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Experimental analysis of magnetic properties of electrical steel sheets under temperature and pressure coupling environment
Journal of Magnetism and Magnetic Materials 475 (2019) 282–289
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Research articles
Experimental analysis of magnetic properties of electrical steel sheets under temperature and pressure coupling environment
T
⁎
Lijun Xiao, Guodong Yu , Jibin Zou, Yongxiang Xu, Weiyan Liang Department of Electrical Engineering, Harbin Institute of Technology, Harbin 150001, China
A R T I C LE I N FO
A B S T R A C T
Keywords: Temperature and pressure coupling environment Magnetic properties Electrical steel sheets Ring specimen and rolled specimen
Motor made of electrical steel sheet is sometimes used in extreme environments, for example, submersible motors are operated at temperatures and pressures coupling environment. However, most related reports only consider the effect of single environmental factor (temperature or stress) on the magnetic properties of electrical steel sheets. Therefore, in order to accurately design a motor that can operate at temperatures and pressures coupling environment, the magnetic properties of electrical steel sheets used in the motor should be clarified firstly. In the paper, two kinds of specimens (ring specimen and rolled specimen) are used to measure the magnetic properties under temperature and pressure coupling environment. It not only reveals the influence of temperature and pressure coupling environment on the magnetic properties, but also analyzes the difference between the measurement results obtained by two kinds of measurement samples. The measurement results show that the effect of pressure on magnetic properties decreases with increasing temperature under the conditions of temperature and pressure coupling. According to the domain theory, a reasonable explanation for the influence of temperature and pressure coupling environment on electrical steel sheet is given. Meanwhile, combining the shape and size of the two measurement samples, the possible causes of the differences in the measurement results of the two measurement samples were analyzed in detail.
1. Introduction Electrical steel sheets are sometimes used in temperature and pressure coupling environment, for example, in the case of submersible motors used in oil wells, or in the case of motors used in geological prospecting, etc. Such motors used in special environments (temperature and pressure coupling environment) should consider the effects of environmental factors on the motors during the design phase. However, there is a lack of uniform design standards for the design of such motors. Therefore, it needs to be verified with the most commonly used the finite element method (FEM). But so far, we can clearly know that the influence of temperature on the service life of the motor depends to a large extent on the insulation aging of the motor [1–3]. Meanwhile, the influence of temperature on the permanent magnet of the permanent magnet motor [4,5] (the most serious situation is the irreversible demagnetization of permanent magnets [6]) directly affects the performance of the motor. Various losses in the motor, such as core loss, winding loss, eddy current loss in the permanent magnet, and oil film loss, are also affected by temperature. Moreover, the starting performance and operating characteristics of the motor are also affected by temperature [7–13]. The maximum effect of pressure on the motor is to
⁎
increase the core loss in the motor [14,15]. The increase in core loss will further increase the temperature of the motor [16–18], which will affect the performance of the motor. Based on the above analysis, it can be inferred that when temperature and pressure are coupled together, the motor is highly likely to be more severely affected in terms of service life and performance. However, whether it is suitable for high temperature or high pressure environment, the design of the motor has a relatively successful case [7–18]. Obviously, a prerequisite for obtaining a reliable motor design is that the characteristics of the materials used should be clearly understood from the background of the motor application. However, based on known data, it can be found that the effects of temperature and pressure on the magnetic properties of the electrical steel sheet are very different. In terms of temperature alone, the relative permeability at low flux density is increased with the increase of temperature and that at higher flux density is decreased with temperature [19,20]. Moreover, the relative permeability is not changed much when the temperature is less than 500 °C, but when the temperature exceeds 500 °C, the change in relative permeability is very obvious [19]. The iron loss of electrical steel sheet will be decreased with the increase of temperature [19–21]. In general, the relative permeability and iron loss
Corresponding author. E-mail address: [email protected] (G. Yu).
https://doi.org/10.1016/j.jmmm.2018.11.107 Received 27 May 2018; Received in revised form 19 October 2018; Accepted 21 November 2018 Available online 26 November 2018 0304-8853/ © 2018 Elsevier B.V. All rights reserved.
Journal of Magnetism and Magnetic Materials 475 (2019) 282–289
L. Xiao et al.
of electrical steel sheets are increased at low temperatures (77 K) [22]. For NiFe Steel, both relative permeability and iron loss are decreased with the increase of temperature [23]. At present, the research on the relationship between pressure and magnetic properties of electrical steel sheets is mostly concentrated on non-axial stress or finite axial stress. Under the influence of uniaxial stress, the relative permeability of the electrical steel sheet is decreased with the increase of the compressive stress, and the iron loss is increases with the compressive stress [24,28,30]. However, when the compressive stress exceeds −50 MPa, the effect of compressive stress on relative permeability and iron loss is reduced [24]. The effect of multi-axial stress on the magnetic permeability and core of electrical steel sheet are similar to that of uniaxial stress, but the effect on iron loss can be much more significant than that of uniaxial stress [25]. When the compressive stress is perpendicular to the surface of the electrical steel sheet, the increase in pressure causes the relative permeability to show a phenomenon of increasing first and then decreasing. Meanwhile, the iron loss at low flux density is increased with the increase of stress and that at higher flux density is decreased with stress [26]. When the silicon steel sheet is affected by the tensile stress, the iron loss and the coercive field is gradually increased with the increase of the tensile stress till 400 MPa, but when the tensile stress exceeds 400 MPa, the tensile stress leads to the plastic deformation and appearance of the microstructural defects in the material [27–30]. The magnetic properties of electrical steel sheets are deteriorated remarkably (the relative permeability is decreased and the iron loss is increased) with the increase of bending stress [31]. Through the above analysis, it can be found that not only the effects of temperature and stress on the magnetic properties of electrical steel sheets are different, but also the effects of different forms of stress on the magnetic properties of electrical steel sheets are not the same. Therefore, it is not so sensible to use the magnetic properties of electrical steel sheets measured under normal environments (0.1 MPa and 30 °C) [32–34] or single environmental variables (temperature or pressure) in the analysis of temperature and pressure coupling environment (i.e., simultaneous changes in temperature and pressure). Unfortunately, no data has been found in the published literatures on the effects of temperature and pressure coupling environment on the magnetic properties of electrical steel sheets. Meanwhile, it is also difficult to deduce the magnetic properties of electrical steel sheets under temperature and pressure coupling environment by using known data and hysteresis models. Therefore, in order to improve the design accuracy of motor used in temperature and pressure coupling environment, it is necessary to know the magnetic properties of electrical steel sheets under the same conditions. In this paper, the magnetic properties of electrical steel sheets under temperatures and pressures coupling environment are determined by ring specimen [21,23] and rolled specimen [28]. The relative permeability and iron loss of electrical steel sheets under the conditions of 30 °C to 200 °C and 0.1 MPa to 140 MPa are experimentally determined. The changes in magnetic properties with temperature and pressure are discussed in detail. There is only a vertical relationship between the pressure direction and magnetic field lines in the ring specimen, and the rolled specimen contain vertical and parallel relationships. Therefore, by comparing the measurement results of the two specimens, it is possible to analyze the influence of the relationship between the pressure direction and the magnetic field lines on the magnetic properties under the temperature and pressure coupling conditions.
(a)
(b)
(c)
(e)
(g)
(d)
(f)
(h)
Fig. 1. Ring specimen and rolled specimen. (a) The ring specimen size. (b) The rolled specimen size. (c) The stacked ring specimen. (d) The stacked rolled specimen. RD: rolling direction. SD: stacking direction. (e) Relationship between pressure direction and magnetic field line of ring specimens in Cartesian coordinates. (f) Relationship between pressure direction and magnetic field line of rolled specimens in Cartesian coordinates. Black arrow: pressure direction. Dotted line: magnetic field line. (g) Measuring device using rolled specimen. 1: fixed clamp, 2: magnetic yoke, 3: rolled specimen. (h) The ring specimen.
2. Measurement specimens and measurement system Fig. 1 shows two measurement specimens for measuring the magnetic properties of electrical steel sheets under temperature and pressure coupling environment, and the specimens are cut from the same product lot number. 283
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measurement should be stopped immediately, and the measurement should be continued after the temperature falls back.
In fact, there are many methods that can be utilized for specimen processing, such as punching [35–37], laser cutting [36,38], shearing [39,40], and wire cutting (sparking erosion) [41,42]. However, no matter which processing method is used, the magnetic properties of the specimen are deteriorated, and the effects of punching, laser cutting and shearing on specimen are most pronounced. In order to recover the magnetic properties of the processed specimen, annealing is usually required [42–45]. But, in the sample using the laser cutting method, even if annealing is performed, the magnetic properties of the specimen are lower than those of other processing methods [41,42]. However, whether it is before or after annealing, the magnetic properties of the specimens processed by the wire-cutting method are better than those of other methods (the magnetic changes before and after annealing are very small), which makes the specimens processed by the wire-cutting method usually as reference for studying the effects of other processing methods on materials (The core of an actual motor will also be processed by the wire cutting method) [41,42]. Therefore, the wire cutting method is the most suitable processing method in the paper. The specific grades of the non-oriented electrical steel sheets measured are DW460-50 (thickness: 0.5 mm, iron loss: 4.6 W/kg, 1.5 T, 50 Hz) and then stacked and pasted together in the same manner. The measurement magnetic properties of electrical steel sheets are different when compressive stresses are applied to the specimen in the rolling and transverse directions, respectively. However, when the stress is greater than −50 MPa, the difference in measurement magnetic characteristics in these two directions will become smaller, the most likely cause of the phenomenon is due to the fact that the specimen sufficiently deteriorates at this lager stress, the difference of magnetic properties of both directions is very hardly observed by existing measurement technologies [26]. Therefore, in order to reduce the difference in the magnetic measurement due to the rolling direction and the transverse direction, when the ring specimen and the rolled specimen are stacked and glued, the rolling direction and the transverse direction specimen are alternately placed as shown in Fig. 1c and 1d. The alternate stacking method described above should also be used to make laminated iron cores, which helps to provide a more uniform distribution of the magnetic field in the axial direction of iron core, especially in high pressure environments. In the Cartesian coordinate system of Fig. 1e and 1f, the comparison of the measurement results of the ring specimen and the rolled specimen can be used to analyze the influence of the relationship (vertical or parallel) between the pressure and the magnetic field lines on the magnetic properties. The direction of pressure is always perpendicular to the magnetic field lines in the ring specimen. However, a part of the magnetic field lines in the lamination specimen is perpendicular to the direction of pressure direction, while the other part is parallel. In the measurement process, the temperature of specimens need to be observed in real time, so multiple temperature sensors (PT100) are placed on the surface of the ring specimen and the rolled specimen at equal intervals. Fig. 1g shows the mating devices for rolled specimen. The yokes made of high relative permeability and low iron loss material (nickel–iron alloy) can reduce the error caused by the yokes during the measurement. Fig. 1f shows the ring specimen. Moreover, it is important to note that the magnetic properties of electrical steel sheets should be measured at sinusoidal flux density [21]. Temperature and pressure coupling environment system can be realized through the Ultra-high pressure experiment container (up to 180 MPa), high-pressure pump, air compressor, heater and thermostat, as show in Fig. 2. Closed-loop temperature control can be realized by means of temperature sensor (PT100). During the measurement process, the temperature of the specimens should always be observed to prevent the heat generated by the excitation coil from affecting the temperature of the specimens, thereby affecting the accuracy of the measurement results. When it is found that the temperature deviates from the predetermined value, the
3. Measurement results and discussion 3.1. Determination of measurement parameters The induction coil (copper wire with high-temperature insulation) for measuring the magnetic flux density B is evenly wound on the specimen and calculated by Eq. (1).
Bm =
U2 4.44fN2 S
(1)
where Bm is the maximum flux density, U2 is the induction voltage of induction coil (B coil), f is the frequency of magnetizing current, N2 is the turn number of B coil, S is cross section of specimen along the direction of magnetizing path. The exciting coil is uniformly wound outside of the induction coil, and the double root winding method is used to increase the current density for achieving the required magnetic flux density in the specimen. Meanwhile, the turn number, wire gauge and insulation grade of the exciting coil are the same as the induction coil. And the magnetic field strength Hb is determined by the magnetizing current, which is given by the Eq. (2).
Hb =
N1 I1 L
(2)
where Hb is the magnetic field strength at the instant when the magnetic flux density is the maximum value Bm , N1 is the turn number of exciting coil, I1 is the effective value of magnetizing current, L is the length of magnetic path. The iron loss of electrical steel sheet can be calculated by Eq. (3).
PT =
1 N1 Tm N2
∫0
T
i1 (t ) U2 (t ) dt
(3)
where T is the cycle of magnetizing current, m is the weight of specimen, i1 (t ) is the magnetizing current. 3.2. Measurement results The magnetic properties of the ring specimen and rolled specimen of non-oriented electrical steel sheet DW460-50 is measured. Fig. 3 shows the specific relative permeability μr , iron loss of rolled specimen at 50 Hz (30 °C). The relative permeability μr at low flux density (Fig. 3a) is decreased with the increase of pressure, and the difference among relative permeability under different pressures is significant. However, the difference becomes smaller at high magnetic flux density (over 1 T). The iron loss is increased with pressure (Fig. 3b). It can be found that the effect of pressure (equivalent to infinite axial compressive stress) on magnetic properties under normal temperature conditions (30 °C) is similar to the effect of finite axial compressive stress [26]. However, the effect of pressure on relative permeability is weaker than the effect of finite axial stress. The possible causes of this phenomenon are on the one hand the difference in the specimens and on the other hand the difference in the direction of the pressure on the specimens. Fig. 4 shows the measured magnetic properties of rolled specimen at 50 Hz (128 °C). The relative permeability at low flux density (Fig. 4a) is decreased with the pressure and that at high flux density (over 1 T) is almost constant with pressure. The iron loss is also increased with pressure (Fig. 4b). By comparing the measurement results in Figs. 3 and 4, the influence of temperature and pressure coupling on magnetic properties can be found. The relative permeability (Figs. 3a and 4a) is decreased with the temperature, and difference is decreased among the relative permeability under different pressure conditions. The flux density 284
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Fig. 2. The temperature and pressure coupling environment system.
corresponding to the peak relative permeability is also decreased accordingly. The change of iron loss (Figs. 3b and Fig. 4b) with temperature is similar to that of the relative permeability (The iron loss is decreased with the temperature, and the difference among the iron loss under different pressure is also decreased.). It also means that the pressure sensitivity of the magnetic properties of the non-oriented electrical steel sheet (amount of change with the increase of pressure) is decreased with the temperature. For example, the pressure sensitivity of iron loss decreases from + 2.19 × 10−3W·kg−1·MPa −1 at 30 °C to + 1.39 × 10−3W·kg−1·MPa −1 at 128 °C when the flux density is 1 T. The pressure sensitivity of relative permeability is decreased from −9.04 MPa−1 to −1.92 Mpa−1. In order to highlight the effect of temperature and pressure coupling on magnetic properties of rolled specimen of non-oriented electrical steel sheet, the typical parameter (relative permeability and iron loss) values corresponding to flux density of 1 T are presented in Table 1. The relative permeability is decreased with the increase of temperature under different pressures, but with the increase of pressure, the degree of decrease in amplitude is decreased from 55% to 38.92%. The iron loss is also decreased with the increase of temperature under different pressures. Meanwhile, the percentage of decrease is far less than the relative permeability, and the maximum is only 19.17%. Fig. 5 shows the magnetic properties of the ring specimen at 50 Hz (30 °C). The relative permeability (Fig. 5a) is decreased with the increase of pressure in the condition of low pressure (less than 60 MPa) and low flux density (less than 1.1 T), whereas the relative permeability is changed little under high pressure (more than 60 MPa) conditions. Taking into account, the effects of measurement errors and unexpected Table 1 Comparison of measurement results of rolled specimen under different temperature at Bm = 1T . “−” indicates that the parameter is decreased after the temperature is raised. “ε ” represents that the percentage of difference in the parameters at 30 °C and 128 °C. P (MPa)
0.1 30 60 90 120 140
Fig. 3. Measurement results of magnetic properties of rolled specimen at 50 Hz (30 °C). (a) Relative permeability. (b) Iron loss.
285
W
μr 30 °C
128 °C
ε (%)
30 °C
128 °C
ε (%)
3138 2869 2639 2270 1988 1873
1412 1285 1107 1220 1039 1144
−55.00 −55.21 −58.05 −46.25 −47.74 −38.92
0.4162 0.4844 0.5434 0.6295 0.6783 0.7224
0.3894 0.4175 0.4774 0.5096 0.5587 0.5839
−6.44 −13.81 −12.14 −19.05 −17.63 −19.17
Journal of Magnetism and Magnetic Materials 475 (2019) 282–289
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Fig. 4. Measurement results of magnetic properties of rolled specimen at 50 Hz (128 °C). (a) Relative permeability. (b) Iron loss.
Fig. 5. Measurement results of magnetic properties of ring specimen at 50 Hz (30 °C). (a) Relative permeability. (b) Iron loss.
factors (There are two possible causes of unexpected factors. One reason is that the relative permeability may be affected by high pressure, but the regularity of this effect is very small and therefore difficult to be determined. The other reason is that the relative permeability of the ring specimen have deteriorated sufficiently under high pressure conditions, and the influence of the further increase in pressure on the magnetic properties has been difficult to observe), it can be assumed that the relative permeability is not changed under high pressure conditions. The iron loss (Fig. 5b) is changed very little with the increase of pressure (the difference among iron losses does not exceed 6%). Fig. 6 shows the relative permeability μr and iron loss of ring specimen at 50 Hz (128 °C). When the pressure is less than 60 MPa, the relative permeability is decreased with the increase of the pressure (Fig. 6a), but when the pressure is increased to 90 MPa, the relative permeability is decreased only in the range of 0.5 T < B < 1 T. When the pressure is further increased to 120 MPa or 140 MPa, a part of the relative permeability in this range (0.5 T < B < 1 T) will be slightly higher than the relative permeability under the condition of 60 MPa (Although the proportion of this part is very small), the most obvious of which is the relative permeability at B = 0.75 T. It can be seen from the measurement results in Fig. 5a that under normal temperature conditions, when the pressure exceeds 90 MPa, the specimen may have deteriorated sufficiently, and it is difficult to observe the influence of pressure on the magnetic permeability of the specimen. Through the
published data [23], it can be found that when the flux density is low, the temperature causes a slight increase in the relative permeability. Therefore, it can be inferred that temperature is the most likely cause of the occurrence of such an abnormal phenomenon. The iron loss (Fig. 6b) is not changed with the increase of pressure. By comparing the measurement results in Figs. 5 and Fig.6, the effect of temperature and pressure coupling on magnetic properties of ring specimen can be analyzed. The relative permeability (Figs. 5a and 6a) is increased slightly at different pressures with the increase of temperature, but the amplitude of increase is smaller. While the iron loss Figs. 5b and 6b) is decreased, but the amplitude of decrease is smaller. In order to highlight the effect of the temperature and pressure coupling on magnetic properties of ring specimen, the typical parameter (relative permeability and iron loss) values corresponding to flux density of 1 T are presented in Table 2. It can be noticed that the pressure sensitivity of relative permeability of ring specimen is increased with the increase of temperature when the flux density is 1 T (from − 1.82 MPa −1 at 30 °C to − 2.69 MPa −1 at 128 °C). However, the iron loss is changed very little and there is no obvious regularity. Comparing the measurement results in Fig. 3, Fig. 4, Fig. 5, and Fig. 6, it can be noticed that the relative permeability and iron loss of the non-oriented electrical steel sheet measured by the rolled specimen and the ring specimen are completely different. 286
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degree of change is also smaller than that of the rolled specimen (except for the iron loss at 0.1 MPa). From the measured data in Table 3, it can be seen more clearly that the measurement results of the rolled and ring specimens are different under the temperature and pressure coupling environment. The iron loss of the ring specimen is about 2–4 times as large as that of the rolled specimen (30 °C and 128 °C), and the relative permeability is about 1.5 times (30 °C) at Bm = 1T and 50 Hz. In the edge of the sample, a certain amount of striped domains are produced due to the pressure acting in the rolling direction of the sample (or perpendicular to the rolling direction). Moreover, the magnetic poles at the grain boundaries (resulting in an increase in static magnetic energy) and the magnetic anisotropy of the grains also hinder the movement of the domain walls, thereby lowering the magnetic permeability of the sample. However, when the pressure is further increased, the inverse magnetostriction effect causes the magnetization to switch to the direction of 〈1 1 0〉 or 〈1 1 1〉, and the magnetization in the 〈1 1 0〉 or 〈1 1 1〉 direction is easy due to pressure, which obviously hinders the domain wall movement in the 〈1 0 0〉 and 〈0 1 0〉 directions. The above reasons appear to be the reason for the change in the magnetic permeability of the rolled specimen and the ring specimen [46,48]. For polycrystalline materials such as electrical steel sheet, the behavior of the change in elastic deformation is largely dependent on the crystal orientation of the grains, which causes most of the pressure to concentrate near the grain boundaries when pressure is applied to the sample. It is precisely because of the relatively concentrated stress near the grain boundaries that an uneven magnetic distribution is caused, which in turn leads to an increase in iron loss. However, when the pressure is further increased, the difference between the inside and the boundary of the grain is significantly reduced, and the influence of the grain size is further reduced. Meanwhile, the pressure perpendicular to the surface of the sample causes the direction to become hard axis due to the magneto-elastic energy, and the amount of perpendicular magnetization change caused by the pressure is correspondingly reduced during magnetization [47,49,50]. The temperature accelerates the movement of the molecules in the sample, causing the size of the domains to decrease, and the size of the grains to become large, so that the iron loss is thereby reduced. The movement of the molecules is further enhanced with the increase of the temperature, which obviously hinders the change in the direction of the domains, causing permeability of the sample to decrease (the magnetization field is greater than 0.5 T). Comparing the results of this study, it can be clearly found that in terms of iron loss, the effect of pressure is higher than that of temperature [51]. For ring specimen, the thickness (5 mm) is smaller than the laminate specimen (minimum 10 mm), so the proportion of the stress-affected zone at the boundaries is much higher than that of the rolled specimen. On the one hand, the difference between the inside and the boundary of grain in the ring specimen is smaller than that of the rolled specimen. On the other hand, the pressure near the grain boundary of the ring specimen is more concentrated, and the magnetic distribution is more uneven. These factors make the difference in iron loss of the ring specimen at different pressures not only much smaller than the rolled specimen, but also numerically larger than the rolled specimen. When the pressure is low, the strip domain generated at the edge of the ring specimen occupies a higher proportion in the entire sample than the rolled specimen, which causes the effects of magnetic poles at the grain boundaries and the magnetic anisotropy of the grains on the domain wall motion are also higher than that of the rolled specimen. Therefore, the permeability of the ring specimen is lower than that of the rolled specimen. As the pressure increases, the effect of the inverse magnetostriction effect on the ring specimen is also higher than that of the rolled specimen, but the effect among the different pressures is slightly smaller than that of the rolled specimen. As the temperature increases, the effect of the pressure on the sample will also increase as the size of
Table 2 Comparison of measurement results of ring specimen under different temperature at Bm = 1T . “+” represents that the parameter rises after the temperature rises, “−” indicates that the parameter decreases after the temperature rises. P (MPa)
0.1 30 60 90 120 140
W
μr 30 °C
128 °C
ε (%)
30 °C
128 °C
ε (%)
1543 1440 1320 1300 1232 1289
1816 1538 1468 1412 1456 1440
+17.69 +6.81 +11.21 +8.61 +18.18 +11.71
1.526 1.505 1.506 1.587 1.531 1.551
1.388 1.442 1.388 1.424 1.424 1.395
−9.04 −4.19 −7.83 −10.27 −6.99 −10.05
Fig. 6. Measurement results of magnetic properties of ring specimen at 50 Hz (128 °C). (a) Relative permeability. (b) Iron loss.
