Transient electromagnetic field analysis method for non-ferromagnetic abrasive particle motion effect and time-harmonic field coupling

Abstract

The invention discloses a non-ferromagnetic abrasive particle motion effect and time-harmonic field coupled transient electromagnetic field analysis method, and relates to the technical field of three-coil electromagnetic abrasive particle sensor simulation. In order to solve the defect that induced voltage generated by moving abrasive particles cannot be accurately analyzed in the prior art, the technical scheme provided by the invention comprises the following steps: collecting an incident magnetic field vector generated by an excitation coil in a spherical conductor area; eddy current distribution generated by the non-ferromagnetic abrasive particles under the independent action of the exciting coil 1 and the exciting coil 2 is obtained; establishing a magnetic vector potential control equation and performing Fourier transform to obtain a general solution; solving space magnetic vector potential change; calculating equivalent voltage in the induction coil; and integration is carried out on the equivalent excitation source in the non-ferromagnetic abrasive particles, and induced voltage generated when the non-ferromagnetic abrasive particles pass through the sensor is obtained. The method is suitable for high-precision modeling and simulation analysis work of the dynamic induced voltage of the abrasive particles in a non-ferromagnetic abrasive particle online monitoring system.

Description

Technical Field

[0001] This invention relates to the field of simulation technology for three-coil electromagnetic abrasive sensors, and belongs to a transient electromagnetic field analysis method that couples the motion effect of non-ferromagnetic abrasive particles with a time-harmonic field. Background Technology

[0002] Abnormal wear of critical components is a major cause of equipment failure during operation. To improve equipment reliability and reduce maintenance costs, the industry widely adopts online lubricating oil abrasive particle monitoring technology to assess equipment health. This technology determines the degree of component wear by detecting parameters such as the size, material, and concentration of abrasive particles (i.e., metal particles generated by wear) mixed in the lubricating oil, and has become an important means of condition monitoring and fault early warning.

[0003] Among existing abrasive sensors, inductive abrasive sensors are widely used due to their advantages such as non-contact operation, fast response, and suitability for online monitoring. These sensors generally employ a multi-coil structure, with the three-coil structure being the most representative—excitation coils on both sides and an induction coil in the middle. Their basic working principle involves passing a high-frequency current through the excitation coil to create an alternating magnetic field. When an abrasive particle enters the sensor and cuts the magnetic lines of force, an induced voltage change is generated in the induction coil, thereby enabling the identification and parameter estimation of the abrasive particle.

[0004] Currently, many studies have established simulation models of the electromagnetic field of abrasive particles based on the static time-harmonic electromagnetic field theory, which can effectively explain the generation process of induced signals from ferromagnetic abrasive particles. For example, some scholars have analyzed the scattering behavior of ferromagnetic spherical particles under a static magnetic field by modeling, and used the induced voltage response characteristics to distinguish different types of abrasive particles. However, most of these models ignore the motion state of the abrasive particles inside the sensor, and therefore cannot accurately predict the dynamic induced voltage during the motion process.

[0005] Some studies have attempted to introduce motion corrections into time-harmonic fields, such as calculating the induced voltage generated by moving abrasive particles in a static field using Faraday's law of induction. However, this approach remains within the basic framework of static fields, treating only the effects of motion as a correction quantity, and does not construct a complete dynamic model of motion-electromagnetic coupling. Therefore, it suffers from incomplete physical meaning and limited computational accuracy. Especially for non-ferromagnetic abrasive particles, whose induction intensity is weak, the eddy currents they generate are difficult to accurately predict by static models, resulting in insufficient detection sensitivity and a high risk of missed detections.

[0006] In summary, the existing technology has the drawback of failing to construct a transient electromagnetic model that couples the motion of non-ferromagnetic abrasive particles with a time-harmonic electromagnetic field, thus making it impossible to accurately analyze the induced voltage generated by the moving abrasive particles. Summary of the Invention

[0007] To address the shortcomings of existing technologies that fail to construct a transient electromagnetic model coupling non-ferromagnetic abrasive particle motion with a time-harmonic electromagnetic field, thus hindering accurate analysis of the induced voltage generated by the moving abrasive particles, the present invention provides the following technical solution: A transient electromagnetic field analysis method coupling nonferromagnetic abrasive particle motion effect with time-harmonic field includes: The steps for acquiring the incident magnetic field vector generated by the excitation coil within the spherical conductor region; Based on the incident magnetic field vector, the steps are as follows: to obtain the eddy current distribution generated by nonferromagnetic abrasive particles under the individual action of excitation coil 1 and excitation coil 2; The steps are as follows: the internal eddy current of nonferromagnetic abrasive grains is equivalent to a new excitation source, the magnetic vector potential control equation is established and the general solution is obtained by Fourier transform. The steps for solving the spatial magnetic vector potential change by performing inverse Fourier transform using boundary conditions; The steps for calculating the equivalent voltage of an induction coil based on the principle of electromagnetic induction; The step of integrating the equivalent excitation source inside the non-ferromagnetic abrasive grains to obtain the induced voltage generated when the non-ferromagnetic abrasive grains pass through the sensor.

