Electromagnetic sensor signal analysis method and system based on real abrasive particle dynamic trajectory and time-harmonic field intensity coupling

Abstract

The invention discloses an electromagnetic sensor signal analysis method and system based on real abrasive particle dynamic trajectory and time-harmonic field intensity coupling, and belongs to the field of mechanical equipment state monitoring and sensor simulation. The method comprises the following steps: firstly, based on a CFD-DEM coupling theory, combining abrasive particle multi-physical field stress, and accurately reconstructing a real three-dimensional dynamic track in a complex flow field of a lubricating oil pipeline; and establishing a three-dimensional time-harmonic magnetic field analysis model based on magnetic vector potential and a modified Bessel function, constructing a dynamic mapping relation between the transient position of the abrasive particles and a non-uniform magnetic field, quantifying the disturbance characteristic of the abrasive particle eddy current to the magnetic field, and solving the transient response of the sensor induced electromotive force. Abrasive particle size, material conductivity and magnetic conductivity parameter correction are fused, simulation distortion caused by a simplified motion model and neglect of radial magnetic field difference in a traditional theory is overcome, and high-precision prediction of dynamic signals of the whole process that the abrasive particles pass through the sensor is achieved. The method is suitable for health monitoring of aero-engines and industrial gearboxes.

Description

Technical Field

[0001] This invention relates to the field of mechanical equipment condition monitoring and sensor simulation technology, specifically to an electromagnetic sensor signal analysis method based on the coupling of real abrasive particle dynamic trajectory and time-harmonic field strength. Background Technology

[0002] During long-term operation, critical friction pairs of mechanical equipment inevitably experience wear, generating tiny metal particles that circulate in the lubricating oil system, carrying crucial information about the equipment's health status. Online lubricating oil wear particle monitoring technology effectively provides early warning of faults by detecting changes in the size, material, and concentration of wear particles in the oil in real time. Among these technologies, the three-coil inductive sensor is widely used in health monitoring of aero-engines and industrial gearboxes due to its simple structure, resistance to high temperatures and pressures, and insensitivity to oil transmittance.

[0003] However, with the increasing demands for monitoring accuracy, existing simulation and signal analysis methods for three-coil abrasive sensors have gradually revealed serious limitations, failing to meet the high-precision prediction requirements under complex working conditions. Specifically, existing sensor simulation studies, whether based on the finite element method or traditional analytical methods, mostly employ idealized motion assumptions when dealing with the process of abrasive particles passing through the sensor's sensitive area. This assumption presupposes that the abrasive particles move at a constant velocity along the central axis of the sensor's flow channel or a fixed parallel straight line. This assumption deviates significantly from the actual physical process because the lubricating oil pipeline environment in actual engineering is extremely complex, typically including structures such as bends, variable cross-section necks, and static mixers, with flow field morphologies encompassing laminar, transitional, and even turbulent flow. According to the coupling theory of fluid dynamics and discrete elements, abrasive particles suspended in oil are actually subjected to the combined effects of multiple physical fields during their motion, including gravity, fluid drag, Saffman shear lift, virtual mass force, and pressure gradient force. In particular, the presence of Saffman shear lift causes significant radial migration of abrasive particles in the shear flow field of the pipe wall. As a result, the actual trajectory of the abrasive particles when passing through the sensor coil is often a complex spatial curve rather than an ideal straight line. Consequently, the probability distribution of abrasive particles appearing at different radial positions of the sensor deviates greatly from the ideal model.

[0004] Meanwhile, traditional analytical electromagnetic field models, in order to reduce computational complexity, are mostly based on simplified one-dimensional or two-dimensional theories, which can only calculate the magnetic field distribution along the central axis of the sensor, ignoring the three-dimensional non-uniformity of the magnetic field inside the sensor. In fact, inside a three-coil sensor, especially in the interface region between the excitation coils at both ends and the induction coil in the middle, the radial component of the magnetic induction intensity is strongest at the inner edge of the coil wall, while approaching zero at the axis. When abrasive particles are deflected near the pipe wall by the lift force of the fluid, the amplitude and waveform characteristics of the induced electromotive force generated by cutting high-gradient magnetic field lines are completely different from those at the axis. For example, the signal of non-ferromagnetic abrasive particles under the edge trajectory will exhibit a characteristic bimodal distortion. Since fluid dynamics (focusing on the force trajectory of discrete particles) and time-harmonic electromagnetic field theory (focusing on continuous field distribution) belong to completely different physical domains, there are natural technical barriers between them in numerical calculation methods and underlying data interaction structures. It is difficult to achieve efficient real-time mapping between the dynamic Lagrangian coordinates of massive discrete abrasive particles and the Eulerian grid of the continuous magnetic field space, and strong coupling analysis is often accompanied by extremely high algorithmic complexity and computational resource consumption. Limited by the aforementioned physical span and computational gap, existing technologies are forced to adopt simplified "decoupling" processes, resulting in a long-standing disconnect between fluid simulation and electromagnetic simulation. There is a lack of a strongly coupled analysis method that can directly map the real spatiotemporal coordinates of abrasive particles calculated by CFD-DEM as dynamic variables to a three-dimensional time-harmonic electromagnetic field analytical model in real time. This makes it impossible to quantify the specific impact of random changes in the radial position of abrasive particles on the output signal, often leading to significant amplitude errors and waveform distortions between simulation results and experimental data. Therefore, there is an urgent need for an electromagnetic field analysis method that integrates the coupling of real motion trajectories and time-harmonic fields to overcome these technical bottlenecks. Summary of the Invention

