Force Analysis of Gear Meshing in Planetary Gear Transmission

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Force Analysis of Gear Meshing in Planetary Gear Transmission

Planetary gear transmission is widely applied in wind power, automotive, aerospace and industrial machinery fields due to its advantages of compact structure, high power density, large transmission ratio and load distribution. Its core advantage lies in the power split transmission through multiple planetary gears, while this parallel structure also makes the force analysis of the system more complex. Mastering the meshing force analysis of planetary gear transmission is the theoretical foundation for the design, strength check and fault diagnosis of planetary transmission systems.

1 Basic Structure and Terminology

1.1 Main Components

Sun gear: Located at the center of the system, it is usually used as the input shaft of the transmission system.
Planetary gear: Meshes with both the sun gear and the ring gear at the same time. Generally, 3 to 6 planetary gears are evenly distributed in the system, and they perform both rotation and revolution movements during operation.
Ring gear: An internal gear ring, which is usually fixed in most working conditions, and can also serve as the input or output end of power according to different transmission schemes.
Planet carrier: A structural component that connects and supports all planetary gears, and is commonly the output shaft of the planetary transmission system.

1.2 Meshing Relationship

The meshing between the sun gear and planetary gears belongs to external meshing.
The meshing between the planetary gears and ring gear is internal meshing.

1.3 Typical Transmission Schemes and Ratios

The transmission ratio of the planetary gear system varies with different combinations of driving, driven and fixed components, where the parameter a is the ratio of the number of teeth of the ring gear to the sun gear, namely a = Zr/Zs, Zr refers to the number of teeth of the ring gear and Zs is the number of teeth of the sun gear.

When the sun gear is the driving part, the planet carrier is the driven part and the ring gear is fixed, the transmission ratio is 1+a, realizing deceleration and torque increase. When the ring gear is the driving part, the planet carrier is the driven part and the sun gear is fixed, the transmission ratio is (1+a)/a. When the sun gear is the driving part, the ring gear is the driven part and the planet carrier is fixed, the transmission ratio is -a.

When the planet carrier is the driving part, the ring gear is the driven part and the sun gear is fixed, the transmission ratio is a/(1+a), achieving acceleration and torque reduction. When the planet carrier is the driving part, the sun gear is the driven part and the ring gear is fixed, the transmission ratio is 1/(1+a). When the ring gear is the driving part, the sun gear is the driven part and the planet carrier is fixed, the transmission ratio is -1/a.

If any two components are connected as a whole, the transmission ratio is 1, which is the direct gear mode. If no component is braked and no two components are connected together, the system is in neutral gear with three components rotating freely and no fixed transmission ratio.

2 Basic Assumptions for Force Analysis

To simplify the force analysis process and ensure the clarity of theoretical derivation, an ideal mechanical model of the planetary gear transmission system is established with the following basic assumptions:

Friction neglect: Ignore the friction loss in gear meshing and bearing rotation processes.
Static equilibrium: Analyze the static equilibrium state of the system under constant load conditions.
Ideal load sharing: Initially assume that the total load of the system is evenly distributed among all planetary gears.
Force symmetry: For the evenly distributed planetary gears, their stress states show circumferential symmetry in the system.

3 Force Analysis of a Single Planetary Gear

The single planetary gear is the core force-bearing unit of the entire planetary transmission system. The forces acting on it are mainly derived from three parts, and the force balance relationship is the basis of the whole system's force analysis.

3.1 Force Decomposition

: Meshing force from the sun gear to the planetary gear, whose direction is along the common normal (meshing line) at the meshing point of the sun gear and the planetary gear.
: Meshing force from the ring gear to the planetary gear, whose direction is along the common normal at the meshing point of the ring gear and the planetary gear.