Читать книгу Hydraulic Fluid Power - Andrea Vacca - Страница 89

The hydraulic schematic of the lifting system considered in this problem introduces the symbolic representation of components that will be described in more detail in the next chapter of this book. However, for the reader, the functioning of the system should be quite intuitive: a hydraulic pump P is driven by a prime mover (an electric motor) M to supply flow to a hydraulic control valve, DCV. The hydraulic control valve is manually activated, and it determines the direction of the supply flow: in one position, it implements the cylinder extension, and in the other, the retraction. Centering springs ensure the valve blocks the cylinder work ports in case of no valve actuation.

A pressure relief valve is installed at the pump outlet, to protect the pump from overpressurization.

Considering the rest position, the supply part of the hydraulic system is isolated through the DCV, so that the problem can be simplified by considering the following schematic:

1 If a motion of the piston would occur in rest conditions the steady‐state form of the conservation of mass at both Vpist and Vrod would apply:(E4.4.1) (E4.4.2) The above equations were derived in Chapter 3, when analyzing the basic functioning of a linear actuator. The flow QLEAK is the flow rate through the laminar orifice that represents the internal leakages inside the cylinder.(E4.4.3) From the above (E4.4.1) and (E4.4.2), being Apist ≠ Arod, it is clear that the only possible solution for the leakage flow is QLEAK = 0 l/min. This means that even if there is an opening between the two chambers of a differential cylinder actuator, there are no internal leakage inside the actuator. This means that v = 0 m/s, meaning that the piston will remain in standstill.

2 The above Equation (E4.4.3) implies thatRecognizing that prod = pA and ppist = pB, we haveThe two pressure gages will give the same reading, which can be determined by the force balance of the piston (assuming no friction):

Further considerations:

 This example shows how the presence of internal leakages paths inside a differential cylinder do not prevent realizing a perfect load holding, as long as the hydraulic circuit properly blocks the cylinder work ports. This is why load handling hydraulic machines can safely use even worn cylinders, as long as the connecting hydraulic valves can achieve a perfect sealing.

 The answer is true only after the system reaches a stationary condition. A very fast transient will actually happen when the valve is brought to rest, or in case of a variation of the load. During this transient, the pressure inside the piston and rod chamber will equalize. This process involves a small mass exchange between Vpist and Vrod (therefore a QLEAK ≠ 0 for a short interval) related to the compressibility of the fluid.