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Simpson Gear

The Simpson Gear component is composed of two planetary gear sets (rear and front). The rear and front Sun gears rotate together. The front carrier is connected to the rear ring. The gear ratios are uniquely defined by specifying the rear and front planetary gear ratios (i.e. Ring/Sun gear ratios).

This compound planetary gear set is constructed from four gear pairs; two Planet Ring gears, and two Planet Planet gears as shown in the diagram below.

Internal Structure

Internal Settings

 Component ${\mathbf{PPG}}_{\mathbf{1}}$ PR${\mathbf{G}}_{\mathbf{1}}$ ${\mathbf{PPG}}_{\mathbf{2}}$ ${\mathbf{PRG}}_{\mathbf{2}}$ , ${r}_{\mathrm{fR}/S}$ $\mathrm{ideal}=\mathbf{true}$ $\mathrm{ideal}=\mathbf{true}$ $\mathrm{ideal}=\mathbf{true}$ $\mathrm{ideal}=\mathbf{true}$ $\mathrm{ideal}=\mathbf{true}$ $\mathrm{ideal}=\mathbf{false}$   $\mathrm{η}\left(\mathrm{ω}\right)$, d $\mathrm{ideal}=\mathbf{false}$ $\mathrm{η}\left(\mathrm{ω}\right)$ $\mathrm{ideal}=\mathbf{false}$ $\mathrm{η}\left(\mathrm{ω}\right)$ $\mathrm{ideal}=\mathbf{false}$ $\mathrm{η}\left(\mathrm{ω}\right)$ $\mathrm{ideal}=\mathbf{false}$ $\mathrm{η}\left(\mathrm{ω}\right)$ $\mathrm{ideal}=\mathbf{false}$ $\mathrm{ideal}=\mathbf{false}$ $\mathrm{ideal}=\mathbf{false}$ $\mathrm{ideal}=\mathbf{false}$ $\mathrm{ideal}=\mathbf{false}$ 

Connections

 Name Condition Description ID $-$ Rear Carrier flange rear_carrier  $-$ Front Ring flange front_ring Rear Sun and Front Sun gears are connected) - Sun flange sun Rear Ring (rR) (the same as Front Carrier) $-$ Rear Ring flange rear_ring Rear planet flange rear_planet Front planet flange front_planet $\mathrm{ideal}\mathbf{=}\mathbf{false}$ Conditional real output port for power loss lossPower

Parameters

Symbol

Condition

Default

Units

Description

ID

$\mathrm{ideal}$

-

$\mathrm{true}$

-

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 [GUI]
 • by an attachment [attachment]
 • by an external file [file]

datasourcemode

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

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 [$=\mathbf{false}$].

SameMeshingEfficiency

${r}_{\mathrm{rR}/S}$

-

$2$

-

Rear ring/Sun Gear ratio

ratio2

${r}_{\mathrm{fR}/S}$

$-$

$2$

$-$

Front Ring/Sun Gear ratio

ratio1

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

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

$1$

$-$

Number of planet pair gears for both front and rear planetary gears

numberofPlanets

$\mathrm{\eta }\left(\mathrm{ω}\right)$

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

same loss data = true

data source = GUI

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

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

Defines all velocity dependant meshing efficiencies.

The columns are:

[${\mathrm{\omega }}_{}$      (${\mathrm{\eta }}_{1}$ ($\mathrm{ω}$ )     ${\mathrm{\eta }}_{2}$ ($\mathrm{ω}$ )]

Five options are available:

 • 1 by 1 array:

Entered value is taken as the constant efficiency for forward and backward cases

${\mathrm{\eta }}_{1}$ ($\mathrm{ω}$ ) = ${\mathrm{\eta }}_{2}$ ($\mathrm{ω}$ ) = ${\mathrm{\eta }}_{}$

 • 1 by 2 array:

First entered value is taken as the constant efficiency for forward case and the second for backward cases

${\mathrm{\eta }}_{1}$ ($\mathrm{\omega }$) =  ($\mathrm{ω}$ ) = ${\mathrm{\eta }}_{2}$

 • 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:

2nd column is forward and backward efficiency

$\mathrm{η}$ ($\mathrm{ω}$) = ${\mathrm{\eta }}_{1}$ ($\mathrm{\omega }$ ) = ${\mathrm{\eta }}_{2}$($\mathrm{ω}$ )

 • n by 3 array:

2nd column is forward efficiency

${\mathrm{\eta }}_{1}$ ($\mathrm{ω}$)

3rd column is backward efficiency

${\mathrm{\eta }}_{2}$ ($\mathrm{\omega }$ )

meshinglossTable5

ideal = false

same loss data = true

data source = attachment

-

Defines velocity dependant meshing efficiency

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

(See $\left[\mathrm{η}\right]$ below)

data5

ideal = false

same loss data = true

data source = file

-

fileName5

$\left[\mathrm{η}\right]$

ideal = false

same loss data = true

data source = attachment or file

$\left[2,3\right]$

-

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 (

columns5

${\mathrm{η}}_{\mathrm{rR}/P}\left({\mathrm{\omega }}_{\mathrm{rR}/C}\right)$

ideal = false

same loss data = false

data source = GUI

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

Defines rear Ring/rear Planet velocity dependant meshing efficiency as a function of  ${\mathrm{\omega }}_{\mathrm{rR}/C}$ .

