Spool Edge with Notches (IL)

The figure shows the definition of overlap:

Parameter value Underlap corresponding to zero displacement — this is the relative position between the edge of the recess or the edge of the spool (in the case of a spool without recesses) and the port for the inlet of the isothermal fluid, if the position set in the port RA is 0. Parameter value Underlap corresponding to maximum area — this is the overlap value at which the flow cross-sectional area reaches its maximum value. This parameter can be used to simulate the effect of geometric features of the spool or housing that restrict the flow of liquid (for example, when the hole begins to have a minimum cross-section at a given position of the spool).

Note that the cross-sectional area of the flow should be an increasing function of the overlap value. In particular, it is assumed that the recess will never be blocked by the housing if the overlap is positive (as shown in the figure: with a slight shift to the left, the recess of the spool will be blocked by the housing). In any case, this hole in the housing is not modeled, so it is simply impossible to determine, for example, its diameter and, consequently, the moment when the flow cross-sectional area should decrease after reaching the maximum value at the maximum overlap value. This hypothesis should not cause problems in real systems, since they are not designed for such large overlap values.

Parameter Number of slots sets the number of recesses on the spool edge. It is assumed that all recesses have the same geometry. Note that adding additional recesses only leads to an increase in the flow cross-sectional area for a given spool position. The angular position of the recesses on the spool circumference does not affect the simulation results and is not set in the block.

The notch is created by adding simple shapes called areas to each other. The number of areas is set in the parameter Number of regions. For each area, you can set geometric characteristics in the corresponding parameter group. The documentation provides a group of parameters for the first area only. Define Geometry Region 1 the others differ only in their ordinal number. The shape of the area is set in the parameter Shape selection R1 and it can take the following values: Circular, Triangular, Rectangular, Trapezoidal, Trapezoidal with rounded edges. A notch is a collection of areas of different geometries, as shown in the figure.

Each area has its own radial depth (parameter value Radial depth R1), which is constant along the axis of the spool for all geometries, with the exception of rectangular geometry, which allows a linear change in depth along the axis. In any case, the width of the recess perpendicular to the radial direction remains constant along the radial direction.

circular area

The geometry of the circular area is shown in the figure.

The triangular area

The geometry of the triangular area is shown in the figure.

The rectangular area

The geometry of the rectangular area is shown in the figure.

trapecial region

The geometry of the trapezoidal area is shown in the figure.

trapect -shaped area with rounded sides

The geometry of the trapezoidal area with rounded sides is shown in the figure.

If the check box is Moving body removed and the body movement is not simulated, the overlap value is defined as

where

If the check box is Moving body If installed and the body movement is simulated, then the overlap value is defined as

where — moving the case in port CA.

The length of the camera is defined as

where — the length of the camera at zero offset, the value of the parameter Chamber length at zero displacement.

The formula for calculating the volume of the camera depends on the parameter value Evaluate pressure resultant force and volume variation:

In these formulas

The block evaluates various areas as a function of overlap, depending on geometric parameters.

For each floor with a recess, the block searches for the minimum area. between two candidate squares:

Hydraulic diameter It is calculated based on the cross-sectional area and the perimeter of the wetted surface as follows:

In the case of a simple spool valve with sharp edges, the flow area is calculated as described in the block Spool with Annular Orifice (IL).

Flow coefficient calculated as

where

Expense ratio calculated as

where

For meaning practically does not change. For low meaning it changes linearly with the change .

A reasonable value the default is 1000. However, for holes with complex (rough) geometry, it may be smaller. 50. For very smooth geometry, it can be set to 50000.

The average fluid velocity is

Consumption is determined by the following factors:

If the check box is selected Evaluate pressure resultant force and volume variation, then the contribution to the flow rate due to the movement of the spool is calculated as

where — the speed of the spool movement.

The hydrodynamic force acting on the spool is determined by estimating the change in momentum. This force tends to close the valve. For a steady-state fluid flow, the hydrodynamic force is

where — the angle of the jet.

Dependence of the hydrodynamic force from overlap It is defined as follows:

Check the box Couette effect allows you to take into account the Couette effect, that is, to take into account the contribution of the Couette current to the force of viscous friction.:

where

The force in the port RA is calculated taking into account the force in the port RB, the pressure force (if the check box is selected Evaluate pressure resultant force and volume variation), viscous friction forces (if the check box is selected Couette effect) and hydrodynamic force as

If the check box is selected Moving body and the hull movement is modeled, then the force in port CA is calculated based on the force in port CB: