Iron loss modelling which includes the impact of punching, applied to high-efficiency induction machines

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1 Iron loss modelling which includes the impact of punching, applied to high-efficiency induction machines Lode Vandenbossche, Sigrid Jacobs ArcelorMittal Global R&D, Gent, Belgium Xavier Jannot, Mike McClelland, Jacques Saint-Michel Leroy Somer, Angoulême, France Emmanuel Attrazic ArcelorMittal St-Chély d Apcher Saint-Chély d Apcher, France Abstract Within the market evolution towards higher efficiency machines, there is a need for more precise modelling tools, taking also higher frequency power supplies into account. This paper implements the effect of cut edge degradation, due to punching, on the local magnetization curve and local losses, aiming at improved calculation of magnetization current and machine iron losses. For an induction machine, defined by Leroy Somer and a high efficiency electrical steel, selected from ArcelorMittal s range, this study combines advanced material characterization with improved modelling techniques, and is validated by selected machine testing procedures. For the sake of clear loss separation a machine with slotless rotor was characterized at two conditions regarding speed and excitation. The loss model, including already the effect of rotational losses and higher harmonics, was enhanced with the punching effect, which led to a model accuracy of 86% at synchronous speed when compared to the measured losses. This study also led to further insights in local magnetization behaviour, to be used in further design optimization. Keywords electrical steel; induction machine; punching; iron loss; magnetic modelling; influence of production processes I. INTRODUCTION The past few years have seen significant improvements in the efficiency rating of electrical machines. In addition the use of variable speed drives continues to grow leading to the need for standard motors with no thermal de-rating. An understanding of iron loss at supply frequencies and pulse width modulation (PWM) frequencies is fundamental to achieve the lowest loss which will lead to further improvements in efficiency and thermal performance. Over the past three decades significant improvements have been made to the iron loss calculation method for both sinusoidal and non-sinusoidal flux waveforms [1-11]. Less attention has been paid to the impact of manufacturing processes on the performance of a real electric machine: most published work in this area has focused on the impact of cutting, punching and assembly stresses on the magnetic steel characteristics as such [1-17]. Only some literature combines both aspects, in other words an improved iron loss modelling approach taking into consideration a material property description depending on the manufacturing processes, aiming at a detailed consideration of their impact on electric machine performance [18-]. Recent work [1, 16] by researchers at ArcelorMittal has studied the impact of the industrial processing of steel laminations (cutting, punching, etc.) which causes a significant degradation of its magnetic material properties. Locally near the cut edge the microstructure of the steel (dislocations, internal stresses, grain morphology) is affected by the mechanical cutting or punching, which results in a decrease of magnetic permeability and an increase of hysteresis losses in the region near the cutting edge [1-]. Small machines and those with fine tooth geometries are particularly affected by punch hardening effects. For example the magnetic degradation due to the cut edge can extend several millimeters from the edge [1-16]. This means that for many motors with distributed windings a large part of the tooth will be subjected to an increase in loss and a decrease in permeability. The use of finite-element analysis allows a detailed understanding of the flux density distribution in the electrical lamination steel. Faster computers allow higher mesh densities to be processed with reasonable calculation times. High tooth mesh densities mean that changes in magnetic properties as a function of distance from the cut-edge can be modeled more accurately. The work presented here describes the initial calculation and experimental phase of a larger research project which has the objective of characterizing the cut-edge effect on the machine performance for a standard induction motor manufactured by Leroy Somer. The objective of this study is to compare the improved iron loss modelling results including the cut edge effect (as described in section 3) with the measured iron loss occurring in the electrical machine under study. A slotless rotor, induction motor is manufactured in order to avoid rotor bar eddy current losses, in other words to isolate the iron losses due to stator tooth punch hardening from those of the rotor slot and bars. This avoids the difficult and inaccurate process of separating the iron losses occurring in stator and rotor laminations from the resistive rotor bar losses.

