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In the previous sections, we devoted ourselves to the analysis of behavior of the healthy induction motor in different possible operating modes including transient and rated operations each having their own effects on the electrical, magnetic and mechanical quantities of the motor. In this section, we deal with an easy and comprehensible way of formulating and describing motor quantities by means of very useful mathematical equations. The goal is initially to see how motor quantities might vary in time and partly in frequency domains. However, the frequency domain is only mentioned as a black box while there would be a sufficient discussion in the next section corresponding to various time, frequency and time frequency processors. The materials provided earlier in the previous sections were interesting and, of course an essential step through understanding the induction motor faults and the corresponding fundamentals. By ''fundamentals,'' the causes, the effects and also any development related to the faults are targeted. Moreover, various types of the supply modes including the line-start, open-loop and closed loop applications were discussed in the previous section to wrap up what happens in industry in terms of the motor control strategies. So, a potential reader of this guide will get used to the terminologies and possible motor-drive interactions.
A general guideline based on which the motor operations are justified in different modes were provided as well. As the goal of this guide is not to discuss every single aspect of drive circuits and also the control strategies, they were explained in a way to cover a great portion of existing operations.
On the other hand, drive circuits are not directly related to the fault diagnosis procedure of induction motors. They mostly apply a kind of impact on the quantities of the faulty motor. It means that the drive and the inverter are not usually involved in the diagnosis procedure. However, they definitely affect the process in comparison to a line-start application. Having discussed and investigated the behavior of the healthy induction motor, now it is time to go through the theoretical and practical aspects of the faulty induction motor. This is a step-by-step process which illustrates and formulates various faults and their effects on the magnetic, electrical, mechanical and also thermal, of course if possible, quantities. Unfortunately, the fault diagnosis of electrical machines really suffers from lack of knowledge in terms of thermal analysis of induction motors. Therefore, the main focus will be on the analysis of other types of physics. In the meanwhile, you will sometimes find a subsection related to some specific aspects of thermal modeling or analysis of a faulty motor.
According to the early materials of Section 2, any induction motor, regardless of the type and the configuration, consists of two main parts, the stator and the rotor each having their own particular components. Depending on the location and the type of the component, various faults might occur. The magnetic, thermal, electrical and also mechanical stresses are the major causes of faults in induction motors. Generally, there are two types of faults as follows:
--Electrical faults: Any type of fault which has an electrical source is called an ''electrical fault.'' The most important and well-known kind of this type of fault is the ''short-circuit'' or ''interturn'' fault. This fault is common for all types of machines which include windings and coils. The main cause of the interturn fault is the deterioration or damage of winding insulations. Over voltages or over-currents are the main causes. In fact, if the voltage applied to the turns of windings goes over the tolerable thresholds of insulations, insulations fail. Over-current, which is the main cause of heat-up in the machine core and winding materials, is another factor in damaging insulations. As a result of this phenomenon, two or more coils in a winding or even between two windings are short-circuited, and an uncontrollable large current circulates through the windings without contributing to the main torque component of the motor. Therefore, it is only considered as a source of losses, unbalanced operation and failure in the symmetrical operation of the motor. This is why, this kind of unbalanced/asymmetrical operation is called ''fault.'' There are also other causes which lead to an unbalanced electrical operation of the motor quantities, mainly the magnetic flux density. The best examples are an unbalanced supply voltage, reversed-phase voltages as well as the gearbox fault. However, they have nothing to do with the internal structure of the motor. Therefore, they should not be considered as a type of fault assigned to the motor because the source is not located inside the motor. Unfortunately, some of research works take them as a kind of motor fault by mistake. In this guide, the term ''fault'' refers to a phenomenon which directly affects an interior motor component so that a change in the shape, the material or the motor operation takes place. Basically, if an external factor leads to a harsh motor operation, it does not necessarily damage the motor components, consequently, if the factor is removed, the motor will be back to its normal, symmetrical and balanced operation. Nonetheless, if the harsh conditions go on for a while, the external factor might lead to a destruction of the building blocks of the motor. This is exactly what we call the ''fault.'' Therefore, all the materials of this guide are valid as internal faults take place. This discussion necessitates the presence of an early fault diagnosis procedure usually called an ''incipient fault diagnosis'' which should be an essential part of any diagnosis task. Incipient diagnosis is an extremely important condition monitoring process existing in high-power applications. In fact, diagnosing the transition from a healthy state to a faulty one is always appreciate in industry.
--Mechanical faults: In this case, the main cause of the fault has a mechanical nature. The ''broken bar,'' ''broken end-ring'' and ''eccentricity'' faults are the best examples of the kind. There is no shortage of agreement that all the mechanical faults are caused by a corrosion, improper casting or unsuitable placement of the components. Sometimes, an internal defect of the motor materials also produces a mechanical fault. For instance, the bearing fault sometimes is a result of a partial breakage of the interior balls. The broken bar fault is generally assigned to the event of disjoining the end-rings and the bars in the rotor. As the bars are connected to the rings through a molded or casted area, they are likely subjected to a breakage if an overwhelming tension is applied to the joints. Unbalanced magnetic pulls (UMP) are mostly the main reasons. The UMP itself can be an output of a misaligned or eccentric rotor.
When a rotor center is not aligned with that of the stator, the motor air-gap experiences an UMP around the outer circumference of the rotor. As a result, the bars and the rings are impacted. When a broken bar motor comes across an eccentric rotor, it is expected to observe a higher level of the broken bar indicators. It is worth noting that any mechanical or even electrical fault eventually contributes to an improper magnetic and/or thermal tension and imbalance. Undoubtedly, the UMP is the best example of the magnetic imbalance. In terms of the thermal stress, the short-circuited turns or windings reveal a hot spot adjacent to the fault area and introduce the possibility of a molded silicon steel material due to the high temperatures around the faulty region. Hence, some specific types of fault faults might create another type of fault. Thus, any methodology leading to a fast, reliable and most importantly early detection of the fault is much respected.
In general, three major types of defects, namely the broken bars/end-rings, the eccentricity/misalignment and the short-circuit faults are going to be investigated in this guide in details. The materials of this section are sort in the way described below:
--the broken bars/end-ring fault
--the eccentricity/misalignment fault
--the short-circuit fault.
Each type will be analytically and experimentally dealt with. The broken bars fault is practically the most tackled and analytically addressed one, and the other two types somehow contain fewer databases in terms of analytical extensions and also the drive-connected problems. Nevertheless, the authors try to gather up every required detail for the purpose of providing the fundamentals of advanced knowledge of the field. To this end, it is preferred to first discuss the basics of all types of fault and then move toward some of the analytical demonstrations of the faulty motor behavior. Then, the experimental approaches corresponding to the laboratory-scale implementation of various faults, along with the required sampling and processing tools and equipment, are studied. Hence, this section seems to be interesting and, for sure, indispensable for almost all of the readers who are amateurs. If the readers already have the idea of how faults are examined, the current section might be skipped. Here are the main outlines of this section:
--to investigate the fundamental concepts of fault occurrence
--to study the time-domain effects of the faults on the motor quantities
--to provide some important analytical descriptions of the faulty motor behavior
--to provide the guidelines of the experimental implementation of various faults in a laboratory
--to explain how the faulty motor signals are measured and then processed experimentally
--to discuss various type of sensors such as the wireless apparatus which could be used during the sampling and measurement task
--to go through the advantages and disadvantages of the measurement techniques provided in this section and then introduce the most competent one.
As the starting point of the discussion, the broken bar fault is targeted as follows.
3.2 Broken bar/end-ring fault in induction motors
Bars breakage usually takes place in applications which specifically require high-power motors, and a highly stressful environment normally exists.
In such conditions, oscillating loads, improper motor assembly, mechanical stresses, as well as the hysteresis stresses, might weaken the joints connecting the bars and the end-rings. Consequently, weakly connected bars might be disconnected from end-rings in one or both of the motor ends. This phenomenon, which partially or fully eliminates the current in the broken bar or bars, is known as the ''broken bars/end-rings'' (see Fig. 1). Sometimes, there can also be a crack or breakage in the end-ring, not in the location of the bar/end-ring joint, but somewhere between two bars. This type is usually caused by improper casting process during the motor construction. Equally important, the air bubbles located inside the joints or the materials could be a decisive factor in increasing the breakage likelihood. As it is conveyed by the name of this type of fault, it only affects the motors with a squirrel-cage rotor, and because the squirrel-cage motors are widely and prominently used in industry, the broken bars fault is very common.
The term ''partially'' which was assigned to the broken bar fault in the previous statements reinforces the idea that there might be a partial or full broken bar or bars. What happens in the case of partial broken bar is that the connection between the bar and the end-ring still exists, although the breakage has already happened and caused to disconnect a part of the joint. As a result, the partial broken bars fault is introduced. Likewise, when there is a fully disconnected joint from which the bar current is not able to flow, the full broken bars fault is introduced.
Depending on the severity of the breakage, different levels of the partial broken bar are addressed and investigated in the literature. Moreover, more than one breakage might also be present at the same time. However, increasing the number of broken bars, whether partial or full breakage, does not necessarily mean that the effect of the fault on the motor quantities increases as well. It sometimes depends on another factor which is the location of the bars in the rotor across the rotor circumference.
So, a new influential factor is introduced as well; that is the fault location. It should be noted that increasing the severity of the breakage in the case of partial broken bar always amplifies the fault effect, while it is not always the case where the number of broken bars increases.
In Section 2, the rotor circuit was modeled and represented by an impedance network containing one impedance per bar or one end-ring (see Fig. 2.5). In the same fashion, the broken bar rotor is modeled in a way that the bar subjected to a full breakage is totally removed from the network. Instead, the current previously flowing in the broken bar finds a pathway through the adjacent bars leading to an increase in the bar currents close to the breakage, and the removed current is modeled by a current source in Fig. 2. The amount of the current source should be ideally equal to the bar current removed from the circuit. The main reason for the increase in the current level of the adjacent bars is the elimination of the armature reaction generated by the broken bar in a healthy case. The voltages applied to the adjacent bars increase; hence, their total current increases as well.
The amount of divergence forming a symmetric and healthy motor depends on the severity of the breakage. The more sever the joint is broken, the larger the asymmetry of the motor variables will be.
The first variable affected by the broken bar is the current space distribution.
Then, the corresponding magnetic field pattern is distorted. The development process of the broken bars fault is as follows:
Mechanical asymmetry ? Electrical distortion? Magnetic distortion? Thermal stress At the final stage of this fault, due to the dramatically increased magnetic saturation caused by the over-current phenomenon, the local losses and subsequently the local temperature increase as well. This is the general qualitative flow observed in any broken bar event.
Now, it is time to take a bit distance from the philosophical aspects of the broken bars fault and move along with the real-world happenings in terms of formulating this kind of fault. Without exception, if a symmetric, healthy and single harmonic motor is under investigation, the ideal magnitude of the back ward field should be zero. The term ''backward'' is assigned to a field which rotates in the opposite direction to that of the synchronous speed or frequency.
When an inherent asymmetry such as the nonsinusoidal spatial distribution of the bars exists, a very well-known backward field whose frequency is equal to sfs is produced (see Fig. 3, the clock-wise rotating sfs components). The other sfs component always exists in a motor.
According to the fundamentals of induction motor, the following relations hold:
Stator electrical frequency: fs Rotor rotating electrical frequency: fr 1 s fs Motor slip: s fs fr fs Rotor bar electrical frequency: sfs
Two magnetic fields, Bs and Br, which are spatially placed with a specific angle, q, with respect to each other produce the electromagnetic torque. In fact, in electrical motors, the electromagnetic torque is produced by cross product of two fields generated by the stator and the rotor. Like Bs, the forward magnetic field produced by the rotor rotates with the electrical frequency of fs fr sfs (3.2)
There is another backward field, Br_fault, which rotates in the direction opposite to the main rotor and stator fields. Therefore, the resultant electrical frequency in the stator reference frame is equal to fr sfs (1 2s) fs which is an indication of the armature reaction of the clock-wise rotating backward field on the stator variables including its current and back-EMF. This is actually the basis of investigating an asymmetry in the rotor. Not only the fault, but also the rotor inherent asymmetries produce a backward field causing additional harmonic components of the motor.
Thus, it is expected to observe the backward field in the case of a healthy motor as manufacturing process does not guarantee a hundred percent ideal rotor design.
Given the fact that even healthy motors consist of the backward fields, the fault occurrence only amplifies the magnitude of the corresponding field and has nothing to do with creating the frequency component. Most of the time, researchers make this big mistake that the broken bar/end-ring fault generates the backward sfs component, while this is a totally wrong notion. In reality, the broken bars fault only impacts the magnitudes of some existing harmonic components which are normally the outcomes of the motor structure.
By means of the overviewed concept and also the one related to the single harmonic motor model investigated in Section 2, one can develop the fundamental formulas of the induction motor with broken bars assuming a linear silicon steel material with a constant permeability of both the stator and the rotor. This makes the process of relating the magnetic field to their producing currents a simple one.
The fundamental component of the model reveals a synchronous frequency of fs in the stator. Therefore, the fundamental harmonic component of the air-gap flux density produced by the stator current is B fundamental Bmsin wst (3.3)
where Bm is the magnitude of the fundamental component of the flux density at the air gap. On the other hand, there is a flux density component with the frequency of (1 2s)fs produced by the rotor backward field . Hence, the corresponding flux density is formulated as the following:
B backward Bmbsin 1 2s wst aB backward (3.4)
where aB_backward is the electrical phase angle of the backward field. Bmb is the magnitude of backward magnetic flux density caused by rotor asymmetry. The assumption of a linear magnetic material leads to NI kB yR (3.5)
where I, N, k, y and R are the current, number of turns, constant coefficient and reluctance of the flux path, respectively. So the motor current is related to the magnetic flux density as follows:
As far as the material is linear, the superposition is applicable. Taking advantage of the superposition rule, each component of the magnetic flux density, the synchro nous and fault-related components, could be separately substituted in (3.4). If it is applied to the fault component, the following equation is achieved.
…where I sideband is a current component with the frequency and magnitude of (1-2s) fs and Im sideband, respectively. This component is the outcome of the backward rotating field. The term ''Sideband'' is assigned to this component because it is located within a specific frequency range around the fundamental component if the current spectrum is analyzed. For the moment, we do not intend to talk about the frequency-domain analysis and will only stick to the time-domain variations for justifications.
Suppose, there was an asymmetry in the rotor, whether a fault or inherent casting problem. Then, we ended up with the fact that describes the reason for the existence of a backward field and subsequently the corresponding (1-2s)fs components of the flux density and the current. This clearly proves that the sideband components are always present in a motor with asymmetries, regardless of the rotor fault occurrence. Nevertheless, the broken bar/end-ring fault, a kind of asymmetry in the rotor, helps the component get stronger compared to a healthy motor. Again, it should be noted that a healthy motor is different from an ideal motor in which the forward rotating fields are only observable.
