Planet Ring Gear
Planet Ring Gear component
The Planet Ring Gear component models a set of carrier, ring, and planet gear wheels with specified ringplanet gear ratio without inertia, elasticity or backlash. The inertia of the gears and carrier may be included by attaching the Inertia components to the ‘planet’, ‘ring’ or ‘carrier’ flanges respectively. The damping in the bearing connecting the planet(s) to the carrier can be included via the component options. Bearing friction on the ‘ring’ and ‘carrier’ shafts may be included by attaching the Bearing Friction component(s) to these flanges.
Note 1: Since the planet’s mass is rotating at a distance from the planet ring gear axis, ensure that when adding inertia to the ‘planet', 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, the configuration shown in the figure below should be used to correctly account for the relative velocity of the planet with respect to the carrier.
Including Planet/Carrier Bearing Friction
Kinematic Equation
where
is the gear ratio and is defined as:
where is the number of teeth of the outer planet gear and
is the number of teeth of the inner planet gear.
Also and are defined as the rotation angles of the carrier, outer planet, and inner planet, respectively.
Torque Balance Equation (No Inertia)
where , and are the torques applied to the carrier, ring, and planet, respectively and is the number of identical planets meshing with the ring.
Also is the loss torque and is defined as:
Also
= 
= 
where
,
Power Loss:
The power loss () is calculated as:
Connections
Name

Condition

Description

ID




Carrier flange

carrier




Planet flange

planet

ring



Ring flange

ring



Conditional real output port for power loss

lossPower


data source = input port

Conditional real input port for meshing loss data

lossdata



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:
•

entered via GUI [data entered via GUI]

•

by an attachment [data is attached to model]

•

by an external file [data is stored in a file]

•

an input port [input port]


datasourcemode


data source = input port




Number of efficiency inputs
•

1 input:

•

2 inputs:


inputNo







Gear ratio

ratio





Number of planet gears

numberofPlanets


data source = GUI



Defines Ring/Planet velocity dependant meshing efficiency as a function of .
The columns:
[ ( ( ) ( )]
First column is angular velocity of inner 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
( )

meshinglossTable

data source = attachment



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

data

data source = file



fileName


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 (

columns1

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 one.
See Also
MapleSim Driveline Library Overview
MapleSim Library Overview
1D Mechanical Overview
Basic Gear Sets
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.