The relative permeability at different pressures measured by the rolled specimen is higher than that of the ring specimen, and the iron loss is smaller than that of the ring specimen, under normal temperature conditions (30 °C). Moreover, the magnetic properties of rolled specimen are more sensitive to pressure than ring specimen. After the temperature is increased (128 °C), the relative permeability and iron loss of the rolled specimen under different pressures are decreased. However, the relative permeability of the ring specimen is slightly increased, while the change in iron loss is the opposite, and the 287
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Table 3 Comparison of measurement results of rolled specimen and ring specimen at Bm = 1T and 50 Hz. “+” represents that the parameter rises after the temperature rises, “−” represents that the parameter decreases after the temperature rises. P (MPa)
0.1 30 60 90 120 140
W
μr Rolled specimen 30 °C
Ring specimen 30 °C
ε (%)
Rolled specimen 128 °C
Ring specimen 128 °C
ε (%)
Rolled specimen 30 °C
Ring specimen 30 °C
ε (%)
Rolled specimen 128 °C
Ring specimen 128 °C
ε (%)
3138 2869 2639 2270 1988 1873
1543 1440 1320 1300 1232 1289
−50.83 −49.81 −49.98 −42.73 −38.03 −31.18
1412 1285 1107 1220 1039 1144
1816 1538 1468 1412 1456 1440
+28.61 +19.69 +32.61 +15.74 +40.13 +25.87
0.4161 0.4844 0.5434 0.6295 0.6783 0.7226
1.631 1.578 1.592 1.659 1.531 1.55
+291.97 +225.76 +192.97 +163.54 +125.71 +114.50
0.4161 0.4844 0.5434 0.6295 0.6783 0.7226
1.388 1.442 1.388 1.424 1.424 1.395
+133.57 +195.25 +155.43 +126.21 +109.94 +93.05
c) In the temperature and pressure coupling environment, the difference between the measurement results of the ring specimen and rolled specimen is not only related to the pressure and temperature (pressure is the main factor), but also related to the shape and size of the two samples. d) When analyzing the characteristics of the motor under temperature and pressure coupling environment, the iron core made of non-oriented electrical steel sheet should be divided into tooth (magnetic properties are measured by rolled specimen) and yoke (magnetic properties measured are by ring specimen).
the domains become smaller, but it is obviously only applicable to the case where the pressure is low. In addition, the magnetization direction of the rolled specimen is along the rolling direction (or perpendicular to rolling direction), and there is a certain angle between the magnetization direction of the ring specimen and the rolling direction (or perpendicular to rolling direction). Therefore, under the same magnetization conditions, the movement of the domain walls in the rolled specimen is much easier than the movement of the domain walls in the ring specimen, and the energy required is also small. This also causes some differences in the measurement results of the rolled specimen and the ring specimen. Another possible reason is that a part of stress may be introduced in the sample due to the processing method of the excitation coil and B coil (directly wound on the specimens), and the accuracy of measurement is affected. The coils of the ring specimen are evenly wound around the whole specimen, while the coils of the rolled specimen are wound only on the middle part (the stress distribution may not be uniform), and the number of turns are much smaller than that of the ring specimen. All of these may be the reasons that the magnetic properties of ring specimen are worse than that of rolled specimen. Meanwhile, because the insulating tapes are set between specimen and B coil, a certain calculation error may be introduced in the determination of the sectional area of the B coil. Comparing the iron core of motor with the two specimens used in this article, it is not difficult to find that the shape of the yoke is similar to the ring specimen, and the shape of the tooth is similar to the rolled specimen. Through the above analysis, it can be seen that the magnetic properties of the non-oriented electrical steel sheet measured by the two specimens are different under temperature and pressure coupling environment. Therefore, when analyzing a motor operating in a temperature and pressure coupling environment, the iron core should be segmented into tooth and yoke and given the different magnetic properties of non-oriented electrical steel sheet measured by the rolled and ring specimens, respectively.
Acknowledgment This work was supported in part by National Key R&D Plan 2017YFC0307103, in part by the National Natural Science Foundation of China under Grant 51437004. References [1] Reza Soltani, Eric David, Laurent Lamarre, Temperature Effect on Dielectric Characteristics of Large Rotating Machines Insulation, in: Conference Record of the 2008 IEEE International Symposium on Electrical Insulation, (2008) pp. 280–283. [2] M.S. Ballal, Z.J. Khan, H.M. Suryawanshi, R.L. Sonolikar, Induction motor: fuzzy system for the detection of winding insulation condition and bearing wear, Electr. Power Compon. Syst. 34 (2006) 159–171. [3] Vadim Iosif, Daniel Roger, Stéphane Duchesne, Assessment and improvements of inorganic insulation for high temperature low voltage motors, IEEE Trans. Diele. Elec. Insul. 23 (2016) 2534–2542. [4] P. Zhou, D. Lin, Y. Xiao, N. Lambert, M.A. Rahman, Temperature-dependent demagnetization model of permanent magnets for finite element analysis, IEEE Trans. Magn. 48 (2012) 1031–1034. [5] Sami Ruoho, Jere Kolehmainen, Jouni Ikäheimo, D. Antero Arkkio, Interdependence of demagnetization, loading, and temperature rise in a permanentmagnet synchronous motor, IEEE Trans. Magn. 46 (2010) 949–953. [6] Myung-Ki Seo, Tae-Yong Lee, Young-Yoon Ko, Yong-Jae Kim, Sang-Yong Jung, Irreversible demagnetization analysis with respect towinding connection and current ripple in brushless DC motor, IEEE Trans. Appl. Super. 28 (2018) 5203604. [7] F.A. Khalifa, S. Serry, M.M. Ismail, B. Elhady, Effect of temperature rise on the performance of induction motors, in: 2009 International Conference on Computer Engineering & Systems, (2009) pp. 549–552. [8] Tomy Sebastian, Temperature effects on torque production and efficiency of PM motors using NdFeB magnets, IEEE Trans. Indus. Appl. 31 (1995) 353–357. [9] Xiaoguang Kong, Fengxiang Wang, Junqiang Xing, Temperature rise calculation of high speed PM machine based on thermal-circuit method and 3D fluid field method, ICEMS 2011 (2011) 1–5. [10] Z.Q. Zhu, D. Howe, Instantaneous magnetic field distribution in brushless permanent magnet DC motors. II. Armature-reaction field, IEEE Trans. Magn. 29 (1993) 136–140. [11] Yao Atsushi, Yao Atsushi, Yao Atsushi, Iron loss and hysteretic properties under PWM inverter excitation at high ambient temperature, IEEJ J. Indus. Appl. 7 (2018) 298–304. [12] Shi-Bin Zhang, Xiao-Wen Zheng, Li-Jie Feng, Yan-Feng Wang, Zhen-Feng Liu, The design and experimental research of cooling structure in deep well submersible motor, J. Discrete Math. Sci. Cryptogr. 29 (2016) 838–848. [13] Patricio Peralta, Tobias Wellerdieck, Daniel Steinert, Thomas Nussbaumer, Johann W. Kolar, Ultra-High Temperature (250 ◦C) Bearingless Permanent Magnet Pump for Aggressive Fluids, IEEE/ASME Trans. Mechatronics 15 (2010) 97–107. [14] Jibin Zou, Wenjuan Qi, Xu. Yongxiang, Xu. Fei, Yong Li, Jianjun Li, Design of deep sea oil-filled brushless DC motors considering the high pressure effect, IEEE Trans. Magn. 48 (2012) 4220–4223.
