(2) Difference of Volumetric Elasticity Coefficient:
Atmosphere b 0 ¼ 7 Â 10
5
$ 14 Â 10
5 Pa
½ ;
Actuating Oil of Hydraulic System b ¼ 1:4 Â 10
9
$ 1:86 Â 10
9 Pa
½ ;
The difference is about 2000 times.
(3) From the Eqs. (8.11) and (8.15), it can be seen that the natural frequencies of
cylinders and pneumatic cylinders are about
ffiffiffiffiffiffiffiffiffiffi
2000
p
times (45 times) different
for actuators of the same size.
(4) Difference of Piston Positions at the Minimum Natural Frequency:
i. Pneumatic: The minimum natural frequencies of symmetrical and asymmetrical cylinders occur when the piston is in the middle of the cylinder.
When analyzing the stability of the pneumatic system, only the piston in the
neutral position of the cylinder needs to studied.
ii. Hydraulic: The minimum natural frequency of a symmetrical cylinder
occurs when the piston is in the middle of the cylinder. However, the
minimum natural frequency of an asymmetric cylinder occurs somewhere in
which the piston deviates from the middle of the cylinder. When analyzing
the stability of hydraulic system, the symmetrical cylinder only needs to
study that the piston is in the neutral position of the cylinder; the asymmetrical cylinder needs to study that the piston deviates from the neutral
position of the cylinder.
(5) The mechanical structure of hydraulic cylinder and cylinder is basically the
same.
8.1.5 Conclusions
By analyzing the natural frequencies of pneumatic cylinder and hydraulic cylinder
when the piston is in or off the central position of the actuator with asymmetric
effective area on both sides, the following results can be obtained by comparing and
analyzing them:
(1) When the piston is in different positions, the natural frequencies of pneumatic
cylinder or hydraulic cylinder are completely different. When the piston is in
the position of both ends of the end cap of the actuator, the natural frequency
reaches the maximum.
(2) When the piston of pneumatic single acting cylinder is in the end position, the
natural frequency reaches the maximum. When the piston is in the middle
position, the natural frequency of the double acting cylinder reaches the minimum, whether the symmetrical cylinder A 1 ¼ A 2 or the asymmetrical cylinder
A 1 ¼ 2A 2 . Symmetrical hydraulic cylinder, such as A 1 ¼ A 2 , when the piston is
in the central position, the natural frequency reaches the minimum. For
asymmetric cylinders, such as A 1 ¼ 2A 2 , the minimum natural frequency
12
8 Pneumatic Actuators, Driving Elements and Accessories
Atmosphere b 0 ¼ 7 Â 10
5
$ 14 Â 10
5 Pa
½ ;
Actuating Oil of Hydraulic System b ¼ 1:4 Â 10
9
$ 1:86 Â 10
9 Pa
½ ;
The difference is about 2000 times.
(3) From the Eqs. (8.11) and (8.15), it can be seen that the natural frequencies of
cylinders and pneumatic cylinders are about
ffiffiffiffiffiffiffiffiffiffi
2000
p
times (45 times) different
for actuators of the same size.
(4) Difference of Piston Positions at the Minimum Natural Frequency:
i. Pneumatic: The minimum natural frequencies of symmetrical and asymmetrical cylinders occur when the piston is in the middle of the cylinder.
When analyzing the stability of the pneumatic system, only the piston in the
neutral position of the cylinder needs to studied.
ii. Hydraulic: The minimum natural frequency of a symmetrical cylinder
occurs when the piston is in the middle of the cylinder. However, the
minimum natural frequency of an asymmetric cylinder occurs somewhere in
which the piston deviates from the middle of the cylinder. When analyzing
the stability of hydraulic system, the symmetrical cylinder only needs to
study that the piston is in the neutral position of the cylinder; the asymmetrical cylinder needs to study that the piston deviates from the neutral
position of the cylinder.
(5) The mechanical structure of hydraulic cylinder and cylinder is basically the
same.
8.1.5 Conclusions
By analyzing the natural frequencies of pneumatic cylinder and hydraulic cylinder
when the piston is in or off the central position of the actuator with asymmetric
effective area on both sides, the following results can be obtained by comparing and
analyzing them:
(1) When the piston is in different positions, the natural frequencies of pneumatic
cylinder or hydraulic cylinder are completely different. When the piston is in
the position of both ends of the end cap of the actuator, the natural frequency
reaches the maximum.
(2) When the piston of pneumatic single acting cylinder is in the end position, the
natural frequency reaches the maximum. When the piston is in the middle
position, the natural frequency of the double acting cylinder reaches the minimum, whether the symmetrical cylinder A 1 ¼ A 2 or the asymmetrical cylinder
A 1 ¼ 2A 2 . Symmetrical hydraulic cylinder, such as A 1 ¼ A 2 , when the piston is
in the central position, the natural frequency reaches the minimum. For
asymmetric cylinders, such as A 1 ¼ 2A 2 , the minimum natural frequency
12
8 Pneumatic Actuators, Driving Elements and Accessories