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Evaluation of local magnetic degradation by interlocking electrical steel sheets for an effective modelling of electrical machines
Journal of Magnetism and Magnetic Materials 500 (2020) 166372
Contents lists available at ScienceDirect
Journal of Magnetism and Magnetic Materials journal homepage: www.elsevier.com/locate/jmmm
Research articles
Evaluation of local magnetic degradation by interlocking electrical steel sheets for an effective modelling of electrical machines
T
⁎
S. Imamoria,b, , S. Aiharac, H. Shimojid, A. Kutsukaked, K. Hameyerb a
Advanced Technology Laboratory, Fuji Electric Co., Ltd., Hino, Japan Institute of Electrical Machines (IEM), RWTH Aachen University, Aachen, Germany c BRIGHTEC Co., Ltd., Oita, Japan d Oita Industrial Research Institute (OIRI), Oita, Japan b
A R T I C LE I N FO
A B S T R A C T
Keywords: Electrical steel sheet Laminated core Manufacturing process Interlocking BH curve Iron loss Electrical machine
Interlocking electrical steel sheets degrades magnetic characteristics of laminated cores. In this paper, local magnetic characteristics of laminated cores with interlocking have been measured. The size of the damaged region has been determined according to the measurement results in order to calculate the average magnetic characteristics of the region, which have been applied to the simulation of an electrical machine with interlocking. The results demonstrate that it is important to consider the influence of interlocking for accurate calculations of motor characteristics.
1. Introduction Manufacturing processes of laminated cores have a significant impact on magnetic characteristics, leading to low performance of electrical machines [1–3]. Detailed magnetic characteristics under the influence of cutting [4] and compressive stress [5], which is often induced by shrink fitting, have been reported. When it comes to the fixing process of stacked electrical steel sheets, interlocking is a promising method because this method is suitable for mass production. This process, however, also alters soft magnetic properties of electrical steel sheets. It is thus important to know detailed information about the magnetic degradation for accurate modelling and simulation of electrical machines. In our previous study [6], BH and iron loss characteristics of laminated cores with interlocking have been studied by using interlocked ring cores. The measurement results are in good agreement with the proposed model and thus indicate that magnetic degradation due to interlocking is local. Stack length dependence of iron loss implies that interlaminar eddy current loss plays a minor role in the laminated cores studied in [6]. However, information from macroscopic magnetic measurements is not always sufficient for the design of electrical machines; distributions of magnetic characteristics have not been clarified in the study. For measuring such distributions, many methods have been proposed. The
⁎
most conventional method is to use search coils. This method, however, requires holes in the sample for the search coils, which degrade magnetic properties near the measured region and make it difficult to improve spatial resolution. To solve these problems, local magnetic measurements with needle probes and double H-coils are discussed [7–12]. In this paper, needle probes and double H-coils are used for the measurement of local magnetic properties near interlocks. With this method, the size of the damaged region induced by interlocking, which is not determined by macroscopic measurements [6], is discussed. Thereafter, the average magnetic properties in the damaged region are calculated. The results are used for the calculation of motor characteristics. 2. Experimental setup 2.1. Measurement method As shown in Fig. 1(a), the needle probes are in contact with the sample surface during the measurements. The contact force between the needles and the sample are controlled to reduce the measurement errors. The flux density in the sample is estimated with the voltage induced between the needles. The relation between the induced voltage and the flux density is as follows.
Corresponding author at: Fuji Electric. Co., Ltd., 1, Fuji-machi, Hino-City, Tokyo 191-8502, Japan. E-mail address: [email protected] (S. Imamori).
https://doi.org/10.1016/j.jmmm.2019.166372 Received 11 August 2019; Received in revised form 25 December 2019; Accepted 28 December 2019 Available online 07 January 2020 0304-8853/ © 2020 Elsevier B.V. All rights reserved.
Journal of Magnetism and Magnetic Materials 500 (2020) 166372
S. Imamori, et al.
Fig. 1. (a) Needle probes for the measurement of flux density and a double H-coil for the measurement of magnetic field. (b) The picture of the whole sensor. (b) The picture of the double H-coil.
Bi =
2 SBi
T
∫ eBi dt
35A. The die used for producing these samples is the same as that for ring cores shown in [6], which restricts the structure of the samples. Wire cutting was applied to cut out single sheets and laminated cores to minimize the magnetic degradation in the cutting process. The rolling direction is horizontal in this figure. The width of these cores is 6 mm, the same as that of ring cores shown in [6]. The length and width of each interlock, a and b respectively, are 4 mm and 1 mm. The overall height of the stack T is approximately 5 mm. The height of the protrusion shown in Fig. 3(c) is 0.35 mm. The photo of a sample with windings is shown in Fig. 3.
(1)
0
where eBi is the induced voltage, SBi is the area of the loop formed by the needles and the sample, T is the inverse of frequency f, and i is the in-plane components of the Cartesian coordinate system. The magnetic field in the sample is estimated with the voltage induced in the double H-coil, which is placed on the sample. The strength of magnetic field is calculated by
Hi =
1 SHi NHi
T
∫ eHi dt
(2)
0
3. Results of local magnetic measurements and discussions
where eHi is the induced voltage of the H-coils and SHiNHi is the effective area turns of each coil. The iron loss W is calculated by
W=
1 ρT
T
x ∫ ⎛Hx dB dt ⎜
0
+ Hy
⎝
dB y ⎞ ⎟
dt ⎠
Fig. 4 shows Bmax, Hmax, and W distributions for a single sheet without interlocking. Bmax and Hmax are defined by the following equations.
dt (3)
where ρ is the density of the sample. With this method, Enokizono, et al. [9] and Mori, et al. [10] measured local magnetic properties in a model core of a three-phase induction motor and discussed the influence of anisotropy in non-oriented electrical steel sheets. Aihara, et al. [11] and Ooka, et al. [12] studied local magnetic properties in a joint region of a three-phase transformer core made of grain-oriented electrical steel sheets. The sensor used for the measurements shown in Fig. 1(b) has following characteristics; the distance between the needles is 3.5 mm. The Hx-coil was wound on a ceramic plate, and the Hy-coil was wound around the Hx-coil. As shown in Fig. 1(c), the length of each coil is approximately 2 mm. The number of turns and the diameter of each coil were 560 and 0.01 mm, respectively. The effective area turns of the Hxand Hy-coils were 855 × 10−6 m2 and 595 × 10−6 m2, respectively. The distance between the surface of the whole sensor and the center of the double H-coil is 0.75 mm. To reduce the measurement errors, the distance between the double H-coil and the sample surface is set to be as small as possible.