[0008] Furthermore, a preferred embodiment is provided in which the solution of the incident magnetic field vector includes the steps of equivalently converting the air-core cylindrical excitation coil into multiple single-turn circular coils and performing integration.

[0009] Furthermore, a preferred embodiment is provided in which the calculation of the nonferromagnetic abrasive eddy current is based on Ohm's law for a moving conductor, and takes into account the magnitude of the coil current, the coil density, the abrasive velocity, and the spatial position relationship.

[0010] Furthermore, a preferred embodiment is provided in which the magnetic vector potential is constrained to not diverge at ρ=0 and to decay to zero as ρ approaches infinity during the process of obtaining the general solution by performing Fourier transform.

[0011] Furthermore, a preferred embodiment is provided in which the solution of the equivalent voltage in the induction coil is based on the turns density, length and relative position of the abrasive grains of the induction coil, and is integrated in combination with the trend of the change of magnetic vector potential over time.

[0012] Furthermore, a preferred embodiment is provided, which obtains the voltage response curve of the nonferromagnetic abrasive grains after induced voltage and outputs it over time, for dynamic feature recognition under different nonferromagnetic abrasive grain parameters.

[0013] Based on the same inventive concept, this invention also provides a transient electromagnetic field analysis device coupling non-ferromagnetic abrasive particle motion effect with a time-harmonic field, comprising: A module for acquiring the incident magnetic field vector generated by the excitation coil within the spherical conductor region; Based on the incident magnetic field vector, a module is obtained to obtain the eddy current distribution generated by non-ferromagnetic abrasive particles under the individual action of excitation coil 1 and excitation coil 2. The module that treats the internal eddy currents of nonferromagnetic abrasive grains as a new excitation source, establishes the magnetic vector potential control equation, and obtains the general solution by performing Fourier transform. A module that uses boundary conditions to perform inverse Fourier transform to solve for the change in spatial magnetic vector potential; A module that calculates the equivalent voltage in an induction coil based on the principle of electromagnetic induction; A module that integrates the equivalent excitation source inside the non-ferromagnetic abrasive grains to obtain the induced voltage generated when the non-ferromagnetic abrasive grains pass through the sensor.

[0014] Based on the same inventive concept, the present invention also provides a computer storage medium for storing a computer program, wherein when the computer program is read by a computer, the computer executes the method described thereon.

[0015] Based on the same inventive concept, the present invention also provides a computer, including a processor and a storage medium, wherein when the processor reads a computer program stored in the storage medium, the computer executes the method described thereon.

[0016] Based on the same inventive concept, the present invention also provides a computer program product, which, when executed, implements the method described.

[0017] Compared with the prior art, the advantages of the technical solution provided by the present invention are as follows: This approach constructs an analytical model of the transient electromagnetic field under the motion of non-ferromagnetic abrasive particles. By treating the eddy currents induced by the particle motion as a new excitation source and modifying the governing equations, the calculation of the induced voltage more closely reflects the actual physical process. Compared to traditional models based on static time-harmonic fields, this method can more accurately reveal the dynamic coupling relationship between the particle motion and the induced signal, effectively improving the simulation accuracy of the induced voltage of non-ferromagnetic abrasive particles.

[0018] This scheme employs Fourier transform and inverse Fourier transform to solve the governing equations, and constrains the magnetic vector potential distribution through boundary conditions to ensure that the solved physical solution is finite and stable in space. This approach overcomes the problem of numerical divergence caused by inadequate boundary treatment in the magnetic vector potential solution of traditional models, thereby improving the stability and accuracy of the analytical model.

[0019] This approach incorporates the structural characteristics of a three-coil sensor, separately solving for the eddy currents generated by the two excitation coils inside the non-ferromagnetic abrasive grains. The superposition principle is then used to accurately reconstruct the total eddy current field, thus more realistically simulating the disturbance of the sensor's magnetic field by the abrasive grains. This method differs from existing research that simplifies multiple coils to an equivalent single coil, avoiding simplification errors in the magnetic field distribution modeling process and making the model more consistent with the actual device structure.

[0020] This scheme explicitly considers the influence of abrasive material parameters (conductivity, permeability), geometric dimensions, and motion speed on eddy current density and induced voltage. It proposes a time-varying mechanism for the dynamic variable H(t) in the induced voltage expression, achieving time-varying voltage response modeling. Compared to traditional static induced voltage models, this approach better reflects the real-time response characteristics of abrasive particles traversing the sensor region, improving detection accuracy and dynamic tracking capabilities.

[0021] This scheme refines the calculation method of the magnetic vector potential of the excitation coil, modeling the multi-layer coil as a continuously distributed coil that integrates along a rectangular cross-section, effectively reducing the computational complexity caused by double integration. Compared with existing numerical methods based on finite element discrete integration, this analytical approach not only improves simulation efficiency but also reduces the model's dependence on computational resources, making it suitable for rapid simulation and online identification system design requirements.

[0022] It is suitable for high-precision modeling and simulation analysis of dynamic induced voltage of abrasive particles in online monitoring systems for non-ferromagnetic abrasive particles. Attached Figure Description

[0023] Figure 1 This is a schematic diagram of a three-coil abrasive sensor structure; Where Drivecoil1 is the excitation coil 1; Pick-upcoil is an induction coil; Drivecoil2 is the excitation coil 2; The insulation layer is an insulating layer. Wearparticles are abrasive particles; v is the velocity of the abrasive particles; z represents the axial direction of the sensor; The coil frame is the coil skeleton; This is the initial distance between the centroid of the abrasive grain and the left edge of the excitation coil 1; This is the axial distance from the left edge to the right edge of excitation coil 1; This is the total axial distance from the left edge of excitation coil 1 to the right edge of excitation coil 2; L d1The length of excitation coil 1; L p The length of the induction coil; L d2 The length of excitation coil 2; Let the inner and outer radii be the excitation coil 1; Let be the inner and outer radii of the induction coil; Let be the inner and outer radii of the excitation coil 2.

[0024] Figure 2 The flowchart shows the transient electromagnetic field analysis method for coupling the motion effect of nonferromagnetic abrasive particles with time-harmonic fields. Detailed Implementation

[0025] To make the advantages and benefits of the technical solution provided by the present invention clearer, the technical solution provided by the present invention will now be described in further detail with reference to the accompanying drawings, specifically: Implementation Method 1: This implementation method provides a transient electromagnetic field analysis method for the coupling of nonferromagnetic abrasive particle motion effects with time-harmonic fields, including: The steps for acquiring the incident magnetic field vector generated by the excitation coil within the spherical conductor region; Based on the incident magnetic field vector, the steps are as follows: to obtain the eddy current distribution generated by nonferromagnetic abrasive particles under the individual action of excitation coil 1 and excitation coil 2; The steps are as follows: the internal eddy current of nonferromagnetic abrasive grains is equivalent to a new excitation source, the magnetic vector potential control equation is established and the general solution is obtained by Fourier transform. The steps for solving the spatial magnetic vector potential change by performing inverse Fourier transform using boundary conditions; The steps for calculating the equivalent voltage of an induction coil based on the principle of electromagnetic induction; The step of integrating the equivalent excitation source inside the non-ferromagnetic abrasive grains to obtain the induced voltage generated when the non-ferromagnetic abrasive grains pass through the sensor.

[0026] The solution for the incident magnetic field vector includes the steps of equating the air-core cylindrical excitation coil to multiple single-turn circular coils and performing integration.

[0027] The calculation of the nonferromagnetic abrasive eddy current is based on Ohm's law for a moving conductor and takes into account the magnitude of the coil current, the coil density, the abrasive velocity, and the spatial position relationship.

[0028] In the process of obtaining the general solution by performing Fourier transform, the magnetic vector potential is constrained to not diverge at ρ=0 and to decay to zero as ρ approaches infinity.

[0029] The solution for the effective voltage in the induction coil is based on the coil’s turns density, length, and relative position of the abrasive grains, and is integrated in conjunction with the time-varying trend of the magnetic vector potential.

[0030] The voltage response curve of the output after obtaining the induced voltage of nonferromagnetic abrasive particles as a function of time is used for dynamic feature identification under different nonferromagnetic abrasive particle parameters.

[0031] Implementation Method Two: This implementation method is a further detailed description of the technical solution provided in Implementation Method One, specifically: A transient electromagnetic field analysis method for coupling nonferromagnetic abrasive particle motion effect with time-harmonic field is proposed, applicable to inductive abrasive sensor with a three-coil structure. It aims to accurately simulate the dynamic correlation mechanism between the motion process of nonferromagnetic abrasive particles in the sensor and the induced voltage.

