Translational Position

Forced movement of a flange according to a reference position

 Description The Translational Position (or Position) component generates a forced translation at the flange according to an input signal, ${s}_{\mathrm{ref}}$ The $\mathrm{Exact}$ boolean parameter determine how ${s}_{\mathrm{ref}}$ is used: When $\mathrm{Exact}$ is true, ${s}_{\mathrm{ref}}$ is used as-is. The input signal must be twice-differentiable. When $\mathrm{Exact}$ is false (the default), ${s}_{\mathrm{ref}}$ is filtered and the second derivative of the filtered curve is used to compute the reference acceleration of the flange. This second derivative is not computed by numerical differentiation but rather by a second-order Bessel filter. The critical frequency of the filter (cut-off frequency) is defined by the parameter ${f}_{\mathrm{crit}}$. This frequency should be higher than the essential low frequencies in the signal. 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 $\left\{\begin{array}{cc}\left\{\begin{array}{c}s={s}_{\mathrm{ref}}\\ v=0\\ a=0\end{array}& \mathrm{exact}\\ \left\{\begin{array}{c}a=\left(\left({s}_{\mathrm{ref}}-s\right){w}_{\mathrm{crit}}-{a}_{f}v\right)\frac{{w}_{\mathrm{crit}}}{{b}_{f}}\\ \stackrel{.}{v}=a\\ \stackrel{.}{s}=v\end{array}& \mathrm{otherwise}\end{array}$ ${w}_{\mathrm{crit}}=2\mathrm{\pi }{f}_{\mathrm{crit}}$ $\mathbf{if}\mathrm{Use Support Flange}\mathbf{then}{f}_{\mathrm{support}}=-f$ $s={s}_{\mathrm{flange}}-\left\{\begin{array}{cc}{s}_{\mathrm{support}}& \mathrm{Use Support}\\ 0& \mathrm{otherwise}\end{array}$

Variables

 Name Units Description Modelica ID $a$ $\frac{m}{{s}^{2}}$ If $\mathrm{Exact}$ is false, absolute acceleration of flange else 0 a $f$ $N$ Accelerating force acting at flange f ${f}_{\mathrm{support}}$ $N$ Force acting at support support.f $s$ $m$ Distance between flange and support s ${s}_{\mathrm{flange}}$ $m$ Position of flange flange.s ${s}_{\mathrm{support}}$ $m$ Position of support support.s $v$ $\frac{m}{s}$ If $\mathrm{Exact}$ is false, absolute velocity of flange else 0 v

Connections

 Name Description Modelica ID $\mathrm{flange}$ Flange of component flange ${s}_{\mathrm{ref}}$ Real input; reference position of flange in $m$ s_ref $\mathrm{support}$ support

Parameters

 Name Default Units Description Modelica ID Exact $\mathrm{false}$ True (checked) means the reference position is treated exactly exact ${f}_{\mathrm{crit}}$ $50$ $\mathrm{Hz}$ Critical frequency of input signal when exact is set to false f_crit Use Support Flange $\mathrm{false}$ True (checked) means the support flange is enabled useSupport

Constants

 Name Value Units Description Modelica ID ${a}_{f}$ $1.3617$ $1$ Coefficient of $s$ in Bessel filter af ${b}_{f}$ $0.618$ $1$ Coefficient of ${s}^{2}$ in Bessel filter bf

 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.