CA2292341C - Method of testing rotor bars in a squirrel cage electric motor - Google Patents

Abstract

A method of testing rotor bars in a squirrel cage electric motor. An electric current is passed through a rotor cage, so that current flows through the rotor bars being tested. A
relative strength of flux generated by the electric current passing through the rotor bars is compared. A marked difference in flux strength indicates a broken rotor bar. The method is of sufficient resolution as to leave no doubt as to when a rotor bar is damaged. By way of example, in one test a broken rotor bar recorded a reading of 25 millivolts, as compared with readings of 140 millivolts for all of the other rotor bars.

Description

TITLE OF THE INVENTION:
Method Of Testing Rotor Bars In A Squirrel Cage Electric Motor NAMES) OF INVENTOR(S):
Jan Krepela FIELD OF THE INVENTION
The present invention relates to a method of testing rotor io bars in a squirrel cage electric motor.
BACKGROUND OF THE INVENTION
A rotor in a squirrel cage electric motor has a plurality of rotor bars which may vary in number from as few as 36 or less to as many as 200 or more. An electric motor with a broken rotor bar does not perform to its designed capability. LEXSECO, a leading manufacturer of testing equipment, has developed a methodology for testing a rotor of an electric motor to detect broken rotor bars.
The method involves directing a current through the rotor shaft.
2o The rotors are then examined for "hot spots". The instructions issued by LEXSECO indicate that hot spots develop in the vicinity of a break in a rotor bar, due to increased resistance. The method teaches that the hot spots may become so intense as to produce smoke.
The described method is criticized as not producing an acceptable degree of resolution. Interpretation of "hot spots" is sometimes totally erroneous. A technician can never be absolutely certain that the results obtained are accurate, as many factors 3o can adversely affect the test results. However, to this point in time there has not been an alternative methodology capable of producing a higher degree of resolution.
SU1~IARY OF THE INVENTION
What is required is a method of testing rotor bars in a squirrel cage electric motor which has a higher degree of resolution than the above described methodology.

According to the present invention there is provided a method of testing rotor bars in a squirrel cage electric motor.
An electric current is passed through a rotor cage, so that current flows through the rotor bars being tested. A relative strength of flux generated by the electric current passing through the rotor bars is compared. A marked difference in flux strength indicates a broken rotor bar.
Although beneficial results may be obtained through the use io of the above described method, the method is most effective when the difference in flux strength can be objectively quantified.
Even more beneficial results may, therefore, be obtained when the comparing of the relative strength of the flux generated by the electric current passing through the rotor bars is performed with i5 a testing instrument in order to provide objective data of the flux strength. Beneficial results have been obtained through the use of a testing instrument recording voltage readings induced by proximity of the testing instrument to the flux of one of the rotor bars. The difference in resolution is dramatic, leaving 20 little doubt as to when a rotor bar is broken. For example, in tests of one type of rotor a broken rotor bar recorded a reading of 25 millivolts, as compared with readings of 140 millivolts for all of the other rotor bars.

These and other features of the invention will become more apparent from the following description in which reference is made to the appended drawings, wherein:
FIGURE 1 is a side elevation view, in section, of a rotor 3o from a squirrel cage electric motor.
FIGURE 2 is a side elevation view, in section, of the rotor illustrated in FIGURE 1, connected to a power source for testing in accordance with the teaching of the present method.
FIGURE 3 is a detailed end elevation view, in section, of 35 the rotor illustrated in FIGURE 1.
FIGURE 4 is a detailed perspective view, in section, of the rotor illustrated in FIGURE 1, with a test instrument.

