Performance Analysis of Double Cage Induction Motor with Broken Bar Faults in Outer Cage

Induction motors are one of the most commonly used motor in the industry. For this reason, a fault (electrical or mechanical) inside or outside of the motor can cause the motor to go out of power and even cause the production losses inside the factory. Although there are many studies on single-cage induction motor failures in the literature, double cage motor failures are not a frequent subject of study. Therefore, in this study, it was investigated how the outer cage slot faults in a double cage induction motor affect the motor performance. Analyses were performed using Finite Element Method (FEM). 1, 2, 3 and 4 outer cage broken bars in the rotor slot were investigated. Rotor currents, magnetic vector potential values, magnetic flux distributions, current densities, radial forces and torque-speed graphs of the motor models were obtained and compared for both healthy and failure motors. The results show that as the number of broken bar in the rotor increased, a significant reduction was observed in all three torque (starting, maximum and nominal) values. It has been observed that the starting torque decreased by 13.77% for the 4 broken outer cage rotor bars motor according to the healthy motor.


INTRODUCTION
The three phase squirrel cage induction motor is now one of the most reliable, efficient and cost effective electric machines which is the largest electrical energy consumer in the industry (Tudorache et al., 2006;Wang et al., 2018). Induction motors have many advantages thanks to their easy and robust construction. This type of machine is extensively used in many industrial applications (Nakamura and Mizuno, 2013;Roubache et al., 2016;Brooks et al., 2018). In general, induction motors are manufactured in two ways with squirrel cage and wound rotor. Although the single cage structure in the industry is used more and more, the double cage rotor structure has a few applications (Lorenzani et al., 2012). Some of these applications can be given as follows: conveyors, crushers, mixers, compressors, loaded pumps and the likes (Gyftakis et al., 2012). The double cage rotor is an effective technique that improves the starting performance of induction motors (Yamamoto et al., 2017), which provides high starting torque and low starting current (Guru et al., 2013). Double cage rotors are characterized by the large outer (starting) bar resistance and large inner (running) bar leakage inductance, as shown in Figure 1. The high starting torque is obtained by confining the current to the high resistance outer cage during the startup transient at high slip when the inductive impedance is dominant over the resistive impedance as shown in Figure 1 (Lorenzani et al., 2012). In the figure, Vs is voltage, Is is stator current, Ir is rotor current, Rs is stator resistance, Xs is stator reactance, Xm is magnetization reactance, Rr1 and Xr1 are outer cage resistance and reactance, Rr2 and Xr2 are inner cage resistance and reactance, s is slip value and Im is magnetization current. Double cage induction motors can be divided into two categories depending on the structure of the rotor cage. If both, the outer and the inner bar, are from the same material, they are short circuited to the same end-ring and the rotor has one cage, similar to the standard "A" class induction motor. On the other hand, if the two bars are from different materials, then the outer bars are short circuited independently from the inner bars and the rotor is manufactured with two cages. Usually, when two different conducting materials are implemented into the rotor, the material of the greatest resistivity, forms the outer cage, in order to improve the motor's starting behavior. Furthermore, since the cost of production increases with the double cage structure, special attention should be paid to the design process not only for the electromagnetic properties of these motors but also for their general behavior (thermal, vibration, etc.) and their reliability (Gyftakis et al., 2012). The flux distributions that occur during starting and operation of a double cage induction motor are given in Figure 2 (Jahic et al., 2015). The geometries used in induction motors as double cages are given in Figure 3. It is seen that the outer and inner cage geometries are generally preferred for the circle and rectangular slot types. In this study, the structure of Figure 3 (i) is used for the rotor slot geometry.  (Bernatt and Bernatt, 2013;Boughrara and Ibtiouen, 2014;Jahic et al., 2015;Preez, 2016;Yamamoto et al., 2017) In the literature, it is seen that single cage rotor structures are generally used for rotor fault analysis of three phase induction motors. These failures are usually 1, 2 or 3 broken rotor bars or end ring failures (Hamdani et al., 2008;Xie et al., 2012;Pezzani et al., 2014;Ishikawa, 2015;Xie et al., 2018;Yetgin, 2019 In this study, the effects of broken bars on motor performance were investigated in detail by performing an analysis of the outer cage faults which may occur in a double cage induction motor. Healthy motor and 1, 2, 3 and 4 outer cage broken bar motor models were analyzed with FEM. Magnetic vector potential, magnetic field, flux distributions, inner and outer cage rotor currents, torquespeed graphs analysis were obtained for each motor model. In this study, it contributes to the literature because it investigates the effects of double layer broken rotor bar failures on the motor instead of single layer broken rotor bar failures, which is the subject of many studies in the literature.

