Basic Gear
Basic Gear component
The Basic Gear component models two meshing gears without inertia, elasticity or backlash. Gear and bearing friction inertia may be included by attaching the Inertia and Bearing Friction components to either ‘flange_a’ or ‘flange_b’, respectively.
Kinematic Equation
ϕa = −rb/a·ϕb
Where rb/a is the gear ratio and is defined as:
rb/a=NbNa
Where Na is the number of teeth of the a-side gear and Nb is the number of teeth of the b-side gear. Also, ϕa and ϕb are defined as
ϕx = ϕfx −ϕsupport use Support = true0otherwise , x ∈ a,b
Where ϕfa and ϕfb are the absolute rotation angles of flange_a and flange_b, respectively.
Torque Balance Equation (No Inertia)
τb=rb/a·τa−τloss
Where τa and τb are the torques applied to flange_a and flange_b, respectively.
Also τloss is the meshing loss torque and is defined as:
τloss=(1−η1(ωa)) · τa ωa·τa≥0 (1−1η2(ωa) )·τa ωa·τa<0
Where
ωa = ⅆⅆ t ϕa =ϕ·a
When useSupport = true, the following equation is added to calculate the support reaction torque:
τsupport = − τa+τb
Power Loss:
The power loss (Ploss) is calculated as:
Ploss = 0 ideal=true1−η1 · τa· ωa τa· ωa≥0 1−1η2 · τa· ωa τa· ωa<0
Connections
Name
Condition
Description
ID
flangea
-
Flange to driver shaft
flange_a
flangeb
Flange to driven shaft
flange_b
support
use support=true
Conditional Support Flange
Loss Power
ideal=false
Conditional real output port for power loss
lossPower
Loss Data
data source = input port
Conditional real input port for loss data
lossdata
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 [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
ninputs
1
Number of inputs
One input (ninputs=1): Forward and backward efficiencies are the same:η=η1 = η2
Two inputs (ninputs=2): Forward and backward efficiencies are given independently: η1 , η2
inputNo
use support
false
Enables/disables the support flange
useSupport
rb/a
Gear ratio
ratio
ηωa
data source = GUI
0,1,1
rads,−,−
Defines velocity dependant meshing efficiency
The columns:
[ωa (η1 (ωa ) η2 (ωa )]
Five options are available:
1 by 1 array: entered value is taken as the constant efficiency for forward and backward cases
η1 (ωa ) = η2 (ωa ) = η
1 by 2 array: first entered value is taken as the constant efficiency for forward case and the second for backward cases
η1 (ωa ) = η1 , η2 (ωa ) = 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 (ωa ) = η1 (ωa ) = η2(ωa )
n by 3 array:
2nd column is forward efficiency
η1 (ωa )
3rd column is backward efficiency
η2 (ωa )
Note: The rows of the array are ordered according to ωa, with the first row having the smallest |ωa|
meshinglossTable
data source = attachment
First column is angular velocity (ωa )
(See col η below)
data
data source = file
fileName
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:
1 by 1 array:
Data column corresponding to the column number is used for both forward and backward efficiencies (η=η1 = η2)
1 by 2 array:
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)
columns
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
Note: The ratio (rb/a) must be non-zero. Negative values are permissible. For (rb/a) < 0, the Basic Gear component resembles the Ideal Gear (when ideal = true) and Lossy Gear (ideal = false).
See Also
Driveline Library Overview
MapleSim Library Overview
1-D Mechanical Overview
Basic Gear Sets
Ideal Gear
Lossy 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. 257-266.
Download Help Document