FIGURE 5 is a perspective view of the test instrument illustrated in FIGURE 4.
FIGURE 6 is an end elevation view, in section, of the rotor illustrated in FIGURE 3, with circuit detail superimposed thereon.
s FIGURE 7 is a circuit diagram of current flow during testing in accordance with the teachings of the present method.
FIGURE 8 is identical to FIGURE 3 with dimensions added for calculations.
1o DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT
The preferred method of testing rotor bars in a squirrel cage electric motor, will now be described with reference to FIGURES 1 through 8.
1s Referring to FIGURE l, a rotor for a squirrel cage electrical motor, generally identified by the reference numeral 10, includes a laminated cylindrical body 12, an axial shaft 14 and several rotor bars 16 in a regularly spaced apart parallel relation to shaft 14 within body 12. Laminated cylindrical body 20 12 is constructed of a plurality of steel sheets insulated from each other by thin layers of insulation. A first end 18 of shaft 14 extends past a first end 20 of body 12. A second end 22 of shaft 14 extends past a second end 24 of body 12. A length of each of rotor bars 16 extends throughout the length of body 12.
2s An end ring 26 is secured to each of first end 20 and second end 24 of body 12. Each end ring 26 is in electrical contact with and covers the corresponding end of each of rotor bars 16. A
plurality of cooling fins 28 is located at a remote face 30 of each of end rings 26. Rotor 10 rotates about a longitudinal axis 3o indicated by broken line 32.
Referring to FIGURE 2, the method of testing rotor bars 16 in a squirrel cage electric motor includes passing an electric current through a rotor cage, so that current flows through rotor 35 bars 16 being tested. A source of electrical power 34 for generating an alternating current is provided. A first electrode 36 is connected by electrical wiring 38 to cooling fins 28 at first end 20 of body 12. A second electrode 40 is connected by electrical wiring 38 to cooling fins 28 at second end 24 of body 12. An electrical circuit is thereby formed, comprising source of electrical power 34, wiring 38, cooling fins 28, and rotor bars s 16. When source of electrical power 34 is activated, an alternating current flows through the circuit.
Referring to FIGURE 3, when a current flows through rotor bars 16, a magnetic flux 40 is generated around each of rotor bars 16. A strength of flux 40 in the vicinity of rotor bar 16 is proportional to the current flowing through said rotor bar 16.
Flux 40 extends into the region 39 past an outer surface 41 of body 12 in the vicinity of each of rotor bars 16. When the current flowing through one of rotor bars 16 differs from the i5 current flowing through another of rotor bars 16, flux 40 in region 39 in the vicinity of the one rotor bar 16 differs from flux 40 in region 39 in the vicinity of the another rotor bar 16.
When the current in rotor bar 16 is an alternating current, flux 40 generated by the flow of current through said rotor bar is an 2o alternating flux.
Referring to FIGURE 2, when one of rotor bars 16 has a break 44, an electrical resistance of broken rotor bar 46 is higher than a resistance of unbroken rotor bar 16. The higher resistance 2s causes a markedly reduced current in broken rotor bar 46 compared with a current in unbroken rotor bar 16. As a consequence, there is a marked reduction in a strength of flux 40 in region 39 in the vicinity of broken rotor bar 46 when compared with a strength of flux 40 in region 39 in the vicinity of unbroken rotor bar 16.
3o Referring to FIGURE 4, a relative strength of flux 40 generated by the electric current passing through rotor bars 16 is compared by use of a magnetic probe 42. Magnetic probe 42 is made from a material that can be magnetized, and so interacts with flux 40.
Magnetic probe 42 in region 39 vibrates as a consequence of 5 interaction between magnetic probe 42 and alternating flux 40. A
strength of vibration of magnetic probe 42 provides a diagnostic non-quantitative indication of the presence of break 44 in broken rotor bar 46.

The method is most effective when the difference in flux strength can be objectively quantified. Even more beneficial results may, therefore, be obtained when the comparing of the s relative strength of flux 40 generated by the electric current passing through rotor bars 16 is performed with a testing instrument in order to provide objective data of the flux strength. Beneficial results have been obtained through the use of a testing instrument recording voltage readings induced by to proximity of the testing instrument to the flux of one of the rotor bars. Referring to FIGURE 5, a length of insulated electrically conducting wire 48 is wound as several turns longitudinally around magnetic probe 42. Each of ends 50 of length of wire 48 is electrically connected to a different contact 52 of i5 an electrical meter 54. Magnetic probe 42 wound with length of wire 48 is situated in region 39 in the vicinity of one of rotor bars 16 and is aligned substantially parallel to said rotor bar 16, as illustrated in FIGURE 4. Alternating flux 40 is generated when alternating current passes through rotor bar 16. Alternating 2o flux 40 interacts with turns of length of wire 48 to generate an electrical potential that is measured using electrical meter 54.
A potential generated when the magnetic probe 42 is in region 39 in the vicinity of one unbroken rotor bar 16 is substantially the same as a potential generated in region 39 in the vicinity of 2s another unbroken rotor bar 16. A significantly lower potential is generated when magnetic probe 42 wound with coils of length of wire 48 is in region 39 in the vicinity of broken rotor bar 46.
The difference in resolution is dramatic, leaving little doubt as to when a rotor bar is broken. For example, in tests of one type 30 of rotor 10 a broken rotor bar 46 recorded a reading of 25 millivolts, as compared with readings of 140 millivolts for all of the other rotor bars 16.
When a rotor 10 has n rotor bars 16, none of which is 35 broken, and a total alternating current IT is generated from power source 34, the current through each rotor bar IB is given by an equation:

