Method for measuring resistivity of permanent magnet cylinder by using alternating current magnetic susceptibility

Abstract

The invention discloses a method for measuring the resistivity of a permanent magnet cylinder by using alternating current magnetic susceptibility. The method comprises the following steps: S1, adjusting input voltages at two ends of a non-inductive resistor under a plurality of set frequencies, and adjusting a phase angle of the non-inductive resistor to be zero; s2, measuring whether there is an induced electromotive force of a sample in a J coil or not under the same condition; s3, obtaining the magnetic moment induced electromotive force of the sample according to the existence of the induced electromotive force of the sample; s4, according to the sample magnetic moment induced electromotive force and the like, orthogonal magnetic susceptibility and in-phase magnetic susceptibility under each set frequency are obtained through calculation; and S5, if the orthogonal magnetic susceptibility included in each AC magnetic susceptibility calculated under each set frequency and corresponding input voltage is in a constant relation with the frequency and the in-phase magnetic susceptibility is in a linear relation with the frequency, according to the same excitation magnetic field intensity effective value and under two different set frequencies, determining that the excitation magnetic susceptibility of each AC magnetic susceptibility is equal to the excitation magnetic field intensity effective value. And the resistivity of the permanent magnet cylinder is obtained by calculating the two alternating-current magnetic susceptibilities and the like. The method is simple and convenient in test operation, accurate in test data and good in repeatability.

Description

Technical Field

[0001] The present application relates to the technical field of resistivity measurement, and in particular, to a method for measuring the resistivity of a permanent magnetic cylinder by utilizing AC magnetic susceptibility. Background Art

[0002] The recommended method for measuring the resistivity of rare earth permanent magnet cylinders is the Van der Pauw method. That is, through the four-point probe technology, a high-precision DC power supply is used to apply the same current I of 1 to 5A to the A, B and B, A contacts twice. AB , test the average induced voltage U of the C and D contacts CD ; Then apply the same current I of 1 to 5A to contacts B, C and C, B twice BC , test the average induced voltage U of contacts A and D AD , referring to the average thickness h of the sample, the resistivity ρ is calculated according to the following formula.

[0003]

[0004] This method requires that the surface of the sample to be tested should be flat, and there should be no rust or stains on the surface and around the sample; it also requires that the four contacts be in good electrical contact during the test, and the contact positions are symmetrically distributed around the sample; at the same time, it requires that the appropriate current value be selected according to the thickness of the sample to be tested and the size of the measured voltage signal. Although too much current will increase the voltage signal, it will also cause the sample to heat up and cause the voltage signal to be unstable. These factors make the test operation difficult and the test data repeatability is poor. Summary of the invention

[0005] The present application provides a method for measuring the resistivity of a permanent magnetic cylinder by using AC magnetic susceptibility, so as to solve the technical problems that the existing resistivity measurement method of a rare earth permanent magnetic cylinder has great difficulty in test operation and poor repeatability of test data.

[0006] This application is implemented through the following scheme:

[0007] A method for measuring the resistivity of a permanent magnetic cylinder using AC magnetic susceptibility is based on a rare earth permanent magnetic cylinder AC magnetic susceptibility measuring instrument, the AC magnetic susceptibility measuring instrument includes an excitation power supply, a phase-locked amplifier, a solenoid constant k h A solenoid, a non-inductive standard resistor connected in series with the solenoid, and an air-core J coil consisting of two concentric and coaxial coils connected in series and reversed, whose coil constant is k m The ref end of the phase-locked amplifier is connected to the original input signal output by the excitation power supply as a reference, the A channel of the phase-locked amplifier is connected to both ends of the sampling resistor to measure the input amplified signal of the solenoid end, and the B channel is connected to both ends of the J coil to measure the induction signal of the J coil, including the steps of:

[0008] S1. Adjust the input voltage across the non-inductive resistor at multiple set frequencies and adjust its phase angle to zero, wherein the input voltage is the input voltage required for the corresponding solenoid to reach a specified effective value of the excitation magnetic field strength at each set frequency, and the set frequency is 111 Hz to 888 Hz;

[0009] S2. Measure the induced electromotive force of the air-core J coil Then, the sample magnetized to saturation is inserted into the center of the J coil, and the induced electromotive force of the J coil containing the sample is measured under the same conditions. The sample is a permanent magnetic cylinder in a residual magnetic state after saturation magnetization;

[0010] S3, according to the induced electromotive force of the hollow J coil The induced electromotive force of coil J when containing the sample The sample magnetic moment induced electromotive force

[0011] S4. Induced electromotive force based on the sample magnetic moment The definitions of total AC magnetic flux, magnetic field intensity M of the sample and magnetic susceptibility are calculated to obtain the orthogonal magnetic susceptibility and in-phase magnetic susceptibility contained in the AC magnetic susceptibility at each set frequency and corresponding input voltage;

[0012] S5. If the orthogonal susceptibility included in each AC susceptibility calculated at each set frequency and corresponding input voltage is in a constant relationship with the frequency, and the in-phase susceptibility is in a linear relationship with the frequency, then the resistivity of the permanent magnet cylinder is calculated based on the two AC susceptibilities calculated at the same effective value of the excitation magnetic field intensity and two different set frequencies, combined with the radius and aspect ratio of the permanent magnet cylinder.

[0013] Furthermore, in step S1, the input voltage is calculated based on a specified effective value of the excitation magnetic field strength, a solenoid constant of the solenoid, and a resistance value of a non-inductive standard resistor.

[0014] Furthermore, the input voltage is calculated according to the specified effective value of the excitation magnetic field strength, the solenoid constant of the solenoid and the resistance value of the non-inductive standard resistor, specifically comprising the steps of:

[0015] Measure the voltage across the non-inductive standard resistor at the set frequency and adjust its phase angle to zero, and get the following formula:

[0016]

[0017] in Represents the phasor form of the input voltage across the non-inductive standard resistor, E′ h is the effective value of the input voltage across the non-inductive standard resistor;

[0018] According to the specified excitation magnetic field strength effective value H' a The effective value of the input voltage across the non-inductive standard resistor E′ is calculated by the solenoid constant of the solenoid and the resistance value of the non-inductive standard resistor. h As the input voltage:

[0019] H′ a = k h E′ h / R 0 (2)

[0020] Among them, k h is the solenoid constant of the solenoid, R 0 is the resistance value of a non-inductive standard resistor.

[0021] Furthermore, the step S2 specifically includes the steps of:

[0022] S21. Measure the induced electromotive force of the air-core J coil

[0023] S22, insert the sample into the center of the J coil, and measure the induced electromotive force of the J coil containing the sample under the same conditions Each has two components as follows:

[0024]

[0025] in, The induced electromotive force phasor form of the air-core J coil is represented by E′ e is the orthogonal component of the induced electromotive force of the air-core J coil, E″ e is the in-phase component of the induced electromotive force of the air-core J coil, It represents the induced electromotive force phasor form of coil J when containing the sample, E′ s is the orthogonal component of the induced electromotive force of coil J when containing the sample, E″ s is the in-phase component of the induced electromotive force of coil J when containing the sample.

[0026] Furthermore, the step S3 specifically includes the steps of:

[0027] S31. Calculate the sample magnetic moment induced electromotive force based on the difference in induced electromotive force of the J coil with and without the sample: That is:

[0028] E′ = E′ s - E′ e (5)

[0029] E″ = E″ s - E″ e (6)

[0030] Among them, E' is the orthogonal component of the induced electromotive force of the sample magnetic moment, and E" is the in-phase component of the induced electromotive force of the sample magnetic moment.

[0031] Furthermore, the step S4 specifically includes the steps of:

[0032] S41. Calculate the total AC magnetic flux φ within one cycle:

[0033]

[0034] Where, f is the set frequency;

[0035] S42, the corresponding J coil constant k is known m , sample volume V s , and the expression of magnetic field intensity M of the corresponding sample is obtained:

[0036]

[0037] in, is the induced electromotive force of the sample magnetic moment, u 0 is the vacuum permeability, H′ a is the effective value of the excitation magnetic field strength;

[0038] S43. Substituting equations (7) and (8) into the definition of AC magnetic susceptibility χ = M / H, we can obtain the orthogonal magnetic susceptibility χ′ and the in-phase magnetic susceptibility χ″ contained in the AC magnetic susceptibility at the set frequency and corresponding input voltage:

[0039] χ′ = E″ / c (9)

[0040] χ″ = E′ / c (10)

[0041] in:

[0042] c = 2πμ 0 f s k m H′ a (11).

[0043] Furthermore, the S5 specifically includes the steps of:

[0044] S51. If the orthogonal magnetic susceptibility included in each AC magnetic susceptibility under each set frequency and corresponding input voltage has a constant relationship with the frequency, and the in-phase magnetic susceptibility has a linear relationship with the frequency, then under the same effective value of the excitation magnetic field intensity and two different set frequencies, the orthogonal magnetic susceptibility and the in-phase magnetic susceptibility included in the two AC magnetic susceptibilities are calculated respectively;

[0045] S52. According to the orthogonal magnetic susceptibility and the in-phase magnetic susceptibility included in the two AC magnetic susceptibilities, the radius of the permanent magnetic cylinder, and the aspect ratio, the resistivity of the permanent magnetic cylinder is calculated:

[0046]

[0047] Among them, x″ 1 To set the frequency f 1 The in-phase susceptibility contained in the AC susceptibility obtained under 2 To set the frequency f 2 The in-phase susceptibility contained in the AC susceptibility obtained under the condition, γ is the aspect ratio of the permanent magnetic cylinder, and γ = l s / (2r s ), l s is the length of the permanent magnetic cylinder, r s is the radius of the permanent magnetic cylinder, N m (γ,0) is the magnetometer demagnetization factor of a uniformly magnetized cylinder, and χ′ is the magnetometer demagnetization factor of a permanent magnetic cylinder of the same material at a set frequency f 1 and f 2 The orthogonal magnetic susceptibility included in the obtained AC magnetic susceptibility is a constant.

