A necessary evil: the air gap in rotating machines

Electrical Apparatus, Sep 2005 by Nailen, Richard L

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).