The performance requirements of motors are gradually increasing, and anisotropic soft magnetic materials have been applied in motors to improve performance, The magnetostriction of anisotropic soft magnetic materials is one of the main contributors in extensive research on anisotropic soft magnetic material transformers. Compared to transformers, the magnetic field in motors has more complex harmonic and multi-directional characteristics. In this paper, the magnetic field of motors stator teeth under both no-load and load conditions is calculated and analyzed to research magnetostriction of anisotropic soft magnetic materials in motor magnetic field and predict the NVH performance of anisotropic soft magnetic material motors accurately. Furthermore, the magnetostriction in different magnetization angles is investigated for the multi-directional characteristics, and the result is explained from microscopic principles. This paper focuses on a splicing oriented silicon steel (OSS) motor, the magnetization angle of OSS in motor varying from 0° to 90°. Firstly, the equivalent formulas of magnetic field are obtained under the analytical and finite element calculations. After that, the frequency and direction of experiment magnetic field are confirmed and the magnetostriction of OSS in different magnetization angle and frequency is measured. In the end, the variation character of magnetostriction of OSS is summarized.

Oriented silicon steel (OSS) materials are commonly used in transformer cores due to its high saturation flux density and low core losses in the rolling direction (RD). As the motor performance requirements continue to increase, the OSS started to be used in motor to reduce the core losses and improve the motor performance.1 The vibration and noise of motors are extensively researched topics in a long time. Apart from electromagnetic forces, the magnetostriction of core materials, especially in OSS material, is another cause.2,3

The magnetostriction of OSS and non-oriented silicon steel (NOSS) in electromagnetic equipment, including transformers and motors, is a highly intricate phenomenon.4 Thus, comprehending the magnetostrictive characteristics of OSS can aid in detecting vibration distortion resulting from magnetostriction when designing motors, and facilitate its application in electromagnetic components. The investigation of magnetostriction properties primarily involves material testing and prediction. Lixun Zhu et al.5 have introduced a new circular bi-directional monolithic tester, which provides a broader and more uniform test field for measuring the magnetostrictive properties of OSS, and the magnetostrictive force model was improved and validated in a transformer. Yang Li et al.6 proposed a simulation of the one-dimensional sinusoidal force of OSS under one-dimensional sinusoidal excitation using a dynamic J-A model. Additionally, they presented a model of magnetostrictive force of OSS under the same excitation. Their models considered both the dynamic hysteresis loop excitation and magnetostriction effects of OSS. For the microstructure analysis of OSS, Keiji Iwata et al.7 and other researchers investigated the pattern of variation within the OSS willow leaf domains at temperatures up to 900 °C.

At present, the magnetostriction of OSS is mainly studied within transformer, while the investigation in rotating motors is in its infancy. However, the magnetic field distribution in rotating motors is more intricate compared to that of transformers. Furthermore, although by applying splicing structure to OSS in the stator core can optimize the superior magnetic features of OSS and enhance motor performance.8 it leads to greater complexity in magnetostriction.

This paper investigates the magnetostriction in the OSS motor with a splicing stator. The magnetic field environment of OSS is analyzed under both no-load and load operation conditions in the motor. Experiments are established and conducted to measure the magnetostriction properties of OSS. Finally, the magnetostriction of OSS is analyzed in the motor, which is significant for further research on the vibration noise of the OSS motors.

In this paper, an 8-pole 48-slot tooth -spliced OSS motor is taken as the background. Fig. 1(a) shows the 1/8 topology model of the motor, where both stator yoke and rotor core are still made of NOSS material, while the stator tooth are made of OSS. Fig 1(b) shows the rolling direction of OSS in stator tooth. The parameters of the motor are shown in Table I.

FIG. 1.

(a) Motor structure (b) Stator teeth.

FIG. 1.

(a) Motor structure (b) Stator teeth.

Close modal
TABLE I.

Motor parameters.

ParameterValueParameterValue
Inner/Out radius 60.5 mm/180 mm Rated power 90 kW 
of stator    
Inner/Out radius 25 mm/59.5 mm Rated torque 90 Nm 
of rotor    
Length 120 mm Rated current 150 A 
Teeth width 4.23 mm Busbar voltage 540 V 
ParameterValueParameterValue
Inner/Out radius 60.5 mm/180 mm Rated power 90 kW 
of stator    
Inner/Out radius 25 mm/59.5 mm Rated torque 90 Nm 
of rotor    
Length 120 mm Rated current 150 A 
Teeth width 4.23 mm Busbar voltage 540 V 

The magnetic field of OSS in the motor is generated by the interaction of the permanent magnetic field and the excitation magnetic field. To determine the variation of the magnetic field of the oriented silicon steel material, this paper calculates the magnetic flux density of the teeth of the motor under both no-load and load conditions.

