Keywords

1 Introduction

Modern industrial of “induction motors” are frozen used drive-in manufacturing with several methods. The investigation of motor product has been considered as optimality in the usage. Such type of motor faces many problems in general manufacturing area which considers unwanted phenomena due to motor period time reduction. Hence, the motor rating power monitoring decreases the probability of motor loss life. So, the requirements of “faults diagnosis” in this type of motor could be achieved by many advanced techniques [1]. Then, the harmonic current and other many parameters in the motor stator will affect the motor efficiency due to its increasing and decreasing compared with standard values [2]. Any of these parameters could be used as useful signs of faulty motor “diagnosis” of induction motors. The finding of these catalogues in many ways could suggest solving this problem [3]. The potential magnetic aberration parameters and the spreading of flux are used to overcome many faults in the broken bars of motors [4]. A problem is protecting the motor device indoors from the “air gap” which affect the incoming signals from motor. To sense the rotor bar faults, the turning radius techniques could be used [5, 6]. Consequently, this technique needs more additional devices. Many researchers introduce advanced methods to diagnose the motor faults as in [7,8,9]. One of the more attractive methods in these fields is the consideration of harmonic produced by stator current as in [10, 11]. The investigated method of [12] which used the “inverted fed induction motors” caused an unwanted frequency harmonic. The idea by [13, 14] of in hand fault motor using frequency spectrum illustrates peak power of spectrum and pole number in the motor consideration. The opera-2d programme technique is carried out to sign the faults by means of broken bar rotor routine. The specifications of suggested motor are illustrated in Table 1.

Table 1 Specification of suggested motor
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2 Mechanical Fault Concept

The common things affected on rotor could be simplified and explained briefly in the healthy bars, which are forced to carry high current and high-speed torques. Additionally, the large air in “aluminium” causes uniform bars to expand. The static and dynamic rotor symmetry could affect rubbing the stator winding.

3 Mathematical Model

The most techniques used to model the fault diagnosis and investigate the induction motor damages are the “winding function, equivalent circuit and finite element methods”. The high performance of electromagnet symmetrical in the induction motor could be used in the suggested model, which indicates any asymmetry degree sign as illustrated in Fig. 1.

Fig. 1
A circuit diagram of a symmetrical electromagnetic field. The circuit is labeled as follows: top, R e, L e, R m, and L m; right, R bn, L bn; bottom, R r2, L r2, R r1, and L r1; left, R b2 and L b2. A vertical wire at the center has R b1 and L b1. A curved arrow labeled i superscript r subscript f passes above R b1 from the right to the left.

Allocation structure

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An asymmetrical of electromagnetic field in the motor produces inequalities in the phase resistance as well as in the air-gap electromagnetic field which introduces a harmonic frequency in the current of stator and rotor. This phenomenon could be expressed in the mathematical model which adds extra resistance to phase of rotor as in [15].

$$R_{{\text{bar}}} = \frac{{l_{{\text{bar}}} }}{{{\text{cos}}\alpha_{{\text{skew}}} .\sigma s}}$$
(1)
$$\Delta r_{ra,b,c} = \frac{{3n_{bb} }}{{N_b - 3n_{bb} }}r_r$$
(2)

where \(\Delta r_{ra,b,c}\) phase change of rotor resistance.

The change produced by rotor effects \(\left( {\Delta r_{ra,b,c} } \right)\) is created by rotor effects which are derived depending on the statement of broken bar as touching either resistance of ring end or magnetizing current. A corresponding resistance of healthy machine could write as:

$$r_r = \frac{{\left( {2N_S } \right)^2 }}{N_b /3}\left[ {r_b + \frac{2}{{N_b \left( {2{\text{sin}}\frac{\alpha }{2}} \right)^2 }}r_e } \right]$$
(3)

where

rb and re denote the end-ring resistances and rotor bar,

Ns turns of winding.

To simplify Eq. (2), assume re deserted, then Eq. (2) become:

$$R_{{\text{ring}}} = \frac{{{\text{l}}_{{\text{ring}}} }}{{{\text{cos}}\alpha_{{\text{skew}}} .\sigma s}}$$
(4)
$$r_r \approx \frac{{\left( {2N_s } \right)^2 }}{N_b /3}r_b$$
(5)

and

$$r \approx \frac{{\left( {2N_s } \right)^2 }}{{\frac{N_b }{3} - n_{bb} }}r_b$$
(6)

Hence

$$\Delta_r = r - r_r = \frac{{3n_{bb} }}{{N_b - 3n_{bb} }}$$
(7)

The 2nd measurable fault assessment as suggested by [16,17,18,19,20,21] is:

$$\frac{{I_{bb} }}{I} = \frac{{{\text{sin}}\alpha }}{{P\left( {2\pi - \alpha } \right)}}$$
(8)

which Ibb and I are amplitudes of the sideband frequency \(\alpha\) …… electrical angle.

