Page 481 - Mechatronics with Experiments

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ELECTROHYDRAULIC MOTION CONTROL SYSTEMS 467
pressure is proportional to the lever displacement with its maximum value being the input
pilot pressure. This output pressure is then used to shift the main spool against a centering
spring in order to generate a main spool displacement that is proportional to the lever
displacement.
In pilot valve applications, the input pressure is the pilot supply pressure (p pilot,s ),
and output pressure is the pilot control pressure (p pilot,c ) which is used to shift the spool of
a larger flow control valve,
p pilot,c = (k spring spring )∕A out ≤ p pilot,s (7.172)
x
≈ K ⋅ x spring ≤ p pilot,s (7.173)

A different version of the pilot valve has two inports: pilot pressure supply and tank ports.
The output pilot control pressure is regulated by the lever motion to be between the tank
pressure and pilot supply pressure.
Spring force is due to preloaded displacement (x ) plus the displacement during
preload
pressure regulation, Δx ,
v
F spring = k spring ⋅ (x preload +Δx ) (7.174)
v
While
A out ⋅ p out ≤ k spring ⋅ x preload (7.175)

the valve orifice is fully open with negligible restriction and
p out ≈ p in (7.176)

When,
A out ⋅ p out > k spring ⋅ x preload (7.177)

The force balance to define the position of the spool
A ⋅ p = k ⋅ (x +Δx ) (7.178)
out out spring preload v
p = p − K ⋅ Δx (7.179)
out in vp v
where the last equation states that as the valve spool moves, Δx , due to increased output
v
pressure, the orifice restriction increases (orifice starts to close, gets smaller), and the output
pressure becomes less than the input pressure due to a pressure drop across the smaller
orifice. The gain between the spool displacement and pressure drop, K , is large and
vp
typically much larger than the spring constant, K vp ≫ k spring . This means that the movement
of a spool makes a large difference in the output pressure but not much change in the
spring force. If we eliminate the Δx in the above equations, we can obtain a steady-state
v
relationship between input and output pressures, which can be shown to be
( )
1
A ⋅ p = k ⋅ x + ⋅ (p − p ) (7.180)
out out spring preload in out
K
vp
( )
k spring k spring
A out + ⋅ p out = k spring ⋅ x preload + ⋅ p in (7.181)
K vp K vp
k spring
p out ≈ ⋅ x preload (7.182)
A out
p out ≈ p preload (7.183)
by approximating k spring ∕K vp ≈ 0.0.