[0005] In view of this, the present invention provides an electromagnetic sensor signal analysis method based on the coupling of real abrasive particle dynamic trajectory and time-harmonic field strength, so as to reveal the dynamic correlation mechanism between the real motion state of abrasive particles and the induced signal, and provide theoretical support for improving the accuracy of abrasive particle detection.

[0006] To achieve the above objectives, the present invention provides the following technical solution: In a first aspect, the present invention provides an electromagnetic sensor signal analysis method based on the coupling of real abrasive particle dynamic trajectory and time-harmonic field strength, the method comprising the following steps: Step 1: Construct a fluid-particle two-phase flow dynamics simulation model. Based on the Euler-Lagrange coupling method, establish a motion model of the fluid and abrasive particles within the lubricating oil pipeline. Solve the motion equations of the continuous phase fluid and the dynamic equations of the discrete phase abrasive particles. Introduce a particle shape factor to correct the resultant force on the abrasive particles. Solve the differential equations of motion of the abrasive particles through time-step integration to obtain the motion of the abrasive particles at each time step. t The three-dimensional spatial position coordinates and velocity vector; Step 2: Establish a three-dimensional time-harmonic magnetic field analytical model for the sensor. Based on the Biot-Savart law, the coil is equivalent to a multi-turn circular coil with a rectangular cross section. The modified Bessel function and elliptic integral are introduced to establish an analytical model of the radial and axial magnetic induction intensity generated by a single coil at any position in space. The total magnetic field intensity distribution of the three-coil sensor at the actual trajectory position of the abrasive grain is calculated using the principle of vector superposition. Step 3: Solve for the dynamic induced voltage under the actual trajectory, establish the abrasive particle magnetization model and calculate the complex magnetic susceptibility of the abrasive particles in the alternating magnetic field. Based on the mutual inductance principle and perturbation theory, construct the dynamic mapping relationship between the radial position of the abrasive particles and the radial induced voltage, and between the axial position and the axial induced voltage. Substitute the actual trajectory coordinates of the abrasive particles obtained in Step 1 into the mapping relationship, and perform vector synthesis of the radial and axial induced voltage components to obtain the time-varying signal of the total induced voltage output by the sensor. u ( t ).

[0007] Furthermore, the motion equation of the continuous phase fluid in step one is the Navier-Stokes equation. By solving the Navier-Stokes equation, the velocity vector, pressure gradient, and velocity gradient tensor of any node in the flow field can be obtained. The dynamic equation of the discrete phase abrasive grains considers the forces acting on the abrasive grains as the resultant force of gravity, fluid drag, virtual mass force and pressure gradient force in a complex flow field.

[0008] Furthermore, the discrete phase abrasive particle kinetic equation in step one is:

[0009] in, For abrasive grain quality, For abrasive particle velocity vector, The combined force of gravity and buoyancy. For fluid drag force, For virtual mass force, For pressure gradient force; The virtual mass force The calculation formula is:

[0010] in, The mass of the fluid displaced by the abrasive particles. The fluid velocity vector represents the additional inertial effect generated when the abrasive particles accelerate, causing the surrounding fluid to accelerate as well. The pressure gradient force The calculation formula is:

[0011] in, This force is the substantial derivative of fluid acceleration and represents the driving force caused by the uneven distribution of pressure in the flow field.

[0012] Furthermore, fluid drag The calculation is performed using a modified model that considers the particle Reynolds number and non-spherical characteristics, and the formula is as follows:

[0013] Among them, particle velocity response time With drag coefficient C D The relationship is:

[0014] The drag coefficient C D Based on relative Reynolds number Perform nonlinear correction:

[0015]

[0016] in, For fluid dynamic viscosity, This is the equivalent diameter of the abrasive grain.

[0017] Furthermore, the radial magnetic induction intensity generated by a single coil With axial magnetic induction intensity The analytical calculation formula;

[0018]

[0019] in, The permeability of free space, J For current density, r The radial coordinates of the field point, P ρ and P z To introduce an auxiliary function containing elliptic integrals, R i and Z j These are the normalized coordinate parameters; Total induced voltage output by the sensor under the actual abrasive particle motion trajectory The calculation formula is:

[0020] Among them, the radial induced voltage component With axial induced voltage component for:

[0021] in, The imaginary unit, For the excitation frequency, For abrasive magnetic susceptibility, and This is the integral term that includes coil structure parameters and position functions.