Therefore, the electrical angle could be expressed as:

$$\alpha = \frac{{\pi Pn_{bb} }}{N_b }$$
(9)

4 Tests and Results

The finite element method approach is used to diagnose the effect of broken bars in three-phase induction motor which achieves computing healthy and faulty cases and collects the data as waveforms for magnetic field and air-gap flux. This data could extract different fault type signs without destroying the motor. The programme of opera-2d is used in this work to observe and detect the faults and provide good proof of suggested approach. The plots of rated motor in the case of asymmetrical and symmetrical rotor condition are presented. Hence, a flux density of healthy motors shows a bit unbalance due to rotating field introduced by faulty motor as shown in Fig. 2.

Fig. 2
A line graph plots air gap flux density versus time. Values are estimated. first line, (25, 0.045), (100, 0.08), (350, 0.08); second line, (50, 0.039), (140, 0.03), (350, 0.03); third line, (25, 0.009), (100, 0.018), (200, 0.08), (300, 0.018), (400, 0.008).

Waveform of flux

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Figure 3 illustrated a current through stator in faulty and healthy state under load condition. The stator current increased suggestively associated with a fine rotor because the component of harmonic which caused by faults is superimposed into stator current winding at the frequency fb. Concentrating faults on one pole produce an increase in the value of harmonic mechanisms because the faults cause irregularity of flux spreading, that produce more harmonics. Faults generate amount of frequencies with the rotating flux waveform. The rotating flux waves could encourage currents in equal frequency with the stator current.

Fig. 3
A line graph plots current versus time. The general trend of the graph is a sine wave like formation by the healthy and faulty lines. The height of the wave is between negative 2 to 2 on the vertical axis.

Variation of current

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The difference between two stator amplitudes is due to fault case because of asymmetrical flux distribution case, more harmonic in the faulty motor performance. Hence, increasing the number of broken bars would introduce bad asymmetrical in flux. High rise in the frequency harmonic will appear in the case of increasing the amplitude of harmonic of flux waveforms. As a result, one could observe that the harmonic in the faulty motor appears more asymmetrical compared with healthy motor. Figure 4 illustrates the air-gap harmonic spectrum in healthy and faulty machine and the difference between them is highlighted as well.

Fig. 4
Two vertical bar graphs plot amplitude versus harmonic order. Values are estimated. Graph a, (1, 0.26), (2, 0.02), (3, 0.03), (6, 0.02), (7, 0.06), (9, 0.08), (11, 0.02), (13, 0.01). Graph b, (1, 0.45), (2, 0.1), (5, 0.02), (9, 0.19), (11, 0.02), (12, 0.04).

Harmonic spectrums

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In the faulty machine, the waves of magnetic torque are more compared with healthy motor. The time variation of the torque in the healthy and faulty more is illustrated in Fig. 5. The oscillation of developed torque is increased in case of faulty motor more than traditionally enveloped in the healthy motor as well more values. The time variation of torque shape in faulty motor is seen more than in healthy one and the ripple is high also.

Fig. 5
A line graph plots torque versus time. The healthy and faulty lines form a wave-like formation. Values are estimated. Healthy, (0.05, 40), (0.08, 8), (0.1, 8), (0.15, negative 1), (0.2, 4), (0.3, 0). Faulty, (0.03, 20), (0.05, 51), (0.09, 16), (0.1, 12), (0.2. negative 4), (0.3, 0).

Variation of torque

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5 Conclusion

This paper presents the detection of mechanical faults in induction motor by using the opera-2d programme techniques. This approach will increase the time life and keep the motor efficiency as top as possible. The early detection of the faults in the motor will give enough time to protect the machine and decrease the cost by many phases of running time. The suggested technique provides and enhances the machine researcher to develop the fault detection in the current and future generations of induction motor. This work opens a new window for developing and accelerating the induction motor design process to get efficient motor. The future direction of this study aims to develop a comprehensive database of non-invasive sensor measurements of induction machines with different faults and to understand the effect of faults on each sensor output.