4. Conclusion The magnetic properties of electrical steel sheets (DW460-50) under temperature and pressure coupling environment are measured by using the ring specimen and the rolled specimen. The obtained results can be summarized as follows: a) The relative permeability measured by the rolled specimen is decreased with the increase of pressure while iron loss increases. With the increase of temperature, the relative permeability and iron loss are decreased in value and pressure sensitivity. b) The relative permeability measured by the ring specimen is decreased with the increase of pressure, while the iron loss is almost constant. With the increase of temperature, the value and pressure sensitivity of relative permeability are increased, but the iron loss is only decreased in value. 288
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Research articles
Experimental analysis of magnetic properties of electrical steel sheets under temperature and pressure coupling environment
T
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Lijun Xiao, Guodong Yu , Jibin Zou, Yongxiang Xu, Weiyan Liang Department of Electrical Engineering, Harbin Institute of Technology, Harbin 150001, China
A R T I C LE I N FO
A B S T R A C T
Keywords: Temperature and pressure coupling environment Magnetic properties Electrical steel sheets Ring specimen and rolled specimen
Motor made of electrical steel sheet is sometimes used in extreme environments, for example, submersible motors are operated at temperatures and pressures coupling environment. However, most related reports only consider the effect of single environmental factor (temperature or stress) on the magnetic properties of electrical steel sheets. Therefore, in order to accurately design a motor that can operate at temperatures and pressures coupling environment, the magnetic properties of electrical steel sheets used in the motor should be clarified firstly. In the paper, two kinds of specimens (ring specimen and rolled specimen) are used to measure the magnetic properties under temperature and pressure coupling environment. It not only reveals the influence of temperature and pressure coupling environment on the magnetic properties, but also analyzes the difference between the measurement results obtained by two kinds of measurement samples. The measurement results show that the effect of pressure on magnetic properties decreases with increasing temperature under the conditions of temperature and pressure coupling. According to the domain theory, a reasonable explanation for the influence of temperature and pressure coupling environment on electrical steel sheet is given. Meanwhile, combining the shape and size of the two measurement samples, the possible causes of the differences in the measurement results of the two measurement samples were analyzed in detail.
1. Introduction Electrical steel sheets are sometimes used in temperature and pressure coupling environment, for example, in the case of submersible motors used in oil wells, or in the case of motors used in geological prospecting, etc. Such motors used in special environments (temperature and pressure coupling environment) should consider the effects of environmental factors on the motors during the design phase. However, there is a lack of uniform design standards for the design of such motors. Therefore, it needs to be verified with the most commonly used the finite element method (FEM). But so far, we can clearly know that the influence of temperature on the service life of the motor depends to a large extent on the insulation aging of the motor [1–3]. Meanwhile, the influence of temperature on the permanent magnet of the permanent magnet motor [4,5] (the most serious situation is the irreversible demagnetization of permanent magnets [6]) directly affects the performance of the motor. Various losses in the motor, such as core loss, winding loss, eddy current loss in the permanent magnet, and oil film loss, are also affected by temperature. Moreover, the starting performance and operating characteristics of the motor are also affected by temperature [7–13]. The maximum effect of pressure on the motor is to
⁎
increase the core loss in the motor [14,15]. The increase in core loss will further increase the temperature of the motor [16–18], which will affect the performance of the motor. Based on the above analysis, it can be inferred that when temperature and pressure are coupled together, the motor is highly likely to be more severely affected in terms of service life and performance. However, whether it is suitable for high temperature or high pressure environment, the design of the motor has a relatively successful case [7–18]. Obviously, a prerequisite for obtaining a reliable motor design is that the characteristics of the materials used should be clearly understood from the background of the motor application. However, based on known data, it can be found that the effects of temperature and pressure on the magnetic properties of the electrical steel sheet are very different. In terms of temperature alone, the relative permeability at low flux density is increased with the increase of temperature and that at higher flux density is decreased with temperature [19,20]. Moreover, the relative permeability is not changed much when the temperature is less than 500 °C, but when the temperature exceeds 500 °C, the change in relative permeability is very obvious [19]. The iron loss of electrical steel sheet will be decreased with the increase of temperature [19–21]. In general, the relative permeability and iron loss
Corresponding author. E-mail address: [email protected] (G. Yu).
https://doi.org/10.1016/j.jmmm.2018.11.107 Received 27 May 2018; Received in revised form 19 October 2018; Accepted 21 November 2018 Available online 26 November 2018 0304-8853/ © 2018 Elsevier B.V. All rights reserved.
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of electrical steel sheets are increased at low temperatures (77 K) [22]. For NiFe Steel, both relative permeability and iron loss are decreased with the increase of temperature [23]. At present, the research on the relationship between pressure and magnetic properties of electrical steel sheets is mostly concentrated on non-axial stress or finite axial stress. Under the influence of uniaxial stress, the relative permeability of the electrical steel sheet is decreased with the increase of the compressive stress, and the iron loss is increases with the compressive stress [24,28,30]. However, when the compressive stress exceeds −50 MPa, the effect of compressive stress on relative permeability and iron loss is reduced [24]. The effect of multi-axial stress on the magnetic permeability and core of electrical steel sheet are similar to that of uniaxial stress, but the effect on iron loss can be much more significant than that of uniaxial stress [25]. When the compressive stress is perpendicular to the surface of the electrical steel sheet, the increase in pressure causes the relative permeability to show a phenomenon of increasing first and then decreasing. Meanwhile, the iron loss at low flux density is increased with the increase of stress and that at higher flux density is decreased with stress [26]. When the silicon steel sheet is affected by the tensile stress, the iron loss and the coercive field is gradually increased with the increase of the tensile stress till 400 MPa, but when the tensile stress exceeds 400 MPa, the tensile stress leads to the plastic deformation and appearance of the microstructural defects in the material [27–30]. The magnetic properties of electrical steel sheets are deteriorated remarkably (the relative permeability is decreased and the iron loss is increased) with the increase of bending stress [31]. Through the above analysis, it can be found that not only the effects of temperature and stress on the magnetic properties of electrical steel sheets are different, but also the effects of different forms of stress on the magnetic properties of electrical steel sheets are not the same. Therefore, it is not so sensible to use the magnetic properties of electrical steel sheets measured under normal environments (0.1 MPa and 30 °C) [32–34] or single environmental variables (temperature or pressure) in the analysis of temperature and pressure coupling environment (i.e., simultaneous changes in temperature and pressure). Unfortunately, no data has been found in the published literatures on the effects of temperature and pressure coupling environment on the magnetic properties of electrical steel sheets. Meanwhile, it is also difficult to deduce the magnetic properties of electrical steel sheets under temperature and pressure coupling environment by using known data and hysteresis models. Therefore, in order to improve the design accuracy of motor used in temperature and pressure coupling environment, it is necessary to know the magnetic properties of electrical steel sheets under the same conditions. In this paper, the magnetic properties of electrical steel sheets under temperatures and pressures coupling environment are determined by ring specimen [21,23] and rolled specimen [28]. The relative permeability and iron loss of electrical steel sheets under the conditions of 30 °C to 200 °C and 0.1 MPa to 140 MPa are experimentally determined. The changes in magnetic properties with temperature and pressure are discussed in detail. There is only a vertical relationship between the pressure direction and magnetic field lines in the ring specimen, and the rolled specimen contain vertical and parallel relationships. Therefore, by comparing the measurement results of the two specimens, it is possible to analyze the influence of the relationship between the pressure direction and the magnetic field lines on the magnetic properties under the temperature and pressure coupling conditions.