At rated operation, the saturation of OSS material is not high. As a result, the teeth exhibit a much higher magnetic permeability than the slot, which leads to significantly lower magnetic resistance. Within a range of tooth pitch, nearly all magnetic flux enters the stator yoke via the stator tooth. This means that, regardless of whether the motor is under no-load or load, the magnetic density of the tooth can be expressed as
(1)
Where, B̄i is the magnetic flux density of stator tooth, B̄δ is the air gap magnetic flux density of air gap, lef is the armature calculated length, t is the stator tooth pitch, li is the core axial length, Kfe is the core stacking coefficient, bi is the width of the stator teeth, for this motor, and A is a constant. To determine the magnetic field frequency in OSS within the motor, Fourier decomposition is applied to the magnetic density of the teeth, which can be expressed as
(2)

Figs. 2(a) and (b) shows B̄i under no-load and load conditions, respectively, it can be seen that the magnetic field waveform is non-sinusoidal due to the structure and armature reaction of the motor under both no-load and load, and although the excitation is sinusoidal, the B̄i are still non-sinusoidal. Fig. 2(c) shows the Fourier decomposition outcomes of the magnetic flux density in stator tooth under no-load and load condition, and mainly consists of the magnetic flux density of the fundamental frequency, the third harmonic frequency and the fifth harmonic frequency. And the amplitude of the stator tooth’s magnetic flux density under no-load and load conditions is 1.38 T and 1.6 T, respectively. Furthermore, the magnetic density of motor teeth can be approximated by superimposing magnetic fields of various frequencies through Fourier decomposition.

FIG. 2.

(a) Magnetic flux density of Stator tooth under no-load condition (b) Magnetic flux density of Stator tooth under load condition (c) the Fourier decomposition outcomes of the magnetic flux density in stator tooth under no-load and load condition.

FIG. 2.

(a) Magnetic flux density of Stator tooth under no-load condition (b) Magnetic flux density of Stator tooth under load condition (c) the Fourier decomposition outcomes of the magnetic flux density in stator tooth under no-load and load condition.

Close modal

To determine the magnetization direction of OSS in the motor, the FEA is conducted. Fig 3 shows the magnetic flux path of the motor stator. The result shows that the angle between the direction of the magnetic flux path of OSS and the rolling direction of OSS ranges from 0° to 90°, and primarily in the range of 0° to 40° in motor.

FIG. 3.

Magnetic flux path of stator.

FIG. 3.

Magnetic flux path of stator.

Close modal

The test samples are B23R080 high magnetic susceptibility OSS strips with 100 mm×500 mm. For the aforementioned calculation and analysis of the B̄i of the OSS stator tooth, six magnetization directions were evaluated at angles of α = 0°, 10°, 20°, 30°, 35°, and 40°, with each direction examined at frequency intervals of 50 Hz (covering the range from 50 Hz to 250 Hz) and magnetic flux density intervals of 0.2 T (ranging from 1.2 T to 1.6 T). Meanwhile, a NOSS of identical specification is set up for a magnetostriction comparison test at a magnetization direction of 0°, as the difference in magnetostriction of NOSS between magnetization directions of 0° to 40° is insignificant.9 

Figure 4 shows the magnetostriction testing equipment, which mainly includes the excitation coil, laser vibrometer, magnetostriction damping platform and testing software. In order to better analyze the changes in magnetostriction of OSS, this paper also sets up the metallographic experiment of OSS.

FIG. 4.

Magnetostriction test equipment.

FIG. 4.

Magnetostriction test equipment.

Close modal

From Fig. 5, it can be seen that the λPP, which is defined as the distances between the positive and negative peak values of magnetostriction, has the same rule of change at different frequencies under 1.2 T, 1.4 T and 1.6 T. λPP increases from 50 Hz to 150 Hz and a decrease from 150 Hz to 200 Hz. Figure 6 shows the magnetostrictive butterfly curve of OSS under the magnetization strength of 1.6 T, which is the rated condition of the motor, at different frequencies. The value of the longitudinal coordinate greater than 0 represents elongation of OSS and less than 0 represents contraction. At 50 Hz, the magnetostrictive butterfly curve is basically symmetrical about the y=0 axis, the magnetostriction elongation and contraction are basically equal, and in the range of 50 Hz to 250 Hz, as the frequency increases, the magnetostriction contraction ratio first increases and then decreases, but always exceeds the elongation. The area enclosed by the butterfly loop first narrows and then widens. The reason may be related to the different sensitivity of the elongation and contraction of magnetostriction in oriented silicon steel to different frequencies and excitation amplitudes, but the effect on frequency and tooth magnetic density is significant.