[0048] Furthermore, the orthogonal magnetic susceptibility included in each AC magnetic susceptibility at each set frequency and corresponding input voltage and the frequency presenting a constant relationship specifically refers to:

[0049] The error between the value of the orthogonal magnetic susceptibility included in each AC magnetic susceptibility at each set frequency and corresponding input voltage and a constant is less than a set threshold value;

[0050] If the in-phase magnetic susceptibility contained in each AC magnetic susceptibility at each set frequency and corresponding input voltage has a linear relationship with the frequency, it specifically means:

[0051] The line connecting the in-phase magnetic susceptibility included in each AC magnetic susceptibility at each set frequency and corresponding input voltage is a straight line.

[0052] Furthermore, the permanent magnet cylinder is a rare earth permanent magnet cylinder, including a neodymium iron boron permanent magnet cylinder and a samarium cobalt permanent magnet cylinder.

[0053] Furthermore, the resistance value of the non-inductive standard resistor ranges from 30 to 100 mΩ.

[0054] Compared with the prior art, this application has the following beneficial effects:

[0055] The present application provides a method for measuring the resistivity of a permanent magnetic cylinder using AC magnetic susceptibility. The method can control the excitation power supply to input the same voltage at different low frequencies and the phase-locked amplifier to ensure that the corresponding phase angle is 0, so as to facilitate obtaining the induced voltage of the corresponding coil. Through the calculation formula of the resistivity, the resistivity of the material with low magnetic susceptibility can be obtained quickly, efficiently and accurately, and the measurement of the AC magnetic susceptibility of the permanent magnetic cylinder at different frequencies can be achieved, and the calculation of the resistivity can be completed. The method can realize fast and accurate detection of the resistivity of the permanent magnetic cylinder under the residual magnetic state after saturation magnetization. At the same time, the method is a non-contact measurement, which can reduce the requirements of the existing four-probe DC method (or Van der Pauw method) on the contact points on the sample surface, as well as the difficulty of the test signal being unstable due to excessive current. The test speed is fast and accurate, and the test accuracy and repeatability will be improved. In addition, the equipment required for the method is simple in structure and easy to operate.

[0056] In addition to the above-described purposes, features and advantages, the present application also has other purposes, features and advantages. The present application will be further described in detail with reference to the drawings. BRIEF DESCRIPTION OF THE DRAWINGS

[0057] The drawings constituting a part of the present application are used to provide a further understanding of the present application. The illustrative embodiments of the present application and their descriptions are used to explain the present application and do not constitute an improper limitation on the present application.

[0058] Figure 1 It is a flow chart of a method for measuring the resistivity of a permanent magnetic cylinder using AC magnetic susceptibility according to a preferred embodiment of the present application.

[0059] Figure 2 It is a schematic diagram of the principle of the rare earth permanent magnet cylinder AC magnetic susceptibility measuring instrument of the preferred embodiment of the present application.

[0060] Figure 3 This is a schematic diagram of a lock-in amplifier display.

[0061] Figure 4 It is a schematic diagram of demagnetization factor.

[0062] Figure 5 This is a schematic diagram of the relationship between the orthogonal and in-phase magnetic susceptibility and frequency of NdFeB permanent magnet cylindrical samples.

[0063] Figure 6 This is a schematic diagram of the relationship between the orthogonal and in-phase magnetic susceptibility and frequency of samarium cobalt permanent magnet cylindrical samples.

[0064] In the figure: 1. Excitation power supply; 2. Lock-in amplifier; 3. Non-inductive standard resistor; 4. Solenoid; 5. Sample; 6. J coil. DETAILED DESCRIPTION

[0065] The embodiments of the present application are described in detail below in conjunction with the accompanying drawings, but the present application can be implemented in a variety of different ways defined and covered below.

[0066] like Figure 1 As shown, the preferred embodiment of the present application provides a method for measuring the resistivity of a permanent magnetic cylinder using AC magnetic susceptibility, based on a rare earth permanent magnetic cylinder AC magnetic susceptibility measuring instrument, such as Figure 2 As shown, the AC magnetic susceptibility measuring instrument includes an excitation power supply 1, a phase-locked amplifier 2, a solenoid constant k h The solenoid 4 is provided with a non-inductive standard resistor 3 connected in series with the solenoid 4. The solenoid 4 is inserted with a hollow J coil 6 consisting of two concentric and coaxial coils connected in series and reversely connected. The coil constant is k m The ref end of the phase-locked amplifier is connected to the original input signal output by the excitation power supply as a reference, the A channel of the phase-locked amplifier is connected to both ends of the sampling resistor to measure the input amplified signal of the solenoid end, and the B channel is connected to both ends of the J coil to measure the induction signal of the J coil, including the steps of:

[0067] S1. Adjust the input voltage across the non-inductive resistor at multiple set frequencies and adjust its phase angle to zero, wherein the input voltage is the input voltage required for the corresponding solenoid to reach a specified effective value of the excitation magnetic field strength at each set frequency, and the set frequency is 111 Hz to 888 Hz;

[0068] S2. Measure the induced electromotive force of the air-core J coil Then, the sample magnetized to saturation is inserted into the center of the J coil, and the induced electromotive force of the J coil containing the sample is measured under the same conditions. The sample is a permanent magnetic cylinder in a residual magnetic state after saturation magnetization;

[0069] S3, according to the induced electromotive force of the hollow J coil The induced electromotive force of coil J when containing the sample The sample magnetic moment induced electromotive force

[0070] S4. Induced electromotive force based on the sample magnetic moment The definitions of total AC magnetic flux, magnetic field intensity M of the sample and magnetic susceptibility are calculated to obtain the orthogonal magnetic susceptibility and in-phase magnetic susceptibility contained in the AC magnetic susceptibility at each set frequency and corresponding input voltage;

[0071] S5. If the orthogonal susceptibility included in each AC susceptibility calculated at each set frequency and corresponding input voltage is in a constant relationship with the frequency, and the in-phase susceptibility is in a linear relationship with the frequency, then the resistivity of the permanent magnet cylinder is calculated based on the two AC susceptibilities calculated at the same effective value of the excitation magnetic field intensity and two different set frequencies, combined with the radius and aspect ratio of the permanent magnet cylinder.

[0072] The present embodiment provides a method for measuring the resistivity of a permanent magnetic cylinder using AC magnetic susceptibility. The method can control the excitation power supply to input the same voltage at different low frequencies and the phase-locked amplifier to ensure that the corresponding phase angle is 0, so as to obtain the induced voltage of the corresponding coil conveniently. Through the calculation formula of the resistivity, the resistivity of the material with low magnetic susceptibility can be obtained quickly, efficiently and accurately, and the measurement of the AC magnetic susceptibility of the permanent magnetic cylinder at different frequencies can be achieved, and the calculation of the resistivity can be completed. The method can realize fast and accurate detection of the resistivity of the permanent magnetic cylinder under the residual magnetic state after saturation magnetization. At the same time, the method is a non-contact measurement, which can reduce the requirements of the existing four-probe DC method (or Van der Pauw method) on the contact points of the sample surface, and the difficulty of the test signal being unstable due to excessive current. The test speed is fast and accurate, and the test accuracy and repeatability will be improved. In addition, the equipment required for the method is simple in structure and easy to operate.

[0073] Wherein, in step S1, the input voltage is calculated according to the specified effective value of the excitation magnetic field intensity, the solenoid constant of the solenoid and the resistance value of the non-inductive standard resistor.

[0074] Specifically, the input voltage is calculated according to the specified effective value of the excitation magnetic field strength, the solenoid constant of the solenoid and the resistance value of the non-inductive standard resistor, and specifically includes the steps of:

[0075] Measure the voltage across the non-inductive standard resistor at the set frequency and adjust its phase angle to zero, and get the following formula:

[0076]

[0077] in Represents the phasor form of the input voltage across the non-inductive standard resistor, E′ h is the effective value of the input voltage across the non-inductive standard resistor;

[0078] According to the specified excitation magnetic field strength effective value H' a The effective value of the input voltage across the non-inductive standard resistor E′ is calculated by the solenoid constant of the solenoid and the resistance value of the non-inductive standard resistor. h As the input voltage:

[0079] H′ a = k h E′h / R 0 (2)

[0080] Among them, k h is the solenoid constant of the solenoid, R 0 is the resistance value of a non-inductive standard resistor.

[0081] Preferably, the step S2 specifically comprises the steps of:

[0082] S21. Measure the induced electromotive force of the air-core J coil

[0083] S22, insert the sample into the center of the J coil, and measure the induced electromotive force of the J coil containing the sample under the same conditions Each has two components as follows:

[0084]

[0085] in, The induced electromotive force phasor form of the air-core J coil is represented by E′ e is the orthogonal component of the induced electromotive force of the air-core J coil, E″ e is the in-phase component of the induced electromotive force of the air-core J coil, It represents the induced electromotive force phasor form of coil J when containing the sample, E′ s is the orthogonal component of the induced electromotive force of coil J when containing the sample, E″ s is the in-phase component of the induced electromotive force of coil J when containing the sample.

[0086] In this embodiment, the induced electromotive force is measured under the same conditions when there is a sample in the J coil and when there is no sample. and Induced electromotive force for subsequent sample magnetic moment Provide necessary data preparation.