[0032] It mainly includes the following two core modules: the eddy current analysis module for non-ferromagnetic abrasive particles and the induced voltage solution module. Specifically: Step 1: Establish the sensor excitation field model and calculate the incident magnetic vector. First, the non-ferromagnetic abrasive grains are considered as spherical conductors, and the excitation coil adopts an air-core cylindrical structure, which can be viewed as a superposition of multiple single-turn circular coils. Based on the three-coil sensor structure, the incident magnetic field vectors generated by excitation coil 1 and excitation coil 2 during the abrasive grain movement need to be calculated separately. This magnetic vector is determined by the excitation current, coil density, coil geometric parameters, and the real-time position of the abrasive grain.

[0033] To accurately represent the magnetic vector field distribution of an air-core cylindrical coil, spatial integration along the coil's cross-section is necessary. Since double integration is computationally complex, it is simplified while maintaining physical consistency, resulting in a closed-form expression that can be used for subsequent derivations.

[0034] The output of this step is: the expression of the incident magnetic vector generated inside the spherical abrasive grain by excitation coil 1 and excitation coil 2 respectively, which serves as the input basis for subsequent solution of eddy current distribution.

[0035] Step 2: Solve for the distribution of motion-induced eddy currents inside nonferromagnetic abrasive grains Based on the obtained incident field, the eddy current density inside the non-ferromagnetic abrasive grains is calculated using Ohm's law for moving conductors. Since the overall physical structure is axisymmetric, only the angular component of the eddy current needs to be solved. The solutions are obtained separately for the cases where excitation coil 1 and excitation coil 2 act independently, considering their opposite excitation directions. The overall eddy current expression is obtained through coordinate transformation and the superposition principle.

[0036] The output of this step is: the equivalent eddy current source distribution inside the abrasive grains, which provides a basis for equivalent modeling and boundary problem correction.

[0037] Step 3: Construct an equivalent eddy source model and correct the boundary value problem. By treating the internal eddies of the abrasive grains as a new excitation source, a new boundary value problem is established. This boundary value problem must maintain the finiteness of the magnetic vector potential throughout the entire space and satisfy the physical constraints that it cannot diverge at ρ=0 and the vector potential decays to zero as ρ approaches infinity.

[0038] Based on this, the governing equations are modified, and the Fourier transform method is introduced for solution. The obtained Fourier general solution needs to be obtained in combination with the boundary conditions to obtain its specific form, and the variation of the magnetic vector potential in the spatiotemporal domain is restored by inverse Fourier transform.

[0039] The output of this step is: considering the spatial magnetic vector potential distribution after the motion of non-ferromagnetic abrasive particles, providing a spatial field basis for the calculation of induced voltage.

[0040] Step 4: Calculate the equivalent induced voltage based on the principle of electromagnetic induction. By substituting the known spatial distribution of the magnetic vector potential into the induction coil model, the variation law of the induced voltage on the induction coil is calculated based on the principle of electromagnetic induction. This process needs to consider the dynamic influence of the induction coil's turn density, geometric dimensions, and the relative position of the abrasive grains on the voltage.

[0041] The output of this step is: the expression for the change of induced voltage over time under the equivalent single-turn circular coil.

[0042] Step 5: Integrate to solve for the overall equivalent induced voltage of the nonferromagnetic abrasive particles By spatially integrating the calculated induced voltage expression over the equivalent excitation source inside the abrasive grain, the overall induced voltage response when the non-ferromagnetic abrasive grain passes through the sensor is obtained. This response can be used in a simulation system to verify the sensor's recognition accuracy under different abrasive grain parameters and different movement speeds.

[0043] The output of this step is: the response curve of the nonferromagnetic abrasive particle induced voltage over time, realizing the dynamic sensing model of the abrasive particle passing through the sensor.

[0044] Step Six: Complete parameter mapping and simulation analysis based on different abrasive grain parameters. By adjusting the input parameters, including the magnitude and frequency of the excitation current, the size and position of the coil, the material of the abrasive particles (conductivity, permeability), the speed and size of the abrasive particles, and repeating the above steps, it is possible to simulate the dynamic sensing behavior and extract features of various abrasive particle types, providing theoretical support for abrasive particle recognition algorithms and sensor design.

