Iron loss evaluation method, low iron loss material design method, iron loss evaluation program, low iron loss material design program, low loss soft magnetic material, and low loss soft magnetic powder

Abstract

This iron loss evaluation method includes a step for predicting, on the basis of a modulation factor and a carrier frequency, an iron loss that occurs when a magnetic material is excited by an excitation waveform generated by a PWM inverter that is controlled using PWM parameters including the modulation factor and the carrier frequency.

Description

[Technical Field]

[0001] This disclosure relates to a method and program for evaluating iron loss, which is a problem when exciting a magnetic material with a PWM inverter; a method and program for designing a low iron loss material corresponding to the excitation conditions of a PWM inverter; and a low-loss soft magnetic material and a low-loss soft magnetic powder used as a low iron loss material. [Background technology]

[0002] Generally, the iron loss of soft magnetic materials used as motor cores is evaluated by exciting them with a sinusoidal wave. On the other hand, motor cores used in recent power electronics equipment are excited by inverters. Here, iron loss is a cause of heat generation in power electronics equipment. To improve the accuracy of predicting the amount of heat generated during the actual operation of power electronics equipment, it is essential to evaluate the iron loss when the core is excited by an inverter. As a method for evaluating the iron loss when the core is excited by an inverter, a method is known in which the iron loss is calculated by integrating the excitation waveform synthesized based on the inverter conditions (see Non-Patent Literature 1).

[0003] Here, the most common type of inverter, the PWM (Pulse Width Modulation) inverter, is sometimes used. A PWM inverter generates the excitation waveform as a pulse wave using the PWM method. Specifically, in order to create a sine wave with a maximum magnetic flux density of B1 and a frequency of f1 as the target excitation wave, the PWM inverter compares the height of a modulated wave corresponding to the target excitation wave with a carrier wave, which is a triangular wave with a frequency several times that of the modulated wave. It generates a pulse wave that is at a HI level when the modulated wave is higher than the carrier wave and at a LO level when the modulated wave is lower than the carrier wave. This pulse wave is configured so that the pulse height is constant regardless of time, but the pulse width changes with time. The waveform obtained by taking the time average of the pulse wave thus generated is applied to the iron core as the excitation wave.

[0004] As described above, the excitation wave generated by a PWM inverter corresponds to a waveform in which harmonics originating from the carrier wave are superimposed on the target excitation wave, which is a sine wave. The iron loss in excitation using a PWM inverter is increased compared to the iron loss in excitation using a sine wave by the amount of iron loss caused by the harmonic components.

[0005] Therefore, it is conceivable to improve the accuracy of iron loss calculation by analyzing the excitation wave generated by the PWM inverter. However, analyzing the excitation wave generated by the PWM inverter requires complex waveform analysis. Consequently, it is difficult to perform waveform analysis for each condition when prototyping iron cores under multiple conditions. Therefore, a method for accurately estimating iron loss in a short time has been proposed (see Patent Document 1). [Prior art documents] [Patent Documents]

[0006] [Patent Document 1] Japanese Patent Publication No. 2012-26960 [Non-patent literature]

[0007] [Non-Patent Document 1] G. Bertotti, IEEE TRANSACTIONS ON MAGNETICS, VOL. 24, NO. 1 (1988), p.621-630 [Overview of the Initiative] [Problems that the invention aims to solve]

[0008] As described in Non-Patent Document 1, the method for evaluating inverter iron loss is extremely complicated, involving the synthesis of excitation waveforms based on inverter conditions and then integration of the synthesized waveforms. This hinders the analysis itself, the prototyping of magnetic cores, and their application to evaluation. Furthermore, while Patent Document 1 estimates iron loss by simply representing the harmonic components of the inverter excitation waveform, it is necessary to measure the harmonic components each time iron loss is estimated.

[0009] This disclosure was developed in view of the above-mentioned problems, and aims to clarify the relationship between inverter input conditions and inverter iron loss, and to provide an iron loss evaluation method and iron loss evaluation program that can directly predict iron loss from inverter conditions without measuring the iron loss when an iron core is excited by an inverter. Furthermore, this disclosure aims to provide a low iron loss material design method and low iron loss material design program that use the evaluation results of the above-mentioned iron loss evaluation method and iron loss evaluation program, as well as a low-loss soft magnetic material and low-loss soft magnetic powder designed using the low iron loss material design method and low iron loss material design program. [Means for solving the problem]

[0010] (1) An iron loss evaluation method according to one embodiment of the present disclosure includes the step of predicting the iron loss that occurs when a magnetic material is excited with an excitation waveform generated by a PWM inverter controlled by PWM parameters including modulation rate and carrier frequency, based on the modulation rate and the carrier frequency.

[0011] (2) In the step of predicting the iron loss in the iron loss evaluation method described in (1) above, the iron loss may be predicted based on the ratio of the frequency of the harmonics of the excitation waveform to the carrier frequency.

[0012] (3) In the step of predicting the iron loss in the iron loss evaluation method described in (2) above, the ratio of the frequency of the harmonics of the excitation waveform to the carrier frequency may be determined based on waveform data obtained by measuring the excitation waveform generated by the PWM inverter.

[0013] (4) In the step of predicting the iron loss in the iron loss evaluation method described in any one of (1) to (3) above, if the magnetic material is a compacted magnetic core, the iron loss may be predicted based on the cross-sectional area of ​​the compacted magnetic core that intersects the magnetic flux that energizes the compacted magnetic core.

[0014] (5) A low iron loss material design method according to one embodiment of the present disclosure includes the step of designing the characteristics of a magnetic material to be designed such that the iron loss that occurs when the magnetic material to be designed is excited with an excitation waveform generated by controlling the PWM inverter at a predetermined modulation rate and a predetermined carrier frequency is reduced, based on the results of predicting the iron loss that occurs when each of at least two types of magnetic materials having different characteristics is excited with an excitation waveform generated by controlling the PWM inverter at a predetermined modulation rate and a predetermined carrier frequency, by performing the iron loss evaluation method described in any one of (1) to (4) above.

[0015] (6) In the step of designing the properties of the magnetic material to be designed in the low iron loss material design method described in (5) above, the representative dimensions of the magnetic material to be designed may be designed as properties of the magnetic material to be designed based on the results obtained for each representative dimension of the magnetic material to be designed of the iron loss that occurs when the magnetic material to be designed is excited with a sinusoidal excitation waveform.

[0016] (7) In the low iron loss material design method described in (5) above, the magnetic material to be designed may be a compacted magnetic core made of soft magnetic powder. In the step of designing the properties of the magnetic material to be designed, the representative dimensions of the soft magnetic powder may be designed as a property of the magnetic material.

[0017] (8) In the step of designing the properties of the magnetic material to be designed in the low iron loss material design method described in (7) above, if the magnetic material is a powder core made of soft magnetic powder, the representative dimensions of the soft magnetic powder may be designed as properties of the magnetic material based on the results obtained for each representative dimension of the soft magnetic powder when the powder core is excited with a sinusoidal excitation waveform.

[0018] (9) An iron loss evaluation program according to one embodiment of the present disclosure causes a processor to execute the iron loss evaluation method described in any one of (1) to (4) above.

[0019] (10) A low iron loss material design program according to one embodiment of the present disclosure causes a processor to execute the low iron loss material design method described in any one of (5) to (8) above.

[0020] (11) A low-loss soft magnetic material according to one embodiment of the present disclosure has properties designed by performing the low-iron-loss material design method described in (5) or (6) above.

[0021] (12) A low-loss soft magnetic powder according to one embodiment of the present disclosure has a representative dimension designed by performing the low-iron-loss material design method described in (7) or (8) above. [Effects of the Invention]

[0022] According to the iron loss evaluation method and iron loss evaluation program described herein, the iron loss when the iron core is excited by the inverter is directly predicted from the inverter conditions without measuring the iron loss. According to the low iron loss material design method and low iron loss material design program, as well as the low loss soft magnetic material and low loss soft magnetic powder described herein, the iron loss when the iron core is excited by the inverter is reduced. [Brief explanation of the drawing]

