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Abstract— This paper presents vibration as an efficient tool in detecting electromagnetic faults in electrical machines. Two common electromagnetic faults are considered in this work: a broken rotor bar and inter-turn short circuit in th e stator winding. A 3-D model was developed in COMSOL Multiphysics. As the main sources of vibration in electrical machines, the radial and tangential forces were introduced to the model. Frequency response analysis was then performed to collect acceleration data from the frame surface for each operating conditions. Finally, the simulation results illustrate that vibration is a beneficial signature for fault detection in electrical machines.

I. INTRODUCTION

Diagnostic of electrical machines have been the subject of interest during the last decades. Faults reduce the machines’ life, performance, and their functionality. Moreover, it may cause severe hazards to human and appliances around them. Significant numbers of scientific research have been conducted on several applicable methods to monitor the conditions of electrical machines in a simpler and more reliable way.

Currents, temperatures, voltage, chemical debris, and vibration are known as the most common fault indicators in the electrical machines [1]. Vibration and torque signal analysis, however, have been less scrutinized in studies due to claimed lower sensitivity [2]. Nevertheless, [3], [4] have shown that the machine vibration is a sufficient fault indicator in many cases, but the effect of electrical fault on the vibration is still under investigation. Rodrigues, Belahcen, and Arkkio [5] presented a method for predicting the excited vibration frequencies caused by faults in an induction motor. They concluded that both mechanical and electrical faults could be detected by monitoring the vibration of the machine.

It has been suggested that electromagnetic forces can be used as one of the most accurate electrical-fault indicators in electrical machines [6]. One obstacle in this method is the difficulty of data acquisition, due to low accessibility of electromagnetic forces. However, since these forces generate vibration in the structure of the machine, the fault indicators existing in the forces shall be well-manifested in the vibration pattern. Su, Xi, and Chong [7] presented an online method for fault detection in the induction motor by using vibration spectrum. They verified the computational results with the experimental ones, and proposed that vibration signal analysis could be an effective approach in fault diagnosis, which would be easily applied in real-time.

Different methods exist for analyzing structural vibration. Analytical methods are the oldest types, which can be used only for simple geometries. Another popular vibration analysis method is deterministic numerical method, applicable to most of problems.

In structural dynamic analysis of induction machines, since stator is one of the most relevant elements in generating noise and vibration procedures, it has been of high interest to a large number of researches. Structural dynamic analysis of

induction machines has been largely studied so far, but in most cases, the stator is modeled as multi-connected rings by using 2-D finite-beam element [8].

This work predicts the excited vibration frequencies produced by two common faults in the structure of an induction motor fed from a sinusoidal voltage source. These two common faults are: a broken rotor bar and inter-turn short circuit in the stator winding the motor. COMSOL Multiphysics software is used to simulate the 3-D model of an existing 35 kW cage induction motor.

II. VIBRATION AND NOISE IN INDUCTION MOTOR

When the stator winding of an induction machine is connected to a supply, a rotating magnetic field is generated; inducing a current in the rotor conductor. The induced current then interacts with the rotating magnetic field and generates rotation.

High frequency forces are produced during the interaction between the input current and the magnetic field. These forces act on the inner stator core surface and excite the stator. This causes mechanical vibration, and consequently displacement in the surface of the stator yoke and the frame (as a mechanical system) with frequencies corresponding to the forces frequencies.

Ref. [9], [10] categorized vibration and noise of electrical machines with respect to their sources into three groups:

1. Electromagnetic 2. Mechanical 3. Aerodynamic

Forces with magnetic and mechanical origins produce vibration directly in the structure of the machine. Nevertheless, aerodynamic sources pressurize the air around the machine. The target of this paper is merely on the structural vibration in the stator and the frame of an induction machine.

Faults with mechanical and electrical origin disturb the magnetic field of an electrical machine. This unbalanced magnetic field results in unbalanced induced forces. Thus, when a fault occurs, compared to a normal operation, larger magnetic forces are produced in the air gap of the machines. These forces interact with the inner surface of the stator, excite the machine frame, and change the structural vibration of the electrical machines. Therefore, vibration analysis is beneficial in fault detection of the machines.

