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

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

[0001] The present disclosure relates to a method and program for evaluating iron loss, which becomes a problem when exciting a magnetic material with a PWM inverter, a method and program for designing a low iron loss material that corresponds to the excitation conditions of a PWM inverter, and a low-loss soft magnetic material and low-loss soft magnetic powder used as a low iron loss material.

[0002] Generally, the iron loss of soft magnetic materials used in motor cores and the like is evaluated by excitation with a sine wave. Meanwhile, the iron cores of motors used in recent power electronics devices are excited by inverters. Here, iron loss is a cause of heat generation in power electronics devices. To improve the accuracy of predictions of the amount of heat generated during actual operation of power electronics devices, it is essential to evaluate the iron loss when the iron core is excited by an inverter. A known method for evaluating iron loss when the iron core is excited by an inverter is to calculate the iron loss by integrating an excitation waveform synthesized based on inverter conditions (see Non-Patent Document 1).

[0003] Here, a PWM (Pulse Width Modulation) inverter, which is the most common type of inverter, may be used. A PWM inverter generates an excitation waveform as a pulse wave using the PWM method. Specifically, to create a target excitation wave—a sine wave with a maximum magnetic flux density of B1 and a frequency of f1—a PWM inverter compares the height of a modulation wave corresponding to the target excitation wave with a carrier wave, which is a triangular wave having a frequency several times higher than that of the modulation wave. The PWM inverter generates a pulse wave that is at a high level during periods when the modulation wave is higher than the carrier wave and at a low level during periods when the modulation wave is lower than the carrier wave. This pulse wave is configured so that its pulse height is constant over time and its pulse width varies over time. A waveform obtained by taking the time average of the generated pulse wave is applied to the iron core as the excitation wave.

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

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

[0006] JP 2012-26960 A

[0007] G. Bertotti, IEEE TRANSACTIONS ON MAGNETICS, VOL. 24, NO. 1 (1988), p.621-630

[0008] As in Non-Patent Document 1, the evaluation method for inverter iron loss is extremely complicated, as it involves synthesizing an excitation waveform based on inverter conditions and then integrating the synthesized waveform to calculate it, which poses an obstacle to the application to analysis itself, prototyping of magnetic cores, and evaluation. Furthermore, Patent Document 1 simply expresses the harmonic components of the inverter excitation waveform to estimate iron loss, but it is necessary to measure the harmonic components for each iron loss estimation.

[0009] The present disclosure was developed in consideration of the above-mentioned problems, and aims to provide an iron loss evaluation method and an iron loss evaluation program that clarify the relationship between inverter input conditions and inverter iron loss and that can directly predict iron loss from inverter conditions without measuring iron loss when the iron core is excited by the inverter. The present disclosure also aims to provide a low-iron loss material design method and a low-iron loss material design program that use evaluation results from 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.

[0010] (1) An iron loss evaluation method according to one embodiment of the present disclosure includes a step of predicting, based on a modulation rate and a carrier frequency, iron loss that occurs when a magnetic material is excited with an excitation waveform generated by a PWM inverter controlled by PWM parameters including the modulation rate and a 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 a ratio of a frequency of a harmonic 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, a ratio of a frequency of a harmonic 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 according to any one of (1) to (3) above, when the magnetic material is a powder magnetic core, the iron loss may be predicted further based on a cross-sectional area of ​​the powder magnetic core that intersects with a magnetic flux that excites the powder magnetic core.

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

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

[0016] (7) In the method for designing a low iron loss material described above in (5), the magnetic material to be designed may be a powder magnetic core made of soft magnetic powder. In the step of designing the characteristics of the magnetic material to be designed, a representative dimension of the soft magnetic powder may be designed as the characteristic of the magnetic material.

[0017] (8) In the step of designing the characteristics 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, a representative dimension of the soft magnetic powder may be designed as a characteristic of the magnetic material based on the results of obtaining the iron loss that occurs when the powder core is excited with a sinusoidal excitation waveform for each representative dimension of the soft magnetic powder.

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

[0019] (10) A low iron loss material design program according to an 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 an embodiment of the present disclosure has characteristics designed by carrying out the low iron loss material design method described in (5) or (6) above.

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

[0022] According to the iron loss evaluation method and iron loss evaluation program of the present disclosure, iron loss can be directly predicted from inverter conditions without measuring iron loss when the iron core is excited by an inverter. According to the low iron loss material design method and low iron loss material design program, and the low loss soft magnetic material and low loss soft magnetic powder of the present disclosure, iron loss can be reduced when the iron core is excited by an inverter.

[0023] 1 is a diagram showing an example of operation of a PWM inverter using a triangular wave comparison method; FIG. 2 is a diagram showing an example of a frequency spectrum of an inverter excitation waveform; FIG. 3 is a flowchart showing the procedure of a method for predicting iron loss according to a comparative example; FIG. 4 is a flowchart showing an example of the procedure of a method for evaluating iron loss according to an embodiment of the present disclosure; FIG. 5 is a block diagram showing an example configuration of an information processing system according to an embodiment of the present disclosure; FIG. 6 is a graph showing an example of the relationship between a carrier frequency and a harmonic frequency; FIG. 7 is a graph showing an example of the relationship between a modulation factor and a harmonic frequency; FIG. 8 is a graph showing an example of the relationship between a modulated wave frequency and a harmonic frequency; FIG. 9 is a graph showing an example of the relationship between a carrier frequency and a harmonic magnetic flux density; FIG. 10 is a graph showing an example of the relationship between a modulation factor and a harmonic magnetic flux density; FIG. 11 is a graph showing an example of the relationship between a modulated wave frequency and a harmonic magnetic flux density; FIG. 12 is a graph showing an example of the relationship between an actual measured value and a predicted value of a harmonic magnetic flux density; FIG. 13 is an example of a graph used to determine α in Steinmetz's empirical formula; FIG. 14 is an example of a graph used to determine β in Steinmetz's empirical formula. 18 is a graph showing an example of a relationship between the α value determined for a powder core using pure iron powder and the median diameter of the pure iron powder, using simple regression. FIG. 19 is an example of a graph showing the relationship between the β value determined for a powder core using pure iron powder and the median diameter of the pure iron powder, using simple regression. FIG. 20 is an example of a graph showing the relationship between the γ value determined for a powder core using pure iron powder and the median diameter of the pure iron powder, using simple regression. FIG. 21 is an example of a scatter diagram showing the relationship between the actual measured value of iron loss and the value calculated based on the iron loss prediction formula in Example 1. FIG. 22 is a graph showing an example of the relationship between the median diameter and the predicted value of iron loss in Example 2. FIG. 23 is a graph showing an example of the relationship between the median diameter and the predicted value of iron loss in Example 3. FIG. 24 is a graph in which the actual measured value of iron loss and the value calculated based on the iron loss prediction formula in Example 4 are added to FIG. 18. FIG. 25 is a diagram showing an example of eddy currents flowing in a powder core. FIG. 26 is a diagram showing an example of the configuration of a powder core. FIG. 27 is a scatter diagram showing an example of the relationship between the eddy current loss coefficient of a sinusoidal wave and the cross-sectional area of ​​a powder core. 1 is a scatter diagram showing an example of the relationship between the harmonic eddy current loss coefficient and the cross-sectional area of ​​a powder magnetic core. 2 is a scatter diagram showing an example of the relationship between the actual measured value and the predicted value of the sinusoidal eddy current iron loss in Example 5. 3 is a scatter diagram showing an example of the relationship between the actual measured value of the harmonic eddy current iron loss and the predicted value without taking the harmonic eddy current loss coefficient into consideration in Example 6.10 is a scatter diagram showing an example of the relationship between the measured value of harmonic eddy current iron loss and the value predicted in consideration of the harmonic eddy current loss coefficient in Example 6. FIG. 11 is a scatter diagram showing an example of the relationship between the measured value of iron loss and the predicted value in Example 7.