[0022] Furthermore, the magnetic susceptibility of the abrasive particles The calculation formula is:

[0023] in, Where is the abrasive grain radius. The relative permeability, To match the conductivity of abrasive particles The relevant complex wavenumber, and .

[0024] Furthermore, the method also includes: introducing a Saffman shear lift calculation term into the fluid dynamics model to correct the radial migration trajectory of abrasive particles near the pipe wall; when the actual trajectory of the abrasive particles ( r , z Located on the inner edge of the coil ( When, based on the calculated total induced voltage u ( t Identify the bimodal distortion feature at the center of the waveform; use the mapping relationship between this bimodal feature and the radial position to invert and correct the size and material properties of the abrasive particles.

[0025] Secondly, the electromagnetic sensor signal analysis method based on the coupling of real abrasive particle dynamic trajectory and time-harmonic field strength described in this invention can be fully implemented using computer software. Therefore, correspondingly, this invention also provides an electromagnetic sensor signal analysis system based on the coupling of real abrasive particle dynamic trajectory and time-harmonic field strength.

[0026] Thirdly, the present invention also provides a computer-readable storage medium storing a computer program, which, when executed by a processor, performs the electromagnetic sensor signal analysis method based on the coupling of real abrasive particle dynamic trajectory and time-harmonic field strength as described in any one of the above-mentioned methods.

[0027] Fourthly, the present invention also provides a computer device, which includes a memory and a processor. The memory stores a computer program. When the processor runs the computer program stored in the memory, the processor executes the electromagnetic sensor signal analysis method based on the coupling of real abrasive particle dynamic trajectory and time-harmonic field strength as described in any one of the above claims.

[0028] As can be seen from the above technical solution, the present invention discloses a transient electromagnetic field analysis method coupling non-ferromagnetic abrasive particle motion effect with time-harmonic field, which has the following advantages compared with the prior art: (1) This method firstly considers the multi-physics force mechanism of the abrasive particles in the lubricating oil pipeline, such as gravity, fluid drag, virtual mass force and pressure gradient force, based on the coupled theory of computational fluid dynamics and discrete element model (CFD-DEM), and accurately reconstructs the real three-dimensional dynamic trajectory of the abrasive particles in the complex flow field. Then, it establishes a three-dimensional time-harmonic magnetic field analytical model based on magnetic vector potential and modified Bessel function, constructs the dynamic mapping relationship between the transient spatial position of the abrasive particles and the non-uniform magnetic field, quantifies the disturbance characteristics of the magnetic field distribution caused by the eddy current generated by the abrasive particles at different radial trajectory positions, and thus solves the transient time-varying response of the sensor induced electromotive force.

[0029] (2) It breaks through the idealized assumption of "linear motion" of abrasive particles and significantly improves the simulation realism under complex flow fields.

[0030] (3) It overcomes the defect of "dimensionality deficiency" in traditional electromagnetic field models and realizes high-precision analysis of non-uniform magnetic fields inside sensors.

[0031] (4) A strongly coupled analysis framework of “fluid trajectory-electromagnetic response” was constructed, which greatly improved the prediction accuracy of sensor dynamic signals. Attached Figure Description

[0032] To more clearly illustrate the specific embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the specific embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.

[0033] Figure 1 This is a schematic diagram of the three-coil abrasive sensor structure described in an embodiment of the present invention; Figure 2 This is a flowchart of the electromagnetic sensor signal analysis method for coupling the real abrasive particle dynamic trajectory with the time-harmonic field strength as described in this embodiment of the invention. Detailed Implementation

[0034] The specific implementation details (such as experimental setup, operation procedures, data processing steps, and example parameters) of "An Electromagnetic Sensor Signal Analysis Method and System Based on Coupling of Real Abrasive Particle Dynamics Trajectory and Time-Harmonic Field Strength" provided in this specification below are primarily intended for illustrative purposes rather than limiting definitions, aiming to help those skilled in the art thoroughly understand the principles and implementation of the invention. However, those skilled in the art should understand that these details represent only one feasible embodiment, and the core concept of the invention can be fully realized through other technical means or alternative solutions not described in detail, without departing from its spirit and essence. Furthermore, the omission of details of conventional experimental methods and apparatus known in the art in the specification is to avoid redundant information interfering with the understanding of the innovation points. This does not mean that these known technologies are not required during implementation, and those skilled in the art should be able to supplement and apply them based on their professional knowledge.

[0035] The specific embodiments of the present invention will be further described in detail below with reference to the accompanying drawings. The following examples will help those skilled in the art to further understand the present invention, but do not limit the present invention in any way. It should be noted that those skilled in the art can make several changes and improvements without departing from the concept of the present invention, and these all fall within the protection scope of the present invention.

[0036] Example 1, Combination Figure 1 and Figure 2 This embodiment provides an electromagnetic sensor signal analysis method based on the coupling of real abrasive particle dynamic trajectory and time-harmonic field strength, in order to reveal the dynamic correlation mechanism between the real motion state of abrasive particles and the induced signal, and to provide theoretical support for improving the accuracy of abrasive particle detection.

