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

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

$\{\begin{array}{cc}\left\{{\mathrm{\eta }}_{\mathrm{mf}}\&equals;{\mathrm{\eta }}_{\mathrm{mf1}}\&comma;{\mathrm{\tau }}_{\mathrm{bf}}\&equals;{\mathrm{\tau }}_{\mathrm{bf1}}\right\}& \left({\mathrm{\tau }}_a-{\mathrm{\tau }}_{{\mathrm{bf}}_a}\right)w_a\&gt;0\vee \left({\mathrm{\tau }}_a\&equals;{\mathrm{\tau }}_{{\mathrm{bf}}_a}\wedge w_a\&gt;0\right)\\ \left\{{\mathrm{\eta }}_{\mathrm{mf}}\&equals;{\mathrm{\eta }}_{\mathrm{mf2}}\&comma;{\mathrm{\tau }}_{\mathrm{bf}}\&equals;{\mathrm{\tau }}_{\mathrm{bf2}}\right\}& \left({\mathrm{\tau }}_a-{\mathrm{\tau }}_{{\mathrm{bf}}_a}\right)w_a<0\vee \left({\mathrm{\tau }}_a\&equals;{\mathrm{\tau }}_{{\mathrm{bf}}_a}\wedge w_a<0\right)\\ {\stackrel{\&period;}{w}}_a\&equals;0& \mathrm{otherwise}\end{array}$

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.

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.