Three Port Valve $—$ Three port valve with second-order spool dynamics and nonlinearities

The Three Port Valve component describes a three port valve with second-order spool dynamics. The laminar/turbulent flow through the valve is modeled as flow through an orifice without cavitation.

The commanded relative opening of the valve is input at $\mathrm{command}$. The parameter qnom gives the nominal flow rate of the fully opened valve at the pressure drop dpnom. The parameter ${d}_{\mathrm{leak}}$ gives the equivalent diameter of an orifice to describe the leakage flow if the valve is closed.

${A}_{\mathrm{max}}={q}_{\mathrm{nom}}\sqrt{\frac{1}{2}\frac{\mathrm{\rho }{k}_{2}}{{\mathrm{Δp}}_{\mathrm{nom}}}}$

${A}_{\mathrm{leak}}=\frac{1}{4}\mathrm{\pi }{d}_{\mathrm{leak}}^{2}$

The position of the spool is modeled as a second-order system with natural frequency ${\mathrm{\omega }}_{0}$, damping damp, limits for the velocity, and hysteresis for the position. The input variable is $\mathrm{command}$ and the output variable is $\mathrm{position}$ [-1 ... 1]. The flow area depends linearly on the spool position. For overlap = 0 the flows are given by:

 $\mathrm{position}\le -1$ from $\mathrm{command}\le -1$ Flow from A $\to$ T. Flow area from A $\to$ T: ${A}_{\mathrm{max}}+{A}_{\mathrm{leak}}$. Flow area from P $\to$ A: ${A}_{\mathrm{leak}}$. $-1<\mathrm{position}$ $<$ $0$ from $-1<\mathrm{command}$ $<$ $0$ Flow from A $\to$ T. Leakage from P $\to$ A. Flow area from A $\to$ T: $\frac{{A}_{\mathrm{max}}+{A}_{\mathrm{leak}}}{\mathrm{position}}$. Flow area from P $\to$ A: ${A}_{\mathrm{leak}}$. $\mathrm{position}=0$ from $\mathrm{command}=0$ Leakage from P $\to$ A and from  A $\to$ T. $0<\mathrm{position}$ $<$ $1$ from $0<\mathrm{command}$ $<$ $1$ Flow from P $\to$ A. Leakage from A $\to$ T. $1\le \mathrm{position}$ from $1\le \mathrm{command}$ Flow from P $\to$ A. Leakage from A $\to$ T.

The mass and flow forces are not included. Use the modifier(s)

VolumeA(port_A(p(start=1e5,fixed=true)))

and/or

VolumeP(port_A(p(start=1e5,fixed=true)))

and/or

VolumeT(port_A(p(start=1e5,fixed=true)))

to set the initial condition(s) for the pressure of the lumped volume(s) [Pa].

Related Components

 Name Description Valve with second-order spool dynamics and nonlinearities. Flow area depends linearly on spool position. Valve with second-order spool dynamics and nonlinearities. Flow area depends not linearly on spool position, usually large overlap.

Variables

 Name Value Units Description Modelica ID ${V}_{A}$ VolumeA ${V}_{T}$ VolumeT ${V}_{P}$ VolumeP $\mathrm{spoolDynamics}$ spoolDynamics $\mathrm{valveNoStates}$ valveNoStates ${p}_{A\left(\mathrm{summary}\right)}$ $\mathrm{valveNoStates.port_A.p}$ $\mathrm{Pa}$ Pressure at port A summary_pA ${p}_{P\left(\mathrm{summary}\right)}$ $\mathrm{valveNoStates.p\left[P\right]}$ $\mathrm{Pa}$ Pressure at port P summary_pP ${p}_{T\left(\mathrm{summary}\right)}$ $\mathrm{valveNoStates.port_T.p}$ $\mathrm{Pa}$ Pressure at port T summary_pT ${\mathrm{Δp}}_{\mathrm{PA}\left(\mathrm{summary}\right)}$ [1] $\mathrm{Pa}$ Pressure drop summary_dp_PA ${\mathrm{Δp}}_{\mathrm{AT}\left(\mathrm{summary}\right)}$ [2] $\mathrm{Pa}$ Pressure drop summary_dp_AT ${q}_{\mathrm{PA}\left(\mathrm{summary}\right)}$ $\mathrm{valveNoStates.morpa.q}$ $\frac{{m}^{3}}{s}$ Flow rate flowing port_P to port_A summary_qPA ${q}_{\mathrm{AT}\left(\mathrm{summary}\right)}$ $\mathrm{valveNoStates.morat.q}$ $\frac{{m}^{3}}{s}$ Flow rate flowing port_P to port_A summary_qAT

