Influence of temperature on magnetic properties of silicon steel lamination

Grain-oriented(GO) and non-oriented(NO) silicon steel is widely used as core materials for electromagnetic equipment, such as transformer and motors, because of their attractive characteristics of high magnetic saturation point, good mechanical strength and low cost. Increasing frequency and magnetic induction is the direct way to reduce the volume and weight of magnetic devices. Meanwhile, the increase of power density leads to high loss density, thus higher temperature in the silicon lamination core. A lack of coupled magnetic data of silicon steel couldn’t provide finite element method (FEM) software with precise input, which may prevent researchers from precisely designing and analyzing high power density magnetic device even though advanced analysis and optimization algorithms are adopted.

Some papers focused on soft ferrites addressed this issue,^1–5 literatures Refs. 6 and 7 measured the thermal effect(up to Curie point) on magnetic properties of silicon steel only at 50Hz, and the result shows a significant difference with the properties we have known in the ordinary condition. This paper aims to clearly quantify the thermal effect on magnetization and iron loss (20∼400Hz) of both NO and GO silicon steels, and finally propose a temperature-dependent model for 2D transient magnetic field analysis based on loss separation theory.

Considering most of the magnetic devices operate within temperature range from RT to 200°C because of the winding insulation, we customized a special Epstein frame for examining thermal effect on magnetic properties of silicon steel, whose size is consistent with IEC and Chinese GB standard, illustrated in FIG. 1. The size of specimen mentioned in this paper is 300mm length by 30mm width.

At first, we measured 26 grades of all the Q,QG series(GO) and W series(NO) silicon steel stripe made by Wuhan Iron and Steel Corp.(WISCO), and obtained AC magnetization and iron loss data at 20, 50, 100, 150 and 200°C, respectively. FIG. 2(a) and (b) show that the magnetization curves are more influenced by frequency, and vary little with temperature, especially when the magnetic induction is larger than 1.4T(for NO) and 1.7T(for GO). Iron loss of GO and NO silicon steels at various temperatures and frequencies (20, 50, 100, 200 and 400Hz) is shown in FIG. 2(c) and (d), which indicates that both steels’ iron loss decreases with rising temperature. But iron loss of NO steel decreases more sharply than GO steel when excitation frequency increases from 50 to 400Hz. For example, compared with measurement result at 20°C, NO’s P_1.56/400 at 200°C decreases by 30%, while GO’s P_1.7/400 decreases only by 10%.

Iron loss is the one of the most important indexes for silicon steel. Almost every motor designer knows that classic loss separation formula is used in iron loss calculation,⁸ which can be divided into static and dynamic loss. Static loss is known as hysteretic loss, which is related to energy consumed when domain wall moves and rotates, expressed in (1). Dynamic loss is composed of eddy current loss and excess loss, shown in (2), where unit of iron loss is W/kg. Dynamic loss originates from eddy current and some other non-ideal factors, such as inhomogeneous magnetization.

Here, K_h, x, K_e are loss coefficients fitted by measured loss curve and conductivity of steel specimen. B_p, B and f denote the peak value, instantaneous value of magnetic induction and fundamental frequency. $σ$ and $δ$ are the conductivity and mass density of the steel specimen.

When fed with sinusoidal excitation, expression (1) can be simplified as (3)

Due to lack of detailed datasheet and inhomogeneity of material, it is sometimes difficult for motor designers to get precise conductivity data of the silicon steel, which hinders the application of the iron loss data. Usually, multi-frequency iron loss curves are used to directly determine the above iron loss coefficients by least mean square (LMS) method. Literature Refs. 9 and 10 combined the eddy current loss and excess loss, and designated them as comprehensive eddy current loss expressed in (4), whose time domain and frequency domain expression are shown in (5) and (6), respectively.

It is called modified iron loss model in the following.

Following from TABLE I, TABLE II and FIG. 3, for GO steel, the classic iron loss model is more accurate than the modified one, overall relative error is about 4% smaller than the latter, while for NO steel, the modified iron loss model seem a little bit more precise with overall relative error below 10%. Although the error of both model is significant when B is below 0.5T, it is acceptable because the working point of silicon steel is seldom below 0.5T. From perspective of massive curves fitting involving all series of NO and GO products made by WISCO, the modified iron loss model is recommended to be used for nonoriented silicon steel. For grain oriented one, the classic loss separation model is recommended.

Since the iron loss is composed of static and dynamic component, a natural idea to investigate temperature’s influence on iron loss is to study the thermal effect on each loss components respectively. DC magnetic test under different temperatures is carried out because dynamic loss cannot be measured directly. We used the computerized ballistic method¹¹ to measure the DC hysteresis loss and loop because it is not that demanding as scanning method on zero drift index of flux meter. Theoretically, repeatability and precision of the computerized ballistic method is better on the premise of the same specification of flux meter.

