The air gap in
rotating machines Necessary Evil
But it often gets overlooked when
it should be getting close attention
NOT TOO BIG, NOT TOO SMALL. THE Essential
air gap separating rotor from stator in any electric motor or generator has
several important influences on machine performance-nevertheless, in any design
discussion, few essential details get less attention than the air gap.
Air offers much higher resistance
to the passage of magnetic flux than the so-called "magnetic
materials." Such materials allow a far more intense field to pass through
a given space with a relatively lower driving potential (what we call
magnetomotive force or mmf). That force is measured in ampere-turns within the
electrical circuit causing the magnetization.
Naturally, then, we want to
minimize the intervention of air into the magnetic field path. Yet it can't be
omitted. It can't be too small. Discontinuities or joints in the magnetic core
material are necessary also in a transformer or other "solid-state"
electromagnetic apparatus, but are kept small or in staggered locations, to
minimize their influence.
Special demands of motors and
generators
The electric motor (or generator)
presents the unique necessity for an air gap fully separating a rotating
magnetic structure from a stationary one. Not only must the separation be
complete; it must be large enough so that manufacturing tolerances will not
allow the separated components to come into damaging contact during machine
operation.
As a further complication, these
components exert a strong magnetic attraction on each other. The mechanical
structure-including the shaft of the rotating component-must be stiff enough to
maintain separation despite that pull. In large machines, the magnetic pull is
calculated, then carefully compared to the restraining stiffness, to ensure the
assembly's "magnetic stability." (see Figures 1 and 2.)
The high "reluctance"
of air means that for every unit length of magnetic flux path, the mmf required
to drive flux through the air portion of the path will far exceed (as much as
tenfold) what's needed for the magnetic (steel) portion. Consequently, the
machine's magnetizing current (and the associated PR loss in the winding) will
be determined largely by the size of the air gap. The larger that gap in an
induction motor, the lower the power factor.
That creates an unavoidable
contradiction in the design process. For mechanical reasons, we want to avoid
too small an air gap; for electrical reasons, we don't want it too large.
Attempts to generalize about this
are liable to be wide of the mark, by failing to account for all the influences
at work. For example, when "energy efficient" motors were being
introduced, the claim was often made that they used "smaller air
gaps" to reduce losses. In its 1992 report (TR-101290, Vol. 2) on energy
efficient motors, the Electric Power Research Institute cited a decreased air
gap as one of seven basic ways to increase motor efficiency.
The reasoning is that a smaller
gap meant less magnetizing current and therefore a lower stator copper loss.
That's true. However, in the theoretical calculation of stray load loss for an
induction motor, some component losses vary as the inverse square of
magnetizing current. By increasing that current, a larger gap reduces those loss
components. Some "energy efficient" motors have therefore used larger
air gaps for the best overall effect. In this, as in many other design issues,
the answer to the question "what's best?" is, "that
depends."
A larger air gap can also reduce
electromagnetic noise. Although slot combination and winding configuration
exert major influences on noise production, they're seldom subject to change
after the machine is built. But studies have shown that doubling the air gap
can reduce overall sound pressure level by at least 10 decibels. Although that
large a gap increase is seldom possible, significant noise reduction can occur
with much smaller gap increases.
A necessary compromise
The resulting compromise is a
familiar one. For a given rotor diameter, the slower an a-c machine speed
(meaning the larger the number of magnetic poles in the winding), the smaller
the gap. Horsepower output will be lower, and the power factor lower as well,
so that the electrical effect of a large gap is relatively less acceptable than
for a high-speed, higher-horsepower machine having that same rotor diameter. As
polarity decreases and both speed and horsepower go up, the trend reverses.
In published material on basic
design, the most common guidelines relate power and speed to two basic
dimensions: core diameter squared, and core stack length, or DL in shorthand
notation. There are a couple of variations. Theoretically, the diameter should
be the stator inside diameter, what's often called the bore or gap diameter.
Some designers, however, have used the core outside diameter instead. Also, the
exponent (the power to which the diameter is raised) has been quoted as either
2.0 or 2.5.
Given those properties, the
design practices usually go on to recommend various approaches to selecting the
number and size of slots, the winding configuration, and arriving at estimated
heat dissipation and performance. Seldom, however, is any firm guidance offered
on the selection of air gap.
