that, in this case, the pressure drop across the orifice equals pP, since the pressure downstream the orifice is pT = 0 bar.
the pump curve represented by a horizontal line (constant flow rate). In fact, for this problem the pump provides a constant flow independent on the system pressure.
the relief valve curve, represented by a vertical line. The relief valve, which will be explained more in detail in Chapter 8, limits the maximum pressure at the junction point P to p*.
The behavior of the system can be analyzed for different openings of the variable orifice O.
In case of a large orifice area (Ω = Ω1), the intersection between the pump characteristic and the orifice curve is at X1. This point is located at a pressure lower than p*: the entire pump flow rates QP goes to the orifice (QP = QO); and the relief valve is closed (QRV = 0). In this case, the orifice Eq. (4.5) can be used to find the pressure at the point P:
In this condition, the orifice O behaves as a compensator, since it establishes a pressure drop for a given flow rate.
The situation is similar for the smaller opening area Ω2 < Ω1: the operating point shifts from X1 to X2 at a higher pressure. The relief valve remains closed and the orifice equation can be used again to find p2.
The orifice maintains the compensator function until it reaches the opening area Ω*. This area value is critical, as it corresponds to a pressure at point P equal to p*. When the opening area is Ω*, the full pump flow is still passing through the orifice.
For area values smaller than Ω*, as in the case of Ω3, the intersection between the orifice curve and the pump curve would result in the operating point X3′, which corresponds to a system pressure
The orifice equation in this case can be used to find the flow rate Q3, knowing that the pressure drop across the orifice is defined as Δp3 = p* − pT = p*
A further reduction of the opening area of the orifice (Ω4 < Ω3) results in a reduction of the orifice flow, as visible by the location of the intersection point X4 in the figure.
In these conditions, the orifice behaves as metering, since it establishes a flow rate as a consequence of a given pressure drop.
This example shows how a metering element can be used to regulate flow in a hydraulic system. In this simple case, the orifice flow is directed to tank at null pressure. In general, an actuator can be located downstream of the metering element, which is ultimately used to adjust its speed.
4.5.2 Orifices in Pilot Lines
Pilot lines are used to transmit the value of pressure to different locations of a circuit. In such lines, it is very rare to find orifices working as metering or compensator devices. Instead,
Orifices are used in pilot lines to manipulate the pressure signal, according to two possible function purposes: pressure separators or dynamic orifices.
A pressure separator is an orifice used to decouple the pressure in the working line – where the pilot line is connected – and the pressure transmitted by the pilot line itself, downstream the orifice.
A dynamic orifice is utilized with to modify the rate at which the pressure information is transmitted through the pilot line. Dynamic orifices dampen the pilot pressure information, acting as hydraulic low pass filters. Typically, dynamic orifices are accomplished with two different layout configurations. In the first layout, they are located next to closed‐end connections of the pilot line. Therefore, they do not affect the operation of the system in steady‐state operation, being crossed by zero flow rate in this condition. This kind of dynamic orifice can be neglected while studying the main steady‐state system operation. In the second layout, the dynamic orifice is used in an additional pilot line connection to the reservoir (bleed orifice). Also, a bleed orifice does not affect the steady‐state operation of the system, but it introduces a constant dissipation by bleeding fluid to tank.
Understanding the function of orifices in working lines and pilot lines is not always simple, particularly for the cases of pressure separators and dynamic orifices. For this reason, this book will often point out the function accomplished by the various orifices present in a certain component or system. In this way, the reader will progressively become more familiar with recognizing the different roles of orifices in hydraulic systems.
Example 4.4 Leakage in a Cylinder
Consider the hydraulic system in the figure below. The system is used to lift and lower a vertical load. The system requirement is that no leakage should occur while the system is in rest or standby (directional control valve (DCV) in neutral position). However, the cylinder seal is damaged so that leakages can occur between its piston chamber and its rod chamber. Assuming that the DCV can perfectly block the cylinder work ports, what happens to the piston when the valve is in rest position? Does it fall? Or it remains stand still? Also, provide the value of the reading of the two pressure gages A and B in such condition.
The following data are given: equivalent orifice resistance of the internal cylinder leakage = 50 (bar · min)/l; mass = 1000 kg; piston diameter 100 mm; rod diameter 40 mm.
Given:
The hydraulic schematic of a hydraulic lifting system, the piston diameter of the cylinder D = 100 mm and the rod diameter d = 40 mm. The gravitational load is known M = 10 000 kg. The internal leakage of the cylinder expressed as equivalent orifice resistance
