Page 650 - Mechatronics with Experiments

636 MECHATRONICS
The basic mode of control is the control of current in the coil in order to control the
force. Unlike a rotational DC motor where the current and torque relationship is constant
and independent of the rotary position of the shaft, the force–current relationship of a
solenoid is nonlinear and a function of the rotor (plunger) position (Figure 8.18).
◦
In general the force capacity of the solenoid is rated at 25 C. The force capacity
◦
would typically reduce to 80% value at around 100 C temperature. At a rated current, the
force varies as function of plunger displacement (Figure 8.18). Notice that there is always
a residual flux left in the core when the current is turned OFF (current is zero) due to
the hysteresis nature of electromagnetism. Use of annealed steel for the core and plunger
material minimizes that effect.
In the basic mode of operation, a solenoid is driven by DC voltage, V (i.e., 12 V,
t
24 V, 48 V) at its coil terminals, and steady-state current i is developed by the resistance
ratio (neglecting the inductance of coil),
V t
i = (8.128)
R
coil
The physical size of the solenoid determines the maximum amount of power it can convert
from electrical to mechanical power. The continuous power rating of the solenoid should
not be exceeded in order to avoid overheating,

V 2 t
2
P = R ⋅ i = < P (8.129)
coil rated
R
coil
In some applications, it is desirable to provide a larger current (the in-rush current)
and after the initial movement, the current is reduced to a lower value, called the hold-
ing current. One way to reduce the in-rush current to the holding current is to divide the
coil winding into two resistor sections and provide an electrical contact between the two
series resistor. When a large in-rush current is needed, short circuit via a switch (i.e., elec-
tronic transistor switch) the second resistor section to increase current by reducing effective
resistance. When it is desired to reduce the current, turn OFF the switch to include the
second part of the resistor in the circuit in series, hence reduce the current for the given
terminal voltage. Some solenoids can be driven by 50 Hz or 60 Hz AC voltages (i.e., 24,
120 VAC). Force is related to the square of current. Therefore, the direction of generated
force does not oscillate with the AC current direction change. However, the magntitude
oscillates at twice the frequency of the supply current frequency, that is if the AC supply
is 60 Hz, the force magnitude would oscillate at 120 Hz. In other words, the electromag-
netic circuit of the solenoid acts like a “rectifier” between supply current and generated
force.

8.3.2 DC Solenoid: Electromechanical Dynamic Model

Consider the solenoid shown in Figure 8.17. The electromagnetic energy conversion mech-
anism generates the force as a result of the interaction between the coil generated elec-
tromagnetic field and variable reluctance of the plunger–air gap assembly. Let us consider
the magnetic flux path in the solenoid (Figure 8.17). Assume that the permeability of the
plunger, frame, and stop are very high compared to permeability of air gap, ≫ .We
0
c
can assume the magnetic energy is only stored in the air gap, neglecting the magnetic
energy stored elsewhere. This model is similar to the magnetic circuit shown in Figure 8.12
except that in the case of solenoids, the air gap is variable. Then, the following relations