Planet Planet Gear - MapleSim Help

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Planet Planet Gear

Planet Planet Gear component

The Planet Planet Gear component models a set of carrier, inner planet, and outer planet gear wheels with a specified gear ratio without inertia, elasticity, or backlash. The inertia of the gears and carrier may be included by attaching Inertia components to the ‘inplanet,’ ‘outplanet’, or ‘carrier’ flanges respectively. The damping in the bearing connecting the planet(s) to carrier can be included via the component options. Bearing friction on the ‘inplanet’, ‘outplanet’, and ‘carrier’ shafts may be included by attaching Bearing Friction component(s) to these flanges.

Note 1: Since the outer planet’s mass is rotating at a distance from the Planet Planet gear axis, ensure that when adding inertia to the ‘outer planet', proper inertia is also added to the ‘carrier’.

Note 2: When attaching a bearing friction component to the outer planet shaft to represent outplanet/carrier bearing friction, the configuration shown in the figure below should be used to correctly account for the relative velocity of the outer planet with respect to the carrier.

Including Outer Planet/Carrier Bearing Friction

Kinematic Equation

Where ${r}_{\mathrm{O}/I}$  is the gear ratio and is defined as:

${r}_{\mathrm{O}/I}=\frac{{N}_{\mathrm{O}}}{{N}_{I}}$

Where   ${N}_{\mathrm{O}}$ is the number of teeth of the outer planet gear and     is the number of teeth of the inner planet gear.
Also  and ${\mathrm{\varphi }}_{\mathrm{I}}$ are defined as the rotation angles of the carrier, outer planet, and inner planet, respectively.

Torque Balance Equation (No Inertia)

Where  are defined as the rotation angles of the carrier, outer planet, and inner planet, respectively. is the number of identical outer planets meshing with the inner planet.

Also is the loss torque and is defined as:



Also

${\mathrm{\omega }}_{I/C}$ =  - ${\mathrm{\omega }}_{C}$

${\mathrm{\omega }}_{\mathrm{O}/C}$ =  - ${\mathrm{\omega }}_{C}$

Where

,

Power Loss

The power loss (${P}_{\mathrm{loss}}$) is calculated as:



Connections

 Name Condition Description ID $\mathrm{Carrier}$ - Carrier flange carrier - Inner planet flange inplanet Outer planet - Outer planet flange outplanet $\mathrm{ideal}=\mathbf{false}$ 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

$\mathrm{ideal}$

-

$\mathbf{true}$

-

Defines whether the component is:

true - ideal or

false - non-ideal

ideal

data source

$\mathrm{ideal}=\mathbf{false}$

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

${n}_{\mathrm{inputs}}$

data source = input port

$1$

-

Number of inputs

 • 1 input:
 • 2 inputs:

inputNo

${r}_{\mathrm{O}/I}$

-

$1$

-

Gear ratio

ratio

${n}_{\mathrm{pl}}$

$\mathrm{ideal}=\mathbf{false}$

$1$



Number of planet gears

numberofPlanets

$\mathrm{\eta }\left({\mathrm{\omega }}_{I/C}\right)$

$\mathrm{ideal}=\mathbf{false}$

data source = GUI

$\left[0,1,1\right]$

$\left[\frac{\mathrm{rad}}{s},-,-\right]$

Defines Outer Planet/Inner Planet velocity dependant meshing efficiency as a function of ${\mathrm{\omega }}_{I/C}$ .

The columns:

[${\mathrm{\omega }}_{I/C}$     (${\mathrm{\eta }}_{1}$ (${\mathrm{\omega }}_{I/C}$ )     ${\mathrm{\eta }}_{2}$ (${\mathrm{\omega }}_{I/C}$ )]

First column is angular velocity of inner gear w.r.t. carrier (${\mathrm{\omega }}_{I/C}$)

Five options are available:

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

${\mathrm{\eta }}_{1}$ (${\mathrm{\omega }}_{I/C}$ ) = (${\mathrm{\omega }}_{I/C}$ ) =

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

${\mathrm{\eta }}_{1}$ (${\mathrm{\omega }}_{I/C}$ ) = (${\mathrm{\omega }}_{I/C}$ ) = ${\mathrm{\eta }}_{2}$

 • 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

$\mathrm{η}$ (${\mathrm{\omega }}_{I/C}$ ) = ${\mathrm{\eta }}_{1}$ (${\mathrm{\omega }}_{I/C}$ ) = ${\mathrm{\eta }}_{2}$(${\mathrm{\omega }}_{I/C}$ )

 • n by 3 array:

Second column is forward efficiency

${\mathrm{\eta }}_{1}$ (${\mathrm{\omega }}_{I/C}$)

Third column is backward efficiency

${\mathrm{\eta }}_{2}$ (${\mathrm{\omega }}_{I/C}$ )

meshinglossTable

$\mathrm{ideal}=\mathbf{false}$

data source = attachment

Defines velocity dependant meshing efficiency

First column is angular velocity (${\mathrm{\omega }}_{I/C}$ )

(See $\left[\mathrm{η}\right]$ below)

data

$\mathrm{ideal}=\mathbf{false}$

data source = file

fileName

$\left[\mathrm{η}\right]$

$\mathrm{ideal}=\mathbf{false}$

$\left[2,3\right]$

-

Defines the corresponding data columns used for forward efficiency (${\mathrm{\eta }}_{1}$) and backward efficiency (${\mathrm{\eta }}_{2}$ )

Two options are available:

 • 1 by 1 array:

Data column corresponding to the column number is used for both forward and backward efficiency (

 • 1 by 2 array:

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

$\mathrm{ideal}=\mathbf{false}$

0

$\left[\frac{\mathrm{N}·\mathrm{m}}{\frac{\mathrm{rad}}{s}}\right]$

Linear damping in planet/carrier bearing

d

smoothness

$\mathrm{ideal}=\mathbf{false}$

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 ${r}_{\mathrm{O}/I}$  must be strictly greater than zero.

References

Pelchen C., Schweiger C., and Otter M., “Modeling and Simulating the Efficiency of Gearboxes and Planetary Gearboxes,” 2nd International Modelica Conference, Proceedings, pp. 257-266.