Page 542 - Mechatronics with Experiments

JWST499-Cetinkunt
JWST499-c07
528 MECHATRONICS Printer: Yet to Come October 9, 2014 8:41 254mm×178mm
and the pressure transients in the control volumes on both sides of the cylinder,

̇ p (t) = (−Q (t) − ̇ y(t) ⋅ A ) (7.368)
AT
A
A
(V hose,VA + y(t) ⋅ A )
A

̇ p (t) = (Q (t) + ̇ y(t) ⋅ A ) (7.369)
PB
B
B
(V hose,VB + (l cyl − y(t)) ⋅ A )
B

̇ p (t) = (Q (t) − Q (t) − Q (t) − Q (t)) (7.370)
PB
r
PT
P
P
V hose,pv
where
Q = w pump ⋅ D ( ) (7.371)
P
p
sw
A (x ) √
PT
s
Q PT = Q ⋅ ⋅ (P − P )∕P r (7.372)
r
T
P
A PT,max
A (x ) √
PB
s
Q = Q ⋅ ⋅ (P − P )∕P (7.373)
PB r P A r
A
PB,max
A (x ) √
AT
s
Q AT = Q ⋅ ⋅ (P − P )∕P r (7.374)
T
B
r
A AT,max
Q = Q (p , p ) (7.375)
r r relief p
where the design parameters and variables for the hydraulic system are,
m – inertia,
A , A – cylinder head-end and rod-end cross-sectional area,
A
B
– bulk modulus of hydraulic fluid due to its finite stiffness,
V hose,pv – volume of the hose between pump and valve,
V hose,AV – volume of the hose between valve and cylinder side A,
V – volume of the hose between valve and cylinder side B,
hose,BV
l – the travel range of the cylinder,
cyl
D – flow rating of the pump (Volume/Revolution),
p
Q – rate flow at rated pressure P when valve is fully open,
r r
P – rate pressure,
r
A (x ), A (x ), A (x ), A (x ), A (x ) – valve flow areas as a function of
PA s PB s AT s BT s PT s
spool displacement, between pump, cylinder, and tank,
A PA,max , A PB,max , A AT,max , A BT,max , A PT – maximum value of valve flow areas
when valve is fully open between pump, cylinder, and tank,
Q , Q , Q , Q , Q , Q BT – flow rate from pump, pump-to-tank, pump-to-
PA
PB
AT
P
PT
cylinder and cylinder-to-tank,
x – valve spool displacement,
s
sw – swash plate angle, sw0 constant value of swash plate angle,
y – cylinder displacement,
P , P , P , P – pressure at pump, head-end, rod-end and tank,
P
T
B
A
w pump – speed of the pump,
p relief – the line relief pressure setting on the relief valve.
Relief Valves Relief valves are used to limit the pressure in hydraulic lines, and hence
protect the lines against excessive pressure. The maximum pressure limit of relief valve is