Let us now flash back to the main discussion. Phase angle of faulty current component should be different from that of the flux density as nonlinear relation ship always holds in reality instead of a linear correspondence. This claim can be further discussed by the FFT analysis of both the current and the flux density and will be done in Section 4. For now, we do not miss the chance to continue with the analytical formulations which have been provided so far. Considering the fact that the electromagnetic torque is the main motive force to produce rotation, it is used here. The fundamental and fault-related components of the electromagnetic torque are expressed as follows:
where L fundamental, Lm, aL fundamental , I fundamental , Im, aI fundamental , T and p are the fundamental components of flux linkage, the amplitude of flux linkage, the phase angle of flux linkage, the fundamental current component, the amplitude of fundamental current component, the phase angle of fundamental current component, the developed electromagnetic torque and the number of poles, respectively. Here, the coupling between the fundamental flux linkage component and the stator current variables including the fundamental and sideband components are dealt with. The resultant torque consists of DC, 2wst,2swst and 1 s 2wst components. The DC component produces the average torque required for the main rotor operation. The terms 2wst,1 s 2wst are higher frequency components which are located around twice the fundamental synchronous frequency and are mostly subjected to being filtered out from the motor operating cycle due to the fact that the rotor plus load inertia is so high that the only the low-frequency components with the order of a couple of Hertz would remain in the torque. As a result, the remaining part which comes into considerations and might produce ripples in the motor torque is 2swst.
This is exactly the component which is the consequence of a rotor asymmetry such as the broken bar fault. As it is a linear function of the motor slip, it is located at very small frequencies, typically below 10 Hz, depending on the motor supply frequency and the slip level.
As a very interesting point, the motor torque and its harmonic components are controlled directly by means of a drive circuit. Therefore, any low-frequency fault related component which is located inside the pass band of the PI regulators is normally affected by the closed loop of the drive circuit. As a result, it is not likely to have a lower torque oscillation even in case of higher fault levels. In Section 8 which is related to the fault diagnosis of the broken bar motors, this issue will be discussed in details.
Now, consider the torque fluctuations caused by the 2swst component as follows:
On the other hand, the motor torque and speed are related to each other by the following equation given that the viscosity of the shaft is zero. Then, one comes up with the following equation which is demonstration of speed fluctuations caused by rotor fault.
J is the motor inertia and Dwr is the illustration of the motor speed fluctuations caused by the broken bars fault. It is obviously seen that the asymmetry in the rotor, for example the broken bar fault, brings the speed to oscillate with the frequency of 2sfs. This fluctuation happens over the average value of the speed. As the next step of the analysis, electromotive force (EMF) produced by the speed fluctuations is calculated and added to the fundamental component as follows:
… where wr average is the average speed of the motor. Equation (3.11) reveals a very interesting and significant aspect of the broken bars fault which is actually the production of a sideband component with the frequency of (1 2s)fs. It means that not only does a left sideband component of the fundamental current harmonic exist, but a right sideband component is also produced as a result of the motor-speed fluctuations. Both are the functions of the motor slip. These harmonic components are generally called the sideband components of the motor current shown by the pattern (1-2s) fs. Accordingly, if the speed is fixed by any means, for example, if it is connected to a closed-loop drive with a very well-refined speed control loop, there is no right sideband component, (1 2s) fs or it exists with a considerably small magnitude compared to the left sideband. In practice, eliminating speed fluctuations is impossible. Hence, the right sideband component always exists while its amplitudes would be so much sensitive.
Each sideband component appears as a current component in the stator windings with the same frequency of the mentioned pattern. In turn, the corresponding magnetic flux densities are produced at the air gap (see (3.12)). The corresponding magnetic flux density terms are named the fault component of the flux density as the source could be related to an asymmetry such as the broken bar phenomenon.
Taking this along with the Biot Savart law into account, two terms defining the right and left sideband components of the magnetic flux density are formulated as (3.12). In fact, hereafter, the terms ''right'' and ''left'' sideband components are used to address (1 2s) fs and (1 2s) fs elements in any motor variable, respectively. Accordingly, the left and right sideband components of the magnetic flux density are as follows:
where Bfault , Bmleft , Bmright , aBleft and aBright are the fault component of flux density, the amplitude of left sideband component, the amplitude of right sideband component, the phase angle of left sideband component and the phase angle of right sideband component, respectively. In a similar fashion the current components are formulated as follows:
where Ifault , Imleft , Imright , aIleft and aIright are the fault components of motor current, the amplitude of left sideband component, the amplitude of right sideband component, the phase angle of left sideband component and the phase angle of right sideband component, respectively. So the total motor current containing the fundamental and faulty components is as follows:
On the basis of the fact that the motor flux has been affected by the sideband components, (3.15) is conducted. It is the output of a fundamental electromagnetic rule based on which the product of a flux and flux-producing current results in an electromagnetic torque if the corresponding flux vectors make a specific angle. Therefore, as both the flux and the current are affected by the fault, the left and right sideband components contribute to the motor torque production as follows:
The above demonstration of the electromagnetic torque is the more comprehensive case compared to the simple representation in which all the flux and current signals were ideal and healthy. In the last illustration of the electromagnetic torque, (3.15), there are nine terms added up. By means of (3.16), the mentioned terms are separated into their fundamental terms expressing the corresponding frequencies.
Tbl. 3.1 Frequency components of the motor torque caused by the faulty current and flux signals
DC component corresponds to the average motor torque. The higher order harmonic components present themselves in the shape of fluctuations carried by the average value. The amplitude of fluctuations increases with the increase in fault level. As mentioned before and what will be proved in Section 4, the high-order harmonic components of the motor torque including 2fs,(1 s)2fs and (1 2s)2fs are usually filtered by the motor transfer function which is in practice a low-pass filter. So the only remaining components are those which are the product of the motor slip. If one takes electromagnetic torque spectrum, s/he will notice the higher harmonic components as well. The reason is that usually the motor mechanical torque is measured in which high-order harmonic components eliminate, depending on rotor and coupling inertias. The calculated electromagnetic torque will, of course, contain the high-order components.
Finally, the active power of the motor could be calculated mathematically by multiplying the torque and speed equations. There should certainly be an average value providing the motor with an active power to run. The active or sometimes the reactive power of the motor gives us the opportunity to discriminate between the fault-related 2sfs component and the one produced by an oscillating load. In fact, any load oscillating with the frequency of 2ksfs introduces some levels of change of the sideband components. Thus, they might be mistaken as the real broken bar fault if simply the motor current signature analysis (MCSA) is used. In this case, the motor power spectrum is usually preferred, of course in the steady-state regime, to find the principle source of sideband components change.
As shown in (3.11), the backward field whose frequency is equal to (1 2s)fs generates the right sideband component with the frequency of (1 2s)fs. This was revealed by substituting speed fluctuations caused by 2sfs component with the EMF equation (see (3.11)). If such a trend is repeated for the 4sfs component existing in motor torque equation, the corresponding torque and EMF will contain new components with the frequency of 4sfs and (1 4s)fs, respectively. On closer inspection, if one continues the process of mutation of the sideband components repeatedly, the following pattern is introduced and could be extracted by the frequency analysis of motor current and EMF.
Frequency pattern of the sideband components: 1 2ks fs (3.17) where k is an integer starting from 1. This pattern exists in the vicinity of the fundamental component of the current and the flux. However, it might be seen around the products of the fundamental components including the third, fifth, seventh product and so forth. Equation (3.17) prepares a very significant engineering basis for the starting point of the fault diagnosis procedure in terms of the broken bars fault. Actually, the amplitudes of these components are the key feature in the fault diagnosis procedure. The point is that the amplitudes are functions of so many influential factors including the fault severity, the fault location, the load level, the speed level, the supply mode, the motor voltage and the motor structure. Therefore, so many efforts have been made so far to find a meaningful trend of variations between the influential factors and the corresponding amplitude of indicator. The studies include the time, frequency and time-frequency processors which deal with stationary and non-stationary operations.
3.2.1 Time-domain behavior of induction motors with broken bar/end-ring faults
A very useful analytical approach has been already provided for understanding what theoretically happens to the motor quantities due to the broken bar/end-ring fault occurrence. The statements should be completed by additional schematic illustration of the motor quantities such as current. Fig. 4 presents the current, torque, speed and flux signals for an induction motor with one broken bar.
The investigated motor is the same as the one with the power of 11 kW used in Section 2. This motor consists of 28 rotor bars along with 36 stator slots. The broken bar characteristics reflected in the motor variables are listed below.
Transient operation is always a tricky and challenging mode of diagnosis in every type of fault as the corresponding faulty signals are only present for a very short period of time. As a result, it is often impossible to track the frequency components dealing with the fault. Besides, the fault components have no fixed amplitude and frequency wise, and they reveal a dramatically changing trend. Thus, diagnosing the faults in the transient regime is still one of the trending aspects of the field. This is not merely restricted to the broken bars fault and is a matter of all the types.
On the other hand, although no/light-load operating condition might be very helpful in diagnosing the faults such as the eccentricity, it diminishes or at least reduces the possibility of detecting the broken bars fault. It is generally because of the masking effects of the fundamental harmonic component which is very close to the fault-related patterns, specifically if the motor current is the signal which is used for the diagnosis purposes. In the no/light-load condition, the slip value is so small that the sideband components almost stick to the fundamental component and they are hopelessly undetectable unless a frequency-domain analysis is hired ( Fig. 5).
The hints are provided here in terms of the theoretical and schematic behavioral study of an induction motor with one full broken bar. There are several other aspects associated with this problem such as:
--the location of multiple broken bars
--the partial broken bar fault
--the effect of various supply modes including the open- or closed-loop modes
--the effect of the drive reference parameters on the diagnosis procedure.
Having provided the fashion based on which the motor faults could be studied, let us move on to the next type of faults which corresponds to the rotor shaft and its displacement from the stator center. This is called the ''misalignment fault'' or generally the ''eccentricity fault.'' First, a set of mathematical developments are addressed; then a couple of illustrations are provided in terms of the behavioral study of the faulty motor.
3.3 Eccentric/misaligned and bearing faults in induction motors
In induction motors, there are three physical dimensions x, y and z indicating the Cartesian axes in 3D space (see Fig. 6(a)). In addition, the 2D demonstration is also provided in Fig. 6(b) which illustrates the rotor symmetry center (Ar), the stator symmetry center (As) and the rotor rotation/whirling center (Aw). Besides, the Cartesian axes are highlighted in the following fashion:
--The x-axis is aligned with the spatial axis of the phase ''a'' of the stator.
--The y-axis is located exactly 90 mechanical degrees away, in a counter clock wise direction, from the x-axis.
--The z-axis is perpendicular to both of the x and y axes in the direction of the motor shaft.
In healthy motors all the three centers perfectly coincide with the spatial center of the stator, i.e., As, which is fixed in one point. This point is the origin of any mechanical displacement analysis. So the air-gap length, highlighted in Fig. 6(a), would be the same all over across the stator circumference and equals to g0.
The rotational movement of the rotor does not disturb this uniformity while a hundred percent match between the mentioned centers is impractical due to several imperfections such as the improper assembly or placement of the bearings. This is the reason that the bearing fault could also be a potential source of eccentricity fault.
This phenomenon could be easily detected even in the case of healthy and new brand motors. This type of eccentricity is called the inherent eccentricity. Other factors including the misalignment of the load and the shaft axes, as well as the mechanical stresses and imbalances, fortify the situation. Consequently, the eccentricity fault takes place, and the uniformity of the flux distribution in the air gap is distorted. This literally means that the air-gap length is not uniform across the stator circumference. Using a very acceptable approximation of the air-gap length variation, the following representation should always hold correctly [29-35 ]: g j; jm; r g0 1 rcos j jm (3.18)
where g0, r, j and jm are the uniform air-gap length in healthy condition, the ratio of the distance of the rotor and stator centers over g0 (the severity of the eccentricity fault), the mechanical angle of the rotating and nonrotating point is the stator reference frame and the angle separating the stator and rotor centers in the direction of the rotation, respectively (see Fig. 6(b)). It is obvious that the distance between the stator and rotor center could not exceed g0. As a result, r should geometrically remain within the range [0-1 ] if the rotor is locked. However, while the rotor rotates, the UMP, along with the centrifugal force, leads to the increase in the fault severity, so r might not go beyond 0.72 (proved by the experiments). In such situation, the rotor touches the inner surface of the stator at both ends while the motor operates.
The center of rotation of the rotor has not been taken into account yet and it has only been assumed that Aw is fixed. In fact, it is the position of Aw which defines the type of the eccentricity fault. If the center of rotation remains concentric with As, it is called the ''static eccentricity.'' The term static conveys the idea that although the air-gap length is nonuniform across the stator circumference, it is fixed and does not change with time. However, if the center of rotation is aligned with the stator center during any eccentric condition, it is called ''dynamic eccentricity'' fault. In this case, the rotor center rotates about the stator center with the same frequency as that of the rotor. As a result, the nonuniform air-gap length rotates by rotating the rotor, and the air-gap length is not fixed anymore. For example, jm which is the position of the minimum air-gap length, increases by the rotor speed as follows:
--the level of the eccentricity fault (r)
--the spatial distribution of the nonuniform air gap.
Considering this point, r and j are generally formulated as follows [36-38 ]:
where rs is the ratio of the distances of Aw and As from g0. rd and js are the ratio of the distances of Aw and Ar from g0 and the angle along which Aw and As diverge, respectively. The static and dynamic eccentricities are only some simpler forms of the mixed eccentricity fault where rd or rs are equal to zero. Therefore, rs defines the severity of the static eccentricity fault. Likewise, rd defines the severity of the dynamic eccentricity fault. If (3.20) and (3.21) are substituted with (3.18), the real value of the air-gap length is obtained as a function of the rotor position, the static eccentricity severity and also the dynamic eccentricity severity. The inverse function of (3.18) is called the inverse air-gap function or the permeance function which plays a vital role in analyzing the eccentricity fault as well as the misalignment fault which is a rather complex version of the eccentricity fault in which the motor shaft bends toward the z-axis shown in Fig. 6(a). This issue will be further investigated.
Depending on the values of rs and rd, one of the following three cases is possible:
(a) rd > rs In this case, the dynamic eccentricity dominates the static one. Using the equations represented so far, the air-gap function, along with its position, can be calculated upon changing the rotor position (see Fig. 7). This figure illustrates such calculation according to which the minimum air-gap length oscillates between two extreme points including g0(1 rd rs ) and g0 (1 rd rs) with respect to the rotor rotation. The frequency of jm is the same as that of the rotor rotation.
(b) rd rs
This situation is usually called a balanced mixed eccentricity fault. The corresponding variations of gmin and jm are shown in Fig. 8. As seen, gmin oscillates within the range g0(1 rd rs), and g0 and jm are limited to the [ p/2, p/2 ] period. Therefore, the minimum air-gap length is eliminated where the rotor position equals one of the odd factors of p. Again, the frequency of jm is the same as that of the rotor rotation.
(c) rd < rs
In the above situations, the static component of the eccentricity dominates the dynamic one, and the corresponding air-gap length looks like Fig. 9.
Accordingly, the minimum air-gap length oscillates between two extreme points including g0(1 rd rs) and g0(1 rd rs) with respect to the rotor rotation. The range of variations of jm is relatively small and it oscillates very close to js. The movement looks like a pendulous oscillation, and the corresponding frequency is again equal to the rotor frequency.
Three general cases, namely a dominant dynamic, a dominant static, as well as a balanced mixed eccentricity fault, were discussed. Considering the dis cussed cases, the air-gap length affected by the eccentricity fault could have several different shapes each having its own effect on the motor quantities.
It should be mentioned that many assumptions are associated with the analysis such as:
--ignoring saturation effect
--ignoring slotting effect
--ignoring end winding effect
--the static or dynamic eccentricity level is applied to the rotor along the z-axis, and the rotor should be displaced from the origin. This means there is still symmetry in z-direction, and all the 2D analyses are still valid in 3D if the thermal issues are not of interest.