2 As a consequence a higher accuracy measurement can be expected as described in section 4. The prototype machine is operated at two distinctly different operating conditions: (1) No load (synchronous speed), with a conventional three-phase rotational field; directly from the progressive die with an outside diameter punched to the size of the stator bore. The blanks are assembled into a stack, pressed onto a shaft and finish machined to give the standard air gap. Iron loss is measured using the method described in section 4 below. () Blocked rotor (zero speed), with a pulsating singlephase field. For each operating condition two iron loss calculations are made: (a) Ideal case, with model data based on homogeneous material properties; (b) Including the cut edge effect, with material properties which depend on the distance from the cut edge. This paper focuses on the effect of the local degradation of the magnetic properties due to punching on the machine s performance. The effect of additional eddy current losses due to parasitic interlaminar contacts due to the burrs at the punched edges [1] is not taken into account in this study. II. THE PROTOTYPE MOTOR WITH SLOTLESS ROTOR The prototype machine is derived from an existing 3kW four pole induction motor whose main characteristics are summarized in Table I. For the prototype machine under study, standard rotor laminations are replaced with slotless laminations. The resulting geometry is shown in Fig. 1. TABLE I. PROTOTYPE MAIN CHARACTERISTICS Stator slot number 48 Rotor original slot number 8 Stator outer diameter 145 mm Airgap.5 mm Lamination steel thickness.5 mm Pole number 4 poles Stack length 16 mm Rated power 3 kw Rated voltage 4 V Rated frequency 5 Hz The lamination steel for stator and rotor is selected from the ArcelorMittal range of high efficiency Electrical Steels (ES), based on the loss and the magnetization characteristics determined using Epstein frame measurements. The punching and machining of the laminations uses an identical process to that used to manufacture the standard motor. A serial production progressive die with clearances optimized for.5mm steel sheet is used. The prototype laminations are punched during a standard production run and within the scheduled maintenance interval for regrinding (to compensate for punch wear). Stator laminations are punched, stacked and welded, then insulated and wound using the standard production process. The wound stator is then hot pressed into an aluminium housing. Rotor blanks are recovered Fig. 1. Sketch of the cross section of the magnetic laminations used in the prototype. III. IMPROVED IRON LOSS MODELLING APPROACH Magnetic losses or iron losses of ferromagnetic materials are usually measured and theoretically described under welldefined, standardized conditions such as the Epstein frame test [IEC 644-], carried out under unidirectional, homogeneous and sinusoidal magnetic polarization conditions resulting in the specific iron losses (in W/kg) of a particular electrical steel grade for a given magnetic polarization amplitude and frequency value. Moreover according to this international standard procedure, cutting the material to the standardized sample dimensions should be performed with the greatest care in order to minimize the local degradation of the intrinsic material properties due to sample preparation. However in rotating electrical machines, the magnetic flux paths, flux waveforms, steel part geometries, lamination manufacturing techniques and mechanical constraints are far more complex than those encountered in the laboratory for Epstein frame measurements. Hence the actual iron core losses (in W) dissipated in electrical machines cannot be related in a simple and straight-forward way to the Epstein loss data. To be more specific, compared to the standardized Epstein iron loss measurements there are a lot of additional factors influencing the iron losses in machines: The magnetic flux waveforms occurring in electrical machines due to the applied rotational fields via threephased windings are not simply sinusoidal and unidirectional, but contain higher harmonics in time (due to saturation effects, stator slotting, power electronics such as PWM, skin effect), giving rise to additional harmonic losses; Moreover, the magnetic fields can become, in some regions of the machine, vector properties (known as rotational