[0024] In recent years, power electronics, which utilizes the switching function of semiconductors to efficiently control power, has rapidly developed. Power electronics technology allows for AC-to-DC converters, DC-DC converters, DC-to-AC inverters, and AC frequency conversion (matrix converters) to be easily achieved using relatively simple circuits. Furthermore, increasing the switching frequency reduces the inductance or capacitance of passive elements required for circuits. Reducing the inductance or capacitance of passive elements enables the miniaturization of equipment. Toward the realization of a carbon-neutral society, there is a strong global demand for efficient use of electricity and the miniaturization and weight reduction of equipment. Power electronics technology is now being widely applied not only in the power equipment, railways, and industrial fields where it has been prioritized until now, but also in electrical equipment used in everyday life, such as automobiles and home appliances.

[0025] Inverters are one of the important circuits used in power electronics devices. They not only convert direct current (DC) to alternating current (AC), but also efficiently control AC output. Familiar examples of inverters include the electric compressors in inverter air conditioners and induction motors used to drive electric vehicles (EVs), contributing significantly to energy conservation. Pulse Width Modulation (PWM), which controls AC output by modulating the pulse width of a constant voltage, is widely used to control inverter output. Commonly used induction motors rotate their rotors by applying AC currents of tens to hundreds of hertz (Hz). PWM inverters, on the other hand, generate AC from DC currents to be applied to the induction motor to rotate the rotor. Therefore, PWM inverters switch at frequencies several times higher than the AC frequency 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. A triangular wave comparison PWM inverter outputs a pulse waveform generated by comparing a target AC waveform with a triangular wave and switching DC. The time-averaged waveform of the output pulse waveform is a waveform that approximates the target AC waveform. The target AC waveform is also called a modulation wave. The triangular wave compared with the target AC waveform is also called a carrier wave. In other words, a triangular wave comparison PWM inverter can convert DC into an AC waveform and output it by switching the DC based on the comparison result between the modulation wave and the carrier wave.

[0027] In this embodiment, the PWM inverter generates an output pulse waveform by further utilizing a pulse waveform generated by comparing a waveform of the opposite phase of the modulated wave with a triangular wave. Specifically, the PWM inverter outputs a pulse waveform that is the difference between a pulse waveform obtained by inputting the modulated wave and a carrier wave to a comparator and switching DC based on the output of the comparator, and a pulse waveform obtained by inputting the waveform of the opposite phase of the modulated wave and the carrier wave to a comparator and switching DC based on the output of the comparator.

[0028] An example of the operation of a PWM inverter using a triangular wave comparison method will be described with reference to Figure 1. The graph shown in Figure 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 signal strength.

[0029] The top graph shows the waveform of the carrier wave, the waveform of the modulated wave, and the waveform of the opposite phase of the modulated wave. ｃ The frequency of the triangular carrier wave is f ｃ The peak-to-peak value of the carrier wave waveform is E ｃ Let it be expressed as:

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

[0031] E ｃ E for ｓ The ratio of E is also called the modulation factor and is expressed as m. In other words, the modulation factor (m) is the voltage amplitude ratio of the modulating wave to the carrier wave, and E ｓ / E ｃ It is calculated as follows.

[0032] The PWM inverter is a converter that uses a modulation factor (m) and a carrier frequency (f ｃ By controlling the modulation factor (m) and carrier frequency (f ｃ ) are also referred to as PWM parameters. The PWM parameters are included in the inverter conditions. The inverter conditions include not only PWM parameters but also parameters of the modulated wave. When the modulated wave is a sine wave, the parameters of the modulated wave are also referred to as sine wave conditions. In other words, the inverter conditions include PWM parameters and sine wave conditions.

[0033] The second graph shows a pulse waveform generated based on a comparison between the waveform of the carrier wave and the waveform of the modulated wave. The pulse waveform generated based on a comparison between the waveform of the carrier wave and the waveform of the modulated wave is P ｓ１ It is assumed that the equation is expressed as follows: P ｓ１ are represented as black rectangles in FIG.

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

[0035] The third graph shows a pulse waveform generated based on a comparison between the waveform of the carrier wave and the waveform of the opposite phase of the modulated wave. The pulse waveform generated based on a comparison between the waveform of the carrier wave and the waveform of the opposite phase of the modulated wave is P ｓ２ It is assumed that the equation is expressed as follows: P ｓ２ is represented in FIG. 1 as a rectangle hatched with diagonal lines slanting downward to the right.

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

[0037] The fourth graph shows P ｓ１ From the pulse waveform of P ｓ２ , which shows the pulse waveform generated by subtracting the pulse waveform of P ｓ１ From the pulse waveform of P ｓ２ The pulse waveform generated by subtracting the pulse waveform of P ｓ It is assumed that the equation is expressed as follows: P ｓ is represented in FIG. 1 as a rectangle with cross hatching.

[0038] Specifically, P ｓ１ In the pulse waveform of P1, the pulse waveform of the circled dashed line is ｓ２By subtracting the pulse waveform of the dashed circled area represented by P2 from the pulse waveform of ｓ In the pulse waveform of P3, the pulse waveform of the circled portion of the dashed line is generated. ｓ１ and P ｓ２ If P ｓ The value of P becomes 0. ｓ１ is 1 and P ｓ２ If is 0, P ｓ The value of P is 1. ｓ１ is 0 and P ｓ２ If is 1, P ｓ The value of P becomes -1. ｓ A pulse waveform in which P is 1 is a positive pulse waveform. ｓ A pulse waveform where P is -1 is a negative pulse waveform. ｓ is a pulse waveform that combines a positive pulse waveform and a negative pulse waveform.

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

[0040] Here, it is assumed that a PWM inverter equipped with a SiC power semiconductor and outputting the output waveform shown in FIG. 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 was measured by inverter exciting the magnetic material to be measured by outputting an excitation waveform based on the output waveform shown in FIG. 1 using an excitation power supply equipped with a PWM inverter. In this embodiment, the frequency of the modulated wave is f １ The frequency of the modulating wave (f １ ) is included in the sine wave condition. For a modulated wave with a frequency range of 400 Hz to 1 kHz, the carrier wave frequency (f ｃ The modulation factor (m) was controlled in the range of 0.4 to 1.25.

[0041] As described above, the excitation power supply of the high-frequency iron loss measuring device inverter-excites the magnetic material based on the output waveform of the PWM inverter. The waveform output when the magnetic material is inverter-excited is also referred to as the inverter excitation waveform. The inverter excitation waveform may be considered to be a waveform generated by a PWM inverter. Hereinafter, it is assumed that the PWM inverter generates the inverter excitation waveform.

[0042] Here, as an example, the PWM inverter has a carrier frequency (f ｃ ) is 20 kHz and the modulation rate (m) is 0.4, and １ Assume that an inverter excitation waveform is generated based on a modulation wave having a frequency of 1 kHz. The inverter excitation waveform generated in this embodiment is represented as a frequency spectrum illustrated in FIG. 2 by Fourier transform. In FIG. 2, the horizontal axis corresponds to frequency, represented as f. The unit of frequency is assumed to be kilohertz (kHz). The vertical axis corresponds to the intensity of each frequency component, represented as B. The intensity of each frequency component is assumed to be in tesla (T).

[0043] The frequency spectrum of the inverter excitation waveform generated in this embodiment is mainly in the frequency range of f １ The modulated wave component with frequency f ２ 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 B １ The intensity of the modulated wave component is also called the excitation magnetic flux density. １ ) is included in the sine wave condition. The intensity of the first harmonic component is B ２ Let it be expressed as:

[0044] In the frequency spectrum of FIG. 2, the frequency of the first harmonic component (f ２ ) is calculated as the average frequency of the strongest component other than the modulating wave component and the frequency of the component with an intensity of 50% or more of 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 (f ｃ) is twice as much.

[0045] Harmonics include not only the first-order component 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 component. Therefore, in this embodiment, only the first-order harmonic component is 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 iron core materials under sinusoidal excitation is published, and motors are designed based on this data. However, as mentioned above, the inverter excitation waveform using a PWM inverter is not a smooth sinusoidal wave but contains harmonics due to the switching operation of semiconductors. Therefore, the iron loss generated in the magnetic core during 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 iron loss due to the harmonic component increases the heat generation rate beyond that expected at the time of design. This increase in heat generation may require cooling measures not anticipated at the time of design. If a design is made with a margin in mind, taking into account the iron loss due to harmonics, the equipment using inverter-driven motors will become larger. Given the strong demand for equipment miniaturization and high efficiency, it is necessary to accurately estimate inverter iron loss when designing equipment.

[0047] When designing a motor, if a magnetic core material suitable for the motor's drive conditions is to be selected, 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, the excitation magnetic flux density (B １ ) is 1.0T, and the frequency (f １ ) represents the iron loss when the frequency is 400 Hz. １０／４００ However, W １０／４００ The iron loss data generally disclosed as above is data obtained with sinusoidal excitation, not inverter excitation. Therefore, when designing a motor driven by an inverter, it is necessary to take into account the increase in iron loss caused by harmonics.

[0048] If a motor were connected to an inverter circuit that would actually be used and the iron loss or heat generation of the magnetic core were measured, it would be possible to directly evaluate the iron loss that occurs during inverter excitation. However, directly evaluating iron loss requires a great deal of cost and man-hours. It is unrealistic to repeatedly prototype a motor in order to directly evaluate iron loss from the stage of selecting the magnetic core material in the motor design process.

[0049] Alternatively, the iron loss of a test piece can be evaluated using an excitation power supply that simulates a PWM inverter. Iron loss during inverter excitation can also be evaluated by integrating an inverter excitation waveform synthesized based on PWM parameters. However, this method is difficult to implement because it requires specialized evaluation equipment and the analysis method is complicated.

[0050] For these reasons, there is a need for a simple method for evaluating iron loss during inverter excitation.

[0051] Here, the PWM inverter can control the output by changing the modulation factor (m) from 0 to 1 while keeping the pulse voltage height constant. Also, the PWM inverter can control the carrier frequency (f ｃ ) can be used to control the output. When evaluating iron loss, a specific inverter excitation waveform is applied to the magnetic material. Specifically, the excitation conditions for evaluating iron loss are the frequency (f １ ) and excitation magnetic flux density (B １ ) is set.

[0052] The frequency of the modulation wave of the inverter excitation waveform (f １ ) and excitation magnetic flux density (B １ ) with modulation rate (m) and carrier frequency (f ｃ ) is set independently. In other words, the excitation magnetic flux density (B １ ) and modulation factor (m) do not correspond one-to-one. １The modulation factor (m) may be set to a smaller or larger value relative to the iron loss. The value of the modulation factor (m) is set based on the output fluctuation range of the motor whose iron loss is to be evaluated or the design concept of the circuit.

[0053] Inverter excitation waveform excitation magnetic flux density (B １ When the modulation factor (m) is set to a large value (close to 1) relative to the excitation magnetic flux density (B １ ) is set in the high magnetic flux density region, the modulation factor (m) exceeds 1, resulting in an overmodulation state, and power control becomes unstable. Conversely, when the modulation factor (m) is set to a small value (a value close to 0), the excitation magnetic flux density (B １ ) in the high magnetic flux density region, power control is stabilized, but inverter iron loss increases.

[0054] Carrier frequency (f ｃ ) is set to a high frequency, the intensity of the harmonic components of the inverter excitation waveform (B ２ ) is reduced, and the increase in iron loss due to harmonics is suppressed. However, the heat generated by the switching elements increases, and the loss of the entire circuit also increases.

[0055] As described above, the PWM inverter uses one excitation condition for evaluating iron loss as modulation factor (m) or carrier frequency (f ｃ The iron loss generated by inverter excitation is a function of the modulation factor (m) and the carrier frequency (f ｃ Therefore, even if the excitation conditions are the same, the modulation factor (m) and carrier frequency (f) set by the PWM inverter to realize those excitation conditions may differ. ｃ ) must be taken into account when evaluating iron loss.

[0056] Therefore, the iron loss evaluation method according to the present disclosure is to evaluate the iron loss by adjusting the frequency (f １ ) and excitation magnetic flux density (B １ ), the modulation rate (m) and carrier frequency (f ｃ) can be used to easily predict iron loss caused by inverter excitation with high accuracy. Furthermore, the low iron loss material design method according to the present disclosure can design the characteristics of a low iron loss material based on the iron loss prediction results, and provide a low iron loss material.

[0057] (Iron Loss Evaluation Method According to the Present Disclosure) The iron loss evaluation method according to the present disclosure estimates iron loss without measuring the excitation waveform when a magnetic material is inverter-excited, by measuring the modulation factor (m) and carrier frequency (f 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 σ is constructed in the following procedure.

[0059] First, by Fourier analysis of the excitation waveform synthesized under multiple excitation conditions of the inverter excitation by the PWM inverter, the magnetic flux density of the first harmonic (B ２ ) and frequency (f ２ In this case, it is desirable to analyze an excitation waveform synthesized under three or more excitation conditions. The excitation conditions are the modulation factor (m) and the carrier frequency (f ｃ ) is assumed to be identified.

[0060] Next, the magnetic flux density of the first harmonic (B ２ ) and frequency (f ２ ) and the excitation conditions are substituted into Steinmetz's empirical formula and rearranged to generate a prediction formula for iron loss.

[0061] The iron loss prediction formula according to the present disclosure, generated by the above procedure, can calculate the predicted value of inverter iron loss directly from the excitation conditions of inverter excitation by the PWM inverter, without analyzing the excitation waveform.

[0062] As a comparative example, it is conceivable to perform extremely complicated calculations for analyzing the excitation waveform and measure harmonic components for each excitation condition in order to predict iron loss. The iron loss prediction method according to the comparative example includes the steps shown in FIG.

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

[0064] As described above, the method according to the comparative example requires measurement of the excitation waveform and integration of the waveform data, whereas the iron loss evaluation method according to the present disclosure is performed using only the procedure shown in FIG.

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

[0066] As described above, the prediction formula according to the present 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 according to the present disclosure can be expanded to one that reflects the characteristics of the raw materials that make up the magnetic material, as will be described later. By reflecting the characteristics of the raw materials in the prediction formula, the iron loss that occurs when the magnetic material is inverter excited is reduced, and guidelines for designing a magnetic material suitable for inverter excitation can be obtained from the prediction formula.

