# 4-Way Ideal Valve

Hydraulic 4-way critically-centered valve

## Library

Directional Valves

## Description

The 4-Way Ideal Valve block represents a 4-way critically-centered valve, where initial openings of all four variable orifices are equal to zero. This significantly simplifies the model of a 4-way directional valve and makes it especially suitable for real-time and HIL (hardware-in-the-loop) simulation, where such assumption is applicable.

The flow rate is computed with the equation:

`$q=x{C}_{D}b\sqrt{\frac{1}{\rho }\left({p}_{S}-abs\left({p}_{A}-{p}_{B}\right)\right)}sign\left({p}_{A}-{p}_{B}\right)$`

where

 q Flow rate x Valve displacement, –xmax <= x <= xmax b Orifice width, b = Amax / xmax Amax Maximum orifice area xmax Valve maximum opening CD Flow discharge coefficient ρ Fluid density pS Pressure supply pA,pB Pressures at the load ports A and B, respectively

Connections A and B are conserving hydraulic ports associated with the valve load ports. Connections P and S are the physical signal input ports that provide supply pressure and valve displacement values, respectively.

## Basic Assumptions and Limitations

• The valve is of a critically-centered type, that is, all initial openings are equal to zero.

• The return pressure is assumed to be very low and can be treated as a zero pressure.

• All the orifices are assumed to have the same shape and size, that is, the valve is symmetrical.

## Dialog Box and Parameters

Valve passage maximum area

Specify the area of a fully opened valve. The parameter value must be greater than zero. The default value is `5e-5` m^2.

Valve maximum opening

Specify the maximum displacement of the control member. The parameter value must be greater than zero. The default value is `0.005` m.

Flow discharge coefficient

Semi-empirical parameter for valve capacity characterization. Its value depends on the geometrical properties of the valve, and usually is provided in textbooks or manufacturer data sheets. The default value is `0.7`.

## Global Parameters

Parameter determined by the type of working fluid:

• Fluid density

Use the Hydraulic Fluid block or the Custom Hydraulic Fluid block to specify the fluid properties.

## Ports

The block has the following ports:

`A`

Hydraulic conserving port associated with the actuator connection port.

`B`

Hydraulic conserving port associated with the actuator connection port.

`P`

Physical signal port that controls the supply pressure.

`S`

Physical signal port that controls spool displacement.

## Examples

The Closed-Loop Hydraulic Actuator Model for Real-Time Simulation example is an example of using this valve, along with other blocks optimized for real-time and HIL simulation.