Spool valves and hydraulic circuits

Determination of clearances and tolerances

Spool valves are normally designed so that leakage in the spool is small compared to the hydraulic system flow rate, but it is helpful to know what the leakage is and to be able to control the tolerances on the clearance in a rational manner.

Bores are machined and then honed, to control size and also surface finish, typically 8 to 16 micro-inches. Running clearance and tolerances on bore and lands can be determined using the following procedure.

Due to tooling and gauging considerations, it is usually practical to violate convention by assigning a nominal size, or a size found to be repeatably attainable, to the bore, and then grinding the spool land diameter to suit.

Spool valves have a leakage path around their assembly clearance. For a rectangular gap of upstream-downstream length L, radial clearance t, and width b, then for a fluid of viscosity μ, then pressure P will drive a leakage flow rate of Q according to the equation shown. Of course a spool valve can be idealized with this equation by using b = 2πr.

Note the t³ term: leakage increases as to the cube of the clearance, to a point: once the static pressure has been converted entirely to velocity head (Bernoulli), then increasing the clearance further will only increase the leakage linearly in t.

Also, leakage converts static pressure into velocity head, which drops the static pressure in the leakage path. If the spool is off-center in its bore, then the leakage flow rate will be greater on the side with the larger gap: this reduces the pressure here, which in turn exerts a large force on the spool tending to center it.

For eccentric gaps, the above equation can be integrated around the circumference of the spool, and it can be shown that when the spool is offset to make contact with its bore on one side, the leakage flow rate is exactly twice that of a perfectly centered spool. Thus it is conservative to assume that the leakage flow will be double of that calculated.

Timing

The axial location of ports (i.e. holes) in a valve block presents a practical machining problem: hydraulic passages are small diameter bores with long lengths; drills tend to wander so accurate location of the break-out points is difficult to hold.

To address this, most spool valve bores have stepped-up grooves into which the drilled holes break out. The grooves are cut with a boring bar and can be located far more accurately than a hole break-out (the boring bar is far more rigid and any bending deflection will tend to affect the depth of the cut, which is not critical, not its axial location).

When a land covers a groove, there is minimal leakage: minimal flow through the spool, and the valve is said to be closed. When an inlet and outlet groove are not separated by a tightly fit land, then there will be substantial flow and minimal flow restriction, and the valve is open.

However, between the closed an open states, when the land just opens a small gap to a groove, it is tempting to think of the valve as “partially open”, however this is not the case. The equation in the above section can be applied to this geometry, and it can be shown that the axial distance in which there is a non-trivial flow restriction, is small: a large flow restriction from a partially-opened valve only persists for a few thousandths of an inch!

Therefore, spool valves are to be treated as “Boolean” “on/off” devices, rather than analog pressure-reducing valves in which the pressure is varied using the valve.

Inlet port timing

Most spool valves are designed to have the inlet and outlet ports open simultaneously. However, it is better to consider the axial tolerance stackup of the grooves and lands, and design to ensure that the inlet is open before the outlet: in other words, time your circuit using the outlet ports not the inlet ports.

Depending on where the spool is placed: between a return line and the pump, or between the pump and the load: the inlet might be at a low, often tank or reservoir pressure, which  is not in general known to you, the designer. It is very easy to accidentally choke the inlet due to pipe flow losses and velocity head. 15 psi, for example, might be an insignificant loss for a 500 psi system, but in the case of inlet design, a partially opened port can (will) restrict the flow due to Bernoulli. It is better practice to arrange the inlet port to be substantially open before the outlet starts to open.

Hydraulic circuit linearity and analog to Kirchoff’s Laws

A consequence of the equation above, which applies to a range of low-Reynolds number hydraulic components, is that most of the complex geometry terms are constant once the valve has been built. This reduces the equation to P = Q*R, where R is the “fluid resistance”. Clearly this is an analog to Ohm’s Law.

Thus, Kirchoff’s Current Law (a.k.a. the equation of continuity) and Kirchoff’s Voltage Law (the sum of the pressure drops around any closed loop must be zero) hold. This allows the use of linear algebra to model complex hydraulic circuits in steady state. The introduction of transient devices, such as accumulators, would render this simplification invalid.