Spool_4_3_A $—$ Spool with 4 ports and 3 stable positions; when in the  middle position, ports A, B, T and P closed

The Spool_4_3_A component describes the spool of a directional control valve with 4 ports and 3 stable positions. When in the middle position, ports A, B, P and T are closed.

The laminar/turbulent flow through the valve is modeled as flow through orifices without cavitation. The opening of the valve is input at the port ${\mathrm{spool}}_{\mathrm{position}}$  ($-1\le {\mathrm{spool}}_{\mathrm{position}}$ $\le$ $1$).

The parameter ${q}_{\mathrm{nom}}$ gives the nominal flow rate of the fully opened flow path at the pressure drop $\mathrm{dpnom}$.

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

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

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

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

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

The diameter depends on the spool position as given in the figure below.

There is leakage flow modeled when the respective flow path is nominally closed.

Input signal: ${\mathrm{spool}}_{\mathrm{position}}$.

When ${\mathrm{spool}}_{\mathrm{position}}=-1$, the left square of the valve icon describes the flow paths.

When ${\mathrm{spool}}_{\mathrm{position}}=0$, the middle square of the valve icon describes the flow paths.

When ${\mathrm{spool}}_{\mathrm{position}}=1$, the right square of the valve icon describes the flow paths.

Intermediate positions and their respective connections are modeled and shown below.

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

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).

Note: There are some valves that open the path to the tank before they open the path to the pump.

Events

There is a new boolean reduceEvents (selected by default) in the Advanced section under the Properties tab ( ). Selecting reduceEvents lets the model use noEvents(expr) to generate fewer events for boolean expressions that should not generate events. In some cases the solver might reduce the stepsize too much and generate a lot of steps. If this happens, try clearing reduceEvents.

Variables

 Name Value Units Description Modelica ID ${\mathrm{mor}}_{\mathrm{PA}}$ mor_P_A ${\mathrm{mor}}_{\mathrm{BT}}$ mor_B_T ${\mathrm{mor}}_{\mathrm{PB}}$ mor_P_B ${\mathrm{mor}}_{\mathrm{AT}}$ mor_A_T ${\mathrm{mor}}_{\mathrm{AB}}$ mor_A_B ${\mathrm{mor}}_{\mathrm{PT}}$ mor_P_T $\mathrm{checkFlow}$ checkFlow ${\mathrm{command}}_{\mathrm{diameter}}$ command_diameter ${\mathrm{port}}_{\mathrm{pressure}}$ port_pressure ${\mathrm{port}}_{\mathrm{flow}}$ port_flow ${p}_{P\left(\mathrm{abs}\right)}$ ${p}_{P}+\mathrm{oil.p_atm}$ $\mathrm{Pa}$ Absolute pressure at port P pP_abs ${p}_{\mathrm{sat}}$ [1] $\mathrm{Pa}$ Gas saturation pressure p_sat ${p}_{A\left(\mathrm{summary}\right)}$ ${p}_{A}$ $\mathrm{Pa}$ Pressure at port A summary_pA ${p}_{B\left(\mathrm{summary}\right)}$ ${p}_{B}$ $\mathrm{Pa}$ Pressure at port B summary_pB ${p}_{P\left(\mathrm{summary}\right)}$ ${p}_{P}$ $\mathrm{Pa}$ Pressure at port P summary_pP ${p}_{T\left(\mathrm{summary}\right)}$ ${p}_{T}$ $\mathrm{Pa}$ Pressure at port T summary_pT ${\mathrm{Δp}}_{\mathrm{PA}\left(\mathrm{summary}\right)}$ ${p}_{A}-{p}_{P}$ $\mathrm{Pa}$ Pressure drop summary_dp_PA ${\mathrm{Δp}}_{\mathrm{PB}\left(\mathrm{summary}\right)}$ ${p}_{B}-{p}_{P}$ $\mathrm{Pa}$ Pressure drop summary_dp_PB ${\mathrm{Δp}}_{\mathrm{AT}\left(\mathrm{summary}\right)}$ ${p}_{T}-{p}_{A}$ $\mathrm{Pa}$ Pressure drop summary_dp_AT ${\mathrm{Δp}}_{\mathrm{BT}\left(\mathrm{summary}\right)}$ ${p}_{T}-{p}_{B}$ $\mathrm{Pa}$ Pressure drop summary_dp_BT ${q}_{\mathrm{PA}\left(\mathrm{summary}\right)}$ $\mathrm{mor_PA.q}$ $\frac{{m}^{3}}{s}$ Flow rate flowing port_P to port_A summary_qPA ${q}_{\mathrm{PB}\left(\mathrm{summary}\right)}$ $\mathrm{mor_PB.q}$ $\frac{{m}^{3}}{s}$ Flow rate flowing port_P to port_B summary_qPB ${q}_{\mathrm{AT}\left(\mathrm{summary}\right)}$ $\mathrm{mor_AT.q}$ $\frac{{m}^{3}}{s}$ Flow rate flowing port_A to port_T summary_qAT ${q}_{\mathrm{BT}\left(\mathrm{summary}\right)}$ $\mathrm{mor_BT.q}$ $\frac{{m}^{3}}{s}$ Flow rate flowing port_B to port_T summary_qBT

[1] $\mathrm{oil.gasSaturationPressure}\left(T={\mathrm{oil.T}}_{0}+{\mathrm{ΔT}}_{\mathrm{system}},{v}_{\mathrm{gas}}={\mathrm{oil.v}}_{\mathrm{gas}}\right)$

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 ${\mathrm{spool}}_{\mathrm{position}}$ Command signal for spool position spool_position $\mathrm{oil}$ oil

Parameters

General Parameters

 Name Default Units Description Modelica ID flow path A to B $\mathrm{false}$ There is a spool position with flow from port A to B flowPath_AB flow path P to T $\mathrm{false}$ There is a spool position with flow from port P to T flowPath_PT ${\mathrm{ΔT}}_{\mathrm{system}}$ $0$ $K$ Temperature offset from system temperature dT_system

 Name Default Units Description Modelica ID reduce events $\mathrm{true}$ If true, reduce event generation reduceEvents

Flow Parameters

 Name Default Units Description Modelica ID use CheckFlow $\mathrm{true}$ True, if a warning should be printed to user useCheckFlow ${\mathrm{Δp}}_{\mathrm{nom}}$ $7.·{10}^{5}$ $\mathrm{Pa}$ 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 ${P}_{\mathrm{max}}$ $1.26·{10}^{5}$ $W$ 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 dleak