[0023] [Figure 1] This figure shows an example of operation of a triangular wave comparison type PWM inverter. [Figure 2] This figure shows an example of the frequency spectrum of an inverter excitation waveform. [Figure 3] This flowchart shows the procedure for predicting iron loss in the comparative example. [Figure 4] This flowchart shows an example of a procedure for an iron loss evaluation method according to one embodiment of the present disclosure. [Figure 5] This is a block diagram showing an example configuration of an information processing system according to one embodiment of the present disclosure. [Figure 6] This graph shows an example of the relationship between carrier frequency and harmonic frequency. [Figure 7] This graph shows an example of the relationship between modulation index and harmonic frequencies. [Figure 8] This graph shows an example of the relationship between the frequency of the modulated wave and the frequency of its harmonics. [Figure 9] This graph shows an example of the relationship between carrier frequency and harmonic magnetic flux density. [Figure 10] This graph shows an example of the relationship between modulation index and harmonic magnetic flux density. [Figure 11] This graph shows an example of the relationship between the frequency of a modulated wave and the magnetic flux density of its harmonics. [Figure 12] This graph shows an example of the relationship between measured and predicted values ​​of harmonic magnetic flux density. [Figure 13] This is an example of a graph used to determine α in Steinmetz's empirical formula. [Figure 14] This is an example of a graph used to determine β in Steinmetz's empirical formula. [Figure 15] This is an example of a graph showing the relationship between the defined value of α and the median diameter of the pure iron powder in a powdered magnetic core using pure iron powder, expressed using simple regression. [Figure 16] This is an example of a graph showing the relationship between the defined β value and the median diameter of the pure iron powder in a compacted magnetic core using pure iron powder, expressed using simple regression. [Figure 17] This is an example of a graph showing the relationship between the defined γ value and the median diameter of the pure iron powder for a powdered magnetic core using pure iron powder, expressed using simple regression. [Figure 18] This is an example of a scatter plot showing the relationship between the measured iron loss in Example 1 and the value calculated based on the iron loss prediction formula. [Figure 19] This graph shows an example of the relationship between median diameter and predicted iron loss in Example 2. [Figure 20] This graph shows an example of the relationship between median diameter and predicted iron loss in Example 3. [Figure 21] Figure 18 is a graph that adds the measured iron loss values ​​from Example 4 and the values ​​calculated based on the iron loss prediction formula. [Figure 22] This figure shows an example of eddy currents flowing within a compacted magnetic core. [Figure 23]This figure shows an example of the structure of a compacted magnetic core. [Figure 24] This scatter plot shows an example of the relationship between the sinusoidal eddy current loss coefficient and the cross-sectional area of ​​the compacted magnetic core. [Figure 25] This is a scatter plot showing an example of the relationship between the harmonic eddy current loss coefficient and the cross-sectional area of ​​the compacted magnetic core. [Figure 26] This is a scatter plot showing an example of the relationship between measured and predicted sinusoidal eddy current iron loss in Example 5. [Figure 27] This scatter plot in Example 6 shows an example of the relationship between the measured value of harmonic eddy current iron loss and the predicted value without considering the harmonic eddy current loss coefficient. [Figure 28] This scatter plot in Example 6 shows an example of the relationship between the measured value of harmonic eddy current iron loss and the value predicted considering the harmonic eddy current loss coefficient. [Figure 29] This is a scatter plot showing an example of the relationship between measured and predicted iron loss values ​​in Example 7. [Modes for carrying out the invention]

[0024] In recent years, power electronics, which efficiently controls power using the switching function of semiconductors, has been developing rapidly. By utilizing power electronics technology, conversion from AC to DC (converters), DC voltage conversion (DC-DC converters), DC to AC conversion (inverters), and AC frequency conversion (matrix converters) can be easily realized with relatively simple circuits. Furthermore, by increasing the frequency of switching, the inductance or capacitance of passive elements required in the circuit is reduced. This reduction in the inductance or capacitance of passive elements makes it possible to miniaturize equipment. Amidst the strong global demand for efficient use of electricity and miniaturization and weight reduction of equipment in order to realize a carbon-neutral society, power electronics technology is being widely applied not only to power equipment, railways, and industrial fields where it has been preferentially applied until now, but also to electrical equipment used in daily life, such as automobiles and home appliances.

[0025] Inverters are a crucial circuit used in power electronics equipment. They not only convert direct current (DC) to alternating current (AC), but also efficiently control AC output. Common examples include the control of electric compressors in inverter air conditioners and induction motors for electric vehicles (EVs), significantly contributing to energy savings. Pulse Width Modulation (PWM), which controls AC output by modulating the pulse width of a constant voltage, is widely used for inverter output control. Generally, induction motors rotate their rotors by applying AC at tens to hundreds of hertz (Hz). On the other hand, PWM inverters generate the AC applied to the induction motor to rotate the rotor from DC. Therefore, in PWM inverters, switching is performed at a frequency several times higher than the frequency of the AC applied to the induction motor. PWM inverters are also called PWM inverters.

[0026] In this embodiment, the PWM inverter operates using a triangular wave comparison method. The triangular wave comparison method PWM inverter outputs a pulse waveform generated by switching DC by comparing the target AC waveform with a triangular wave. The time-averaged waveform of the output pulse waveform approximates the target AC waveform. The target AC waveform is also called the modulated wave. The triangular wave compared with the target AC waveform is also called the carrier wave. In other words, the triangular wave comparison method PWM inverter can convert DC to an AC waveform and output it by switching DC based on the comparison result between the modulated wave and the carrier wave.

[0027] Also, in this embodiment, the PWM inverter further utilizes a pulse waveform generated by comparing the waveform of the opposite phase of the modulation wave with the triangular wave to generate an output pulse waveform. Specifically, the PWM inverter inputs the modulation wave and the carrier wave into a comparator and switches DC based on the output of the comparator to obtain a pulse waveform, and outputs a pulse waveform that is the difference between the pulse waveform obtained by inputting the waveform of the opposite phase of the modulation wave, the carrier wave, and the comparator, and switching DC based on the output of the comparator.

[0028] Referring to FIG. 1, an operating example of a triangular-wave comparison type PWM inverter will be described. The graph shown in FIG. 1 is a graph in which five graphs are arranged on the same time scale. The horizontal axis of each graph represents time (t). The vertical axis of each graph represents the signal intensity.

[0029] The uppermost graph shows the waveform of the carrier wave, as well as the waveform of the modulation wave and the waveform of the opposite phase of the modulation wave. The waveform of the carrier wave is represented as e c Let the frequency of the carrier wave, which is a triangular wave, be represented by f c Let the peak-to-peak value of the waveform of the carrier wave be represented by E c

[0030] The waveform of the modulation wave, which is a sine wave represented by a solid line, is represented as e s1 Also, the waveform of the opposite phase of the modulation wave, which is a sine wave represented by a dashed line, is represented as e s2 Let the peak-to-peak value of the waveforms of the modulation wave and the opposite phase of the modulation wave be represented by E s

[0031] E c The ratio of E s to E s / E c is also referred to as the modulation ratio and is represented by m. In other words, the modulation ratio (m) is the voltage amplitude ratio of the modulation wave to the carrier wave and is calculated as E

[0032] The PWM inverter uses the modulation ratio (m) and the carrier frequency (f​​c By controlling the modulation index (m) and carrier frequency (f), the waveform of the output AC can be controlled. c These are also called PWM parameters. PWM parameters are included in the inverter conditions. In addition to PWM parameters, the inverter conditions also include the parameters of the modulating wave. If the modulating wave is a sine wave, the parameters of the modulating wave are also called the sine wave conditions. In other words, the inverter conditions include both PWM parameters and sine wave conditions.

[0033] The second graph shows the pulse waveform generated based on a comparison between the carrier wave waveform and the modulated wave waveform. The pulse waveform generated based on a comparison between the carrier wave waveform and the modulated wave waveform is P s1 Let it be expressed as P s1 This is represented as a black rectangle in Figure 1.

[0034] Specifically, P s1 The pulse is generated such that it is 1 during the period when the intensity of the modulated wave waveform is greater than or equal to the intensity of the carrier wave waveform, and 0 during the period when the intensity of the modulated wave waveform is less than the intensity of the carrier wave waveform. A pulse of 1 may be replaced with a HI signal. A pulse of 0 may be replaced with a LO signal.

[0035] The third graph shows the pulse waveform generated based on a comparison between the carrier wave waveform and the out-of-phase waveform of the modulated wave. The pulse waveform generated based on a comparison between the carrier wave waveform and the out-of-phase waveform of the modulated wave is P s2 Let it be expressed as P s2 This is represented in Figure 1 as a rectangle with a downward-sloping hatching line.

[0036] Specifically, P s2 This is generated such that it becomes 1 during the period when the intensity of the waveform opposite in phase to the modulated wave is greater than or equal to the intensity of the carrier wave waveform, and 0 during the period when the intensity of the modulated wave waveform is less than the intensity of the carrier wave waveform.

[0037] The graph in the fourth row is P s1From the pulse waveform P s2 This shows the pulse waveform generated by subtracting the pulse waveform of P. s1 From the pulse waveform P s2 The pulse waveform generated by subtracting the pulse waveform of P s Let it be expressed as P s This is represented in Figure 1 as a rectangle with shaded hatching.

[0038] Specifically, P s1 In the pulse waveform, the pulse waveform of the area enclosed by the dashed line, represented by P1, is P s2 In the pulse waveform, by subtracting the pulse waveform of the area enclosed by the dashed line P2, P s In the pulse waveform, the pulse waveform of the area enclosed by the dashed line, represented by P3, is generated. s1 and P s2 If the values ​​are the same, P s The value of P becomes 0. s1 is 1, and P s2 If P is 0, s The value of P becomes 1. s1 If is 0, and P s2 If P is 1, s The value of P becomes -1. s A pulse waveform in which this value becomes 1 is a positive pulse waveform. s A pulse waveform in which P is -1 is a negative pulse waveform. In other words, P s This is a pulse waveform that combines a positive pulse waveform and a negative pulse waveform.

[0039] The graph in the fifth row is P s This shows the time-averaged waveform of the pulse waveform. s The time-averaged waveform of the pulse waveform is also called the output waveform. The output waveform approximates the modulated wave.

