Chamber $—$ Oil-filled chamber with a moveable piston and pressure-dependent compressibility

The Chamber component describes an oil-filled chamber that has a moveable, frictionless, and massless piston. The volume is given by

${V}_{\mathrm{eff}}={V}_{\mathrm{dead}}+\left({s}_{b}-{s}_{a}-{\ell }_{\mathrm{rod}}\right){A}_{\mathrm{piston}}$

There is a check whether

$\mathrm{stroke}={s}_{b}-{s}_{a}-{\ell }_{\mathrm{rod}}$

is greater than zero during the simulation.

To compute the pressure in the chamber, an equation for the bulk modulus is needed. It uses the oil model defined on the system level. The bulk modulus is given by

$\mathrm{\beta }=\mathrm{\beta }\left({p}_{A}\right)$

The calculated pressure is not limited to the vapor pressure but can reach unlimited negative values. A limitation is done for the computed force where the relevant pressure is limited by the vapor pressure. Another limitation is implemented in TwoPortComp where all pressures used to compute the differential pressure between the ports are limited to the vapor pressure. Detailed information about the bulk modulus of the oil is given in the documentation for OilVolume. Use the modifier

port_A(p(start=2e6,fixed=true))

to set the initial condition for the pressure in the chamber in $\mathrm{Pa}$.

 Equations $\mathrm{msim/FOR}\left(\mathrm{msim/IN}\left(\mathrm{i#1},1..{n}_{\mathrm{ports}}\right),p=\mathrm{port_A\left[i#1\right].p}\right)$ $\mathrm{\beta }={\mathrm{\beta }}_{\mathrm{oil}}\left(p={p}_{\mathrm{abs}},T=T,{v}_{\mathrm{air}}={v}_{\mathrm{gas}\left(\mathrm{oil}\right)},{p}_{\mathrm{sat}}={p}_{\mathrm{sat}}\right)$ $\mathrm{\rho }={\mathrm{\rho }}_{\mathrm{oil}}\left(p={p}_{\mathrm{abs}},T=T,{v}_{\mathrm{air}}={v}_{\mathrm{gas}\left(\mathrm{oil}\right)},{p}_{\mathrm{sat}}={p}_{\mathrm{sat}}\right)$ $T={T}_{0\left(\mathrm{oil}\right)}+{\mathrm{ΔT}}_{\mathrm{system}}$ $f=\mathrm{max}\left(p,{p}_{\mathrm{vapour}\left(\mathrm{oil}\right)}-{p}_{\mathrm{atm}\left(\mathrm{oil}\right)}\right){A}_{\mathrm{piston}}$ $\mathrm{stroke}={s}_{\mathrm{rel}}-{\ell }_{\mathrm{rod}}$ ${V}_{\mathrm{eff}}=\mathrm{stroke}{A}_{\mathrm{piston}}+{V}_{\mathrm{dead}}$ ${p}_{\mathrm{abs}}=p+{p}_{\mathrm{atm}\left(\mathrm{oil}\right)}$ ${q}_{\mathrm{cham}}=-{v}_{\mathrm{rel}}{A}_{\mathrm{piston}}$ ${s}_{\mathrm{rel}}=\mathrm{switch}\left(\mathrm{flange_b.s}-\mathrm{flange_a.s}\right)$ ${v}_{\mathrm{rel}}={\partial }_{t}\left({s}_{\mathrm{rel}}\right)$ $\mathrm{flange_a.f}\mathrm{switch}=f$ $\mathrm{flange_a.f}+\mathrm{flange_b.f}=0$ ${\partial }_{t}\left(p\right)=\frac{\mathrm{\beta }\left(\frac{{\sum }\phantom{\rule[-0.0ex]{5.0px}{0.0ex}}{m}_{\mathrm{flow}\left(A\right)}}{\mathrm{\rho }}+{q}_{\mathrm{cham}}\right)}{{V}_{\mathrm{eff}}}$

Variables

 Name Value Units Description Modelica ID ${s}_{\mathrm{rel}}$ $m$ Relative position s_rel $f$ $N$ Force between flanges f ${v}_{\mathrm{rel}}$ $\frac{m}{s}$ Relative velocity between flange flange_a and flange_b v_rel $\mathrm{stroke}$ $m$ Stroke of chamber stroke ${V}_{\mathrm{eff}}$ ${m}^{3}$ Effective volume = dead volume + stroke  piston_area EffVolume $\mathrm{qcham}$ $\frac{{m}^{3}}{s}$ Induced flowrate because of piston movement qcham ${p}_{\mathrm{abs}}$ $\mathrm{Pa}$ Absolute pressure, used for all property calls p_abs $p$ $\mathrm{Pa}$ Pressure in Chamber p $\mathrm{\beta }$ $\mathrm{Pa}$ Bulk modulus beta $T$ $K$ Local temperature T $\mathrm{\rho }$ $\frac{\mathrm{kg}}{{m}^{3}}$ Density rho ${p}_{\mathrm{sat}}$ [1] $\mathrm{Pa}$ Gas saturation pressure p_sat $\mathrm{oilWarnings}$ oilWarnings $\mathrm{pressureSensor}$ pressureSensor ${p}_{A\left(\mathrm{summary}\right)}$ $p$ $\mathrm{Pa}$ Pressure at port A summary_pA ${T}_{\mathrm{summary}}$ $T$ $K$ Local temperature summary_T ${\mathrm{\beta }}_{\mathrm{summary}}$ $\mathrm{\beta }$ $\mathrm{Pa}$ Bulk modulus of oil summary_beta ${\mathrm{\rho }}_{\mathrm{summary}}$ $\mathrm{\rho }$ $\frac{\mathrm{kg}}{{m}^{3}}$ Density summary_rho ${P}_{\mathrm{hyd}\left(\mathrm{summary}\right)}$ $p{v}_{\mathrm{rel}}{A}_{\mathrm{piston}}$ $W$ Hydraulic power summary_HP

[1] $\mathrm{oil.gasSaturationPressure}\left(T=T,{v}_{\mathrm{gas}}={\mathrm{oil.v}}_{\mathrm{gas}}\right)$

Connections

 Name Description Modelica ID $\mathrm{oil}$ oil ${\mathrm{flange}}_{a}$ flange_a ${\mathrm{flange}}_{b}$ flange_b ${\mathrm{port}}_{A}$ Port A, where oil flows into the component ($0, ${p}_{B}<{p}_{A}$ means $0<\mathrm{Δp}$) port_A

Parameters

General Parameters

 Name Default Units Description Modelica ID $\mathrm{reverse}$ $\mathrm{false}$ Reverse the sign convention, see documentation for details reverse ${n}_{\mathrm{ports}}$ $0$ Number of ports nPorts ${A}_{\mathrm{piston}}$ $0.01$ ${m}^{2}$ Piston area piston_area ${\ell }_{\mathrm{rod}}$ $0.005$ $m$ Rod length RodLength ${V}_{\mathrm{dead}}$ ${10}^{-6}$ ${m}^{3}$ Dead volume for stroke = 0 dead_volume ${\mathrm{ΔT}}_{\mathrm{system}}$ $0$ $K$ Temperature offset from system temperature dT_system