A. Magnetic Forces

Followings are different kinds of magnetic forces in electrical machines [11]:

1. The reluctance force 2. The Lorentz force 3. The magnetostrictive force Comparing the magnitude of these forces, reluctance force

has the greatest magnitude, and is the major cause of magnetic vibration and noise. The area where this force acts on is the

Vibration as Fault Indicator in Electrical Machines Mehrnaz Farzam Far1, Anouar Belahcen1, Antero Arkkio1, Janne Roivainen2

1 Aalto University (Finland), 2 ABB Motors and Generators (Finland)

mehrnaz.farzam.far@aalto.fi

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air gap between the stator and the rotor. The Lorentz force, which acts on the machine winding, can be neglected due to the small flux density in a slot. The magnetostrictive force acts inside the iron core. This force is not considered in this work, due to its complexity.

The reluctance force, as a 3-D vector, is divided into three components: radial, tangential, and axial. Usually, radial forces have the largest magnitude, whereas axial components are so small that could be neglected.

Calculating the magnetic fields and the reluctance forces produced in the air gap of electrical machines have been of interest to a large number of researchers for the last decades. Gair and Yang [12] suggested a technique using a 2-D image of the magnetic field in the air gap of a rotating machine to calculate the resultant forces acting on the surfaces of rotor and stator. Amrhein and Krein [13] used a 3-D magnetic equivalent circuit model together with Maxwell stress tensor method to approach an accurate way for force calculation. Moreover, they compared forces obtained from 3-D and 2-D models.

B. Forces acting on teeth

The magnetic forces operate on teeth, poles, and core of the rotor and stator. These forces are transferred to the stator body and its frame. Belahcen and Arkkio [14] worked on the calculation of teeth forces and concluded that forces on the tooth-tip areas are much stronger than forces on the rest of the tooth. This section describes tooth force calculation by using Maxwell stress tensor.

Studying tooth force requires knowledge of the flux densities (B ) in the machine. Hence, the conversion of the

magnetic vector potential (A ) to flux density in the Cartesian coordinate system can be represented as

A Ax yxy

∂ ∂= −

∂∂B u u (1)

By applying flux densities, Maxwell stress tensor (τ ) in Cartesian system is defined as [15]

0

12 22

12 22

12 22

1

B B B B B Bx x y x z

B B B B B By x y y z

B B B B B Bz x z y z

µ

−

= −

−

τ (2)

To calculate tooth force, Gauss theorem converts the total force acting on the volume V of a body to the force acting on its surface S (the surface encloses the volume). This is expressed as

. .fd V d V d SV SV

= = ∇ =∫ ∫∫F nτ τ (3)

where f is force density,n is unit normal vector on the

surfaceS . Expressing the flux density distribution in the form of

normal nu and tangential tu components

n n t tB B= −B u u (4)

The flux densities are calculated at the edges of the

elements and integrated numerically along path C (as in Fig. 1). Thus, the tooth force is

2 2T n t n n t n

0 0

1 1( )

2C

d CL B B B B uµ µ

= − +

∫F u (5)

whereL is the axial length of the stator core.

Fig. 1. The integration path (C) in 2-D cross section of a tooth.

Considering cylindrical coordinates (havingru as the radial

unit vector and ϕu as the tangential unit vector), (5) will be

T r r ,e φF Fϕ= +F u u (6)

Note that, in general, ,eFϕ and φ

F are not equal [11].

This is due to the fact that the radial Maxwell stress component might not be symmetrically distributed at the tooth

tip (P). ,eFϕ is defined as

Te

TF

hϕ , = −T

(7)

where TT is the vector magnitude of the tooth torque and

Th is the tooth length (Fig 1)..

III. SIMULATION METHOD AND PROCEDURE

As discussed before, the radial and tangential magnetic forces in the air gap of stator and rotor are the main sources of vibration in electrical machines. Therefore, the initial step in vibration analysis is to compute these forces. These forces were calculated by an in-house software FCSMEK code. This software uses the Maxwell stress method to compute the magnetic forces acting on the magnetized iron. Due to the shape of poles and also the interaction between the rotor and the stator, flux waves can be considered as a series of harmonics functions independent from the axial position. Consequently, the magnetic excitation forces are calculated by using 2-D model. In the 2-D study, the code integrates the tooth forces and torque directly from the stresses on element edges. These are the forces which excite the structure. The unit of the forces is Newton per tooth.

The electromagnetic forces were calculated for an existing cage induction motor under load and no load conditions, during three different operation status of the motor: healthy motor, motor with a broken rotor bar, and motor with a shorted turn in the stator winding. Table I presents the

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parameters of the motor used in this study.