3 magnetization). These non-unidirectional magnetization conditions give rise to additional so-called rotational losses; In some regions of the machines, elevated magnetic induction levels occur. It is clear that a sufficiently accurate estimation of iron losses occurring in the machine s stator/rotor parts, taking into account the above-mentioned aspects, is indispensable to effectively carry out the design of electric machines. Further in subsection A we will show how we tackle this issue of improving the estimation of the iron losses by numerical methods, giving rise to the basic version of the presented iron loss modelling approach. Moreover, also stator/rotor lamination cutting processes such as punching [1-], and assembly stresses (radial compression applied to the steel lamination when fitting it into the machine housing and/or axial compression when performing stack assembly) [19-], affect the magnetization processes in the machines and have impact on the resulting machine s iron losses. In order to take into account both the above-mentioned machine operation conditions together with the machine manufacturing aspects affecting the magnetic losses of electrical machines, ArcelorMittal R&D developed further its generic numerical approach to be able to predict the iron losses more accurately. These additional effects are incorporated into the iron loss description. Furthermore, such additional loss descriptions need the input of non-standard material data of ArcelorMittal s products, based on advanced experimental characterization methodologies. Subsection B describes the extension of the iron loss model to incorporate the cut edge effect on the local magnetization curve and on the local iron losses in the vicinity of the cut edge. A. Iron Loss Modelling with Homogeneous Magnetic Properties of the Electrical Steel The basic version of the iron loss model with homogeneous material properties, improving in relatively wide operational ranges of magnetic polarization J and frequency f the estimation of iron losses occurring in rotating electrical machines, can be seen as a further elaborated Bertotti-based loss-separation model [1]. Bertotti s original approach does not take into account rotational losses and higher harmonics, so estimated loss values are expected to be smaller than the losses occurring in reality. These limitations underline the need to extend the loss model by describing also these mentioned effects which additionally contribute to the iron losses. The ArcelorMittal improved iron loss model on the other hand includes the most relevant additional aspects which influence the actual iron losses occurring in rotating machines: (a) elevated magnetic induction levels (b) higher harmonics in time and space (c) spatial vector fields; rotational magnetization ArcelorMittal s iron loss description comprises five material dependent parameters ( s eddy, s hyst, s exc, α and β ) and reads as follows: P( J, f + eddy n= 1 ( α + βj p ) ( 1+ ( r( J ) 1 c) J ) = shyst p ) s J p, n 1.5 ( nf ) ( ) sexc J p, n nf p n= 1 taking into account the following definitions: s eddy : is calculated from electrical conductivity, thickness and mass density of the electrical steel laminations [1] s hyst, s exc, α and β are fitted material parameters for the studied electrical steel grade, based on measured Epstein data (as a function of peak magnetic polarization J p and frequency f ) J p : peak value or amplitude of the ground (first) harmonic component of the magnetic polarization [T] J p, n : amplitude of the n-th harmonic component of the magnetic polarization, with J p,n = ( J p, n, x + J p, n, y ) based on its x- and y-components f : fundamental frequency, in Hertz [Hz] c : flux distortion factor at every location in the stator or rotor parts, defined as c = J min J : minimum of the absolute value of the magnetic min polarization, evaluated over one electrical period [T] r ( J p ) : rotational loss factor (empirical function, experimentally determined on a few grades []) Here, the exponent of J p for the hysteresis loss term is not a fixed value or one single parameter but a linear function of J p, which makes the loss model suitable for a wider range of magnetic polarization values. Fig.. General overview of the numerical scheme of the ArcelorMittal iron loss modelling approach. The general framework of the proposed calculation method for the improved estimation of iron losses in electrical machines is shown in fig., and is based on three main parts: (1) finite element calculations of the magnetization distribution occurring in the machine, () loss calculations via postprocessing routines, and (3) last but not least the material characterization, serving as input for the other two tasks. J p f (1)

4 The methodology with properties discussed here in subsection A consists of using the specific loss W(J,f) characteristics obtained by standardized Epstein frame measurements, in order to fit the material parameters of the improved iron loss description (equation 1). As been said, this iron loss description accounts for the presence of the real life conditions occurring in electrical machines such as in some regions of the ES elevated magnetic induction levels, waveforms with higher harmonics and rotational magnetization patterns. On the other hand, the magnetization curves J(H,f) also obtained by the standard Epstein measurements serve as input for the D finite element computations of the electrical machine under evaluation, identifying the local flux densities for each time step during one electrical period. The magnetization curves obtained from the Epstein frame are modified for use in FEA in order to account for the stack factor (corresponding to the actual manufacturing process). For one particular working point of the