[0037] The signal analysis method is as follows Figure 2 As shown, it includes the following steps: Step 1: Construct a fluid-particle two-phase flow dynamics simulation model. Based on the Euler-Lagrange coupling method, establish a motion model of the fluid and abrasive particles within the lubricating oil pipeline. Solve the motion equations of the continuous phase fluid and the dynamic equations of the discrete phase abrasive particles. Introduce a particle shape factor to correct the resultant force on the abrasive particles. Solve the differential equations of motion of the abrasive particles through time-step integration to obtain the motion of the abrasive particles at each time step. t The three-dimensional spatial position coordinates and velocity vector; Step 2: Establish a three-dimensional time-harmonic magnetic field analytical model for the sensor. Based on the Biot-Savart law, the coil is equivalent to a multi-turn circular coil with a rectangular cross section. The modified Bessel function and elliptic integral are introduced to establish an analytical model of the radial and axial magnetic induction intensity generated by a single coil at any position in space. The total magnetic field intensity distribution of the three-coil sensor at the actual trajectory position of the abrasive grain is calculated using the principle of vector superposition. Figure 1 This is a schematic diagram of a three-coil abrasive sensor structure; Step 3: Solve for the dynamic induced voltage under the actual trajectory, establish the abrasive particle magnetization model and calculate the complex magnetic susceptibility of the abrasive particles in the alternating magnetic field. Based on the mutual inductance principle and perturbation theory, construct the dynamic mapping relationship between the radial position of the abrasive particles and the radial induced voltage, and between the axial position and the axial induced voltage. Substitute the actual trajectory coordinates of the abrasive particles obtained in Step 1 into the mapping relationship, and perform vector synthesis of the radial and axial induced voltage components to obtain the time-varying signal of the total induced voltage output by the sensor. u ( t ).

[0038] Furthermore, the signal analysis method is more specifically as follows: Step 1: Construct a fluid-particle two-phase flow dynamics simulation model (CFD-DEM). Based on the Eulerian-Lagrangian coupling method, establish a motion model of the fluid and abrasive particles within the lubricating oil pipeline. Solve the Navier-Stokes equations for the continuous phase fluid (lubricating oil) to obtain the velocity vector, pressure gradient, and velocity gradient tensor at any node in the flow field. Construct the dynamic equations for the discrete phase abrasive particles, calculate the resultant forces of gravity, fluid drag, virtual mass force, and pressure gradient force acting on the abrasive particles in the complex flow field, and introduce particle shape factor correction. Solve the differential equations of motion for the abrasive particles through time-step integration to obtain the motion of the abrasive particles at each time step. t True three-dimensional spatial coordinates r p , z p and velocity vector v p It is worth noting that, in order to solve for the incident magnetic vector of the 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.

[0039] The discrete phase abrasive kinetic equation is as follows:

[0040] in, For abrasive grain quality, For abrasive particle velocity vector, The combined force of gravity and buoyancy. For fluid drag force, For virtual mass force, For pressure gradient force; The virtual mass force The calculation formula is:

[0041] in, The mass of the fluid displaced by the abrasive particles. The fluid velocity vector represents the additional inertial effect generated when the abrasive particles accelerate, causing the surrounding fluid to accelerate as well. The pressure gradient force The calculation formula is:

[0042] in, This force is the substantial derivative of fluid acceleration and represents the driving force caused by the uneven distribution of pressure in the flow field.

[0043] Furthermore, fluid drag The calculation is performed using a modified model that considers the particle Reynolds number and non-spherical characteristics, and the formula is as follows:

[0044] Among them, particle velocity response time With drag coefficient C D The relationship is:

[0045] The drag coefficient C D Based on relative Reynolds number Perform nonlinear correction:

[0046]

[0047] in, For fluid dynamic viscosity, This is the equivalent diameter of the abrasive grain.

[0048] Step 2: Establish a three-dimensional time-harmonic magnetic field analytical model for the sensor. Based on the Biot-Savart law, the coil is equivalent to a multi-turn circular coil with a rectangular cross-section. By introducing the modified Bessel function and elliptic integral, an analytical model of the radial and axial magnetic induction intensity generated by a single coil at any position in space is established. Using the principle of vector superposition, the total magnetic field intensity distribution of a three-coil sensor containing two excitation coils and one induction coil at the actual trajectory position of the abrasive grain is calculated. Among them, the radial magnetic induction intensity generated by a single coil With axial magnetic induction intensity The analytical calculation formula;

[0049]

[0050] in, The permeability of free space, J For current density,r The radial coordinates of the field point, P ρ and P z To introduce an auxiliary function containing elliptic integrals, R i and Z j These are the normalized coordinate parameters; Total induced voltage output by the sensor under the actual abrasive particle motion trajectory The calculation formula is:

[0051] Among them, the radial induced voltage component With axial induced voltage component for:

[0052] in, The imaginary unit, For the excitation frequency, For abrasive magnetic susceptibility, and This is the integral term that includes coil structure parameters and position functions.