[0040] Here, a PWM inverter equipped with a SiC power semiconductor, which outputs the output waveform exemplified in Figure 1, is attached to the excitation power supply of a high-frequency iron loss measuring device. Excitation based on the output waveform of a PWM inverter is also called inverter excitation. The iron loss of the magnetic material to be measured was measured by inverter-exciting the magnetic material to be measured using an excitation waveform based on the output waveform exemplified in Figure 1, using the excitation power supply to which the PWM inverter is attached. In this embodiment, the frequency of the modulated wave is represented by f1 and set to 400Hz to 1kHz. The frequency of the modulated wave (f1) is included in the sinusoidal wave condition. For a modulated wave with a frequency range of 400Hz to 1kHz, the frequency of the carrier wave (f c The frequency response (kHz) was controlled within the range of 5 kHz to 100 kHz. The modulation index (m) was controlled within the range of 0.4 to 1.25.

[0041] As described above, the excitation power supply for the high-frequency iron loss measuring device inverter-excites the magnetic material based on the output waveform of a PWM inverter. The waveform output when the magnetic material is inverter-excited is also called the inverter excitation waveform. The inverter excitation waveform can be considered to be the waveform generated by the PWM inverter. Hereafter, we will assume that the PWM inverter generates the inverter excitation waveform.

[0042] Here, as one embodiment, the PWM inverter has a carrier frequency (f c Let's assume that the inverter excitation waveform is generated based on a carrier wave with a frequency (f1) of 20 kHz and a modulation index (m) of 0.4, and a modulated wave with a frequency (f1) of 1 kHz. The inverter excitation waveform generated in this embodiment is represented as the frequency spectrum exemplified in Figure 2 by performing a Fourier transform. In Figure 2, the horizontal axis corresponds to frequency and is represented as f. The unit of frequency is assumed to be kilohertz (kHz). The vertical axis corresponds to the intensity of each frequency component and is represented as B. The intensity of each frequency component is assumed to be Tesla (T).

[0043] The frequency spectrum of the inverter excitation waveform generated in this embodiment mainly consists of a modulated wave component with frequency f1 and a first harmonic component with frequency f2. In other words, the inverter excitation waveform is a waveform in which harmonics are superimposed on a modulated wave. The intensity of the modulated wave component is denoted by B1. The intensity of the modulated wave component is also called the excitation magnetic flux density. The excitation magnetic flux density (B1) is included in the sinusoidal wave condition. The intensity of the first harmonic component is denoted by B2.

[0044] In the frequency spectrum of Figure 2, the frequency of the first harmonic component (f2) is calculated as the average of the frequency of the strongest component other than the modulated wave component and the frequency of the component having 50% or more intensity than that component. The frequency of the harmonic component included in the frequency spectrum of Figure 2 is 40 kHz. In other words, the frequency of the first harmonic component is the carrier frequency (f2). c It is twice the amount of ).

[0045] Harmonics include not only first-order components but also second-order and higher-order components. However, the second-order and higher-order harmonic components are negligibly small compared to the first-order harmonic components. Therefore, in this embodiment, only the first-order harmonic components are considered. In the following description, the first-order harmonic component will be simply referred to as the harmonic component.

[0046] Generally, data on the magnetic properties of core materials under sinusoidal excitation is publicly available, and motors are designed based on this data. However, as mentioned above, the inverter excitation waveform using a PWM inverter is not a smooth sinusoid, but includes harmonics resulting from the switching operation of semiconductors. Therefore, the iron loss generated in the magnetic core under inverter excitation is the sum of the iron loss due to the sinusoidal component and the iron loss due to the harmonic component. As a result, in inverter-driven motors using inverter excitation, the amount of heat generated is greater than assumed during the design phase due to the iron loss due to the harmonic component. This increase in heat generation may necessitate cooling measures that were not anticipated during the design phase. If iron loss due to harmonics is taken into account and designed with a margin of safety, the size of equipment using inverter-driven motors will increase. Given the strong demand for miniaturization and increased efficiency of equipment, it is necessary to accurately estimate inverter iron loss and design equipment accordingly.

[0047] When designing a motor and selecting a core material that suits the motor's driving conditions, the iron loss under frequently used excitation conditions is often used as an evaluation index, rather than the iron loss under high magnetic flux density excitation conditions corresponding to the motor's maximum output. The iron loss under frequently used excitation conditions is, for example, W, which represents the iron loss when the excitation magnetic flux density (B1) is 1.0T and the frequency (f1) is 400Hz. 10 / 400 That's fine. However, W 10 / 400 The iron loss data that is generally disclosed, as shown above, is obtained using sinusoidal excitation, not inverter excitation. Therefore, in the design of inverter-driven motors, it is necessary to consider the increase in iron loss caused by harmonics.

[0048] If we were to connect a motor to an inverter circuit that would actually be used and measure the iron loss or heat generation of the magnetic core, we could directly evaluate the iron loss caused by inverter excitation. However, directly evaluating iron loss would require a great deal of cost and manpower. In motor design, it is impractical to repeatedly prototype motors from the stage of selecting the magnetic core material in order to directly evaluate iron loss.

[0049] Alternatively, the iron loss of a test specimen can be evaluated using an excitation power supply that simulates a PWM inverter. Furthermore, the iron loss in inverter excitation can be evaluated by integrating the inverter excitation waveform synthesized based on the PWM parameters. However, this is difficult to implement due to the need for specialized evaluation equipment and the complexity of the analysis methods.

[0050] Therefore, a simple method for evaluating iron loss in inverter excitation is required.

[0051] Here, the PWM inverter can control its output by keeping the pulse voltage height constant and varying the modulation index (m) from 0 to 1. Furthermore, the PWM inverter controls the carrier frequency (f c The output can be controlled by changing the ). When evaluating iron loss, a specific inverter excitation waveform is applied to the magnetic material. Specifically, the excitation conditions for evaluating iron loss are set to the frequency (f1) of the modulated wave of the inverter excitation waveform applied to the magnetic material and the excitation magnetic flux density (B1).

[0052] For the frequency (f1) and excitation flux density (B1) of the modulated wave of the inverter excitation waveform, the modulation rate (m) and carrier frequency (f c These are set independently. In other words, the excitation flux density (B1) and modulation index (m) of the inverter excitation waveform, which are the excitation conditions for evaluating iron loss, do not have a one-to-one correspondence. The modulation index (m) may be set to a smaller or larger value relative to the excitation flux density (B1). The value of the modulation index (m) is set based on the output fluctuation range of the motor or the design concept of the circuit for which iron loss is being evaluated.

[0053] When the modulation index (m) is set to a large value (close to 1) relative to the excitation flux density (B1) of the inverter excitation waveform, inverter iron loss tends to decrease. However, when the excitation flux density (B1) is set to a high flux density range, an overmodulation state occurs where the modulation index (m) exceeds 1, causing power control to become unstable. Conversely, when the modulation index (m) is set to a small value (close to 0), power control stabilizes when the excitation flux density (B1) is set to a high flux density range, but inverter iron loss increases.

[0054] Carrier frequency (f c When the frequency is set to a high frequency, the intensity of the harmonic component (B2) of the inverter excitation waveform decreases, suppressing the increase in iron loss caused by harmonics. However, the heat generated by the switching element increases, and the overall loss of the circuit also increases.

[0055] As described above, a PWM inverter uses either the modulation rate (m) or the carrier frequency (f) as the excitation condition for which iron loss is evaluated. c This can be achieved by various combinations of values ​​where the values ​​of ) are different. Iron loss that occurs in inverter excitation is due to the modulation rate (m) and carrier frequency (f c This includes iron loss caused by harmonics, which are determined according to the following. Therefore, even if the excitation conditions are the same, the modulation rate (m) and carrier frequency (f) set by the PWM inverter to achieve those excitation conditions will be different. c It is necessary to evaluate the iron loss taking this into consideration.

[0056] Therefore, the iron loss evaluation method according to this disclosure is based on the modulation frequency (f1) and excitation magnetic flux density (B1) of the modulated wave, which are the excitation conditions for which iron loss is to be evaluated, and the modulation rate (m) and carrier frequency (f c Based on the value of ), the iron loss caused by inverter excitation can be predicted with high accuracy and in a simple manner. Furthermore, the low iron loss material design method according to this disclosure can design the characteristics of a low iron loss material based on the iron loss prediction result and provide a low iron loss material.

[0057] (Method for evaluating iron loss related to this disclosure) The iron loss evaluation method described herein predicts iron loss without measuring the excitation waveform when a magnetic material is excited by an inverter, using the modulation rate (m) and carrier frequency (f), which are control parameters of a PWM inverter. c A prediction formula is used that can calculate the predicted value of iron loss based on the value of ).

[0058] Modulation rate (m) and carrier frequency (f) c A prediction formula for predicting iron loss based on the value of ) is constructed using the following procedure.

[0059] First, by performing a Fourier analysis on the excitation waveform synthesized under multiple excitation conditions for inverter excitation using a PWM inverter, the magnetic flux density (B2) and frequency (f2) of the first harmonic, which contribute significantly to iron loss, can be identified. In this case, it is desirable to analyze the excitation waveform synthesized under three or more excitation conditions. Furthermore, the excitation conditions include the modulation index (m) and carrier frequency (f2). c It is assumed that it will be identified by ).

[0060] Next, the relationship between the magnetic flux density (B2) and frequency (f2) of the first harmonic, which contribute significantly to iron loss, and the excitation conditions is substituted into Steinmetz's empirical formula and rearranged to generate a predictive formula for iron loss.

