Planetary Gear
Planetary Gear component
The Planetary Gear component models a gearbox without inertia, elasticity, or backlash. It consists of an inner sun wheel, an outer ring wheel, and a planet wheel located between sun and ring wheel. The bearing of the planet wheel shaft is fixed in the planet carrier.
The component can be connected to other elements at the sun, ring and/or carrier flanges. An option is provided to activate a planet flange. If inertia is taken into consideration, the sun, ring, and carrier inertias can be added by attaching the Inertia component to the corresponding connectors. The inertia of the planet wheels are included by attaching an Inertia component to the planet flange. The damping in the bearing connecting the planet(s) to carrier can be included via the component options. Bearing friction of the ‘ring’ and ‘carrier’ shafts may be included by attaching the Bearing Friction component(s) to these flanges.The icon of the planetary gear signals that the sun and carrier flanges are on the left side and the ring flange is on the right side of the gear box. However, this component is generic and is valid independently to how the flanges are actually placed (for example, the sun wheel may be placed on the right side instead on the left side). According to the overall convention, the positive direction of all relevant vectors, namely, the absolute angular velocities and cuttorques in the flanges are along the axis vector shown in the icon.
Note 1: Since the planet’s mass is rotating at a distance from the planetary gear axis, ensure that when adding inertia to the ‘planet' that the proper inertia is also added to the ‘carrier’.
Note 2: When attaching a Bearing Friction component to the planet shaft to represent planet/carrier bearing friction, use the configuration shown in the figure below to correctly account for the relative velocity of the planet with respect to the carrier.
Including Planet/Carrier Bearing Friction
Kinematic Equation
The gear ratio of the planetary gear is and is defined by:
Where
is the number of ring teeth and
is the number of sun teeth.
The number of planet teeth
has to fulfill the following relationship:
There are two types of kinematic equations depending whether the Planet flange is disabled or enabled:
Note: When the Planet flange is enabled () an extra equation is added.
Planet flange is disabled
Planet flange is enabled
Where , and are defined as the rotation angles of the carrier, outer planet, and inner planet, respectively
Internal Structure
Torque Balance Equation (No Inertia)
There are two sets of kinematic torque balance equations depending on whether the Planet flange is disabled or enabled:
Planet flange is disabled
Planet flange is enabled
Where are defined as the rotation angles of the carrier, ring, sun, and planet respectively. is the number of identical planets meshing with the ring and sun gears.
Also is the loss torque and is defined as:
Where is the number of planets meshing with the Sun and the Ring gears, and
Where and are the forward and backward Ring/Planet meshing efficiency, respectively and and are the forward and backward Sun/Planet meshing efficiency, respectively.
Also
= 
= 
= 
=
Where
,
Power Loss
The power loss () is calculated as:
Where
Connections
Name

Condition

Description

ID



Carrier flange

carrier



Planet flange

planet

Ring


Ring flange

ring



Sun flange

sun



Conditional real output port for power loss

lossPower



Parameters
Symbol

Condition

Default

Units

Description

ID







Defines whether the component is:
true  ideal or
false  nonideal

ideal

data source


GUI



Defines the source for the loss data:
•

by an attachment [attachment]

•

by an external file [file]


datasourcemode



true



Defines whether one efficiency data table is used for all meshing loss calculations [] or the efficiency of each meshing gear pair is given by a separate data table [].

