Planetary gear#

The Planetary gear block models a gear train consisting of a sun gear, planet gears, and a ring gear. The satellites are mounted on the planet carrier, which is connected to the drive shaft and ensures their joint movement.

This block is a structural component consisting of the blocks Sun-planet and Ring-planet Fig. 1 :

In this model of planetary gear, two kinematic and two geometric constraints are imposed (1) :

(1)#\[\begin{split}r_{вод.} \cdot \omega_{вод.}= r_{сол.} \cdot \omega_{сол.} +r_{сат.} \cdot \omega_{сат.}\\r_{корон.} \cdot ω_{корон.}= r_{вод.} \cdot ω_{вод.} + r_{сат.} \cdot ω_{сат.}\\r_{вод.}= r_{сол.}+ r_{сат.} \\r_{корон.}= r_{вод.} + r_{сат.}\end{split}\]

where:

\(r_{car.}\) – distance from the transmission axis to the satellite axis (satellite installation radius);

\(\omega_{car.}\) – angular velocity of the carrier;

\(r_{crown.}\) – radius of the crown gear;

\(\omega_{crown.}\) – angular velocity of the crown gear;

\(r_{sun}\) – radius of the sun gear;

\(\omega_{sun}\) – angular velocity of the sun gear;

\(r_{sat.}\) – satellite radius;

\(ω_{sat.}\) – angular velocity of the satellite.

Rear to sun gear ratio (2):

(2)#\[g = \frac{N_{корон.}}{N_{сол.}} = \frac{r_{корон.}}{r_{сол.}}\]

where \(N\) is the number of teeth of the corresponding gear.

As a result, the four degrees of freedom of the system are reduced to two independent ones

Through this relationship, the basic kinematic relationship is established (3):

(3)#\[(1+g) \cdot \omega_{вод.} = \omega_{сол.} + g \cdot \omega_{корон.}\]

Torque transmission occurs according to the equation (4):

(4)#\[g \cdot M_{сол.} + M_{корон.} - M_{потери} = 0\]

where:

\(M_{sun}\) – transmission moment for the sun gear;

\(M_{crown.}\) – transmission moment for the crown gear;

\(M_{losses}\) – moment of loss (equal to zero in the ideal case).

Restrictions:

The inertia of the components is negligible;
The components are considered absolutely rigid.

1. Properties#

Property	Default Value	Description	Units of measurement
Ring (R) to sun (S) teeth ratio (N_R/N_S)	2.0	-	-

2. Inputs and outputs#

Parameters	Input/Output	Description	Units of measurement	Port type
Carrier (C)	Input	-	-	Rotational motion
Ring (R)	Output	-	-	Rotational motion
Sun (S)	Output	-	-	Rotational motion

In order to see the connection capabilities of the block, you need to go to page Description of block ports