 Lossy Gear - MapleSim Help

# Online Help

###### All Products    Maple    MapleSim

Home : Support : Online Help : MapleSim : MapleSim Component Library : 1-D Mechanical : Rotational : Bearings and Gears : componentLibrary/1Dmechanics/rotational/bearingsGears/LossyGear

Lossy Gear

Gear with mesh efficiency and bearing friction (stuck/rolling possible)  Description

The Lossy Gear component models the gear ratio and the losses of a standard gear box in a realistic way, including the stuck phases that may occur at zero speed. The gear boxes that can be handled are fixed in the ground or on a moving support, have one input and one output shaft, and are essentially described by the equations

${\mathrm{\phi }}_{a}=r{\mathrm{\phi }}_{b}$

$-{\mathrm{\tau }}_{b}=r\left({\mathrm{\eta }}_{\mathrm{mf}}{\mathrm{\tau }}_{a}-{\mathrm{\tau }}_{\mathrm{bf}}\right)$

where $r$ is constant gear ratio, ${\mathrm{\eta }}_{\mathrm{mf}}$ is the efficiency due to mesh friction, and ${\mathrm{\tau }}_{\mathrm{bf}}$ is the bearing friction torque.

Loss Table

The Loss Table parameter is five-column table that defines the loss terms ${\mathrm{\eta }}_{\mathrm{mf}}$ and ${\mathrm{\tau }}_{\mathrm{bf}}$ in terms of the absolute value of the input shaft speed, ${w}_{a}$, and of the energy flow direction. Its columns are $\left[|{w}_{a}|,{\mathrm{\eta }}_{\mathrm{mf1}},{\mathrm{\eta }}_{\mathrm{mf2}},{\mathrm{\tau }}_{\mathrm{bf1}},{\mathrm{\tau }}_{\mathrm{bf2}}\right]$ with

 $\left|{w}_{a}\right|$ $\frac{\mathrm{rad}}{s}$ Angular speed of ${\mathrm{flange}}_{a}$ ${\mathrm{\eta }}_{\mathrm{mf1}}$ $1$ Mesh efficiency when input shaft is driving ${\mathrm{\eta }}_{\mathrm{mf2}}$ $1$ Mesh efficiency when output shaft is driving ${\mathrm{\tau }}_{\mathrm{bf1}}$ $Nm$ Absolute bearing friction torque when input shaft is driving ${\mathrm{\tau }}_{\mathrm{bf2}}$ $Nm$ Absolute bearing friction torque when output shaft is driving

The rows of the Loss Table are ordered according to ${\mathrm{\omega }}_{a}$, with the first row having the smallest ${\mathrm{\omega }}_{a}$. The values for ${\mathrm{\eta }}_{\mathrm{mf1}}$, ${\mathrm{\eta }}_{\mathrm{mf2}}$, ${\mathrm{\tau }}_{\mathrm{bf1}}$, and ${\mathrm{\tau }}_{\mathrm{bf2}}$ at a particular shaft speed are interpolated from the values in the table.

To add rows to the table, right-click on the value and select Edit Matrix Dimension.

With these variables, the mesh efficiency and the bearing friction are formally defined as

$\left\{\begin{array}{cc}\left\{{\mathrm{\eta }}_{\mathrm{mf}}={\mathrm{\eta }}_{\mathrm{mf1}},{\mathrm{\tau }}_{\mathrm{bf}}={\mathrm{\tau }}_{\mathrm{bf1}}\right\}& \left({\mathrm{\tau }}_{a}-{\mathrm{\tau }}_{{\mathrm{bf}}_{a}}\right){w}_{a}>0\vee \left({\mathrm{\tau }}_{a}={\mathrm{\tau }}_{{\mathrm{bf}}_{a}}\wedge {w}_{a}>0\right)\\ \left\{{\mathrm{\eta }}_{\mathrm{mf}}={\mathrm{\eta }}_{\mathrm{mf2}},{\mathrm{\tau }}_{\mathrm{bf}}={\mathrm{\tau }}_{\mathrm{bf2}}\right\}& \left({\mathrm{\tau }}_{a}-{\mathrm{\tau }}_{{\mathrm{bf}}_{a}}\right){w}_{a}<0\vee \left({\mathrm{\tau }}_{a}={\mathrm{\tau }}_{{\mathrm{bf}}_{a}}\wedge {w}_{a}<0\right)\\ {\stackrel{.}{w}}_{a}=0& \mathrm{otherwise}\end{array}$

Losses are modeled in a physically meaningful way taking into account that at zero speed the movement may be locked due to the friction in the gear teeth and/or in the bearings.

Variables

 Name Units Description Modelica ID ${\mathrm{\phi }}_{x}$ $\mathrm{rad}$ Absolute angle of ${\mathrm{flange}}_{x},x\in \left\{a,b\right\}$ flange_x.phi ${\mathrm{\phi }}_{\mathrm{support}}$ $\mathrm{rad}$ Absolute angle of support flange support.phi ${\mathrm{\tau }}_{x}$ $Nm$ Torque applied to ${\mathrm{flange}}_{x},x\in \left\{a,b\right\}$ flange_x.tau

Connections

 Name Description Modelica ID ${\mathrm{flange}}_{a}$ Flange of left shaft flange_a ${\mathrm{flange}}_{b}$ Flange of right shaft flange_b $\mathrm{support}$ support $\mathrm{heatPort}$ heatPort

Parameters

 Name Default Units Description Modelica ID $r$ $1$ $1$ Transmission ratio ($\frac{{\mathrm{\phi }}_{a}}{{\mathrm{\phi }}_{b}}$) ratio $\mathrm{Loss Table}$ $\left[0.,1.,1.,0.,0.\right]$ Matrix for mesh efficiencies and bearing friction depending on speed lossTable Use Heat Port $\mathrm{false}$ True (checked) means heat port is enabled useHeatPort Use Support Flange $\mathrm{false}$ True (checked) enables the support flange useSupport

Constants

 Name Value Units Description Modelica ID $\mathrm{Unknown}$ $3$ Value of mode is not known Unknown $\mathrm{Free}$ $2$ Element is not active Free $\mathrm{Forward}$ $1$ w_a > 0 (forward rolling) Forward $\mathrm{Stuck}$ $0$ w_a = 0 (forward rolling, locked or backward rolling) Stuck $\mathrm{Backward}$ $-1$ w_a < 0 (backward rolling) Backward $\mathrm{unitAngularAcceleration}$ $1$ $\frac{\mathrm{rad}}{{s}^{2}}$ unitAngularAcceleration $\mathrm{unitTorque}$ $1$ $Nm$ unitTorque

 Modelica Standard Library The component described in this topic is from the Modelica Standard Library. To view the original documentation, which includes author and copyright information, click here.

 See Also