[0068] <Example of Hardware Configuration for Realizing Iron Loss Evaluation Method> The iron loss evaluation method according to the present disclosure may be realized by an information processing system 1 exemplified in Fig. 5. The information processing system 1 includes an information processing device 10, an excitation device 20, and a measurement device 30.

[0069] The excitation device 20 includes a PWM inverter and an excitation power supply. The PWM inverter may be realized by 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 a magnetic flux based on an output waveform from the PWM inverter and apply the magnetic flux to the magnetic material. The excitation power supply may be configured to pass a current corresponding to the output waveform from the PWM inverter through the excitation coil, for example.

[0070] The measuring device 30 is configured to measure the magnetic flux density when the magnetic material is inverter-excited. The measuring device 30 may include various magnetic sensors such as a flux gate or a Hall element.

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

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

[0073] The storage unit 14 stores various types of 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 a work memory for the processor 12. The storage unit 14 may be configured to include, for example, a semiconductor memory, but is not limited to this. The storage unit 14 may be configured, for example, as an 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-transitory readable medium. The storage unit 14 may be configured integrally with the processor 12 or as a separate entity from the processor 12.

[0074] The interface 16 may be configured to include a communication interface for communicating with other devices, such as the excitation device 20 or the measurement device 30, via a wired or wireless connection. The communication interface may be configured to be able to communicate with other devices via a network. The interface 16 may be configured to include an input / output port for inputting and outputting data to and from other devices. The interface 16 may communicate based on a wired communication standard or based on a wireless communication standard. For example, the wireless communication standard may include cellular phone communication standards such as 3G, 4G, and 5G. Furthermore, for example, the wireless communication standard may include IEEE 802.11, Bluetooth (registered trademark), and the like. The interface 16 may support one or more of these communication standards. The interface 16 is not limited to these examples and may communicate with other devices or input and output data based on various standards.

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

[0076] The interface 16 may include an input device that accepts input from a user. The input device may include, for example, a keyboard or physical keys, a touch panel or touch sensor, or a pointing device such as a 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 the iron loss evaluation method. The iron loss evaluation method may be realized as an iron loss evaluation program. The processor 12 may notify the user of the predicted value of iron loss calculated by executing the iron loss evaluation method via the interface 16, output the predicted value to an external device, or store the predicted value in the storage unit 14.

[0078] <Example of Developing Iron Loss Prediction Formula> Hereinafter, an example of developing a prediction formula will be specifically described.

[0079] First, a magnetic material was prepared by heat-treating a powder compact as a magnetic core for evaluating iron loss. The powder compact was made by compacting iron powder into a ring shape under a pressure of 980 MPa.

[0080] This magnetic material was excited by applying, for example, the output waveform of a PWM inverter shown in Figure 1 as an inverter excitation waveform. The inverter excitation waveform is a waveform in which harmonics resulting from semiconductor switching are superimposed on a modulated wave. The inverter excitation waveform is a waveform in which harmonics are superimposed on a modulated wave when, for example, the frequency of the modulated wave (f １ ) and harmonic frequencies (f ２ ) component is larger.

[0081] << Harmonic frequency (f ２ ) and inverter conditions >> As mentioned above, the frequency (f ２ ) is 40 kHz. In other words, the harmonic frequency (f ２ ) is the carrier frequency (f ｃ ) as illustrated in FIG. ｃ The harmonic frequencies (f ２ ) and carrier frequency (f ｃ ) In the graph of FIG. 6, the horizontal axis is the carrier frequency (f ｃ The vertical axis represents the frequency of the harmonic (f ２) represents

[0082] The frequency of the harmonic (f ２ ) is the carrier frequency (f ｃ ) but does not depend on the modulation factor (m). This can be seen from the fact that, as shown in FIG. 7, when a PWM inverter is controlled with a plurality of PWM parameters with different modulation factors (m) to excite a magnetic material, the harmonic frequencies (f ２ ) and modulation factor (m). In the graph of FIG. 7, the horizontal axis represents modulation factor (m), and the vertical axis represents harmonic frequency (f ２ The points plotted on the graph indicate the frequency of the harmonics (f ２ ) is confirmed to be unchanged.

[0083] In addition, the frequency of the harmonic (f ２ ) is the frequency of the modulating wave (f １ ) as well. This is because, as shown in FIG. １ The frequency of the harmonics (f ２ ) and the frequency of the modulating wave (f １ In the graph of FIG. 8, the horizontal axis represents the frequency of the modulating wave (f １ The vertical axis represents the frequency of the harmonic (f ２ The points plotted on the graph indicate the frequency of the modulating wave (f １ Regardless of the change in the frequency of the harmonic (f ２ ) is confirmed to be unchanged.

[0084] Based on the above-mentioned relationship, the frequency of the harmonic (f ２ ) is the carrier frequency (f ｃ ), and depends on the modulation rate (m) and the frequency of the modulating wave (f １ ) is expressed by the following equation (1).

[0085]

[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 (f ２ ) is expressed by the following formula (2).

[0087]

[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 is set to 1 when the PWM inverter is a single-phase half-bridge circuit. The proportionality constant is the ratio of the frequency of the harmonics of the excitation waveform to the carrier frequency. The proportionality constant may be set by directly confirming the type of PWM inverter. The proportionality constant may be determined by Fourier analysis of waveform data obtained by measuring the excitation waveform at least once when the magnetic material is inverter-excited by the PWM inverter, without directly confirming the type of PWM inverter. In other words, the proportionality constant may be determined based on waveform data obtained by measuring the excitation waveform generated by the PWM inverter.

[0089] As mentioned above, the frequency of the harmonic (f ２ ) is the inverter condition of the carrier frequency (f ｃ ) is determined by

[0090] <<Harmonic magnetic flux density (B ２ ) and inverter conditions >> As shown in Figure 9, the magnetic flux density of the harmonic (B ２ ) is the carrier frequency (f ｃ ) is proportional to the inverse of the harmonic magnetic flux density (B ２ ) is the carrier frequency (f ｃ ) is inversely proportional to the carrier frequency (f ｃ The vertical axis represents the magnetic flux density of the harmonic (B ２ ) represents

[0091] As shown in FIG. 10, the magnetic flux density of the harmonic (B ２) changes along an exponential function with the modulation factor (m) as a variable. The exponent value ranged from -1.64 to -1.65. In the graph of FIG. 10, the horizontal axis represents the modulation factor (m), and the vertical axis represents the magnetic flux density (B ２ ) represents

[0092] As shown in FIG. 11, the magnetic flux density of the harmonic (B ２ ) is the frequency of the modulating wave (f １ In the graph of FIG. 11, the horizontal axis represents the frequency of the modulating wave (f １ The vertical axis represents the magnetic flux density of the harmonic (B ２ ) represents

[0093] Based on the above-mentioned relationship, the magnetic flux density of the harmonic (B ２ ) is the carrier frequency (f ｃ ), modulation rate (m) and frequency of modulating wave (f １ ) is expressed by the following equation (3). １ is the proportionality constant.

[0094]

[0095] Here, the excitation power supply excites the magnetic material by applying a voltage to the excitation coil. The maximum value of the voltage applied by the excitation power supply is also called the maximum excitation voltage and is expressed as V. The maximum excitation voltage (V) and the frequency of the modulating wave (f １ ) and excitation magnetic flux density (B １ ) and V ∝ B １ ×f １ The relationship between the carrier frequency (f ｃ ) is changed, V ∝ B ２ ×f ｃ From the above, the relationship V ∝ B １ ×f １ ∝B ２ ×f ｃ It is assumed that the following relationship holds: Under this assumption, the following equation (4) holds:

[0096]

[0097] Furthermore, it is assumed that the following equation (5) holds when equation (4) is applied to equation (3): γ used in equation (5) is a proportionality constant.