FIG. 5.

λPP at different frequencies.

FIG. 5.

λPP at different frequencies.

Close modal
FIG. 6.

Magnetostrictive butterfly curve at different frequencies.

FIG. 6.

Magnetostrictive butterfly curve at different frequencies.

Close modal

Figure 7 shows the λPP of OSS at different magnetization directions. It can be seen that as the magnetization angle increases, the λPP of OSS increases rapidly, the growth rate decreases significantly when the magnetization angle reaches 20°, and then decreases when the magnetization angle is between 30° and 40°.

FIG. 7.

λPP in magnetic direction from 0° to 40° at magnetic field of 1.2 T, 1.4 T, 1.6 T.

FIG. 7.

λPP in magnetic direction from 0° to 40° at magnetic field of 1.2 T, 1.4 T, 1.6 T.

Close modal

Fig. 8(a) shows the magnetostrictive butterfly curve under different magnetization angles at the magnetic flux density of 1.4 T and the frequency of 50 Hz. It can be seen that as the magnetization angle increases from 0° to 40°, the shape of the butterfly curve varies greatly. And this is because the magnetization direction has different effects on the harmonics of magnetostriction. but in general, the butterfly curve first becomes longer and then shorter.

FIG. 8.

(a) Magnetostrictive butterfly curve of OSS at magnetization direction from 0° to 40°(b) Magnetostrictive butterfly curve of NOSS at a magnetization direction of 0°.

FIG. 8.

(a) Magnetostrictive butterfly curve of OSS at magnetization direction from 0° to 40°(b) Magnetostrictive butterfly curve of NOSS at a magnetization direction of 0°.

Close modal

Fig. 8(b) shows the magnetostrictive butterfly curve of NOSS with magnetization angle of 0° at the magnetic flux density of 1.4 T and the frequency of 50 Hz. At this point, the magnetostrictive strain of NOSS is dominated by the elongation, which is 1871.18 nm/m, greater than that of OSS. However, as the magnetization angle increases, the magnetostrictive strain of OSS far exceeds that of NOSS.

As the external magnetic field varies, the magnetic domains of OSS exhibit different degrees of rotation and domain wall motion, resulting in deformation of the magnetic domain-containing grains and macroscopic magnetostriction.

As shown in Figure 9, the grains in B23R080 (the mean size of the grains is 0.67 cm) are significantly larger than those found in NOSS (the mean size of the grains is 88.8 μm). Furthermore, the magnetic domains exhibit a higher degree of alignment. The main magnetic domains of OSS are predominantly the 180° domains, which are parallel to [001]. When the magnetization direction is the same as the rolling direction of OSS, the magnetostriction mainly relies on the domain wall motion of the 180° main magnetic domain, resulting in smaller magnetostriction than in NOSS.

FIG. 9.

(a) Metallographic observation result of OSS (b) Metallographic observation result of NOSS.

FIG. 9.

(a) Metallographic observation result of OSS (b) Metallographic observation result of NOSS.

Close modal

There is a damping nature between the magnetic domains magnetization and magnetostrictive strain as the frequency of the external magnetic field changes, the delay between the magnetization and the strain macroscopically changes, resulting in a change in the area enclosed by the magnetostrictive butterfly curve.

In OSS, the main magnetic domain of 180° is almost the same as the rolling direction, besides the 180° main magnetic domain, there are also 90° magnetic domains, and the magnetostriction during magnetization is produced by the coupled action of these two magnetic domains. As the angle between the magnetization direction and the rolling direction of oriented silicon steel increased, magnetostriction is dominated by the magnetic domain rotation of the 90° magnetic domains. The magnetostriction is predominantly contractional and reaches its maximum at magnetization angles between 30° and 40°. As the magnetization angle is further increased, the angle between the main magnetic domains and the magnetization direction continues to increase, domain wall motion of the magnetic domains gradually dominates, and the contraction of magnetostriction begins to decrease.

The following 3 points are summarized:

  1. The magnetic field of OSS in a motor is more complex than in a transformer, because of motor structure and armature reaction. and in the motor, the angle between the direction of the magnetic field and the rolling direction of the OSS varies from 0° to 90°.

