Prop Valve $—$ Propoprtional valve with second-order spool dynamics and nonlinearities

The Prop Valve component describes a proportional valve with second-order spool dynamics and nonlinearities. The laminar/turbulent flow through the valve is modeled as flow through orifices without cavitation. Flow forces are not modeled. The commanded relative opening of the valve is input at $\mathrm{command}$. The parameter ${q}_{\mathrm{nom}}$ gives the nominal flow rate of the fully opened valve at the pressure drop ${\mathrm{Δp}}_{\mathrm{nom}}$. 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.

Input signal: $\mathrm{command}$.

Output signal: $\mathrm{position}$.

The flow area depends nonlinearly on the spool position (parabola).

For overlap = 0 the flows are given by:

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

VolumeB(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) $\left[\mathrm{Pa}\right]$.

Related Components

 Name Description Three port valve with second-order spool dynamics and nonlinearities. Valve with second-order spool dynamics and nonlinearities. Flow area depends linearly on spool position.

Variables

 Name Value Units Description Modelica ID ${V}_{A}$ VolumeA ${V}_{B}$ VolumeB ${V}_{T}$ 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 ${p}_{B\left(\mathrm{summary}\right)}$ $\mathrm{valveNoStates.port_B.p}$ $\mathrm{Pa}$ Pressure at port B summary_pB ${p}_{P\left(\mathrm{summary}\right)}$ $\mathrm{valveNoStates.p\left[P\right]}$ $\mathrm{Pa}$ 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 ${q}_{\mathrm{PA}\left(\mathrm{summary}\right)}$ $\mathrm{valveNoStates.morpa.q}$ $\frac{{m}^{3}}{s}$ Flow rate flowing port_P to port_A summary_qPA ${q}_{\mathrm{PB}\left(\mathrm{summary}\right)}$ $\mathrm{valveNoStates.morpb.q}$ $\frac{{m}^{3}}{s}$ Flow rate flowing port_P to port_B summary_qPB ${q}_{\mathrm{AT}\left(\mathrm{summary}\right)}$ $\mathrm{valveNoStates.morat.q}$ $\frac{{m}^{3}}{s}$ Flow rate flowing port_A to port_T summary_qAT ${q}_{\mathrm{BT}\left(\mathrm{summary}\right)}$ $\mathrm{valveNoStates.morbt.q}$ $\frac{{m}^{3}}{s}$ Flow rate flowing port_B to port_T summary_qBT

Connections

 Name Description Modelica ID ${\mathrm{port}}_{A}$ Port A, one of valve connections to actuator or motor port_A ${\mathrm{port}}_{B}$ Port B, one of valve connections to actuator or motor port_B ${\mathrm{port}}_{P}$ 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 B $\mathrm{true}$ If true, a volume is present at port_B useVolumeB 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 ${V}_{B}$ ${10}^{-6}$ ${m}^{3}$ Geometric volume at port B volumeB ${V}_{P}$ ${10}^{-6}$ ${m}^{3}$ 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 use hysteresis $\mathrm{true}$ Use hysteresis in model useHysteresis ${\mathrm{\omega }}_{0}$ $500$ $\frac{\mathrm{rad}}{s}$ Natural frequency of spool omega0 $\mathrm{damp}$ $\frac{7}{10}$ Damping coefficient of spool damp $\mathrm{overlap}$ $\frac{1}{10}$ Overlap relative to max. displacement = 1 overlap $\mathrm{hyst}$ $0.05$ Half of hysteresis width hyst ${v}_{\mathrm{max}}$ $100$ Max. spool velocity [1/s] vmax

Flow Parameters

 Name Default Units Description Modelica ID ${q}_{\mathrm{nom}\left(\mathrm{PA}\right)}$ $8.33·{10}^{-4}$ $\frac{{m}^{3}}{s}$ Nominal flow rate qnompa ${\mathrm{Δp}}_{\mathrm{nom}\left(\mathrm{PA}\right)}$ $1.5·{10}^{6}$ $\mathrm{Pa}$ Pressure drop at qnom dpnompa ${q}_{\mathrm{nom}\left(\mathrm{BT}\right)}$ $8.33·{10}^{-4}$ $\frac{{m}^{3}}{s}$ Nominal flow rate qnombt ${\mathrm{Δp}}_{\mathrm{nom}\left(\mathrm{BT}\right)}$ $1.5·{10}^{6}$ $\mathrm{Pa}$ Pressure drop at qnom dpnombt ${q}_{\mathrm{nom}\left(\mathrm{PB}\right)}$ $8.33·{10}^{-4}$ $\frac{{m}^{3}}{s}$ Nominal flow rate qnompb ${\mathrm{Δp}}_{\mathrm{nom}\left(\mathrm{PB}\right)}$ $1.5·{10}^{6}$ $\mathrm{Pa}$ Pressure drop at qnom dpnompb ${q}_{\mathrm{nom}\left(\mathrm{AT}\right)}$ $8.33·{10}^{-4}$ $\frac{{m}^{3}}{s}$ Nominal flow rate qnomat ${\mathrm{Δp}}_{\mathrm{nom}\left(\mathrm{AT}\right)}$ $1.5·{10}^{6}$ $\mathrm{Pa}$ Pressure drop at qnom dpnomat ${k}_{1\left(\mathrm{PA}\right)}$ $10$ 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 ${k}_{1\left(\mathrm{PB}\right)}$ $10$ Laminar part of orifice model k1pb ${k}_{2\left(\mathrm{PB}\right)}$ $2$ Turbulent part of orifice model, ${k}_{2}=\frac{1}{{C}_{d}^{2}}$ k2pb ${C}_{d\left(\mathrm{PB}\right)}$ $\frac{1}{\sqrt{{k}_{2\left(\mathrm{PB}\right)}}}$ Max discharge coefficient C_dpb ${\mathrm{\lambda }}_{c\left(\mathrm{PB}\right)}$ $\frac{2{k}_{1\left(\mathrm{PB}\right)}}{\sqrt{{k}_{2\left(\mathrm{PB}\right)}}}$ Critical flow number lambdacpb ${k}_{1\left(\mathrm{BT}\right)}$ $10$ Laminar part of orifice model k1bt ${k}_{2\left(\mathrm{BT}\right)}$ $2$ Turbulent part of orifice model, ${k}_{2}=\frac{1}{{C}_{d}^{2}}$ k2bt ${C}_{d\left(\mathrm{BT}\right)}$ $\frac{1}{\sqrt{{k}_{2\left(\mathrm{BT}\right)}}}$ Max discharge coefficient C_dbt ${\mathrm{\lambda }}_{c\left(\mathrm{BT}\right)}$ $\frac{2{k}_{1\left(\mathrm{BT}\right)}}{\sqrt{{k}_{2\left(\mathrm{BT}\right)}}}$ Critical flow number lambdacbt ${k}_{1\left(\mathrm{AT}\right)}$ $10$ 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 ${\mathrm{\rho }}_{\mathrm{nom}}$ $865$ $\frac{\mathrm{kg}}{{m}^{3}}$ Nominal density rhonom ${d}_{\mathrm{leak}}$ $1.67·{10}^{-5}$ $m$ Diameter of equivalent orifice to model leakage of closed valve dleak $\mathrm{Transition}$ $1$ Transition model Transition