Rotational Position

Forced movement of a flange according to a reference angle signal

 Description The Rotational Position (or Position) component generates a forced angular position at the flange according to an input signal that specifies a reference angle. The $\mathrm{Exact}$ boolean parameter determine how ${\mathrm{\phi }}_{\mathrm{ref}}$ is used: When $\mathrm{Exact}$ is true, ${\mathrm{\phi }}_{\mathrm{ref}}$ is used as-is. The input signal must be twice-differentiable. When $\mathrm{Exact}$ is false (the default), ${\mathrm{\phi }}_{\mathrm{ref}}$ 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.
 Equations $\left\{\begin{array}{cc}\left\{\begin{array}{c}\mathrm{\phi }={\mathrm{\phi }}_{\mathrm{ref}}\\ w=0\\ a=0\end{array}\right\}& \mathrm{exact}\\ \left\{\begin{array}{c}a=\left(\left({\mathrm{\phi }}_{\mathrm{ref}}-\mathrm{\phi }\right){w}_{\mathrm{crit}}-{a}_{f}w\right)\frac{{w}_{\mathrm{crit}}}{{b}_{f}}\\ \stackrel{.}{w}=a\\ \stackrel{.}{\mathrm{\phi }}=w\end{array}\right\}& \mathrm{otherwise}\end{array}$ ${w}_{\mathrm{crit}}=2\mathrm{\pi }{f}_{\mathrm{crit}}$ $\mathbf{if}\mathrm{Use Support Flange}\mathbf{then}{\mathrm{\tau }}_{\mathrm{support}}=-\mathrm{\tau }$ $\mathrm{\phi }={\mathrm{\phi }}_{\mathrm{flange}}-\left\{\begin{array}{cc}{\mathrm{\phi }}_{\mathrm{support}}& \mathrm{Use Support}\\ 0& \mathrm{otherwise}\end{array}$

Variables

 Name Units Description Modelica ID $a$ $\frac{\mathrm{rad}}{{s}^{2}}$ If Exact is false, angular acceleration of flange with respect to support else 0 a $\mathrm{\phi }$ $\mathrm{rad}$ 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 $w$ $\frac{\mathrm{rad}}{s}$ If Exact is false, angular velocity of flange with respect to support else 0 w

Connections

 Name Description Modelica ID $\mathrm{flange}$ Flange of shaft flange $\mathrm{support}$ support ${\mathrm{\phi }}_{\mathrm{ref}}$ Real input; reference angle in $\mathrm{rad}$ phi_ref

Parameters

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

Constants

 Name Value Units Description Modelica ID ${a}_{f}$ $1.3617$ s coefficient of Bessel filter af ${b}_{f}$ $0.618$ ss coefficient of 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.