Literature Ref. 9 reported that temperature has little effect on static hysteresis loss of NO steel. To clarify thermal effect on GO steel, here we take 30Q130 silicon steel as the example. FIG. 4(a) shows that static hysteresis loss of GO steel decreases with rising temperature, when field strength H_dc is kept constant. But the fact is that magnetic induction B_dc also decreases at the same time. As iron loss curve always takes magnetic induction as the abscissa, we continue to explore the hysteresis loss versus B_dc. FIG. 4(b) shows static hysteresis loss remains almost invariant for GO steel around working point of 1.7T when temperature changes from 25∼150°C. Obviously, judging from the measured result, dynamic loss is responsible for the decline of GO’s iron loss when temperature increases, which is consistent with the result in a preceding study about NO steels.⁹ This could explain the phenomenon observed in Section II that the higher the frequency is, the more the iron loss decreases when temperature rises. Because static hysteresis loss is proportional to frequency, dynamic loss is proportional to 1.5∼2 power of frequency. Therefore, with the frequency increasing, the dynamic loss component takes more share of total iron loss. The dynamic loss component decreases with rising temperature, but the static hysteresis loss component almost remains invariant when temperature rises.

If excitation frequency is zero, only magnetic field is involved in the magnetizing process, iron loss is equal to static hysteresis loss. Otherwise, electric field is also involved, for silicon steel is a good conductor, both current and ohmic loss exist. Based on the fact above, the resistivity is the physical cause of dynamic loss. We assumed that resistivity increases when temperature increases. Thus, we introduced a temperature coefficient k for resistivity in classic and modified iron loss model. In (7), T and T₀ are the actual and base temperature value, respectively.

Substituting (2) and (4) into (7), respectively, we can obtain the temperature-dependent model for GO and NO silicon steels.

The temperature-dependent iron loss model was validated by 26 grades of all the Q, QG series(GO) and W series(NO) silicon steel stripe made by WISCO. For each grade, several hundreds of test combinations of various temperatures, magnetic inductions and frequencies are validated. Model prediction error is defined as (8), where N denotes the total counts of iron loss measurement.

FIG. 5 shows the predicted and measured iron loss of NO and GO steel at 200°C. TABLE III shows that the overall relative error of temperature-dependent iron loss model for 50DW465(NO) and 30Q130(GO) within the range of 0∼2T, 20∼400Hz, 20∼200°C is within 10%. While from TABLE I and TABLE II, we see that the relative error of iron loss model without considering temperature is already 8.79% for 50DW465 and 9.3% for 30Q130. This means that the temperature-dependent model can accommodate more temperature-dependent test samples without reducing the accuracy significantly.

The classic iron loss model is a 2-factor model, which can only describe the influence of frequency and magnetic induction on iron loss. The proposed temperature-dependent iron loss model is a 3-factor model, can be applied in the electromagnetic and thermal coupled analysis of motor. Though the value of k is mathematically determined, in fact it has a physical meaning, which can be explained as temperature coefficient of effective resistivity of silicon steel lamination. If k is positive, iron loss decreases with rising temperature, if negative, iron loss increases with rising temperature. The larger |k| is, iron loss varies more sharply with rising temperature. Most importantly, temperature coefficient k is a constant, which is meaningful to reduce the model complexity.

Considering static hysteresis loss is proportional to frequency, while dynamic loss is proportional to 1.5∼2 power of frequency, so with the frequency increasing, dynamic loss is dominant. However, dynamic loss decreases with rising temperature, while static loss doesn’t vary with temperature. So, when excitation frequency goes up or high order harmonics exist, the percentage of dynamic loss component of iron loss increase, thermal effect on iron loss will be more obvious. It also indicates that for loss frequency applications, the thermal effect on iron loss can be neglected. The proposed method can be applicable to other types of magnetic materials as long as whose resistivity rate exhibits approximately linear thermal dependence on a temperature range of 20∼200°C.

Based on DC magnetic measurement result and loss separation theory, we studied the temperature influence on iron loss of both NO and GO silicon steels. For both steels static hysteresis loss is not influenced by temperature within the range of 20∼200°C. By massive curves fitting, we found that the classic iron loss model is more suitable for GO, while a modified iron loss model is more appropriate for NO steel. Considering the results above, a temperature-dependent iron loss model for silicon steel is proposed by introducing temperature coefficient k to consider thermal effects on dynamic loss. The proposed model is very simple, effective and easy to implement in time-stepping electromagnetic FEM software.

This work was supported in part by the National Key Basic Research Program 973 Project of China under Grant 2013CB035601, Chinese Scholarship Council, National Natural Science Foundation of China under Grant 51137005, 51377086, 51407180, 51407188, 51407192 and 51507181, and Foundation for the Author of National Excellent Doctoral Dissertation of China under Grant 201152. The authors would like to thank Mr. Zhu and Hunan Forever Elegance Corporation for their assistance in experimental setup and magnetic measurement.