Bmax = max{ Bx2 + By2 }
(4)
Hmax = max{ Hx2 + Hy2 }
(5)
The frequency of excitation was 50 Hz. The maximum flux density measured by the search coil shown in Fig. 3 was controlled at 1.4 T. This measurement has 86 and 3 measurement points for longitudinal and transverse directions, respectively. As shown in Fig. 5(a), the distances between the adjacent measurement points are approximately 1 mm and 0.75 mm for longitudinal and transverse directions, respectively. In Fig. 4, the measurement results for each points are shown by colored rectangles. The rectangles are located at the center of the measurement points. Although the size of the sensor restricts the measurable area, local magnetic characteristics near the cut edge (or the interlocking shown below) can be deduced by comparing neighboring points. This figure shows that local magnetic distribution is well measured by this method; flux density at the corners is lower than that in the other regions. Fig. 6 shows Bmax distributions for interlocked samples. The maximum flux density measured by the search coil was controlled at 1.4 T. This measurement has 93 and 3 measurement points for longitudinal and transverse directions, respectively. As shown in Fig. 5(b), the distances between the adjacent measurement points are approximately 0.5 mm and 0.75 mm for longitudinal and transverse directions, respectively. Here we should note that the positions of cut edges and interlocks in this figure are just guide for the eye. Fig. 6(a) and (b) show the results for the front and back of a single sheet with interlocks perpendicular to the longitudinal direction. The definitions of front and back are shown in Fig. 7. Bmax for this sheet is much lower than 1.4 T. Because this sample configuration strongly blocks the flux of single
2.2. Sample preparation In our previous study [6], laminated ring cores with interlocks are used to measure macroscopic soft magnetic properties. For such measurements, ring cores are suitable because the influence of magnetic anisotropy is averaged. In contrast, local magnetic measurements detect magnetic anisotropy, which makes it difficult to discuss the influence of interlocking in ring cores. Rectangular samples are thus better for local magnetic measurements. Fig. 2 shows the schematic picture of the samples. The grade of the electrical steel sheets under study is M3602
Journal of Magnetism and Magnetic Materials 500 (2020) 166372
S. Imamori, et al.
Fig. 2. The schematic pictures of the samples. (a) The sample with interlocks parallel to flux. (b) The sample with interlocks perpendicular to flux. (c) The cross section of the interlocked region in a laminated core.
figures is due to the asymmetric structure of interlocking in the stack direction as shown in Fig. 2(c). Bmax distribution at the center of the lamination is probably similar to the average of these figures. Fig. 6(g) and (h) show the results for the front and back of a laminated core with interlocks parallel to the longitudinal direction. Bmax for laminated cores is higher than that for single sheets, because laminated cores have interlaminar magnetic paths and thus the influence of “blocking” flux by interlocking is not significant. Similar to the case of single sheets, Bmax for a sample with interlocks perpendicular to the longitudinal direction is lower than that for a sample with interlocks parallel to the longitudinal direction. In Fig. 6(c), (d), (g), and (h), flux density close to the interlocks is larger than the other area. Possible reasons for this phenomenon are the improvement of permeability caused by the tensile stress in the longitudinal direction induced by the interlocking process and the disturbance by inter-laminar eddy current due to the short circuits. Clarifying the mechanism by using X-ray stress measurement [13] or 3D simulation of eddy current will be an interesting future research topic.
Fig. 3. A sample with windings. The maximum flux density measured by the search coil was controlled at 1.4 T.
sheets, a significant amount of leakage flux exists, leading to low Bmax. Fig. 6(c) and (d) show the results for the front and back of a single sheet with interlocks parallel to the longitudinal direction. Bmax for this sheet is higher than that in Fig. 6(a) and (b), because this sample configuration does not block flux significantly. Fig. 6(e) and (f) show the results for the front and back of a laminated core with interlocks perpendicular to the longitudinal direction. The difference between these
(a) The front of a single sheet with interlocks perpendicular to the longitudinal direction. (b) The back of a single sheet with interlocks perpendicular to the longitudinal direction. (c) The front of a single sheet with interlocks parallel to the longitudinal direction.
Fig. 4. Measurement results of local magnetic characteristics for a single sheet without interlocking. (a) Bmax distribution. (b) Hmax distribution. (c) W distribution. 3
Journal of Magnetism and Magnetic Materials 500 (2020) 166372
S. Imamori, et al.
Fig. 5. Measurement points. Each square has an area of 3.5*3.5 mm2 and shows a measurement area of B. (a) For samples without interlocking. (b) For samples with interlocking.
(d) The back of a single sheet with interlocks parallel to the longitudinal direction. (e) The front of a laminated core with interlocks perpendicular to the longitudinal direction. (f) The back of a laminated core with interlocks perpendicular to the longitudinal direction. (g) The front of a laminated core with interlocks parallel to the longitudinal direction. (h) The back of a laminated core with interlocks parallel to the longitudinal direction.
Fig. 7. Definition of front and back.