Induction Motor Faults
Induction motors are the most preferred electric motors in the industry due to their robust construction and not easy failure. However, for unexpected reasons, faults that may occur inside or outside of the motor prevent the operating efficiently. There are several methods for detecting faults that may occur in induction motors. Thanks to these methods, the motor can be deactivated without failure.
Detection of motor faults in the initial phase is important because it leads to increased reliability and low failure time. Motor failure could not be determined in the first step can lead to disaster and induction motor can be seriously damaged (Kathir et al., 2012). Induction motor faults are divided into electrical and mechanical faults.
General failures in inductions motors can be given as follows (Alsaedi, 2015;Huang et al., 2016):  Stator faults resulting in the opening or shorting of one or more of a stator phase winding.  Abnormal connection of the stator windings.  Shorted rotor field winding.  Broken rotor bar or cracked rotor end rings.  Eccentricity (Static and/or dynamic air gap irregularities).  Bent shaft.  Bearing and gearbox failures.

Rotor Bar Faults
The broken bars cause, a strong dissymmetry of the magnetic field into machine air gap which creates the rotate flux harmonics. In this situation, the machine consumes a lot of reactive power and this becomes presently dominant than the active power, which conducts to reduce the torque capabilities of the motor (Said, 2004). Cracked or broken rotor bars and end rings failure are common faults in the three phase squirrel cage induction motors. Generally, 1, 2, 3 or more broken rotor bar are generated in the rotor bars for the single cage induction motor (Pezzani et al., 2014;Ishikawa, 2015;Hamdani et al., 2008;Miceli et al., 2014;Gritli et al., 2013). This is shown in Figure 4. . Healthy rotor and rotors with one, two and three broken bars (Pezzani et al., 2014) The temperature rise around the cracked bars may eventually break the bars and the electric arc occurs around the broken bars. This may damage the laminations of the rotor body close to the broken bar region. The following reasons can lead to cracking or breakage of the rotor bars (Faiz et al., 2007):  Thermal stress due to over-load, non-uniform heat distribution, hot spot and arc.  Magnetic stresses due to electromagnetic forces, magnetic asymmetry forces, noises and electromagnetic vibrations.  Residual stress from the fabrication process.  Dynamic stress due to rotor axial torque and centrifugal forces.  Circumferential stress due to wearing and pollution of rotor material by chemical materials and humidity.  Mechanical stress due to mechanical fatigue of different parts, ball-bearing damage, loosens laminations etc.
Rotor faults are caused by a combination of various stresses acting on the rotor. These stresses can be electromagnetic, thermal, residual, dynamic, environmental and mechanical. However, induction motor rotor faults usually start from a small break in the rotor bar or from a high resistance point. When such a fault increases, the magnetic field becomes increasingly asymmetrical due to the absence of induced currents in the broken rotor bars. This leads to local saturation and disproportionate magnetic distribution in the stator and rotor teeth near the broken bars. The increase of high harmonic components can trigger several electromagnetic events, such as the development of inverse magnetic field, torque pulse, and unbalanced magnetic attraction. All these events are not desirable because they reduce the reliability of the induction motor. The resistance of the broken bars is very high compared to the value of the healthy rotor bars. This is very likely to cause disproportionate distribution of rotor currents. The parts of rotor currents that are not flowing in the broken bars due to high resistance flow in the bars next to the broken. This results in an increase in the value of these bars. Although the broken bar currents flow in adjacent bars, the sum of the rotor currents is lower than in the healthy rotor. Very high current density causes overheating in the bar (Vaimann and Kallaste, 2011). It can cause torque and speed fluctuations, noise and unstable stator currents, reduce average torque (Maouche et al., 2014).

MATERIAL AND METHODS
In recent years, finite element method has been used frequently in the analysis, simulation and modelling of electrical machines. The simulation results are sensitive to the quality of the Finite Element (FE) model, thus critical parameters for FE model have to be specified carefully .
In this study, finite element method was used for the analysis of the healthy motor and the outer cage broken bar motor. Finite element analysis is a computer based numerical technique for calculating the parameters of electromagnetic devices. It can be used to calculate the flux density, flux linkages, inductance etc. In the finite element method, the large electromagnetic device is broken down into many small elements. The equations describing the behavior of the individual elements are joined into an extremely large set of equations that describe the whole device. The computer can solve this large set of simultaneous equations. From the solution, the computer extracts the behavior of the individual elements. Finite element methods of analysis have emerged in the past decades as the useful numerical methods for magnetic field analysis of electrical machines (Sudar et al., 2012).
Magnetic field waveform contains full information about the stator and rotor positions and mechanical parts of the motor. Distribution of the magnetic flux density (B) is calculated from the magnetic vector potential (A) as follows in Equation (1) (Faiz and Ebrahimi, 2009).