(a)
(b)
(c)
(e)
(g)
(d)
(f)
(h)
Fig. 1. Ring specimen and rolled specimen. (a) The ring specimen size. (b) The rolled specimen size. (c) The stacked ring specimen. (d) The stacked rolled specimen. RD: rolling direction. SD: stacking direction. (e) Relationship between pressure direction and magnetic field line of ring specimens in Cartesian coordinates. (f) Relationship between pressure direction and magnetic field line of rolled specimens in Cartesian coordinates. Black arrow: pressure direction. Dotted line: magnetic field line. (g) Measuring device using rolled specimen. 1: fixed clamp, 2: magnetic yoke, 3: rolled specimen. (h) The ring specimen.
2. Measurement specimens and measurement system Fig. 1 shows two measurement specimens for measuring the magnetic properties of electrical steel sheets under temperature and pressure coupling environment, and the specimens are cut from the same product lot number. 283
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measurement should be stopped immediately, and the measurement should be continued after the temperature falls back.
In fact, there are many methods that can be utilized for specimen processing, such as punching [35–37], laser cutting [36,38], shearing [39,40], and wire cutting (sparking erosion) [41,42]. However, no matter which processing method is used, the magnetic properties of the specimen are deteriorated, and the effects of punching, laser cutting and shearing on specimen are most pronounced. In order to recover the magnetic properties of the processed specimen, annealing is usually required [42–45]. But, in the sample using the laser cutting method, even if annealing is performed, the magnetic properties of the specimen are lower than those of other processing methods [41,42]. However, whether it is before or after annealing, the magnetic properties of the specimens processed by the wire-cutting method are better than those of other methods (the magnetic changes before and after annealing are very small), which makes the specimens processed by the wire-cutting method usually as reference for studying the effects of other processing methods on materials (The core of an actual motor will also be processed by the wire cutting method) [41,42]. Therefore, the wire cutting method is the most suitable processing method in the paper. The specific grades of the non-oriented electrical steel sheets measured are DW460-50 (thickness: 0.5 mm, iron loss: 4.6 W/kg, 1.5 T, 50 Hz) and then stacked and pasted together in the same manner. The measurement magnetic properties of electrical steel sheets are different when compressive stresses are applied to the specimen in the rolling and transverse directions, respectively. However, when the stress is greater than −50 MPa, the difference in measurement magnetic characteristics in these two directions will become smaller, the most likely cause of the phenomenon is due to the fact that the specimen sufficiently deteriorates at this lager stress, the difference of magnetic properties of both directions is very hardly observed by existing measurement technologies [26]. Therefore, in order to reduce the difference in the magnetic measurement due to the rolling direction and the transverse direction, when the ring specimen and the rolled specimen are stacked and glued, the rolling direction and the transverse direction specimen are alternately placed as shown in Fig. 1c and 1d. The alternate stacking method described above should also be used to make laminated iron cores, which helps to provide a more uniform distribution of the magnetic field in the axial direction of iron core, especially in high pressure environments. In the Cartesian coordinate system of Fig. 1e and 1f, the comparison of the measurement results of the ring specimen and the rolled specimen can be used to analyze the influence of the relationship (vertical or parallel) between the pressure and the magnetic field lines on the magnetic properties. The direction of pressure is always perpendicular to the magnetic field lines in the ring specimen. However, a part of the magnetic field lines in the lamination specimen is perpendicular to the direction of pressure direction, while the other part is parallel. In the measurement process, the temperature of specimens need to be observed in real time, so multiple temperature sensors (PT100) are placed on the surface of the ring specimen and the rolled specimen at equal intervals. Fig. 1g shows the mating devices for rolled specimen. The yokes made of high relative permeability and low iron loss material (nickel–iron alloy) can reduce the error caused by the yokes during the measurement. Fig. 1f shows the ring specimen. Moreover, it is important to note that the magnetic properties of electrical steel sheets should be measured at sinusoidal flux density [21]. Temperature and pressure coupling environment system can be realized through the Ultra-high pressure experiment container (up to 180 MPa), high-pressure pump, air compressor, heater and thermostat, as show in Fig. 2. Closed-loop temperature control can be realized by means of temperature sensor (PT100). During the measurement process, the temperature of the specimens should always be observed to prevent the heat generated by the excitation coil from affecting the temperature of the specimens, thereby affecting the accuracy of the measurement results. When it is found that the temperature deviates from the predetermined value, the
3. Measurement results and discussion 3.1. Determination of measurement parameters The induction coil (copper wire with high-temperature insulation) for measuring the magnetic flux density B is evenly wound on the specimen and calculated by Eq. (1).
Bm =
U2 4.44fN2 S
(1)
where Bm is the maximum flux density, U2 is the induction voltage of induction coil (B coil), f is the frequency of magnetizing current, N2 is the turn number of B coil, S is cross section of specimen along the direction of magnetizing path. The exciting coil is uniformly wound outside of the induction coil, and the double root winding method is used to increase the current density for achieving the required magnetic flux density in the specimen. Meanwhile, the turn number, wire gauge and insulation grade of the exciting coil are the same as the induction coil. And the magnetic field strength Hb is determined by the magnetizing current, which is given by the Eq. (2).
Hb =
N1 I1 L
(2)
where Hb is the magnetic field strength at the instant when the magnetic flux density is the maximum value Bm , N1 is the turn number of exciting coil, I1 is the effective value of magnetizing current, L is the length of magnetic path. The iron loss of electrical steel sheet can be calculated by Eq. (3).
