Chuck Yung
EASA Technical Support Specialist 

Occasionally, someone asks how much current a squirrel cage rotor bar carries. That’s an interesting question, and the answer depends on several factors. The rotor kVA* of a wound rotor motor is typically about 0.8 times the stator kVA. 

The rotor rated voltage is open circuit—a condition than cannot exist in a functional squirrel cage rotor— and the amps are at rated-load; the two don’t “coincide,” thus the 0.8 factor. For a squirrel-cage induction rotor, a multiplier of 0.96 is used because the magnetizing current comes from the stator rather than from the rotor. 

Since the rotor is the secondary winding to the primary stator wind­ing, the turns ratio of the stator to the rotor can be calculated if we know the stator winding data and the number of rotor bars. (See Figure 1.) To determine the rotor bars/pole: 

Count the rotor bars, divide by the number of poles, and then divide the result by 2 (because each bar is only a half-turn.) The result is the number of rotor turns/pole. Because of slip**, the poles rotate slightly faster than the rotor itself, so it is not uncommon for the above calculation to result in fractional turns. 

Since the stator and rotor have the same number of poles, we can ignore poles when making the calculations. To calculate the approximate rotor bar current, use the following equation: (.96 x stator slots x turns/coil x stator amps)  [(rotor bars / 2) x stator circuits x k] 
where k = 1.0 for a wye connection and k = 1.732 for a delta connection

For example, consider a 100 hp, 4-pole motor with 48 slots, 11 turns/ coil, and connected 2-delta @ 460 volts and rated 120 amps. The rotor has 39 bars. 
(.96 x 48 x 11 x 120)  [(39/2) x 2 x 1.732] = 900 rotor amps 

The effect of open bars 
Open rotor bars can reduce torque, causing increased slip. It is the nature of an induction motor to try to produce the torque required by the load. It accomplishes this by slipping more. Increased slip causes more current in both the rotor and stator which in turn produces heat. 

So, what happens when a rotor bar becomes open and can no longer carry its share of the current? The nearby bars, under the same magnetic pole as the open bar, must carry the additional current that should have passed through the open bar (Figure 2). More current raises the temperature of those bars, increasing the chance of failure. Subsequent rotor bar failures occur close to the first one(s). Because of slip, bars within half a pole-pitch either side of the open bar can be directly affected. The bars in parallel with that open bar are continuously changing; visualize a crowd doing the “wave” at a football game. That is why we often see clusters of failed bars. 

Of course, fabricated rotors may also fail because of metal fatigue— strictly a mechanical failure. Each bar in the rotor is subject to the same fatigue and thermal cycles, so random distribution of broken bars does occur. Even so, the combination of fatigue and increased thermal stress can accelerate the failure rate for bars under the same pole-pitch as each failed bar. 

Increased rotor current in those bars also affects stator current. Current signature analysis can reliably detect the resulting pole-modulated fluctuation in stator current. Other technologies (vibration analysis, growler, core tester, so-called black boxes, etc.) might reveal a defective rotor—or not. There are several technologies other than current signature analysis that can reveal a defect. For more information, refer to Tech Note 23: Testing of Squirrel Cage Rotors under “Tech Notes” in the “Members Only” section of EASA’s Web site at www.easa.com. Unfortunately, even if multiple technologies do not reveal a defective rotor, it does not necessarily mean the rotor is good. However, when the results of several technolo­gies agree, the confidence level increases. 

Progressive bar failures 
Each additional open bar changes the stator slot-rotor bar combination. Eventually, the combination causes electrical noise, cogging or a cusp (Table 1). The customer might not realize there is a problem until the motor either fails to start, or fails to accelerate the load. If the faulty rotor causes the stator windings to fail, an open rotor is easy to miss. Because a rotor design could have any number of bars, there is no quick answer to the question “How many rotor bars can break without affecting motor perfor­mance?” For one design, a single open rotor bar can spell trouble.

For another design, several open bars may have no apparent effect on performance. 

Using a transformer comparison, what happens when we energize the primary winding with the secondary open? Only magnetizing current (“no­load amps”) develops. If you were to try the same thing with a closed secondary winding (secondary leads connected to­gether—and definitely not suggested), the primary winding draws short-circuit magnitude current. The results for a wound-rotor motor are similar. The locked rotor current of the stator is much higher when the rotor leads are shorted together than with the rotor leads open. 

When an induction motor attempts to deliver the torque required by the load, current increases with slip. This remains true as additional bars become open. If an endring literally falls off—or if most of the rotor bars become open—the stator current would decrease, as the motor ap­proaches the “open secondary” condition of our transformer / wound rotor examples. And the rotor would stop rotating. 

Referring back to Figure 1, it is evident that the endring carries current for the distance of the pole-pitch. The more poles the motor has, the shorter the pole-pitch, and the fewer the bars connected within the pole-pitch. The required endring cross-section therefore decreases. 

Given a 3-phase machine, a common estimate for the required endring area of 2- or 4-pole machines is the total area of all the bars, divided by 3x the poles. For slower machines (6 poles or more), use 1.5x the area of a single bar instead. Note that these estimates are only useful when the endrings and bars are of same material. 

Conclusion 
The next time a customer insists that he has seen motors run with broken rotor bars, you can tell him that you have seen people cross the street without looking, too – but you don’t recommend either one. The fact is that a motor could operate with open rotor bars, if the torque require­ment was much less than rated; or with poor performance due to increased slip, increased heating and reduced efficiency—and premature failure of the stator windings likely. 

Categories: Rotors, Repair procedures & tips

Tags: Rotor design

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