machine, the magnetic induction values in every finite element of the machine s stator lamination are retrieved, and this is repeated at different time instants during one electrical period. These magnetic induction values (as function of time and finite element index) then serve as input for the post-processing tool implemented into the numerical environment at ArcelorMittal Research Gent, which can run independently from the FEM calculations to calculate the iron losses according to the ArcelorMittal iron loss model of equation 1. This method is validated with higher harmonic magnetic measurements, resulting in good accuracy and reliability. Single Sheet Tester (SST) magnetic loss measurements were performed for which the magnetic polarization waveform corresponds with the actual waveform occurring in three specific points in the stator geometry and these measured losses were compared with the calculated values computed by utilizing equation (1). The difference is always less than 4%. These calculations can then be repeated for different operational points as a function of torque (current) and speed (frequency) and all such results can be combined in so-called efficiency maps. Using these efficiency maps the influence of different ES grades on the performance of rotating electrical machines can be studied. An example of such a study is given in [9]. B. Iron Loss Modelling, including the Local Degradation of Magnetic Properties near the Cut Edge As been said, the machine manufacturing aspects affecting the magnetic losses of electrical machines (such as lamination punching) can be implemented into the iron loss modelling approach as an upgrade to the basic model version described in subsection A. Modifications are necessary on the iron loss description, as well as on the material input data, which are obtained based on advanced characterization. At the vicinity of lamination edges due to the cutting/punching process [1-], two phenomena occur: dependence of both the local magnetic permeability and the local iron loss on the distance x from the cut edge. Indeed, the industrial processing of steel laminations (cutting, punching, etc.) causes - locally near the cut edge due to local plastic deformation - significant changes of the microstructure of the steel (dislocations, internal stresses, grain morphology), which results in a degradation of the magnetic properties in the region near the cut edge. The iron loss description is modified accordingly: the magnetization polarization is depending on the distance from the cut edge, as well as the micro-structurally dependent iron loss parameters s hyst, s exc, α and β : P( x, J ( x), f ) = s + s eddy n= 1 ( J p, n hyst ( x)) J ( x) 1+ ( r 1) J min p ( x) J ( x) ( α ( x) + β ( x) J p ( x) ) ( x) f 1.5 ( nf ) ( ) sexc( x) ( J p, n( x)) nf Both the magnetization polarization as a function of x as well as the iron loss parameters depending on the distance from the cut edge can be determined based on magnetic measurements. Samples were cut with a guillotine shear which was adjusted so that the local profile of the micro-vickers hardness of the cut samples corresponds to the local hardness profile of the punched edge of stator laminations produced during series production at Leroy Somer on the same ArcelorMittal fully processed electrical steel grade as the one studied here. The average losses as well the average magnetic polarization over the sample s cross section are measured with a SST on different sample sets with different ratios of degraded vs. non-degraded material, at various frequencies and at various values of the applied magnetic field H. As reference, an unaffected sample of 8mm wide was cut by spark erosion. In addition, five samples were prepared with the same cumulative width, but cut by guillotine shear in a number of less wide strips: as such, samples with, 4, 8, 16 and cut edges were prepared, where it is anticipated based on earlier results [1, 16] that the first three samples (, 4 and 8 cut edges) are a combination of cut edges with also some unaffected material, whereas for the last two samples (16 and cut edges) the strip width becomes so small that the degraded zones of both sides of the strip overlap. Having samples of both categories is necessary for the determination of the local properties (both J(H,x) as well as the loss parameters as a function of x) [16]. Starting from the experimental data, a numerical method is proposed in [16] to determine the local magnetization curves J(H,x), as function of distance from the cut edge. At 5Hz the impact of cutting is observed over a degraded region as deep as 6.9mm from the cut-edge inwards when this method is used for the electrical steel grade selected for testing during the study. This result is in agreement with the study on another grade reported in [16]. As the distribution is parabolic as a function of x, the most significant material degradation occurs over the first few mm. The local magnetization curves depending on the distance from the cut edge, are then used as inputs for the finite element computation of the field distribution in electrical machines. During this study for instance the stator and rotor design is split in five different zones, see Fig. 3, starting from the cut edge towards the bulk of the lamination, and for each of these zones the corresponding magnetization characteristic is used, see Fig. n= 1 p ()