(e) The front of a laminated core with interlocks perpendicular to the longitudinal direction. (f) The back of a laminated core with interlocks perpendicular to the longitudinal direction. (g) The front of a laminated core with interlocks parallel to the longitudinal direction. (h) The back of a laminated core with interlocks parallel to the longitudinal direction.
Fig. 8 shows Hmax distributions for the interlocked samples. Increases in Hmax close to the interlocks are observed in every measurement result. Fig. 9 shows W distributions for the interlocked samples. Increases in W close to the interlocks are observed for every measurement result. (a) The front of a single sheet longitudinal direction. (b) The back of a single sheet longitudinal direction. (c) The front of a single sheet itudinal direction. (d) The back of a single sheet itudinal direction.
with interlocks perpendicular to the (a) The front of a single sheet with interlocks perpendicular to the longitudinal direction. (b) The back of a single sheet with interlocks perpendicular to the longitudinal direction. (c) The front of a single sheet with interlocks parallel to the longitudinal direction. (d) The back of a single sheet with interlocks parallel to the
with interlocks perpendicular to the with interlocks parallel to the longwith interlocks parallel to the long-
Fig. 6. Bmax distributions for interlocked samples. 4
Journal of Magnetism and Magnetic Materials 500 (2020) 166372
S. Imamori, et al.
Fig. 8. Hmax distributions for interlocked samples.
interlocks are larger than those close to the short sides of interlocks. This result is reasonable because the long sides of interlocks were separated from the other region in the interlocking process in contrast to the case of short sides. In this paper, magnetic characteristics have been measured only when the flux is mainly in the rolling direction. Measuring characteristics when the flux is in the cross direction is an interesting future research topic.
longitudinal direction. (e) The front of a laminated core with interlocks perpendicular to the longitudinal direction. (f) The back of a laminated core with interlocks perpendicular to the longitudinal direction. (g) The front of a laminated core with interlocks parallel to the longitudinal direction. (h) The back of a laminated core with interlocks parallel to the longitudinal direction.
(a) The front of a single sheet with interlocks perpendicular to the longitudinal direction. (b) The back of a single sheet with interlocks perpendicular to the longitudinal direction. (c) The front of a single sheet with interlocks parallel to the longitudinal direction. (d) The back of a single sheet with interlocks parallel to the longitudinal direction. (e) The front of a laminated core with interlocks perpendicular to the longitudinal direction. (f) The back of a laminated core with interlocks perpendicular to the
Although Hmax and W distributions show clearly that magnetic degradation by interlocking is local, it is difficult to determine the size of damaged regions with these figures, because Hmax and W distributions depend not only on magnetic degradation but also on Bmax. In this paper, Bmax dependence of the material iron loss without degradation is γ simply expressed by W = KBmax . γ for the material studied is calculated to be approximately 1.66 by fitting Bmax dependence of W without γ material degradation in the region from 0.8 T to 1.4 T. K = W / Bmax is shown in Fig. 10 to see intrinsic material degradation by interlocking. These figures show that the damaged regions close to the long sides of
Fig. 9. W distributions for interlocked samples. 5
Journal of Magnetism and Magnetic Materials 500 (2020) 166372
S. Imamori, et al.
γ Fig. 10. Distributions of K = W / Bmax for interlocked samples calculated by the results shown in Figs. 6 and 9.
magnetic characteristic of the damaged region for this model is calculated. First, it is assumed that the interlocked ring core is represented by a magnetic series circuit with undamaged and damaged regions as shown in Fig. 11. If there is no leakage of flux from the ring core, the measured permeability and iron loss are expressed by the following equations.
l Nd l − Nd = + μa μ'' μ' Wa =
Nd '' l − Nd W + W' l l
(6)
(7)
where μa and Wa are the measured permeability and iron loss. μ'' and μ' are the permeability of damaged and undamaged regions. W’’ and W’ are the iron losses of damaged and undamaged regions. N is the number of interlocks in a ring core. l is the average length of the entire magnetic circuit, which is approximated by the following equation.
Fig. 11. The schematic picture of a ring core with four interlocks. The interlocks are parallel to flux.
longitudinal direction. (g) The front of a laminated core with interlocks parallel to the longitudinal direction. (h) The back of a laminated core with interlocks parallel to the longitudinal direction.
l = (do + di ) π /2
(8)
where do and di are the outer and inner diameter, respectively. d is the length of a damaged region, which is calculated with the angle of this region α .
4. Modelling of interlocking
d = (do + di ) α /4
4.1. Calculation of magnetic characteristics in damaged regions
(9)
Eqs. (6) and (7) show that the inverse of permeability and iron loss should increase linearly with the increasing number of interlocks N. The linear behaviors shown in Fig. 12(a) and (b) obtained by measurements of ring cores demonstrate that this modelling is appropriate and thus
In this chapter, the modelling method for a magnetic circuit (a ring core in this case) with interlocking [6] is briefly explained and the
Fig. 12. N dependence of measured values for ring cores. The interlocks are parallel to flux. (a) Required magnetic fields to reach specific B. (b) Iron loss at 50 Hz. 6
Journal of Magnetism and Magnetic Materials 500 (2020) 166372
S. Imamori, et al.
Fig. 13. A damaged region due to interlocking. (a) Parallel to flux. (b) Perpendicular to flux.
Fig. 14. Average magnetic characteristics in the damaged region. (a) BH curve. (b) Iron loss at 50 Hz.