PT =
1 N1 Tm N2
∫0
T
i1 (t ) U2 (t ) dt
(3)
where T is the cycle of magnetizing current, m is the weight of specimen, i1 (t ) is the magnetizing current. 3.2. Measurement results The magnetic properties of the ring specimen and rolled specimen of non-oriented electrical steel sheet DW460-50 is measured. Fig. 3 shows the specific relative permeability μr , iron loss of rolled specimen at 50 Hz (30 °C). The relative permeability μr at low flux density (Fig. 3a) is decreased with the increase of pressure, and the difference among relative permeability under different pressures is significant. However, the difference becomes smaller at high magnetic flux density (over 1 T). The iron loss is increased with pressure (Fig. 3b). It can be found that the effect of pressure (equivalent to infinite axial compressive stress) on magnetic properties under normal temperature conditions (30 °C) is similar to the effect of finite axial compressive stress [26]. However, the effect of pressure on relative permeability is weaker than the effect of finite axial stress. The possible causes of this phenomenon are on the one hand the difference in the specimens and on the other hand the difference in the direction of the pressure on the specimens. Fig. 4 shows the measured magnetic properties of rolled specimen at 50 Hz (128 °C). The relative permeability at low flux density (Fig. 4a) is decreased with the pressure and that at high flux density (over 1 T) is almost constant with pressure. The iron loss is also increased with pressure (Fig. 4b). By comparing the measurement results in Figs. 3 and 4, the influence of temperature and pressure coupling on magnetic properties can be found. The relative permeability (Figs. 3a and 4a) is decreased with the temperature, and difference is decreased among the relative permeability under different pressure conditions. The flux density 284
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Fig. 2. The temperature and pressure coupling environment system.
corresponding to the peak relative permeability is also decreased accordingly. The change of iron loss (Figs. 3b and Fig. 4b) with temperature is similar to that of the relative permeability (The iron loss is decreased with the temperature, and the difference among the iron loss under different pressure is also decreased.). It also means that the pressure sensitivity of the magnetic properties of the non-oriented electrical steel sheet (amount of change with the increase of pressure) is decreased with the temperature. For example, the pressure sensitivity of iron loss decreases from + 2.19 × 10−3W·kg−1·MPa −1 at 30 °C to + 1.39 × 10−3W·kg−1·MPa −1 at 128 °C when the flux density is 1 T. The pressure sensitivity of relative permeability is decreased from −9.04 MPa−1 to −1.92 Mpa−1. In order to highlight the effect of temperature and pressure coupling on magnetic properties of rolled specimen of non-oriented electrical steel sheet, the typical parameter (relative permeability and iron loss) values corresponding to flux density of 1 T are presented in Table 1. The relative permeability is decreased with the increase of temperature under different pressures, but with the increase of pressure, the degree of decrease in amplitude is decreased from 55% to 38.92%. The iron loss is also decreased with the increase of temperature under different pressures. Meanwhile, the percentage of decrease is far less than the relative permeability, and the maximum is only 19.17%. Fig. 5 shows the magnetic properties of the ring specimen at 50 Hz (30 °C). The relative permeability (Fig. 5a) is decreased with the increase of pressure in the condition of low pressure (less than 60 MPa) and low flux density (less than 1.1 T), whereas the relative permeability is changed little under high pressure (more than 60 MPa) conditions. Taking into account, the effects of measurement errors and unexpected Table 1 Comparison of measurement results of rolled specimen under different temperature at Bm = 1T . “−” indicates that the parameter is decreased after the temperature is raised. “ε ” represents that the percentage of difference in the parameters at 30 °C and 128 °C. P (MPa)
0.1 30 60 90 120 140
Fig. 3. Measurement results of magnetic properties of rolled specimen at 50 Hz (30 °C). (a) Relative permeability. (b) Iron loss.
285
W
μr 30 °C
128 °C
ε (%)
30 °C
128 °C
ε (%)
3138 2869 2639 2270 1988 1873
1412 1285 1107 1220 1039 1144
−55.00 −55.21 −58.05 −46.25 −47.74 −38.92
0.4162 0.4844 0.5434 0.6295 0.6783 0.7224
0.3894 0.4175 0.4774 0.5096 0.5587 0.5839
−6.44 −13.81 −12.14 −19.05 −17.63 −19.17
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Fig. 4. Measurement results of magnetic properties of rolled specimen at 50 Hz (128 °C). (a) Relative permeability. (b) Iron loss.
Fig. 5. Measurement results of magnetic properties of ring specimen at 50 Hz (30 °C). (a) Relative permeability. (b) Iron loss.
factors (There are two possible causes of unexpected factors. One reason is that the relative permeability may be affected by high pressure, but the regularity of this effect is very small and therefore difficult to be determined. The other reason is that the relative permeability of the ring specimen have deteriorated sufficiently under high pressure conditions, and the influence of the further increase in pressure on the magnetic properties has been difficult to observe), it can be assumed that the relative permeability is not changed under high pressure conditions. The iron loss (Fig. 5b) is changed very little with the increase of pressure (the difference among iron losses does not exceed 6%). Fig. 6 shows the relative permeability μr and iron loss of ring specimen at 50 Hz (128 °C). When the pressure is less than 60 MPa, the relative permeability is decreased with the increase of the pressure (Fig. 6a), but when the pressure is increased to 90 MPa, the relative permeability is decreased only in the range of 0.5 T < B < 1 T. When the pressure is further increased to 120 MPa or 140 MPa, a part of the relative permeability in this range (0.5 T < B < 1 T) will be slightly higher than the relative permeability under the condition of 60 MPa (Although the proportion of this part is very small), the most obvious of which is the relative permeability at B = 0.75 T. It can be seen from the measurement results in Fig. 5a that under normal temperature conditions, when the pressure exceeds 90 MPa, the specimen may have deteriorated sufficiently, and it is difficult to observe the influence of pressure on the magnetic permeability of the specimen. Through the
published data [23], it can be found that when the flux density is low, the temperature causes a slight increase in the relative permeability. Therefore, it can be inferred that temperature is the most likely cause of the occurrence of such an abnormal phenomenon. The iron loss (Fig. 6b) is not changed with the increase of pressure. By comparing the measurement results in Figs. 5 and Fig.6, the effect of temperature and pressure coupling on magnetic properties of ring specimen can be analyzed. The relative permeability (Figs. 5a and 6a) is increased slightly at different pressures with the increase of temperature, but the amplitude of increase is smaller. While the iron loss Figs. 5b and 6b) is decreased, but the amplitude of decrease is smaller. In order to highlight the effect of the temperature and pressure coupling on magnetic properties of ring specimen, the typical parameter (relative permeability and iron loss) values corresponding to flux density of 1 T are presented in Table 2. It can be noticed that the pressure sensitivity of relative permeability of ring specimen is increased with the increase of temperature when the flux density is 1 T (from − 1.82 MPa −1 at 30 °C to − 2.69 MPa −1 at 128 °C). However, the iron loss is changed very little and there is no obvious regularity. Comparing the measurement results in Fig. 3, Fig. 4, Fig. 5, and Fig. 6, it can be noticed that the relative permeability and iron loss of the non-oriented electrical steel sheet measured by the rolled specimen and the ring specimen are completely different. 286