[0087] Preferably, the step S3 specifically comprises the steps of:

[0088] S31. Calculate the sample magnetic moment induced electromotive force based on the difference in induced electromotive force of the J coil with and without the sample That is:

[0089] E′ = E′ s - E′ e (5)

[0090] E″ = E″ s - E″ e (6)

[0091] Among them, E' is the orthogonal component of the induced electromotive force of the sample magnetic moment, and E" is the in-phase component of the induced electromotive force of the sample magnetic moment.

[0092] In this embodiment, the sample magnetic moment induced electromotive force is calculated based on the difference in induced electromotive force of the J coil when there is a sample and when there is no sample. Provide necessary data preparation for the subsequent calculation of the orthogonal susceptibility and in-phase susceptibility included in the AC susceptibility at the set frequency and corresponding input voltage.

[0093] Preferably, the step S4 specifically comprises the steps of:

[0094] S41. Calculate the total AC magnetic flux φ within one cycle:

[0095]

[0096] Where, f is the set frequency;

[0097] S42, the corresponding J coil constant k is known m , sample volume V s , and the expression of magnetic field intensity M of the corresponding sample is obtained:

[0098]

[0099] in, is the induced electromotive force of the sample magnetic moment, u 0 is the vacuum permeability, H′ a is the effective value of the excitation magnetic field strength;

[0100] S43. Substituting equations (7) and (8) into the definition of AC magnetic susceptibility χ = M / H, we can obtain the orthogonal magnetic susceptibility χ′ and the in-phase magnetic susceptibility χ″ contained in the AC magnetic susceptibility at the set frequency and corresponding input voltage:

[0101] χ′ = E″ / c (9)

[0102] χ″ = E′ / c (10)

[0103] in:

[0104] c = 2πμ 0 f s k m H′ a (11).

[0105] This embodiment uses the definition of total AC magnetic flux, AC magnetic susceptibility, magnetic field strength of the corresponding sample and sample magnetic moment induced electromotive force The orthogonal susceptibility and in-phase susceptibility included in the AC susceptibility at the set frequency and corresponding input voltage are obtained jointly.

[0106] Furthermore, the S5 specifically includes the steps of:

[0107] S51. If the orthogonal magnetic susceptibility included in each AC magnetic susceptibility under each set frequency and corresponding input voltage has a constant relationship with the frequency, and the in-phase magnetic susceptibility has a linear relationship with the frequency, then under the same effective value of the excitation magnetic field intensity and two different set frequencies, the orthogonal magnetic susceptibility and the in-phase magnetic susceptibility included in the two AC magnetic susceptibilities are calculated respectively;

[0108] S52. According to the orthogonal magnetic susceptibility and the in-phase magnetic susceptibility included in the two AC magnetic susceptibilities, the radius of the permanent magnetic cylinder, and the aspect ratio, the resistivity of the permanent magnetic cylinder is calculated:

[0109]

[0110] Among them, x″ 1 To set the frequency f 1 The in-phase susceptibility, x, included in the AC susceptibility obtained under 2 To set the frequency f 2 The in-phase susceptibility contained in the AC susceptibility obtained under the condition, γ is the aspect ratio of the permanent magnetic cylinder, and γ = l s / (2r s ), l s is the length of the permanent magnetic cylinder, r s is the radius of the permanent magnetic cylinder, N m (γ,0) is the magnetometer demagnetization factor of a uniformly magnetized cylinder, and χ′ is the magnetometer demagnetization factor of a permanent magnetic cylinder of the same material at a set frequency f 1 and f 2 The orthogonal magnetic susceptibility included in the obtained AC magnetic susceptibility is a constant.

[0111] In this embodiment, under the condition that there is a constant orthogonal magnetic susceptibility at low frequency and an in-phase magnetic susceptibility that is linearly related to the frequency, the set frequency f is measured at the same effective value of the excitation magnetic field intensity H′a. 1 The in-phase susceptibility x″ contained in the AC susceptibility obtained under 1 , set frequency f 2 The in-phase susceptibility x″ contained in the AC susceptibility obtained under 2 , the resistivity ρ of the permanent magnetic cylinder can be calculated by formula (12). The reason why the resistivity of the permanent magnetic cylinder can only be calculated by formula (12) under the premise that there is a constant orthogonal magnetic susceptibility and an in-phase magnetic susceptibility that is linearly related to the frequency at low frequency is that the magnetic properties of general permanent magnetic materials such as NdFeB are generally reflected in the axial direction, while the magnetic field in the orthogonal direction does not change much.

[0112] Among them, N m (γ,0) is the magnetometer demagnetization factor of a uniformly magnetized cylinder, see Figure 4 The schematic diagram of the demagnetization factor coefficient is shown, which is obtained by looking up the table according to the current aspect ratio γ and the magnetic susceptibility x.

