Page 649 - Mechatronics with Experiments

ELECTRIC ACTUATORS: MOTOR AND DRIVE TECHNOLOGY 635
ON or fully OFF, then the displacement of the plunger can be controlled proportionally
instead of two or three discrete positions. This is the method used in proportional valves.
The solenoids are rated in terms of their coil voltage (i.e., 12 VDC, 24 VDC), maximum
plunger displacement (i.e., 1∕4 in), and maximum force (i.e., 0.25 oz to 20 lb range). There
are two major differences between ON/OFF type and proportional type solenoids:

1. the solenoid mechanical construction where the plunger, coil, and frame design
provides a different flux path (Figure 8.18i-iii, the proportional solenoids are generally
of type shown in Figure 8.18iiic)).
2. the current in the coil is controlled either in ON/OFF mode or in proportional mode.

The coil acts as the electromagnet in all electric actuators. Current (i), number of
turns (n ), and the effective permeance of the magnetic medium (core material, air gap,
coil
etc.) determine the strength of the electromagnetic field generated by the coil. At the same
time, there are mechanical size and thermal considerations. The rated current determines
the minimum diameter requirement of the conductor wire. The wire diameter and the
number of turns determines the mechanical size of the coil. In general, the insulation
material increases the effective conductor diameter by about 10%. Different insulation
◦
◦
materials have different temperature ratings (i.e., 105 C for formvar, 200 C for thermalex
insulation material compounds commonly used industry). Once the coil wire diameter,
number of turns, and mechanical size is known, the resistance of the coil is determined.
Hence, the resistive heat dissipation is known. In order to make sure the temperature of the
coil stays within the limits of its coil insulation rating, the thermal heat conducted from the
coil should balance the resistive heat. The coil design requires the balancing of electrical
capacity (current and number of turns), mechanical size, and thermal heat. In other words,
the designer must find a balance between the mechanical dimension constraint, thermal
heat dissipation capacity, and electrical power conversion capability for a coil design. In
order to increase the MMF, we need a large number of turns, n coil , which means diameter,
d, of the coil wire should be small. However, as d gets smaller, resistance R increases, hence
the maximum current we can pass through must be smaller in order to stay within the heat
dissipation capacity of the solenoid,
MMF = n coil ⋅ i (8.124)
2
R ⋅ i < P rated (8.125)
In order to increase MMF, we can decrease d so that n is large. But this results in an
coil
increase in R which in turn requires lower i, which then reduces MMF.
The force generated by a solenoid is a function of the current in the coil (i),
the number of turns in the coil (n ), the magnetic reluctance (R , which is a func-
coil B
tion of the plunger displacement, x, the design shape, and material permeability, ), and
temperature (T)

F = F (i, n , R (x, ), T) (8.126)
sol sol coil B
For a given solenoid, the n coil is fixed, R (x, ) varies with the displacement of the plunger
B
and the air gap between the winding coil and the plunger. The main effect of temperature is
the change in the resistance of the coil. This leads to a change in current for a given terminal
voltage. If the control system regulates the current in the coil, the effect of temperature on
force other than its effect on resistance is negligable. Therefore, for a given solenoid, the
generated force is a function of operating variables as follows,

F sol = F (i, x) (8.127)
sol