[0061] The iron loss prediction formula generated by the above procedure, as described in this disclosure, can directly calculate the predicted value of inverter iron loss from the excitation conditions of inverter excitation using a PWM inverter, without omitting the analysis of the excitation waveform.

[0062] As a comparative example, one might consider performing extremely complex calculations for analyzing the excitation waveform or measuring harmonic components for each excitation condition in order to predict iron loss. The iron loss prediction method in the comparative example includes the procedure shown in Figure 3.

[0063] First, PWM parameters are set as inverter conditions for the PWM inverter (step S1). A sinusoidal wave condition may also be set as an inverter condition. The magnetic material is inverter-excited by the waveform output by the PWM inverter with the set PWM parameters (step S2). The excitation waveform applied to the magnetic material is measured (step S3). The waveform data of the measured excitation waveform is integrated (step S4). Based on the result of integrating the excitation waveform, the iron loss when the magnetic material is inverter-excited with the set PWM parameters is predicted (step S5).

[0064] As described above, the method relating to the comparative example requires measurement of the excitation waveform and integration of the waveform data. In contrast, the iron loss evaluation method relating to this disclosure can be performed using only the procedure shown in Figure 4.

[0065] First, the PWM parameters are set as the inverter conditions for the PWM inverter (step S11). A sinusoidal wave condition may also be set as an inverter condition. The set PWM parameters are input into a pre-prepared prediction formula (step S12). Based on the calculation results of the prediction formula, the iron loss when the magnetic material is inverter-excited with the set PWM parameters is predicted (step S13).

[0066] As described above, the prediction formula relating to this disclosure can predict iron loss with high accuracy and in a simple manner without analyzing the excitation waveform.

[0067] Furthermore, the iron loss prediction formula relating to this disclosure can be extended to a prediction formula that reflects the properties of the raw materials constituting the magnetic material, as will be described later. By reflecting the properties of the raw materials in the prediction formula, guidelines for designing magnetic materials suitable for inverter excitation, which reduce the iron loss that occurs when the magnetic material is inverter-excited, can be obtained from the prediction formula.

[0068] <Example of hardware configuration for implementing an iron loss evaluation method> The iron loss evaluation method relating to this disclosure may be implemented by the information processing system 1 illustrated in Figure 5. The information processing system 1 comprises an information processing device 10, an excitation device 20, and a measuring device 30.

[0069] The excitation device 20 comprises a PWM inverter and an excitation power supply. The PWM inverter may be implemented using various circuits, such as a single-phase full-bridge circuit or a single-phase half-bridge circuit. The excitation power supply is configured to generate magnetic flux based on the output waveform from the PWM inverter and apply the magnetic flux to the magnetic material. The excitation power supply may be configured, for example, to supply current to the excitation coil according to the output waveform from the PWM inverter.

[0070] The measuring device 30 is configured to measure the magnetic flux density when a magnetic material is excited by an inverter. The measuring device 30 may be equipped with various magnetic sensors such as fluxgates or Hall elements.

[0071] The information processing device 10 comprises a processor 12, a storage unit 14, and an interface 16.

[0072] The processor 12 may include, for example, a CPU (Central Processing Unit) or a GPU (Graphics Processing Unit) to control and manage various functions of the information processing device 10. The processor 12 may realize the functions of the information processing device 10 by reading and executing programs stored in the memory unit 14.

[0073] The storage unit 14 stores various information or data used by the information processing device 10. The storage unit 14 may store, for example, a program executed by the processor 12, or data or processing results used in processing executed by the processor 12. The storage unit 14 may function as the work memory of the processor 12. The storage unit 14 may include, but is not limited to, semiconductor memory. The storage unit 14 may be configured as, for example, the internal memory of the processor 12, or as an electromagnetic recording medium such as a hard disk drive (HDD) accessible from the processor 12. The storage unit 14 may be configured as a non-temporary readable medium. The storage unit 14 may be configured integrally with the processor 12, or as a separate unit from the processor 12.

[0074] Interface 16 may include a communication interface for communicating with other devices, such as the excitation device 20 or the measuring device 30, by wire or wireless connection. The communication interface may be configured to communicate with other devices via a network. Interface 16 may include input / output ports for inputting and outputting data to and from other devices. Interface 16 may communicate based on wired communication standards or based on wireless communication standards. For example, wireless communication standards may include cellular phone communication standards such as 3G, 4G, and 5G. Also, for example, wireless communication standards may include IEEE 802.11 and Bluetooth®. Interface 16 may support one or more of these communication standards. Interface 16 may communicate with other devices and input / output data based on various standards, but is not limited to these examples.

[0075] Interface 16 may be configured to output information acquired from processor 12. Interface 16 may notify the user of information by outputting visual information such as characters, figures, or images, either directly or via external devices. Interface 16 may include a display device, or may be connected to a display device by wire or wireless. The display device may include various displays such as liquid crystal displays. Interface 16 may notify the user of information by outputting auditory information such as sound, either directly or via external devices. Interface 16 may include an audio output device such as a speaker, or may be connected to an audio output device by wire or wireless. Interface 16 may notify the user of information not only by outputting visual or auditory information, but also by outputting information that the user can perceive, either directly or via external devices.

[0076] Interface 16 may include an input device that accepts input from the user. The input device may include, for example, a keyboard or physical keys, or a pointing device such as a touch panel or touch sensor or mouse. The input device is not limited to these examples and may include various other devices.

[0077] The processor 12 of the information processing device 10 may execute an iron loss evaluation method. The iron loss evaluation method may be implemented as an iron loss evaluation program. The processor 12 may notify the user of the predicted iron loss calculated by executing the iron loss evaluation method via the interface 16, output it to an external device, or store it in the storage unit 14.

[0078] <Example of constructing a prediction formula for iron loss> The following provides a detailed explanation of how to construct a prediction formula.

[0079] First, a magnetic material was prepared as the magnetic core to be evaluated for iron loss, which was obtained by heat-treating a compacted powder. The compacted powder was formed by applying a pressure of 980 MPa to iron powder and shaping it into a ring.

[0080] The magnetic material was excited by applying, for example, the output waveform of the PWM inverter shown in Figure 1 as the inverter excitation waveform. The inverter excitation waveform is a waveform in which harmonics caused by semiconductor switching are superimposed on the modulated wave. The fact that the inverter excitation waveform is a waveform in which harmonics are superimposed on the modulated wave can be confirmed, for example, by the fact that the frequency component of the modulated wave (f1) and the frequency component of the harmonics (f2) are large in the frequency spectrum graph shown in Figure 2.

[0081] <<Relationship between harmonic frequency (f2) and inverter conditions>> As mentioned above, the frequency (f2) of the harmonic component appearing in the frequency spectrum of Figure 2 is 40 kHz. In other words, the harmonic frequency (f2) is equal to the carrier frequency (f c This is twice the carrier frequency (f). This relationship is illustrated in Figure 6, c The harmonic frequency (f2) and carrier frequency (f) when a magnetic material is excited by controlling a PWM inverter with multiple PWM parameters that have different values. c This is confirmed by the relationship with (). In the graph in Figure 6, the horizontal axis is the carrier frequency (f c The vertical axis represents the frequency of the harmonic (f2).

[0082] The harmonic frequency (f2) is, as mentioned above, the carrier frequency (f c It depends on the modulation index (m), but not on the modulation index (m). This is confirmed by the relationship between the harmonic frequency (f2) and the modulation index (m) when a magnetic material is excited by controlling a PWM inverter with multiple PWM parameters that have different modulation indexes (m), as illustrated in Figure 7. In the graph in Figure 7, the horizontal axis represents the modulation index (m), and the vertical axis represents the harmonic frequency (f2). The points plotted on the graph confirm that the harmonic frequency (f2) does not change regardless of the change in modulation index (m).

[0083] Furthermore, the harmonic frequency (f2) does not depend on the modulating wave frequency (f1). This is confirmed by the relationship between the harmonic frequency (f2) and the modulating wave frequency (f1) when a magnetic material is excited with excitation waveforms that have different modulating wave frequencies (f1), as illustrated in Figure 8. In the graph in Figure 8, the horizontal axis represents the modulating wave frequency (f1), and the vertical axis represents the harmonic frequency (f2). The points plotted on the graph confirm that the harmonic frequency (f2) does not change regardless of the change in the modulating wave frequency (f1).

[0084] Based on the relationships described above, the harmonic frequency (f2) is equal to the carrier frequency (f c It is expressed by the following equation (1), which depends on ) and does not depend on the modulation rate (m) and the frequency of the modulated wave (f1).

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[0086] However, the proportionality constant used in equation (1) may differ depending on the type of PWM inverter. By generalizing the proportionality constant, the harmonic frequency (f2) can be expressed by the following equation (2).

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[0088] The proportionality constant (u) used in equation (2) is set to 2 when the PWM inverter is a single-phase full-bridge circuit, and to 1 when the PWM inverter is a single-phase half-bridge circuit. The proportionality constant is the ratio of the harmonic frequencies of the excitation waveform to the carrier frequency. The proportionality constant may be set by directly checking the PWM inverter configuration. Alternatively, the proportionality constant may be determined by performing a Fourier analysis on waveform data obtained by measuring the excitation waveform once or more times when a magnetic material is inverter-excited by a PWM inverter, without directly checking the PWM inverter configuration. In other words, the proportionality constant may be determined based on waveform data measured from the excitation waveform generated by the PWM inverter.