6 mm as shown in Fig. 13 makes it easy to calculate average magnetic properties in the damaged regions because the width of the damaged regions is the same as that of the samples used in this study. Under this assumption, the distance between the edge of the damaged region and the long side of the interlock is 2.5 mm and that between the edge of the damaged region and the short side of the interlock is 1 mm. However, it should be noted that the size of the damaged region depends on the dimensions of the interlock. Based on Fig. 12, Eqs. (6) and (7), the average magnetic properties in the damaged regions are calculated. Fig. 14 shows the BH curves and iron losses at 50 Hz in the damaged region, which are used for the calculation of motor characteristics. This figure demonstrates significant reduction of permeability and increase of iron loss in the damaged region. The small anisotropy in Fig. 14 agrees well with the discussions in the previous chapter. 4.2. Application of the modelling to the simulation of an electrical machine
Fig. 15. The schematic picture of the electrical machine under study (1/4 model).
The magnetic characteristics of the damaged region calculated in 4.1 is used for the simulation of an electrical machine. The schematic picture of the machine under study is shown in Fig. 15. Table 1 shows the specifications of this machine. The stator core of this machine is composed of 12 pieces. Each piece has three interlocks; two in the yoke and one in the tooth. The damaged regions with a size of 6 mm*6 mm caused by interlocking is also shown in Fig. 15. To simplify the calculation, the average data of magnetic characteristics for parallel and perpendicular directions shown in Fig. 14 were used for the isotropic characteristics in the damaged regions in Fig. 15. Fig. 16 shows calculation results of no-load characteristics for this machine. The rotation speed is 1500 rpm. Fig. 16(a) demonstrates that interlocking increases the amplitude of cogging torque in this machine. This behavior is explained by the non-linearity of the BH curve in the stator core [3]. Fig. 16(b) demonstrates that interlocking increases iron
Table 1 Specifications of the electrical machine. Outer diameter of stator Core length Rated power
124 mm 50 mm 1 kW
Magnet Stator core Rotor core
Nd-Fe-B M360-35A M1300-50A
magnetic damage by interlocking is local. In this case the interlocks are parallel to flux. Similar results are obtained for ring cores with interlocks perpendicular to flux. From the discussions in the preceding chapter, it is reasonable to define that the damaged region is square, although the interlock has an anisotropic structure. In addition, assuming that the length of the side is 7
Journal of Magnetism and Magnetic Materials 500 (2020) 166372
S. Imamori, et al.
Fig. 16. No-load characteristics of the electrical machine. (a) Cogging torque. (b) Iron loss.
doi.org/10.1016/j.jmmm.2019.166372.
loss under no-load condition. Both results clearly show that it is important to consider the influence of interlocking for accurate calculations of motor characteristics. Optimizing position of interlocks in electrical machines by using this modelling will be an interesting future topic.
References [1] N. Takahashi, H. Morimoto, Y. Yunoki, D. Miyagi, Effect of shrink fitting and cutting on iron loss of permanent magnet motor, J. Magn. Magn. Mater. 320 (20) (2008) e925–e928. [2] A. Cavagnino, R. Bojoi, Z. Gmyrek, M. Lefik, Stator lamination geometry influence on the building factor of synchronous reluctance motor cores, IEEE Trans. Magn. 53 (4) (2017) 3394–3403. [3] S. Imamori, H. Ohguchi, M. Shuto, A. Toba, Relation between magnetic properties of stator core and cogging torque in 8-pole 12-slot SPM synchronous motors, IEEJ J. Ind. Appl. 4 (6) (2015) 696–702. [4] F. Ossart, E. Hug, O. Hubert, C. Buvat, R. Billardon, Effect of punching on electrical sheets: experimental and numerical coupled analysis, IEEE Trans. Magn. 36 (5) (2000) 3137–3140. [5] Y. Kai, Y. Tsuchida, T. Todaka, M. Enokizono, Influence of stress on vector magnetic property under alternating magnetic flux conditions, IEEE Trans. Magn. 47 (10) (2011) 4344–4347. [6] S. Imamori, S. Steentjes, K. Hameyer, Influence of interlocking on magnetic properties of electrical steel laminations, IEEE Trans. Magn. 53 (11) (2017) 8108704. [7] E. Werner, Einrichtung zur Messung magnetischer Eigenschaften von Blechen bei Wechselstrommagnetisierung, Austrian Patent 191015 (1957). [8] H. Pfützner, G. Krismanic, The needle method for induction tests: source of error, IEEE Trans. Magn. 40 (3) (2004) 1610–1616. [9] M. Enokizono, M. Morikawa, S. Fujiyama, J. Sievert, I. Serikawa, Distribution of local magnetic properties in three-phase induction motor model core, IEEE Trans. Magn. 35 (5) (1999) 3937–3939. [10] Y. Mori, H. Shimoji, A. Ikariga, T. Todaka, M. Enokizono, Measured distributions of two-dimensional magnetic properties in a three phase induction motor model core by using a V-H sensor, International Conference on Electrical Machines and Systems (ICEMS), 2007, pp. 1013–1018. [11] S. Aihara, H. Shimoji, T. Todaka, M. Enokizono, Measurement of local vector magnetic properties in laser scratched grain-oriented silicon steel sheet with a vector-hysteresis sensor, IEEE Trans. Magn. 48 (11) (2012) 4499–4502. [12] K. Ooka, T. Kajiwara, S. Aihara, M. Enokizono, Control of rotating magnetic flux distribution in a transformer model core by laser irradiation, IEEE Trans. Magn. 50 (4) (2012) 8400204. [13] S. Zeze, Y. Kai, T. Todaka, M. Enokizono, Vector magnetic characteristic analysis of a PM motor considering residual stress distribution with complex-approximated material modeling, IEEE Trans. Magn. 48 (11) (2012) 3352–3355.
