Fourier components of the measured stator current.
This chapter investigates the diagnosis of not only broken bar but also broken end ring faults in an induction motor. The difference between the broken bars and broken end ring segments is experimentally clarified by the Fourier analysis of the stator current. This difference is verified by two-dimensional finite element (FE) analysis that takes into consideration the voltage equation and the end ring. The electromagnetic field in the undamaged motor and the motor with broken bars and broken end ring segments is analyzed. The effect of the number of broken bars and broken end ring segments on the motor performance is clarified. Moreover, transient response is analyzed by the wavelet analysis.
- Failure diagnosis
- finite element method
- motor current signature analysis
- wavelet analysis
Squirrel-cage induction motors are widely used in many industrial applications because they are cost effective and mechanically robust. However, production will stop if these motors fail. Therefore, early detection of motor faults is highly desirable. Induction motor faults are summarized in  and , and rotor failures account for approximately 10% of the total induction motor failures. Several studies have carried out diagnosis of induction machines using motor current signature analysis (MCSA). For example, Davio et al. proposed a method to diagnose rotor bar failures in induction machines based on the analysis of the stator current during start-up using the discrete wavelet transform (DWT) . Moreno et al. developed an automatic online diagnosis algorithm for broken-rotor-bar detection, which was optimized for single low-cost field-programmable gate array implementation . Guasp et al. proposed a method based on the identification of characteristic patterns introduced by fault components in the wavelet signals obtained from the discrete wavelet transformation of transient stator currents . Kia et al. proposed a time-scale method based on DWT to make the broken-bar fault diagnosis slip independent . Gritli et al. carried out diagnosis of induction machines using DWT under a time-varying condition . However, most of the literature has studied only broken-bar faults, and broken end ring faults have been marginally dealt with. For example, Bouzida et al. dealt with the fault diagnosis of induction machines with broken rotor bars and end ring segment and loss of stator phase during operation using DWT . Concerning the FE analysis of rotor failures in induction motors, several papers have been presented. For example, Mohammed et al. studied the broken rotor bar and stator faults using FE and discrete wavelet analyses . Weili et al. analyzed the flux distribution in the air gap of an induction motor with one and two broken rotor bars . Faiz et al. analyzed the stator current under different numbers of broken bars and different loads of an induction motor . They dealt with broken rotor bars but not a broken end ring.
This chapter addresses not only broken bar but also broken end ring faults. First, we manufacture some rotors with broken bars or end rings . Next, the difference between the broken end ring segments and broken bars is verified by MCSA . The electromagnetic field in the rotor is analyzed to clarify the effect of the number of broken bars and broken end ring segments on the motor performance . Moreover, the stator voltage and current waveforms in a transient response are analyzed by the wavelet analysis.
2. Induction motor with broken rotor and experimental system
Figure 1 shows the photographs of a rotor with broken bars and a broken end ring segments that we have manufactured . Figure 1(a) shows a rotor with one broken bar drilled at the center of the rotor, and Fig. 1(b) shows a rotor with two broken bars drilled at the adjacent aluminum bars. Figure 1(c) shows a rotor with a broken segment in the end ring, which is made by cutting aluminum. Figure 1(d) shows a rotor with two broken segments in the end ring, which are separated by two rotor bars. Figure 1(e) shows a rotor with two broken segments in the end ring whose distance is 45 degrees, that is, 90 electrical degrees. The experimental motor shown in Fig. 2 has the following specifications: 50 Hz, 200 V, 400 W, four poles, and 1,400 min-1 speed.
Figure 3 shows the experimental system for the failure diagnosis, which is composed of a 200-V 1.1-kVA 3-A inverter, an induction motor, a torque meter, and a servo motor used as load. Figure 4 shows the developed measurement system using NI cDAQ and Lab VIEW . Lab VIEW is a system design platform and development environment for visual programming language and can be easily used for data acquisition in Microsoft Windows. Figure 4(a) shows the interface part, which is composed of a channel selector,
3. Fourier analysis of the measured data
Figure 5 shows the Fourier analysis of the stator current at a rated speed of 1,400 min-1, where the Fourier component of several rotors is shown at every 0.33 Hz to easily compare the broken situations. Here, 1 bar, 2 bars, 1 ring, 2 rings, and 2 rings (2) mean one broken bar [see Fig. 1(a)], two adjacent broken bars [Fig. 1(b)], end ring broken at one position [Fig. 1(c)], end ring broken at two positions separated by two rotor bars [Fig. 1(d)], and end ring broken at two positions separated by five rotor bars, that is, 90 electrical degrees [Fig. 1(e)], respectively.
In Fig. 3, the inverter rating is 1.1 kVA, which is a sufficient capacity for the 400-W experimental induction motor. Therefore, the Fourier analysis of the stator voltage did not include the (1 ± 2
We found 50 ± 6.67 Hz components, that is, (1 ± 2
In each fault, the components at 50 - 6.67 Hz, that is, (1 - 2
|Healthy||0.0010 A||2.818 A||0.0009 A|
|1 bar||0.0135 A||2.755 A||0.0119 A|
|2 bars||0.0176 A||2.890 A||0.0193 A|
|1 ring||0.0286 A||2.872 A||0.0258 A|
|2 rings||0.0306 A||2.725 A||0.0333 A|
|2 rings (2)||0.0076 A||2.760 A||0.0072 A|
Figure 6 shows the Fourier analysis of the stator current under a no-load condition. The rotating speed of 1,495 min-1 was almost the same. We also find 50 ± 0.33 Hz components, that is, (1 ± 2
Figure 7 shows the Fourier analysis of the torque at the rated speed of 1,400 min-1. We find 6.67 Hz components, that is, 2
4. Simulation of induction motor with broken rotor bars and broken end ring segments
4.1. Analysis method
The experimental motor has rotor skew of one slot pitch. Although a three-dimensional FE analysis is necessary to consider the rotor skew, it is very time consuming. This study calculates the electromagnetic field in the motor using a two-dimensional FE method, which considers the voltage equation and the rotor end ring. The cross section of the motor is shown in Fig. 8. The stator has 36 slots, and the rotor has 44 slots. The following assumptions have been made:
Two-dimensional analysis is employed, and the skew in the rotor is ignored.