[0113] Specifically, the orthogonal magnetic susceptibility included in each AC magnetic susceptibility at each set frequency and corresponding input voltage and the frequency present a constant relationship specifically means:

[0114] The error between the value of the orthogonal magnetic susceptibility included in each AC magnetic susceptibility at each set frequency and corresponding input voltage and a constant is less than a set threshold value;

[0115] If the in-phase magnetic susceptibility contained in each AC magnetic susceptibility at each set frequency and corresponding input voltage has a linear relationship with the frequency, it specifically means:

[0116] The line connecting the in-phase magnetic susceptibility included in each AC magnetic susceptibility at each set frequency and corresponding input voltage is a straight line.

[0117] Preferably, the permanent magnet cylinder is a rare earth permanent magnet cylinder, including a neodymium iron boron permanent magnet cylinder, a samarium cobalt permanent magnet cylinder, and the like.

[0118] Preferably, the resistance value range of the non-inductive standard resistor is 30 to 100 mΩ. The purpose is: the general resistance should not be too large to prevent excessive current and heat. At the same time, in order to meet the requirement of not crossing the level within the 200 mV range of the phase-locked amplifier, a resistance of 30 to 100 mΩ can be selected. If the resistance is too small, phase shift is likely to occur, so it cannot be too small either.

[0119] In another preferred embodiment of the present application, standard NdFeB and SmCo cylindrical samples with a diameter of 10 mm and a height of 10 mm are selected for analysis and measurement. The entire measurement experiment uses a computer display, an excitation power supply, a lock-in amplifier, and an excitation test coil.

[0120] The lock-in amplifier, also known as the phase detector, measures the in-phase and quadrature components of the fundamental voltage (rated voltage or voltage RMS) and is a device that can extract the amplitude and phase information of weak signals in an extremely noisy environment. In this embodiment, we will calculate the signal feedback of the A channel (input end) and the B channel (sensing output end) of the lock-in amplifier at different reference frequencies.

[0121] The ref end of the lock-in amplifier is connected to the original input signal as a reference, the A channel is used to measure the input amplified signal at the solenoid end, and the B channel is used to measure the induction signal of the magnetic moment coil.

[0122] In this embodiment, we select a 50mΩ non-inductive standard resistor as the load to collect the input voltage signal, and determine the current solenoid coil constant k according to the calibration method of the solenoid coil constant. h 1119.63m-1 , the same J coil constant k m 1243Wb / m 3 / T(or m -1 ). In the experiment, standard NdFeB permanent magnet cylinders and SmCo permanent magnet cylinders were first magnetized and then the external field was removed to make the samples in a remanent magnetic state.

[0123] Based on the above preparation, the subsequent specific steps of this method include:

[0124] A. Set the effective value H'a of the excitation magnetic field strength generated by the solenoid to 4000Am, and calculate the corresponding input voltage E' according to formulas (1) and (2): h Need to be fixed at 125.88mV, this voltage E' h Refers to the voltage value that the corresponding solenoid needs to reach at different frequencies.

[0125] B. Connect the reference terminal (ref) of the phase-locked amplifier to the input terminal of the excitation power supply, connect channel A to both ends of the sampling resistor, and connect channel B to both ends of the J coil.

[0126] C. Set the test frequency. In this embodiment, the test is performed at 111Hz, 222Hz, 444Hz, and 888Hz respectively. The input voltage signal at both ends of the non-inductive standard resistor is controlled to reach the required voltage value of 125.88mV by adjusting the output frequency and output voltage of the excitation power supply. During operation, the phase angle of the phase-locked amplifier needs to be rotated so that the phase angle of the input voltage signal is close to 0. The input interface of the phase-locked amplifier is as follows: Figure 3 In the figure, CH-A is the input signal (channel A). During the test, the phase angle of the lock-in amplifier needs to be adjusted to 0, that is, the corresponding "Y" component voltage is close to 0mV.

[0127] D. Measure the induced voltage of the air-core J coil at 111 Hz, 222 Hz, 444 Hz, and 888 Hz, and the induced voltage of the J coil with the sample. According to formulas (9) and (10), the corresponding orthogonal magnetic susceptibility χ′ and in-phase magnetic susceptibility χ″ can be obtained. The corresponding dot-line graph is shown in the figure below: Figure 5 and Figure 6 As shown. Figure 5 and Figure 6 It can be seen that the orthogonal magnetic susceptibility χ′ of the saturated magnetized NdFeB permanent magnet cylinder and SmCo permanent magnet cylinder samples has a constant relationship with the frequency, while their in-phase magnetic susceptibility χ″ has a linear relationship with the frequency.