5. Conclusions Local magnetic measurements of laminated cores with interlocking by using needle B probes and H-coils show that magnetic degradation due to interlocking is local and that the damaged regions close to the long sides of interlocks are larger than those close to the short sides of interlocks. The results are used for the modelling of interlocking, which are applied to simulations of electrical machines. The simulation results demonstrate the importance of considering the influence of interlocking. CRediT authorship contribution statement S. Imamori: Conceptualization, Formal analysis, Investigation, Methodology, Writing - original draft, Writing - review & editing. S. Aihara: Data curation, Resources. H. Shimoji: Visualization, Software. A. Kutsukake: Validation. K. Hameyer: Supervision. Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Appendix A. Supplementary data Supplementary data to this article can be found online at https://
8
Contents lists available at ScienceDirect
Journal of Magnetism and Magnetic Materials journal homepage: www.elsevier.com/locate/jmmm
Research articles
Evaluation of local magnetic degradation by interlocking electrical steel sheets for an effective modelling of electrical machines
T
⁎
S. Imamoria,b, , S. Aiharac, H. Shimojid, A. Kutsukaked, K. Hameyerb a
Advanced Technology Laboratory, Fuji Electric Co., Ltd., Hino, Japan Institute of Electrical Machines (IEM), RWTH Aachen University, Aachen, Germany c BRIGHTEC Co., Ltd., Oita, Japan d Oita Industrial Research Institute (OIRI), Oita, Japan b
A R T I C LE I N FO
A B S T R A C T
Keywords: Electrical steel sheet Laminated core Manufacturing process Interlocking BH curve Iron loss Electrical machine
Interlocking electrical steel sheets degrades magnetic characteristics of laminated cores. In this paper, local magnetic characteristics of laminated cores with interlocking have been measured. The size of the damaged region has been determined according to the measurement results in order to calculate the average magnetic characteristics of the region, which have been applied to the simulation of an electrical machine with interlocking. The results demonstrate that it is important to consider the influence of interlocking for accurate calculations of motor characteristics.
1. Introduction Manufacturing processes of laminated cores have a significant impact on magnetic characteristics, leading to low performance of electrical machines [1–3]. Detailed magnetic characteristics under the influence of cutting [4] and compressive stress [5], which is often induced by shrink fitting, have been reported. When it comes to the fixing process of stacked electrical steel sheets, interlocking is a promising method because this method is suitable for mass production. This process, however, also alters soft magnetic properties of electrical steel sheets. It is thus important to know detailed information about the magnetic degradation for accurate modelling and simulation of electrical machines. In our previous study [6], BH and iron loss characteristics of laminated cores with interlocking have been studied by using interlocked ring cores. The measurement results are in good agreement with the proposed model and thus indicate that magnetic degradation due to interlocking is local. Stack length dependence of iron loss implies that interlaminar eddy current loss plays a minor role in the laminated cores studied in [6]. However, information from macroscopic magnetic measurements is not always sufficient for the design of electrical machines; distributions of magnetic characteristics have not been clarified in the study. For measuring such distributions, many methods have been proposed. The
⁎
most conventional method is to use search coils. This method, however, requires holes in the sample for the search coils, which degrade magnetic properties near the measured region and make it difficult to improve spatial resolution. To solve these problems, local magnetic measurements with needle probes and double H-coils are discussed [7–12]. In this paper, needle probes and double H-coils are used for the measurement of local magnetic properties near interlocks. With this method, the size of the damaged region induced by interlocking, which is not determined by macroscopic measurements [6], is discussed. Thereafter, the average magnetic properties in the damaged region are calculated. The results are used for the calculation of motor characteristics. 2. Experimental setup 2.1. Measurement method As shown in Fig. 1(a), the needle probes are in contact with the sample surface during the measurements. The contact force between the needles and the sample are controlled to reduce the measurement errors. The flux density in the sample is estimated with the voltage induced between the needles. The relation between the induced voltage and the flux density is as follows.
Corresponding author at: Fuji Electric. Co., Ltd., 1, Fuji-machi, Hino-City, Tokyo 191-8502, Japan. E-mail address: [email protected] (S. Imamori).
https://doi.org/10.1016/j.jmmm.2019.166372 Received 11 August 2019; Received in revised form 25 December 2019; Accepted 28 December 2019 Available online 07 January 2020 0304-8853/ © 2020 Elsevier B.V. All rights reserved.
Journal of Magnetism and Magnetic Materials 500 (2020) 166372
S. Imamori, et al.
Fig. 1. (a) Needle probes for the measurement of flux density and a double H-coil for the measurement of magnetic field. (b) The picture of the whole sensor. (b) The picture of the double H-coil.
Bi =
2 SBi
T
∫ eBi dt
35A. The die used for producing these samples is the same as that for ring cores shown in [6], which restricts the structure of the samples. Wire cutting was applied to cut out single sheets and laminated cores to minimize the magnetic degradation in the cutting process. The rolling direction is horizontal in this figure. The width of these cores is 6 mm, the same as that of ring cores shown in [6]. The length and width of each interlock, a and b respectively, are 4 mm and 1 mm. The overall height of the stack T is approximately 5 mm. The height of the protrusion shown in Fig. 3(c) is 0.35 mm. The photo of a sample with windings is shown in Fig. 3.
(1)
0
where eBi is the induced voltage, SBi is the area of the loop formed by the needles and the sample, T is the inverse of frequency f, and i is the in-plane components of the Cartesian coordinate system. The magnetic field in the sample is estimated with the voltage induced in the double H-coil, which is placed on the sample. The strength of magnetic field is calculated by
Hi =
1 SHi NHi
T
∫ eHi dt
(2)
0
3. Results of local magnetic measurements and discussions
where eHi is the induced voltage of the H-coils and SHiNHi is the effective area turns of each coil. The iron loss W is calculated by
W=
1 ρT
T
x ∫ ⎛Hx dB dt ⎜
0
+ Hy
⎝
dB y ⎞ ⎟
dt ⎠
Fig. 4 shows Bmax, Hmax, and W distributions for a single sheet without interlocking. Bmax and Hmax are defined by the following equations.
