Page 128 - Servo Motors and Industrial Control Theory -

7.4 Hydraulic Servo Motors 123

Fig. 7.5 A typical static characteristic of an axial piston type motor

where λ is the motor leakage coefficient which is usually provided by manufac-
m
turers. When oil is discharged from a motor at high pressure, there will be some
compression of oil volume due to slight compressibility of the oil at high pressure.
The pressure involved is in the range of 3000 psi (100–150 bar). A volume of oil V
o
at atmospheric pressure will be reduced to a volume V, at a gauge pressure p, ac-
cording to the relation,
 p 
v: = v · 1 − B  (7.16)
o 


where B is the bulk modular of compressibility. It should be noted that V is the
o
total volume of oil which includes the inlet and outlet ports. Because although the
inlet side goes under high pressure oil, at the outlet section the high pressure oil is
discharged and the oil expands for continuity purpose. The rate of change of vol-
ume with pressure is then can be calculated by first differentiating Eq. (7.16) with
respect to pressure and the flow rate is then obtained by differentiating with respect
to time:
d v: = − v o
dp B

or,

d − V d
v: = o p (7.17)
dt B dt