In most textbooks on electric
machinery design and performance, the air gap is considered a
"given." Much attention is paid to calculation of losses and
performance involving air gap flux density and ampere-turns, reactances,
excitation requirements, and so on. But mention is almost never made of either
the rationale for choosing air gap size, or the range of sizes typically used
in design.
One of the more popular texts,
first published in 1936, offers only this advice:
". . . it is necessary (for
low magnetizing current) to use small (but not too small) air gap length. . . .
The [air gap] must be so selected that the exciting current and machine
reactances conform to the performance desired. Reduced gaps may increase motor
noise and tooth-face losses. . . ."
According to another design
textbook, "It is impossible at the present time to derive a satisfactory
equation, directly from theoretical considerations, for determining the proper
length of gap." This "empirical" (based on experience) equation
is often considered accurate enough:
Air gap, inch = 0.005 0.0003D
0.001 L 0.003V
in which D = rotor O.D., inches
L = core stack length, inches
V = rotor peripheral velocity in
thousands of ft/min.= D(RPM/12,000)
Figure 3 illustrates typical
design air gaps for four-pole polyphase squirrel-cage induction machines that
are fairly consistent with that equation. How these will vary with speed is
evident from Figure 4.
Whatever the nominal gap, it must
be uniform. Eccentricity drives up stray loss. Other characteristics are also
affected. One 800 hp four-pole motor developed a vibration problem (up to 0.3
inches/second at running speed) that could not be solved by rebalancing. The
vibration disappeared when the rotor was machined to correct a 7 mil runout. A
non-uniform air gap also tends to increase noise; Figure 5 illustrates the relationship
developed experimentally by one motor manufacturer.
Anyone dealing with other types
of motors will recognize that these air gaps are much smaller than in either
a-c synchronous machines or d-c motors. Here's why: In a synchronous motor or
generator, two separate magnetic fields exist in the air gap, supplied from two
separate sources. The d-c excitation field, produced by the winding on each
rotor pole, is concentrated along the central axis of the pole itself. The
"armature field," created by the polyphase stator winding, has its
axis half a pole pitch away. The net effect is a distortion in the overall air
gap field, weakening its effect and (in a motor) reducing the available torque.
This is referred to as armature
reaction-the reaction of the stator field against the rotor field. To minimize
this, the air gap must be large enough to keep the ratio of air gap
ampere-turns to armature reaction ampere-turns per pole above an empirical
limit, often taken as 1.0. The higher that ratio, the less the influence of
armature reaction, and the more sinusoidal the flux waveform under load. For a
highly stable machine, a ratio of 2 to 3 may be needed. Hence, for any given
rotor diameter, a synchronous machine's air gap may be two or more times that
of an induction machine (see Figure 6
As in the induction machine, of
course, the increased gap means more rotor field ampere-turns (and current) are
required to drive the desired flux across that gap. That increases both power
usage and cost of the field winding, as well as the short-circuit current the
machine will supply to a fault on the power supply circuit.
In a d-c motor, armature reaction
of the same sort takes place, the difference being that the main field is
stationary while the armature rotates. Again, achieving the desired motor
performance requires a relatively large air gap. Typical values in industrial
d-c motors range from 1/8 to 1/4 inch. (Contrast that with Figure 4.)
Obviously, with a given stator
and rotor, decreasing the original air gap is impossible, except in d-c
machines, where pole shims can be used. Increasing the gap, however, is
possible by either boring out the stator or turning down the rotor. Regardless
of the reasons for doing so, either procedure presents problems for
squirrel-cage machines.
The first is the tendency for
adjacent laminations to "smear" together at the surface during
machining. That effectively short-circuits the interlaminar insulation, and can
escalate surface losses enough to bring the steel to red heat. Grinding, rather
than turning, is less likely to cause trouble.
However, machining the stator in
any way risks damage to the slot wedges. That's not a concern for a
squirrel-cage rotor-where two other related problems may arise. If the rotor
contains a cast aluminum cage in partially open slots, the machining operation
may not only smear the laminations themselves, but also spread a film of
aluminum over the finished surface, forming an even more troublesome conductive
layers.