3.3.1 Misalignment inclined rotor
The main focus has been already on a symmetric z-directional eccentricity fault which guarantees the symmetry in the third dimension of the motor. However, in a specific situation, an asymmetric distribution of the motor air-gap length along the z-axis might also be dealt with (see Fig. 10). Although Fig. 10 is a kind of exaggerated representation of the mentioned defect, it easily and clearly conveys the issue according to which the rotor axis Ar, inclines and takes a distance from As.
b is the amount of divergence from the concentric point, but it is totally different from a simple static eccentricity as the rotor ends move in the opposite directions, i.e., one goes up and the other falls down. So along the z-axis, the eccentricity severity of the fault is not constant anymore. In this case, we only refer to a static misaligned/inclined rotor to make sure that the analytical descriptions are easily extractable while a mixed misalignment fault should always take place in reality.
Some of the most important causes are as follows:
--bearings wear caused by aging
--swinging mechanical loads
--inherent assembly and manufacturing defects.
After a long motor operation, these factors result in a mechanical failure of the motor if a proper diagnostic and maintenance process is not held. The misaligned rotor not only harms the motor itself, but also produces an extensively fluctuating movement of loads leading to an improper operation outside the motor as well. This might be the most compelling evidence which necessitates the fault diagnosis procedures. Now, we would like to formulate the air-gap length in a misaligned motor, using the assumption that only the static form of the fault exists and there is no additional swing caused by a dynamic movement of the rotor center. In this case, there is an air-gap length distribution similar to (3.18) but with a variable r along the third dimension (z) of the motor. The air-gap length and consequently the corresponding permeance are the functions of b.
…where rs0 is the static eccentricity fault severity right in the middle of the rotor. Ls is the motor stack length, and z is the distance from the origin shown in Fig. 10.
According to the above equations, the air-gap length is not fixed in different motor cross-sections. For the future analysis, if the permeance function is required, (3.22) should be used but in an inverse form. Incorporating the dynamic eccentricity into the misalignment formulations should be so sufficient that you might not be able to find a suitable theoretical resource in this field. Therefore, it is preferred to skip the philosophical discussion of the eccentricity/misalignment fault at this point and switch to the mathematical and physical descriptions of the phenomenon by working on the impacted motor quantities including the magnetic flux density and the current. Then, we will end up with a pretty closed-form formula associated with the UMP existing in an eccentric induction motor. What is provided there is an intensive analytical representation of the eccentricity fault and its resultant components; then a few motor signals are illustrated to justify the effects in the time domain.
3.3.2 Theoretical analysis of eccentric induction motor
The basis for providing the materials is introduced by the Ampere's law.
The main assumption here is the presence of a single-harmonic motor model based on which all the healthy motor signals only contain a single sinusoidal distribution.
So the stator current density should also follow the same rule. It is noted that the statement is true if the discussion is held in the steady-state mode. Considering this, the current density of the stator windings can be formulated as (3.24).
(3.24) where Jsm and j are the stator current density (in A/mm^2 ), the synchronous field position (in wst, t is time). jm is equal to pky where k is the inverse air-gap function, and y is the linear distance around the stator circumference. Using the Ampere's circuital law and also neglecting the angular component of the air-gap flux density which is practically a correct assumption, one will end up with the following equation.
where y; t is the permeance function described previously in this section. As seen, the magnetic flux density is related to the current density by an integral operator over the stator circumference. Reforming (3.18)-(3.21) returns, the following representation of the air-gap length demonstrating the components corresponding to the static and dynamic eccentricities:
It is assumed that the air-gap variation is a sinusoidal function if the stator and rotor slotting effects are not taken into account. Otherwise, the air-gap length must be equal to sum of many sinusoidal terms expressing the Fourier transform of the air gap function. This matter will be discussed later. It might also be noted that experiments and investigations show that the above assumption is correct in the case of a nonsalient pole machine. wr, rs, rd and g0 are rotor rotational speed, static eccentricity severity, dynamic eccentricity severity and average air-gap length in healthy condition, respectively. To avoid stator-rotor rub term (rs rd) < 1 must hold. Under small values of eccentricity fault, inverse air-gap function is approximated as follows:
In practice, if the eccentricity fault severity goes beyond 30%, rotor may rub the stator and probably fail to operate appropriately. By combining (3.24)-(3.27), one obtains:
Bs is the stator magnetic field observed at the air-gap level considering the presence of a mixed dynamic eccentricity fault. Multiplying the left cosine term by the terms residing inside the righter parentheses leads to an almost straightforward formulation of the magnetic flux density produced by the stator as follows:
There are five components associated with the calculated eccentricity-related magnetic flux density. From left to right of the left-hand side term, they are accordingly produced by the fundamental component, the static eccentricity and the dynamic eccentricity fault, respectively. It is clearly observable that the static eccentricity components, the ones with the magnitude of Bp 1 sm s m0Jsm 2kpg0 rs, merely depend on the functions of the synchronous frequency and have nothing to do with the rotor speed or position. On the other hand, the dynamic eccentricity fault related components, the ones with the magnitude of Bp 1 sm d m0Jsm 2kpg0 rd, are imposed to be the functions of the rotor position as well as the synchronous speed of the stator. This is another proof of the dependency of the motor quantities on the rotor rotation in the case of dynamic eccentricity fault. The developed and discussed formulation is a pure analytical practice with a lot of imprecise assumptions made just to allow us to extract a closed-form relationship. Therefore, although the magnitudes (see (3.30)) provide a useful common basis to compare the healthy and fault-related components, are not accurate in terms of the absolute values. However, the Bp 1 sm s and Bp 1 sm d are smaller than Bp sm m0Jsm kpg0 , proving the fact that the fundamental component still possesses the largest magnitude among the motor frequency components. As another perceivable fact, the fault-related components are indeed number-of-poles dependent. In fact, two faulty terms are separately assigned to each of the static and dynamic eccentricities. In the case of dynamic eccentricity, these terms are located within a specific frequency range, scaled by (ws wr), of the fundamental component.
So far, the air-gap field produced by the stator current, which in turn applies a specific level of the EMF to the rotor bars, has been evaluated. Inspecting a short circuited rotor circuit, the voltages induced by the mentioned EMF produce the bar currents flowing into the rotor circuits. The same principle is valid for a wound rotor. The point is that the calculations provided so far are based on a stator reference frame while the rotor-related calculations require to transfer the quantities from the stator to the rotor side. As a result, (3.29) should be mapped on the rotor reference frame using a wise substitution of ky wrt ky and wr 1 s p ws with (3.29). The stator magnetic flux density formulated in the stator reference frame is converted to (3.31).
A very clear interpretation of (3.31) is that the rotating frequency corresponding to the magnetic flux density is of course slip-dependent. This arises from the previous transformation from the stator to rotor reference frame. The induced EMF is derived by taking derivative of (3.31) with respect to time.
It is really important to realize that unlike the magnetic flux density, the amplitude of the induced EMF is the function of the motor slip, so increasing the motor slip should practically lead to an increase in the magnitude of the induced EMFs regardless of the fault type [44-46 ]. Thus, the rotor current must increase as well.
This is consistent with the fact that increasing the motor load requires a larger current flowing into the windings and bars as a larger slip is needed. Following the explanations, the rotor bar or winding currents are simply calculated by dividing the EMFs with a factor of rotor bar or winding resistance while neglecting the phase shift between the EMF and the current caused by the inductive nature of the rotor. Then, rotor bar current densities would be obtained as follows:
Equation (3.34) has been developed in rotor reference frame based on the stator supply frequency. a1, a2, a3, a4 and a5 are the phase angle of the rotor bar currents with respect to the induced EMF from the stator side. If it is assumed that the rotor inductance is very smaller than its resistance as rotor electric frequency is a fraction of rated frequency, the amplitude of harmonic components of bar current, i.e., Jrm p , Jrm(s) p 1 , Jrm(s) p 1 , Jrm(d) p 1 , Jrm(d) p 1 , could be simply obtained by dividing the induced EMFs by rotor bar resistance as follows:
where Rbar is the rotor bar resistance in the rotor reference frame. Generally, there are three current components rotating with the frequency of sws, 1 p 1 s p ws and 1 p 1 s p ws. Although this is a very rough approximation, it could be insightful.
The last two frequencies correspond to the static eccentricity fault while the dynamic eccentricity is of the same nature of the fundamental frequency. Rotor bar currents produce their own magnetic fields in the motor air gap and then induce the corresponding MMFs into the stator winding through being modulated by the air gap permeance similar to what has been previously done in (3.28). Working on the formulations and extracting the terms related to the non-supply-frequency components and also the p pole-pair components, we will end up with the following equations:
(3.37) From (3.36), it is seen that the rotor magnetic flux density waves caused by the static eccentricity are regulated with the dynamic component of the eccentricity and produce the sideband current components with the frequency pattern of ( fs fr).
The point is that the components listed in (3.36) do not contribute to the torque developing process as the number of poles is not equal to that of the stator, whereas (3.37) illustrates the torque-generating fault components containing the same frequency pattern as that of (3.36).
The ( fs fr) pattern is the very well-known index to diagnose the eccentricity fault; of course, in the case of a mixed eccentricity fault, both the static and dynamic types have some level of correlation with the mentioned pattern.
This pattern is also a function of the motor slip revealing a non-constant frequency position if the motor slip is changed by any means. Moreover, the corresponding magnitudes are load-dependent deduced from the rotor current densities in (3.37).
It should also be remembered that an UMP which results in additional noise or vibration is an output of any eccentricity fault. Nowadays, due to the lack of engineering importance, very little is known about the subject of noise in electrical machines. All motor designers treated noise mitigation as an art-like cookery. For example, they had a list of low-noise empirical rules and some forbidden combi nations of stator and rotor slots. All that was perfectly clear. However, these are some general laws that do not aim at explicitly describing the faulty motor behavior which is the main focus of the guide. Therefore, due to the significance of the pre-drawn topic, we are seeking to provide a satisfactory on the vibration and probably noise analysis throughout this guide. The starting point is to calculate the magnetic force between rotor and stator by means of the following commonly used approximation of the magnetic force.
where B radial is the radial component of the air-gap flux density all over the stator inner circumference. Considering a mixed eccentric rotor, 4 main flux components other than the fundamental one are present as the spatial harmonics of the flux density according to (3.29). It is worth noting that it is the interaction between the rotor and the stator flux densities which finally produces the net flux density at the air gap. So on the basis of the existing components shown in (3.29), the net flux density should also contain the same harmonics, but with different values of the magnitude and the phase angles. The general formulation should be as follows:
By replacing (3.39) with (3.38) and simplifying the equation, a closed-form expression of the radial forces at the motor air gap is obtained where the fault is present.
The most significant aspects in terms of the above expression are as follows:
--The minimum frequency included in the magnetic force is the same as that of the rotor mechanical quantities, i.e., fr.
--The maximum available frequency is equal to twice the synchronous frequency, for example if there is a supply frequency of 50 Hz, the largest observable frequency will be 100 Hz.
--There are also some medium frequency components including 2fs fr , 2fs fr ,2 fs fr ,2 fs fr and 2fr.
--Not all the frequency components would probably be detected in the vibration signal analysis of induction motors, and it actually depends on the motor structure, the mechanical damping factors, etc.
--Practically, relying on 2fs component to detect the fault is somehow a wrong technique as it cannot be clearly diagnosed most of the time.
According to the literature, the vibration signal is usually considered as one of the most interesting signals available throughout the sensors mounted in the motor body.
This is not only the case in induction motors; and vibration and subsequently noise analysis have been a matter of various investigations in terms of different types of machines. However, we do not aim at discussing the diagnosis procedures in this section; they will be dealt with in the next sections. For the time being, it seems terrific to have an insight into the real motor quantities including the current, the torque, the speed and even the motor flux when the eccentricity fault exists.
Therefore, we aim at providing finite element (FE) results of 28-bar, 36-slot and delta-connected induction motor to which 30% dynamic eccentricity fault is applied. A 2D FE analysis is conducted as a complete 3D one will be so time consuming that it might not be handled by means of low-power computational devices. A quasi-2D model in which several slices of one single motor in z-direction are modeled, paralleled and simulated at the same time is also an appropriate alternative of a 3D operation. However, there is still a high computational demand compared to 2D simulations. Considering these points, the motor is modeled in 2D. This is an acceptable approximation as long as the stack length is not small compared to the stator diameter. If so, the z-axis component of the motor quantities would be symmetric to that of the 2D simulations to a great extent.
Otherwise, the z-axis should be definitely modeled due to the fact that z-axis components play a vital role in motor operation. With this in mind, a group of results illustrated in Fig. 11 in terms of an eccentric motor are provided.
Fig. 11 shows the motor quantities in the no-load and full-load conditions.
The simulated motor has already been discussed in Fig. 4. The difference is that the skewing effect resulting in a smoother response as well as a larger motor rise time has not been considered in the FE-based represented plots in Fig. 11.
Therefore, it is expected to observe more fluctuations in terms of the variables illustrated in Fig. 11 compared to Figures 3.4 and 3.5. Significantly, skew effect is always used to reduce the magnitude of undesirable higher order spatial harmonic components caused by the slotting and nonsinusoidal distribution of winding effects while the magnitude of the fundamental component is reduced accordingly as well. So it is obvious that the motor torque production capability degrades by decreasing the fundamental magnetic field which leads to an increase in the motor rise time. These comments are made here to prepare minds for the next sections in which a comprehensive discussion on the analytical and FE-based modeling of the healthy and faulty induction motors is going to be included. So different aspects including the winding topology, the skewing effect, the material modeling, and the fault modeling will be further discussed. Now, take a look at the following features extracted from Fig. 11.
--Then again, the current decreases considerably by reducing the load. It gets more and more small up to the no-load current in which the steady-state cur rent signal diverges from a pure sinusoidal curve and turns into a flat top signal. The situation gets worse if the phase current of the motor is investigated. If a 3D model is used, the shape will be certainly more sinusoidal due to the fact that the skewing effect is incorporated. Otherwise, the uncomplicated model should always reveal higher signal ripple. However, a flat top no-load signal is expected even in practice. This is caused due to the presence of the harmonic components, which are powerful enough to change the shape of the signal other than the fundamental one. In view of the fault-related oscillations, the current envelope is not a good medium for reflecting the eccentricity fault as the effect is not clearly distinguishable. It, of course, leads to some sort of fluctuations, not very useful to follow up the fault.
--The motor rise-time is considerably larger than that of Figs 4 and 5.
This evidently proves the claim based on which the fundamental component of the magnetic flux is weakened if the skewing effect is applied. In Fig. 11, the skewing effect has been completely ignored.
--The time-domain representation of the motor signals, except that of the flux, clearly conducts the distinction of the no- and full-load condition in terms of the eccentricity fault and its effect on the motor. In contrast to the broken bar fault, connecting a larger load to the motor shaft lowers the impact of the eccentricity fault on the time-domain signals. In other words, increasing the load damps the oscillations caused by the eccentricity fault.
--The effect of the sideband components produced by the eccentric rotor and discussed throughout (3.24)-(3.39) is not properly distinguishable in time domain signals. This might be because of the smaller magnitude of the eccentricity fault compared to that of the broken bar fault. Notably, the side band components associated with the eccentricity fault are not generated or produced by the fault. They are already there in the motor structure while their magnitude is changed if a fault takes place.