5 4. Next, the losses are computed during post-processing for each zone separately, making use of iron loss parameters depending on the distance from the cut edge. function of x, whereas the markers indicate which fixed values are actually used to calculate the losses separately for each of the 5 zones as determined in the geometry. It can be noted that mainly the hysteresis loss parameter changes a lot in the affected zone. The excess loss parameter also increases, but to a lesser extent for the.5mm thick electrical steel grade under study here. The relative importance of excess losses when compared to the total losses, evaluated at 5Hz, is rather low. Moreover the excess losses are partly defined by microstructural features and partly by the electrical conductivity, which is not affected by cutting. 5. zone 1 zone zone 3 zone 4 zone 5 (unaffected) Fig. 3. Division of the stator and rotor geometry into 5 zones.. Zone 5 corresponds to the unaffected bulk material properties. The stator yoke width is larger than twice 6.9mm hence all zones are represented in the yoke. The stator tooth width is small and therefore the teeth are only represented by zone 1 and partly by zone. For the rotor, the 5 zones are only used around the outer diameter. 1.8 loss parameters (x) / unaffected loss parameters alpha(x) beta(x) shyst(x) sexc(x) alpha (5 zones) beta (5 zones) shyst (5 zones) sexc (5 zones) distance from cut edge (m) magnetic polarization J (T) J(H,x) zone 1 (<x<1mm) J(H,x) zone (1<x<mm) J(H,x) zone 3 (<x<4mm) J(H,x) zone 4 (4<x<6mm) J(H,x) zone 5 (x>6mm) unaffected magnetic field H (A/m) Fig. 4. Result of the J(H,x) determination is a set of five J(H) magnetization curves, one for each zone defined in both the stator and the rotor geometry. The iron loss parameters depending from the distance from the cut edge, are determined by assuming that their x- dependence is a decaying exponential one. Furthermore the unknowns are determined by minimizing the discrepancy between the measured iron losses for a certain (H p, f) set point and the calculated ones by incorporating the actual J(H,x) dependence (not just only the stepwise J(H) for the five FEMzones as shown in Fig. 4) into equation (). The magnetic measurements are performed with sinusoidal and unidirectional flux, hence the rotational part of the hysteresis losses as well as the higher harmonic part of both dynamic losses can be omitted during parameter fitting (as is also the case during the determination of the unaffected loss parameters based on Epstein data). Fig. 5 shows the result of this fitting, normalized to the loss parameters for unaffected material. The curves in Fig. 5 represent the continuous function of the loss parameters as a Fig. 5. x-dependence of the iron loss parameters, relatively compared to the loss parameters for unaffected material. The full curves represent the continuous function of the loss parameters as a function of x, whereas the markers indicate which fixed values are actually used to calculate the losses separately for each of the 5 zones as determined in the geometry. As a reminder s eddy is not affected by punching, hence this parameter is not depending on x. Remember that the depth of the affected zone is 6.9mm. Once the local iron loss parameters and the local magnetization curve (as continuous functions) are known, the changes in local total losses can be visualized under the same conditions as the SST magnetic measurement. This means the peak value of magnetic field is kept constant across the cross section of the strip. Fig. 6 shows the local loss distribution depending on the distance from the cut edge for different values of peak value of magnetic field. Both magnetic properties depending on the cut edge being the local iron loss parameters as well as the local magnetization curve have a signature in the local loss signature distribution. As can be noticed on Fig. 5, the iron loss parameters deviate most from the unaffected ones for x<3mm; as a result the local losses increase towards the cut edge. On the other hand, the J(H,x) behavior gives rise - especially for intermediate H p values (for instance for H p values between 1 and 3A/m for the grade under consideration, see Fig. 4), to local J values which decrease for decreasing x, a feature which is apparent throughout the complete affected zone of 6.9mm in depth. This explains why for 3<x<6.9mm and for intermediate H p values, the local losses first decrease a little for decreasing x, because in that zone the magnetic polarization is somewhat less than in the unaffected bulk material, whereas for 3<x<6.9mm the iron loss parameters are close to the unaffected ones; both aspects combined give rise to local losses which are somewhat lower for 3<x<6.9mm and for intermediate H p values.

