Double Acting Cylinder

Ideal transformation between hydraulic and 1-D translational work

 Description The Double Acting Cylinder component models a double-acting translational actuator. It transforms energy between the hydraulic and translational domains. Optional end cushions restrict the stroke length of the piston.
 Equations ${q}_{a}={A}_{a}{v}_{\mathrm{rel}}\phantom{\rule[-0.0ex]{3.5ex}{0.0ex}}{q}_{b}=-{A}_{b}{v}_{\mathrm{rel}}$ ${s}_{\mathrm{rel}}={s}_{b}-{s}_{a}\phantom{\rule[-0.0ex]{2.5ex}{0.0ex}}{v}_{\mathrm{rel}}=\frac{\mathrm{d}{s}_{\mathrm{rel}}}{\mathrm{d}t}$ ${f}_{a}=-{f}_{b}=\left\{\begin{array}{cc}f+{f}_{{e}_{1}}+{f}_{{e}_{2}}& \mathrm{Use end cushions}\\ f& \mathrm{otherwise}\end{array}$ $f={A}_{a}{p}_{a}-{A}_{b}{p}_{b}-d{v}_{\mathrm{rel}}$ ${f}_{{e}_{1}}=\left\{\begin{array}{cc}0& 0\le {f}_{{c}_{1}}+{f}_{{d}_{1}}\\ {f}_{{c}_{1}}+\mathrm{max}\left({f}_{{c}_{1}},{f}_{{d}_{1}}\right)& \mathrm{otherwise}\end{array}\phantom{\rule[-0.0ex]{3.0ex}{0.0ex}}{f}_{{e}_{2}}=\left\{\begin{array}{cc}0& {f}_{{c}_{2}}+{f}_{{d}_{2}}\le 0\\ {f}_{{c}_{2}}+\mathrm{min}\left({f}_{{c}_{2}},{f}_{{d}_{2}}\right)& \mathrm{otherwise}\end{array}$ ${f}_{{c}_{1}}=\left\{\begin{array}{cc}-{k}_{c}\left({s}_{\mathrm{rel}}-{L}_{\mathrm{max}}\right)& {L}_{\mathrm{max}}<{s}_{\mathrm{rel}}\\ 0& \mathrm{otherwise}\end{array}\phantom{\rule[-0.0ex]{5.0ex}{0.0ex}}{f}_{{c}_{2}}=\left\{\begin{array}{cc}-{k}_{c}\left({s}_{\mathrm{rel}}-{L}_{\mathrm{min}}\right)& {s}_{\mathrm{rel}}<{L}_{\mathrm{min}}\\ 0& \mathrm{otherwise}\end{array}$ ${f}_{{d}_{1}}=\left\{\begin{array}{cc}-{c}_{c}{v}_{\mathrm{rel}}& {L}_{\mathrm{max}}<{s}_{\mathrm{rel}}\\ 0& \mathrm{otherwise}\end{array}\phantom{\rule[-0.0ex]{7.5ex}{0.0ex}}{f}_{{d}_{2}}=\left\{\begin{array}{cc}-{c}_{c}{v}_{\mathrm{rel}}& {s}_{\mathrm{rel}}<{L}_{\mathrm{min}}\\ 0& \mathrm{otherwise}\end{array}$

Variables

 Name Units Description Modelica ID ${p}_{x}$ $\mathrm{Pa}$ Pressure port $x,x\in \left\{A,B\right\}$ portx.p ${q}_{x}$ $\frac{{m}^{3}}{s}$ Flow rate through port $x,x\in \left\{A,B\right\}$ portx.q ${s}_{\mathrm{rel}}$ $m$ Relative distance from flange a to b s_rel ${v}_{\mathrm{rel}}$ $\frac{m}{s}$ Relative velocity of flanges v_rel

Connections

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

Parameters

Basic Parameters

 Name Default Units Description Modelica ID ${A}_{a}$ $0.01$ ${m}^{2}$ Effective area of piston - side A Aa ${A}_{b}$ $0.008$ ${m}^{2}$ Effective area of piston - side B Ab $d$ $0$ $N\frac{s}{m}$ Piston viscous friction coefficient d

End Cushions Parameters

 Name Default Units Description Modelica ID Use end cushions $\mathrm{false}$ True adds cushions to the cylinder and enables ${L}_{\mathrm{max}}$, ${L}_{\mathrm{min}}$, ${k}_{c}$, and ${c}_{c}$ parameters useEndCushions ${L}_{\mathrm{max}}$ $1$ $m$ Maximum piston position Lmax ${L}_{\mathrm{min}}$ $0$ $m$ Minimum piston position Lmin ${k}_{c}$ $1·{10}^{10}$ $\frac{N}{m}$ End cushion stiffness kc ${c}_{c}$ $1·{10}^{6}$ $N\frac{s}{m}$ End cushion damping cc