[0128] E. Based on the above relationship, according to the definition of resistivity ρ in formula (12), refer to the demagnetization factor correction table N m The value of (λ,0) finally results in the resistivity of the NdFeB permanent magnet cylindrical sample being 1.24x10-6 Ωm, the result is similar to the resistivity of general NdFeB, which is usually between 1.2 and 1.6×10 -9 kΩm; the resistivity of the tested SmCo permanent magnet cylindrical sample is 8.05×10 -7 kΩm, and the resistivity of general SmCo permanent magnet cylindrical samples is usually: 8×10 -7 69×10 -7 It is worth noting that the AC method tests the magnetic permeability of the cylinder as the annular resistivity, which is more suitable for the analysis of actual eddy currents.

[0129] The results of the above embodiments also prove that the method for measuring the resistivity of permanent magnetic cylindrical samples with small magnetic susceptibility using AC magnetic susceptibility at low frequencies is feasible.

[0130] Although the preferred embodiments of the present application have been described, those skilled in the art may make other changes and modifications to these embodiments once they have learned the basic creative concept. Therefore, the appended claims are intended to be interpreted as including the preferred embodiments and all changes and modifications falling within the scope of the present application.

[0131] Obviously, those skilled in the art can make various changes and modifications to the present application without departing from the spirit and scope of the present application. Thus, if these modifications and variations of the present application fall within the scope of the claims of the present application and their equivalents, the present application is also intended to include these modifications and variations.

Claims

1. A method for measuring the resistivity of a permanent magnetic cylinder using AC magnetic susceptibility, based on a rare earth permanent magnetic cylinder AC magnetic susceptibility measuring instrument, the AC magnetic susceptibility measuring instrument comprising an excitation power supply, a phase-locked amplifier, a solenoid constant k h A solenoid, a non-inductive standard resistor connected in series with the solenoid, and an air-core J coil consisting of two concentric and coaxial coils connected in series and reversed, whose coil constant is k m The ref end of the phase-locked amplifier is connected to the original input signal output by the excitation power supply as a reference, the A channel of the phase-locked amplifier is connected to both ends of the sampling resistor to measure the input amplified signal at the solenoid end, and the B channel is connected to both ends of the J coil to measure the induction signal of the J coil, characterized in that: Includes steps: S1. Adjust the input voltage across the non-inductive resistor at multiple set frequencies and adjust its phase angle to zero, wherein the input voltage is the input voltage required for the corresponding solenoid to reach a specified effective value of the excitation magnetic field strength at each set frequency, and the set frequency is 111 Hz to 888 Hz; S2. Measure the induced electromotive force of the air-core J coil Then, the sample magnetized to saturation is inserted into the center of the J coil, and the induced electromotive force of the J coil containing the sample is measured under the same conditions. The sample is a permanent magnetic cylinder in a residual magnetic state after saturation magnetization; S3, according to the induced electromotive force of the hollow J coil The induced electromotive force of coil J when containing the sample The sample magnetic moment induced electromotive force S4. Induced electromotive force based on the sample magnetic moment The definitions of total AC magnetic flux, magnetic field intensity M of the sample and magnetic susceptibility are calculated to obtain the orthogonal magnetic susceptibility and in-phase magnetic susceptibility contained in the AC magnetic susceptibility at each set frequency and corresponding input voltage; S5. If the orthogonal susceptibility included in each AC susceptibility calculated at each set frequency and corresponding input voltage is in a constant relationship with the frequency, and the in-phase susceptibility is in a linear relationship with the frequency, then the resistivity of the permanent magnet cylinder is calculated based on the two AC susceptibilities calculated at the same effective value of the excitation magnetic field intensity and two different set frequencies, combined with the radius and aspect ratio of the permanent magnet cylinder.

2. The method for measuring the resistivity of a permanent magnetic cylinder using AC magnetic susceptibility according to claim 1, characterized in that: In step S1, the input voltage is calculated according to a specified effective value of the excitation magnetic field strength, a solenoid constant of the solenoid, and a resistance value of a non-inductive standard resistor.

3. The method for measuring the resistivity of a permanent magnetic cylinder using AC magnetic susceptibility according to claim 2, characterized in that: The input voltage is calculated according to the specified effective value of the excitation magnetic field strength, the solenoid constant of the solenoid and the resistance value of the non-inductive standard resistor, and specifically includes the steps of: Measure the voltage across the non-inductive standard resistor at the set frequency and adjust its phase angle to zero, and get the following formula: in Represents the phasor form of the input voltage across the non-inductive standard resistor, E′ h is the effective value of the input voltage across the non-inductive standard resistor; According to the specified excitation magnetic field strength effective value H' a The effective value of the input voltage across the non-inductive standard resistor E′ is calculated by the solenoid constant of the solenoid and the resistance value of the non-inductive standard resistor. h As the input voltage: H′ a =k h IS' h / R0 (2) Among them, k h is the solenoid constant of the solenoid, and R0 is the resistance value of the non-inductive standard resistor.

