DCV_4_3_D $—$ Directional Control Valve with first-order spool dynamics and a spool with 4 ports and 3 stable positions; when in the middle position, ports A and B are closed and ports T and P are connected

The DCV_4_3_D component describes a directional control valve with first-order spool dynamics and a spool with 4 ports and 3 stable positions. When in the middle position, ports A and B are closed and ports P and T are connected. The laminar/turbulent flow through the valve is modeled as flow through orifices without cavitation. The commanded opening of the valve is input at $\mathrm{commandA}$ or $\mathrm{commandB}$, respectively. The parameter qnom gives the nominal flow rate of the fully opened flow path at the pressure drop ${\mathrm{Δp}}_{\mathrm{nom}}$.

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

${d}_{\mathrm{max}}=2\sqrt{\frac{{A}_{\mathrm{max}}}{\mathrm{\pi }}}$

For example, the maximum diameter for the flow path from P to B is given by ${d}_{\mathrm{max}\left(\mathrm{PB}\right)}$:

${A}_{\mathrm{max}\left(\mathrm{PB}\right)}={q}_{\mathrm{nom}\left(\mathrm{PB}\right)}\sqrt{\frac{1}{2}\frac{\mathrm{\rho }{k}_{2}}{{\mathrm{Δp}}_{\mathrm{nom}}}}$

${A}_{\mathrm{max}\left(\mathrm{PB}\right)}={q}_{\mathrm{nom}\left(\mathrm{PB}\right)}\sqrt{\frac{1}{2}\frac{\mathrm{\rho }{k}_{2}}{{\mathrm{Δp}}_{\mathrm{nom}}}}$

${d}_{\mathrm{max}\left(\mathrm{PB}\right)}=2\sqrt{\frac{{A}_{\mathrm{max}\left(\mathrm{PB}\right)}}{\mathrm{\pi }}}$

There is leakage flow modeled when the respective flow path is nominally closed. The position of the spool is modeled as a first-order system.

Input signals: $\mathrm{commandA}$ and $\mathrm{commandB}$.

When $\mathrm{commandA}=\mathrm{true}$ and $\mathrm{commandB}=\mathrm{false}$, the left square of the valve icon describes the flow paths.

When $\mathrm{commandA}=\mathrm{false}$ and $\mathrm{commandB}=\mathrm{true}$, the right square of the valve icon describes the flow paths.

Otherwise, the middle square of the valve icon describes the flow paths.

Intermediate positions and the respective connections are modeled and shown in the following figure. (See DCV_4_3_X for general information on valve diagrams.)

Figure Flow paths in the valve as a function of spool position. 1 means completely open, 0 means completely closed.

 Command signals Flow paths and diameter of metering orifice $\mathrm{commandA}=\mathrm{true}$ and $\mathrm{commandB}=\mathrm{false}$ Flow from P $\to$ A, B $\to$ T. Flow diameter from P $\to$ B: $\mathrm{dleak}$. Flow diameter from A $\to$ T: $\mathrm{dleak}$. Flow diameter from P $\to$ A: $\mathrm{dmax_P_A}+\mathrm{dleak}$. Flow area from B $\to$ T: $\mathrm{dmax_B_T}+\mathrm{dleak}$. Flow area from P $\to$ T: $\mathrm{dleak}$. $\mathrm{commandA}=\mathrm{false}$ and $\mathrm{commandB}=\mathrm{false}$ Flow from P $\to$ T. Flow diameter from P $\to$ B: $\mathrm{dleak}$. Flow diameter from A $\to$ T: $\mathrm{dleak}$. Flow diameter from P $\to$ A: $\mathrm{dleak}$. Flow diameter from B $\to$ T: $\mathrm{dleak}$. Flow diameter from P $\to$ T: $\mathrm{dmax_P_T}+\mathrm{dleak}$. $\mathrm{commandA}=\mathrm{false}$ and $\mathrm{commandB}=\mathrm{true}$ Flow from P $\to$ B, A $\to$ T. Flow diameter from P $\to$ B: $\mathrm{dmax_P_B}+\mathrm{dleak}$. Flow diameter from A $\to$ T: $\mathrm{dmax_A_T}+\mathrm{dleak}$. Flow diameter from P $\to$ A: $\mathrm{dleak}$. Flow diameter from B $\to$ T: $\mathrm{dleak}$. Flow diameter from P $\to$ T: $\mathrm{dleak}$.

When the pump pressure and the flow rate are high, the unbalanced forces and flow forces acting on the spool are higher than the force generated by the solenoid and the valve is partially closed. The effect can be modeled by the parameters P_max and coeff_P. Specify the maximum hydraulic power in $W$ (where the valve is still completely open) and use coeff_P to adjust the model to the manufacturer's data. When the specified hydraulic power is exceeded, a warning is printed in the log window (Mode Simulation / Simulation / Show Log).

The movement of the spool is described by a first-order system. This is appropriate for valves that are directly actuated by a spool. The times to shift from the neutral position to an end position (${\mathrm{\tau }}_{\mathrm{opening}}$) may be different than the time to shift to the neutral position (${\mathrm{\tau }}_{\mathrm{closing}}$).

