Page 104 - Robotics Designing the Mechanisms for Automated Machinery
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3.5 Pneumodrive 93
For the supercritical regime, the pressure p l in the cylinder input orifice is constant,
i.e.,
Substituting p l from Equation (3.113) into Equation (3.111), we obtain, for the super-
critical flow rate G cr
Under standard conditions (T r = 293°K) we have
Now let us find the time required to fill the cylinder from the initial value of the pres-
sure p 0 to the final value p l (p r < 0.528^) while the air temperature remains constant.
For a cylinder volume V c we have
where
G c = instantaneous value of the air weight, and
T= the air temperature.
During an infinitesimal time period dt the pressure will change over a value dp,
and the amount of air will change by G cr dt. Thus,
Substituting Equation (3.116) from Equation (3.117), we obtain
By integration we obtain
By substituting Equation (3.115) into Equation (3.119), we finally reach
When time ^ has passed, two outcomes are possible:
1. The piston begins its movement earlier than ^ (i.e., the movement begins before
pressure p l appears in the cylinder volume).
2. The pressure in the cylinder is still not sufficient to initiate the movement of
the piston.