TABLE I

RATED PARAMETERS OF INDUCTION MOTOR

Parameter

Connection Star Power 35 kW Voltage 400 V Supply frequency 100 Hz Number of phase 3 Number of poles 4 Number of stator slots 48 Rated slip 0.029

The obtained forces had the excitation frequency in the

range 0-6000 Hz with a domain interval of 4.98 Hz. Fig. 2 and Fig. 3 are examples of the calculated radial and the tangential forces spectrum, applied in frequency domain to one of the tooth surface of healthy motor operating with load, respectively.

Fig. 2. Radial force applied on a tooth surface of healthy motor with load.

Fig. 3. Tangential force applied on a tooth surface of healthy motor without load.

To investigate the faults vibration of the motor, a 3-D

model of the given motor was simulated using COMSOL Multiphysics software. The major models were the frame, the stator core, and the stator teeth. The rotor package was not considered in this work, since the rotor has less contribution in generating magnetic origin noises. Fig. 4 shows the finite element mesh of the complete model. The color of the figure illustrates the element shape quality. The motor feet were modeled as four bolts on the four end points of the frame cylinder. These points were the only connections of the model with outside environment. Three of these bolts are shown in the mesh figure by arrows.

Fig. 4. FE mesh of the 3-D model.

A MATLAB program was written to import the extracted

data from FCSMEK to COMSOL. The forces were then defined as “Boundary Load” acting on the teeth surfaces of the COMSOL model. The model had total number of 48 teeth and each boundary load had a complex value of radial and tangential forces.

The next step for the purpose of studying the structural vibration would be frequency response analysis. Frequency response analysis measures system response to linearized steady-state oscillatory excitation. Frequency response analysis leads to important results such as the forces and the stresses of elements, displacement, velocities, and accelerations of nodal points. In this project, the response analysis was performed on a point at the middle of the frame surface. Vibration acceleration data were collected from this point for different operating status of the motor. This point is shown in Fig. 4, where a vibration transducer can be located for monitoring the vibration data.

The frequency response analysis was performed by utilizing the “Frequency Domain Modal” study of COMSOL Multiphysics. The Frequency Domain Modal is a mean of modal superposition, and it has two study steps: one for computing the eigenfrequencies, and the other for the model response. Frequency Domain Modal uses eigenfrequency analysis to decrease the model to a few modes.

IV. SIMULATION RESULTS

Subsections bellow provide the simulated vibration acceleration results of the motor working in various conditions (healthy motor, motor with broken bar, and motor with shorted turn in stator winding - in both full load and no load cases). The simulated data were collected from a transducer point on the surface of the frame as shown in Fig. 4.

A. Healthy Motor

Fig. 5 illustrates the vibration acceleration signal of the healthy induction machine. The peak of the acceleration curve is at 200 Hz, which is twice the supply frequency (100 Hz). Twice supply frequency is one of the most important

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components in vibration analysis the induction motor vibration spectrum. This component is for all alternate current electrical machinery vibration spectra and is a consequence of the structure response to variable electromagnetic forces [16]. According to [16], the main origins of vibration at twice life frequency are radial and tangential electromagnetic forces. These attraction forces act on the stator and induce the vibration on the motor frame, which results in significant peak at double of the supply frequency.

The interesting point is that load does not affect this working principle; electromagnetic forces are independent from load, and are approximately the same for both no load and full load. This independency can be explained by the fact that when load is introduced to the motor, stator and rotor currents are raised at same time and balance each other. As a result, there will be no significant changes in flux and twice line frequency vibration does not change with load. The vibration acceleration spectrum of healthy motor with no-load is featured in Fig. 6. The peak values of no-load cases curves are very high, therefore, the vertical axis of no-load acceleration spectrums are plotted in log scale.

Fig. 5. Vibration acceleration spectrum of healthy motor operating at full load.

Fig. 6. Vibration acceleration spectrum of healthy motor operating at no load.

B. A Broken Rotor Bar

If the rotor cage is healthy, the magnetic stress around the

rotor is symmetric, and as a result, the resultant magnetic force is zero. However, in the case of broken rotor bars, magnetic asymmetry produces an unbalanced magnetic force, which is rotating at the rotational frequency and modulated with a frequency equal to the slip frequency times the number of poles [17].

In vibration analysis, the most important signature in fault diagnosis is the increment of amplitude. Fig. 7 shows the simulation result of vibration acceleration of a broken rotor bar at full load operation. Comparing this figure to the acceleration results of the full load healthy motor, a large increase in the acceleration amplitude can be observed at both

rotational frequency (r

f ) and twice the rotational frequency

(r

f2 ). Therefore, the vibration at frequencies corresponding

to the rotational speed is a clear signature for detection of broken rotor bar.