[0089] As described above, the harmonic frequency (f2) is the carrier frequency (f) among the inverter conditions. c It can be seen that this is determined by ).

[0090] <<Relationship between harmonic magnetic flux density (B2) and inverter conditions>> As shown in Figure 9, the harmonic magnetic flux density (B2) is equal to the carrier frequency (f c It is proportional to the reciprocal of the carrier frequency (f). In other words, the harmonic magnetic flux density (B2) is proportional to the carrier frequency (f). c ) is inversely proportional to the carrier frequency (f). In the graph in Figure 9, the horizontal axis is the carrier frequency (f c The vertical axis represents the harmonic magnetic flux density (B2).

[0091] As shown in Figure 10, the harmonic magnetic flux density (B2) changes along an exponential function with respect to the modulation index (m). The exponential value was in the range of -1.64 to -1.65. In the graph of Figure 10, the horizontal axis represents the modulation index (m), and the vertical axis represents the harmonic magnetic flux density (B2).

[0092] As shown in Figure 11, the harmonic magnetic flux density (B2) is proportional to the frequency (f1) of the modulated wave. In the graph in Figure 11, the horizontal axis represents the frequency (f1) of the modulated wave, and the vertical axis represents the harmonic magnetic flux density (B2).

[0093] Based on the relationships described above, the magnetic flux density of the harmonics (B2) is equal to the carrier frequency (f c It is expressed by the following equation (3), using the modulation index (m) and the frequency of the modulated wave (f1). The γ1 used in equation (3) is the proportionality constant.

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[0095] Here, the excitation power supply excites the magnetic material by applying a voltage to the excitation coil. The maximum voltage applied by the excitation power supply is also called the maximum excitation voltage and is represented by V. The relationship V∝B1×f1 holds between the maximum excitation voltage (V), the frequency of the modulated wave (f1), and the excitation magnetic flux density (B1). Also, the carrier frequency (f) is set so that the maximum excitation voltage (V) remains constant. c Assuming that ) changes, V∝B²×f c The following relationship holds: V∝B1×f1∝B2×f c It is assumed that the following relationship holds. Under this assumption, the following equation (4) holds.

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[0097] Furthermore, by applying equation (4) to equation (3), it is assumed that the following equation (5) holds. The γ used in equation (5) is the proportionality constant.

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[0099] The γ included in equation (5) was determined by performing a regression analysis using equation (5) on the relationship between the harmonic magnetic flux density (B2) obtained by Fourier analysis of the excitation waveform when a magnetic material was inverter-excited under various inverter conditions. Then, the harmonic magnetic flux density (B2) was predicted using equation (5) with the determined γ. The predicted value of the harmonic magnetic flux density (B2) is denoted as [B2] in square brackets. Figure 12 shows an example of the relationship between the measured value and the predicted value of the harmonic magnetic flux density (B2). In the graph of Figure 12, the horizontal axis represents the measured value of the harmonic magnetic flux density (B2). The vertical axis represents the predicted value of the harmonic magnetic flux density ([B2]). It can be seen that the measured value of the harmonic magnetic flux density is proportional to the predicted value.

[0100] <<Calculation of iron loss considering harmonics>> The iron loss that occurs when a magnetic material is excited by an inverter is expressed based on Steinmetz's empirical formula, which is shown as equation (6) below.

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[0102] In equation (6), α and β are constants determined when the magnetic material is excited with a sinusoidal excitation waveform rather than inverter excitation. In other words, equation (6) does not consider harmonics in inverter excitation and represents the iron loss in sinusoidal excitation. The first term of equation (6) corresponds to hysteresis loss, W 1.h It is expressed as follows. The second term corresponds to the eddy current loss, W 1.e It is represented as follows.

[0103] Hysteresis loss (W 1.h ) is as shown in Figure 13, f1·B1 1.6 It has been confirmed by measurements using a DC magnetization measuring device that the constant α is proportional to [the specified value]. Therefore, the constant α may be determined based on the measurement results illustrated in Figure 13.

[0104] Eddy current loss (W) 1.e The constant β of ) is as shown in Figure 14, f12 B1 2 And, W1-α·f1·B1 1.6 The relationship can be determined by performing a regression analysis.

[0105] Iron loss considering inverter excitation is W inv It is expressed as (W) and is also called inverter iron loss. Inverter iron loss (W inv ) is the harmonic iron loss (W1) of sinusoidal excitation, which takes into account the effect of harmonics in inverter excitation. har It can be expressed by the following equation (7) with the addition of ).

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[0107] Harmonic iron loss (W har The harmonics that cause this are considered to be sine waves with a frequency different from that of the modulating wave. When harmonics are considered to be sine waves, the harmonic iron loss (W) har It is assumed that the harmonic iron loss (W1) can be separated into hysteresis loss and eddy current loss, similar to the iron loss (W1) in sinusoidal excitation. Under this assumption, the harmonic iron loss (W1) har ) is expressed by the following equation (8).

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[0109] Inverter iron loss (W inv ) is the frequency of the modulated wave (f1), the excitation magnetic flux density (B1), and the carrier frequency (f c It is calculated based on various inverter conditions that combine (w) and modulation rate (m). Inverter iron loss (W) inv ) can be expressed as the following equation (9) by substituting equations (1), (5), (6), and (8) into equation (7) above.

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[0111] In Equation (9), p h = 2 × γ 1.6 × m -2.62 × (f1 / f c ) 0.6 , and p e = 4 × γ 2 × m -3.28 holds. The component of the harmonic iron loss due to hysteresis loss is represented by p h . Also, the component of the harmonic iron loss due to eddy current loss is represented by p e .

[0112] Predicting the inverter iron loss (W inv ) based on the modulation ratio and the carrier frequency corresponds to calculating the inverter iron loss (W inv ) using the above-mentioned Equation (9). The inverter iron loss (W inv ) is the iron loss that occurs when a magnetic material is excited by an excitation waveform generated by a PWM inverter controlled under inverter conditions including the modulation ratio (m) and the carrier frequency (f c ).

[0113] <<Parentheses>> As described above, by calculating the inverter iron loss (W inv ) using Equation (9), the iron loss is predicted considering the harmonic iron loss caused by harmonics in the inverter excitation. In Equation (9), the constants α, β, and γ are determined in advance. Therefore, by substituting the carrier frequency (f c ), the modulation ratio (m), and the frequency of the modulation wave (f1) as variables into Equation (9), the predicted value of the inverter iron loss (W inv ) is calculated. In other words, without substituting the value based on the measured data of the excitation waveform into Equation (9), by substituting only the inverter conditions, the inverter iron loss (W inv ) is predicted. As a result, the iron loss generated in the inverter excitation is predicted with high accuracy and simply without analyzing the excitation waveform.

[0114] (Low-loss material design method related to this disclosure) Based on the iron loss evaluation method described above, equation (9) was constructed as a prediction formula that can predict iron loss in inverter excitation using only the inverter conditions. The constants α and β included in the iron loss prediction formula change depending on the properties of the magnetic material being excited. Therefore, by identifying the relationship between the constants and the properties of the magnetic material, information that serves as a guideline for designing the properties of the magnetic material to minimize the predicted iron loss can be obtained using the predicted iron loss. Below, a material optimization method based on the prediction of iron loss using equation (9) will be explained. Material optimization includes not only determining the properties of the material to a single optimal property, but also determining the acceptable range for the optimal property. The material optimization method is also called a low-loss material design method.

[0115] When the magnetic material is a compacted magnetic core, the relationship between α and the median diameter of the iron powder that is the raw material for the compacted magnetic core is expressed by the following equation (10).

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[0117] The median diameter is the volume-based median of the particle size of iron powder. That is, the median diameter is the particle size at which, when iron powder is divided into two parts from a certain particle size, the total volume of the larger particle side is equal to the total volume of the smaller particle side. The particle size of iron powder is the diameter of the longest part of the iron powder. The median diameter is D 50 It is expressed as follows. C1 and C2 are constants. Figure 15 shows the value of α defined for a powdered magnetic core using pure iron powder, and the median diameter (D) of the pure iron powder. 50 A graph showing the relationship between C1 and ) using simple linear regression is shown. From this graph, C1 is 1.19 × 10 -6 It is set to 0.0603, and C2 is set to 0.0603.

[0118] Furthermore, when the magnetic material is a compacted magnetic core, the relationship between β and the median diameter of the iron powder that is the raw material for the compacted magnetic core is expressed by the following equation (11).

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[0120] In equation (11), n ​​is set to a value between 1 and 2. C3 is a constant. Figure 16 shows the value of β set for a powdered magnetic core using pure iron powder, and the median diameter (D) of the pure iron powder. 50 A graph showing the relationship with ) using simple linear regression is presented. From this graph, C3 is determined to be 7.65 and n is determined to be 1.46.

[0121] Figure 17 shows the value of γ, a constant included in the iron loss prediction formula, for a compacted magnetic core using pure iron powder, and the median diameter (D) of the pure iron powder. 50 A graph showing the relationship between γ and the median diameter (D) is shown. From this graph, the value of γ is shown as the median diameter (D). 50 It was found to be almost constant regardless of the value, and the average value was set at 0.093.