dt (3)
where ρ is the density of the sample. With this method, Enokizono, et al. [9] and Mori, et al. [10] measured local magnetic properties in a model core of a three-phase induction motor and discussed the influence of anisotropy in non-oriented electrical steel sheets. Aihara, et al. [11] and Ooka, et al. [12] studied local magnetic properties in a joint region of a three-phase transformer core made of grain-oriented electrical steel sheets. The sensor used for the measurements shown in Fig. 1(b) has following characteristics; the distance between the needles is 3.5 mm. The Hx-coil was wound on a ceramic plate, and the Hy-coil was wound around the Hx-coil. As shown in Fig. 1(c), the length of each coil is approximately 2 mm. The number of turns and the diameter of each coil were 560 and 0.01 mm, respectively. The effective area turns of the Hxand Hy-coils were 855 × 10−6 m2 and 595 × 10−6 m2, respectively. The distance between the surface of the whole sensor and the center of the double H-coil is 0.75 mm. To reduce the measurement errors, the distance between the double H-coil and the sample surface is set to be as small as possible.
Bmax = max{ Bx2 + By2 }
(4)
Hmax = max{ Hx2 + Hy2 }
(5)
The frequency of excitation was 50 Hz. The maximum flux density measured by the search coil shown in Fig. 3 was controlled at 1.4 T. This measurement has 86 and 3 measurement points for longitudinal and transverse directions, respectively. As shown in Fig. 5(a), the distances between the adjacent measurement points are approximately 1 mm and 0.75 mm for longitudinal and transverse directions, respectively. In Fig. 4, the measurement results for each points are shown by colored rectangles. The rectangles are located at the center of the measurement points. Although the size of the sensor restricts the measurable area, local magnetic characteristics near the cut edge (or the interlocking shown below) can be deduced by comparing neighboring points. This figure shows that local magnetic distribution is well measured by this method; flux density at the corners is lower than that in the other regions. Fig. 6 shows Bmax distributions for interlocked samples. The maximum flux density measured by the search coil was controlled at 1.4 T. This measurement has 93 and 3 measurement points for longitudinal and transverse directions, respectively. As shown in Fig. 5(b), the distances between the adjacent measurement points are approximately 0.5 mm and 0.75 mm for longitudinal and transverse directions, respectively. Here we should note that the positions of cut edges and interlocks in this figure are just guide for the eye. Fig. 6(a) and (b) show the results for the front and back of a single sheet with interlocks perpendicular to the longitudinal direction. The definitions of front and back are shown in Fig. 7. Bmax for this sheet is much lower than 1.4 T. Because this sample configuration strongly blocks the flux of single
2.2. Sample preparation In our previous study [6], laminated ring cores with interlocks are used to measure macroscopic soft magnetic properties. For such measurements, ring cores are suitable because the influence of magnetic anisotropy is averaged. In contrast, local magnetic measurements detect magnetic anisotropy, which makes it difficult to discuss the influence of interlocking in ring cores. Rectangular samples are thus better for local magnetic measurements. Fig. 2 shows the schematic picture of the samples. The grade of the electrical steel sheets under study is M3602
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Fig. 2. The schematic pictures of the samples. (a) The sample with interlocks parallel to flux. (b) The sample with interlocks perpendicular to flux. (c) The cross section of the interlocked region in a laminated core.
figures is due to the asymmetric structure of interlocking in the stack direction as shown in Fig. 2(c). Bmax distribution at the center of the lamination is probably similar to the average of these figures. Fig. 6(g) and (h) show the results for the front and back of a laminated core with interlocks parallel to the longitudinal direction. Bmax for laminated cores is higher than that for single sheets, because laminated cores have interlaminar magnetic paths and thus the influence of “blocking” flux by interlocking is not significant. Similar to the case of single sheets, Bmax for a sample with interlocks perpendicular to the longitudinal direction is lower than that for a sample with interlocks parallel to the longitudinal direction. In Fig. 6(c), (d), (g), and (h), flux density close to the interlocks is larger than the other area. Possible reasons for this phenomenon are the improvement of permeability caused by the tensile stress in the longitudinal direction induced by the interlocking process and the disturbance by inter-laminar eddy current due to the short circuits. Clarifying the mechanism by using X-ray stress measurement [13] or 3D simulation of eddy current will be an interesting future research topic.
Fig. 3. A sample with windings. The maximum flux density measured by the search coil was controlled at 1.4 T.
sheets, a significant amount of leakage flux exists, leading to low Bmax. Fig. 6(c) and (d) show the results for the front and back of a single sheet with interlocks parallel to the longitudinal direction. Bmax for this sheet is higher than that in Fig. 6(a) and (b), because this sample configuration does not block flux significantly. Fig. 6(e) and (f) show the results for the front and back of a laminated core with interlocks perpendicular to the longitudinal direction. The difference between these
(a) The front of a single sheet with interlocks perpendicular to the longitudinal direction. (b) The back of a single sheet with interlocks perpendicular to the longitudinal direction. (c) The front of a single sheet with interlocks parallel to the longitudinal direction.
Fig. 4. Measurement results of local magnetic characteristics for a single sheet without interlocking. (a) Bmax distribution. (b) Hmax distribution. (c) W distribution. 3
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Fig. 5. Measurement points. Each square has an area of 3.5*3.5 mm2 and shows a measurement area of B. (a) For samples without interlocking. (b) For samples with interlocking.
(d) The back of a single sheet with interlocks parallel to the longitudinal direction. (e) The front of a laminated core with interlocks perpendicular to the longitudinal direction. (f) The back of a laminated core with interlocks perpendicular to the longitudinal direction. (g) The front of a laminated core with interlocks parallel to the longitudinal direction. (h) The back of a laminated core with interlocks parallel to the longitudinal direction.
Fig. 7. Definition of front and back.
