carrier) achieves load balance.
Elastic Element Device: Planet gears are mounted on elastic mandrels, non-metallic elastic bushings, or use "oil film elastic floating" structures.
Lever Linkage Device: Equipped with eccentric planet gear shafts and lever systems to automatically adjust load distribution, with good balance effect but complex structure.

4. Transmission Ratio Calculation

4.1 Basic Idea

Convert the planetary gear train into a fixed-axis gear train (called the converted mechanism) by subtracting the angular velocity of the planet carrier (omega_H) from all components.

4.2 Calculation Formula

For the converted mechanism (fixed-axis gear train), the transmission ratio is: (i_{13}^H = frac{omega_1 - omega_H}{omega_3 - omega_H} = -frac{z_2 z_3}{z_1 z_2} = -frac{z_3}{z_1}), where (i_{13}^H) is the transmission ratio between the sun gear 1 and the ring gear 3 relative to the planet carrier H.

5. Manufacturing and Assembly Key Points

5.1 Precision Requirements

Gear precision: Not lower than Grade 6 (GB/T 10095).
Planet gear phase angle error: Less than 5'.

5.2 Key Fits

Clearance between planet gear and pin: H7/g6.
Position accuracy of planet carrier holes: Φ0.02mm.

5.3 Lubrication Design

Oil Immersion Lubrication: Oil level reaches 1/3 of the planet gear diameter.
Oil Injection Lubrication: Nozzles aligned with the meshing points.

6. Common Problems and Solutions

Problem Phenomenon	Possible Causes	Solutions
Excessive Noise	Large Tooth Profile Error	Improve gear precision
High Temperature Rise & Obvious Vibration	Poor Lubrication	Optimize the lubrication system
Uneven Load Sharing	Malfunction of Floating Mechanism	Inspect and maintain the floating mechanism
Insufficient Service Life	Material Defects	Improve heat treatment process