[0122] As described above, α and β, which are included as constants in equation (9), can be replaced with mathematical formulas that represent the properties of the magnetic material. By replacing α and β in equation (9) with equations (10) and (11), the inverter conditions and the median diameter (D) of the raw material powder can be determined. 50 The following equation (12) is derived as a prediction formula for inverter iron loss with ) as the variable.

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[0124] In the examples described above, the median diameter (D) of the particles constituting the compacted magnetic core 50 α and β were formulated by ). The values ​​representing the properties of a magnetic material may depend on the grain size, even when the magnetic material is a compacted magnetic core. Also, the values ​​representing the properties of a magnetic material may depend on the thickness of the laminated steel plates when the magnetic material is a laminated magnetic core. Therefore, the values ​​representing the properties of a magnetic material are determined by the median diameter (D 50It is not limited to ). Therefore, by expressing the properties of the magnetic material in terms of a representative dimension (D), equation (13), which is a generalization of equation (12), is derived.

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[0126] By using equation (13), guidelines can be obtained for designing the magnetic material used as the core to optimize its properties according to the inverter conditions of inverter excitation. The optimization of the magnetic material properties may be carried out by calculating values ​​that represent the material properties so that the predicted value of iron loss is minimized or reduced, as will be described later as an example.

[0127] In other words, the iron loss that occurs when at least two types of magnetic materials having different characteristics are excited with an excitation waveform generated by controlling a PWM inverter at a predetermined modulation rate and predetermined carrier frequency may be predicted by performing the iron loss evaluation method described above. Based on the predicted value of iron loss, the characteristics of the magnetic material under design may be designed such that the iron loss that occurs when the magnetic material under design is excited with an excitation waveform generated by controlling a PWM inverter at a predetermined modulation rate and predetermined carrier frequency is reduced. In addition, representative dimensions of the magnetic material under design may be designed as characteristics of the magnetic material under design. If the magnetic material under design is a steel plate, the representative dimensions may be the thickness of the steel plate, etc. If the magnetic material under design is a compacted magnetic core, the representative dimensions may be the grain size of the compacted magnetic core, etc.

[0128] Furthermore, if the magnetic material is a compacted magnetic core composed of soft magnetic powder, the iron loss generated when the compacted magnetic core is excited with a sinusoidal excitation waveform may be obtained for each representative size of the soft magnetic powder. Based on the iron loss for each representative size, the representative size of the soft magnetic powder may be designed as a characteristic of the magnetic material. Similarly, if the magnetic material is a steel plate, the iron loss generated when the steel plate is excited with a sinusoidal excitation waveform may be obtained for each representative size of the steel plate. Based on the iron loss for each representative size, the representative size of the steel plate may be designed as a characteristic of the magnetic material.

[0129] The processor 12 of the information processing device 10 may execute a low-loss material design method. The low-loss material design method may be implemented as a low-loss material design program. The processor 12 may notify the user of the material properties determined by executing the low-loss material design method via the interface 16, output it to an external device, or store it in the storage unit 14.

[0130] A low-loss soft magnetic material or low-loss soft magnetic powder may be manufactured as a magnetic material having the properties designed by implementing the low-loss material design method described above.

[0131] (Examples) Examples are described below.

[0132] <Example 1> A test compacted core with an outer diameter of 38 mm, an inner diameter of 25 mm, and a height of 6 mm was fabricated by pressurizing insulating coated pure iron powder, which has an average particle size of 96.8 μm, at 980 MPa. The iron loss of the test compacted core was measured using an inverter iron loss measuring device at arbitrary PWM parameters, and the iron loss was calculated based on the iron loss prediction formula (9) by performing the iron loss evaluation method according to this disclosure.

[0133] Figure 18 shows an example of a scatter plot illustrating the relationship between the measured iron loss and the value calculated based on prediction formula (9). In the graph of Figure 18, the horizontal axis represents the measured iron loss (W invThe vertical axis represents the value calculated based on the iron loss prediction formula (9) ([W inv ]) represents.

[0134] The value calculated based on the iron loss prediction formula (9) is the predicted value of iron loss ([W inv Corresponds to the measured value of iron loss (W). inv ) and predicted value ([W inv It was found that there is a roughly proportional relationship between the measured value of iron loss (W). inv ) and predicted value ([W inv This matches well.

[0135] <Example 2> Compacted magnetic cores were prepared using material powders of various median diameters. Each compacted magnetic core using material powder of a median diameter was subjected to a magnetic excitation flux density (B1) of 1.0T, a modulated wave frequency (f1) of 1kHz, and a carrier frequency (f c The predicted value of the iron loss when the inverter is excited under inverter conditions where the frequency (m) is 20 kHz and the modulation index (m) is 0.4 was calculated using the inverter iron loss prediction formula (9).

[0136] Figure 19 shows the relationship between median diameter and predicted iron loss. In the graph in Figure 19, the horizontal axis represents the median diameter (D 50 The vertical axis represents the predicted value of iron loss ([W inv This represents [W]). In the graph of Figure 19, there exists a median diameter that minimizes the predicted value of iron loss. The minimum value of the predicted value of iron loss is [W inv ] min It is represented as follows.

[0137] Here, we assume that the predicted value of iron loss is allowed to increase by up to approximately 3% from its minimum value. The value that is 3% higher than the minimum predicted value of iron loss is plotted on the vertical axis as [W inv ] min It is expressed as ×1.03. The range of median diameter required to keep the predicted value of iron loss within the acceptable range is the range of median diameter when the predicted value of iron loss increases by no more than 3% from its minimum value, D 50_rThis is represented by [formula]. In Figure 19, it can be seen that the acceptable median diameter range is 46 μm to 113 μm. This median diameter range can be used as a guideline for material design when forming a compacted magnetic core.

[0138] <Example 3> Compacted magnetic cores were prepared using material powders of various median diameters. Each compacted magnetic core using material powder of a median diameter was subjected to a magnetic excitation flux density (B1) of 1.0T, a modulated wave frequency (f1) of 1kHz, and a carrier frequency (f c The predicted iron loss when the inverter is excited under inverter conditions where the modulation index (m) is 20 kHz and the modulation rate (m) is 0.4 or 0.6 was calculated using the inverter iron loss prediction formula (9). Predicted iron loss values ​​were calculated for both the case where the modulation rate (m) is 0.4 and the case where the modulation rate (m) is 0.6. In addition, the predicted iron loss when sine wave excitation is used instead of inverter excitation was calculated using the iron loss prediction formula (6), which does not include harmonic iron loss.

[0139] Figure 20 shows the relationship between median diameter and predicted iron loss. In the graph in Figure 20, the horizontal axis is median diameter (D 50 The graph shows the predicted value of iron loss. The vertical axis represents the predicted value of iron loss. The dashed line graph shows the predicted value of iron loss when sinusoidal excitation is performed. The solid line graph shows the predicted value of iron loss when inverter excitation is performed with a modulation rate (m) of 0.4. The dashed line graph shows the predicted value of iron loss when inverter excitation is performed with a modulation rate (m) of 0.6.

[0140] The minimum predicted value of iron loss when sinusoidal excitation is IL on the vertical axis. min_sin It is expressed as follows: The minimum predicted value of iron loss when the inverter is excited with a modulation rate (m) of 0.4 is IL on the vertical axis. min_m0.4 It is expressed as follows: The minimum predicted value of iron loss when the inverter is excited with a modulation rate (m) of 0.6 is IL on the vertical axis. min_m0.6 It is represented by the median diameter (D) from which the minimum value of each predicted value is obtained. 50It can be seen that the median diameter changes. This change in median diameter can be used as a guideline for material design for forming the compacted magnetic core.

[0141] <Example 4> The same test compacted core as in Example 1 was used, with an excitation magnetic flux density (B1) of 0.5T, a modulated wave frequency (f1) of 400Hz, and a carrier frequency (f c The measured and predicted values ​​of inverter iron loss were obtained when the inverter was excited under inverter conditions where the frequency (W) was 20 kHz and the modulation index (m) was 0.4. Figure 21 shows a scatter plot of Figure 18, illustrated in Example 1, with solid triangles added to represent the relationship between the measured and predicted values ​​of inverter iron loss obtained under the above conditions. Measured value of iron loss (W) inv ) and predicted value ([W inv The fact that the added point lies on the line representing the proportional relationship between ]) indicates that the predicted value of inverter iron loss agrees well with the measured value even when the excitation magnetic flux density (B1) is other than 1.0T.

[0142] (Prediction formula for inverter iron loss considering the cross-sectional area of ​​the magnetic core) The prediction formula described above is designed to predict inverter iron loss under different excitation conditions, assuming that the shape or magnetic properties of the magnetic core remain unchanged. Here, the iron loss that occurs when inverter excitation is performed on a compacted magnetic core may be affected by the cross-sectional area of ​​the magnetic core. The cross-sectional area of ​​the magnetic core is the area of ​​the cross section that intersects the magnetic flux that excites the magnetic core. The cross-sectional area of ​​the magnetic core may also be the area of ​​the cross section perpendicular to the magnetic path passing through the magnetic core. Below, based on experimental results confirming the relationship between the iron loss that occurs in the magnetic core when inverter excitation is performed and the cross-sectional area of ​​the magnetic core, it will be explained how to extend the inverter iron loss prediction formula to a form that takes the cross-sectional area of ​​the magnetic core into consideration.