--The transient mode is apparently the best candidate for demonstrating the differences between the no- and full-load conditions. The differences are less observable in the steady-state operation. According to the transient parts of the signals, the amplitude of the fluctuations in the no-load condition is more than that of the full-load condition. This conveys the fact that the motor load acts as a damping factor in terms of the mechanical faults. This is also true in terms of the steady-state analysis. However, the simulated FE model, due to the absence of the skewing effect, does not represent the idea.
--A very interesting plot is the one related to the magnetic force applied to the inner surface of the stator as shown in Fig. 11(e). The applied force of the no-load motor is obviously more fluctuating than that of the stator in the transient mode of operation. This is the net value of the applied force to the stator surface.
Generally, time-domain signals do not provide a reliable fault detection approach in terms of the dynamic eccentricity fault. They can only be considered as tools to detect a defection or improper operation. Nevertheless, some esoteric fault indicators such as the Gyration Radius (GR) address some unknown time-domain aspects of the eccentricity fault. However, these kinds of indicators are not popular anymore nowadays. A more reliable frequency-based diagnosis is usually preferred.
Having discussed and explained the eccentricity fault's commitment to the unsafe and unreliable performance of the motor, we now prefer to concisely talk about one of the major causes of eccentricity which is called ''bearing fault.'' Bearing fault itself produces additional noise and consequently vibration in the motor body. Depending on the location of fault, inner or outer race, various frequency patterns are provoked and used to detect the fault, but what is interesting is the contribution of this fault to the future eccentricity fault, and this is exactly what has been greatly focused in the literature.
3.3.3 Bearing faults in induction motor
Bearings are indeed one of the most important parts of an induction motor in maintaining the reliability and safety of the machine performance. They should be checked constantly to make sure if the motor operation will not fail. What makes them highly significant is their mechanical operation and being subjected to higher levels of friction leading to wear and tear of their internal and external part. In fact, no rotation exits unless something holds the rotor concentric with respect to the stator and this crucial task is handled by bearings which not only take care of maintenance of a symmetrical operation but also tolerate the rotor weight which might run over hundreds of kilograms. The studies show a considerably high percentage, almost 40%, of contribution of bearing fault to induction motor failures.
Fig. 12 shows a general bearing structure which consists of the following main parts:
--the outer raceway
--the inner raceway
More often, three types of faults are associated with bearings as follows:
--outer raceway defect
--inner raceway defect
Noticeably, any bearing defect is of a mechanical nature which makes the motor vibrate due to the presence of a radially unbalanced force caused by the defect. This statement reminds the term UMP which was previously discussed in terms of an eccentric motor. So the final result of any bearing defect is somehow converted to an eccentricity type of fault based on which some principle harmonic components are used to detect the fault. Resulting from an eccentric-like fault, it is expected to observe a general frequency pattern of f bearing fs m fi;o
(3.41) where m 1, 2, 3, . . . and fi,o is a frequency characterizing and modulating bearing dimension into the motor variables. As a very well-known practice, the corresponding value is obtained as follows:
where Nb,fr,Db,Dc and b are the number of bearing balls, the mechanical rotor speed in Hz, the ball diameter, the bearing pitch diameter and the contact angle of the balls, respectively. The mentioned frequencies are the so-called ''characteristic frequencies.'' Although different bearings produce different characteristic frequencies, depending on the number of ball and their dimensions, as a rule of thumb, the corresponding values can be calculated as follows if the number of balls is between six and twelve.
Although the simplification is brief, it is certainly convincing and no more discussion seems to be necessary at this point. Just as a hint, vibration and noise analysis is one of the best approaches to detect this kind of fault.
3.4 Short-circuit fault in induction motors
One of the phenomenon which has been carefully addressed so far is the problem of short-circuit fault in induction motors [47-50 ]. Due to the dramatically wide application of induction motors in industry and also bring up the safety features among which the short-circuit fault relays or indicators are the most significant ones, we also aim at including this topic in the guide. This type of fault is interesting enough due to the fact that it might similarly happen in both rotor and stator if a wound rotor is targeted. Otherwise, it is restricted to stator side if a cage induction motor is analyzed. Although the wound-rotor motors are less requested, they are promising apparatuses to provide a higher starting torque respecting to a minimum starting current. However, in addition to the stator, the short-circuit fault can also take place in the rotor. The literature shows that the effect of the short-circuit fault in the stator is very higher than that of the rotor.
According to the investigations, almost 37% of the induction motor faults are related to its insulation failure leading to a short-circuit fault [51-54 ]. As a result of this kind of failure, the current density of coils/windings runs over the rated values dangerously causing a hot spot area around and through the faulty coil/winding.
This is one of the major sources of degradation and also aging of motor coils/ windings.
In general, there are specific types of this fault including:
Regardless of the type, the nature of the abovementioned faults is the same.
Actually, a considerably high current level circulates inside the windings without contributing to the torque production capability of the motor. So, it is considered as a kind of loss. The only difference is the severity of the fault which increases with the increase in the number of short-circuited turns as well as the decrease in the short-circuiting path resistance. Ignoring the fault and letting it progress might also cause an irreversible damage to the motor tank and bearings. Therefore, diagnosis of the short-circuit fault is of great importance.
The following are some of the main reasons of generating the fault.
--Thermal stresses: These are produced by thermal aging or over-loading.
Respecting to a 10 C of increase in temperature, insulation lifetime reduced by a factor of two. A better class insulation is recommended if the motor is going to be used in a highly stressful environment.
--Electrical stresses: This type of stress is usually classified into two general categories, namely the insulation breakdown and the partial discharge. When a relatively large voltage variation rate, i.e., dv=dt, is applied, insulations are subjected to a breakdown and destruction. This is usually the case where the voltage goes beyond 5 kV.
--Mechanical stresses: This kind of stress is predominantly caused by several start-stop operations of the motor causing frequent warm-up and cool-down of insulations. As a result, cracks are produced and become larger if start-stop operations are not avoided.
--Environmental stresses: External and polluting substances can also disturb the motor operation. For example, pollution might cause an improper thermal exchange between motor and surrounding environment and consequently it leads to motor temperature rise. This in turn increases the risk of electrical failure of coils/windings.
Many efforts have been already undertaken just in case of analyzing different aspects of short-circuit fault. We are going to focus more on the original fault related harmonic components which are the results of the short-circuit fault. like all the other types of faults, the natural frequencies which are used for detecting the short-circuit fault are present in the motor structure and are the functions of the number of poles, the number of slots as well as the saturation profile of the machine. The presence of the short-circuit fault only changes the amplitude of the harmonic components and it has nothing to do with creating new components.
This was also the case in previous types of faults including the broken bar and eccentricity faults. So, it is time to address a part of principle harmonics generated by geometrical placement of the rotor and stator slots and windings. These harmonic components are called principle slot harmonics (PSH) which are some times used to detect a specific type of fault. Both stator and rotor introduce their own PSHs.
It is very well known that induction machines, of course in healthy case, consists of a sort of MMF components formulated as (3.44):
where p is the number of pole pairs, ws is the fundamental angular frequency and m 6g 1, g 0, 1, 2, . . . . Assuming that the number of rotor loops is n, the MMF component corresponding to the first rotor loop is obtained in the rotor reference frame as follows:
where Irmax is the magnitude of the rotor bar current. Following the same fashion, the MMF component of the neighboring rotor loop is analytically derived as follows:
It is worth noting that the upper index of the summation is set at infinity due to the fact that the rotor loop MMFs looks like a spike which can only be modeled accurately by incorporating infinite terms of its Fourier transform. The total MMF produced by rotor is calculated by adding up the loop MMF.
On the basis of the derived closed-form representation of the rotor MMF waves, it is clearly observed that MMF waves are only present for the cases u p; u p ln and u p ln; l 1; 2; 3; ....As u can only take positive integers, it follows that only for u p and J ln p the MMF waves exist.
Therefore, in addition to the fundamental rotor harmonic component for u p which deals with the armature reaction of the fundamental component of the stator, the rest obtained by u ln p demonstrate the rotor slot harmonics (RSH).
Regarding the stator reference frame, the RSH is expressed as follows:
Coupled with previous formulation, the higher frequency MMF waves produced by higher order components are given by:
The corresponding frequency is the same, but the number of effective pole pairs differ. Multiplying the MMF components by the air-gap permeance, which is a con tent term in a healthy idea motor, returns the magnetic flux density wave which produces the EMFs and subsequently the currents in the stator. From (3.48) and (3.49), it is comprehensible that the stator EMFs and currents will only contain the additional slot frequencies 1 l n p 1 s fs which are now the time harmonic components extractable using a Fourier transform. As seen, the spatial components introduced by the slotting effect are eventually reflected into the time-domain signals.
Under short-circuited turns or phases, a new set of waves will apply changes to the stator MMFs described as:
Accordingly, there exist the MMF waves at all numbers of pole pairs and direction of rotations. One of the waves rotates with the same frequency of the fundamental component but in an opposite direction. If a normalized Fourier transform is used, no change will be observed in the current spectrum as it is always normalized to zero. However, there should be a change in the magnitude of the RSH. No new frequency should be added to the current spectrum if the short-circuit fault takes place in the stator. The fault only contributes to an increase in the RSHs.
In the first instance, consideration is given to the simplest case where the coil has only one turn from which it is possible to draw some important conclusions.
Fig. 13, however, shows one-phase group of three coils. It is assumed that interturn short-circuit arises between points a and b, as illustrated. It is clear that the circulating current has a closed path. From simple theory, it is clear that the path A-X can be expanded to two independent circuits. From Fig. 13, we can say that the phase current and the current which flows through the short circuited coil, produce opposite MMF. Therefore, interturn short-circuits have a cumulative effect in decreasing the MMF in the vicinity of the short-circuited turn(s). First, when a short-circuit occurs, the phase winding has less turns and less MMF. Second, the MMF of short-circuited part is opposite to the MMF of the phase winding. Clearly, interturn shorts with more turns can be analyzed in a similar manner.
In most commercially available induction motors, coils are insulated from one another in slots as well as in the end winding region. Therefore, the highest probability for the occurrence of interturn fault is between turns in the same coil.
Here, it is assumed that the interturn short-circuit is between two turns in the same coil, and that one-half of the coil is short-circuited; this means that approximately 8% of turns of one phase are short-circuited. Simulation was carried out for this condition.
As a consequence of the interturn short-circuit, the MMF of the phase winding in which interturn short circuit exists changes, as does the mutual inductance between that phase and all other circuits in the machine. In addition, a new ''phase,'' which we call the short-circuited phase D is introduced. It should be assumed that for modeling, this phase has no conductive contact with other phases, but it is mutually coupled with all other circuits on both the stator and rotor sides.
The currents in stator circuits and rotor loops are assumed independent.
The machine with the following specifications is analyzed using the numerical model based on multiple coupled circuit approach and winding function analysis.
3kW; 415V; D; 50Hz; p 3 six poles machine S 36 stator slots R 32 rotor bars Stator phase winding consists of 6 coils, 1 coil per pole with 77 turns in one coil, i.e., N 462 series turns per pole per phase. Stator phase A winding scheme is:
A 1 6 12 7 13 18 24 19 25 30 36 31
The connection diagram of the stator windings of the experimental machine is additionally shown in Fig. 14.
Motor is loaded with 30 N m under the steady-state condition. Fault is made on such manner that 38 out of 77 turns is short-circuited in one stator phase coil, under one pole. We provide an interesting illustration of the healthy and faulty motors for different load (see Fig. 15) By referring to Fig. 15, it is observed that
--Increasing the load level leads to an increase in the motor current regardless of the short-circuit fault.
--The current reveals an increasing trend in both the transient and steady-state region upon the fault occurrence.
--The average developed electromagnetic torque is almost the same for the faulty and healthy conditions. However, the faulty motor contains some sort of low frequency harmonic components carried by the average value. This clear illustration of harmonic components in time domain is only achievable by the analytical models such as the winding function theory or the magnetic equivalent circuit. If an FE model shown in Fig. 11 is used for simulations, the torque ripple caused by slotting and saturation usually dominates the fault component unless the fault severity becomes very high.
--Similar oscillations are observed in the speed. Surprisingly, the average steady state speed decreases by the fault. This increases the power losses caused by the slip.
--The phase D (short-circuited phase) current is considerably more than that of the rest of the windings. The current circulates and makes the thermal stress so worse that the other healthy insulations also fail to operate well.
--Not all the motor signals get larger by the fault. The phase D current marks down probably due to the increase in the armature reaction in the rotor side.
So far, a lot of contexts have been mentioned in terms of the motor harmonic components, the PSH, the fault-related harmonic components etc., without directly addressing how these frequency-domain signals might be observed or studied. A couple of spectra regarding the motor current signal are put forward without going in depth of how they are calculated to explain first what a spectrum is and second how different frequency analyses are performed by means of a frequency spectrum.
To this end, refer to Fig. 16.
The output of a Fourier transform is usually demonstrated by frequency and magnitude planes. Normally, the horizontal axis is an indication of frequency contents of the processed signal, for example the current and the vertical axis shows the corresponding power or the magnitude. Therefore,
--The synchronous frequency, i.e., 50 Hz for the tested motor, possesses the largest magnitude in the spectrum. That is why it is called the fundamental component (see Fig. 16(a)).
--The rest of the spectrum drops down the mentioned fundamental component in terms of the magnitude. This distinctly explains the lower interest of higher order components in forming the shape of the current which is the processed signal.
--The entire spectrum is an almost featureless curve representing negligible information in terms of the higher order components. This arises from the fact that the number of rotor bars and pole pairs are equal to 32 and 3, respectively.
So none of the principal RSH could be expected. In order that lower rotor slot harmonic exists in stator current spectrum, the following condition should be fulfilled:
--For p 3 and n 1, 2, . . . , the lower RSH (RL_RSH) is equal to 24, 42, . . . . On the other hand, the condition for the existence of the upper RSH is satisfied for rotors with the following number of bars.
--This leads to RU_PSH 12, 30, 48, . . . for a six-pole machine.
However, in a faulty motor, as a consequence of interturn short circuit, there are all harmonics of ''phase'' D MMF. In other words, in the following magnetic flux density waves,
The order of space harmonic n could be u 1/3, 2/3, 1, 4/3, . . . So in general, the RSH could arise in current spectrum ( Fig. 17).
For u 1/3 and l 1 lower rotor slot harmonic exists:
Fig. 17 MMF of ''phase'' D - as analyzed motor is motor with p 3, fundamental harmonic n 1 means six poles. In case of short circuit in one coil, it means that phase D also produces subharmonics
Therefore, in healthy machine with S 36, R 32 and p 3, none of RSHs exists, as it could be seen in Fig. 16(a). However, in case of interturn short-circuit, both of RSHs exist in the line current spectrum, i.e., Fig. 16(b), and they are very prominent. This effect could be additionally amplified by permeance harmonics waves:
In addition, new harmonic component in current spectrum appears due to the saturation phenomenon.
(3.61) now could attain 1 for u 1, u 2 1 2 1 (3.62) which means that new harmonic component at 150 Hz could appear as a result of the fault due to the following flux density wave:
However, this component does not exist in models in which the saturation is neglected. To validate the results from the dynamic model, an experimental investigation was conducted. The experiment was performed in the following manner. A standard commercially available motor was dismantled and isolation of the few turns from the same coil (in the end region) was mechanically injured, i.e., scratched. These spots were soldered conductors which were taken out from the motor. Short circuit was made between these conductors. Therefore, turns were shorted externally. By measuring EMF between conductors and having known winding details, we were able to conclude how many turns in one coil were shorted.