[0053] Furthermore, auxiliary functions P ρ ( R , Z ) and P z ( R , Z The specific expression for ) is:

[0054] in, The integral term is obtained through Gauss-Legendre Numerical solutions are obtained using the quadrature formula.

[0055] Step two aims to construct a semi-analytical mathematical model that can accurately characterize the magnetic field distribution within and around the sensor, providing a high-precision field foundation for subsequent coupled motion trajectories. The specific implementation path is as follows: First, the physical structure of the sensor is geometrically equivalent and its parameters are defined. Both the excitation coil and the induction coil in the sensor are equivalent to multi-turn circular coils with rectangular cross-sections, and a cylindrical coordinate system is established at the geometric center of the sensor. The physical parameters involved in the model include the inner diameter, outer diameter, height, and total number of turns of each coil. Simultaneously, the current flowing through the excitation coil is defined as a time-harmonic current with a specific frequency and amplitude, and based on the coil's geometry, it is equivalent to a current density uniformly distributed within the cross-section.

[0056] Secondly, based on the Biot-Savart law and the theory of magnetic vector potential, an analytical expression for the magnetic field generated by a single coil at any observation point in space is derived. Due to the axisymmetry of the model, the magnetic vector potential only has a circumferential component in space. By performing double integration over the rectangular cross-sectional region of the coil and introducing first and second kind of complete elliptic integrals to handle the nonlinear terms in the integration, a mapping relationship between the magnetic vector potential and the spatial position coordinates is established. To further improve the computational efficiency and convergence of the model in computer simulation, this embodiment also introduces a mathematical transformation method based on modified Bessel functions, transforming the complex integral operations into an analytical expression containing zero-order and first-order modified Bessel functions.

[0057] Next, by utilizing the curl relationship between magnetic flux density and magnetic vector potential, the radial and axial magnetic flux density components at arbitrary spatial locations are further derived. This model can accurately describe the non-uniform characteristics of the magnetic field inside the sensor, especially the high-gradient edge magnetic field near the inner wall of the coil, which is impossible to achieve with the traditional one-dimensional long solenoid approximation model. This is also the key basis for subsequent analysis of signal distortion caused by the radial displacement of abrasive particles.

[0058] Finally, the total field of the multi-coil sensor is reconstructed using the principle of linear vector superposition. For a three-coil sensor structure consisting of two anti-tandem excitation coils and a central induction coil, the magnetic field vectors generated by the two excitation coils at the same instant are superimposed. Considering the time-harmonic characteristics of the excitation current, the total magnetic induction field, which varies periodically with time and is spatially non-uniformly distributed in three dimensions, is finally obtained. After this analytical model is established, the instantaneous magnetic field vector at the location of the abrasive grain can be directly calculated based on the real-time spatiotemporal coordinates of the abrasive grain obtained in step one, thereby completing the dynamic mapping of fluid trajectory data to the electromagnetic field domain. Step 3: Solve for the dynamic induced voltage under the actual trajectory. Establish a wear particle magnetization model and calculate the complex magnetic susceptibility of the wear particle in an alternating magnetic field. Based on the mutual inductance principle and perturbation theory, construct dynamic mapping relationships between the radial position and radial induced voltage, and between the axial position and axial induced voltage of the wear particle. Substitute the actual trajectory coordinates solved in Step 1 into the mapping relationship, perform vector synthesis of the radial and axial induced voltage components, and solve for the time-varying signal of the total induced voltage output by the sensor. u ( t ); Furthermore, a Saffman shear lift term is introduced into the fluid dynamics model to correct the radial migration trajectory of abrasive particles near the pipe wall; when the actual trajectory of the abrasive particles ( r , z Located on the inner edge of the coil ( When, based on the calculated total induced voltage u ( t)Identify the double-peak distortion feature that appears at the center of the recognition waveform; utilize the mapping relationship between this double-peak feature and the radial position to inversely correct the size and material properties of the abrasive particles.

[0059] Embodiment 2: This embodiment provides the specific operation process of an electromagnetic sensor signal analysis method based on the coupling of the true abrasive particle dynamics trajectory and the time-harmonic field strength; Step 1: Construct a fluid-particle two-phase flow dynamics simulation model (CFD-DEM).

[0060] This part aims to accurately reconstruct the true motion trajectory of abrasive particles in the lubricating oil pipeline through numerical calculations. Different from the traditional method that assumes the abrasive particles move in a uniform straight line, this embodiment adopts the Eulerian-Lagrangian method, regards the lubricating oil as the continuous phase, and the abrasive particles as the discrete phase, fully considering the multi-physical field coupling effect between the fluid and the particles. First, establish the flow channel geometric model of the sensor monitoring area, and this model is three-dimensionally digitized and reconstructed based on the physical parameters of the lubricating oil pipeline supporting the actual sensor. Its key construction parameters include the inner diameter of the flow channel D (determining the fluid flow area and Reynolds number distribution), the total length of the monitoring area L and the lengths of the inlet and outlet buffer sections (used to eliminate the disturbance of the boundary conditions on the core area). After completing the geometric modeling, use the computational grid generation technology to divide the internal space of the flow channel, and perform boundary layer grid encryption processing on the near-wall area close to the pipe wall (i.e., the shear flow area where the Saffman shear lift on the abrasive particles is most significant) to ensure the high-precision extraction of the velocity gradient tensor.