IB = IT I n When one or more of the rotor bars is broken, the current through broken bar 46 is significantly lower than the current through each s of unbroken bars 16, and the above equation is no longer valid.
Some current still passes through broken bar 46, but not an amount of current equal to that which passes through unbroken bars 16.
The theory behind the testing instrument can be expressed as io follows. A current I passing through N turns of wire generates an magnetomotive force Fm, as given by an equation: Fm = N.I
Alternating current generates an alternating magnetic flux that is related to magnetomotive force Fm by magnetic 15 reluctance Rm, as given by an equation: Fm=~.Rm Alternating current through rotor bar 16 results in magnetomotive force Fm, which in turn generates alternating flux and thereby induces an electrical signal detected by 2o electrical meter 34.
For the bar test to be really effective, the flux around the solid (unbroken) bar and the broken bar must be sufficiently different. The flux around the bar can be used as a 2s proof of the rotor bar condition. In order to estimate the ratio of the flux around the broken and unbroken bar, one can use the Hopkinson's Law, which is an equivalent of the Ohm Law:
Ohms Law : U = I * R
3 o Hopkinson' s Law : Fm = ~ * Rm Where:
Fm = Magnetomotive force, magnetic equivalent of the voltage in [Amps] ; R"~ =NI
35 N - number of turns I - current Magnetic flux in Wb (Webber) Rm - Reluctance, magnetic equivalent of resistance in [H-1 ](1 / Henry) Now referring to FIGURE 6, bars 16 are in deep open slots between the teeth 21 of the rotor. The width of an opening 19 of the slot is marked b3. The reluctance of the tooth is lumped into Rmb. The reluctance above the bar, consisting mainly to of the reluctance of the slot opening b3, is markedRma. Each bar, when carrying current is a source of a magnetic flux. This is expressed on FIGURE 6 as a "battery" marked Fm . It can also be seen that the reluctance of the rotor yoke is neglected.
Considering the cross section of the tooth and the rotor yoke it i5 is certainly justified. We are not seeking accurate calculations, but a good estimate.
In case of a rotor with N bars, an equivalent diagram of FIGURE 7 applies. For solution we can use the "mesh currents", 2o actually "mesh fluxes". In FIGURE 7, all teeth reluctances are considered equal, also all reluctances above the bars are equal.
However the magnetic voltages Fmn are considered non-equal. It means that the currents in each bar are different. The "mesh flux" in each loop is marked Win.
25 Note 1: It may not be clear why are the "batteries"
representing the bar current positioned in the equivalent diagram as they are. Since the cage is during the test fed from a separate source, we have to consider a complete circuit. This complete circuit is created not only by the rotor bars, but also 3o the leads to the power source. Hence the exciting "coil" is "wound" around the rotor slot opening, not around the tooth or the rotor yoke. Also the polarity of the "batteries" must be the same, because during the test the source of the current in each bar is identical.
35 Note 2: As drawn in FIGURE 6, rotor has open slots.

But majority of the rotor slots is closed, particularly on rotors with cast aluminium bars. However the cross section of the iron above the bar is very small and can be saturated very easily.
Hence even when the physical opening does not exist, there is an "air gap" for the magnetic flux.
The solution is the simplest the least bars are on the rotor. Let's consider a rotor with only 3 bars. We can write the 3 equations to solve the flux ~1, ~2, ~3~
to (W -~3)Rmb +(~~ -~z)Rmb +Rma~i =Fmi ( (~2 - ~1)Rmb +' (~2 - ~3~Rmb + Rma~2 - Fm2 ( 2 ) (~3 - ~2 )Rmb + (~3 - ~1 )Rmb + Rma~3 - Fm3 ( 3 ) It can be also easily seen that a forth equation can be written following the loop through reluctance Rm~.
(~1 + ~2 + ~3 )Rma = Fml + Fm2 + Fm3 ( 4 ) In the case of a "healthy" cage, the currents in each bar will be equal, hence there is no reason for the fluxes not to be the same.
From the equation (4) it follows that the flux in each loop is:
~._F"~
Rma (5) The situation will be much different if one bar is broken. Let's say that the bar 1 does not conduct the current. Then:
Fmk O (6) and for the reason of symmetry:
Fm2 Fm3 Fm ( ,7 ) s and also:
~2 - ~3 - ~m (8) to We can rewrite the (4) as:
(~1 + 2~,n )Rma = ZFm (9) Similarly we can manipulate equation (1) into a form:
(~1 - ~m )2Rm6 + Rn,a~l = 0 (10) After some manipulations and considering eq. (5):
= 2 Fm . Rmb = 2~. Rmb Rma Rma + 3Rmb Rma + 3Rmb (11) Fm (Rma + ZRmb ) _ ~. (Rma + ZRm6 ) m Rma . (Rma + 3Rmb ) (Rma + 3Rmb ) (12) The above equations were derived for rotor with 3 bars only. For arbitrary number of bars the equations would be derived in a similar manner. Unfortunately as the number of bars increases the complexity of the equations increase also. In order to simplify the equations we have consider the ratio r1= Rmb.
Rma When the slot is open the reluctance Rma includes gap b3. It is then obvious that the r1 is very small, in the order of 1/100.
5 But even when the slot is closed, the ratio r1 can be very small if saturation takes effect. Of course for the saturation to occur, the test current has to be high enough.
It can be than shown, that even for arbitrary number of to bars the equations (11) and (12) can be simplified into forms:
~1 - 2~. Rmb Rma (13) and:
~m =

