## Modeling Hydraulic Directional Valves

### Classifying Directional Valves

Directional valves connect different flow paths based on the displacement of a central control member. They can be proportional, such as a 4-way directional valve, or control flow switching, such as a shuttle valve. Proportional directional valves are configured based on the flow paths that open and close when the control member displaces, and are classified by:

• The number of external paths or connecting ports.

• The number of positions the valve can assume.

• Being continuous or discrete.

The amount of open orifice at a given time is determined by:

`$h={x}_{0}+{x}_{sp}\epsilon ,$`

where:

• h is the current open orifice distance.

• x0 is the initial orifice offset. This value is positive for underlapped (initially open) valves and negative for overlapped (initially closed) valves.

• xsp is the spool displacement from its original position.

• ε is the orifice orientation. It is `+1` is the orifice opens when the spool displaces in the positive direction and `-1` if the orifice closes when the spool displaces in the positive direction.

The directional valves in the Simscape™ Fluids™ Hydraulics (Isothermal) library comprise two-way, three-way, four-way, and six-way directional valves with a single, continuous spool control member. Block ports are named to correspond with common connections:

• P — Pump or Pressure port

• T — Tank or Return port

• A, B — Load ports

• X, Y — Pilot ports

### 4-Way Directional Valve Schematic

A proportional flow directional valve is characterized by its initial open flow path, the flow paths that open or close with positive or negative control member displacement, and the orifice opening offset. The relationship between the control member stroke and the opening identifies whether an orifice is overlapped, underlapped, or neutral.

One configuration of a 4-way, 3-position directional valve connected to a double-acting cylinder can be connected with all four ports closed in the neutral position. The valve looks like this:

When the control member displaces in the positive direction, to the right in the valve diagram, the flow paths P-A and B-T open. When the control member displaces in the negative direction, to the left in the valve diagram, flow paths B-P and A-T open. This configuration for positive and negative displacement is schematically is represented as:

where the box on the right represents the positive spool displacement connections, and the box on the left represents the negative spool displacement connections.

The 4-Way Directional Valve block models this and ten additional configurations, specified in the following table.

The 4-Way Directional Valve Configurations

NoConfigurationInitial Openings
1

All four orifices are overlapped in neutral position:

• Orifice P-A initial opening < 0

• Orifice P-B initial opening < 0

• Orifice A-T initial opening < 0

• Orifice B-T initial opening < 0

2

All four orifices are open (underlapped) in neutral position:

• Orifice P-A initial opening > 0

• Orifice P-B initial opening > 0

• Orifice A-T initial opening > 0

• Orifice B-T initial opening > 0

3

Orifices `P-A` and `P-B` are overlapped. Orifices `A-T` and `B-T` are overlapped for more than valve stroke:

• Orifice P-A initial opening < 0

• Orifice P-B initial opening < 0

• Orifice A-T initial opening < – `valve_stroke`

• Orifice B-T initial opening < – `valve_stroke`

4

Orifices `P-A` and `P-B` are overlapped, while orifices `A-T` and `B-T` are open:

• Orifice P-A initial opening < 0

• Orifice P-B initial opening < 0

• Orifice A-T initial opening > 0

• Orifice B-T initial opening > 0

5

Orifices `P-A` and `A-T` are open in neutral position, while orifices `P-B` and `B-T` are overlapped:

• Orifice P-A initial opening > 0

• Orifice P-B initial opening < 0

• Orifice A-T initial opening > 0

• Orifice B-T initial opening < 0

6

Orifice `A-T` is initially open, while all three remaining orifices are overlapped:

• Orifice P-A initial opening < 0

• Orifice P-B initial opening < 0

• Orifice A-T initial opening > 0

• Orifice B-T initial opening < 0

7

Orifice `B-T` is initially open, while all three remaining orifices are overlapped:

• Orifice P-A initial opening < 0

• Orifice P-B initial opening < 0

• Orifice A-T initial opening < 0

• Orifice B-T initial opening > 0

8

Orifices `P-A` and `P-B` are open, while orifices `A-T` and `B-T` are overlapped:

• Orifice P-A initial opening > 0

• Orifice P-B initial opening > 0

• Orifice A-T initial opening < 0

• Orifice B-T initial opening < 0

9

Orifice `P-A` is initially open, while all three remaining orifices are overlapped:

• Orifice P-A initial opening > 0

• Orifice P-B initial opening < 0

• Orifice A-T initial opening < 0

• Orifice B-T initial opening < 0

10

Orifice `P-B` is initially open, while all three remaining orifices are overlapped:

• Orifice P-A initial opening < 0

• Orifice P-B initial opening > 0

• Orifice A-T initial opening < 0

• Orifice B-T initial opening < 0

11

Orifices `P-B` and `B-T` are open, while orifices `P-A` and `A-T` are overlapped:

• Orifice P-A initial opening < 0

• Orifice P-B initial opening > 0

• Orifice A-T initial opening < 0

• Orifice B-T initial opening > 0

Additionally, the Hydraulics (Isothermal) library has nine additional 4-way directional valve blocks, the 4-Way Directional Valves A - K, shown in the following table.

4-Way Directional Valves A - K Configurations

Block NameConfigurationDescription

4-Way Directional Valve A

Contains two additional normally-open, sequentially-located orifices. Valve displacement to the left or to the right closes the path to tank.

4-Way Directional Valve B

Ports P and A are permanently connected through fixed orifice. Orifices `P-B` and `B-T` are initially open (underlapped).

4-Way Directional Valve C

Ports P and B are permanently connected through fixed orifice. Orifices `P-A`, `A-T` and `B-T` are initially open (underlapped).

4-Way Directional Valve D

Two orifices are installed in the P-A link. Port A never connects to port T.

4-Way Directional Valve E

Two orifices are installed in the P-B link. Port B never connects to port T.

4-Way Directional Valve F

Two parallel orifices in the P-A arm and two series orifices in the A-T arm.

4-Way Directional Valve G

Two parallel orifices in the P-B arm and two series orifices in the B-T arm.

4-Way Directional Valve H

Two parallel orifices in the P-B arm and two series orifices in the P-T arm.

4-Way Directional Valve K

Two parallel orifices in the P-A arm and two series orifices in the P-T arm.

### Building a Custom Directional Valve

Directional valves can be modeled as a collection of orifices in series and parallel. Available building blocks in the Hydraulics (Isothermal) library for building directional valves are:

#### Fundamental Directional Valve Composite Structures

The four-way, three-position valve introduced above:

can be modeled as a collection of Variable Orifice blocks:

A different valve that starts with closed load ports and an open connection between the pump and tank is:

When the control member displaces in the positive direction, the flow paths P-A and B-T open. When the control valve displaces in the negative direction, flow paths B-P and A-T open. In the neutral position, flow path P-T is open. This is represented schematically as:

It can be built with a collection of Orifice with Variable Area Round Holes blocks. T1 corresponds to an intermediate point between the pump and tank.

#### Custom Directional Valve for a Front Loader

The front loader shown below handles lift and the tilt actuation with two 6-way 3-position directional valves. If both valves are in the neutral position, the pump port connects to the tank port. The pump is disconnected from the tank if either of the two valves moves from the neutral position.

The valve looks like this:

and is represented schematically as:

It can be modeled as a combination of Orifice with Variable Area Round Holes blocks and a Check Valve block.

All of the orifices, except `P_T1_1` and `P_T1_2`, are overlapped when the valve is in the neutral position. Orifices `P_T1_1` and `P_T1_2` begin the simulation with an opening offset (underlapping) that allows pump delivery at low pressure to the tank.