Sun-planet#

The Sun-planet block is a component of a planetary gear set consisting of a carrier, a planet, and a sun gear. The planetary gear is mounted on the planet carrier and rotates relative to it. The planetary gear and sun gear rotate relative to the planet carrier at a fixed gear ratio, specified by the user.

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

(1)#\[r_{вод.} \cdot \omega_{вод.} = r_{сат.}\cdot \omega_{сат.} +r_{сол.} \cdot \omega_{сол.}\]

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

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

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

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

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

As a result, the system’s three degrees of freedom are reduced to two independent degrees of freedom. To denote a pair of gears, the convention (1,2) = (sun, sat.) is used, where sun is the sun gear, sat. is the satellite (4):

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

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

\(M_{sat.}\) – transmission moment for satellites;

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

Limitations:

• The inertia of the components is negligible;

• Components are considered absolutely rigid.

1. Properties#

Property	Default Value	Description	Units of measurement
Planet (P) to sun (S) teeth ratio (N_P/N_S)	2.0	-	-

2. Inputs and outputs#

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