[0045] Implementation Method 3: Combination Figure 1-2 This embodiment describes the technical solution provided above in further detail through specific examples. Specifically: A transient electromagnetic field analysis method coupling nonferromagnetic abrasive particle motion effect with time-harmonic field includes the following specific steps: Solve for the incident magnetic vector of a single-turn circular coil within a spherical conductor region; Since the coil actually used is an air-core cylindrical coil, it can be regarded as the superposition of multiple single-turn current-carrying circular coils; To solve for the incident magnetic vector of an air-core cylindrical coil, the incident magnetic field potential of the air-core cylindrical coil can be integrated along the rectangular cross-section of the driving coil. Since the incident magnetic vector potential of the air-core cylindrical coil involves double integrals, further simplification of the calculation is required. Since the eddy currents in the conducting sphere are generated as it cuts through the incident field, the eddy current density generated when a moving nonferromagnetic abrasive particle passes through a single coil can be calculated according to Ohm's law for a moving conductor. The magnitude of the eddy current inside the abrasive grain under the action of excitation coil 1 alone is determined. The formula for calculating the eddy current inside abrasive particles still contains an integral term, which further simplifies the calculation. Since the excitation directions of the excitation coils on both sides of the three-coil abrasive sensor are opposite, the magnitude of the eddy current inside the abrasive grain under the action of excitation coil 2 alone can be solved by using the reverse direction of the excitation and the coordinate change. The three-coil abrasive sensor consists of three independent coils, with two excitation coils on both sides. When a non-ferromagnetic abrasive particle passes through the sensor, the superposition principle is used to calculate the magnitude of the eddy current generated inside the sensor when the abrasive particle passes through it. The internal eddy currents of the abrasive grains are treated as a new excitation source, and the new boundary value problem is then treated as solving the magnetic field distribution of a single-turn circular coil in air, thus correcting the governing equations. Find the general solution of the governing equations and perform a Fourier transform; The change in magnetic vector potential of a single-turn coil is obtained by using boundary conditions and inverse Fourier transform. The voltage generated by an equivalent single-turn coil is determined using the principle of electromagnetic induction. By integrating the equivalent excitation source inside the abrasive grain, the induced voltage generated when the non-ferromagnetic abrasive grain passes through the sensor is obtained. Among them, the incident magnetic vector of the single-turn circular coil in the spherical conductor region A inc for:

[0046] The incident magnetic vector potential of the air-core cylindrical coil can be calculated by integral along the rectangular cross-section of the driving coil using the following formula:

[0047] The simplified result of the incident magnetic field vector potential of the air-core cylindrical coil is:

[0048] in , μ 0 is the permeability of free space. j 2 =-1, N 1 represents the number of turns of excitation coil 1. I d1 To excite the current in coil 1, c d1 The density of coil 1 is... c d1 = N 1 / [( R 2– R 1) L d1 ], L 0 represents the distance from the centroid of the nonferromagnetic abrasive grain to the left edge of excitation coil 1. L d1 For the length of excitation coil 1, v The velocity of nonferromagnetic abrasive particles. H 1( t )= L 0- as , H 2( t )= L 0+ L d1 - as , I 1( x )and K 1( x These are the first and second kind of first-order modified Bessel numbers, respectively. α The value ranges from -300 to 300; The internal vortex of the abrasive grain under the sole action of the excitation coil 1 J e1 The calculation formula is:

[0049] Since the overall physical model is an axisymmetric structure, only... Φ Directional components; The internal vortex of the abrasive grain under the sole action of the excitation coil 1 J e1 The simplified result is:

[0050] The internal vortex of the abrasive grains under the independent action of the excitation coil 2 J e2 The result is:

[0051] in, μ 0 is the permeability of free space. j 2 =-1, N 2 represents the number of turns of excitation coil 2. I d2 To excite the current in coil 2, c d2 For coil density 2, that is c d2 = N 2 / [( R 5– R 6) L d2 ], L 0 represents the distance from the centroid of the nonferromagnetic abrasive grain to the left edge of excitation coil 1. L d1 For the length of excitation coil 1, L d1 For the length of excitation coil 2, L p The length of the induction coil, m For the gap between the sensor coils, v The velocity of nonferromagnetic abrasive particles. H 5( t )= L 0+ L d1 + L p +2 m - as , H 4( t )= L 0+ L d1 + L d2 + L p +2 m - as , I 1( x )and K 1( x These are the first and second kind of first-order modified Bessel numbers, respectively. α The value ranges from -300 to 300; The formula for calculating the eddy currents generated when the abrasive particles pass through the sensor is as follows:

[0052] The modified governing equation expression is as follows:

[0053] The general solution obtained using Fourier transform is:

[0054] Since the magnetic vector potential must remain at a finite value throughout the entire space, ρ The magnetic vector potential at =0 cannot diverge, when The magnetic vector potential should tend to 0. When this happens, it will lead to divergence, hence C2=0; similarly, when

[0055] When this happens, it will cause divergence, hence C3=0; The boundary condition expression is:

[0056] in ; The solution obtained by the inverse Fourier transform of f is:

[0057] The calculated result of the equivalent single-turn circular coil induced voltage is as follows:

[0058] The number of turns density of the induction coil c p = N p / [( R 4- R 3) H p ], H 3( t )= L 0+ L d1 + m - as , H 4( t )= L 0+ L d1 + L p + m - as , L 0 represents the distance from the centroid of the nonferromagnetic abrasive grain to the left edge of excitation coil 1. L d1 For the length of excitation coil 1, L p The length of the induction coil, m For the gap between the sensor coils, v The velocity of nonferromagnetic abrasive particles; The equivalent induced voltage of the nonferromagnetic abrasive particles is:

[0059] The expression for the moving Ohm's law is:

[0060] in σ For the electrical conductivity of abrasive particles of different materials; The principle of electromagnetic induction is as follows:

[0061] in Φ s It is magnetic flux; The Fourier transform is:

[0062] Analysis module for eddy currents inside nonferromagnetic abrasive grains and equivalent induced voltage solution module; Specifically, global parameters are input into the analysis module of the eddy current inside the non-ferromagnetic abrasive grains to solve for the incident magnetic vector of the single-turn circular coil within the spherical conductor region. A inc ; Solve for the incident magnetic vector of an air-core cylindrical coil A d The incident magnetic vector potential of an air-core cylindrical coil can be integrated along the rectangular cross-section of the driving coil. Since the incident magnetic vector potential of the air-core cylindrical coil involves double integrals, further simplification of the calculation is required. Since the eddy currents in the conducting sphere are generated as it cuts through the incident field, the eddy current density generated when a moving nonferromagnetic abrasive particle passes through a single coil can be calculated according to Ohm's law for a moving conductor. Solve for the magnitude of the eddy current inside the abrasive grain under the action of excitation coil 1 alone. J e1 ; The formula for calculating the eddy current inside abrasive particles still contains an integral term, which further simplifies the calculation. Since the excitation coils on both sides of the three-coil abrasive sensor are excited in opposite directions, the magnitude of the eddy current inside the abrasive grain under the action of excitation coil 2 alone can be calculated by using the reverse direction of the excitation and the coordinate change. J e2 ; The three-coil abrasive sensor consists of three independent coils, with two excitation coils on either side. When a non-ferromagnetic abrasive particle passes through the sensor, the magnitude of the eddy current generated inside the sensor is calculated using the superposition principle. J e ; The internal eddy currents of the abrasive grains are treated as a new excitation source, and the new boundary value problem is then treated as solving the magnetic field distribution of a single-turn circular coil in air, thus correcting the governing equations. Find the general solution of the governing equations and perform a Fourier transform; The change in magnetomotive force of a single-turn coil is obtained by solving for boundary conditions and inverse Fourier transform. A 2φ ; Solving for the equivalent single-turn coil voltage using the principle of electromagnetic induction u s ( t ); By integrating the equivalent excitation source inside the abrasive grains, the induced voltage generated when non-ferromagnetic abrasive grains pass through the sensor can be obtained. u ( t ); like Figure 1 , Figure 2 As shown, the specific steps include the following: Step 1: Determine the incident magnetic vector of a single-turn circular coil within a spherical conductor region; Since the coil actually used is an air-core cylindrical coil, it can be regarded as the superposition of multiple single-turn current-carrying circular coils; To solve for the incident magnetic vector of an air-core cylindrical coil, the incident magnetic field potential of the air-core cylindrical coil can be integrated along the rectangular cross-section of the driving coil. Since the incident magnetic vector potential of the air-core cylindrical coil involves double integrals, further simplification of the calculation is required. Since the eddy currents in the conducting sphere are generated as it cuts through the incident field, the eddy current density generated when a moving nonferromagnetic abrasive particle passes through a single coil can be calculated according to Ohm's law for a moving conductor. The magnitude of the eddy current inside the abrasive grain under the action of excitation coil 1 alone is determined. The formula for calculating the eddy current inside abrasive particles still contains an integral term, which further simplifies the calculation. Since the excitation directions of the excitation coils on both sides of the three-coil abrasive sensor are opposite, the magnitude of the eddy current inside the abrasive grain under the action of excitation coil 2 alone can be solved by using the reverse direction of the excitation and the coordinate change. The three-coil abrasive sensor consists of three independent coils, with two excitation coils on both sides. When a non-ferromagnetic abrasive particle passes through the sensor, the superposition principle is used to calculate the magnitude of the eddy current generated inside the sensor when the abrasive particle passes through it. Among them, the incident magnetic vector of the single-turn circular coil in the spherical conductor region A inc for:

[0063] The incident magnetic vector potential of the air-core cylindrical coil can be calculated by integral along the rectangular cross-section of the driving coil using the following formula:

[0064] The simplified result of the incident magnetic field vector potential of the air-core cylindrical coil is:

[0065] in , μ 0 is the permeability of free space. j 2 =-1, N 1 represents the number of turns of excitation coil 1. I d1 To excite the current in coil 1, c d1 The density of coil 1 is... c d1 = N 1 / [( R 2– R 1) L d1 ], L 0 represents the distance from the centroid of the nonferromagnetic abrasive grain to the left edge of excitation coil 1. L d1 For the length of excitation coil 1, v The velocity of nonferromagnetic abrasive particles. H 1( t )= L 0- as , H 2( t )= L 0+ L d1 - as , I 1( x )and K 1( x These are the first and second kind of first-order modified Bessel numbers, respectively. α The value ranges from -300 to 300; The internal vortex of the abrasive grain under the sole action of the excitation coil 1 J e1 The calculation formula is:

[0066] Since the overall physical model is an axisymmetric structure, only... Φ Directional components; The internal vortex of the abrasive grain under the sole action of the excitation coil 1 J e1 The simplified result is:

[0067] The internal vortex of the abrasive grains under the independent action of the excitation coil 2 J e2 The result is:

[0068] in, μ 0 is the permeability of free space. j 2 =-1, N 2 represents the number of turns of excitation coil 2. I d2 To excite the current in coil 2, c d2 For coil density 2, that is c d2 = N 2 / [( R 5– R 6) L d2 ], L 0 represents the distance from the centroid of the nonferromagnetic abrasive grain to the left edge of excitation coil 1. L d1 For the length of excitation coil 1, L d1 For the length of excitation coil 2, L p The length of the induction coil, m For the gap between the sensor coils, v The velocity of nonferromagnetic abrasive particles. H 5( t )= L 0+ L d1 + L p +2 m - as , H 4( t )= L 0+ L d1 + L d2 + L p +2 m - as , I 1( x )and K 1( x These are the first and second kind of first-order modified Bessel numbers, respectively. α The value ranges from -300 to 300; The formula for calculating the eddy currents generated when the abrasive particles pass through the sensor is as follows:

[0069] In addition, global parameters include: (1) Sensor excitation coil parameters: coil inner diameter, coil outer diameter, coil length, coil thickness, and number of coil turns; (2) Sensor coil parameters: coil inner diameter, coil outer diameter, coil length, coil thickness, and number of coil turns; (3) Sensor structural parameters: coil gap; (4) Excitation current parameters: current magnitude, current frequency; (5) Abrasive properties: abrasive size, abrasive permeability, abrasive conductivity; (6) Other parameters: vacuum permeability.

[0070] Step 2: Treat the eddy current inside the abrasive grains as a new excitation source, and then treat the new boundary value problem as solving the magnetic field distribution of a single-turn circular coil in the air, and modify the governing equations. Find the general solution of the governing equations and perform a Fourier transform; The change in magnetic vector potential of a single-turn coil is obtained by using boundary conditions and inverse Fourier transform. The voltage generated by an equivalent single-turn coil is determined using the principle of electromagnetic induction. By integrating the equivalent excitation source inside the abrasive grain, the induced voltage generated when the non-ferromagnetic abrasive grain passes through the sensor is obtained. The modified governing equation expression is as follows:

[0071] The general solution obtained using Fourier transform is:

[0072] Since the magnetic vector potential must remain at a finite value throughout the entire space, ρ The magnetic vector potential at =0 cannot diverge, when The magnetic vector potential should tend to 0. When this happens, it will lead to divergence, hence C2=0; similarly, when When this happens, it will cause divergence, hence C3=0; The boundary condition expression is:

[0073] in ; The solution obtained by the inverse Fourier transform of f is:

[0074] The calculated result of the equivalent single-turn circular coil induced voltage is as follows:

[0075] The number of turns density of the induction coil c p = N p / [( R 4- R 3) H p ], H 3( t )= L 0+ L d1 + m - as , H 4( t )= L 0+ L d1 + L p + m - as , L 0 represents the distance from the centroid of the nonferromagnetic abrasive grain to the left edge of excitation coil 1. L d1 For the length of excitation coil 1, L p The length of the induction coil, m For the gap between the sensor coils, v The velocity of nonferromagnetic abrasive particles; The equivalent induced voltage of the nonferromagnetic abrasive particles is:

[0076] If the calculation of the equivalent induced voltage solution model has been completed, then output the result of the magnitude of the induced voltage and keep it.