In the case of inrush current which was experienced particularly when two turns which are in the neighborhood (in the electrical sense) were shorted, the short circuit current was reduced by means of an externally placed resistor. In these cases, current was limited to the value of double-rated current for a short time during the experiment.
Fig. 18 shows the spectra of line current for a loaded machine for a healthy and a faulty condition, respectively. Fig. 18(a) shows that in a healthy machine, frequency components, the result of the saturation of magnetic material (150, 250, 350 Hz, etc.), exist. In the healthy condition, only the upper rotor slot harmonic is visible at 568 Hz (s 2.8%). From Fig. 18(b), it is clear that as it is predicted in the simulation model, the most significant changes arise at harmonic components of (1 lR(1 s)/p)fs. Now, the lower rotor slot harmonic (at 469 Hz) is prominent and the upper harmonic has risen. Moreover, the 150-Hz harmonic component is considerably higher under the fault condition.
What has been already proposed in terms of PSHs existing in induction motors is actually the basis for future analysis not only in the case of short-circuit fault but also in the case of other types of faults. Furthermore, the appreciable practice of the frequency-domain analysis of the motor current was extracted and analyzed. What is not really deductible about faults in a time-domain analysis can be somehow easily detected, followed and analyzed by means of a frequency domain. The PSHs related to the short-circuit fault are the best examples of this kind and in the same fashion, the broken bar and eccentricity fault will be addressed shortly in the next sections. Considering the mentioned points, three apparently distinct but inherently correlated processing domains including time, frequency and time-frequency ones are going to be discussed in Sections 8-10. In the current section, the time-domain variations are emphasized more while the frequency analysis will be further studied and combined with the time-domain information to introduce a generalized solution to fault diagnosis challenges.
Measuring the magnetic, electrical, mechanical and partly thermal quantities of the motor, we will also go directly through the property of time and frequency components of every single motor variable to see how different faults apply changes to motor variables, how the fault information could probably be extracted and how the extracted information is used for a precise detection, determination and diagnosis procedure.
3.5 Laboratory-sale implementation of induction motor faults
Any fault diagnosis procedure will be nonsense if experimental investigations and validations are not included in the procedure. In fact, after all the theoretical and simulation-based analysis, what really matters in industry is measurements reflecting the real motor behavior in faulty conditions. Moreover, although developing the basic ideas mathematically or even by means of simulations, whether accurate FE or analytical models, helps researchers and industries investigate practically the impossible number of situations, models still suffer from some sort of inaccuracy depending on the number of assumptions made to build models.
Therefore, experimental study of what happens in reality should be an inseparable part of any diagnosis procedure of electrical machines. More importantly, some of the real world influential factors such as the thermal stresses, the non-homogenous magnetic materials and also every single multi-physics-related problem cannot be analyzed accurately unless a real motor and drive system is incorporated. This discussion necessitates presence of a straightforward implementation of the motor- drive systems along with the corresponding faulty conditions including all three major types of fault discussed in this section.
There are some prerequisites which should be considered prior to any setup preparation for the experimental test rig. The prerequisites are as follows:
--The motor should not be so small that implementing the fault is difficult or practically impossible. This really makes sense as motors in which the faults take place are of a large power, for instance hundreds of kilowatts.
--The motor should not be very large because of two main reasons. First, as the focus is on preparing a logical laboratory-scale setup, dealing with a relatively large motor during the fault implementation will be a very tricky and over whelming task. Second, the larger the motor is, the higher the investment will be. Most of the time, academic research budgets are limited, and having a solid investment plan is essential.
--Peak a motor for which an industrial drive could be easily found. Do not go through specifically dedicated motors built for special applications such as ultrahigh speed ones. Catching a drive for this kind of applications is not easy; moreover, research output will not probably be general enough to be used in other applications.
--Sometimes, more than one rotor is required if the goal is to study the effect of various broken bar positions. Therefore, include the corresponding prices in the investment plan.
--Keep in mind to apply reversible faults such as eccentricity prior to applying an irreversible defect like bar breakage if more than one type of fault should be investigated.
--Take the safe side and start from the low fault levels. Even if a reversible fault such as eccentricity of the rotor is studied, the reassembled healthy motor might not be as the same as it was initially right after the factory production.
If a higher fault level is applied, the motor might be subjected to un-repairable damage and not be able to be used later.
--Again, choosing a medium or not very small power motor is usually preferred as it is also robust enough against the environment noise which might affect the faulty motor signals and consequently the diagnosis procedure.
--Try to prepare a general application drive such ABB ACS800 which can be applied to all types of motors regardless of their specifications. The only restricting factor in choosing general application drives is their power limits which should be matched with the motor power.
--Try to prepare a drive consisting of both the open- and closed-loop control strategies. Unfortunately, there is only a DTC or FOC strategy implemented in one single drive. If one looks for a wider range of useful strategies, s/he should go through providing more than one drive. It is not recommended to build the drive on your own. If you wish so, make sure to implement every influential factor which might be included in an industrial drive. Otherwise, the results might not be convincing.
--In the case of a line-start application, make sure to have balanced three-phase network. Otherwise, the diagnosis results achieved from one phase might be different from the one obtained from another phase. To deal with an unbalanced network, using an autotransformer is a good solution. In the case of inverter-fed applications, it is not a requirement as the drive itself outputs balanced three-phase signals unless a switch fault or problem occurs.
--Prepare safe data acquisition instruments.
--Prepare a processor such as a computer or digital signal processors (DSP) to process the measured data to extract the fault indicators. A very useful and comprehensive discussion on this topic will be shortly provided in this section.
Tbl. 3.2 Induction motor specifications Fig. 19 (a) Tested induction motor and (b) corresponding winding layout 3.5.1 Three-phase induction motor The key element of any test rig built for the diagnosis purposes targeted in this guide is an induction motor. The discussion is continued by considering a three-phase induction motor with the following specifications (see Tbl. 3.2):
The real motor is shown in Fig. 19. This is exactly the same motor as what was previously simulated using the FE approach. So it consists of 28 rotor bars and 36 stator slots. The stator and rotor are both made of silicon steel. The rotor bars are made of aluminum. The rotor consists of two cages facilitating the motor start-up by increasing the start-up resistance of the rotor. The number of slots per pole per phase is equal to 3, so the winding layout should be the same as Fig. 19(b) as it consists of a concentric single layer winding topology. In high-power applications, double layer winding topology is more popular. By ''layer,'' we mean the number of separate layers of phases placed inside one single stator slot. The available network to supply the motor contains three phases with an effective value of 380 V. There fore, the peak value of the supply voltage is equal to 538 V. The network should be connected to the motor terminals with a delta connection (see Fig. 19(a)). For a star connection, the motor operation will be degraded due to the lack of supply voltage. Coupled with the mentioned points, presence of a rigid bench to which the motor is hanged firmly is another crucial requirement which reduces the unwanted vibrations caused by improper or loose motor placement. The more the degree of freedom of the bench is, the more flexible the motor assembling and disassembling would be.
Fig. 20 shows a typical autotransformer used in this study. There is one input and one output set containing four terminals three of which is related to phases, and the remaining one is the ground terminal if required. The adjusting wheel is used to control the voltage level. An autotransformer is an electrical device with only one single coil per phase and one or more terminals at the secondary to provide various voltage levels for the user. The utilized autotransformer consists of the adjusting wheel instead of the output terminals to make it possible to obtain smoothly vari able voltage range. The network voltage is applied to the primary winding(s) and the secondary winding(s) returns the required voltage(s). The scale of the voltage change applied by the transformer is not considerably large in fault diagnosis procedures. The main responsibility of this device is to stabilize the voltage amplitude partly different from the rated one. This apparatus has nothing to do with the supply frequency and is simply used to control the voltage level.
SAFETY NOTE: Before turning on the setup, ascertain that the adjusting wheel is located in a fair position in terms of the ratio of turns. Autotransformers are normally capable of increasing the voltage up to three times the rated one and this might cause life-threatening risk if it is not taken into account.
Another key point to be considered is how the motor is managed to be used in inverter-fed applications. To do so, a very famous drive, i.e., ABB ACS800 is used in this study (see Fig. 21).
ACS800 is an industrial drive including the following features:
--controlling the time-domain characteristics of the motor speed and torque
--regenerative Braking mode
--DC magnetization to obtain the maximum torque capabilities of the motor
--flux weakening mode
--parallel motor control mode.
One of the most incredible advantages of this inverter is its ability to control motor speed in sensor-less method. In fact, there is no resolver or encoder connected to the motor shaft to measure its mechanical speed, although it is also applicable using this inverter. Mechanical speed is estimated by measuring electrical variables with a very high precision. The operating mode can also be selected among SCALAR and DTC. The main circuit of the drive is shown in Fig. 22. The significant parts are listed as follows:
--the control panel
--the start-up prevention switch (X41)
--the I/O board
--the input, output, DC bus and external braking resistor connections
--the six-step inverter.
The starting point of any motor-drive operation is to define the motor parameters including the rated values as well as its electrical quantities, namely the resistance and inductance of the drive, using the control panel. This is a must-do step prior to any other progress. The entered values facile the torque and speed estimation per formed internally by the drive if a sensor-less control strategy is used. Otherwise, the speed and torque signals can be passed to the drive through the I/O board using sensors which are going to be discussed shortly. Moreover, the estimated torque and speed signals are likewise available in the I/O board. So the I/O board is really helpful in case if an advanced data acquisition hardware is not accessible. Different drives provide different numbers and types of I/Os. Therefore, it is proposed to refer to the user manual to be informed of details. Furthermore, input and output power cables should be connected to the embedded ports shown in Fig. 21.
There are also three other output ports allowing users to access the DC bus voltage and also connect the external braking resistor to the drive. The latter is used to consume large regenerated braking power with the goal avoiding higher thermal tensions applied to the drive.
It is very important to know that there are some safety rules to follow. For example, the drive should always be installed inside a grounded metal frame (see Fig. 23) to prevent the external noise which might affect the control-level measurements. In addition, the life-threatening risk is reduced due to the fact that the frame voltage is deliberately brought to zero by connecting a ground wire to the body. A very important practical aspect is that if you use a computer to analyze the sampled motor signals, computer supply plug must be different from that of drive.
Otherwise, you will observe a very undesirable signal to noise ratio in your sampled signals. Another alternative is to use three-phase chock.
Generally, the installation steps are as follows:
--Identify the frame size based on the user's manual.
--Select the required cables including the power and control cables depending on the motor-drive ratings the environmental conditions.
--Check for the availability of the entire necessary module in the drive box.
--Prepare a chock to prevent inter-circuital interference between the drive and the data acquisition power supplies.
--Install the drive inside the metal frame.
--Connect the grounding cable of the frame.
--Connect and shield power cables. It is essential to use shielded power cables specifically where a long cable should be placed between the motor and the drive. This is the major requirement to surpass the radio frequency emissions radiated from the drive signals.
--Follow the cabling instruction to avoid improper installing angle of the cables at joints.
--Connect an external braking resistor if you might have a regenerative braking operation. This mostly happens when another drive which acts as the motor load is connected in parallel to the main drive. In this case, two drives share the DC bus voltage.
Finally, the motor is connected to the drive as shown in Fig. 24. A set of fuses should be necessarily utilized as an electric safe guard in case if any undesirable over-currents take place (see Fig. 24). The positive terminal of the braking resistor is regularly connected to the positive terminal of the DC bus, and a built-in terminal is embedded into the drive for the negative terminal. Both the motor and the drive bodies must be grounded together.
Usually two types of reference values are implemented in every drive, speed and torque reference values. Depending on the application in which the motor- drive system is used, different reference values might be chosen. Then, the rest of the operation is handled by the drive for controlling the motor speed or torque. It should be noted that precise determination of the motor quantities such as the stator inductance and the resistance are the essential task for presetting the drive.
Otherwise, the drive might fail to estimate the motor flux, torque and speed accurately. As a result, all the control process should be questioned.
Another must-remember point is the acceleration profile adjustment which takes place at the very beginning step of parameter determination for the drive.
Usually two general choices are available, linear and user-defined curves. The state of the art is to use a linear acceleration or even de-acceleration profile. However, various control strategies certainly lead to a different profile of the motor quantities. This makes the diagnosis procedure a very complex task. Investigating the motor-drive behavior in the faulty modes is still an open area of research and readers are referred to the author's publications to find the potential research areas.
3.5.4 Motor load
This is one of the most demanding aspects required to be as precise as possible if an accurate diagnosis investigation is really needed. First, it is the motor load level which affects all the motor quantities, so the necessity of presence of an accurate equipment for applying loads is one of the concerns. In addition, there are several types of equipment functioning as a load for any type of motors including:
--AC machines controlled by a drive
--advanced programmable dynamometers.
These are the general types of loads functioning in different ways but fulfilling the same goal which is fixing the motor load level at a specific value or changing the load based on a specific requirement such as oscillating load. Now, we are going to discuss each of the available options one by one from the simplest to the most advanced one sorted above.
184.108.40.206 DC machines
This type of loads includes DC generators which are mechanically coupled to the shaft of induction motors, using a coupling device as shown in Fig. 25. The more reliable the coupler is, the less the amount of unwanted oscillations caused by improper placement of the motor or the generator on the bench will be. It is highly recommended that the motor and the generator be aligned along their shaft.
Otherwise, not only do undesirable oscillations harm the diagnosis procedure, but they also cause future mechanical defects if the system is used for a long time. DC machines are probably the simplest apparatus by means of which the motor load can be controlled. The underlying idea is to make the machine operate as a generator while it supplies a resistive load like what is shown in Fig. 26.
Significantly, the field and armature windings of the unitized DC machine should have a shunt nature as a series-connected topology suffers from the lack of field strength during the full-load operation. As a result, increasing the load, which is in turn achievable by adding a parallel resistive branch illustrated in Fig. 26, leads to a dramatic reduction of the field of a series-connected topology; hence, the generator starts to be demagnetized. This means that the DC machine would not be able to compensate for the increased load level, and the total system load drops down the desired value. This only happens if the rated power of the DC machine is almost close to that of the motor. To come up with a solution, a considerably larger DC machine is recommended. Otherwise, a shunt topology should be used.
One of the drawbacks associated with the mentioned approach of load control is that the load level indicator is the induction motor current or speed while what really matters in fault diagnosis applications is the motor slip. Nevertheless, the proposed system seems to be very simple and straightforward while some precautions in terms of the appropriate load-level control should be always kept in mind.
The shaft speed can also be measured by a tachometer.
The proposed scheme is considered as of the unsafe approaches if an amateur practitioner uses the equipment. The reasons are the naked terminals of both the induction and DC motor along with the fact that the load should be changed manually by switching the resistors. Therefore, the user should be alert enough to avoid undesirable risks.