[1] $\mathrm{valveNoStates.port_P.p}-\mathrm{valveNoStates.port_A.p}$

[2] $\mathrm{valveNoStates.port_A.p}-\mathrm{valveNoStates.port_T.p}$

Connections

 Name Description Modelica ID ${\mathrm{port}}_{A}$ Port A, one of valve connections to actuator or motor port_A ${\mathrm{port}}_{P}$ Port P, where oil enters the component from the pump port_P ${\mathrm{port}}_{T}$ Port T, where oil flows to the tank port_T $\mathrm{command}$ Command signal for valve position command $\mathrm{oil}$ oil

Parameters

General Parameters

 Name Default Units Description Modelica ID use volume A $\mathrm{true}$ If true, a volume is present at port_A useVolumeA use volume P $\mathrm{true}$ If true, a volume is present at port_P useVolumeP use volume T $\mathrm{true}$ If true, a volume is present at port_T useVolumeT ${V}_{A}$ ${10}^{-6}$ ${m}^{3}$ Geometric volume at port A volumeA ${V}_{P}$ ${10}^{-6}$ ${m}^{3}$ Geometric volume at port P volumeP ${V}_{T}$ ${10}^{-6}$ ${m}^{3}$ Geometric volume at port T volumeT ${\mathrm{ΔT}}_{\mathrm{system}}$ $0$ $K$ Temperature offset from system temperature dT_system

Actuation Parameters

 Name Default Units Description Modelica ID ${\mathrm{\omega }}_{0}$ $500$ $\frac{\mathrm{rad}}{s}$ Natural frequency of spool omega0 $\mathrm{damp}$ $\frac{7}{10}$ Damping coefficient of spool damp $\mathrm{overlap}$ $0.02$ Overlap relative to max. displacement = 1 overlap $\mathrm{hyst}$ $0.005$ Half of hysteresis width hyst ${v}_{\mathrm{max}}$ $100$ Max. spool velocity [1/s] vmax

Flow Parameters

 Name Default Units Description Modelica ID ${d}_{\mathrm{leak}}$ ${10}^{-6}$ $m$ Diameter of equivalent orifice to model leakage of closed valve dleak ${q}_{\mathrm{nom}\left(\mathrm{PA}\right)}$ $8.33·{10}^{-4}$ $\frac{{m}^{3}}{s}$ Nominal flow rate qnompa ${\mathrm{Δp}}_{\mathrm{nom}\left(\mathrm{PA}\right)}$ $3.5·{10}^{6}$ $\mathrm{Pa}$ Pressure drop at qnom dpnompa ${k}_{1\left(\mathrm{PA}\right)}$ $10$ Laminar part of orifice model k1pa ${k}_{2\left(\mathrm{PA}\right)}$ $2$ Turbulent part of orifice model, ${k}_{2}=\frac{1}{{C}_{d}^{2}}$ k2pa ${C}_{d\left(\mathrm{PA}\right)}$ $\frac{1}{\sqrt{{k}_{2\left(\mathrm{PA}\right)}}}$ Max discharge coefficient C_dpa ${\mathrm{\lambda }}_{c\left(\mathrm{PA}\right)}$ $\frac{2{k}_{1\left(\mathrm{PA}\right)}}{\sqrt{{k}_{2\left(\mathrm{PA}\right)}}}$ Critical flow number lambdacpa ${q}_{\mathrm{nom}\left(\mathrm{AT}\right)}$ $8.33·{10}^{-4}$ $\frac{{m}^{3}}{s}$ Nominal flow rate qnomat ${\mathrm{Δp}}_{\mathrm{nom}\left(\mathrm{AT}\right)}$ $3.5·{10}^{6}$ $\mathrm{Pa}$ Pressure drop at qnom dpnomat ${k}_{1\left(\mathrm{AT}\right)}$ $10$ Laminar part of orifice model k1at ${k}_{2\left(\mathrm{AT}\right)}$ $2$ Turbulent part of orifice model, ${k}_{2}=\frac{1}{{C}_{d}^{2}}$ k2at ${C}_{d\left(\mathrm{AT}\right)}$ $\frac{1}{\sqrt{{k}_{2\left(\mathrm{AT}\right)}}}$ Max discharge coefficient C_dat ${\mathrm{\lambda }}_{c\left(\mathrm{AT}\right)}$ $\frac{2{k}_{1\left(\mathrm{AT}\right)}}{\sqrt{{k}_{2\left(\mathrm{AT}\right)}}}$ Critical flow number lambdacat $\mathrm{Transition}$ $1$ Transition model Transition