[0098]

[0099] The magnetic flux density (B) of harmonics obtained by Fourier analysis of the excitation waveform when the magnetic material is inverter excited under various inverter conditions. ２ ) was determined by performing a regression analysis using equation (5) on the relationship between the magnetic flux density (B ２ ) was predicted. ２ ) predicted values ​​are shown in brackets [B ２ ]. In FIG. 12, the magnetic flux density of the harmonic ２ 12 shows an example of the relationship between the measured value and the predicted value of the magnetic flux density of the harmonic. ２ The vertical axis represents the predicted value of the magnetic flux density of the harmonic ([B ２ ]) It can be seen that the measured values ​​of the magnetic flux density of the harmonics are proportional to the predicted values.

[0100] <<Calculation of Iron Loss Taking Harmonics into Account>> Iron loss that occurs when a magnetic material is excited by an inverter is expressed based on the Steinmetz empirical formula shown as the following equation (6).

[0101]

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

[0103] Hysteresis loss (W １．ｈ ) is expressed as f １ ・B １ １．６It has been confirmed by measurements using a DC magnetization measurement device that the constant α is proportional to the following: Therefore, the constant α may be determined based on the measurement results illustrated in FIG.

[0104] Eddy current loss (W １．ｅ ) is determined by the constant β of f １ ２ ・B １ ２ And, W １ -α f １ ・B １ １．６ The relationship between the sigma and the sigma may be determined by performing a regression analysis.

[0105] The iron loss taking into account inverter excitation is W ｉｎｖ and is also called inverter iron loss. ｉｎｖ ) is the iron loss of sinusoidal excitation (W １ ) taking into account the influence of harmonics in inverter excitation, ｈａｒ ) is expressed by the following equation (7).

[0106]

[0107] Harmonic iron loss (W ｈａｒ ) are considered to be sinusoidal waves with frequencies different from the frequency of the modulating wave. When the harmonics are considered to be sinusoidal waves, the harmonic iron loss (W ｈａｒ ) is the iron loss of sinusoidal excitation (W １ ) can be separated into hysteresis loss and eddy current loss. Under this assumption, the harmonic iron loss (W ｈａｒ ) is expressed by the following equation (8).

[0108]

[0109] Inverter iron loss (W ｉｎｖ ) is the frequency of the modulating wave (f １ ), excitation magnetic flux density (B １ ), carrier frequency (f ｃ The inverter iron loss (W ｉｎｖ) is expressed as the following equation (9) by substituting equations (1), (5), (6), and (8) into the above equation (7).

[0110]

[0111] In addition, in the formula (9), p ｈ = 2 × γ １．６ ×m －２．６２ × (f １ / f ｃ ) ０．６ , and p ｅ = 4 × γ ２ ×m －３．２８ The element of harmonic iron loss that is caused by hysteresis loss is p ｈ In addition, the harmonic iron loss component caused by eddy current loss is expressed as p ｅ It is expressed as:

[0112] Based on the modulation rate and carrier frequency, inverter iron loss (W ｉｎｖ ) can be predicted by using the above-mentioned equation (9) to calculate the inverter iron loss (W ｉｎｖ ) corresponds to calculating the inverter iron loss (W ｉｎｖ ) is the modulation factor (m) and carrier frequency (f ｃ ) is the iron loss that occurs when a magnetic material is excited with an excitation waveform generated by a PWM inverter controlled under inverter conditions including

[0113] <<Summary>> As described above, inverter iron loss (W ｉｎｖ ) is calculated, the iron loss is predicted taking into account the harmonic iron loss caused by the harmonics in the inverter excitation. In equation (9), the constants α, β, and γ are determined in advance. Therefore, the carrier frequency (f ｃ ) and modulation rate (m) and frequency of modulating wave (f １ ) are substituted as variables into equation (9), the inverter iron loss (W ｉｎｖ In other words, if only the inverter conditions are substituted into equation (9) without substituting values ​​based on the measured data of the excitation waveform, the predicted value of the inverter iron loss (W ｉｎｖAs a result, iron loss generated by inverter excitation can be predicted with high accuracy and ease without analyzing the excitation waveform.

[0114] (Low-Loss Material Design Method According to the Present Disclosure) Using the iron loss evaluation method described above, Equation (9) was constructed as a prediction formula that can predict iron loss during inverter excitation based solely on inverter conditions. The constants α and β included in the iron loss prediction formula vary depending on the characteristics of the magnetic material to be excited. Therefore, by identifying the relationship between the constants and the characteristics of the magnetic material, information that serves as a guide for designing the characteristics of the magnetic material so that the predicted iron loss value is reduced can be obtained using the predicted iron loss value. Below, a material optimization method based on iron loss prediction using Equation (9) is described. Material optimization involves not only determining a single optimal material characteristic, but also determining an acceptable range for the optimal characteristic. The material optimization method is also called a low-loss material design method.

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

[0116]

[0117] The median diameter is the volumetric median of the particle diameters of iron powder. That is, the median diameter is the particle diameter determined so that when iron powder is divided into two particles of a certain particle diameter, the total volume of the larger particle diameter side is equal to the total volume of the smaller particle diameter side. The particle diameter of iron powder is the diameter of the longest part of the iron powder. The median diameter is determined by D ５０ It is expressed as follows. １ and C ２ is a constant. Figure 15 shows the relationship between the value of α determined for a dust core using pure iron powder and the median diameter (D ５０ ) is shown in a graph that shows the relationship between C １ is 1.19 x 10 －６ stipulated in C ２ is set to 0.0603.

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

[0119]

[0120] In formula (11), n ​​is set to a value between 1 and 2. ３ is a constant. Figure 16 shows the relationship between the value of β determined for a dust core using pure iron powder and the median diameter (D ５０ ) is shown in a graph that shows the relationship between C ３ is set to 7.65 and n is set to 1.46.

[0121] Regarding γ, a constant included in the iron loss prediction formula, Fig. 17 shows the value of γ determined for a dust core using pure iron powder and the median diameter (D ５０ ) is shown in a graph that shows the relationship between the median diameter (D ５０ ), and is determined to be an average value of 0.093.

[0122] As described above, the constants α and β included in formula (9) are replaced with mathematical expressions that represent the characteristics of the magnetic material. By replacing α and β in formula (9) with formulas (10) and (11), the inverter conditions and the median diameter (D ５０ The following equation (12) is derived as a prediction equation for inverter iron loss using the variables:

[0123]

[0124] In the examples described above, the median diameter (D ５０ ) are used to formulate α and β. The values ​​representing the properties of a magnetic material may depend on the crystal grain size even when the magnetic material is a powder magnetic core. Furthermore, the values ​​representing the properties of a magnetic material may depend on the thickness of the laminated steel sheets when the magnetic material is a laminated magnetic core. Therefore, the values ​​representing the properties of a magnetic material can be calculated by the median diameter (D ５０Therefore, by expressing the characteristics of the magnetic material in terms of a characteristic dimension (D), the following generalized equation (12) is derived:

[0125]

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

[0127] In other words, the iron loss generated 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 a predetermined carrier frequency may be predicted by executing the above-described iron loss evaluation method. Then, based on the predicted iron loss value, the characteristics of the magnetic material to be designed may be designed so that the iron loss generated when the magnetic material to be designed is excited with an excitation waveform generated by controlling a PWM inverter at a predetermined modulation rate and a predetermined carrier frequency is reduced. Furthermore, the representative dimensions of the magnetic material to be designed may be designed as the characteristics of the magnetic material to be designed. If the magnetic material to be designed is a steel plate, the representative dimensions may be the thickness of the steel plate, etc. If the magnetic material to be designed is a powder magnetic core, the representative dimensions may be the crystal grain size of the powder magnetic core, etc.