220.127.116.11 AC machines controlled by a drive
This scheme of loading the induction motor is very straightforward, useful, safe enough, but a little costly (see Fig. 27). The required ingredients of the scheme are as follows:
--tested induction motor as the main machine
--another AC machine, preferably a synchronous one, as the generator acting as a load
The whole system is supplied by only one three-phase network connected to the machines and the drives through a set of fuses preventing the electrical stresses in the network side if any over currents happen in the system. Note that the fuses are supposed to be there any time. The three-phase fuse set should be used; moreover, two other fuses should connect the positive and the negative terminals of the DC buses of two drives. A choke is also required to prevent high-frequency PWM signals from circulating through the network. Drive#1 controls the induction motor while Drive#2 is connected to the AC machine, acting as the load, whether synchronous or asynchronous. The second motor-drive system should be set at torque control mode while the first system can be used in either torque or speed control mode depending on the test requirement. Preferably, the power, speed and torque ratings of the second motor-drive system which is used to act as the load should be similar to that of the induction motor. Otherwise, the AC machine power should be necessarily larger than that of the induction motor. Moreover, if there is so much difference of speed between the machines, a gearbox whose main operation is to change the speed while ideally transferring the same power is used to couple the shafts mechanically.
Due to its unique capability in accurate control of the torque or speed quantities, the closed-loop strategy should be hired in the load side. Otherwise, it is not guaranteed that a constant load is applied to the shaft if an open-loop strategy is used. So make sure to prepare a drive which is capable of handling closed-loop strategies, no matter if it is of a DTC or FOC nature, both work well. To reduce the budget, look for a drive with a sensor-less control included. Otherwise, a resolver or encoder should be prepared as well.
Whenever a single drive is connected to the network and the load is provided by the first scheme, the DC machine, all the required currents including the transient one come from the network and if a large power motor is utilized, other network-connected utilities might be affected harmfully due to the loading effect of the motor test setup. However, the second scheme, two motor-drive systems, is as demanding as the first scheme as the induction motor current is partly supplied by the AC machine which operates as a generator. So the current is circulated among two machines, and the network is only responsible for the power supply of drives.
The situation is somewhat different in transient start-ups while once the system comes to a stable point, the network normally operates with a minimum current defined by the drives.
A programmable drive #2 which facilitates applying a non-constant load to the system is recommended. This kind of drive is useful when phenomena such as oscillating loads are studied. Otherwise, studies should be limited to a constant but altering load level which means a part of actual operations are neglected. So the generality of the investigations directly depends on the capability of drives. This is an important feature which we are aiming at in this guide. With the use of the DC machine scheme, it is almost impossible to apply an oscillating load. This is another shortcoming of the first scheme highlighting it as an inefficient way of tackling fault diagnosis matters. To put it differently, it is not mainly proposed to go through the first scheme of motor loading.
On the other hand, the second scheme does not essentially ask for an auto transformer connecting the network to drive systems. The reason is that the drive itself takes care of stabilization of its own terminal voltages and eliminates the need for an extra stabilizing tool. This is another advantage of the mentioned motor- drive systems in use. Furthermore, the braking resistor is not required anymore if the motor and AC machines powers are properly matched, or in the best case, the AC machine power exceeds that of the induction motor.
There is one important question ''Is it possible to test a line-start induction motor, using the second scheme?'' The answer is ''YES.'' By removing the drive#1 and separately supplying the induction motor and the drive#2 to the network, a very fantastic line-start setup by means of which a pure constant load level can be easily applied is achieved. Do not forget to set the drive#2 at the torque control mode.
18.104.22.168 Advanced programmable dynamometers
This is certainly the most accurate and appealing way of applying various load levels to an induction motor under the test. Dynamometers generally operate on the basis of absorbing the energy of the motor shaft and acting as a load. There are able to operate at various torque-speed profiles providing the commanded mechanical load for motors. Sometimes, there are measurement devices implemented to mea sure speed and torque to provide a proper command while some of the types of dynamometers do not necessarily require a speed measure ( Fig. 28).
Regardless of what is connected to the dynamometer shaft, it operates as a load-producing equipment guaranteeing a specific torque on the shaft. On the basis of what structure or material produces the braking force acting as a load connected to the shaft, various dynamometers are available. Three important ones are as follows:
--Hysteresis brake dynamometers
This is a perfect choice for experimenting motors ranging from fractions of a kilowatt to medium-power applications. A full range of motor speed including the free-run to locked rotor can be easily controlled by means of a hysteresis dynamometer. This is possible just because hysteresis dynamometers do not generally need a speed measurement to precisely output a torque. They are indeed accurate, and the maximum error, depending on the size and accuracy of the configuration, does not go beyond 1%. Considering the nature of hysteresis dynamometers, they can be programmed to be even used in varying load applications.
--Eddy-current brake dynamometer
The main feature of this type is the dependency of its torque to speed of rotation. It is something like fans in which the developed load is proportional to square of speed. So not all range of torque-speed profiles might be covered by this means. However, if a high-speed application should be tested, eddy current dynamometers are the best.
--Powder brake dynamometers
This type is usually recommended for a considerably high torque application such as traction motors while the corresponding speed level should not be so much high. Again, a very well-designed dynamometer of this type might reach a maximum error of 1% in the worst-case scenario.
Dynamometers usually come with a comprehensive measurement and analysis package called power and spectrum analyzers by means of which all the ordinary motor signals including the voltage, the current, the active and reactive power, the inductance and also the corresponding frequency and time-domain variations are explored. This gives users the opportunity to access the essential mediums of fault diagnosis procedure straightforwardly. However, such a measurement and loading equipment is supposed to be very expensive. An example will be provided later in this section.
3.5.5 Implementation of broken bar fault
Initially, let us provide a complete 2D view of an induction motor cross-section shown in Fig. 29(a). The stator and the rotor consist of 36 slots and 28 bars, respectively. Every 9 slots and 7 bars form pole out of 4 poles of the motor. Due to the symmetry of the rotor, it is not important which bar is assigned as the first bar of the rotor. Then, the other bars are numbered clockwise or counter clockwise from 2 to 28. The air-gap length of the motor is equal to 0.45 mm ( Fig. 29(b)), and the bars possess one upper and one lower parts dealing with the motor start-up and steady-state operation, respectively.
The air gap is normally so small that even a very negligible amount of bearing defect or eccentricity fault leads to a considerable percentage of air-gap distortion causing an unbalanced motor operation. A very promising way of doing this is to fix the motor housing on the working bench and clamp the shaft from both ends and then try to loosen and open the plates. To perform it more smoothly, preheat the plates close to the bearing area to make sure the bearing nests are loose enough.
Prior to any fault implementation, the first step is to disassemble the motor by opening the two end plates. Preferably, start with the load-end plate. Make sure to clamp the rotor shaft and not to release it while opening two end plates. Even if you intend to release the shaft and put it on inner surface of the stator, do it safely to prevent the stator material from being damaged or rubbed. If not so, the stator would be apparently useless for future fault diagnosis attempts. Finally, take the entire rotor body out and put it somewhere safe. Make sure to do it gently with the goal of protecting the rotor material. By ''material,'' we mean the silicon steel material, not the bar material because the bars are often intact and inaccessible while the outer layers of the silicon steel materials are of course in contact. The bearings are mainly attached and fixed to the two shaft ends. So leave them the same unless an eccentric rotor should be investigated (see Fig. 30).
In this specific rotor, the bars are in the shape of a deep bar which consists of two parts, the upper and the lower cages, as shown in Fig. 31. This makes the fault implementation somewhat tricky as there is not a uniform distribution of the bar cross-section across the rotor bar depth. So while applying the partial broken bar, it is not a 100% accurate practice. Nevertheless, applying a full broken bar is easy and precise. The main aspect of implementing the breakage is to know the exact dimension and shape of bars, as it is visible from outside of the rotor.
Therefore, having the structural map of the motor in hand is essential.
Considering the double cage rotor bars shown in Fig. 31, the maximum diameters of the upper and lower cages are equal to 6.2 and 5.4 mm, respectively.
So, it is obvious that a full broken bar requires an elimination of a crosssection covered by a width 6.2 mm, while the partial broken bar only asks for a smaller portion of the mentioned value. The question is that how the removal of the crosssection is done. Actually, the goal is to partially or fully eliminate the bar current and prevent the corresponding bar from contributing to the magnetic field generation. How is it handled? To apply broken bars fault to the rotor, the rotor bar should be drilled to pre vent the current from passing through the bar from one end to the other end. In general, there are two main locations to make the desired hole ( Fig. 32):
--somewhere between two end-rings along the bar length
--right at the connection of bar and end-rings joints.
The latter is the most probable location of the fault in real motors ( Fig. 32(a)).
The joint between bar and end-ring is not always as strong as it should be due to some internal cracks or bad welding or casting process. When the motor is subject to undesirable thermal or mechanical stress, the joint is broken and it is literally said that the bar is broken. It is not proposed to drill the hole at the joint of bar and end-ring as it probably damages the end-ring which leads to a worse fault level.
First of all, it is better to make a very small hole on the rotor bar, somewhere between two end-rings, using a very thin drill. Do not put so much pressure on the drill because the bar is made of aluminum which is a really soft and easily drilled material. Keep in mind to use fixture to prevent the rotor from moving when it is drilled. Otherwise, the silicon steel material might be damaged. If so, not only the core losses but also the flux distribution will dramatically be increased. To make sure that you are just drilling the bar not the core, you have to keep eye on color of swarf coming out of the drill. If the color is bright, it is the aluminum which is drilled. Otherwise, if it is dark gray, you are drilling the core material. So you have to stop immediately. Be careful to drill the bar with a very high speed and low force level to guarantee that the drill would not brake and stick into the bar.
Depending on the diameter of drilling area, different levels of the breakage is applied. Fig. 31 clearly illustrates four different possibilities, namely the 25%, 50%, 75% and 100% breakage.
The formal course of drilling action is to utilize a stand-up drill like what is shown in Fig. 33. Do not lose the sight of the fact that the rotor should be certainly fixed by means of a fixture. Act very gently and smoothly! If you are going to investigate different fault levels ranging from partial to several full broken bars, go ahead with the smallest fault level, for example 25% partial breakage. Then, move toward the higher levels to keep the tested rotor less damaged. Note that the broken bars fault is an irreversible kind of fault leading to a permanent damage.
A very critical point is to get more than one rotor ready for experiments as you might also intend to study more than one breakage at different poles. So one single rotor is not enough to fulfill the requirements.
Partial and full breakages are two types of broken bars. If it is a partial breakage, it is called partial broken bar in which a fraction of healthy current passes through the bar. By increasing the level of partial breakage, the bar resistance is increased up to almost infinity. Sometimes, there is full broken bar. This is simply known as broken bar fault. It is mostly considered that the resistance of a broken bar is infinite and no current passes through it, although it is not infinite when the bar is partially broken. What really happens is a bit different due to the existence of interbar currents. Although the current might not be able to pass through one bar in full breakage case, it might enclose its pass through cracks existing in core between two or more bars. This phenomenon has not yet been studied deeply, but the effects of interbar currents have been observed in different tests. On the basis of this claim, the resistance of a broken bar is not infinite at all. If you need to simulate the broken bar fault, you might choose a larger value compared to that of the healthy motor. This value will be discussed in the next sections. Sometimes, more than one broken bar, for example 2, 3 or more, might exist or happen in a rotor. The broken bars could be in adjacent or nonadjacent locations. So the broken bars fault is categorized into three main groups as follows:
Fig. 35 Broken bar (bb) locations (a) healthy, (b) 1 bb, (c) 2 adjacent bbs (case 1), (d) 2 bbs at half pole-pitch distance (case 2), (e) 2 bbs at one pole-pitch distance (case 3) and ( f) 2 bbs at two pole-pitch distance (case 4). (bb: Broken Bar)
Fig. 34 shows partial, 1, 2, 3, 4 adjacent broken bars. As the entire rotor circumference cannot be shown in 3D figures, the nonadjacent broken bars located at different poles are shown in Fig. 35 by means of a 2D representation. P1, P2, P3 and P4 stand for first, second, third and fourth poles, respectively. Each small gray circle is the symbol of one bar. Red color means that the bar is broken.
The number of nonadjacent broken bars might vary from 2 to larger numbers. (Instead of color, special signs must be used to have clear figures in the black and white hard copy of the guide.) As you notice, there could be various degrees, numbers and locations of the broken bars. So three totally different concepts, briefly addressed before, are introduced as follows:
--Detection: Monitoring incipient broken bars fault occurrence
--Determination: Monitoring number of broken bars
--Fault-location: Monitoring location of the broken bars.
Combination of ''detection,'' ''determination'' and ''fault-location'' procedures builds a very comprehensive advanced industrial concept which is called ''Diagnosis.'' The same is valid for the other types of motor faults. Diagnosis is not a specific process of monitoring for electric machines. It is a very complicated process which is required in all engineering and medical applications to provide a safe and reliable operating condition not only for devices but also for technicians.
Taking the possibility of having different levels and locations of the fault into account, one can easily understand the struggling of the diagnosis procedures based on which users, researchers and technicians are trying to detect, determine and even locate the fault. It is a really overwhelming task unless a clear interpretation of faults and their effects on the motor signals is prepared. That is why a very basic to advanced discussion of every influential factor of motors, drives and faults have been and will be discussed in this guide. Ignoring one important aspect, something like the location of the fault, would probably result in unsatisfactory outputs leading to an incorrect maintenance process.
Having provided the experimental details in terms of the setup preparation and also the broken bar implementations, now it is time to tackle the eccentricity fault and its experimental sides. To learn more, have a look at the next subsection.
3.5.6 Implementation of eccentricity fault
So far, different ways of producing eccentricity fault in a laboratory scale have been proposed in the literature. For example, static eccentricity can be the output of the following approaches:
--to use a faulty bearing
--to design and build specific plates enabling us to change the vertical position of the bearings
--to replace the bearing cage by an eccentric one and then use concentric rings around the cage to fill the empty spaces
--to place the concentric bearing cage between the eccentric rings inside and outside the cage
--to remove the plates, fix the rotor on stands and the stator on adjustable stand In addition, the following approaches can be used to apply a dynamic eccentricity:
--to couple an unbalanced load to motor
--to chisel the bearings housing and fill the empty spaces by means of eccentric rings
--to chisel the bearings housing and make an eccentric space and fill the empty spaces by means of non-eccentric rings
--to replace the bearing by bearings with a larger inner race diameter and fill the empty space by means of eccentric rings.
Using one static and one dynamic approach simultaneously introduces a mixed eccentricity fault. Some of the mentioned approaches are destructive. This means that the motor structure is damaged permanently after applying the fault. In the case of destructive approaches, returning the motor to its healthy state will be almost impossible. Moreover, the fault level cannot even be changed if a destructive approach is used. Some of the approaches require a sophisticated measurement tool to measure the level of eccentricity applied to bearings.
We decide to stick to an approach which reduces the number of disadvantages mentioned above. Mainly, the approach should not be destructive and not require a specific measurement tool. So various types and levels of eccentricity can be applied and eventually removed from the motor to get it back to a healthy operation. It is an extension of the forth dynamic approach. For this purpose, instead of the main bearing with the code 6309, another bearing called 6011 whose inner race diameter is 10 mm larger and outer race diameter is 10 mm smaller than that of 6309 is utilized. Placing the new bearing helps us with two empty spaces inside and outside it and allows us to fill both spaces by means of rings leading to the possibility of both the static and dynamic eccentricities. So the steps are as follows:
--to install a concentric ring inside and an eccentric ring outside the bearing to produce a static eccentricity. The fault severity is controlled by means of the level the eccentricity of the outer ring.
--to install an eccentric ring inside and a concentric ring outside the bearing to produce a dynamic eccentricity. The fault level is controlled by means of the level of eccentricity of the inner ring.
