x ¼ x min ¼
ffiffiffiffiffiffiffiffiffiffiffiffiffiffi
4nA 1 p 1
sM
r
It can be seen from the above equation that when the piston is in the central
position of the cylinder, the natural frequency reaches the minimum, whether the
double acting symmetrical cylinder or the double acting asymmetrical cylinder. The
influence of piston initial position and cylinder initial pressure on frequency
characteristics is shown in Fig. 8.6. The higher the initial value of cylinder gas
pressure, the greater the natural frequency of cylinder.
8.1.3 Natural Frequency of Hydraulic Cylinder
The structure of hydraulic cylinder is similar to that of pneumatic cylinder.
Hydraulic cylinder uses hydraulic oil as a working medium and cylinder uses
compressed gas such as air as a working medium, but the basic characteristics of the
two are quite different. The compressibility of hydraulic cylinders is generally
shown in the dynamic characteristics of the cylinder system. The volume elasticity
atural frequency
Initial position of piston
0
Fig. 8.5 Natural frequency characteristics of pneumatic double acting cylinder (A 1 ¼ A 2 or
A 1 6 ¼ A 2 )
Table 8.2 Effect of initial pressure on natural frequency characteristics of dual acting cylinder
(A 1 ¼ A 2 or A 1 6 ¼ A 2 ; V 10 ¼ V 20 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 %
∞
167
125
109
103
100
103
109
125
167
∞
8
8 Pneumatic Actuators, Driving Elements and Accessories