4. The method for measuring the resistivity of a permanent magnetic cylinder using AC magnetic susceptibility according to claim 3, characterized in that: The step S2 specifically includes the following steps: S21. Measure the induced electromotive force of the air-core J coil S22, insert the sample into the center of the J coil, and measure the induced electromotive force of the J coil containing the sample under the same conditions Each has two components as follows: in, The induced electromotive force phasor form of the air-core J coil is represented by E′ e is the orthogonal component of the induced electromotive force of the air-core J coil, E″ e is the in-phase component of the induced electromotive force of the air-core J coil, It represents the induced electromotive force phasor form of coil J when containing the sample, E′ s is the orthogonal component of the induced electromotive force of coil J when containing the sample, E″ s is the in-phase component of the induced electromotive force of coil J when containing the sample.

5. The method for measuring the resistivity of a permanent magnetic cylinder using AC magnetic susceptibility according to claim 4, characterized in that: The step S3 specifically comprises the following steps: S31. Calculate the sample magnetic moment induced electromotive force based on the difference in induced electromotive force of the J coil with and without the sample: That is: E′=E′ s -AND' e (5) E″=E″ s -AND" e (6) Among them, E' is the orthogonal component of the induced electromotive force of the sample magnetic moment, and E" is the in-phase component of the induced electromotive force of the sample magnetic moment.

6. The method for measuring the resistivity of a permanent magnetic cylinder using AC magnetic susceptibility according to claim 5, characterized in that: The step S4 specifically comprises the following steps: S41. Calculate the total AC magnetic flux φ within one cycle: Where, f is the set frequency; S42, the corresponding J coil constant k is known m , sample volume V s , and the expression of magnetic field intensity M of the corresponding sample is obtained: in, is the induced electromotive force of the sample magnetic moment, u0 is the vacuum magnetic permeability, H′ a is the effective value of the excitation magnetic field strength; S43. Substituting equations (7) and (8) into the definition of AC magnetic susceptibility χ = M / H, we can obtain the orthogonal magnetic susceptibility χ′ and the in-phase magnetic susceptibility χ″ contained in the AC magnetic susceptibility at the set frequency and corresponding input voltage: χ′=E″ / c (9) χ″=E′ / c (10) in: c=2πμ0fV s k m H′ a (11)。 7. The method for measuring the resistivity of a permanent magnetic cylinder using AC magnetic susceptibility according to claim 6, characterized in that: The S5 specifically includes the steps of: S51. If the orthogonal magnetic susceptibility included in each AC magnetic susceptibility under each set frequency and corresponding input voltage has a constant relationship with the frequency, and the in-phase magnetic susceptibility has a linear relationship with the frequency, then under the same effective value of the excitation magnetic field intensity and two different set frequencies, the orthogonal magnetic susceptibility and the in-phase magnetic susceptibility included in the two AC magnetic susceptibilities are calculated respectively; S52. According to the orthogonal magnetic susceptibility and the in-phase magnetic susceptibility included in the two AC magnetic susceptibilities, the radius of the permanent magnetic cylinder, and the aspect ratio, the resistivity of the permanent magnetic cylinder is calculated: Wherein, x″1 is the in-phase susceptibility contained in the AC susceptibility obtained at the set frequency f1, x″2 is the in-phase susceptibility contained in the AC susceptibility obtained at the set frequency f2, γ is the aspect ratio of the permanent magnetic cylinder, and γ=l s / (2r s ), l s is the length of the permanent magnetic cylinder, r s is the radius of the permanent magnetic cylinder, N m (γ,0) is the magnetometer demagnetization factor of the uniformly magnetized cylinder, and χ′ is the orthogonal susceptibility contained in the AC susceptibility obtained by the permanent magnetic cylinder of the same material at the set frequencies f1 and f2, and the orthogonal susceptibility is a constant.

8. The method for measuring the resistivity of a permanent magnetic cylinder using AC magnetic susceptibility according to claim 1 or 7, characterized in that: The orthogonal magnetic susceptibility included in each AC magnetic susceptibility at each set frequency and corresponding input voltage has a constant relationship with the frequency, which specifically means: The error between the value of the orthogonal magnetic susceptibility included in each AC magnetic susceptibility at each set frequency and corresponding input voltage and a constant is less than a set threshold value; If the in-phase magnetic susceptibility contained in each AC magnetic susceptibility at each set frequency and corresponding input voltage has a linear relationship with the frequency, it specifically means: The line connecting the in-phase magnetic susceptibility included in each AC magnetic susceptibility at each set frequency and corresponding input voltage is a straight line.

9. The method for measuring the resistivity of a permanent magnetic cylinder using AC magnetic susceptibility according to claim 1, characterized in that: The permanent magnet cylinder is a rare earth permanent magnet cylinder, including a neodymium iron boron permanent magnet cylinder and a samarium cobalt permanent magnet cylinder.

10. The method for measuring the resistivity of a permanent magnetic cylinder using AC magnetic susceptibility according to claim 1, characterized in that: The resistance value of the non-inductive standard resistor ranges from 30 to 100 mΩ.

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