The last key point on the operating envelope is the condition of impending cavitation. It is found by setting the pressure in the powered end of the cylinder to zero, then solving for the conditions that will produce the condition. In that development, we find that the maximum deceleration force (over-running load) without cavitation is given by:
fL,max = (1+ρv2/ρc3) APE × PS
which applies to both extension and retraction with the proper interpretation of the valve and cylinder ratios. The amount of the overrunning load force must be less than the value calculated in the above equation, because no good comes of cavitation.
But in the world of servo and proportional valve control, if the valve truly controls the flow into the actuator, then the pressure drop across the valve be must be substantial. In fact, in a true valve controlled system, the pressure drop across the valve will normally vary from nearly zero to nearly the supply pressure as the load moves, accelerates, decelerates, and stops. This means that the velocity term (also called the force loss term) cannot be ignored. Instead, it is essential, because it is the means by which the valve asserts its control function into the circuit.
This is the so-called velocity term. It should be looked at in the context of the entire VCCM equation. Note that if velocity, v, is zero, the entire velocity term is zero. That is, at zero speed, there is no pressure loss across the valve’s metering lands. This is not a profound conclusion. Zero speed is also the stall condition, where the load force is so great that system pressure acting on the cylinder area cannot move the piston.
If the load force is relaxed, the speed will increase, and a larger and larger value for the velocity term will be subtracted from the stall force, leaving less force available at the cylinder rod. Note that the velocity term (force loss) increases by the square of the speed.
An interesting side note to the velocity term is its role in conventional” hydraulics. In such scenarios, it is not at all unusual to select valves that have such a great degree of opening that they result in negligible pressure drop. In terms of the VCCM equation and the velocity term, this is a situation in which KVPL is so large as to make the velocity term small. The point is that the VCCM equation is very general and applies both to conventional as well as servo or proportional hydraulics. The bottom line, though, is that with the best valve control that modern technology has to offer — control by means of electrically modulated valves — there must be substantial pressure, force, and power loss to avoid sacrificing good control.
High efficiency and pressure compensation from a fixed displacement pump?
Designing a successful closed-loop electrohydraulic motion control system usually starts with providing a constant pressure source. The traditional solution has been to provide a variable-displacement pump and accumulators in the hydraulic power unit.
However, a textbook written by well-known fluid power author and lecturer Jack Johnson, P.E. and Brian Johnson provides a detailed engineering study of a pressure-compensated system that uses a fixed-displacement pump and no relief valves. Titled An Engineering Analysis of the Pulse Width Modulation Method of Controlling Output Pressure of a Hydraulic Power Supply, it is as efficient as a conventional pressure compensated pump.
You can read about the complete test results, but more importantly, you can learn all you need to design and build your own low cost, efficient constant pressure power units for both servo and conventional applications.