[0128] Furthermore, if the magnetic material is a powder magnetic core made of soft magnetic powder, the iron loss generated when the powder magnetic core is excited with a sinusoidal excitation waveform may be obtained for each representative dimension of the soft magnetic powder. Then, based on the iron loss for each representative dimension, the representative dimension of the soft magnetic powder may be designed as a characteristic of the magnetic material. Furthermore, 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 dimension of the steel plate. Then, based on the iron loss for each representative dimension, the representative dimension 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 realized 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 the properties to an external device, or store them 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 designed characteristics by carrying out the low-loss material design method described above.

[0131] (Example) An example will be described below.

[0132] Example 1: A test dust core having an outer diameter of 38 mm, an inner diameter of 25 mm, and a height of 6 mm was produced by compressing and molding an insulating-coated pure iron powder having an average particle diameter of 96.8 μm as the material powder at 980 MPa. The iron loss of the test dust core was measured using an inverter iron loss measurement device at any PWM parameter, and the iron loss was calculated based on the iron loss prediction formula (9) by executing the iron loss evaluation method according to the present disclosure.

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

[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 iron loss value (W ｉｎｖ ) and predicted value ([W ｉｎｖ ]) is roughly proportional to the measured iron loss value (W ｉｎｖ ) and predicted value ([W ｉｎｖ ]) is in good agreement.

[0135] <Example 2> Powder magnetic cores were prepared by compacting material powders having various median diameters. The powder magnetic cores using material powders having each median diameter were measured for the excitation magnetic flux density (B１ ) is 1.0T, and the frequency of the modulating wave (f １ ) is 1 kHz, and the carrier frequency (f ｃ The predicted value of iron loss when the inverter is excited under inverter conditions where the frequency (Hz) is 20 kHz and the modulation factor (m) is 0.4 was calculated using inverter iron loss prediction formula (9).

[0136] The relationship between the median diameter and the predicted value of iron loss is shown in Figure 19. In the graph of Figure 19, the horizontal axis represents the median diameter (D ５０ ) The vertical axis represents the predicted value of iron loss ([W ｉｎｖ In the graph of FIG. 19, there is a median diameter at which the predicted value of iron loss is minimum. The minimum predicted value of iron loss is [W ｉｎｖ ] ｍｉｎ It is expressed as:

[0137] Here, it is assumed that the predicted value of iron loss is allowed to increase by about 3% from its minimum value. The value that increases by 3% from the minimum predicted value of iron loss is represented by [W ｉｎｖ ] ｍｉｎ The range of the median diameter for keeping the predicted value of iron loss within the allowable range is the range of the median diameter when the predicted value of iron loss increases by no more than 3% from its minimum value, and D ５０＿ｒ 19, it can be seen that the allowable range of the median diameter is 46 μm to 113 μm. This range of median diameter may be referred to as a guideline for designing materials for forming a powder magnetic core.

[0138] <Example 3> Powder magnetic cores were prepared by compacting material powders having various median diameters. The powder magnetic cores using material powders having each median diameter were measured for the excitation magnetic flux density (B １ ) is 1.0T, and the frequency of the modulating wave (f １ ) is 1 kHz, and the carrier frequency (f ｃThe predicted value of iron loss when inverter excitation is performed under inverter conditions where the frequency (Hz) is 20 kHz and the modulation factor (m) is 0.4 or 0.6 was calculated using inverter iron loss prediction formula (9). The predicted value of iron loss was calculated for each of the cases where the modulation factor (m) is 0.4 and where the modulation factor (m) is 0.6. In addition, the predicted value of iron loss when sinusoidal excitation is used instead of inverter excitation was calculated using iron loss prediction formula (6) that does not include harmonic iron loss.

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

[0140] The minimum predicted value of iron loss when sinusoidal excitation is IL on the vertical axis. ｍｉｎ＿ｓｉｎ The minimum predicted value of iron loss when the inverter is excited with a modulation factor (m) of 0.4 is expressed as IL ｍｉｎ＿ｍ０．４ The minimum predicted value of iron loss when the inverter is excited with a modulation factor (m) of 0.6 is IL ｍｉｎ＿ｍ０．６ The median diameter (D ５０ ) changes. This change in median diameter may be used as a guideline for designing materials for forming a powder magnetic core.

[0141] Example 4 The same test dust core as in Example 1 was subjected to an excitation magnetic flux density (B １ ) is 0.5T, and the frequency of the modulating wave (f １ ) is 400 Hz, and the carrier frequency (f ｃThe actual measured values ​​and predicted values ​​of inverter iron loss were obtained when the inverter was excited under the inverter conditions that the frequency (W) was 20 kHz and the modulation factor (m) was 0.4. Fig. 21 shows a scatter diagram in which points representing the relationship between the actual measured values ​​and predicted values ​​of inverter iron loss obtained under the above conditions are added as solid triangles to the scatter diagram of Fig. 18 shown in Example 1. The actual measured values ​​of iron loss (W ｉｎｖ ) and predicted value ([W ｉｎｖ ]), the point is located on the line that shows the proportional relationship between the excitation magnetic flux density (B １ ) other than 1.0 T, the predicted values ​​of inverter iron loss were shown to agree well with the measured values.

[0142] (Inverter iron loss prediction formula taking into account the cross-sectional area of ​​the magnetic core) The prediction formula described above was designed to be able 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 generated when inverter excitation is performed on a powder 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 ​​a cross section that intersects with the magnetic flux that excites the magnetic core. The cross-sectional area of ​​the magnetic core may also be the area of ​​a cross section that is perpendicular to the magnetic path passing through the magnetic core. Below, we will explain how to expand the inverter iron loss prediction formula to a form that takes into account the cross-sectional area of ​​the magnetic core, based on the results of experiments that confirmed the relationship between the iron loss generated in the magnetic core when inverter excitation is performed and the cross-sectional area of ​​the magnetic core.

[0143] A magnetic material obtained by heat-treating a powder compact was prepared as a sample magnetic core to be evaluated for iron loss occurring when inverter excitation was performed. The powder compact was composed of a plurality of iron powder particles 100, as illustrated in FIG. 22 . A pressure of 980 MPa was applied to the powder compact, thereby forming a ring-shaped powder core 200, as illustrated in FIG. 23 . The cross section 210 of the powder core 200 illustrated in FIG. 23 , which intersects with the circumferential direction, has a rectangular shape. The shape of the cross section 210 is not limited to a rectangle, and various other shapes may be used.

[0144] 22 , the eddy currents flowing in the powder core 200 include intragranular eddy currents I1 that flow within the individual iron powder particles 100, and intergranular eddy currents I2 that flow between the iron powder particles 100. The loss due to the intergranular eddy currents I2 is significantly larger than the loss due to the intragranular eddy currents I1. Therefore, the iron loss due to the eddy currents flowing in the powder core 200 depends on the area of ​​the cross section 210 of the powder core 200, i.e., the core cross-sectional area. The core cross-sectional area is represented by S. As samples with different core cross-sectional areas S, multiple powder cores 200 with different heights H of the cross sections 210 were produced.

