Quadratic dependency of torque versus speed

 Description The Quadratic Speed Dependent Torque component models a torque that is quadratically dependent on the angular velocity of the flange. The Torque Direction parameter determines the sign of the torque when the velocity is reversed. The Use Support Flange boolean parameter enables a support flange on the housing. When true (checked) the support flange must be connected in the drawing. When false the component is internally fixed to ground.
 Equations $\mathrm{\tau }=-{\mathrm{\tau }}_{\mathrm{flange}}=-\frac{{\mathrm{\tau }}_{\mathrm{nom}}}{{\mathrm{\omega }}_{\mathrm{nom}}^{2}}\left\{\begin{array}{cc}1& \mathrm{Torque Direction}=\mathrm{true}\\ \mathrm{sign}\left(\mathrm{\omega }\right)& \mathrm{otherwise}\end{array}$ $\mathrm{\omega }=\stackrel{.}{\mathrm{\phi }}$ $\mathbf{if}\mathrm{Use Support Flange}\mathbf{then}{\mathrm{\tau }}_{\mathrm{support}}=-\mathrm{\tau }$ $\mathrm{\phi }={\mathrm{\phi }}_{\mathrm{flange}}-\left\{\begin{array}{cc}{\mathrm{\phi }}_{\mathrm{support}}& \mathrm{Use Support}\\ 0& \mathrm{otherwise}\end{array}$

Variables

 Name Units Description Modelica ID $\mathrm{\omega }$ $\frac{\mathrm{rad}}{s}$ Angular velocity of flange with respect to support w $\mathrm{\phi }$ $\mathrm{rad}$ Angle of flange with respect to support phi ${\mathrm{\phi }}_{\mathrm{flange}}$ $\mathrm{rad}$ Angle of flange flange.phi ${\mathrm{\phi }}_{\mathrm{support}}$ $\mathrm{rad}$ Angle of support support.phi $\mathrm{\tau }$ $Nm$ Accelerating torque acting at flange tau ${\mathrm{\tau }}_{\mathrm{flange}}$ $Nm$ Torque at flange flange.tau ${\mathrm{\tau }}_{\mathrm{support}}$ $Nm$ Torque at support support.tau

Connections

 Name Description Modelica ID $\mathrm{flange}$ Flange of shaft flange $\mathrm{support}$ support

Parameters

 Name Default Units Description Modelica ID ${\mathrm{\tau }}_{\mathrm{nom}}$ $Nm$ Nominal torque tau_nominal ${\mathrm{\omega }}_{\mathrm{nom}}$ $\frac{\mathrm{rad}}{s}$ Nominal speed w_nominal $\mathrm{Torque Direction}$ $\mathrm{true}$ True (checked) means the sign of the torque is independent of direction of rotation TorqueDirection Use Support Flange $\mathrm{false}$ True (checked) enables the support flange useSupport

 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.