SameMeshingEfficiency







Gear ratio

ratio





Number of planet gears

numberofPlanets


same loss data = true
data source = GUI



Defines all velocity dependant meshing efficiencies.
The columns:
[ ( ) ( )]
Five options are available:
•

1 by 1 array: entered value is taken as the constant efficiency for forward and backward cases

( ) = ( ) =
•

1 by 2 array: first entered value is taken as the constant efficiency for forward case and the second for backward cases

() = ( ) =
•

1 by 3 array: first column is ignored and the second and third values are taken as constant efficiencies for forward and backward cases, respectively

•

n by 2 array: Second column is forward and backward efficiency

() = ( ) = ( )
Second column is forward efficiency
()
Third column is backward efficiency
( )

meshinglossTable3

same loss data = true
data source = attachment



Defines velocity dependant meshing efficiency
First column is angular velocity ()
(See below)

data3

same loss data = true
data source = file



fileName3


same loss data = true
data source = attachment or file




Defines the corresponding data columns used for forward efficiency () and backward efficiency ( )
Two options are available:
Data column corresponding to the column number is used for both forward and backward efficiency (
)
Data column corresponding to the first column number is used for forward efficiency () and data column corresponding to the second column number is used for backward efficiency ()

columns3


same loss data = false
data source = GUI



Defines Ring/Planet velocity dependant meshing efficiency as a function of .
The columns are:
[ ( ) ( )]
First column is angular velocity of the ring gear w.r.t. the carrier ()
Five options are available:
•

1 by 1 array: entered value is taken as the constant efficiency for forward and backward cases

( ) = =
•

1 by 2 array: first entered value is taken as the constant efficiency for forward case and the second for backward cases

( ) =( ) =
•

1 by 3 array: first column is ignored and the second and third values are taken as constant efficiencies for forward and backward cases, respectively.

•

n by 2 array: Second column is forward and backward efficiency

( ) = ( ) = ( )
Second column is forward efficiency
( )
Third column is backward efficiency
( )

meshinglossTable1

same loss data = false
data source = attachment



Defines the velocity dependent meshing efficiency
First column is angular velocity ( )
(See below)

data1

same loss data = false
data source = file



fileName1


same loss data = false
data source = attachment or file




Defines the corresponding data columns used for forward () and backward () friction torques.
Two options are available:
Data column corresponding to the column number is used for both forward and backward efficiency (
Data column corresponding to the first column number is used for forward efficiency () and
Data column corresponding to the second column number is used for backward efficiency ()

columns1


same loss data = false
data source = GUI



Defines Planet/Sun velocity dependant meshing efficiency as a function of .
The columns are:
[ ( ) ( )
First column is angular velocity of the sun gear w.r.t. carrier ()
Five options are available:
•

1 by 1 array: entered value is taken as the constant efficiency for forward and backward cases

( ) = =
•

1 by 2 array: first entered value is taken as the constant efficiency for forward case and the second for backward cases

( ) =( ) =
•

1 by 3 array: first column is ignored and the second and third values are taken as constant efficiencies for forward and backward cases, respectively.

•

n by 2 array: Second column is forward and backward efficiency

( ) = ( ) = ( )
Second column is forward efficiency
( )
Third column is backward efficiency
( )

meshinglossTable2

same loss data = false
data source = attachment



Defines the velocity dependent meshing efficiency
First column is angular velocity ( )
(See below)

data2

same loss data = false
data source = file



fileName2


same loss data = false
data source = attachment or file




Defines the corresponding data columns used for forward () and backward () efficiency
Two options are available:
Data column corresponding to the column number is used for both forward and backward efficiency (
Data column corresponding to the first column number is used for forward efficiency () and
Data column corresponding to the second column number is used for backward efficiency ()

columns2

d


0


linear damping in planet/carrier bearing

d

smoothness


Table points are linearly interpolated



Defines the smoothness of table interpolation
There are two options:
•

Table points are linearly interpolated

•

Table points are interpolated such that the first derivative is continuous


smoothness



Note: Gear ratio must be strictly greater than zero.
See Also
MapleSim Driveline Library Overview
MapleSim Library Overview
1D Mechanical Overview
Basic Gear Sets
Planet Planet Gear
Planet Ring Gear
References
Pelchen C., Schweiger C., and Otter M., “Modeling and Simulating the Efficiency of Gearboxes and Planetary Gearboxes,” 2nd International Modelica Conference, Proceedings, pp. 257266.