6 iron loss density (W/kg) 1 8 Prototype motor 6 Hp = 97 A/m Hp = 4699 A/m Hp = 1764 A/m Hp = 559 A/m Hp = 48A/m Hp = 149 A/m Hp = 17A/m 4 Hp = 81 A/m Load machine Hp = 61 A/m distance from cut edge (m) Fig. 6. Local loss distribution depending on the distance x from the cut edge for different values of peak value of magnetic field. This visualization is only valid for the condition during the SST magnetic measurement, this means the peak value of magnetic field is kept constant across the cross section of the strip. Remember that the depth of the affected zone is 6.9mm. IV. MACHINE MEASUREMENT APPROACH Iron loss measurements and iron loss calculations are performed for two different operating conditions. The first consists of a locked rotor with a non-rotating, single-phase field. This allows losses due to a simple pulsating field to be measured thus avoiding rotational losses and loss components due to stator slotting. One phase winding is connected in series with the other two connected in parallel or in other words a star connection with two of the phases connected together. This arrangement is connected to a singlephase, 4V, 5Hz supply. It is this machine operating condition which best approaches the conditions used by the electrical steel supplier to measure the intrinsic magnetic losses of the material according to the international standard for Epstein frame measurements [IEC 644-]: unidirectional magnetization and sinusoidal magnetic flux density at 5Hz. The second operating condition consists of a conventional rotating field with the slotless rotor driven by a separate motor running close to its no-load speed. This test gives rise to rotational losses in the stator and losses in the machined rotor surface due to stator slotting (higher order space harmonics). The test bench used to perform the measurements at noload speed consists of the prototype, a coupling and a load machine, as pictured in Fig. 7. Before the test, the resistance is measured by means of the four-terminal sensing method using the micro-ohmmeter AOIP OM-1. The load machine is run up to synchronous speed and power is supplied to the prototype. Only electrical measurements need to be made at the prototype terminals: electric power, voltage and current are recorded using the power analyzer N4L KinetiQ PPA63. All measurements are made automatically; this allows measurements to be taken quickly thus avoiding the heating of the motor. Hence the prototype can be considered to be at room temperature (a maximum change of 5K is observed during the measurement interval). Fig. 7. Test bench used for the no load and rotating field test. As long as there are no slots on the rotor, the prototype cannot produce torque. This means that no torque measurement is necessary. Iron loss can be deduced from the electrical measurements using the same approach as the one described in the loss separation method in [IEC ]. Firstly, one needs to calculate the stator copper loss: PJS = 3 Rll I, (3) Rll being the line-to-line measured resistance of the prototype. Then the iron losses are the remaining losses; indeed as long as there is no cage, there are no rotor conductor losses and the mechanical losses are provided by the load machine. The iron losses are determined according the following formula: Piron = Pinput PJS, (4) where Pinput is the electrical power input to the prototype machine. The test bench used to perform the blocked rotor test is different because it needs a fixture to lock the rotor. Nevertheless the same electrical equipment is used for measurements, to reduce differences in characterization methodologies of both machine conditions. The same quantities are measured, in the same thermal conditions, and the iron losses are derived in the same way. V. STUDY 1: BLOCKED ROTOR & PULSATING FIELD A. Electromagnetic modelling results For the specific condition of machine operation with blocked rotor and single-phase (non-rotating but pulsating) field excitation - as was introduced in section 4 - Table II summarizes the calculated iron losses obtained with both iron loss modelling approaches ( properties, versus degraded material properties due to cut edge effect included).

7 TABLE II. CALCULATED IRON LOSSES, FOR THE BLOCKED ROTOR & PULSATING FIELD CONDITION, OBTAINED WITH BOTH IRON LOSS MODELLING APPROACHES (HOMOGENEOUS MATERIAL PROPERTIES, VERSUS DEGRADED MATERIAL PROPERTIES DUE TO CUT EDGE EFFECT INCLUDED). cut edge effect included stator rotor both stator Rotor both P hyst P hyst,rot P class,f P class,hh P exc,f P exc,hh P total As anticipated, the dominant loss components are the hysteresis losses and the dynamic loss components corresponding with the fundamental frequency: the sum of P hyst, P class,f and P exc,f contributes to 98% of the total losses for the specific condition of blocked rotor and pulsating field. As can be noticed in Table II, due to the pulsating field combined with the zero speed, rotational hysteresis losses are almost absent (indeed, for a pulsating field, twice per period the amplitude of J is zero in all elements of the geometry), as well as higher order space harmonic components of the classical eddy current losses and the excess losses are hardly noticeable (indeed the waveforms of J evaluated over the entire electrical period at each finite element, are nearly sinusoidal, for the blocked rotor condition). When comparing both modelling approaches it can be seen that including the cut edge effect gives rise to an additional 33% of the total