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

Variables

 Name Value Units Description Modelica ID $\mathrm{p_A}\left(\mathrm{summary}\right)$ $\mathrm{spool_43.p_A}$ $\mathrm{Pa}$ Pressure at port A summary_pA $\mathrm{p_B}\left(\mathrm{summary}\right)$ $\mathrm{spool_43.p_B}$ $\mathrm{Pa}$ Pressure at port B summary_pB $\mathrm{p_P}\left(\mathrm{summary}\right)$ $\mathrm{spool_43.p_P}$ $\mathrm{Pa}$ Pressure at port P summary_pP $\mathrm{p_T}\left(\mathrm{summary}\right)$ $\mathrm{spool_43.p_T}$ $\mathrm{Pa}$ Pressure at port T summary_pT ${\mathrm{Δp}}_{\mathrm{PA}\left(\mathrm{summary}\right)}$ [1] $\mathrm{Pa}$ Pressure drop summary_dp_PA ${\mathrm{Δp}}_{\mathrm{PB}\left(\mathrm{summary}\right)}$ [2] $\mathrm{Pa}$ Pressure drop summary_dp_PB ${\mathrm{Δp}}_{\mathrm{AT}\left(\mathrm{summary}\right)}$ [3] $\mathrm{Pa}$ Pressure drop summary_dp_AT ${\mathrm{Δp}}_{\mathrm{BT}\left(\mathrm{summary}\right)}$ [4] $\mathrm{Pa}$ Pressure drop summary_dp_BT ${V}_{A}$ VolumeA ${V}_{B}$ VolumeB ${V}_{P}$ VolumeP $\mathrm{coil}$ coil $\mathrm{spool_43}$ spool_4_3 ${V}_{T}$ VolumeT $\mathrm{q_PA}\left(\mathrm{summary}\right)$ $\mathrm{spool_43.mor_PA.q}$ $\frac{{m}^{3}}{s}$ Flow rate flowing port_P to port_A summary_qPA $\mathrm{q_PB}\left(\mathrm{summary}\right)$ $\mathrm{spool_43.mor_PB.q}$ $\frac{{m}^{3}}{s}$ Flow rate flowing port_P to port_B summary_qPB $\mathrm{q_AT}\left(\mathrm{summary}\right)$ $\mathrm{spool_43.mor_AT.q}$ $\frac{{m}^{3}}{s}$ Flow rate flowing port_A to port_T summary_qAT $\mathrm{q_BT}\left(\mathrm{summary}\right)$ $\mathrm{spool_43.mor_BT.q}$ $\frac{{m}^{3}}{s}$ Flow rate flowing port_B to port_T summary_qBT $\mathrm{q_PT}\left(\mathrm{summary}\right)$ $\mathrm{spool_43.mor_PT.q}$ $\frac{{m}^{3}}{s}$ Flow rate flowing port_P to port_T summary_qPT

[1] $\mathrm{spool_43.port_P.p}-\mathrm{spool_43.port_A.p}$

[2] $\mathrm{spool_43.port_P.p}-\mathrm{spool_43.port_B.p}$

[3] $\mathrm{spool_43.port_A.p}-\mathrm{spool_43.port_T.p}$

[4] $\mathrm{spool_43.port_B.p}-\mathrm{spool_43.port_T.p}$

Connections

 Name Description Modelica ID ${\mathrm{port}}_{A}$ Port A, one of valve connections to actuator or motor port_A ${\mathrm{port}}_{B}$ 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 $\mathrm{commandB}$ Command signal for valve commandB $\mathrm{commandA}$ Command signal for valve commandA $\mathrm{oil}$ 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

Dynamic Parameters

 Name Default Units Description Modelica ID ${\mathrm{\tau }}_{\mathrm{opening}}$ $0.03$ $s$ Switching time to open valve 95 % tau_opening ${\mathrm{\tau }}_{\mathrm{closing}}$ $0.02$ $s$ Switching time to close valve 95 % tau_closing

Flow Parameters

 Name Default Units Description Modelica ID ${\mathrm{Δp}}_{\mathrm{nom}}$ $7.·{10}^{5}$ $\mathrm{Pa}$ Pressure drop at nominal flow rate qnom dpnom ${q}_{\mathrm{nom}\left(\mathrm{PA}\right)}$ $0.00158$ $\frac{{m}^{3}}{s}$ Nominal flow rate from P -> A qnom_P_A ${q}_{\mathrm{nom}\left(\mathrm{PB}\right)}$ ${q}_{\mathrm{nom}\left(\mathrm{PA}\right)}$ $\frac{{m}^{3}}{s}$ Nominal flow rate from P -> B qnom_P_B ${q}_{\mathrm{nom}\left(\mathrm{AT}\right)}$ ${q}_{\mathrm{nom}\left(\mathrm{PA}\right)}$ $\frac{{m}^{3}}{s}$ Nominal flow rate from A -> T qnom_A_T ${q}_{\mathrm{nom}\left(\mathrm{BT}\right)}$ ${q}_{\mathrm{nom}\left(\mathrm{PA}\right)}$ $\frac{{m}^{3}}{s}$ Nominal flow rate from B -> T qnom_B_T ${q}_{\mathrm{nom}\left(\mathrm{PT}\right)}$ $0$ $\frac{{m}^{3}}{s}$ Nominal flow rate from P -> T qnom_P_T ${P}_{\mathrm{max}}$ $1.26·{10}^{5}$ $W$ Max. hydraulic power P_max ${\mathrm{coeff}}_{P}$ $10$ Influence of hydraulic power on flow rate coeff_P ${k}_{1}$ $10$ Laminar part of orifice model k1 ${k}_{2}$ $2$ Turbulent part of orifice model, ${k}_{2}=\frac{1}{{C}_{d}^{2}}$ k2

Spool Geometry Parameters

 Name Default Units Description Modelica ID ${d}_{\mathrm{leak}}$ $1.67·{10}^{-5}$ $m$ Diameter of equivalent orifice to model leakage of closed valve; P -> A, P -> B,A -> T, B -> T dleak