Читать книгу Hydraulic Fluid Power - Andrea Vacca - Страница 71

This example shows two possible cases of poppet valve design. With poppet valves, the flow exit area can be almost perfectly sealed when the valve is closed (poppet against the seat). This feature is very difficult to achieve with the spool valve geometries in Figure 3.17, due to the necessary clearance between the spool and the valve body.

Flow force derivation – Case A

Equation (3.43) can be applied to the CV shown in the figure above, with the same assumptions illustrated in the previous paragraphs. This provides the expression of Eq. (3.48) for the flow force in steady state conditions:

The flow force, in this case, tends to close the valve poppet.

Flow force derivation – Case B

Additionally, in this case, Eq. (3.43) can be applied to the CV shown in figure; however, it has to be noted that the Eq. (3.47) includes the overall contribution of the solid walls:

For this case, the pressure acting on CV at the left side (next to the entrance) is not acting on the sliding element, but on the valve body. It can be assumed that this pressure is equal to the entrance pressure p₁ and uniformly distributed at the surface (i.e. small opening area Ω). Next, assuming that with the whole poppet downstream, the flow area Ω is at the pressure p₂:

For typical valve geometries, it is easy to show that the first term is generally higher than the second one so that in this case the flow force tends to open the poppet.

This can be proven by writing the orifice equation that relates Q and Δp:

and considering that generally