(e) The front of a laminated core with interlocks perpendicular to the longitudinal direction. (f) The back of a laminated core with interlocks perpendicular to the longitudinal direction. (g) The front of a laminated core with interlocks parallel to the longitudinal direction. (h) The back of a laminated core with interlocks parallel to the longitudinal direction.
Fig. 8 shows Hmax distributions for the interlocked samples. Increases in Hmax close to the interlocks are observed in every measurement result. Fig. 9 shows W distributions for the interlocked samples. Increases in W close to the interlocks are observed for every measurement result. (a) The front of a single sheet longitudinal direction. (b) The back of a single sheet longitudinal direction. (c) The front of a single sheet itudinal direction. (d) The back of a single sheet itudinal direction.
with interlocks perpendicular to the (a) The front of a single sheet with interlocks perpendicular to the longitudinal direction. (b) The back of a single sheet with interlocks perpendicular to the longitudinal direction. (c) The front of a single sheet with interlocks parallel to the longitudinal direction. (d) The back of a single sheet with interlocks parallel to the
with interlocks perpendicular to the with interlocks parallel to the longwith interlocks parallel to the long-
Fig. 6. Bmax distributions for interlocked samples. 4
Journal of Magnetism and Magnetic Materials 500 (2020) 166372
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Fig. 8. Hmax distributions for interlocked samples.
interlocks are larger than those close to the short sides of interlocks. This result is reasonable because the long sides of interlocks were separated from the other region in the interlocking process in contrast to the case of short sides. In this paper, magnetic characteristics have been measured only when the flux is mainly in the rolling direction. Measuring characteristics when the flux is in the cross direction is an interesting future research topic.
longitudinal direction. (e) The front of a laminated core with interlocks perpendicular to the longitudinal direction. (f) The back of a laminated core with interlocks perpendicular to the longitudinal direction. (g) The front of a laminated core with interlocks parallel to the longitudinal direction. (h) The back of a laminated core with interlocks parallel to the longitudinal direction.
(a) The front of a single sheet with interlocks perpendicular to the longitudinal direction. (b) The back of a single sheet with interlocks perpendicular to the longitudinal direction. (c) The front of a single sheet with interlocks parallel to the longitudinal direction. (d) The back of a single sheet with interlocks parallel to the longitudinal direction. (e) The front of a laminated core with interlocks perpendicular to the longitudinal direction. (f) The back of a laminated core with interlocks perpendicular to the
Although Hmax and W distributions show clearly that magnetic degradation by interlocking is local, it is difficult to determine the size of damaged regions with these figures, because Hmax and W distributions depend not only on magnetic degradation but also on Bmax. In this paper, Bmax dependence of the material iron loss without degradation is γ simply expressed by W = KBmax . γ for the material studied is calculated to be approximately 1.66 by fitting Bmax dependence of W without γ material degradation in the region from 0.8 T to 1.4 T. K = W / Bmax is shown in Fig. 10 to see intrinsic material degradation by interlocking. These figures show that the damaged regions close to the long sides of
Fig. 9. W distributions for interlocked samples. 5
Journal of Magnetism and Magnetic Materials 500 (2020) 166372
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γ Fig. 10. Distributions of K = W / Bmax for interlocked samples calculated by the results shown in Figs. 6 and 9.
magnetic characteristic of the damaged region for this model is calculated. First, it is assumed that the interlocked ring core is represented by a magnetic series circuit with undamaged and damaged regions as shown in Fig. 11. If there is no leakage of flux from the ring core, the measured permeability and iron loss are expressed by the following equations.
l Nd l − Nd = + μa μ'' μ' Wa =
Nd '' l − Nd W + W' l l
(6)
(7)
where μa and Wa are the measured permeability and iron loss. μ'' and μ' are the permeability of damaged and undamaged regions. W’’ and W’ are the iron losses of damaged and undamaged regions. N is the number of interlocks in a ring core. l is the average length of the entire magnetic circuit, which is approximated by the following equation.
Fig. 11. The schematic picture of a ring core with four interlocks. The interlocks are parallel to flux.
longitudinal direction. (g) The front of a laminated core with interlocks parallel to the longitudinal direction. (h) The back of a laminated core with interlocks parallel to the longitudinal direction.
l = (do + di ) π /2
(8)
where do and di are the outer and inner diameter, respectively. d is the length of a damaged region, which is calculated with the angle of this region α .
4. Modelling of interlocking
d = (do + di ) α /4
4.1. Calculation of magnetic characteristics in damaged regions
(9)
Eqs. (6) and (7) show that the inverse of permeability and iron loss should increase linearly with the increasing number of interlocks N. The linear behaviors shown in Fig. 12(a) and (b) obtained by measurements of ring cores demonstrate that this modelling is appropriate and thus
In this chapter, the modelling method for a magnetic circuit (a ring core in this case) with interlocking [6] is briefly explained and the
Fig. 12. N dependence of measured values for ring cores. The interlocks are parallel to flux. (a) Required magnetic fields to reach specific B. (b) Iron loss at 50 Hz. 6
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Fig. 13. A damaged region due to interlocking. (a) Parallel to flux. (b) Perpendicular to flux.
Fig. 14. Average magnetic characteristics in the damaged region. (a) BH curve. (b) Iron loss at 50 Hz.
6 mm as shown in Fig. 13 makes it easy to calculate average magnetic properties in the damaged regions because the width of the damaged regions is the same as that of the samples used in this study. Under this assumption, the distance between the edge of the damaged region and the long side of the interlock is 2.5 mm and that between the edge of the damaged region and the short side of the interlock is 1 mm. However, it should be noted that the size of the damaged region depends on the dimensions of the interlock. Based on Fig. 12, Eqs. (6) and (7), the average magnetic properties in the damaged regions are calculated. Fig. 14 shows the BH curves and iron losses at 50 Hz in the damaged region, which are used for the calculation of motor characteristics. This figure demonstrates significant reduction of permeability and increase of iron loss in the damaged region. The small anisotropy in Fig. 14 agrees well with the discussions in the previous chapter. 4.2. Application of the modelling to the simulation of an electrical machine
Fig. 15. The schematic picture of the electrical machine under study (1/4 model).
