Translational Hardstop

Double-sided translational mechanism that restricts motion to a set length

 Description The Translational Hardstop component represents a double-sided translational mechanism that restricts the motion to a set length. The mechanism is assumed to be in the center of this region so that the solid connector, ${\mathrm{flange}}_{a}$, is attached to the center of the gap, and the hollow connector, ${\mathrm{flange}}_{b}$, is attached to the frame that is moving back and forth. The hardstop is modeled as a stiff spring-damper. The compliance of the mechanism can be controlled by adjusting the stiffness ($c$) and damping ($d$) coefficients in the component parameters.
 Equations ${s}_{\mathrm{rel}}={s}_{b}-{s}_{a}\phantom{\rule[-0.0ex]{3.5ex}{0.0ex}}{v}_{\mathrm{rel}}={\stackrel{.}{s}}_{\mathrm{rel}}$ $F={F}_{b}=-{F}_{a}=\left\{\begin{array}{cc}\left\{\begin{array}{cc}c\left({s}_{\mathrm{rel}}-\frac{b}{2}\right)+d{v}_{\mathrm{rel}}& {s}_{\mathrm{rel}}>\frac{b}{2}\\ c\left({s}_{\mathrm{rel}}+\frac{b}{2}\right)+d{v}_{\mathrm{rel}}& {s}_{\mathrm{rel}}<\frac{b}{2}\\ 0& \mathrm{otherwise}\end{array}& b>2{10}^{-10}\\ c{s}_{\mathrm{rel}}+d{v}_{\mathrm{rel}}& \mathrm{otherwise}\end{array}$

Variables

 Name Units Description Modelica ID $F$ $N$ Force at ${\mathrm{flange}}_{b}$ F ${F}_{x}$ $N$ Force at flange $x,x\in \left\{a,b\right\}$ flange_x.f ${s}_{\mathrm{rel}}$ $m$ Distance between flanges s_rel ${s}_{x}$ $m$ Position of flange $x,x\in \left\{a,b\right\}$ flange_x.s

Connections

 Name Description Modelica ID ${\mathrm{flange}}_{a}$ Left flange of compliant 1-dim. translational component flange_a ${\mathrm{flange}}_{b}$ Right flange of compliant 1-dim. translational component flange_b

Parameters

General Parameters

 Name Default Units Description Modelica ID $b$ $1$ $m$ Distance between stops b $c$ $1·{10}^{10}$ $\frac{N}{m}$ Spring constant c $d$ $1·{10}^{10}$ $\frac{Ns}{m}$ Damping constant d

 Name Default Units Description Modelica ID $\mathrm{prefer}$ Prioritize ${s}_{\mathrm{rel}}$ and ${v}_{\mathrm{rel}}$ as states stateSelect ${s}_{\mathrm{nominal}}$ $1·{10}^{-4}$ $m$ Nominal value of s_rel (used for scaling) s_nominal