[0143] As a sample of a magnetic core to be evaluated for the iron loss that occurs when inverter excitation is performed, a magnetic material obtained by heat-treating a compacted powder was prepared. The compacted powder is composed of multiple iron powders 100, as illustrated in Figure 22. Furthermore, by applying a pressure of 980 MPa to the compacted powder, a ring-shaped compacted magnetic core 200, as illustrated in Figure 23, was formed. The shape of the cross-sections 210 intersecting in the circumferential direction of the compacted magnetic core 200 illustrated in Figure 23 is rectangular. The shape of the cross-sections 210 is not limited to a rectangle and may be various other shapes.

[0144] As illustrated in Figure 22, the eddy currents flowing through the compacted magnetic core 200 include intragranular eddy currents I1 flowing through individual iron particles 100 and intergranular eddy currents I2 flowing between the iron particles 100. The loss due to intergranular eddy currents I2 is significantly larger than the loss due to intragranular eddy currents I1. Therefore, the iron loss due to eddy currents flowing through the compacted magnetic core 200 depends on the area of ​​the cross-section 210 of the compacted magnetic core 200, i.e., the magnetic core cross-sectional area. Let the magnetic core cross-sectional area be represented by S. As samples with a changed magnetic core cross-sectional area S, several compacted magnetic cores 200 with different heights H of the cross-section 210 were created.

[0145] Harmonic eddy current loss W har.e When the second term on the right-hand side of equation (9) above is expanded, the element p due to eddy current loss is obtained. e Using terms containing , it can be expressed by the following equation (14). In equation (14), p e =4γ 2 ·m -3.28 And, γ = 0.093 holds true.

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[0147] Eddy current loss W of sinusoidal powder core 1.e This is the intragranular eddy current loss W 1.e_intra And, interparticle eddy current loss W 1.e_inter The sum of these is calculated using the following formula (15).

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[0149] Intragranular eddy current loss W of a sinusoidal wave 1.e_intra This is calculated using the following formula (16). Here, D 50 ρ is the median diameter of 100 units of iron powder, C4 is a constant, and ρ intra D is the resistivity within the particle. p This is the magnetic core density.

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[0151] Sinusoidal interparticle eddy current loss W 1.e_inter This is calculated by the following equation (17). Here, C5 is a constant, and ρ inter This is the resistivity of the entire magnetic core.

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[0153] Here, the median diameter D of iron powder 100 50 Assume that the square of is proportional to the cross-sectional area of ​​iron powder 100. Equations (15), (16), and (17) above are given by W, which is included in equation (6) above. 1.e =β(f1·B1) 2 By applying this relationship and rearranging, the eddy current loss coefficient β can be derived as shown in equation (18) below.

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[0155] To investigate the possibility that the interparticle eddy current loss changes with the change in cross-sectional area, D in equation (18) 50 and, ρ intra and, ρ interAssuming that and are constant, the eddy current loss coefficient β can be expressed as a linear function of S as shown in equation (19) below.

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[0157] Here, in order to determine the relationship between the cross-sectional area S of the powder core and the eddy current loss coefficient β, the eddy current loss was measured in powder cores fabricated at four different heights. The powder cores used to measure the eddy current loss were four types of test powder cores formed by pressurizing a powder compact made of insulating coated pure iron powder with a median diameter of 87.7 μm at 980 MPa. The outer diameter of the four test powder cores was a common 38 mm, and the inner diameter was a common 25 mm. The heights of the four test powder cores were 4 mm, 6 mm, 10 mm, and 18 mm, respectively. The cross-sectional area of ​​the four test powder cores was 25 mm². 2 , 38mm 2 , 64mm 2 , and 116mm 2 That is the case.

[0158] The eddy current loss coefficient β is calculated from the measured eddy current loss when sinusoidal excitation is performed on a powder core. Figure 24 shows a scatter plot illustrating an example of the relationship between the value of β calculated from the measured eddy current loss when sinusoidal excitation is performed on powder cores manufactured with four different heights, and the cross-sectional area S of the powder core. By performing a simple linear regression analysis on the four points plotted in the scatter plot, the coefficients when approximating the relationship with the cross-sectional area S of the powder core using equation (19) are found to be a = 0.325 and b = 7.25 × 10⁻⁶. -6 This was the calculated result.

[0159] Here, applying the eddy current loss coefficient β, expressed by equation (19), to equation (14), we obtain the harmonic eddy current loss W. har.e This was predicted. [W] is the predicted value of the harmonic eddy current loss. har.e ] is the harmonic loss W obtained from inverter iron loss measurement. har W is the measured value of the eddy current loss. har.eWhen compared, it was found that the prediction accuracy of the harmonic eddy current loss was low. The reason for the low prediction accuracy of the harmonic eddy current loss is partly due to the eddy current loss coefficient β. Specifically, when assuming that the eddy current loss coefficient β depends on the material but not on the excitation conditions, it is expressed as the above-mentioned formula (19). That is, applying the same value as the eddy current loss coefficient β in the case of sine wave excitation and the case of inverter excitation is partly the reason for the low prediction accuracy of the harmonic eddy current loss.

[0160] Conversely, the low prediction accuracy of the harmonic eddy current loss suggests that in the case of inverter excitation, it is necessary to separately calculate the eddy current loss due to the sine wave component and the eddy current loss due to the harmonic component. Therefore, the eddy current loss coefficient β can be distinguished into the eddy current loss coefficient β sin of the sine wave and the eddy current loss coefficient β har of the harmonic. The eddy current loss coefficient β sin of the sine wave is assumed to be the same as β expressed by the above-mentioned formula (19).

[0161] In the prediction formula of the inverter iron loss considering the cross-sectional area S of the compressed powder core, the inverter iron loss prediction formula applying the harmonic eddy current loss coefficient β har is expressed as the following formula (20).

[0162]

Number

[0163] The harmonic eddy current loss coefficient β har is expressed as the following formula (21) in accordance with the form of the eddy current loss coefficient β sin of the sine wave, that is, β expressed by formula (19).

[0164]

Number

[0165] From the measured value of the eddy current loss when performing inverter excitation on the compressed powder core, the harmonic eddy current loss coefficient β harThe following is calculated. Figure 25 shows the β calculated from the measured values ​​of eddy current loss when inverter excitation was performed on powder cores manufactured with four different heights. har A scatter plot is shown illustrating an example of the relationship between the value of and the cross-sectional area S of the compacted magnetic core. By performing a simple linear regression analysis on the four points plotted in the scatter plot, the coefficients when approximating the relationship with the cross-sectional area S of the compacted magnetic core using equation (21) are found to be a'=0.860 and b'=2.02×10 -6 This was the calculated result.

[0166] Here, the β included in equation (20) sin Applying β from equation (19) to β har β in equation (21) har By applying this, the prediction formula for inverter iron loss, with inverter conditions and the cross-sectional area S of the compacted magnetic core as parameters, can be expressed as shown in equation (22) below.

[0167]

number

[0168] As described above, the correlation between the harmonic eddy current loss coefficient and the cross-sectional area of ​​the powder core is reflected in the prediction formula. This allows the phenomenon where the measured eddy current loss increases exponentially with increasing cross-sectional area of ​​the powder core to be reflected in the prediction of harmonic eddy current loss. As a result, the prediction accuracy of high-frequency eddy current loss is improved.

[0169] <Example 5> As a sample of the magnetic core, a test compacted core was prepared by pressurizing a compacted body of insulating coated pure iron powder with a median diameter of 87.7 μm at 980 MPa. The test compacted core has a ring shape with an outer diameter of 38 mm, an inner diameter of 25 mm, and a height of 10 mm. The cross-sectional area of ​​the test compacted core intersecting in the circumferential direction is 64 mm². 2 That is the case.

[0170] The measured eddy current iron loss of a test compacted powder core under arbitrary sinusoidal excitation conditions was actually measured using a sinusoidal iron loss measuring device. Furthermore, the predicted value of the eddy current iron loss of a test compacted powder core under arbitrary sinusoidal excitation conditions was calculated using the sinusoidal eddy current loss prediction formulas (15) and (19) described above.

[0171] Figure 26 shows the measured value of the sinusoidal eddy current iron loss W. 1.e and predicted value [W 1.e A scatter plot illustrating an example of the relationship between [ ] is shown. In the graph in Figure 26, the horizontal axis represents the measured value W of sinusoidal eddy current iron loss. 1.e This represents the predicted value of sinusoidal eddy current iron loss [W]. The vertical axis is the predicted value of sinusoidal eddy current iron loss. 1.e This represents the measured value of sinusoidal eddy current iron loss (W). 1.e and predicted value [W 1.e A generally proportional relationship can be observed between [ ] and [ ]. Furthermore, the measured value of sinusoidal eddy current iron loss W 1.e and predicted value [W 1.e This matches well.

[0172] <Example 6> As a sample of the magnetic core, the same test compacted core as in Example 5 was prepared.

[0173] The measured eddy current iron loss of a test compacted powder core at arbitrary PWM parameters was actually measured using an inverter iron loss measuring device. In addition, the predicted eddy current iron loss of a test compacted powder core at arbitrary PWM parameters was calculated using the harmonic eddy current loss prediction formulas (14) and (19) described above.