iron losses. In line with the changes of the different iron loss parameters as a function of distance from the cut edge, most of the additional losses due to cutting are hysteresis losses. loss density (W/kg) = (loss per zone) / (zone weight) incl. cut edge effect R5 R4 R3 R R1 S1 S S3 S4 S5 Fig. 8. Loss density for each zone for both modelling approaches (with and without cut edge effect included), for the blocked rotor & pulsating field. Loss density is defined as the loss in W calculated for each zone separately, divided by the corresponding zone weight. Fig. 8 shows the loss density for each zone for both modelling approaches (with and without cut edge effect included), it can be seen that most of the loss increase is concentrated close to the air gap (i.e. for zone 1 and in both the stator and the rotor). Notice that the iron losses in zones S4 and S5 (these are the central parts of the stator yoke, see Fig. 3) are also slightly higher, although the iron loss parameters in these zones are almost equal to the unaffected ones of the. The underlying reason is that due to the cut edge effect on the magnetization curve J(H,x) the distribution of the J across the yoke is such that the amplitude of J becomes higher in the centre of the yoke and less at the sides (see also the J-histogram of Fig. 9). As such this increased J gives rise to increased losses at the centre of the yoke, although the iron loss parameters for these depths are almost unaffected. relative occurence of J p (%) 1% 9% 8% 7% 6% 5% 4% 3% % 1% % incl. cut edge effect (+) amplitude of magnetic polarization, J p (T) Fig. 9. For the blocked rotor and pulsating field: histogram of the amplitude of J in the stator, for both approaches (with and without cut edge effect included). The peak at 1.47T corresponds to the J value of the yoke (when the yoke is homogeneously magnetized). When cut edge effect is included, J increases for the central parts of the yoke (~1.53T), whereas J decreases closer to the edges (~1.39T). B. Comparison of measured versus modelled iron losses The iron losses determined experimentally by the machine measurement approach described in section 3, can now be compared with both modelling approaches, see Table III. The most precise model with cut edge effect included is able to predict 7% of the measured iron losses. This could be partly due to the modelling simplification of splitting the geometry and the corresponding continuously and locally varying material properties into only 5 zones (hence stepwise material behaviour). Moreover, the model does not yet incorporate the following features, which could increase the calculated iron loss (hence the associated additional losses are measured but not modeled): (1) additional machining of the rotor outer diameter to fine-tune the air gap which can lead to a surface loss component; () press fitting of stator in housing; (3) press fitting of rotor on shaft; (4) local material degradation due welding; (5) additional eddy current losses, due to eddy current paths which could close themselves over the electrically conducting shaft. (-) (+)

8 Features (3) and (5) could explain the difference between modeled and measured which is bigger for the blocked/pulsating condition (see next section: for the noload/rotating condition where modeled iron loss is 86% of the measured iron loss). In the case of the pulsating field, the rotor lamination is subject to a time varying field close to the shaft (a location where the degradation due to punching is not taken into account here) whereas for the no-load/rotating condition this is not the case. TABLE III. FOR THE BLOCKED ROTOR AND PULSATING FIELD: COMPARISON OF THE MEASURED VERSUS THE MODELLED IRON LOSSES. iron losses determined via machine measurements ArcelorMittal iron loss model, ArcelorMittal iron loss model, cut edge effect included VI. stator iron rotor iron total iron STUDY : SYNCHRONOUS SPEED & ROTATING FIELD A. Electromagnetic modelling results The second operating condition consists of a conventional rotating field with the slotless rotor driven by a separate motor running close to its no-load speed. Table IV summarizes the calculated iron losses obtained with both iron loss modelling approaches ( properties, versus degraded material properties due to cut edge effect included). TABLE IV. CALCULATED IRON LOSSES, FOR THE SYNCHRONOUS SPEED & ROTATING FIELD CONDITION, OBTAINED WITH BOTH IRON LOSS MODELLING APPROACHES (HOMOGENEOUS MATERIAL PROPERTIES, VERSUS DEGRADED MATERIAL PROPERTIES DUE TO CUT EDGE EFFECT INCLUDED). cut edge effect included stator rotor both stator rotor both P hyst P hyst,rot P class,f P class,hh P exc,f P exc,hh P total As can be noticed this condition gives rise to rotational losses in the stator, and losses in the machined rotor surface due to stator slotting (higher order space harmonics give rise to higher harmonic eddy current and excess losses; mainly in the rotor). Indeed when evaluating the waveforms of J over the entire electrical period at each finite element for the zone R1 (part of the rotor closest to the air gap), mainly 6 th and 4 th harmonics due stator winding and slotting harmonics are visible (corresponds to 3Hz and 1Hz respectively). The maximum value of the amplitude of the 4 th harmonic is around.4t (for a J bias at about.75t). On the other hand the higher harmonic content is less for the stator. Remark: rotor losses are determined starting from a FEM computation with stator moving and rotor fixed. When comparing both