[0061] Among them, the solution of the continuous phase (lubricating oil) flow field: Solve the velocity field and pressure field of the lubricating oil based on the Navier-Stokes equation. For an incompressible fluid, its mass conservation equation (continuity equation) is:

[0062] Its momentum conservation equation is:

[0063] Among them, is the fluid density, is the fluid velocity vector, is the static pressure, is the gravitational acceleration. In this control equation set, the operator This represents the partial derivative of a physical quantity with respect to time. Its physical meaning is the rate of change of a fluid physical parameter (such as momentum or local density) with time at a fixed observation point in space. In unsteady flow simulations, this term characterizes the transient pulsation characteristics of the flow field over time, and is a key foundation for accurately capturing the unsteady and nonlinear motion trajectories of abrasive particles caused by instantaneous fluctuations in the flow field. It is worth noting that the effective dynamic viscosity is introduced in the formula. (Including molecular viscosity and turbulent eddy viscosity) and the transpose of the velocity gradient tensor This is to accurately describe the shear stress distribution inside the fluid. The finite volume method (FVM) is used to iteratively solve the above equations to obtain the flow velocity at any node in the flow field. ,pressure and velocity gradient .

[0064] Discrete-phase (abrasive) dynamics solution: After obtaining the convergent flow field solution, the abrasive particle motion is tracked based on the discrete element method (DEM). This embodiment constructs a full-force model incorporating various physical mechanisms, and the translational equations of the abrasive particles follow Newton's second law: +

[0065] The specific calculation methods for each force are as follows: (1) The resultant force of gravity and buoyancy ( ):

[0066] In the formula, d p The equivalent physical diameter of the abrasive grain (abrasive grain diameter) determines the volume and force-bearing area of ​​the abrasive grain in the flow field. The physical density of abrasive materials (abrasive density), which is related to fluid density. The difference determines the tendency of abrasive particles to settle or float in lubricating oil.

[0067] (2) Fluid drag ( The shape factor (BF) characterizes the driving effect of fluid viscosity on abrasive particles, representing the dominant force driving the abrasive particles to follow the fluid's motion. To accommodate the common plate-like or needle-like abrasive particles in engineering, this embodiment specifically introduces a shape factor correction model for non-spherical particles.

[0068] in, A p This represents the projected area (frontal area) of the abrasive grain in the direction of motion. For non-spherical abrasive grains, this area changes dynamically with the relative motion between the abrasive grain and the fluid, and is a key geometric feature parameter for calculating the magnitude of fluid drag.

[0069] Where the drag coefficient C D The Haider-Levenspiel correlation is used for calculation, which is the particle relative Reynolds number. Re p With sphericity Φ Functions:

[0070] In the formula A , B , C , D This is a constant that is only related to particle shape.

[0071] (3) Virtual mass force This term characterizes the additional inertial effect generated when abrasive particles accelerate in an unsteady flow field, causing the surrounding fluid layer to accelerate as well. This term cannot be ignored when there are abrupt changes in the sensor's flow channel cross-section, the presence of eddies, or when abrasive particles pass through the coil at high speed.

[0072] In the formula, The virtual mass coefficient (or additional mass coefficient) is a dimensionless coefficient used to characterize the additional inertial effect generated by the fluid during acceleration. Under common lubricating oil conditions, it is typically taken as 0.5. (Operator) D / Dt The mass derivative (also known as the volume derivative) represents the total rate of change of flow field physical quantities with respect to the motion of fluid particles, including local variations over time and convection terms with respect to space; operator d / dt Represents the constant derivative (or time derivative), which here indicates the rate of change of the velocity of the discrete abrasive grains with time, i.e., the instantaneous acceleration of the abrasive grains.

[0073] (4) Pressure gradient force ): Characterizes the additional driving force on abrasive particles caused by uneven pressure distribution within the flow field itself (such as the shift of high-pressure areas to low-pressure areas due to velocity variations).

[0074] (5) Saffman shear lift ( This characterizes the lateral lift force of abrasive particles in a shear flow field within a pipe wall, caused by the velocity difference between the upper and lower surfaces of the particles. This is the key force leading to cross-stream migration of abrasive particles, and its direction is perpendicular to the flow direction.

[0075] Solving the above system of differential equations using the time-step integration method yields the results of the abrasive particles' behavior during the process. t 0, t 1, …, t n The actual three-dimensional spatial coordinates (rt, zt) at each moment.

