#### What is in this article?:

- Sizing a motion control system
- How many KVs are there?

Multiple calculations for closed-loop electrohydraulic servo systems are presented, including a detailed explanation of the VCCM equation.

Matching the performance characteristics of a servo or proportional valve to the performance needs of an application requires at least two major system design steps:

1. The valve and cylinder must be sized so that the cylinder transmits enough power to the load to simultaneously meet the worst case force and speed design target.

2. There is sufficient bandwidth (frequency response) in the valve and load-compressibility resonance to accurately regulate the output (let us assume it to be cylinder position) at the target value.

The sizing problem is greatly facilitated by adopting the concept of valve flow coefficient rather than the valve flow rating process that is popular with valve manufacturers. We can develop a set of design formulas to derive the valve coefficient, which is not practical with the flow rating method. That’s because servo and proportional valves are flow rated at different pressures. Furthermore, ISO 10770-1 requires that the “valve total pressure drop be set to 1 MPa or 7 MPa, as appropriate.”

A test procedure that specifies only total valve pressure drop does not accommodate valves that are deliberately designed with asymmetrical valve coefficients. Such valves are useful in special applications — for example, when trying to reduce the likelihood of cavitation from an over-running load. Another example is an application that cannot withstand the “turnaround bump” that accompanies cylinder motion when symmetrical valves control asymmetrical (single rod) cylinders.

The asymmetrical valve can be the perfect solution. In the asymmetrical valve, the individual internal metering lands do not open to equal flow areas even though they are all connected to the same spool. Such asymmetry is achieved by using differing numbers of slots or notches on the valve body (sleeve) or on the spool.

The beauty of the valve coefficient approach is that both servo and proportional valves can be accommodated with one set of formulas —equally important, so can symmetrical and non-symmetrical valves and symmetric or non-symmetric cylinders.

### Pressure and flow relationships

Most fluid mechanics professors express the characteristics of an orifice in terms of its geometry, contraction coefficient (based on geometric dimensions), and the velocity coefficient. However, in Hydraulic Control Systems, H. E. Merritt convincingly explains his conclusion that most hydraulic valves behave as knife-edged orifices. Furthermore, the relationship between pressure and flow can be approximated by the simple formula:

*Q = 100 × A*(

_{Q}

*P* – P

_{1}

_{2}

^{½}

*where* ,

100 is a constant, lb-in.-sec,

*A*_{Q}^{2},

*P*_{1} – *P*_{2}*P*_{1}*P*_{2}

*Q* is the resulting flow, in.^{3}/sec.

To properly size a servo or proportional control valve, I propose making a simple substitution in the above equation to introduce the valve coefficient, K_{V}

*K*

_{V}= 100 × A

_{Q}.

The relationship is only approximate, but countless valve manufacturers accept the idea that the flow through a typical hydraulic control valve follows the square root of the differential pressure drop. So I propose a definition to make valve sizing and selection more predictable. I propose defining KV empirically and applying it to valves that can be tested now, rather than for designing a new valve:

*K*

_{V}= Q

_{r}÷ (∆P

*Q*)

_{r}

^{1/2}

where *K*_{V}^{3}/sec) ÷ (∆P)^{1/2}

*Q _{r}* is the rated flow of the orifice as verified by actual test while the valve is operated at its flow rating pressure, in.

^{3}/sec, and

*PQ*

_{r}The flow rating differential pressure distinguishes between the rated pressure of the valve and the pressure drop used for determining or verifying the rated flow of the valve. In the case of servovalves, if you are determining the flow coefficient of the “total valve,” then the flow rating pressure is 1000 psid (7 MPa).

If you are looking at only one of the valve’s two metering lands, with one direction of spool shift, then the flow rating differential pressure is one-half the total, or 500 psid (3.5 Mpa). For proportional valves, the flow rating pressure is 145 psid (1 MPa) for the total valve, but only half that, or 72.5 psid (0.5 MPa), for just one of the two internal metering lands.

This approach removes some of the confusion surrounding high pressure drop valves. It also removes confusion when the valve’s lands are not all of equal flow area. Furthermore, the design formulas that come up later apply to all types of valves, making design and sizing straightforward. If valve manufacturers would publish their empirically derived KVs for their products, then applying them would be much easier.

Manufacturers publish rated flow for valves as a convenience to their users. Unfortunately, it implies that

• it is the maximum flow,

• the pressure drop remains constant,

• it is the only flow allowed, or

• some other misconception. Rated flow is not a property of the valve. It is something the valve has if, and only if, it is operated at its flow rating pressure.

*K*_{V}*K*_{V} of the valve allows calculating the flow and pressure at all operating conditions, not just flow rating conditions.