Rotor bars and end ring are insulated from the rotor core, and no current flows from the rotor bars to the rotor core.
The rotating speed is constant.
The supply voltage is assumed to be sinusoidal.
Although the motor is fed by a pulse width modulation (PWM) inverter, the Fourier components of the measured stator current around the switching frequency differ very slightly among the rotor fault types. Therefore, the PWM inverter does not affect the harmonic components of the stator current.
Figure 9 shows the FE analysis region and the connection of the end ring segments in the rotor where 44 bars are included in the FE analysis. Because the end ring is connected to each rotor bar, it is represented by 44 conductor segments whose resistance is
where of aluminum is.
4.2. Analysis results
Figure 10 shows the Fourier analysis of the calculated stator current at the rated speed of 1,400 min-1. We find the (1 ± 2
|Healthy||0.0002 A||2.455 A||0.0003 A|
|1 bar||0.0326 A||2.434 A||0.0030 A|
|2 bars||0.0701 A||2.411 A||0.0079 A|
|1 ring||0.1637 A||2.390 A||0.0488 A|
|2 rings||0.1477 A||2.374 A||0.0618 A|
|2 rings (2)||0.0807 A||2.335 A||0.0222 A|
4.3. Electromagnetic field in the motor calculated by FEM
An example of the magnetic flux and eddy current distribution in the healthy motor under the rated speed with rated-load condition is shown in Fig. 11. Because this motor is a four-pole machine, the magnetic flux distribution is periodic in every one-fourth region, that is, in every nine stator slots. Here, we denote the number of stator slots in the same group of magnetic flux lines as
Figure 12 shows the distribution of the magnetic flux and eddy current in the motor with two broken bars under different rotor positions, namely, that where the magnetic flux does not pass through the broken bars [Fig. 12(a)] and that where it passes through the broken bars [Fig. 12(b)]. In Fig. 12(a), the eddy current distribution in the rotor bars is approximately the same as that in the healthy motor shown in Fig. 11, and the
Figure 13 shows the distribution of the magnetic flux and eddy current in the motor with a broken end ring segment under different rotor positions. No rotor bar exhibits a very high eddy current density, and the number of stator slots included in the flux lines for each pole is different. The
4.4. Effect of the number of broken bars and end ring segments
Next, we discuss the effect of the number of broken bars and broken end ring segments on the motor performance. Figure 14 shows the Fourier components of the stator current and torque for different numbers of broken bars. The fundamental components of the stator current and the average torque decrease, and the (1 ± 2
5. Wavelet analysis
We have discussed about the failure diagnosis of broken end ring segments and broken bars in induction motor at the steady state using the Fourier analysis. In this section, the transient performance of an inverter-fed induction motor is discussed by using the wavelet analysis. There are two kinds of wavelet transform; continuous and discrete ones.
5.1. Continuous wavelet analysis
Let us make a brief introduction of continuous wavelet transform. Figure 16 shows the waveform of a signal and its wavelet analysis, which shows equipotential lines in the frequency and time plane. Although there are several kinds of Wavelet function – Morlet, Paul, and Derivative of Gaussian – Fig. 16 is the result of using the Morlet function, where the number of waves is 30. We can find high value region around 100 Hz and from 0.3 to 0.6 s and around 400 Hz and from 0.4 to 0.7 s.
We investigate transient response of an inverter-fed induction motor, where the control strategy is an open loop and the motor has no-load. The step responses of the stator voltage, stator current, and motor speed were measured when a start signal was input to the inverter. Figures 17 and 18 show the Wavelet analysis of the stator current
5.2. Discrete wavelet analysis
The discrete wavelet transform of a signal is calculated by passing it through a series of filters. As it is well known, the use of wavelet signals, that is, approximation and high-order details, resulting from discrete wavelet transform constitutes an interesting advantage because these signals act as filters. Moreover, the computational time of discrete wavelet transform is much shorter than that of continuous wavelet transform. Figure 19 shows the discrete wavelet analysis for the same signal as shown in Fig. 16. It is found that the component of 100 Hz appears in d6 and signal of 450 Hz component appears in d4 detail.
Table 3 shows frequency bands by decomposition in multi-levels. Figures 20 and 21 show discrete wavelet signals of stator current
|a10||0 – 24|
|d10||24 – 49|
|d9||49 – 98|
|d8||98 – 195|
|d7||195 – 391|
|d6||391 – 781|
|d5||781 – 1,563|
|d4||1,563 – 3,125|
|d3||3,125 – 6,250|
|d2||6,250 – 12,500|
|d1||12,500 – 25,000|
This study has analyzed the Fourier components of broken end ring segments and compared them with those of the broken bars. We have verified, by both experiment and simulation, that the components of (1 ± 2
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