[0174] Figure 27 shows the measured value of harmonic eddy current iron loss W. har.e and predicted value [W har.e A scatter plot illustrating an example of the relationship between [ ] is shown. In the graph in Figure 27, the horizontal axis represents the measured value W of harmonic eddy current iron loss. har.e This represents the predicted value of harmonic eddy current iron loss [W]. The vertical axis is the predicted value of harmonic eddy current iron loss. har.e This represents the measured value of harmonic eddy current iron loss W. har.e and predicted value [W har.e A generally proportional relationship can be observed between [W] and the predicted value. har.e ] is the measured value W har.eThis value is approximately half of the original value. In other words, the prediction accuracy of harmonic eddy current iron loss when using β, which is expressed in equation (19), is low.

[0175] On the other hand, the predicted value of the eddy current iron loss of the test compacted powder core at any PWM parameter is given by β, which is expressed by equation (19), i.e., β sin In addition, β represented by the above-mentioned formula (21) har It was calculated using the second term on the right-hand side of equation (22), which was obtained by applying the formula. Figure 28 shows the measured value of harmonic eddy current iron loss W. har.e and predicted value [W har.e A scatter plot illustrating an example of the relationship between [ ] is shown. In the graph in Figure 28, the horizontal axis represents the measured value W of harmonic eddy current iron loss. har.e This represents the predicted value of harmonic eddy current iron loss [W]. The vertical axis is the predicted value of harmonic eddy current iron loss. har.e This represents the predicted value [W] in Figure 28. har.e ] is the measured value W har.e This is approximately 1.07 times the value. Compared to the case where only β is used for prediction as described above, sin and β har The prediction accuracy of harmonic eddy current iron loss is higher when using β. har Applying this to the prediction formula improves prediction accuracy.

[0176] <Example 7> As a sample of the magnetic core, the same test compacted core as in Example 5 was prepared.

[0177] The measured iron loss of a test compacted powder core, which is the sum of eddy current loss and hysteresis loss, was actually measured using an inverter iron loss measuring device at arbitrary PWM parameters. In addition, the predicted value of the iron loss of the test compacted powder core at arbitrary PWM parameters was calculated using the inverter iron loss prediction formula (22) described above.

[0178] Figure 29 shows the measured value of inverter iron loss W. inv and predicted value [W inv A scatter plot illustrating an example of the relationship between [ ] is shown. In the graph in Figure 29, the horizontal axis represents the measured value W of the inverter iron loss. inv This represents the predicted value of inverter iron loss [W]. The vertical axis is the predicted value of inverter iron loss. invThis represents the measured value of inverter iron loss (W). inv and predicted value [W inv A generally proportional relationship can be observed between [ ] and [ ]. Also, the measured value of inverter iron loss W inv and predicted value [W inv This matches well.

[0179] (Summary of inverter iron loss predictions considering the cross-sectional area of ​​the magnetic core) As described above, predicting the inverter iron loss when a powder core is inverter-excited based on the cross-sectional area of ​​the powder core improves the accuracy of predicting the inverter iron loss when the cross-sectional area of ​​the powder core changes. For example, using a prediction formula created based on measured values ​​of inverter iron loss for a sample of a powder core with a small cross-sectional area, the inverter iron loss of a powder core with a large cross-sectional area used in a motor can be predicted with high accuracy.

[0180] The above-mentioned inverter iron loss prediction formula is based on the case where the median diameter of the iron powder, which is the material of the compacted magnetic core, is a specific value. sin and β har It is expressed using a mathematical formula. In other words, a prediction formula for inverter iron loss may be created for each median diameter of the iron powder.

[0181] While embodiments of this disclosure have been described based on the drawings and examples, it should be noted that those skilled in the art can make various modifications or alterations based on this disclosure. Therefore, it should be noted that these modifications or alterations are included within the scope of this disclosure. For example, the functions included in each component or step can be rearranged in a logically consistent manner, and multiple components or steps can be combined into one or divided. Embodiments relating to this disclosure can also be realized as programs executed by a processor in the device or as storage media recording such programs. These should also be understood to be included within the scope of this disclosure.

[0182] The mathematical formulas used in the embodiments described above can be modified in various ways.

[0183] For example, the exponent "1.6" used in the first term (hysteresis loss term) of Steinmetz's empirical formula may be replaced with other values.

[0184] p included in Equation (9) etc. h and p e Regarding p h =u×(γ×m s ) 1.6 ×(f1 / f c ) 0.6 and, p e =(u×γ×m s ) 2 It may be formulated to use u, which is a coefficient determined by the form of the inverter circuit, or to make the ratio of the exponent of m to the exponent of γ equal to s. u, which is a coefficient determined by the form of the inverter circuit, is the ratio of the frequency (f2) of the fundamental harmonic contained in the inverter excitation waveform to the carrier frequency (f c ). Also, γ and s are represented by the mathematical formula (B2×f c ) / (B1×f1)=γ×m s and are values determined based on the form of the target inverter circuit or values calculated based on a prior waveform analysis using a circuit of the same form.

Explanation of Signs

[0185] 1 Information processing system 10 Information processing device (12: Processor, 14: Storage unit, 16: Interface) 20 Excitation device 30 Measuring device

Claims

1. The procedure includes the step of predicting the iron loss that occurs when a magnetic material is excited with an excitation waveform generated by a PWM inverter controlled by PWM parameters including modulation rate and carrier frequency, based on the modulation rate and the carrier frequency, A method for evaluating iron loss, comprising the step of predicting the iron loss based on the ratio of the frequency of the harmonics of the excitation waveform to the carrier frequency.

2. The iron loss evaluation method according to claim 1, wherein in the step of predicting the iron loss, the ratio of the frequency of the harmonics of the excitation waveform to the carrier frequency is determined based on waveform data obtained by measuring the excitation waveform generated by the PWM inverter.

3. The procedure includes the step of predicting the iron loss that occurs when a magnetic material is excited with an excitation waveform generated by a PWM inverter controlled by PWM parameters including modulation rate and carrier frequency, based on the modulation rate and the carrier frequency, An iron loss evaluation method in which, in the step of predicting the iron loss, if the magnetic material is a powdered magnetic core, the iron loss is further predicted based on the cross-sectional area of ​​the powdered magnetic core that intersects the magnetic flux that energizes the powdered magnetic core.

4. A low iron loss material design method, comprising the step of designing the characteristics of a magnetic material to be designed such that the iron loss that occurs when the magnetic material to be designed is excited with an excitation waveform generated by controlling the PWM inverter at a predetermined modulation rate and a predetermined carrier frequency is reduced, based on the results of predicting the iron loss that occurs when each of at least two types of magnetic materials having different characteristics is excited with an excitation waveform generated by controlling the PWM inverter at a predetermined modulation rate and a predetermined carrier frequency, by performing the iron loss evaluation method described in claim 1.

5. The process includes the step of designing the characteristics of a magnetic material to be designed such that the iron loss that occurs when the magnetic material to be designed is excited with an excitation waveform generated by controlling a PWM inverter, which is controlled by PWM parameters including modulation rate and carrier frequency, at a predetermined modulation rate and a predetermined carrier frequency, is reduced, based on the results of predicting the iron loss that occurs when each of at least two types of magnetic materials having different characteristics is excited with an excitation waveform generated by controlling the PWM inverter at a predetermined modulation rate and a predetermined carrier frequency, A low iron loss material design method, comprising the step of designing the properties of the magnetic material to be designed, wherein the iron loss that occurs when the magnetic material to be designed is excited with a sinusoidal excitation waveform is obtained for each representative dimension of the magnetic material to be designed, and the representative dimensions of the magnetic material to be designed are designed as properties of the magnetic material to be designed.

6. The magnetic material to be designed is a compacted magnetic core composed of soft magnetic powder. The low iron loss material design method according to claim 4, wherein in the step of designing the properties of the magnetic material to be designed, the representative dimensions of the soft magnetic powder are designed as properties of the magnetic material.

7. The process includes the step of designing the characteristics of a magnetic material to be designed such that the iron loss that occurs when the magnetic material to be designed is excited with an excitation waveform generated by controlling a PWM inverter, which is controlled by PWM parameters including modulation rate and carrier frequency, at a predetermined modulation rate and a predetermined carrier frequency, is reduced, based on the results of predicting the iron loss that occurs when each of at least two types of magnetic materials having different characteristics is excited with an excitation waveform generated by controlling the PWM inverter at a predetermined modulation rate and a predetermined carrier frequency, The magnetic material to be designed is a compacted magnetic core composed of soft magnetic powder. A low iron loss material design method, comprising the step of designing the properties of the magnetic material to be designed, wherein the representative dimensions of the soft magnetic powder are designed as properties of the magnetic material based on the results obtained when the powder core is excited with a sinusoidal excitation waveform, and the iron loss occurring for each representative dimension of the soft magnetic powder.

8. An iron loss evaluation program that causes a processor to execute the iron loss evaluation method described in any one of claims 1 to 3.

9. A low iron loss material design program that causes a processor to execute the low iron loss material design method described in any one of claims 4 to 7.

10. A low-loss soft magnetic material having properties designed by performing the low-iron-loss material design method described in claim 4 or 5.

11. A low-loss soft magnetic powder having representative dimensions designed by performing the low-iron-loss material design method described in claim 6 or 7.

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