Page 589 - Mechanical Engineers' Handbook (Volume 2)

580 Servoactuators for Closed-Loop Control

dV 2 AV
dt

where A effective area of servomotor piston
B viscous damping coefficient in servomotor
m
C leakage coefficient
2
F force due to Coulomb friction in servomotor
c
F external load force on servomotor piston
e
F force due to stiction in servomotor
ƒ
M mass of moving parts in servomotor
a
P pressure at inlet
1
P pressure at outlet
2
P P P pressure drop across servomotor
2
m
1
Q flow rate into servomotor
1
Q flow rate out of servomotor
2
Q C P internal leakage flow rate
L
m
2
V velocity of servomotor piston
V fluid volume under compression at the inlet
1
V fluid volume under compression at inlet for Y 0
1i
V fluid volume under compression at the outlet
2
V fluid volume under compression at outlet for Y 0
2i
Y linear displacement of servomotor piston from neutral position
fluid bulk modulus of elasticity
fluid mass density at inlet
1
fluid mass density at exit
2
Rotary Servomotor
Torque balance
d 1
(DP B T T T ) (45)
dt J a mm r f c e
Chamber continuity
( ) d
Q 1 2 Q ( V ) (46)
L
11
1
1
2 dt
( ) Q Q d
2
1
2 2
2 L 2 2 dt ( V ) (47)
Equation of state
d 1 dP 1 (48)
1
dt dt
d dP
2 2 2 (49)
dt dt
Chamber volume
V V D (50)
m
1i
1