Spool_4_3_D $—$ Spool with 4 ports and 3 stable positions; in the middle position, ports A and B are closed and ports  T and P are connected

The Spool_4_3_D component describes the spool of a directional control valve 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 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 is 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).

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 $\mathrm{true}$ 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

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 ${q}_{\mathrm{nom}\left(\mathrm{AB}\right)}$ $0$ $\frac{{m}^{3}}{s}$ Nominal flow rate from A -> B qnom_A_B ${q}_{\mathrm{nom}\left(\mathrm{PT}\right)}$ $0$ $\frac{{m}^{3}}{s}$ 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 dleak

Constant Parameters

 Name Default Units Description Modelica ID ${\mathrm{spool}}_{x-\mathrm{axis}}$ [1] Normalized spool position spool_x_axis ${\mathrm{open}}_{\mathrm{PA}}$ [2] Open (1) and closed (0) path P -> A as function of normalized spool position open_P_A ${\mathrm{open}}_{\mathrm{PB}}$ [3] Open (1) and closed (0) path P -> B as function of normalized spool position open_P_B ${\mathrm{open}}_{\mathrm{PT}}$ [4] Open (1) and closed (0) path P -> T as function of normalized spool position open_P_T

[1] $\left[-1.,-0.750,-0.500,-0.250,0.250,0.500,0.750,1.\right]$

[2] $\left[1.,1.,1.,0.,0.,1.,0.,0.\right]$

[3] $\left[0.,0.,1.,0.,0.,1.,1.,1.\right]$

[4] $\left[0.,0.,1.,1.,1.,1.,0.,0.\right]$