The magnetic characteristics of the damaged region calculated in 4.1 is used for the simulation of an electrical machine. The schematic picture of the machine under study is shown in Fig. 15. Table 1 shows the specifications of this machine. The stator core of this machine is composed of 12 pieces. Each piece has three interlocks; two in the yoke and one in the tooth. The damaged regions with a size of 6 mm*6 mm caused by interlocking is also shown in Fig. 15. To simplify the calculation, the average data of magnetic characteristics for parallel and perpendicular directions shown in Fig. 14 were used for the isotropic characteristics in the damaged regions in Fig. 15. Fig. 16 shows calculation results of no-load characteristics for this machine. The rotation speed is 1500 rpm. Fig. 16(a) demonstrates that interlocking increases the amplitude of cogging torque in this machine. This behavior is explained by the non-linearity of the BH curve in the stator core [3]. Fig. 16(b) demonstrates that interlocking increases iron
Table 1 Specifications of the electrical machine. Outer diameter of stator Core length Rated power
124 mm 50 mm 1 kW
Magnet Stator core Rotor core
Nd-Fe-B M360-35A M1300-50A
magnetic damage by interlocking is local. In this case the interlocks are parallel to flux. Similar results are obtained for ring cores with interlocks perpendicular to flux. From the discussions in the preceding chapter, it is reasonable to define that the damaged region is square, although the interlock has an anisotropic structure. In addition, assuming that the length of the side is 7
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Fig. 16. No-load characteristics of the electrical machine. (a) Cogging torque. (b) Iron loss.
doi.org/10.1016/j.jmmm.2019.166372.
loss under no-load condition. Both results clearly show that it is important to consider the influence of interlocking for accurate calculations of motor characteristics. Optimizing position of interlocks in electrical machines by using this modelling will be an interesting future topic.
References [1] N. Takahashi, H. Morimoto, Y. Yunoki, D. Miyagi, Effect of shrink fitting and cutting on iron loss of permanent magnet motor, J. Magn. Magn. Mater. 320 (20) (2008) e925–e928. [2] A. Cavagnino, R. Bojoi, Z. Gmyrek, M. Lefik, Stator lamination geometry influence on the building factor of synchronous reluctance motor cores, IEEE Trans. Magn. 53 (4) (2017) 3394–3403. [3] S. Imamori, H. Ohguchi, M. Shuto, A. Toba, Relation between magnetic properties of stator core and cogging torque in 8-pole 12-slot SPM synchronous motors, IEEJ J. Ind. Appl. 4 (6) (2015) 696–702. [4] F. Ossart, E. Hug, O. Hubert, C. Buvat, R. Billardon, Effect of punching on electrical sheets: experimental and numerical coupled analysis, IEEE Trans. Magn. 36 (5) (2000) 3137–3140. [5] Y. Kai, Y. Tsuchida, T. Todaka, M. Enokizono, Influence of stress on vector magnetic property under alternating magnetic flux conditions, IEEE Trans. Magn. 47 (10) (2011) 4344–4347. [6] S. Imamori, S. Steentjes, K. Hameyer, Influence of interlocking on magnetic properties of electrical steel laminations, IEEE Trans. Magn. 53 (11) (2017) 8108704. [7] E. Werner, Einrichtung zur Messung magnetischer Eigenschaften von Blechen bei Wechselstrommagnetisierung, Austrian Patent 191015 (1957). [8] H. Pfützner, G. Krismanic, The needle method for induction tests: source of error, IEEE Trans. Magn. 40 (3) (2004) 1610–1616. [9] M. Enokizono, M. Morikawa, S. Fujiyama, J. Sievert, I. Serikawa, Distribution of local magnetic properties in three-phase induction motor model core, IEEE Trans. Magn. 35 (5) (1999) 3937–3939. [10] Y. Mori, H. Shimoji, A. Ikariga, T. Todaka, M. Enokizono, Measured distributions of two-dimensional magnetic properties in a three phase induction motor model core by using a V-H sensor, International Conference on Electrical Machines and Systems (ICEMS), 2007, pp. 1013–1018. [11] S. Aihara, H. Shimoji, T. Todaka, M. Enokizono, Measurement of local vector magnetic properties in laser scratched grain-oriented silicon steel sheet with a vector-hysteresis sensor, IEEE Trans. Magn. 48 (11) (2012) 4499–4502. [12] K. Ooka, T. Kajiwara, S. Aihara, M. Enokizono, Control of rotating magnetic flux distribution in a transformer model core by laser irradiation, IEEE Trans. Magn. 50 (4) (2012) 8400204. [13] S. Zeze, Y. Kai, T. Todaka, M. Enokizono, Vector magnetic characteristic analysis of a PM motor considering residual stress distribution with complex-approximated material modeling, IEEE Trans. Magn. 48 (11) (2012) 3352–3355.
5. Conclusions Local magnetic measurements of laminated cores with interlocking by using needle B probes and H-coils show that magnetic degradation due to interlocking is local and that the damaged regions close to the long sides of interlocks are larger than those close to the short sides of interlocks. The results are used for the modelling of interlocking, which are applied to simulations of electrical machines. The simulation results demonstrate the importance of considering the influence of interlocking. CRediT authorship contribution statement S. Imamori: Conceptualization, Formal analysis, Investigation, Methodology, Writing - original draft, Writing - review & editing. S. Aihara: Data curation, Resources. H. Shimoji: Visualization, Software. A. Kutsukake: Validation. K. Hameyer: Supervision. Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Appendix A. Supplementary data Supplementary data to this article can be found online at https://
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