[0076] Step 2: Establish a sensor-induced voltage response model under the actual trajectory of abrasive particles. The true trajectory calculated in the first part ( r t , z t Substitute the sensor's induced voltage response model into the actual trajectory of the abrasive particles and perform a fluid-magnetic coupling solution.

[0077] (1) Abrasive magnetization equivalent Calculate the complex magnetic susceptibility of the abrasive grains under the influence of a magnetic field at the current position. K p ( ω , μ r , σ The abrasive grains are equivalent to having magnetic dipole moments. The secondary field source.

[0078] (2) Synthesis of induced voltage Based on the principle of mutual inductance, the total voltage output by the sensor's sensing coil u ( t This represents the vector superposition of the induced electromotive forces generated by the movement of abrasive particles in different directions.

[0079] Specifically, when CFD simulations show that abrasive particles migrate towards the pipe wall under the influence of Saffman lift, the radial coordinates... Increase. At this time, the induced voltage component generated by the abrasive cutting the radial magnetic field lines increases. This will significantly enhance the overall voltage waveform, resulting in a double-peak distortion at the center.

[0080] Through the above steps, this invention achieves high-precision prediction of the sensing signal of the entire motion process of abrasive particles in a complex flow field, verifies the important influence of the real fluid trajectory on the electromagnetic detection signal, and provides a reliable theoretical basis for the structural optimization design of the sensor.

[0081] Example 3: All of the above examples can be implemented using computer software. Therefore, this example provides an electromagnetic sensor signal analysis system based on the coupling of real abrasive particle dynamics trajectory and time-harmonic field strength.

[0082] Example 4: This example provides a computer-readable storage medium storing a computer program. When the computer program is run by a processor, it executes the electromagnetic sensor signal analysis method based on the coupling of real abrasive particle dynamics trajectory and time-harmonic field strength described in any of the above examples.

[0083] Those skilled in the art will understand that implementing all or part of the processes in the above embodiments can be accomplished by a computer program instructing related hardware. The program can be stored in a computer-readable storage medium, and when executed, it can include the processes of the embodiments of the above methods. The storage medium can be a magnetic disk, optical disk, read-only memory (ROM), random access memory (RAM), flash memory, hard disk drive (HDD), or solid-state drive (SSD), etc.; the storage medium can also include combinations of the above types of memory.

[0084] Example 5: This example provides a computer device, which includes a memory and a processor. The memory stores a computer program. When the processor runs the computer program stored in the memory, the processor executes the electromagnetic sensor signal analysis method based on the coupling of real abrasive particle dynamics trajectory and time-harmonic field strength as described in any of the above examples.

[0085] This embodiment provides a computer device. This part of the hardware device is a general model and is not shown in the figure. The system includes a processor and a memory. The processor and the memory can be connected by a bus or other means. The memory, as a non-transitory computer-readable storage medium, can be used to store non-transitory software programs, non-transitory computer-executable programs and modules, as well as corresponding program instructions / modules. The processor executes various functional applications and data processing by running the non-transitory software programs, instructions and modules stored in the memory, so as to realize the electromagnetic sensor signal analysis method and steps based on the coupling of real abrasive particle dynamic trajectory and time-harmonic field strength in the above method embodiment.

[0086] The memory may include a program storage area and a data storage area, wherein the program storage area may store the operating system and applications required for at least one function; the data storage area may store data created by the processor, etc. Furthermore, the memory may include high-speed random access memory and may also include non-transitory memory, such as at least one disk storage device, flash memory device, or other non-transitory solid-state storage device. In some embodiments, the memory may optionally include memory remotely located relative to the processor, which can be connected to the processor via a network. Examples of such networks include, but are not limited to, the Internet, corporate intranets, mobile communication networks, and combinations thereof.

[0087] One or more modules are stored in the memory. When the processor executes, it performs the method steps in the embodiments. In this way, the invention objective can be achieved through the method, apparatus and process of the present invention. The specific details of the computer device described above can be understood by referring to the relevant descriptions and effects in the embodiments, and will not be repeated here.

[0088] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on its differences from other embodiments. Similar or identical parts between embodiments can be referred to interchangeably. For the apparatus disclosed in the embodiments, since they correspond to the methods disclosed in the embodiments, the description is relatively simple; relevant parts can be referred to the method section.

