Page 124 - Servo Motors and Industrial Control Theory -
P. 124
7.3 Electrohydraulic Servo Valves 119
1 : = b ⋅ (M C⋅ p + M C )⋅ 1 (7.11)
ω 2 n aK A
1
CC⋅ + C C⋅
2 ⋅ ξ : = A + 1 p ⋅ b (7.12)
ω A aK
⋅
n 1
It can be seen that the damping ratio increases as the leakage and viscous friction
increases. The mass of total moving parts reduces the natural frequency. The only
parameter that can vary to obtain the desired behavior is the distance (a) and (b).
The reader is encouraged to obtain the overall transfer function by doing the
algebraic manipulation to ensure that the transfer function is correct.
In deriving the transfer function (7.10), it was assumed that the oil is incompress-
ible. When the mass has to move with high speed, the oil compressibility cannot
be ignored and in fact it may have a dominant contribution to the response. In this
case, the compressibility of oil must be considered. This makes the transfer function
of third-order and stability becomes an important issue. The effect of oil compress-
ibility will be discussed in the next section and in similar way can be implemented
in the flow equation. The reader is encouraged to derive the transfer function of the
servo system discussed in this section after reading the next section.
The flexibility of the transmission mechanism may be necessary to be consid-
ered in some very high performance applications. The procedure is the same as was
derived for DC servo motors. In this case, it is recommended to use state space form
for governing differential equations. This can be done without deriving the overall
transfer function which enables that the state variables may be used as feedback.
The mechanical controller discussed in this chapter may be replaced by electrohy-
draulic servo valves. This will be discussed in the next section.
7.3 Electrohydraulic Servo Valves
Electrohydraulic valves are devices that change a voltage in the range of milliamp
to high pressure oil flow rate. The cross section view of these valves is shown in
Fig. 7.2.
Figure 7.2 shows that there are two sections in any servo valve. One section is
the magnetic torque configuration and the other section is the spool valve. In the
torque motor, there is a magnetic or simple flapper that is connected to two orifices.
When the magnetic torque motor is energized, the flapper moves closer to the ori-
fice. This then causes the pressure behind spool to increase and it moves the spool
valve. The spool valve is spring loaded at both ends and as a result of a magnetic
current the spool moves to a constant position with defined high pressure oil. When