  2. There is a time delay between magnetostrictive strain and magnetization, and the magnetic domain structure is not the same, so, the sensitivity of magnetostriction to the magnetic field frequency is not the same. For the B23R080l, when the applied magnetic field frequency increases from 50 Hz to 250 Hz, λPP of OSS increases from 50Hz to 150Hz and decreases from 150Hz to 200Hz.

  3. When the magnetization direction and the rolling direction of OSS are the same, the λPP of the OSS is smaller than that of the NOSS. As the magnetization direction changes from 0° to 40°, the λPP of the OSS first increases rapidly and then decreases, and when the magnetization direction is in the range of 10° to 40°, the λPP of the OSS is larger than that of the NOSS. In addition, for splicing oriented silicon steel (OSS) motor, the magnetostriction of the NOSS is dominated by elongation and that of OSS is dominated by contraction, so, the magnetostriction of the stator yoke which made of the NOSS may interact with that of the teeth which made of the OSS. Therefore, compared with the transformers and conventional NOSS motors, the magnetostriction problems of oriented silicon steel tooth yoke spliced motors need to be paid more attention.

This research was supported by program of Scholars of the Xingliao Plan (No. XLYC2002113), Shenyang University of Technology Interdisciplinary Team Project (No. 100600453) and Central guide to local science and technology development funds (free exploration class basic research) (No. 2023JH6/100100043).

The authors have no conflicts to disclose.

Yuxiao Li: Writing – original draft (equal); Writing – review & editing (equal). Zhiye Li: Writing – review & editing (supporting). Xusheng Lu: Visualization (supporting). Guangshuai Shao: Software (supporting). Jiaxin Liu: Software (supporting). Ruilin Pei: Data curation (equal).

The data that support the findings of this study are available from the corresponding author upon reasonable request.

1.
O.
Kaneki
,
T.
Higuchi
,
Y.
Yokoi
,
T.
Abe
,
Y.
Miyamoto
, and
M.
Ohto
, “
Performance of segment type switched reluctance motor using grain oriented
,” in
2012 15th International Conference on Electrical Machines and Systems (ICEMS)
(
IEEE
,
2012
), pp.
1
4
.
2.
K.
Delaere
,
W.
Heylen
,
R.
Belmans
et al, “
Comparison of induction machine stator vibration spectra induced by reluctance forces and magnetostriction
,”
IEEE Transactions on Magnetics
38
(
2
),
969
972
(
2002
).
3.
L.
Vandevelde
and
J. A. A.
Melkebeek
, “
Magnetic forces and magnetostriction in electrical machines and transformer cores
,”
IEEE transactions on magnetics
39
(
3
),
1618
1621
(
2003
).
4.
L.
Zhu
,
J.
Li
, and
J.
Zhu
, “
Research on magnetostrictive model for oriented silicon steel under service conditions
,”
Transactions of China Electrotechnical Society
35
(
19
),
4131
4138
(
2020
).
5.
L.
Zhu
,
H. S.
Yoon
,
H. J.
Cho
et al, “
Finite-element analysis of magnetostriction force in power transformer based on the measurement of anisotropic magnetostriction of highly grain-oriented electrical steel sheet
,”
IEEE Transactions on Magnetics
52
(
3
),
6100304
(
2015
).
6.
Y.
Li
,
J.
Zhu
,
L.
Zhu
et al, “
A dynamic magnetostriction model of grain-oriented sheet steels based on Becker–Döring crystal magnetization model and Jiles–Atherton theory of magnetic hysteresis
,”
IEEE Transactions on Magnetics
56
(
3
),
7511405
(
2020
).
7.
K.
Iwata
,
M.
Suzuki
,
M.
Hashimoto
et al, “
Temperature dependence of lancet domains in grain-oriented Fe-3% Si steels
,”
IEEE Transactions on Magnetics
51
(
11
),
2002504
(
2015
).
8.
R.
Pei
,
L.
Zeng
,
S.
Li
, and
T.
Coombs
, “
Studies on grain-oriented silicon steel used in traction motors
,” in
2017 20th International Conference on Electrical Machines and Systems (ICEMS)
(
IEEE
,
2017
), pp.
1
5
.
9.
Z.
Wang
,
Y.
Zhang
,
G.
Yuan
et al, “
Study on magnetostrictive properties of non-oriented electrical steel sheet under mechanical stress
,”
Journal of Electrical Engineering
38
,
5682
(
2023
).