Page 552 - Mechatronics with Experiments

JWST499-Cetinkunt
JWST499-c07
538 MECHATRONICS Printer: Yet to Come October 9, 2014 8:41 254mm×178mm
where Q , Q are rated flow rates for relief valve and main valve, A r,max maximum orifice
rr
vr
opening of the relief valve, A v,max maximum orifice opening of the main valve, Δp rated
rr
pressure difference above the maximum line pressure for the relief valve to open fully, Δp vr
rated pressure differential across the valve used to measure the rated flow through the main
valve. In practice, it is more common to use the rated flow equations instead of the one with
orifice coefficients.
Let the parameters of the relief valve be
K = 10.0 (7.459)
ar
K px = 0.01 (7.460)
A = 1.0mm 2 (7.461)
fb
k = 100 kN∕mm (7.462)
r
2
m = 0.1kN∕(mm∕s ) (7.463)
r
c = 100 kN∕(mm∕s) (7.464)
r
A r,max = 100 mm 2 (7.465)
3
Q = 200 ml∕s = 200 ⋅ 10 −6 m ∕s (7.466)
rr
p = 20 000 kPa (7.467)
max
Δp = 1000 kPa (7.468)
ra
Δp = p = 20 000 kPa (7.469)
rr max
Notice that these parameters indicate that when p (t) − p max =Δp = 1000 kPa, the relief
ra
s
valve will be fully open, x = 10, A = 100 = A r,max .
r
r
Let the parameters of the main valve be:
A v,max = 100 mm 2 (7.470)
3
Q = 200 ml∕s = 200 ⋅ 10 −6 m ∕s (7.471)
vr
Δp = 6895 kPa = 1000 psi (7.472)
vr
The tank pressure is
p = 100 kPa (7.473)
t
The bulk modulus and volume of the fluid in the space between pump and two valves are,

9
6
= 1.5 ⋅ 10 Pa = 1.5 ⋅ 10 kPa (7.474)
2
V hose = (d ∕4) ⋅ (l + l + l ) = 0.001 m 3 (7.475)
2
1
3
Initial conditions for the dynamic models are as follows. For relief valve spool position and
velocity,
x (t ) = 0.0 (7.476)
r 0
̇ x (t) = 0.0 (7.477)
r
and for line pressure
p (t ) = p t (7.478)
s 0
In all of the simulated cases, we are interested in the following variables and their
interaction,

1. D (t), 2. w (t), 3. Q (t), 4. Q (t), 5. Q (t), 6. A (t), 7. A (t), 8. p (t) (7.479)
p shaft p v r v r s