where p A1 ; V A1 —Pressure of nitrogen chamber at a certain working moment and gas
volume at that pressure in descending stage.
For low-pressure accumulators, there are
p LA0 V
n
LA0 ¼ p LA V
n
LA
ð12:18Þ
DV ¼ V LA À V LA0 ¼
p LA0
p LA
1
n À1
"
#
V LA0
¼
Z p
4
D
2
À d
2
À
Á dy f
dt
À Q H
!
dt ¼
p
4
D
2
À d
2
À
Á
y f À
Z
Q H dt
ð12:19Þ
d 1 ! 4:61
ffiffiffiffiffiffi ffi
Q H
v p
s
ð12:20Þ
where
Q H Average flow rate of outlet pipe;
v p Average flow rate of hydraulic oil in tubing. Check the hydraulic technical
manual, the speed of oil return pipeline is 1:7 À 4:5 m=s, take 3 m=s;
d 1 Oil tubing diameter.
Substituting Eqs. (12.19) and (12.20) into Eq. (12.18), the hydraulic pressure of
the oil in the low-pressure accumulator at a certain working hour is obtained.
p LA ¼ p LA0
V LA0
V LA
n
¼ p LA0
V LA0
V LA0 þ
R
p
4 D 2 À d 2
À
Á dy f
dt À Q H
h
i
8
> > <
> > :
9
> > =
> > ;
n
ð12:21Þ
where
p LA0 ; V LA0 Inflatable pressure of low-pressure accumulator and volume at that
pressure is applied;
p LA ; V LA
Pressure of low-pressure accumulator at work and volume at that
pressure.
Substituting Eqs. (12.17) and (12.21) into Eq. (12.13), the dynamic model of the
descending stage is obtained as follows:
m
d
2 y r
dt 2 ¼ mg þ p A0
V A0
V A0 þ
p
4 D 2 H À y f
À
Á
"
# n p
4
D
2
À p LA0
V LA0
V LA0 þ
p
4 D 2 À d 2
ð
Þ y f À
R
Q H dt
"
# n p
4
D
2
À d
2
À
Á
ð12:22Þ
12.2 High-Speed Pneumatic–Hydraulic Composite Hammer
283