modelling approaches it can be seen that including the cut edge effect gives rise to an additional 4% of the total iron losses. Predominantly in the stator the additional loss due to cutting is the largest (+34%). In line with the changes of the different iron loss parameters as a function of distance from the cut edge, most of the additional losses due to cutting are hysteresis losses. loss density (W/kg) = (loss per zone) / (zone weight) incl. cut edge effect R5 R4 R3 R R1 S1 S S3 S4 S5 Fig. 1. Loss density for each zone for both modelling approaches (with and without cut edge effect included), for the synchronous speed & rotational field condition. Loss density is defined as the loss in W calculated for each zone separately, divided by the corresponding zone weight. relative occurence of J p (%) 5% % 15% 1% 5% % (+) (-) incl. cut edge effect amplitude of magnetic polarization, J p (T) Fig. 11. For the synchronous speed and rotating field condition: histogram of the amplitude of J in the stator, for both approaches (with and without cut edge effect included). The peak at 1.34T corresponds to the J value of the yoke (when the yoke is homogeneously magnetized). When cut edge effect is included, J increases for the central parts of the yoke (~1.43T), whereas J decreases closer to the edges (~1.T). Fig. 1 shows the loss density for each zone for both modeling approaches (with and without cut edge effect included), it can be seen that most of the loss increase is concentrated close to the air gap (i.e. zones S1, S and R1). Most of the rotor time varying flux is concentrated in zones R1 and R, hence also the losses. (+)

9 Notice that the iron losses in zones S4 and S5 (these are the central parts of the stator yoke, see Fig. 3) are also slightly higher, although the iron loss parameters in these zones are almost equal to the unaffected ones of the homogeneous material. The underlying reason is that due to the cut edge effect on the magnetization curve J(H,x) the distribution of the J across the yoke is such that the amplitude of J becomes higher in the centre of the yoke and less at the sides (see also the J-histogram of Fig. 11). As such this increased J gives rise to increased losses at the centre of the yoke while the iron loss parameters for these depths are almost unaffected. B. Comparison of measured versus modelled iron losses The iron losses determined experimentally by the machine measurement approach described in section 3, can now be compared with both modelling approaches, see Table V. The most precise model with cut edge effect included is able to predict 86% of the measured iron losses. This could be partly due to the modelling simplification of splitting the geometry and the corresponding continuously and locally varying material properties into only 5 zones (hence stepwise material behaviour). Moreover, the model does not yet incorporate the following features, which could increase the measured iron loss (hence the associated additional losses are measured but not modeled): (1) additional machining of the rotor outer diameter to fine-tune the air gap which can lead to a surface loss component; () press fitting of stator in housing; (3) press fitting of rotor on shaft; (4) local material degradation due welding. Feature (3) has less impact on the rotating field condition under study here since the rotor lamination is not subject to a time varying field close to the shaft. This could explain the difference between modeled and measured which is smaller for the no-load rotating condition. In comparison for the blocked/pulsating condition, the rotor lamination is also magnetized closer to the shaft, and modeled iron loss is 7% of the measured iron loss and in the case of the pulsating field,. TABLE V. FOR THE SYNCHRONOUS SPEED AND ROTATING FIELD CONDITION: COMPARISON OF THE MEASURED VERSUS THE MODELLED IRON LOSSES. iron losses determined via machine measurements ArcelorMittal iron loss model, ArcelorMittal iron loss model, cut edge effect included stator iron rotor iron total iron VII. CONCLUSIONS The current study shows that a structured optimization approach which takes into account a wider range of the relevant material and machine parameters, can lead to a better understanding of the different iron loss mechanisms. First of all it is key to define machine geometries and testing conditions, which allow a clear loss separation in the machine measurement results, to better identify correlations between machine calculations and losses. The results illustrate the improved iron loss prediction capability of the ArcelorMittal material model. In particular the implementation of the punching effect leads to a significant loss prediction improvement for both the cases of synchronous and zero speed. This brings the accuracy of the improved model up to 7% for zero speed and 86% for synchronous speed. Note that these results are obtained without integrating the degradation of the magnetic properties of the electrical steel due to compressive or tensile forces due to machine manufacturing and assembly. Future work will involve the stress relief annealing of the slotless rotor as a whole to mitigate the degraded magnetic properties due to the punching and machining of the rotor. The iron loss measurement will then be repeated and compared with the numerical results already obtained and with new calculations in which the cut edge effect is incorporated for the stator but not for the rotor. 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