[0145] Harmonic eddy current loss W ｈａｒ．ｅ is the element p due to eddy current loss when the second term on the right side of the above-mentioned equation (9) is expanded. ｅ Using terms including p, it is expressed by the following equation (14). ｅ = 4γ ２ ・m －３．２８ , and γ=0.093.

[0146]

[0147] Sinusoidal eddy current loss W in powder magnetic core １．ｅ is the eddy current loss in the grain W １．ｅ＿ｉｎｔｒａ and inter-particle eddy current loss W １．ｅ＿ｉｎｔｅｒ That is, it is calculated by the following formula (15).

[0148]

[0149] Sinusoidal eddy current loss in grains W １．ｅ＿ｉｎｔｒａ is calculated by the following formula (16): ５０ is the median diameter of iron powder 100, and C ４ is a constant, and ρ ｉｎｔｒａ is the resistivity within the particle, and D ｐ is the core density.

[0150]

[0151] Sinusoidal inter-particle eddy current loss W １．ｅ＿ｉｎｔｅｒ is calculated by the following formula (17): ５ is a constant, and ρ ｉｎｔｅｒ is the resistivity of the entire magnetic core.

[0152]

[0153] Here, the median diameter D of the iron powder 100 ５０ It is assumed that the square of is proportional to the cross-sectional area of ​​the iron powder 100. The above equations (15), (16) and (17) are used to calculate W included in the above equation (6). １．ｅ = β(f １ ・B １ ) ２ By applying this relation to the above equation and rearranging it, the eddy current loss coefficient β is derived as shown in the following equation (18).

[0154]

[0155] In order to verify the possibility that the inter-particle eddy current loss changes with the change in cross-sectional area, D in Equation (18) ５０ and ρ ｉｎｔｒａ and ρ ｉｎｔｅｒ Assuming that and are constant, the eddy current loss coefficient β is expressed as a linear function of S as shown in the following equation (19).

[0156]

[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 in powder cores made with four different heights was measured. The powder cores used to measure the eddy current loss were four types of test powder cores made by pressing a powder compact made of an 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 is 38 mm in common, and the inner diameter is 25 mm in common. The heights of the four test powder cores are 4 mm, 6 mm, 10 mm, and 18 mm, respectively. The cross-sectional areas of the four test powder cores are 25 mm ２ , 38mm ２ , 64mm ２ , and 116 mm ２ is.

[0158] The eddy current loss coefficient β is calculated from the measured values ​​of eddy current loss when sinusoidal excitation is performed on the powder core. Fig. 24 shows a scatter diagram illustrating an example of the relationship between the value of β calculated from the measured values ​​of 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 regression analysis on the four points plotted in the scatter diagram, the coefficients when the relationship with the cross-sectional area S of the powder core is approximated by equation (19) are a = 0.325 and b = 7.25 × 10 －６ It was calculated that:

[0159] Here, the eddy current loss coefficient β expressed by the formula (19) is applied to the formula (14) to obtain the eddy current loss W of the harmonic ｈａｒ．ｅ The predicted value of the eddy current loss of the harmonic was [W ｈａｒ．ｅ ] is calculated by measuring the harmonic loss W ｈａｒ The measured value of eddy current loss is W ｈａｒ．ｅ When compared with the above, it was found that the prediction accuracy of harmonic eddy current loss was low. One of the reasons for the low prediction accuracy of harmonic eddy current loss is the eddy current loss coefficient β. Specifically, assuming that the eddy current loss coefficient β depends on the material but not on the excitation conditions, it is expressed as in the above-mentioned equation (19). In other words, applying the same value for the eddy current loss coefficient β to both the sine wave excitation and the inverter excitation is one of the reasons for the low prediction accuracy of harmonic eddy current loss.

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

[0161] In the inverter iron loss prediction formula that takes into account the cross-sectional area S of the powder magnetic core, the harmonic eddy current loss coefficient β ｈａｒ The inverter iron loss prediction equation to which the above formula is applied is expressed as the following formula (20).

[0162]

[0163] Harmonic eddy current loss coefficient β ｈａｒ is the sinusoidal eddy current loss coefficient β ｓｉｎ , that is, in accordance with the form of β expressed in equation (19), it is expressed as the following equation (21).

[0164]

[0165] The harmonic eddy current loss coefficient β was calculated from the measured eddy current loss when inverter excitation was performed on the powder magnetic core. ｈａｒ 25 shows the β calculated from the measured values ​​of eddy current loss when inverter excitation was performed on powder magnetic cores manufactured with four different heights. ｈａｒ A scatter diagram showing an example of the relationship between the value of and the cross-sectional area S of the powder magnetic core is shown. By performing a simple regression analysis on the four points plotted in the scatter diagram, the coefficients when the relationship with the cross-sectional area S of the powder magnetic core is approximated by equation (21) are a' = 0.860 and b' = 2.02 × 10 －６ It was calculated that:

[0166] Here, β included in equation (20) ｓｉｎ Applying β in equation (19) to ｈａｒ to β in equation (21) ｈａｒ By applying the above formula, a prediction formula for inverter iron loss with the inverter conditions and the cross-sectional area S of the powder magnetic core as parameters is expressed as the following formula (22).

[0167]

[0168] By incorporating the correlation between the harmonic eddy current loss coefficient and the cross-sectional area of ​​the powder magnetic core into the prediction formula, the phenomenon in which the measured eddy current loss value increases at an accelerated rate as the cross-sectional area of ​​the powder magnetic core increases is reflected in the prediction of harmonic eddy current loss, thereby improving the prediction accuracy of high-frequency eddy current loss.

[0169] Example 5: A test dust core was produced as a magnetic core sample by pressing a powder compact made of an insulating coated pure iron powder having a median diameter of 87.7 μm at 980 MPa. The test dust core had 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 dust core intersecting the circumferential direction was 64 mm. ２ is.

[0170] The actual eddy current iron loss of the test dust core under any sinusoidal excitation condition was actually measured using a sinusoidal iron loss measurement device. The predicted eddy current iron loss of the test dust core under any sinusoidal excitation condition was calculated using the above-mentioned sinusoidal eddy current loss prediction formula (15) and formula (19).

[0171] Figure 26 shows the measured values ​​of sinusoidal eddy current iron loss W １．ｅ and the predicted value [W １．ｅ 26, the horizontal axis represents the measured value W of the sinusoidal eddy current iron loss. １．ｅ The vertical axis represents the predicted value of sinusoidal eddy current iron loss [W １．ｅ ]. The measured value of sinusoidal eddy current iron loss W １．ｅ and the predicted value [W １．ｅ ] and the measured value of the sinusoidal eddy current iron loss W １．ｅ and the predicted value [W １．ｅ ] are in good agreement.

[0172] Example 6 As a magnetic core sample, a test dust core similar to that of Example 5 was produced.

[0173] The actual eddy current iron loss of the test dust core at any PWM parameter was actually measured using an inverter iron loss measurement device. In addition, the predicted value of the eddy current iron loss of the test dust core at any PWM parameter was calculated using the above-mentioned harmonic eddy current loss prediction formula (14) and formula (19).

