Report of the Second Piloted Aircraft Flight Control System - Acgsc.org

essentially unobstructed. The flow of fluid is then proportional to the
area of the valve opening and the flow coefficient . At constant flow
coefficient therefore the piston velocity is directly proportional to
the valve opening. With rectangular valve ports the open area of the
valve is directly proportional to the error of the piston position. The
velocity of the piston is consequently proportional to the error. In
the no load case therefore, the servomotor will exhibit a traneient
response that is characterized by a linear first order system.
The pressure drop across the motor is divided equally between the
inlet and drain valve ports.
Based on a constant flow coefficient, the piston velocity may then
be equated to the flow through the valve ports by the, following relation:
Equation (1) may be written in the form
where
The analysis of the response of the se~omotor under an inertia
load is considerably more complex than in the no load case. Under an
inertia load the piston is accelerated from zero velocity. There is
consequently an initial period in the response during which the flow
through the- valve ports is laminar, as a result of which the flow coef -
ficient is subject to large variations. After the piaton hae reached
the laaximum velocity in the transient, the momentum of the load may
cause the flow of fluid into the upstream side of the cylinder to cavitate.
The variation of the pressure drop across the piston is therefore
not describable by a continuous function and consequently a single differential
equation cannot be written for the entire traneient.
In spite of the complex nature of the response there are basically
only two phaees in the transient: the acceleration phase and the deceleration'
phase. This conclusion, particularly with reference to a continuous
deceleration phaee without overshoot or oscillat~oii, is baaed
on the assumption of rigid oil and structure end zero leakage. Under
these assuntptions the cylinder pressures during the deceleration phase
are finite but may exceed physical limits.