BA  
(1) In order to calculate the force in induction motors, a circle must be formed in the middle of the air gap section.
These regions must be enclosed by air to get accurate results of the torque. The electromagnetic torque is computed by a volume integration of Maxwell's stress tensor over the selected area. An average valued torque (or weighted torque) is calculated in the time-harmonic simulations. The Maxwell's stress tensor is used to calculate the radial air-gap forces (Fr) in Equation (2) (Wilow, 2014).
Where Bn and Bt are the radial and tangential components of the magnetic flux density, µ0 is the magnetic permeability of free space. The electromagnetic torque is determined by integration of T over the stator and rotor surface (Faiz and Ebrahimi, 2009). In Equation (3), r0 is the radius of the contour and l is the length.
The model of four outer cage broken bar motors used in this study and the mesh structure are given in Figure 5. 87393 nodes and 174625 elements are produced in the modeling. Aluminum material with an electrical conductivity of 34.45 MS/m is used in the rotor slots (URL-1), magnetic material with permeability µx and µy values of 7000 is used in the stator and rotor core parts and in the shaft section. Analysis of electrical machines using the finite element method requires a closed model. For this reason, the outer diameter of the motor must be defined as zero (for boundary condition) in order to keep the magnetic fluxes in the motor. Since the full geometry is addressed in the modelling, the homogeneous Dirichlet boundary condition is defined at the stator outer boundary. FEM analyzes were performed in the Finite Element Method Magnetics (FEMM) program (Meeker, 2014). The motor has 24 stator slots and 18 double cage rotor slots. Motor voltage is 380 V, frequency is 50 Hz, rotor speed is 2850 rpm, the connection is star and the motor power is 800 W.

RESULTS AND DISCUSSION
In this section, the results of analysis of the faults of the outer cage of the induction motor with double cage struc-ture and the effects on the motor performance are explained. Table 1 includes the flux density at different locations of the stator and of the rotor at nominal operating conditions (sn = 0.05) for healthy and 4 broken motor models. When the Table 1 is examined, the average magnetic flux density values of the 4 broken motors at the determined points indicate that the values of the motor have increased significantly according to healthy motor. This situation explains that 4 broken motors have saturation at these points according to healthy motor and have a negative effect on motor performance. Figure 6 shows the magnetic flux distributions obtained from healthy and 4 broken motor models. The flux distributions of the healthy motor are given in Figure 6(a), and the 4 broken motor model is given in Figure 6(b). The maximum flux density value obtained from the healthy motor is 1.68 T, while the value obtained from the 4 rotor bar broken motor is 1.92 T. In order to understand the difference between the magnetic flux densities given in the figure, the lower bound value of the scale is set to zero and the upper bound value is set to 1.95 T. When the figure is examined, it is seen that the flux density values obtained from 4 broken motor models are higher. This figure also shows that the obtained results which consistent with the average flux density values in Table  1.  The current density values for healthy and 4 broken motor models are given in Figure 8. There is a balanced current density in the non-broken rotor bars and current density values are seen to increase gradually in broken bars. This is due to the current accumulation in the bars around the broken rotor bars. In the healthy motor, more balanced current density values are obtained.  The change in rotor currents in each rotor slot are shown in Figure 10. It is seen that the currents change in an unbalanced manner in the broken rotor parts. In the other parts, it is seen that the currents are obtained close to each other. It is seen that the currents in the broken bars 3, 4, 5 and 6 show differences, and the flows are affected by the broken structure in the slots on the right and left sides of the broken bars. Other rotor bars have a balanced current distribution.
The simulated results of the rotor current magnitude for each inner and outer cage bar for a faulty rotor with 4 broken outer bars are shown in Figure 11. While the current values of the broken rotor bars are zero, it is seen that there is a large increase in the current values in the inner cage of the same bar. . Inner and outer cage rotor current graph Figure 12 shows the variation of the magnetic vector potential occurring in the air gap of the induction motor. In the section where the broken bars are deformed, the results obtained in the other parts seem to be equal. This situation also affects the flux distribution negatively. Figure 13 presents the magnetic flux distributions in the air gap obtained from healthy motor and broken motor models. When the shape is examined, it is seen that the flux density values change in the broken parts.   Figure 15 shows the torque-speed curves for each motor model. It is seen that the most important difference is at the starting torque. It is observed that the starting torque obtained from 4 broken motor models leads to a decrease of 13.77% compared to the healthy motor. In the same way, significant differences were obtained in maximum torque values. As the number of broken rotor bar increased, the torque values decreased. Torque values obtained from healthy and broken motor models are given in Table 2.

CONCLUSION
In this study, faults in the outer cage slot of a double cage induction motor are investigated unlike existing single-cage induction motors rotor bar fault in the literature. Healthy and faulty motor models were analyzed by FEM. The effects of faults occurring in outer cage slot on motor performance were investigated. The obtained results show a significant increase in the current values and current density values in the healthy bars around the broken bars. In addition, these imbalances caused on the motor to become saturated in areas with broken parts. Unbalance occurred in magnetic flux distributions. This has led to the deterioration of the magnetic vector potential that should be sinusoidal. In addition, obtained radial forces were larger in the areas with broken parts. However, as the number of broken bars increased, the starting, maximum and nominal torque values decreased. It has been determined that the starting torque obtained from 4 broken motor models leads to a decrease of 13.77% compared to the healthy motor. Similar decreases were observed in maximum and nominal torques.