Home : Support : Online Help : MapleSim Toolboxes : MapleSim Driveline Component Library : Simple Gear Sets : Basic Gear Sets : DrivelineComponentLibrary/basicGear

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

Where   ${r}_{b/a}$  is the gear ratio and is defined as:

${r}_{b/a}=\frac{{N}_{b}}{{N}_{a}}$

Where ${N}_{a}$ is the number of teeth of the a-side gear and ${N}_{b}$ is the number of teeth of the b-side gear. Also,  and ${\mathrm{\varphi }}_{b}$ are defined as

,   $x$ ∈ $\left\{a,b\right\}$

Where ${\mathrm{\varphi }}_{\mathrm{fa}}$ and ${\mathrm{\varphi }}_{\mathrm{fb}}$ are the absolute rotation angles of flange_a and flange_b, respectively.

Torque Balance Equation (No Inertia)

${\mathrm{τ}}_{b}={r}_{b/a}·\left({\mathrm{τ}}_{a}-{\mathrm{τ}}_{\mathrm{loss}}\right)$

Where and ${\mathrm{\tau }}_{b}$ are the torques applied to flange_a and flange_b, respectively.

Also   ${\mathrm{\tau }}_{\mathrm{loss}}$ is the meshing loss torque and is defined as:

Where

${\mathrm{\omega }}_{a}$ =



When useSupport = true, the following equation is added to calculate the support reaction torque:

${\mathrm{\tau }}_{\mathrm{support}}$  =

Power Loss:

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

Connections

 Name Condition Description ID ${\mathrm{flange}}_{a}$ - Flange to driver shaft flange_a ${\mathrm{flange}}_{b}$ - Flange to driven shaft flange_b support support $\mathrm{ideal}=\mathbf{false}$ Conditional real output port for power loss lossPower data source = input port Conditional real input port for 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

 • One input (${n}_{\mathrm{inputs}}$=1): Forward and backward efficiencies are the same:
 • Two inputs (${n}_{\mathrm{inputs}}$=2): Forward and backward efficiencies are given independently:

inputNo

use support

-

$\mathbf{false}$

-

Enables/disables the support flange

useSupport

${r}_{b/a}$

-

$1$

-

Gear ratio

ratio

$\mathrm{η}\left({\mathrm{ω}}_{a}\right)$

data source = GUI

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

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

Defines velocity dependant meshing efficiency

The columns:

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

Five options are available:

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

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

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

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

 • 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

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

 • n by 3 array:

2nd column is forward efficiency

${\mathrm{\eta }}_{1}$ (${\mathrm{\omega }}_{a}$ )

3rd column is backward efficiency

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

Note: The rows of the array are ordered according to ${\mathrm{\omega }}_{a}$, with the first row having the smallest |${\mathrm{\omega }}_{a}$|

meshinglossTable

data source = attachment

Defines velocity dependant meshing efficiency

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

(See $\left[\mathrm{η}\right]$ below)

data

data source = file

Defines velocity dependant meshing efficiency

fileName

$\left[\mathrm{η}\right]$

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 efficiencies ()

 • 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 (${\mathrm{\eta }}_{2}$)

columns

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:  The ratio (${r}_{b/a}$) must be non-zero. Negative values are permissible.  For (${r}_{b/a}$) < 0, the Basic Gear component resembles the Ideal Gear (when ideal = true) and Lossy Gear (ideal = false).

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.