Figure 1. Varying InRush Profiles – Normal vs. Broken Rotor Bars


In the last decade, advancements in motor testing technology have stirred advances in online and offline testing. Online Current Signature Analysis (CSA) is becoming a standard industry practice. Offline tests include advanced inductance measurements to analyze rotor and stator health. The combination of online and offline tests to form a sixfault zone approach offers a more complete analysis of motor health. The six fault zones include power quality, power circuit, stator, air gap, insulation, and rotor. Each fault zone should be analyzed to accurately assess the overall health of a motor.
This paper will examine the rotor fault zone and how it is used to assess motor defects. The rotor fault zone refers to the condition of the rotor bars, rotor laminations and end rings. While contributing minimally to motor problems, rotor faults can influence other fault zones to fail. Inrush current, current demodulation, CSA, rotor influence check (RIC) test, and inductive imbalance are used in testing this fault zone.
InRush Current Profiles
A healthy motor exhibits the current profile shown by the baseline curve in Figure 1. As rotor bars break, the startup current profile changes as less voltage is induced in the rotor cage due to the change in the effective turns ratio. This change in the ratio leaves a higher reflected impedance from rotor to stator. Given a constant load and steady power during startup, the higher reflected impedance lowers the amount of inrush current (see Figure 1). While the current is lower, the same total energy is needed to bring the motor up to speed. With less power from the rotor, the time required to put the same amount of energy (Joules) into the rotor has to increase, as seen in Equation 1.
Joule = watt * second (1)
When applying Equation 2 to the rotor, note that because torque (T) is constant, when power (ERIR) developed in the rotor decreases, the angular velocity (wR) also decreases:
ERIR = wRT (2)
Where:
ER is the voltage developed in the rotor
IR is the current developed in the rotor
wR is the angular velocity of the rotor
T is the torque developed in the rotor and is proportional to output torque
Figure 2. Current Cycling Due to Broken Rotor Bars


Steady State Current Modulation
Healthy motors with no broken rotor bars draw steady current under constant load and power system conditions. Under constant load and power system conditions, cyclical changes (sinusoidal modulations) in current may indicate a broken rotor bar using an enveloped current waveform (see Figure 2). Enveloped current waveform analysis also allows a technician to perform process analysis.
Current Demodulation
Mechanical Components
Load variations are reflected in the stator currents through the motor’s air gap. Current demodulation reveals repetitive load variations, thus enhancing the ability to detect motor speed, polepass, mechanical passthrough, and reflected frequencies. Mechanical and reflected frequencies relate to load variances from items such as belts, gears, pumps, fans, and other mechanical components. A fast fourier transform (FFT) is performed on the demodulated signal, resulting in a frequency spectrum for analysis. Without demodulation, many of these loadrelated frequencies are buried in the noise of the captured data.
Rotor Unbalance/Misalignment
Utilizing current demodulation, the speed of the motor is shown as a peak in the spectrum and is monitored for changes in amplitude. When properly balanced and aligned, a motor has a frequency peak related to its speed that is difficult to find in the spectrum. When out of balance or misaligned, the amplitude of this peak increases. Multiples of the speed frequency develop in the demodulated current spectrum as the condition increases in severity. Figures 3 and 4 show the change in amplitude of the running speed and twotimes the running speed during a precision alignment of a pump and motor.
Figure 3. Demodulated Current Spectrum – Prior To Alignment