[0077] The above description of several specific embodiments further details the technical solution provided by the present invention in order to highlight the advantages and benefits of the technical solution provided by the present invention. However, the above-described specific embodiments are not intended to limit the present invention. Any reasonable modifications and improvements to the present invention, combinations of embodiments, and equivalent substitutions based on the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A transient electromagnetic field analysis method coupling nonferromagnetic abrasive particle motion effect with time-harmonic field, characterized in that, include: The steps for acquiring the incident magnetic field vector generated by the excitation coil within the spherical conductor region; Based on the incident magnetic field vector, the steps are as follows: to obtain the eddy current distribution generated by nonferromagnetic abrasive particles under the individual action of excitation coil 1 and excitation coil 2; The steps are as follows: the internal eddy current of nonferromagnetic abrasive grains is equivalent to a new excitation source, the magnetic vector potential control equation is established and the general solution is obtained by Fourier transform. The steps for solving the spatial magnetic vector potential change by performing inverse Fourier transform using boundary conditions; The steps for calculating the equivalent voltage of an induction coil based on the principle of electromagnetic induction; The step of integrating the equivalent excitation source inside the non-ferromagnetic abrasive grains to obtain the induced voltage generated when the non-ferromagnetic abrasive grains pass through the sensor.

2. The transient electromagnetic field analysis method for the coupling of nonferromagnetic abrasive particle motion effect and time-harmonic field according to claim 1, characterized in that, The solution for the incident magnetic field vector includes the steps of equating the air-core cylindrical excitation coil to multiple single-turn circular coils and performing integration.

3. The transient electromagnetic field analysis method for the coupling of nonferromagnetic abrasive particle motion effect and time-harmonic field according to claim 1, characterized in that, The calculation of the nonferromagnetic abrasive eddy current is based on Ohm's law for a moving conductor and takes into account the magnitude of the coil current, the coil density, the abrasive velocity, and the spatial position relationship.

4. The transient electromagnetic field analysis method for coupling non-ferromagnetic abrasive particle motion effect with time-harmonic field according to claim 1, characterized in that, In the process of obtaining the general solution by performing Fourier transform, the magnetic vector potential is constrained to not diverge at ρ=0 and to decay to zero as ρ approaches infinity.

5. The transient electromagnetic field analysis method for coupling nonferromagnetic abrasive particle motion effect with time-harmonic field according to claim 1, characterized in that, The solution for the effective voltage in the induction coil is based on the coil’s turns density, length, and relative position of the abrasive grains, and is integrated in conjunction with the time-varying trend of the magnetic vector potential.

6. The transient electromagnetic field analysis method for the coupling of nonferromagnetic abrasive particle motion effect and time-harmonic field according to claim 1, characterized in that, The voltage response curve of the output after obtaining the induced voltage of nonferromagnetic abrasive particles as a function of time is used for dynamic feature identification under different nonferromagnetic abrasive particle parameters.

7. A transient electromagnetic field analysis device coupling nonferromagnetic abrasive particle motion effect with a time-harmonic field, characterized in that, include: A module for acquiring the incident magnetic field vector generated by the excitation coil within the spherical conductor region; Based on the incident magnetic field vector, a module is obtained to obtain the eddy current distribution generated by non-ferromagnetic abrasive particles under the individual action of excitation coil 1 and excitation coil 2. The module that treats the internal eddy currents of nonferromagnetic abrasive grains as a new excitation source, establishes the magnetic vector potential control equation, and obtains the general solution by performing Fourier transform. A module that uses boundary conditions to perform inverse Fourier transform to solve for the change in spatial magnetic vector potential; A module that calculates the equivalent voltage in an induction coil based on the principle of electromagnetic induction; A module that integrates the equivalent excitation source inside the non-ferromagnetic abrasive grains to obtain the induced voltage generated when the non-ferromagnetic abrasive grains pass through the sensor.

8. A computer storage medium for storing computer programs, characterized in that, When the computer program is read by the computer, the computer executes the method of claim 1.

9. A computer, comprising a processor and a storage medium, characterized in that, When the processor reads the computer program stored in the storage medium, the computer executes the method of claim 1.

10. A computer program product, as a computer program, is characterized by: When the computer program is executed, it implements the method of claim 1.

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