1. When loaded
p a V a1 ¼ p 1 þ p 2
ð
ÞV 1
ð8:21Þ
2. Load-free (i.e. no-load return)
p a V a2 ¼ p 1 þ p 2
ð
ÞV 2
ð8:22Þ
3. Another expression is obtained by dividing Eqs. (8.21) and (8.22) by the time
t required for working travel:
p a V a1
t 1
¼
p 1 þ p 2
ð
Þ
t 1
V 1
ð8:21’Þ
p a V a2
t 2
¼
p 1 þ p 2
ð
Þ
t 2
V 2
ð8:22’Þ
4. Calculate the volume flow q 1 and q 2 of the gas required for each trip.
Because the volumes on both sides of the piston are
V 1 ¼
pD
2 L
4
and V 2 ¼
p D
2
À d
2
ð
Þ L
4
Under the standard condition, the gas volumetric displacement per unit stroke is,
respectively,
q 1 ¼
V a1
t 1
and q 2 ¼
V a2
t 2
If the unit conversion relation is introduced, the volume flow rate of gas required
to complete a loaded working trip and a no-load return journey can be obtained.
Loaded
Load-free
Fig. 8.14 Working sketch of
cylinder
8.2 Structure and Characteristics of Actuators
17
p a V a1 ¼ p 1 þ p 2
ð
ÞV 1
ð8:21Þ
2. Load-free (i.e. no-load return)
p a V a2 ¼ p 1 þ p 2
ð
ÞV 2
ð8:22Þ
3. Another expression is obtained by dividing Eqs. (8.21) and (8.22) by the time
t required for working travel:
p a V a1
t 1
¼
p 1 þ p 2
ð
Þ
t 1
V 1
ð8:21’Þ
p a V a2
t 2
¼
p 1 þ p 2
ð
Þ
t 2
V 2
ð8:22’Þ
4. Calculate the volume flow q 1 and q 2 of the gas required for each trip.
Because the volumes on both sides of the piston are
V 1 ¼
pD
2 L
4
and V 2 ¼
p D
2
À d
2
ð
Þ L
4
Under the standard condition, the gas volumetric displacement per unit stroke is,
respectively,
q 1 ¼
V a1
t 1
and q 2 ¼
V a2
t 2
If the unit conversion relation is introduced, the volume flow rate of gas required
to complete a loaded working trip and a no-load return journey can be obtained.
Loaded
Load-free
Fig. 8.14 Working sketch of
cylinder
8.2 Structure and Characteristics of Actuators
17