Current Signature Analysis
PolePass Side Bands
A useful indicator of broken rotor bars is the polepass sidebands around line frequency. As shown in Figure 5, these side bands are located in the current spectrum at:
fp = (1 + 2ks)fLine (4)
Where:
fp is the location of the peaks around line frequency
k is the harmonic index 1,2,3...
s is the slip
fLine is the line frequency
Swirl Effect
Another useful spectral tool for detecting broken rotor bars is the swirl effect, which occurs at the fifth harmonic of line frequency (300 Hz on a 60Hz line frequency), as shown in Figure 6. Swirl peaks are a confirming tool for the sidebands around line frequency and occur at:
fswirl = [1 – (2/5)ks]5fLine (5)
Where:
fswirl is the location of the peaks around line frequency
k is the harmonic index 1,2,3...
s is the slip
fLine is the line frequency
Inductance Measurements on Motors
To measure the inductance, impedance is measured on each phase by applying a lowvoltage AC signal of known frequency to the winding and measuring the current that passes through the windings. Resistance of the windings is measured by applying a DC voltage to the windings and measuring the resulting current. From these measurements, inductance is calculated using Equation 6:
L = (XL/w) = [(Vac/Iac)2– (Vdc/Idc) 2]0.5/2pf (6)
Where:
L is the inductance in Henries
XL is the inductive reactance in Ohms
w is 2pf
Vac is the voltage of the AC test signal in Volts
Iac is the current of the AC test signal in Amps
Vdc is the voltage of the DC test signal in Volts
Idc is the current of the DC test signal in Amps
f is the frequency of the test signal in Hertz
Physical Parameters that Affect Inductance
Several physical parameters affect inductance, including the area of the core, number of turns, length of the air gap, length of the magnetic circuit, and the incremental permeability of the steel, as indicated in Equation 7. In a motor, the number of turns, area of the core and the length of the magnetic circuit are constant. The primary parameter that will affect the inductance is the length of the air gap, but the incremental permeability of the steel, especially at the low flux densities used in the inductance measurements, will also affect the inductance. Effects from fringing flux are not included in this formula for simplicity.
L = [3.19N2 Ac x 108]/[lg + (lm/mD] (7)
Where:
L is the inductance in Henries
N is the number of turns
Ac is the area of the core in square inches
lg is the length of the air gap in inches
lm is the length of the magnetic path in inches
mD is the incremental permeability
Influence of Rotor on Measurement of Inductance
The influence of the rotor on the measured inductance offers advantages in detecting the health of a motor. Plotting measured inductance with respect to rotor position (rotation) provides a valuable tool in determining the health of the motor. In this test, the rotor is rotated in discrete increments, and the inductance is measured at each point. The resulting graph of inductance will typically display sinusoidal waveforms that are then analyzed to determine the overall health of the rotor and stator.
Analyzing Inductance Waveforms
When analyzing inductance waveforms, there are three main factors to consider—the amplitude of the inductance waveforms, repeated variations in the waveforms throughout all three phases and the phasing of the waveforms. The amplitude of inductance waveforms depends on the type of motor, its construction, the residual flux on the rotor, and the overall health of the motor. Low amplitudes with very little sinusoidal activity of the inductance waveforms indicate the rotor is of “low influence.” Lowinfluence rotors (LIR) are typically higher quality, have copper bars and have no defects (see Figure 7).
An increase in the amplitude of the inductance waveforms often indicates a developing fault in the motor, especially in rotors that initially have low influence. Rotors that are porous cast aluminum or that have adverse conditions such as broken or cracked rotor bars produce these effects. As the severity of the fault increases, the amplitudes of the waveforms increase, and the waveforms will become sinusoidal in shape (see Figure 8). A baseline test should be performed prior to installation of the motor or as early as practical. Once a baseline test has been established, the motor should be monitored for trends of increasing amplitude and sinusoidal development of the inductance waveforms.
Repeated variations throughout all three phases of inductance waveforms are a strong indicator of developing faults in the rotor, as shown in Figure 9. Repeated variations are caused by the reflected impedance of the cage and the increase in residual flux on the rotor. Evaluate all three inductance waveforms for these repeated variations.
Lastly, evaluate the waveforms for phasing differences. Phasing differences occur when the peak of one waveform will be shifted in phase.
Inductive Imbalance
Using the inductance measurements, percent inductive imbalance is calculated as follows:
%Limb = [(Dmax)/(Lavg)]100% (8)
Where:
% Limb is the inductive imbalance in percent
Dmax is the maximum deviation of inductance from the average inductance in Henries
Lavg is the average inductance in Henries
Percent inductive imbalance is used to determine how well the winding impedances are balanced. Although no specific standards have been established due to the influence of the rotor on the measurement of inductance, in a healthy motor, it is generally accepted that there should be less than a 7percent inductive imbalance for form wound motors and less than 12 percent for random wound motors. Some rotors have half of the cage shifted at the center of the rotor, which, from our experience, tends to create an inductive imbalance of approximately 8 percent to 15 percent between phases.
Figure 4. Current Demodulation Spectrum – After Alignment


Summary
Using a fault zone analysis approach provides a complete analysis of motor health. This paper focuses on using the rotor fault zone to identify potential defects in the motor design; however, all six fault zones should be analyzed to accurately assess the overall health of a motor.
This is an edited version of a paper presented at the Electrical Manufacturing Expo & Technical Conference, held in September 2005. A complete version of the paper, including references, is available from the authors.
Figure 5. PolePass Sidebands


About the Authors
David L. McKinnon is a project manager for hardware and product development of motor test equipment at PdMA Corporation. He received his Bachelor of Science in Electrical Engineering from New Mexico State University and a Master of Business Administration from the University of Phoenix.
Noah Bethel is currently in charge of product development of new and existing PdMA technology for PdMA Corporation. He is a graduate of the University of the State of New York and the Naval Nuclear Power School and Training Unit.
If you wish to contact the authors, please email editor@appliance.com