Fig. 8 compares the vibration acceleration spectrum of the motor with the broken rotor bar at no load condition with the results of healthy motor at both no load and full load operation. The figure illustrates clearly that components at 250, 300, and 350 Hz are influenced by the load.

Fig. 7. Vibration acceleration spectrum of motor with a broken rotor bar, operating at full load.

Fig. 8. Vibration acceleration comparison of a broken bar at full load with healthy-no load and broken bar-no load.

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C. A Shorted Turn in Stator Winding

During inter-turn stator winding fault, an odd distribution of MMF is produced by stator as a result of the additional circulating short circuit current. Thus, the resultant radial magnetic force, exists in the air gap, is not zero, but instead, is proportional to the square of the magnetic flux waves. The changes in the excitation forces will be reflected in the response of the stator to the forces and, hence, in the vibration spectrum of the frame.

Fig. 9 shows the acceleration spectrum of inter-turn short circuit fault. As can be seen, the amplitude of the vibration increases dramatically at twice supply frequency and the variation at other frequencies cannot be observed. However, by plotting the figure in log scale, the amplitude variation can be clearly seen. According to Fig. 10, the components at 50 Hz, 200 Hz, and 400 Hz are corresponding to the fault. These components are in fact the rotational speed and the even harmonics of the rotational speed. In the case of shorted circuit fault, the loading increases the magnitude of vibration components (see Fig. 11).

Fig. 9. Vibration acceleration spectrum of motor with a shorted turn in stator winding, operating at full load.

Fig. 10. Vibration acceleration comparison of a shorted turn in stator winding with healthy motor at full load.

Fig. 11. Vibration acceleration comparison of a shorted turn in the stator winding at full load with healthy-no load and a shorted turn-no load.

V. VIBRATION RESULTS

Fig. 12 - Fig. 14 present 3-D view of the total displacement of the model in three operating statuses. In addition, for each model, the total displacement is recorded from the transducer (see Table I).

Fig. 12. Total displacement of healthy motor-full load at (a) rotating frequency (b) 2×rotating frequency (c) 4×rotating frequency (d) 6×rotating frequency

Fig. 13. Total displacement of motor with a broken rotor bar-full load at (a) rotating frequency (b) 2×rotating frequency.

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Fig. 14. Total displacement of motor with a shorted turn-full load at (a) rotating frequency (b) 2×rotating frequency (c) 4×rotating frequency (d) 6×rotating frequency.

TABLE I

TOTAL DISPLACEMENT (METER) OF THE MOTOR COLLECTED FROM

TRANSDUCER AT FAULT INDICATORS FREQUENCIES

�� ��� ��� ���

Healthy 5.856e-10 5.3233e-9 3.9121e-7 2.6507e-9 A broken bar 1.01012e-5 6.7173e-7 - - Inter -turn shorted circuit 1.3721e-6 1.7621e-8 1.3727e-5 5.3570e-9

As can be seen from Table I, a broken bar and inter turn shorted circuit faults increase the displacement at rotating frequency dramatically. Moreover, motor with shorted turn fault has larger displacement at even harmonic of the rotational speed.

VI. CONCLUSION

This work contributes to utilizing vibration as an indicator in fault detection of induction motors. The radial and tangential magnetic force waves acting on the stator teeth are the main causes of the stator and the frame vibration. An electromagnetic fault distorts these forces and, hence, the spectrum of vibration. The focus of this paper is on two typical faults: a broken rotor bar and a shorted turn in the stator winding.

In order to fulfill the objectives of this paper, a 3-D model of an existing 35 kW cage induction motor was created in COMSOL Multiphysics. The model properties and materials were same as for the existing motor. A MATLAB program was developed to import the magnetic forces given by an in-house FCSMEK program to COMSOL. The forces were then applied as load boundary on the teeth surface in both radial and tangential directions. The model response to the excitation forces was computed. The analyses were performed in different working conditions of healthy and faulty motors in both full-load and no-load cases. After comparing the

vibration acceleration results of each faulty case with the healthy one, an increase in the magnitude of some specific components of acceleration spectrum was observed. This indicated that these components could be used as signatures for fault detection in an induction machine.

VII. ACKNOWLEDGMENT

The authors would like to express their gratitude to the FIMECC/EFFIMA/FOVI project for the funding.

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