(14) We can now examine the ratio of the two fluxes:
__ ~1 __ Rm6 __ r2 ~m 2 Rma 2r1 ( 15 ) Equations (13), (14) and (15) show that the resolution of this testing method is excellent. We have discussed the size of the r1 3o before and decided that it is a very small number in the order of 1/100. The flux over the broken bar is many times smaller compared to solid bar. Hence even such a simple device as a thin steel blade indicates the broken bar with great deal of confidence.
Referring to FIGURE 8, the same features are illustrated as in FIGURE 3 with the addition of values assigned to the various dimensions. W represents the width of the tooth, b2 is the width of the slot at widest point. In this case, the slot is entirely filled with the conductor so h2=b2/2. In some cases when the conductor does not reach all the way to the top of the slot then h2 < b2 l 2 . b3 is the width of the slot opening, h3 is the height of the slot opening, and c is the depth of the slot.
In order to illustrate the ratio of the reluctance r1, to we will actually calculate this ratio for a rotor slot of a sample motor rated 7.5kW motor, 4 pole, 380 V, 50Hz:
To determine the Rma we can use formulas developed for calculation of the stray inductance of the rotor bar. Many of such formulas exist in literature; all are just a good approximation of the reality. They are however more than adequate for our comparison. The following formula includes not only flux across the gap b3, but also the flux across the rest of the slot.
2o Specific magnetic conductivity of the slot:
~.~ _ ~3 + 0.524 - ~2 + 3b ( a ) Inserting the numerical values for the above mentioned 7.5 kW
motor yields:
~~ = 0-55 + 0.524 - 2=9 + 16 =1.277 1.5 5.8 3 * 5.8 The reluctance of the bar is then:
R -_ 1 ma (b) ,up - permeability of vacuum (4~.10-'H/m) Le - length of the bar (we do not need to know this number, because we calculate the ratio only; see below. Let it be =1 m [meter] ) .
to Rma = 1 = 623476H-' 4~t.10-' * 1.277 * 1 Let's now calculate the reluctance of the tooth that is 4.6 mm wide 16 mm tall, and as above the length Le is 1 meter:
h Rmb =
f~rA~ObLe (c) h =length of tooth (radical)= 16 mm=0.016 m b =width of the tooth=4.6mm=0.0046 m fir= relative permeability of the lamination. Since this value so strongly depends on the flux density, we express the total permeability of the material as ratio of the flux density to intensity of the electric field from the curves for the transformer lamination:
f~rf~o - H (d) B=flux density [T] (tesla) H=intensity of mag. field [A/m] (amperes per meter) 0.2 = 0.002H / m f~rf~o = 100 the flux density of 0.2T was chosen. The flux density will be s very low during the test. It follows that:
_ 0.016 _ R"'b 0.002 * 0.0046 1739H
to Finally:

r1 = = 0.00279 =1/358 The estimate of r1 =1100 was obviously justified.
is It will be apparent to one skilled in the art that modifications may be made to the illustrated embodiment without departing from the spirit and scope of the invention as hereinafter defined in the Claims.

Claims (3)

1. A method of testing rotor bars in a squirrel cage electric motor, comprising the steps of:
connecting a rotor cage to an alternating electric current source by means of conductive wiring, maintaining the rotor cage in a static position while applying electric current, so that the electric current flows through rotor bars of the rotor cage being tested; and comparing a relative strength of flux generated by the electric current passing through the rotor bars on the basis that a marked difference in the relative strength of flux indicates a broken rotor bar.

2. The method as defined in Claim 1, wherein comparing the relative strength of flux generated by the electric current passing through the rotor bars is performed with a testing instrument in order to provide objective data of the relative strength of flux.

3. The method as defined in Claim 2, wherein the testing instrument records voltage readings induced by proximity of the testing instrument to the flux of one of the rotor bars.