Ring-planet#

The Ring-planet block models a planetary gear set consisting of a carrier, a satellite, and a ring gear. The satellite is mounted on the carrier and rotates relative to it. The satellite and ring gear rotate with a fixed gear ratio, specified by the user, relative to the planet carrier.

The block imposes one kinematic and one geometric constraint on three connected shafts of the transmission (1):

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

The gear ratio between the ring gear and the satellite is determined by the number of teeth (2) :

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

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

Through this relationship, the basic kinematic relationship between the angular velocities of the shafts (3) is established:

(3)#\[g\cdot ω_{корон.} = ω_{сат.} + (g-1) · ω_{вод.}\]

As a result, the system’s three degrees of freedom are reduced to two independent degrees of freedom. The convention (1,2) = (crown, sat) is used to denote a pair of gears, where crown is the crown gear and sat is the satellite. Torque transmission is described by the expression (4):

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

where in the ideal case \(T_{losses}\) = 0.

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 planet (P) teeth ratio (N_R/N_P)	2.0	-	-

2. Inputs and outputs#

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

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