8.2.2.2 Natural Frequency of Pneumatic Motor
The natural frequencies of pneumatic motors can be given directly by the following
formulas:
Natural frequencies of non-expansive pneumatic motors for adiabatic variation
processes,
x nn ¼ D m
ffiffiffiffiffiffiffi
2kp
VJ
r
ð8:47Þ
Natural frequencies of expansive pneumatic motors for adiabatic variation
processes,
x nc ¼
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
D mv D mt
2kp
VJ
r
ð8:48Þ
where
p
Gas working pressure of pneumatic motor;
D m Gas displacement of pneumatic motor;
D mv Volume flow rate of pneumatic motor;
D mt Torque displacement of pneumatic motor;
V
Average working chamber volume of pneumatic motor;
J
Sum of moment of inertia of rotating parts and load of pneumatic motor;
k
Adiabatic index.
In general, if the size of the pneumatic motor is the same, the natural frequency
of the non-expansion pneumatic motor is higher than that of the expansion pneumatic motor. That is to say, the stiffness of non-expansive pneumatic motor is large.
Of course, when the same output power is achieved, the gas consumption of the
Tube Piston
Seal up
Output shaft
Guide rod
Spiral spline groove
Fig. 8.30 Pneumatic swing motor
38
8 Pneumatic Actuators, Driving Elements and Accessories