[0089] The above description of the technical solution provided by the present invention through several specific embodiments is intended 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, reasonable combinations of implementation methods 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 method for analyzing electromagnetic sensor signals based on the coupling of real abrasive particle dynamics trajectory and time-harmonic field strength, characterized in that, The method is as follows: Step 1: Construct a fluid-particle two-phase flow dynamics simulation model. Based on the Euler-Lagrange coupling method, establish a motion model of the fluid and abrasive particles within the lubricating oil pipeline. Solve the motion equations of the continuous phase fluid and the dynamic equations of the discrete phase abrasive particles. Introduce a particle shape factor to correct the resultant force on the abrasive particles. Solve the differential equations of motion of the abrasive particles through time-step integration to obtain the motion of the abrasive particles at each time step. t The three-dimensional spatial position coordinates and velocity vector; Step 2: Establish a three-dimensional time-harmonic magnetic field analytical model for the sensor. Based on the Biot-Savart law, the coil is equivalent to a multi-turn circular coil with a rectangular cross section. The modified Bessel function and elliptic integral are introduced to establish an analytical model of the radial and axial magnetic induction intensity generated by a single coil at any position in space. The total magnetic field intensity distribution of the three-coil sensor at the actual trajectory position of the abrasive grain is calculated using the principle of vector superposition. Step 3: Solve for the dynamic induced voltage under the actual trajectory, establish the abrasive particle magnetization model and calculate the complex magnetic susceptibility of the abrasive particles in the alternating magnetic field. Based on the mutual inductance principle and perturbation theory, construct the dynamic mapping relationship between the radial position of the abrasive particles and the radial induced voltage, and between the axial position and the axial induced voltage. Substitute the actual trajectory coordinates of the abrasive particles obtained in Step 1 into the mapping relationship, and perform vector synthesis of the radial and axial induced voltage components to obtain the time-varying signal of the total induced voltage output by the sensor. u ( t ).

2. The signal analysis method according to claim 1, characterized in that, The equation of motion for the continuous phase fluid in step one is the Navier-Stokes equation. By solving the Navier-Stokes equation, the velocity vector, pressure gradient, and velocity gradient tensor of any node in the flow field can be obtained. The dynamic equation of the discrete phase abrasive grains considers the forces acting on the abrasive grains as the resultant force of gravity, fluid drag, virtual mass force and pressure gradient force in a complex flow field.

3. The signal analysis method according to claim 2, characterized in that, The discrete phase abrasive kinetic equation described in step one is: in, For abrasive grain quality, For abrasive particle velocity vector, The combined force of gravity and buoyancy. For fluid drag force, For virtual mass force, For pressure gradient force; The virtual mass force The calculation formula is: in, The mass of the fluid displaced by the abrasive particles. The fluid velocity vector represents the additional inertial effect generated when the abrasive particles accelerate, causing the surrounding fluid to accelerate as well. The pressure gradient force The calculation formula is: in, This force is the substantial derivative of fluid acceleration and represents the driving force caused by the uneven distribution of pressure in the flow field.

4. The signal analysis method according to claim 3, characterized in that, Fluid drag The calculation is performed using a modified model that considers the particle Reynolds number and non-spherical characteristics, and the formula is as follows: Among them, particle velocity response time With drag coefficient C D The relationship is: The drag coefficient C D Based on relative Reynolds number Perform nonlinear correction: in, For fluid dynamic viscosity, This is the equivalent diameter of the abrasive grain.

5. The signal analysis method according to claim 1, characterized in that, Radial magnetic flux density generated by a single coil With axial magnetic induction intensity The analytical calculation formula; in, The permeability of free space, J For current density, r The radial coordinates of the field point, P ρ and P z To introduce an auxiliary function containing elliptic integrals, R i and Z j These are the normalized coordinate parameters; Total induced voltage output by the sensor under the actual abrasive particle motion trajectory The calculation formula is: Among them, the radial induced voltage component With axial induced voltage component for: in, The imaginary unit, For the excitation frequency, For abrasive magnetic susceptibility, and This is the integral term that includes coil structure parameters and position functions.

6. The signal analysis method according to claim 5, characterized in that, The magnetic susceptibility of the abrasive particles The calculation formula is: in, Where is the abrasive grain radius. The relative permeability, To match the conductivity of abrasive particles The relevant complex wavenumber, and .

7. The signal analysis method according to claim 1, characterized in that, The method further includes: introducing a Saffman shear lift calculation term into the fluid dynamics model to correct the radial migration trajectory of abrasive particles near the pipe wall; when the actual trajectory of the abrasive particles ( r , z Located on the inner edge of the coil ( When, based on the calculated total induced voltage u ( t Identify the bimodal distortion feature at the center of the waveform; use the mapping relationship between this bimodal feature and the radial position to invert and correct the size and material properties of the abrasive particles.

8. An electromagnetic sensor signal analysis system based on the coupling of real abrasive particle dynamics trajectory and time-harmonic field strength, characterized in that, The system is implemented based on an electromagnetic sensor signal analysis method according to any one of claims 1-7, which is based on the coupling of real abrasive particle dynamic trajectory and time-harmonic field strength.

9. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a computer program that, when executed by a processor, performs the electromagnetic sensor signal analysis method based on the coupling of real abrasive particle dynamic trajectory and time-harmonic field strength as described in any one of claims 1-7.

10. A computer device, characterized in that, The device includes a memory and a processor. The memory stores a computer program. When the processor runs the computer program stored in the memory, the processor executes the electromagnetic sensor signal analysis method based on the coupling of real abrasive particle dynamic trajectory and time-harmonic field strength as described in any one of claims 1-7.

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