cylinder wall and sealing packing. It must be pointed out that the starting delay time
of piston is also related to the back pressure of piston, that is to say, to the exhaust
process.
Generally, the starting delay time t p of the piston of cylinder is between
0.038*0.042 s.
(2) The starting delay time of piston in noncritical (subsonic) flow state. If the
piston starting pressure p p is greater than the critical pressure of the gas flow,
that is, p p [ 0:528; p s ¼ p à , the flow in the cylinder passage is subsonic
(noncritical). Then, Eq. (8.40)’ cannot be used to calculate piston starting delay
time. Therefore, it is necessary to reestablish the analytical formula for calculating piston starting delay time under subsonic flow. The expression of the
weight flow rate for subsonic flow of air through the intake passage into
cylinder (if the gas state change in flow process is a changeable process) is as
follows:
G ¼ c 0 A 0
p s
ffiffiffiffiffiffiffi ffi
RT s
p
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi
2ng
n À 1
p
p s
2=n
À
p
p s
n þ 1
ð
Þ=n
"
#
v
u
u
t
ð8:42Þ
The rate of pressure change (the rate of pressure change) in the working chamber
V 0 caused by the gas mass flow into the cylinder satisfies the following relationship
(if the change of the gas state in chamber V 0 is an isothermal process):
G ¼
V 0
RT 0
dp
dt
ð8:43Þ
So,
c 0 A 0 T 0
V 0
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
2ngR
n À 1
ð
ÞT s
s
dt ¼
dp
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi
p
p s
2=n À
p
p s
n þ 1
ð
Þ=n
r
ð8:44Þ
Because the pressure acting on the piston rises from the initial pressure p 0 to the
piston starting pressure p p , and the piston is stationary before the starting pressure
p p is reached, the time from the beginning of intake to the beginning of piston
operation is t ¼ 0 $ t ¼ t p . The relationship between delay time t p and starting
pressure p p can be obtained by integrating Eq. (8.44):
34
8 Pneumatic Actuators, Driving Elements and Accessories
of piston is also related to the back pressure of piston, that is to say, to the exhaust
process.
Generally, the starting delay time t p of the piston of cylinder is between
0.038*0.042 s.
(2) The starting delay time of piston in noncritical (subsonic) flow state. If the
piston starting pressure p p is greater than the critical pressure of the gas flow,
that is, p p [ 0:528; p s ¼ p à , the flow in the cylinder passage is subsonic
(noncritical). Then, Eq. (8.40)’ cannot be used to calculate piston starting delay
time. Therefore, it is necessary to reestablish the analytical formula for calculating piston starting delay time under subsonic flow. The expression of the
weight flow rate for subsonic flow of air through the intake passage into
cylinder (if the gas state change in flow process is a changeable process) is as
follows:
G ¼ c 0 A 0
p s
ffiffiffiffiffiffiffi ffi
RT s
p
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi
2ng
n À 1
p
p s
2=n
À
p
p s
n þ 1
ð
Þ=n
"
#
v
u
u
t
ð8:42Þ
The rate of pressure change (the rate of pressure change) in the working chamber
V 0 caused by the gas mass flow into the cylinder satisfies the following relationship
(if the change of the gas state in chamber V 0 is an isothermal process):
G ¼
V 0
RT 0
dp
dt
ð8:43Þ
So,
c 0 A 0 T 0
V 0
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
2ngR
n À 1
ð
ÞT s
s
dt ¼
dp
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi
p
p s
2=n À
p
p s
n þ 1
ð
Þ=n
r
ð8:44Þ
Because the pressure acting on the piston rises from the initial pressure p 0 to the
piston starting pressure p p , and the piston is stationary before the starting pressure
p p is reached, the time from the beginning of intake to the beginning of piston
operation is t ¼ 0 $ t ¼ t p . The relationship between delay time t p and starting
pressure p p can be obtained by integrating Eq. (8.44):
34
8 Pneumatic Actuators, Driving Elements and Accessories