8.1.2.2 Natural Frequency of Double Acting Cylinder
Figure 8.4 shows a schematic diagram of a double acting cylinder. It is defined that
the piston stops steadily in the geometric intermediate position of the actuator as the
reference state. The volume of gas is the volume in the pipeline and the volume in
the actuator. The actuator system with different piston rod diameters on both sides
of the actuator piston is equivalent to the equivalent mass–spring system composed
of two equivalent gas springs, whose equivalent spring stiffness is
K eq1 ¼
A
2
1 b 1
V 10 þ A 1 x
ð8:8Þ
K eq2 ¼
A
2
2 b 2
V 20 þ A 2 s À x
ð
Þ
ð8:9Þ
where
V 1 , V 2 Fluid volume of two cavities of actuator, and V 1 ¼ V 10 þ A 1 x,
V 2 ¼ V 20 þ A 2 s À x
ð
Þ;
b 1 ; b 1
Volumetric elastic modulus of gas in two cavities of actuator,
b 1 ¼ np 1 ; b 2 ¼ np 2 ;
A 1 ; A 2
Effective area of two cavities of actuator (m
2 );
Table 8.1 Natural frequency characteristics of pneumatic single acting cylinder system (V 0 ¼ 0)
x/s
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
f%
∞
316
224
183
158
142
129
120
112
106
100
Fig. 8.4 Structural sketch of double acting pneumatic cylinder and double acting hydraulic
cylinder
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8 Pneumatic Actuators, Driving Elements and Accessories