piston diameter.2 Decrease the valve size, thus reducing the valve coefficient k.
3 Reduce the accumulator pressure.
4 Add an orifice in series with the valve (see figure below).
All mentioned solutions are reasonable; however, solutions 1, 2, and 3 require modifications to the existing components. Solution 4 can be a simple way to modify an existing system.
The flow rate through the orifice and the valve can be written as
deq is the diameter of the equivalent orifice given by the series connection of SV and O2. The desired speed of the actuator corresponds to the following flow:
The equivalent series orifice diameter results:
Assuming that both orifices have the same flow coefficient (Cf = 0.7), the diameter of orifice O2 results:
4.5 Functions of Orifices in Hydraulic Systems
Even though the orifice element is described by a single equation (Eq. (4.5)), an orifice can assume different roles in a hydraulic circuit. A first way to classify an orifice function is based on its location in the system: in fact, orifices can be present either in the working and return lines or on the pilot lines of the systems. The working and return lines are represented by the connections to/from the actuators of the system; the power transfer functions achieved by the system occur in these lines. Thus, these lines are usually characterized by significant values of flow rate and pressure. Pilot lines are instead used to transmit pressure information to different locations of the system. These latter lines usually have negligible flow rates and are used for control purposes. According to ISO1219‐1 [1], pilot lines are always indicated with dashed lines, while working and return lines with a solid line.
4.5.1 Orifices in Pressure and Return Lines
When an orifice is used in the working or the return line of a system, it can operate as metering or compensating element.
In principle, if an orifice establishes the flow rate, for a given pressure drop, it functions as a metering element; however, if the orifice defines a certain pressure drop for a given flow rate, it functions as a compensator. In both cases, the relation between pressure drop and flow rate across the orifice is given by Eq. (4.5).
This classification is important to understand several control strategies used in hydraulic systems, as it will be shown in Part II and Part III of the book. A significant example is now provided to clarify the distinction between these different behaviors of an orifice.
Example 4.3 Orifice as a Metering Element or a Compensator
The system in figure consists of a fixed displacement pump and a variable orifice in parallel with a pressure relief valve. The pressure relief valve limits the maximum pressure at the pump outlet to p*. The pump delivers a fixed flow rate QP independently of the pump outlet pressure. Find the flow rate through the orifice, QO, as well as the pump outlet pressure pP, as a function of the orifice area opening, Ω. Describe also the function of the orifice, which can either be metering or compensator.
Given:
The pump flow rate, QP; the setting of the relief valve p*.
Find:
1 The flow rate through the orifice, QO
2 The pressure at pump outlet, pP
3 The orifice function (metering/compensator)
Solution:
Point P is located at the junction of the three main elements of the system (the pump, the relief valve, the variable orifice). Therefore, the operating pressure at point P can be found by intersecting the characteristics curves of these components, while also satisfying the constraints of maximum allowed pressure and available flow.
To clarify this statement, the characteristic curves of the three components in the (Δp, Q) chart are shown in the figure below. In particular,
the orifice characteristic curves are plotted according to the orifice equation 4.5 for decreasing values of the area Ω (Ω1 > Ω2 > Ω3…). This trend is as also shown in the plot of Figure
