Page 611 - Mechatronics with Experiments

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JWST499-Cetinkunt
JWST499-c07
ELECTROHYDRAULIC MOTION CONTROL SYSTEMS 597
Load
m
g
Accumulator
Cylinder
Pump
D Q acc Main valve
p
w (t) Q p P p Q V P-A P B
in
Q r P-B A B
c
l cyl
P relief Relief A-T P
valve A A
B-T A y
T

FIGURE 7.121: One degree of freedom hydraulic system with fixed displacement pump,
closed center valve, a cylinder, and a relief valve.

elseif down motion x < 0.0 (7.779)
s
d
(2) (p (t)) = (−Q (t) − ̇ y(t) ⋅ A ) (7.780)
A
AT
A
dt V + y ⋅ A
hose,VA A
d
(3) (p (t)) = (Q (t) + ̇ y(t) ⋅ A ) (7.781)
B
PB
B
dt V hose,VB + (l cyl − y) ⋅ A B
d
(4) (p (t)) = (Q (t) − (Q (t) + Q (t) + Q (t) + Q (t))) (7.782)
r
P
acc
PT
PB
P
dt V + V
hose,pv acc
end (7.783)
if ideal relief valve (7.784)
(5) if Q (t) > 0.0; then p (t) = p relief (7.785)
P
r
(5) else if p (t) < p relief ; then Q (t) = 0.0 (7.786)
P
r
end (7.787)
else (7.788)
if p (t) ≥ p relief and no transient dynamics (7.789)
P
(5) Q (t) = K relief ⋅ (p (t) − p relief ) (7.790)
r
P
elseif p (t) ≥ p and with transient dynamics (7.791)
P relief
Q (t)
(5) r =−Q (t) + K ⋅ (p (t) − p ) (7.792)
relief r relief P relief
dt
else (7.793)
(5) Q (t) = 0.0 (7.794)
r
end (7.795)
end (7.796)
where (7.797)
(6) Q (t) = D ⋅ w pump (t) (7.798)
P
p
√
(7) Q (t) = (p (t) − p (t))∕Δp = 0.0 (7.799)
PT P T r
x (t) √
(8) Q (t) = Q ⋅ s ⋅ (p (t) − p (t))∕Δp if x > 0 (7.800)
PA r P A r s
x s,max
x (t) √
(9) Q (t) = Q ⋅ s ⋅ (p (t) − p (t))∕Δp if x > 0 (7.801)
BT r B T r s
x s,max