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degree of change is also smaller than that of the rolled specimen (except for the iron loss at 0.1 MPa). From the measured data in Table 3, it can be seen more clearly that the measurement results of the rolled and ring specimens are different under the temperature and pressure coupling environment. The iron loss of the ring specimen is about 2–4 times as large as that of the rolled specimen (30 °C and 128 °C), and the relative permeability is about 1.5 times (30 °C) at Bm = 1T and 50 Hz. In the edge of the sample, a certain amount of striped domains are produced due to the pressure acting in the rolling direction of the sample (or perpendicular to the rolling direction). Moreover, the magnetic poles at the grain boundaries (resulting in an increase in static magnetic energy) and the magnetic anisotropy of the grains also hinder the movement of the domain walls, thereby lowering the magnetic permeability of the sample. However, when the pressure is further increased, the inverse magnetostriction effect causes the magnetization to switch to the direction of 〈1 1 0〉 or 〈1 1 1〉, and the magnetization in the 〈1 1 0〉 or 〈1 1 1〉 direction is easy due to pressure, which obviously hinders the domain wall movement in the 〈1 0 0〉 and 〈0 1 0〉 directions. The above reasons appear to be the reason for the change in the magnetic permeability of the rolled specimen and the ring specimen [46,48]. For polycrystalline materials such as electrical steel sheet, the behavior of the change in elastic deformation is largely dependent on the crystal orientation of the grains, which causes most of the pressure to concentrate near the grain boundaries when pressure is applied to the sample. It is precisely because of the relatively concentrated stress near the grain boundaries that an uneven magnetic distribution is caused, which in turn leads to an increase in iron loss. However, when the pressure is further increased, the difference between the inside and the boundary of the grain is significantly reduced, and the influence of the grain size is further reduced. Meanwhile, the pressure perpendicular to the surface of the sample causes the direction to become hard axis due to the magneto-elastic energy, and the amount of perpendicular magnetization change caused by the pressure is correspondingly reduced during magnetization [47,49,50]. The temperature accelerates the movement of the molecules in the sample, causing the size of the domains to decrease, and the size of the grains to become large, so that the iron loss is thereby reduced. The movement of the molecules is further enhanced with the increase of the temperature, which obviously hinders the change in the direction of the domains, causing permeability of the sample to decrease (the magnetization field is greater than 0.5 T). Comparing the results of this study, it can be clearly found that in terms of iron loss, the effect of pressure is higher than that of temperature [51]. For ring specimen, the thickness (5 mm) is smaller than the laminate specimen (minimum 10 mm), so the proportion of the stress-affected zone at the boundaries is much higher than that of the rolled specimen. On the one hand, the difference between the inside and the boundary of grain in the ring specimen is smaller than that of the rolled specimen. On the other hand, the pressure near the grain boundary of the ring specimen is more concentrated, and the magnetic distribution is more uneven. These factors make the difference in iron loss of the ring specimen at different pressures not only much smaller than the rolled specimen, but also numerically larger than the rolled specimen. When the pressure is low, the strip domain generated at the edge of the ring specimen occupies a higher proportion in the entire sample than the rolled specimen, which causes the effects of magnetic poles at the grain boundaries and the magnetic anisotropy of the grains on the domain wall motion are also higher than that of the rolled specimen. Therefore, the permeability of the ring specimen is lower than that of the rolled specimen. As the pressure increases, the effect of the inverse magnetostriction effect on the ring specimen is also higher than that of the rolled specimen, but the effect among the different pressures is slightly smaller than that of the rolled specimen. As the temperature increases, the effect of the pressure on the sample will also increase as the size of
Table 2 Comparison of measurement results of ring specimen under different temperature at Bm = 1T . “+” represents that the parameter rises after the temperature rises, “−” indicates that the parameter decreases after the temperature rises. P (MPa)
0.1 30 60 90 120 140
W
μr 30 °C
128 °C
ε (%)
30 °C
128 °C
ε (%)
1543 1440 1320 1300 1232 1289
1816 1538 1468 1412 1456 1440
+17.69 +6.81 +11.21 +8.61 +18.18 +11.71
1.526 1.505 1.506 1.587 1.531 1.551
1.388 1.442 1.388 1.424 1.424 1.395
−9.04 −4.19 −7.83 −10.27 −6.99 −10.05
Fig. 6. Measurement results of magnetic properties of ring specimen at 50 Hz (128 °C). (a) Relative permeability. (b) Iron loss.
The relative permeability at different pressures measured by the rolled specimen is higher than that of the ring specimen, and the iron loss is smaller than that of the ring specimen, under normal temperature conditions (30 °C). Moreover, the magnetic properties of rolled specimen are more sensitive to pressure than ring specimen. After the temperature is increased (128 °C), the relative permeability and iron loss of the rolled specimen under different pressures are decreased. However, the relative permeability of the ring specimen is slightly increased, while the change in iron loss is the opposite, and the 287
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Table 3 Comparison of measurement results of rolled specimen and ring specimen at Bm = 1T and 50 Hz. “+” represents that the parameter rises after the temperature rises, “−” represents that the parameter decreases after the temperature rises. P (MPa)
0.1 30 60 90 120 140
W
μr Rolled specimen 30 °C
Ring specimen 30 °C
ε (%)
Rolled specimen 128 °C
Ring specimen 128 °C
ε (%)
Rolled specimen 30 °C
Ring specimen 30 °C
ε (%)
Rolled specimen 128 °C
Ring specimen 128 °C
ε (%)
3138 2869 2639 2270 1988 1873
1543 1440 1320 1300 1232 1289
−50.83 −49.81 −49.98 −42.73 −38.03 −31.18
1412 1285 1107 1220 1039 1144
1816 1538 1468 1412 1456 1440
+28.61 +19.69 +32.61 +15.74 +40.13 +25.87
0.4161 0.4844 0.5434 0.6295 0.6783 0.7226
1.631 1.578 1.592 1.659 1.531 1.55
+291.97 +225.76 +192.97 +163.54 +125.71 +114.50
0.4161 0.4844 0.5434 0.6295 0.6783 0.7226
1.388 1.442 1.388 1.424 1.424 1.395
+133.57 +195.25 +155.43 +126.21 +109.94 +93.05
c) In the temperature and pressure coupling environment, the difference between the measurement results of the ring specimen and rolled specimen is not only related to the pressure and temperature (pressure is the main factor), but also related to the shape and size of the two samples. d) When analyzing the characteristics of the motor under temperature and pressure coupling environment, the iron core made of non-oriented electrical steel sheet should be divided into tooth (magnetic properties are measured by rolled specimen) and yoke (magnetic properties measured are by ring specimen).
the domains become smaller, but it is obviously only applicable to the case where the pressure is low. In addition, the magnetization direction of the rolled specimen is along the rolling direction (or perpendicular to rolling direction), and there is a certain angle between the magnetization direction of the ring specimen and the rolling direction (or perpendicular to rolling direction). Therefore, under the same magnetization conditions, the movement of the domain walls in the rolled specimen is much easier than the movement of the domain walls in the ring specimen, and the energy required is also small. This also causes some differences in the measurement results of the rolled specimen and the ring specimen. Another possible reason is that a part of stress may be introduced in the sample due to the processing method of the excitation coil and B coil (directly wound on the specimens), and the accuracy of measurement is affected. The coils of the ring specimen are evenly wound around the whole specimen, while the coils of the rolled specimen are wound only on the middle part (the stress distribution may not be uniform), and the number of turns are much smaller than that of the ring specimen. All of these may be the reasons that the magnetic properties of ring specimen are worse than that of rolled specimen. Meanwhile, because the insulating tapes are set between specimen and B coil, a certain calculation error may be introduced in the determination of the sectional area of the B coil. Comparing the iron core of motor with the two specimens used in this article, it is not difficult to find that the shape of the yoke is similar to the ring specimen, and the shape of the tooth is similar to the rolled specimen. Through the above analysis, it can be seen that the magnetic properties of the non-oriented electrical steel sheet measured by the two specimens are different under temperature and pressure coupling environment. Therefore, when analyzing a motor operating in a temperature and pressure coupling environment, the iron core should be segmented into tooth and yoke and given the different magnetic properties of non-oriented electrical steel sheet measured by the rolled and ring specimens, respectively.
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4. Conclusion The magnetic properties of electrical steel sheets (DW460-50) under temperature and pressure coupling environment are measured by using the ring specimen and the rolled specimen. The obtained results can be summarized as follows: a) The relative permeability measured by the rolled specimen is decreased with the increase of pressure while iron loss increases. With the increase of temperature, the relative permeability and iron loss are decreased in value and pressure sensitivity. b) The relative permeability measured by the ring specimen is decreased with the increase of pressure, while the iron loss is almost constant. With the increase of temperature, the value and pressure sensitivity of relative permeability are increased, but the iron loss is only decreased in value. 288
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