If the slots are closed or
bridged, even a small reduction in rotor diameter may remove part of the steel
bridge from the laminations (see Figure 7). When that increases the width of
rotor bar exposed at the rotor surface, some stray loss components may increase
considerably. The effect on temperature rise may not be great, but efficiency
suffers, especially if the number of rotor slots exceeds that for the stator.
In addition, the sharp feather
edges of lamination resulting from the severed bridge are liable to eventually
break loose to damage the stator winding. Predicting when a "skim
cut" on the rotor can safely be made without that result is not possible
without design data on the rotor laminations, because the bridge cannot be
measured beforehand.
If the rotor is perfectly
concentric with the stator, the air gap will be the same throughout its 360°
circumference. The magnetic attraction between stator and rotor will therefore
be the same throughout; at any point the pull will be identical to that in the
opposite direction 180° away. The rotor will therefore remain centered.
Some degree of unbalance
inevitable
That ideal situation never
exists, of course, because of manufacturing tolerances, bearing clearance, and
shaft deflection caused by gravity. Some degree of unbalanced pull always
exists, therefore, and the designer's task is to make sure the mechanical
stiffness of the system prevents that unbalance from causing the rotor to move
into destructive contact with the stator. That requires calculation of the
amount of pull involved, which varies inversely with the air gap itself. The
smaller the gap, the greater the pull, and the greater the required mechanical
resistance.
How does the air gap influence
locked-rotor current (and torque)? For gap values within a range that's
practical in view of the other limitations discussed here, the answer is
"not much."
The relationship is not simple.
Several components of both stator and rotor reactance are inversely
proportional to the air gap, while other components are unaffected. But the
amount of change is highly variable depending upon slot dimensions and stator
winding configuration. In any event, an air gap variation of even 20% is
unlikely to make a significant change in locked-rotor performance.
"Increasing the air
gap" often implies simply machining an existing rotor to a smaller
diameter. That decreases the rotor slot reactance (and, as we've seen, several
other consequences can be expected as well). If, however, a machine is designed
and built for a larger gap, the slot configuration-and the associated
reactance-can remain unchanged despite a smaller rotor diameter.
A common limit on measured air
gap variation in an assembled motor is ±10% of the average. However, close
examination of that requirement reveals that it is not as simple as it seems. To
see why, consider some readings for a hypothetical machine. Suppose the gap
intended by design is 0.06 inch. Now suppose a series of measurements yields
these actual values:
0.050, 0.052, 0.061, and 0.064
What is the "average"?
Adding all four readings together and dividing by 4, we get 0.059 (quite close
to the design figure). The 10% variation allows readings to be anywhere from
0.054 to 0.065. Two of the measurements fall below the minimum, which is
unacceptable.
An obvious solution is machining,
to enlarge the gap. Assume the possibility of an increase by 0.006. We would
then get this new set of measurements:
0.056, 0.058, 0.067, and 0.070
Now, the average is 0.063. The
10% limits become 0.057 and 0.069. One reading is still below the minimum, and
now one other reading exceeds the maximum.
What's happening is that any
action taken to bring readings closer to a numerical average will also change
that average. To get past this problem, we can go to the extreme of increasing
the gap by 0.015. The measurements then become:
0.065, 0.067, 0.076, and 0.079
The average is 0.072; limits are
0.065 and 0.079, and all readings are now acceptable (barely)-except that the
average gap has been increased by 25%, which is unacceptable regardless of
eccentricity.
Additional complications
A further complication is the
variation in gap that may occur from one end of the machine to the other. Still
another is the way measurements are made. Actual feeler gauge readings of the
gap in an assembled machine are possible only for the larger horsepower
ratings, and only at certain locations.
An out-of-tolerance value may
exist over only a small area, and therefore have little influence. No single
set of four or eight measurements can establish the condition of the total
peripheral gap area.
In a large, high-speed machine,
with an air gap of 1/8 inch or more, slight changes are seldom troublesome-but
neither are they greatly effective in achieving some desired performance
change.
Ignored in most redesign or
costing procedures, seemingly not a direct influence on temperature or torque
characteristics, the air gap in a motor or generator is nevertheless clearly
important to machine performance. It should not be overlooked.