[0174] Fig. 27 shows the measured values ​​of harmonic eddy current iron loss W ｈａｒ．ｅ and the predicted value [W ｈａｒ．ｅ 27, the horizontal axis represents the measured value W of the harmonic eddy current iron loss.ｈａｒ．ｅ The vertical axis represents the predicted value of harmonic eddy current iron loss [W ｈａｒ．ｅ ]. The measured value of harmonic eddy current iron loss W ｈａｒ．ｅ and the predicted value [W ｈａｒ．ｅ ], there is a roughly proportional relationship between the predicted value [W ｈａｒ．ｅ ] is the actual measurement value W ｈａｒ．ｅ In other words, the prediction accuracy of the harmonic eddy current iron loss is low when β expressed by the formula (19) is used.

[0175] On the other hand, the predicted value of the eddy current iron loss of the test dust core at any PWM parameter is β expressed by equation (19), that is, β ｓｉｎ In addition to this, β ｈａｒ The calculation was performed using the second term on the right side of equation (22) to which the following equation was applied. ｈａｒ．ｅ and the predicted value [W ｈａｒ．ｅ 28, the horizontal axis represents the measured value W of the harmonic eddy current iron loss. ｈａｒ．ｅ The vertical axis represents the predicted value of harmonic eddy current iron loss [W ｈａｒ．ｅ In FIG. 28, the predicted value [W ｈａｒ．ｅ ] is the actual measurement value W ｈａｒ．ｅ This is about 1.07 times the value of β. Compared to the case where prediction is made using only β, ｓｉｎ and β ｈａｒ The prediction accuracy of harmonic eddy current iron loss is high when predicted using β ｈａｒ By applying this to the prediction formula, the prediction accuracy is improved.

[0176] Example 7 As a magnetic core sample, a test dust core similar to that of Example 5 was produced.

[0177] The actual measured value of iron loss, which is the sum of eddy current loss and hysteresis loss of the test dust core at any PWM parameter, was actually measured using an inverter iron loss measuring device. In addition, the predicted value of iron loss of the test dust core at any PWM parameter was calculated using the above-mentioned inverter iron loss prediction formula (22).

[0178] Figure 29 shows the measured values ​​of inverter iron loss W ｉｎｖ and the predicted value [Wｉｎｖ 29, the horizontal axis represents the measured value W of the inverter iron loss. ｉｎｖ The vertical axis represents the predicted value of inverter iron loss [W ｉｎｖ ]. The measured value of inverter iron loss W ｉｎｖ and the predicted value [W ｉｎｖ ] and the actual measured value of inverter iron loss W ｉｎｖ and the predicted value [W ｉｎｖ ] are in good agreement.

[0179] (Summary of inverter iron loss prediction taking into account the cross-sectional area of ​​the magnetic core) As described above, by predicting the inverter iron loss when a powder magnetic core is inverter-excited based additionally on the cross-sectional area of ​​the powder magnetic core, the prediction accuracy of inverter iron loss when the cross-sectional area of ​​the powder magnetic core changes is improved. For example, the inverter iron loss of a powder magnetic core with a large cross-sectional area used in a motor can be predicted with high accuracy using a prediction formula created based on actual measurements of the inverter iron loss of a powder magnetic core sample with a small cross-sectional area.

[0180] The above-mentioned inverter iron loss prediction formula is β when the median diameter of the iron powder, which is the material of the powder magnetic core, is a specific value. ｓｉｎ and β ｈａｒ In other words, a prediction formula for inverter iron loss may be created for each median diameter of iron powder.

[0181] Although the embodiments of the present disclosure have been described based on the drawings and examples, it should be noted that those skilled in the art could make various modifications or alterations based on the present disclosure. Therefore, it should be noted that these modifications and alterations are included within the scope of the present disclosure. For example, the functions included in each component or step can be rearranged so as not to cause logical inconsistencies, and multiple components or steps can be combined or divided into one. The embodiments of the present disclosure can also be realized as a program executed by a processor included in an apparatus or a storage medium on which a program is recorded. It should be understood that these are also included within the scope of the present disclosure.

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

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

[0184] p included in the formula (9) ｈ and p ｅ Regarding p ｈ = u × (γ × m ｓ ) １．６ × (f １ / f ｃ ) ０．６ , and p ｅ = (u × γ × m ｓ ) ２ As shown above, the formula may be formulated so that a coefficient u determined by the type of inverter circuit is used, or the ratio of the exponent of m to the exponent of γ is s. The coefficient u determined by the type of inverter circuit is the frequency of the first harmonic (f ２ ) and carrier frequency (f ｃ ) and γ and s are the magnetic flux density of the first harmonic (B ２ ) and excitation magnetic flux density (B １ ) and the relationship with the formula (B ２ ×f ｃ ) / (B １ ×f １ ) = γ × m ｓ and is a value determined based on the type of inverter circuit in question, or a value calculated based on a prior waveform analysis using a circuit of the same type.

[0185] 1 Information processing system 10 Information processing device (12: processor, 14: storage unit, 16: interface) 20 Excitation device 30 Measuring device

Claims

1. 1. An iron loss evaluation method comprising: a step of predicting, based on a modulation rate and a carrier frequency, iron loss that occurs when a magnetic material is excited with an excitation waveform generated by a PWM inverter controlled by PWM parameters including the modulation rate and a carrier frequency.

2. The iron loss evaluation method according to claim 1 , wherein in the step of predicting the iron loss, the iron loss is predicted based on a ratio of a frequency of a harmonic of the excitation waveform to the carrier frequency.

3. 3. The iron loss evaluation method according to claim 2, wherein in the step of predicting the iron loss, a ratio of a frequency of a harmonic 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.

4. 2. The iron loss evaluation method according to claim 1, wherein in the step of predicting the iron loss, when the magnetic material is a powder magnetic core, the iron loss is predicted further based on a cross-sectional area of ​​the powder magnetic core that intersects with a magnetic flux that excites the powder magnetic core.

5. 2. A low iron loss material design method comprising: a step of designing characteristics of a magnetic material to be designed so that iron loss occurring 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 a result of predicting iron loss occurring when each of at least two types of magnetic materials having mutually different characteristics is excited with an excitation waveform generated by controlling the PWM inverter at the predetermined modulation rate and the predetermined carrier frequency by executing the iron loss evaluation method recited in claim 1.

6. 6. A low iron loss material design method according to claim 5, wherein in the step of designing characteristics of the magnetic material to be designed, a representative dimension of the magnetic material to be designed is designed as a characteristic of the magnetic material to be designed based on results of acquiring iron loss generated when the magnetic material to be designed is excited with a sinusoidal excitation waveform, for each representative dimension of the magnetic material to be designed.

7. the magnetic material to be designed is a powder magnetic core made of soft magnetic powder, 6. The low iron loss material design method according to claim 5, wherein in the step of designing the characteristics of the magnetic material to be designed, a representative dimension of the soft magnetic powder is designed as the characteristic of the magnetic material.

8. 8. The low iron loss material design method according to claim 7, wherein in the step of designing the characteristics of the magnetic material to be designed, a representative dimension of the soft magnetic powder is designed as a characteristic of the magnetic material based on results of acquiring iron loss generated when the powder core is excited with a sinusoidal excitation waveform for each representative dimension of the soft magnetic powder.

9. An iron loss evaluation program that causes a processor to execute the iron loss evaluation method according to any one of claims 1 to 4.

10. A low iron loss material design program that causes a processor to execute the low iron loss material design method according to any one of claims 5 to 8.

11. A low-loss soft magnetic material having characteristics designed by carrying out the low-core-loss material design method according to claim 5 or 6.

12. A low-loss soft magnetic powder having a characteristic dimension designed by carrying out the low iron loss material design method according to claim 7 or 8.