The columns are:

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

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

Five options are available:

 • 1 by 1 array:

Entered value is taken as the constant efficiency for forward and backward cases

${\mathrm{\eta }}_{1}$(${\mathrm{\omega }}_{\mathrm{rR}/C}$ ) =$\left({\mathrm{\omega }}_{\mathrm{rR}/C}\right)$ =

 • 1 by 2 array:

First entered value is taken as the constant efficiency for forward case and the second for backward cases

${\mathrm{η}}_{1}$(${\mathrm{\omega }}_{\mathrm{rR}/C}$ ) =(${\mathrm{\omega }}_{\mathrm{rR}/C}$ ) =

 • 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 efficiencies

(${\mathrm{\omega }}_{\mathrm{rR}/C}$ ) = (${\mathrm{\omega }}_{\mathrm{rR}/C}$ ) = (${\mathrm{\omega }}_{\mathrm{rR}/C}$ )

 • n by 3 array:

Second column is forward efficiency

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

Third column is backward efficiency

(${\mathrm{\omega }}_{\mathrm{rR}/C}$ )

meshinglossTable2

ideal = false

same loss data = false

data source = attachment

-

Defines the velocity dependent meshing efficiency

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

(See $\left[{\eta }_{rR\mathit{/}P2}\right]$ below)

data2

ideal = false

same loss data = false

data source = file

-

fileName2

$\left[{\mathrm{η}}_{\mathrm{rR}\mathit{/}P}\right]$

ideal = false

same loss data = false

data source = attachment or file

$\left[2,3\right]$

-

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 (${\mathrm{\eta }}_{1}$) and

data column corresponding to the second column number is used for backward efficiency (${\mathrm{\eta }}_{2}$)

columns2

${\mathrm{η}}_{\mathrm{fR}/P}\left({\mathrm{\omega }}_{\mathrm{fR}/C}\right)$${}$

ideal = false

same loss data = false

data source = GUI



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

Defines front Ring/front Planet velocity dependant meshing efficiency as a function of  ${\mathrm{\omega }}_{\mathrm{fR}/C}$ .

The columns are:

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

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

Five options are available:

 • 1 by 1 array:

Entered value is taken as the constant efficiency for forward and backward cases

${\mathrm{\eta }}_{1}$(${\mathrm{\omega }}_{\mathrm{fR}/C}$) =$\left({\mathrm{\omega }}_{\mathrm{fR}/C}\right)$ =

 • 1 by 2 array:

First entered value is taken as the constant efficiency for forward case and the second for backward cases

${\mathrm{η}}_{1}$(${\mathrm{\omega }}_{\mathrm{fR}/C}$) =(${\mathrm{\omega }}_{\mathrm{fR}/C}$ ) =

 • 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

(${\mathrm{\omega }}_{S/C}$ ) = (${\mathrm{\omega }}_{\mathrm{fR}/C}$ ) = (${\mathrm{\omega }}_{\mathrm{fR}/C}$ )

 • n by 3 array:

Second column is forward efficiency

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

Third column is backward efficiency

(${\mathrm{\omega }}_{\mathrm{fR}/C}$ )

meshinglossTable1

ideal = false

same loss data = false

data source = attachment

-

Defines the velocity dependent meshing efficiency

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

(See $\left[{\mathrm{\eta }}_{\mathrm{fR}/P}\right]$ below)

data1

ideal = false

same loss data = false

data source = file

-

fileName1

$\left[{\mathrm{\eta }}_{\mathrm{fR}/P}\right]$

ideal = false

same loss data = false

data source = attachment or file

$\left[2,3\right]$

-

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

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 (${\mathrm{\eta }}_{1}$) and

data column corresponding to the second column number is used for backward efficiency (${\mathrm{\eta }}_{2}$)

columns1

${\mathrm{η}}_{\mathrm{rP}\mathit{/}S}\left({\mathrm{\omega }}_{\mathrm{rS}/C}\right)$${}$

ideal = false

same loss data = false

data source = GUI



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

Defines rear Planet/rear Sun velocity dependant meshing efficiency as a function of ${\mathrm{\omega }}_{\mathrm{rS}/C}$ .

The columns are:

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

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

Five options are available:

 • 1 by 1 array:

Entered value is taken as the constant efficiency for forward and backward cases

(${\mathrm{\eta }}_{1}$(${\mathrm{\omega }}_{\mathrm{rS}/C}$ ) =$\left({\mathrm{\omega }}_{\mathrm{rS}/C}\right)$ =)

 • 1 by 2 array:

First entered value is taken as the constant efficiency for forward case and the second for backward cases

(${\mathrm{η}}_{1}$(${\mathrm{\omega }}_{\mathrm{rS}/C}$ ) =(${\mathrm{\omega }}_{\mathrm{rS}/C}$ ) =)

 • 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

((${\mathrm{\omega }}_{\mathrm{rS}/C}$ ) = (${\mathrm{\omega }}_{\mathrm{rS}/C}$ ) = (${\mathrm{\omega }}_{\mathrm{rS}/C}$ ))

 • n by 3 array:

Second column is forward efficiency

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

Third column is backward efficiency

(${\mathrm{\omega }}_{\mathrm{rS}/C}$ )

meshinglossTable4

ideal = false

same loss data = false

data source = attachment

-

Defines the velocity dependent meshing efficiency

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

(See $\left[{\mathrm{\eta }}_{\mathrm{rP}\mathit{/}S}\right]$ below)

data4

ideal = false

same loss data = false

data source = file

-

fileName4

$\left[{\mathrm{η}}_{\mathrm{rP}\mathit{/}S}\right]$

ideal = false

same loss data = false

data source = attachment or file

$\left[2,3\right]$

-

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

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