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
PPG1
PRG1
PPG2
PRG2
rrR/S , rfR/S
rO/I = rfR/S − 12
rR/P = 2 rfR/SrfR/S − 1
rO/I = rrR/S − 12
rR/P = 2 rrR/SrrR/S − 1
ideal=true
ideal=false
same loss data=true
ηω, d
ηωI/C = ηω
d = d
ηωR/C = ηω
d = 0
same loss data= false
ηrP/SωrS/C, ηrR/PωrR/CηfP/SωfS/C, ηfR/PωfR/C
drP/C , dfP/C
ηωI/C = ηfP/SωfS/C
d =dfP/C
ηωR/C = ηfR/PωfR/C d = 0
ηωI/C = ηrP/SωrS/C
d =drP/C
ηωR/C = ηrR/PωrR/C
Connections
Name
Condition
Description
ID
Rear Carrier rC
−
Rear Carrier flange
rear_carrier
Front Ring fR
Front Ring flange
front_ring
Sun S (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 rP
planet port=true
Rear planet flange
rear_planet
Front Planet fP
Front planet flange
front_planet
Loss Power
Conditional real output port for power loss
lossPower
Parameters
Symbol
Default
Units
ideal
true
Defines whether the component is:
true - ideal or
false - non-ideal
data source
GUI
Defines the source for the loss data:
entered via GUI [GUI]
by an attachment [attachment]
by an external file [file]
datasourcemode
same loss data
Defines whether one efficiency data table is used for all meshing loss calculations [same loss data=true] or the efficiency of each meshing gear pair is given by a separate data table [same loss data=false].
SameMeshingEfficiency
rrR/S
2
Rear ring/Sun Gear ratio
ratio2
rfR/S
Front Ring/Sun Gear ratio
ratio1
npl
1
Number of planet pair gears for both front and rear planetary gears
numberofPlanets
ηω
same loss data = true
data source = GUI
0,1,1
rads,−,−
Defines all velocity dependant meshing efficiencies.
The columns are:
[ω (η1 (ω ) η2 (ω )]
Five options are available:
1 by 1 array:
Entered value is taken as the constant efficiency for forward and backward cases
η1 (ω ) = η2 (ω ) = η
1 by 2 array:
First entered value is taken as the constant efficiency for forward case and the second for backward cases
η1 (ω) = η1 , η2 (ω ) = η2
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
η (ω) = η1 (ω ) = η2(ω )
n by 3 array:
2nd column is forward efficiency
η1 (ω)
3rd column is backward efficiency
η2 (ω )
meshinglossTable5
ideal = false
data source = attachment
Defines velocity dependant meshing efficiency
First column is angular velocity (ω)
(See col η below)
data5
data source = file
fileName5
col η
data source = attachment or file
2,3
Defines the corresponding data columns used for forward efficiency (η1) and backward efficiency (η2 )
Two options are available:
Data column corresponding to the column number is used for both forward and backward efficiency (η=η1 = η2)
Data column corresponding to the first column number is used for forward efficiency ( η1)
and data column corresponding to the second column number is used for backward efficiency ( η2)
columns5
ηrR/PωrR/C
same loss data = false
rads,−, −
Defines rear Ring/rear Planet velocity dependant meshing efficiency as a function of ωrR/C .
[ωrR/C (η1(ωrR/C ) η2(ωrR/C )]
First column is angular velocity of the ring gear w.r.t. the carrier (ωrR/C)
η1(ωrR/C ) = η2ωrR/C = η
η1(ωrR/C ) = η1 , η2(ωrR/C ) = η2
First column is ignored and the second and third values are taken as constant efficiencies for forward and backward cases, respectively.
Second column is forward and backward efficiencies
η (ωrR/C ) = η1 (ωrR/C ) = η2 (ωrR/C )
Second column is forward efficiency
η1 (ωrR/C )
Third column is backward efficiency
η2 (ωrR/C )
meshinglossTable2
Defines the velocity dependent meshing efficiency
First column is angular velocity (ωrR/C )
(See col ηrR/P2 below)
data2
fileName2
col ηrR/P
Defines the corresponding data columns used for forward efficiency (η1) and backward efficiency (η2)
Data column corresponding to the column number is used for both forward and backward efficiency (η1=η2 = η)
Data column corresponding to the first column number is used for forward efficiency (η1) and
data column corresponding to the second column number is used for backward efficiency (η2)
columns2
ηfR/PωfR/C
Defines front Ring/front Planet velocity dependant meshing efficiency as a function of ωfR/C .
[ωfR/C (η1(ωfR/C ) η2(ωfR/C )]
First column is angular velocity of the sun gear w.r.t. carrier (ωS/C)
η1(ωfR/C) = η2ωfR/C = η
η1(ωfR/C) = η1 , η2(ωfR/C ) = η2
Second column is forward and backward efficiency
η (ωS/C ) = η1 (ωfR/C ) = η2 (ωfR/C )
η1 (ωfR/C )
η2 (ωfR/C )
meshinglossTable1
First column is angular velocity (ωfR/C )
(See col ηfR/P below)
data1
fileName1
col ηfR/P
Defines the corresponding data columns used for forward (η1) and backward (η2) efficiency
columns1
ηrP/SωrS/C
Defines rear Planet/rear Sun velocity dependant meshing efficiency as a function of ωrS/C .
[ωrS/C (η1(ωrS/C ) η2(ωrS/C )]
First column is angular velocity of the sun gear w.r.t. carrier (ωrS/C)
(η1(ωrS/C ) = η2ωrS/C = η)
(η1(ωrS/C ) = η1 , η2(ωrS/C ) = η2)
(η (ωrS/C ) = η1 (ωrS/C ) = η2 (ωrS/C ))
η1 (ωrS/C )
η2 (ωrS/C )
meshinglossTable4
First column is angular velocity (ωrS/C )
(See col ηrP/S below)
data4
fileName4
col ηrP/S
Data column corresponding to the column number is used for both forward and backward efficiency η1=η2 = η
columns4
ηfP/SωfS/C
rads, N·m, N·m
Defines front Planet/front Sun velocity dependant meshing efficiency as a function of ωfS/C .
[ωfS/C η1ωfS/C η2ωfS/C]
First column is angular velocity of the sun gear w.r.t. carrier (ωfS/C)
Entered value is taken as the constant friction torque for forward and backward cases
η1(ωfS/C ) = η2ωfS/C = η
First entered value is taken as the constant friction torque for forward case and the second for backward cases
η1(ωfS/C ) = η1 , η2(ωfS/C ) = η2
First column is ignored and the second and third values are taken as constant friction torque for forward and backward cases, respectively
η(ωfS/C) = η1 (ωfS/C ) = η2 (ωfS/C )
η1 (ωfS/C )
η2(ωfS/C )
bearinglossTable3
First column is angular velocity (ωfS/C )
(See col ηfP/S below)
data3
fileName3
col ηfP/S
Data column corresponding to the first column number is used for forward friction torque (η1) and data column corresponding to the second column number is used for backward friction torque (η2)
columns3
drP/C
0
N · mrads
Linear damping in rear planet/carrier bearings
d2
dfP/C
Linear damping in front planet/carrier bearings
d1
d
Linear damping in both planet/carrier bearings
d3
smoothness
Table points are linearly interpolated
Defines the smoothness of table interpolation
There are two options:
Table points are interpolated such that the first derivative is continuous
See Also
Driveline Library Overview
MapleSim Library Overview
1-D Mechanical Overview
Gear Sets
Planetary Gear
Planet Planet Gear
Planet Ring Gear
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