--to combine the previous two approaches to apply a mixed eccentricity fault.
Finally, the initial healthy motor can be assembled again using the replacement of faulty bearings by the healthy one. A very clear illustration of the mentioned steps is provided in Fig. 36. The challenging part of the implementation is to appropriately prepare the eccentric rings with an exact level of eccentricity. As the air-gap length is very small, a very accurate tool such as a computerized numeric control machine might be required. This is probably an expensive but appreciable practice.
Now, let us switch to bearing fault and a very simple but intuitive ways of applying defects to it (see Fig. 37). Simply drill the inner or outer race to produce the inner race or outer race fault. To apply a ball defect, it is better to apply a crack or breakage to one of the balls. So it requires disassembling the bearing.
3.5.7 Implementation of interturn short-circuit fault
In a healthy condition, the only accessible parts of the turns or coils are the end terminals allowing us to connect them to the supply while a short-circuit fault stands in need of new electrical connections as shown in Fig. 38. These new connections are definitely different from the terminals and provide a current pass through somewhere in the middle of one of the windings, a, b or c to the same winding, another winding or even the ground (motor housing). Respectively, they are called interturn, phase-to-phase and phase-to-ground fault. Therefore, to apply a short-circuit fault, the insolation of at least two turns should be partly removed to access the turns. So it is certainly a destructive task and needs a careful attention.
Even after removing the insolation, an additional resistance shown by Rf should be used to limit the circulating fault current to a safe value. Actually, if the fault connections are attached to each other, using a low resistance wire, the fault current in the new phase might go beyond control, and the phase winding(s) burns completely. In this case, the motor will be useless.
Depending on the fault severity, location and type, different values of Rf are demanded. For example, when dealing with phase-to-ground short-circuit fault, probably the larger Rf should be used as it is often the electric path with the smallest resistance. Hence, a larger circulating current will flow for a given path voltage.
However, the interturn fault, which is usually the most possible case, is of the smallest current, so the corresponding Rf might also be equal to zero, depending on the insulation quality. This is actually the insulation and partly the copper quality which define the maximum allowable circulating current and subsequently the Rf value. In fact, the more the insulation and copper endurance is against the temperature rise caused by a large circulating current, the smaller the value of Rf needs to be. Therefore, higher levels of fault might also be studied. High-quality insulation also makes it possible to sample a larger time period giving the opportunity to have a better spectral resolution. Rf should be a high-power resistance which is capable of tolerating large power dissipation. Then, Rf is to be electrically connected to the turns which are planned to be short-circuited. As the turns are not accessible through the stator stack length, the only part facilitating the process is the end-winding areas coming out from the stack.
In practice, as investigating real large current faults is impossible due to the fact that the motor will be permanently destructed, the trend is to only analyze lower levels of fault to first find proper indicators and then check how the proposed indicator depends on the fault increase or the other influential factors. The other faults are treated the same while some of them such as eccentricity fault are of a reversible nature pointing it as a motor friendly type of fault.
The aim of this section is to deliver the real sense of fault diagnosis and their laboratory-scale implementations. On the other hand, as the very beginning step of the diagnosis procedure, signals should be prepared for processing step. This is why measuring, or in other words, sampling motor signals including thermal, magnetic, electrical and mechanical signals are of a great interest as they are the mediums reflecting the possible faulty behavior. Motor signals such as voltage and current and their corresponding temporal and spectral variations are kind of signatures for any motor and differ depending on the motor type, the fault type, the processed signal and also the utilized processor.
Basically, an accurate measurement of proper motor signals is the most important concern of any diagnosis procedure. Therefore, we decide to establish a useful and comprehensive analysis of various types of sensing and sampling motor signals. To this end, move toward the next section which discusses signals and the corresponding sensor implementation.
3.5.8 Signals and sensors
One of the most well-known and significant motor signals is probably the voltage which is responsible for providing the amount of torque required for rotation.
Although in line-start applications, there is no point of generally using the voltage as a signal for the diagnosis purposes, in inverter-fed applications it plays a vital role in defining some specific aspects of faults such as justifying the possible differences between various supply modes. However, the voltage might also be useful in a line start application if calculation of quantities such as winding inductances is the main goal. Moreover, the time-domain samples of the line voltage are simply available in the I/O port of drives or by means of built-in packages or interfaces developed for a drive. Therefore, in drive-fed motors, using additional instruments is not recommended, but in case a line-start application is under the test or there is no access to drive interfaces, one might use a ''Voltage Transducer (VT)'' specifically developed for this kind of applications (see Fig. 39). VTs are promising tools to measure and output a scale voltage exactly similar to their inputs which is the motor terminal voltage. A common structure of VTs is illustrated in Fig. 39(a).
Any VT consists of a transformer used for isolating the primary and the secondary windings to increase the safety and also possibility of the measurement, using a small output voltage. The input voltage might be very high. A restricting resistance connects the terminals to the VT and it should have a considerably large value to avoid the loading effect of the VT. Then, the output of transformer is connected to an op-amp for outputting a scaled voltage measured in the M (measurement) terminal. There is also a series-connected measurement resistance to prevent the output current from running above fractions of an ampere. If the output of voltages of transformer becomes larger than the supply voltage of the OP-AMP, the output is saturated and will represent a flat-topped signal. So, make sure the maximum terminal voltage does not go beyond the rated limits of the VT.
Using VTs is very simple and straightforward, and the only necessary additional thing is a DC voltage source to supply the OP-AMP. It is worth noting that the supply provides a positive-negative polarity voltage. Otherwise, one side of the signal, either the positive or negative side, is cut off in the output. The LEM company sells a wide variety of VTs as well as current transducers (CT) ranging from very small to medium ratings (see Fig. 39(b)). Every single product of this company has its own specific datasheet in which the proper usage is provided.
As a principle ingredient of diagnosis procedure, the current should be considered as the most tackled and useful signal in any procedure. Both the time and the frequency analysis of this practically appreciated signal have been matter of various investigations, so an abbreviated term called MCSA which stands for ''motor current signature analysis'' is usually assigned to the process of investigating the fault, using the motor current. The widespread use of the motor current is under lined by the fact that it reflects almost all the essential fault behavior and also it is the easiest and safest signal in terms of sampling. Unlike the motor voltage which might be very dangerous if precautions are not taken into account, the current sampling is painless. The only required instrument is a CT, especially a Hall-effect sensor (see Fig. 40). The connections look similar to that of a VT except the input connections. Instead of a simple isolated transformer, a Hall-effect sensor, which does not require an electric connection in the primary, is implemented. The primary is the motor terminal wires passing through the middle open space of the CT shown in Fig. 40(b). Using the magnetic induction on the secondary winding of the sensor, the transformer output is passed to the OP-AMP and then scaled to the output which is the same as that of VT.
In general, there are two types of torque-measurement sensors as the following:
Invasive type of measurements is normally coupled to the motor shaft mechanically; hence, there is always a mechanical coupling which might affect the motor behavior in a bad way. In fact, there is the possibility of the signals used for the diagnosis being affected. Therefore, it is called ''invasive.'' The terminology of ''invasive measurement'' used in this guide is way broader than what is usually referred to in the literature. In fact, any device or even device placement revealing any kind of potentially harmful or disturbing effect might be included in this category. Otherwise, it is called a ''noninvasive'' technique. Definitely, a non-invasive method should be practically preferred to an invasive one. However, the corresponding noninvasive sensors (see Fig. 41(b)) which are principally based on the Hall-effect do not cover a wide range of applications. So it is recommended to prepare a mechanically coupled sensor (see Fig. 41(a)) if a larger range of torque and speed variations should be investigated.
One of the disadvantages of the mechanically coupled sensors is the presence of a mechanical connection between the motor and the sensor shafts. Thus, if eccentricity is investigated, there is a possibility of a bended sensor shaft as well.
This not only applies asymmetry in a long-term use, but also might reduce the accuracy of the sensor. However, both types are usually robust enough to withstand sever applications up a certain point. Regardless of the type, the associated error of torque sensors today does not usually surpass 1% which is an acceptable range for the diagnosis purposes.
Both types consist of a scaled electrical output to hand in the motor torque instances mostly in an analogue regime. Actually, as they mostly use analogue devices, the output torque has a continuous nature while digital torque sensors providing described signals are also available. Close attention should be paid to the selection of a digital torque sensor in terms of the sampling rate. The higher the sampling rate is, the higher the resolution and the number of observable harmonic orders will be in the torque spectrum.
Encoders and tachometers are two mediums of measuring the motor speed, each having its own advantages and disadvantages (see Fig. 42). Encoders are mechanically coupled devices while tachometer should not necessarily be connected mechanically. What makes a difference between these two types is the way they are used to measure the speed. The following are the main differences:
--Encoders are mechanically connected to the motor shaft; hence, are considered as an invasive method of measurement. On the other hand, tachometers work on the basis of laser light which sends and receives high-frequency waves reflected from the shaft. Normally, unlike encoders, tachometers do not pro vide us with an output port of speed measurement, and they only consist of a digital indicator indicating an average value of speed.
--Encoders are of course capable of sampling the speed variation while tachometers often return one single number in average. So if the goal is to merely define the steady-state speed of the motor shaft, tachometers are the best choices. Otherwise, in case of a need for an accurate time-dependent step-by step speed development of the shaft, encoders should be used undoubtedly.
Discussing the details of operating principles of sensors is not a part of this guide, and the only focus is on their application in accurate signal measurement. For more information about the principles, readers are referred to datasheets distributed by companies.
Magnetic flux density is the key agent of transferring power from the stator to the rotor. Without a magnetic coupling through the motor air gap, electromagnetic energy conversion is stopped and the motor operation fails. This is why it is some times considered as the heart of any electrical machine. On the other hand, although the original signal of supplying the motor power is the terminal voltage, what handles the rotation is the magnetic force or torque developed by the magnetic flux density.
Moreover, previous mathematical and simulation-based developments proved that any fault behavior, either in the stator or the rotor, is somehow transferred to the rotor or the stator only by means of the air-gap magnetic flux. The mentioned point necessitates the utilization of an approach to access the magnetic flux at least at air gap level. To this end, two approaches, namely an FE-based simulation and an experimental sensor, are available. The first approach is the subject of the next sections while here we are going to introduce the second approach.
Observing an induction motor structure, whether wound or cage rotor, one will simply understand that in an ordinary motor, there is no way of accessing the air gap as motors are totally encapsulated by the housing and there is no access inside. So the trick to access the air-gap quantities is to use an invasive technique called ''search coil'' shown in Fig. 43. The approach is called invasive as the motor plates should be opened, and then the search coil is placed around one of the stator teeth.
The larger the number of coils is, the larger the output voltage will be. However, even one turn works very well. Be careful not to increase the number of turns so much that it impacts the flux distribution of the main coils. The search coil provides two open terminals whose differentiated voltages should be equal to its induced voltage on it.
As the search coil is installed as close as possible to the air gap, the most dominant neighboring magnetic field is that of the air gap. According to the Faraday's law, while the magnetic field rotates and passes through the coil, a specific level of EMF is induced and measured at the terminals. This is a highly invasive but very useful technique. The magnetic flux density of the other parts of the motor including the stator tooth, the stator yoke, the rotor tooth and also the rotor yoke is not measurable at least by means of ordinary approaches. It is not also possible to implement such a device in a laboratory scale. This is why researchers rely on 2D or 3D FE simulations to study behavior of faulty motors. Furthermore, in the case of a cage rotor, rotor quantities are actually beyond reach, so the mentioned sensors will be useless unless a pre-implemented sensor, manufactured by factories, is used.
A very important point is to get familiar with the issues associated with magnetic characteristics of faulty induction motors. This is not achievable unless a very comprehensive FE model of motor is investigated. In fact, any posterior analysis including thermal or loss characterization highly depends on an accurate magnetic flux distribution prediction and FE approach makes this possible. Therefore, one complete section will be devoted to basics, formulations, implementation and postprocessing the FE analysis of healthy and faulty induction motors. Along with the other sections, the section related to the FE analysis definitely discriminates this guide from similar guides in which a shallow study of the motor quantities is addressed without providing justifications.
Practically, vibration analysis is the core diagnosis approach of induction motors.
Vibration in vertical, horizontal and axial directions returns astounding information on the motor behavior. Most of the time, it is by mistake assumed that vibration analysis only deals with mechanical defects and has nothing to with electrical faults. However, any type of fault, as what was previously mentioned, produce a specific oscillating trend causing monotonic mechanical pulsation of the motor body. Even the short-circuit fault which is a kind of naturally electrical fault also produces a pulsating air-gap flux density leading to a mechanical vibration. This is exactly what is sensed by a vibration sensor and returned as an electrical signal.
A typical vibration sensor, along with the possible installation locations, is shown in Fig. 44. Accelerometer is the conventional name of vibration sensors. They are magnetically mounted devices which can be rotated by user around the motor to capture vibration patterns of different parts of the motor.
There are types of two implementations of accelerometers, temporary and permanently located sensors, which are used in easily accessible and totally inaccessible operating areas, respectively. In other words, if the motor should be installed once and not accessed easily later on, it is usually preferred to install a permanently mounted wired sensor instead of a rotating accelerometer. If more than one accelerometer is mounted or used to monitor the vibration, data from all sensors is passed to a switch which is connected to a monitor or any kind of indicator. Then, sensors data is monitored one by one by switching between the sensors. Depending on the location of sensors on the motor housing, shaft, plates or even bearings, different patterns each revealing an aspect of faulty motor are achieved. It should be noted that it is also possible to mount a sensor internally inside the motor housing. Nevertheless, this might be considered an invasive technique and is not recommended. Having said that, the placement and location of sensors itself is a cause of decision change of a condition monitoring procedure.
If so, vibration analysis should be included in the category of invasive approaches as the way it is implemented affects the diagnosis procedure. However, once the sensors are implemented and fixed, outputs should be the same for a given faulty condition. So in this sense, it is a noninvasive technique. Equally important, vibration sensors are always mechanically connected to the motor.
Vibration sensors are comparably more expensive than VTs or CTs. Therefore, it might not be affordable by academic research centers whose budgets are limited.
In this case, it is proposed to use a search coil and measure the air-gap flux density.
Then, the radial force can be calculated and assigned as a vibration producing component, using (3.38). As the tangential component of the air-gap flux density is almost zero, this leads to an acceptable approximation of the radial force which is the main reason of the vibration. The other option is to use an accurate FE approach to simulate the vibration signals. However, vibration analysis has been used for several decades and is still of a great interest in industries.
Sound (noise) is a direct consequence of any kind of vibration. So in an environment that there is no additional noise or sound-producing factor except the tested motor, it is a premium approach to the analysis of the fault as it certainly has a noninvasive nature. The corresponding sound or noise sensors are in the form of antenna absorbing the noise or any sound disturbance produced by the fault. The significant requirement of any sound sensing is the presence of a noise-free room (antenna room) in which the motor should be tested. Although the required room should not be very large, it is a very dedicated and expensive facility not found easily everywhere (see Fig. 45). Sound analysis technique is a very promising way of diagnosing motor faults.
