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.
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.