Temperature sensing is one of the common monitoring techniques of electrical machines including motors and generator. Depending on the machine and fault type, different parts of the machine are subjected to a thermal tension requesting for a precaution in terms of possible future defects. In a healthy induction motor, end windings are the highly heated parts due to the higher leakage inductance while in a faulty motor, every part experiencing a dramatically increasing saturation level is the target of thermal tensions. For example, when a broken bar or short-circuit fault occurs, the area neighboring the fault reveals a considerably high temperature leading to an unbalanced temperature distribution of the machine. An eccentricity fault introducing a rotating saturated region called UMP point applies a total temperature rise of the motor. However, the other types of fault are also factors for generally increasing the motor temperature compared to a healthy operation.
Temperature monitoring is not usually performed as a sole-task, and it is combined with some other techniques such as the vibration analysis to return helpful information on motor operation. Moreover, the operating mode and the motor load level should be first defined in any thermal analysis as these are the principle factors in determining the temperature.
There are two basic monitoring approaches dealing with the thermal analysis of an induction motor:
--measuring local temperatures
--measuring a bulk image or motor temperature.
The first approach, which is a kind of invasive technique, requires several thermocouples (see Fig. 46) connected or installed at target part of the motor body including end windings, stator core, rotor core, housing and bearings, etc. This approach is based on a well-known effect called Seebeck which is the direct con version of a difference in temperature between to materials to an electric signal. It literally means that an electrical equivalent value is assigned to heat existing at a joint of two wires with different materials ( Fig. 46(a)). Two metals face the same heat source while the rate of temperature increase is totally different as the materials are not the same. Considering that any temperature change leads to a flow of electrons and assuming two materials with a great difference in their heat transfer capability, an electric voltage difference between two terminals in the measurement side takes place. This is what should be equivalently measured instead of real temperature difference. As thermocouples are very handy and small devices, they can be easily bonded on every part of motors body. This makes them one of the interesting ways of exact temperature monitoring.
Although thermocouples are very easy to use, their lifetime is somehow short compared to the other types of sensors discussed so far. The accuracy of the device might be affected by thermal tensions existing in the test environment. So calibrating the device and making sure if the device works very well should be one of the ongoing steps of using them.
Unlike the local thermal analysis, a global value indicating a total temperature change is sometimes assigned to the motor. The best candidate to reflect the change is the coolant temperature which is usually the air flowing in the air gap or close to it. So one can use a thermometer, regardless of type, to measure the time-dependent change of the motor temperature. This technique has nothing to do with an exact diagnosis procedure as the global temperature variation might be the product of any other unknown reason. Therefore, it is not proposed to go this way. Instead, utilizing a thermography camera is highly recommended (see Fig. 47). It is a potential device to return a very discriminative temperature distribution of motors.
In the case of stationary faults including the stator short circuit and also static eccentricity, it is expected to have a very clear representation of the fault location, and the detection is performed very well. However, if a rotating fault exists, it will not be easily detectable. As the thermal time constant is always larger than the magnetic time constant, incipient faults might not be detected by thermal analysis.
Considering the comments in terms of the motor signals and the corresponding sensing devices, all the sensors return electrical values which are relevant to the measured quantity. The products are electrical signals which should analyzed to conduct a diagnostic task. Therefore, another significantly important step is the so called ''data acquisition'' which is introduced below. This step comes ahead of any signal processing and fault diagnosis step as the latter cases are impossible to be done unless a signal is in hand.
3.5.9 Data acquisition
We prefer to introduce a very useful general application data acquisition (DAQ) device called ''AdvanTech PCI-1710 HG'' which enables us to sample several signals at the same time with difference qualities. A typical device is shown in Fig. 48.
The specifications of the mentioned DAQ device are as follows:
--16 single-ended or 8 differential or a combination of analog inputs
--12-bit A/D converter, with up to 100-kHz sampling rate
--automatic channel/gain scanning
--onboard FIFO memory (4,096 samples)
--two 12-bit analog output channels (PCI-1710/1710HG only)
--16 digital inputs and 16 digital outputs
--onboard programmable counter
--board IDTM switch.
A very compelling aspect of the device is the number of input channels which is equal to 16 if a single-ended topology is used. On the other hand, if a noisy environment exists, the differential topology consisting of 8 channels is recommended. The analogue to digital convertor implemented in this device is capable of sampling at a maximum rate of 100 kHz indicating that a maximum sampling frequency of 6,250 Hz can be assigned to every channel in a single-ended topology.
In the case of differential inputs, 12,500 Hz is the target. The corresponding sampling frequencies cannot be increased over the mentioned values unless some of the channels are free and not used. Then, the sampling frequency of used channels may increase if needed. The more the sampling frequency is, the more information preserved in a sampled signal will be. According to the Nyquist's law, the sampling frequency should be at least equal to twice the maximum frequency which should be included in the spectrum. Considering this fact and also taking the spectral resolution into account, it is suggested to take the safe side and go beyond the Nyquist's law and increase the sampling frequency as much as possible. The upper limit is usually forced by the data storage and also real-time analysis capability. Most of the time, it is favorable to have an online diagnosis technique which is able to detect incipient fault. In this case, there should be a trade-off between the accuracy and the required sampled data. In an offline case, users might even sample tons of data to increase the accuracy of the future investigations.
22.214.171.124 MATLAB_ code for an AdvanTech device
AdvanTech boards always come with a terminal box allowing us to connect the sensors outputs to the AdvanTech board installed inside a personal computer. The interface between the terminal box and the board is implemented by a 68-pin parallel connector shown in Fig. 48(b). The whole system is controlled by the interfaces developed by the company or simply using MATLAB. Fortunately, MATLAB provides a fantastic DAQ interface not only for the AdvanTech products but also for a variety of other DAQ devices. Below is the routine which is used by MATLAB to input or output signals (see Fig. 49). The interfaces taking care of MATLAB/AdvanTech interactions include m-files, data acquisition engines and hardware-driver adaptors. The last two aspects are themselves controlled by m-files or even SIMULINK_ files.
This routine represents the possibility of inputting and outputting data while the focus of our work is on the inputting process. Assuming an inputting process, the steps are as follows:
--connect the sensors outputs to the terminal box
--connect the 68-pin parallel connector to the main AdvanTech board
--before going through defining a DAQ hardware, check if the hardware is available or not using the following command in the command line:
% show and save list of available and installed vendors vendor=daq.getVendors
--open an m-file in a MATLAB environment and start typing the following code:
% Create a session for the required vendor session = daq.createSession('advnatech')
% Add an input digital channel ch1=addDigitalChannel(session,'DeviceID',
% Specify channel specifications ch1.TerminalConfig = 'Differential';
ch1.Range = [-10.0 10.0 ];
% Specify duration of acquisition session.DurationInSeconds = 2;
% Specify the sampling frequency or rate per second session.Rate = 10000;
% Inquire about the limit of sampling rate determined by hardware session.RateLimit
% start session data = startForeground(s);
The steps have been explained as comments shown by percent symbols. Simply, one can call an AdvanTech Package and set the options according to the requirements and then start sampling input signals, using MATLAB. A real-time practice of data acquisition toolbox is also implementable by means of MATLAB/SIMULINK blocks. Moreover, the above-mentioned process shows a digital input scheme while the analogue one is also applicable if needed. For more details, readers are referred to the Mathwork website mathworks.com/help/daq/functionlist.html .
Some technical points while using any acquisition hardware or device should be taken into account:
--Do not touch the input terminals with a bare hand. Static electricity might de-calibrate the device.
--Calibrate the device before using it.
--Scale the input signals applied to the terminal box to a measurable range of the DAQ device, i.e., [ 10, 10 ] V for AdvanTech PCI-1710 HG. In the situation that inputs run over the mentioned range, the sampled signal's top will be cut off and look like a flat-topped curve. Furthermore, relatively large inputs, those which are higher than the tolerable range of the device, might lead to a complete device failure by introducing insulation failure.
--When connecting more than one input, if the number of inputs does not surpass the number of channels, assign distanced channels to inputs to reduce the possibility of loading effects of channels onto each other's signals. However, all the channels should be isolated in the manufacturing process.
What has been already discussed in terms of the DAQ devices is focused on a multitask hardware built by the AdvanTech Corporation. This device does not come with a set of sensors such as VTs or CTs, and one should first prepare the required sensors and then integrate them with a DAQ board. This means that although the provided measurement and acquisition setup components are very handy and useful, they might not perfectly match each other in terms of impedances, calibration, input/ output ranges and so forth. So another comparable option is to use an integrated digital oscilloscope accompanied by a matched set of current and voltage probes.
Tektronix is the best example of manufacturer of this kind. It provides high resolution multichannel digital oscilloscopes; moreover, very accurate current and voltage probes at different ratings are also available. The only drawback is related to the variety of type of probes (sensors) which does not cover the mechanical, magnetic and thermal sensors. So if one looks for a full control of the DAQ devices, the first approach is recommended while the second one is probably easier to use.
After being sampled, all the required motor signals are passed to a processor which can be a simple personal computer or a separate DSP such as those developed by the Texas Instruments company. The diagnosis procedure normally ends with the signal processing and fault indicator extraction step. This is a major step through the final goal of the fault diagnosis. Thus, it will be deeply discussed in Section 7. For now, it is assumed that the corresponding prerequisites are ready to go further through introducing an integrated fault diagnosis scheme below in the next subsection.
3.5.10 Overall scheme of the conventional cabled diagnosis system implementation
Taking all the mentioned aspects of a practical implementation of fault diagnosis procedure into account, a general scheme shown in Fig. 1 is introduced as the final solution for the experimental setup. In a few words, the following step-by-step procedure should be followed up to the end point which is extracting fault information, using a time, frequency or time-frequency analysis ( Fig. 50).
--If the motor is a wound rotor topology, short circuit the rotor windings.
--Connect the tested induction motor to the three-phase network/Drive, using a switch to take care of both the line-start and inverter-fed modes.
--The switch is used to switch between the line-start and inverter-fed modes.
--Connect the drive input to the three-phase network. One might also connect a three-phase choke to reduce the noise applied to the network.
--Connect the drives output terminals to the switch input terminals.
--Use shielded cables.
--Connect the switch output terminals to the motor terminals.
--Determine one of the phases as the diagnosis phase and then pass it through the CT. It is proposed to roll it several times around one leg of the CT to make sure the best primary coupling is made between the phase cable and the CT.
--Connect the test phase to the VT.
--Prior to connecting the electrical inputs of the motor, mechanical parts should be handled very well. It means that the encoder, the torque meter, the coupling and the load should all be connected and checked for being safe first.
--Prior to connecting the drive to the circuit, make sure to adjust the required initial parameters including the rise-time, the motor resistance, the motor inductance and most importantly the operating mode.
--Apply the temperature, flux and also vibration sensors as desired and then route all the sensing signals to the DAQ devices.
--Connect the DAQ devices outputs to a processing hardware which includes an ordinary CPU or a DSP.
--Obviously, the fault should be already applied to the motor. Furthermore, the speed and torque adjustments are supposed to be done.
--Finally, run the system and start sampling and analyzing the motor signals with the goal of extracting proper fault indicators. This step is the main focus of this guide and will be further analyzed, discussed and explained in the next sections.
One of the major aspects of the discussed scheme is the presence of a bunch of probably cumbersome wiring as all the signaling route is handled by means of cables. So if a long-distance analyzing center should be incorporated into the diagnosis procedure, this scheme, although provides a promising infrastructure, it will be somehow challenging in terms of signal routing. Instead, a wireless implementation of a condition monitoring system proposes a very tangible substitute for the conventional approach. The wireless condition monitoring is an almost new topic in the field, and not all researchers or even manufacturers have tried to address this approach. However, the existing literature clearly explains the idea.
3.5.11 Wireless condition monitoring setup
Due to the recent developments achieved in the field of low-cost wireless sensors revealing a great ability in processing and communicating processed data, a couple of research attempts have been devoted to wireless implementation of a diagnosis setup. Consequently, online wired-monitoring systems, which indeed work well, might be totally replaced by wireless network alternatives. The main reason is probably the higher cost of shielded and isolated cable implementation while a wireless system does not require cabling at all. The only cost normally corresponds to the transmitters, receivers and likely the on-sensor processors if utilized.
Another disadvantage associated with the conventional monitoring system is its inability to provide an opportunity for temporary or specialized condition monitoring practices.
Wireless sensor networks (WSN) commonly provide a cheaper system implementation along with a more flexible and re-locatable monitoring system which does not restrict the location of system-utilizing technician. Nevertheless, no one can deny the existing shortcomings such as the potentially short range of operation and also possible electromagnetic interferences. On the other hand, WSNs have considerably constrained resources the significant of which is the associated battery life time. Regardless of its drawbacks, WSNs could definitely play a vital role in simplifying the diagnosis procedure.
In general, there are two kinds of topology for benefiting from a WSN:
In the first topology, the signal processing, feature extraction and likely final fault diagnosis step are performed in the sensor itself. Therefore, sensors should provide an internally implemented microprocessor/microcontroller allowing processing the signals and then transmitting them to the monitoring unit. In the second topology, the sensor is just sensing and transmitting unprocessed signals to the receivers.
Finally, the processing and feature extraction are handled by the monitoring unit which consists of a processing device such as DSPs. What is usually preferred is the first topology due to the fact that the processing unit is fixed and located close to the motor while the monitoring unit can be easily moving around the operating environment. If an off-sensor processing topology is used, the monitoring unit would probably be larger and more difficult to be flexibly moved. Besides, electromagnetic interference, if not dealt with properly, might harm the unprocessed signals and lead to a loss of valuable information during transmission of the signal.
So the first topology is selected and shown in Fig. 51.
For each sensor, one processing and transmitting unit is assigned while there can be only one receiver receiving all the data simultaneously by multiplexing among the inputs. The DAQ, signal processing and feature extraction is handled by a microcontroller or microprocessor, and the extracted features are sent to the transmitter. There are some types of microcontrollers such as Jennic JN5139 which is capable of multitasking. This means that they conduct all the tasks ranging from receiving sensor data to transmitting extracted features at the same time. So not only do they lead to a considerable save in the implementation space, but they also reduce the price of integrating devices. The proposed scheme in Fig. 51 is applied to a line-start motor, but an inverter-fed application is also possible. To understand perfectly how a WSN works and is managed, a knowledge of micro controller programming is also required. At this point, we do not aim at going through the details as it is not the main topic of this guide, and it is assumed that readers have the required knowledge.
A brief overview of the current section reveals the attempts to understand the fundamentals of fault occurrence and the way how fault affects the motor time domain behavior. The attempts were totally devoted to explain the theoretical fault basis and consequently address the most significant time-domain variations by means of which a fault might probably be detected. Nevertheless, not all faults introduce a specifically detectable behavior, at least in a time domain. A step-by step laboratory-scale implementation of various types of faults, along with the required details, was provided. By means of this knowledge, a simple but very useful setup of fault diagnosis based on which one can study different fault aspects is indeed achieved.
Bearing this in mind, in the next three sections, we are going to target the best existing simulation approaches used for accurately modeling faults in induction machines. Not only the fundamental time harmonic components, but also all the possible spatial harmonic components are included and incorporated into the modeling process. The goal is actually to help researchers understand better how internal motor behaves, and it is not easily accessible by means of the existing experimental setups. For example, magnetic flux density at different parts of the motor or even the UMP is not the thing available at a cheap price in any laboratory or industry. Sometimes, it is even impossible unless an accurate modeling and simulation approach is hired. We believe no one's knowledge will get improved unless the upcoming information is studied and kept in mind. Therefore, it is highly proposed to study the following sections first before attempting to read and understand the sections coming after.