Electric vibration table control system modeling method based on electricity-magnetism-structure coupling modeling

Abstract

The invention provides an electric vibration table control system modeling method based on electricity-magnetism-structure coupling modeling. Model equivalence and simplification are carried out on a moving coil, boundary conditions of the moving coil are determined, a dynamic model of the moving coil is established, and the moving coil model is corrected according to a modal test of the moving coil; working points of a magnetic circuit system of the vibration table are determined according to actual conditions of the vibration table, an electromagnetic model of the magnetic circuit system is established, and the electromagnetic model is corrected according to actual magnetic field distribution of air gaps of the vibration table. The physical nature of the electromagnetic vibration table is analyzed, an electricity-magnetism-structure coupling mathematical model is established, the transmission mode between magnetic field exciting force and table surface response data is determined, and electricity-magnetism-structure coupling modeling of the vibration table is achieved. On the basis of establishing an electricity-magnetism-structure coupling model, a complete electric vibration table simulation model is analyzed and established through a control system, and the simulation precision of the electric vibration table is improved.

Description

Technical Field

[0001] The present invention relates to the field of simulation model establishment, and in particular to a modeling method for an electric vibration table control system based on electro-magnetic-structural coupling modeling. Background Art

[0002] With the development of industries such as aerospace and electromechanical, the requirements for the reliability, durability, and safety of products and components are becoming increasingly stringent. Vibration table tests can simulate various complex environments to verify product quality, dynamic strength, reliability, and other performance. Electric vibration tables are widely used in vibration environment experiments due to their advantages such as easy control, wide frequency range, and complete waveforms. However, vibration tests also have limitations such as long vibration cycles and difficulty simulating real-world vibration excitation. Vibration table simulation analysis can provide predictions for vibration table tests, compensate for potential over-testing and under-testing issues that may arise from vibration table tests, and expand the scope of engineering applications of vibration test simulation technology.

[0003] In view of the fact that the coupling effect of traditional electric vibration table simulation modeling is insufficiently considered, the present invention makes the dynamic coil model equivalent and simplified, determines the boundary conditions of the dynamic coil, establishes the dynamic coil's dynamic model, and modifies the dynamic coil model based on the modal test of the dynamic coil; determines the working point of the vibration table's magnetic circuit system based on the actual situation of the vibration table, establishes an electromagnetic model of the magnetic circuit system, and modifies the electromagnetic model based on the actual magnetic field distribution of the vibration table's air gap. The physical nature of the electromagnetic vibration table is analyzed, a mathematical model of the electro-magnetic-structural coupling is established, the transmission method between the magnetic field excitation force and the table surface response data is determined, and the electro-magnetic-structural coupling modeling of the vibration table is realized. Based on the establishment of the electro-magnetic-structural coupling model, a complete electric vibration table simulation model is established through control system analysis to improve the simulation accuracy of the electric vibration table.

[0004] Patent document CN102568769A discloses a method for simulation modeling of a vibration table, including: analyzing the structural characteristics of the vibration table, establishing a finite element model of the vibration table, and realizing partial vibration process simulation through the finite element model. The patent involves the coupling between the model structure and the magnetic field, but the description of the coupling situation in the model establishment is not complete, and the model mechanism is not clear enough. There is still room for improvement in the above aspects.

[0005] Patent document CN103674658A discloses a method for simulating the magnetic field distribution of an electric vibration table, including: analyzing the magnetic field distribution of the vibration table after power is applied, and determining the influence of the magnetic field on the motion of the vibration table's dynamic coil. However, the patent only considers the influence of the magnetic field distribution on the motion of the vibration table's dynamic coil, lacks correlation analysis of the coupling effect, and fails to use model formulas to elaborate on the coupling state in detail. There is still room for improvement in the above aspects.

[0006] The electric vibration table control system modeling method based on electro-magnetic-structural coupling modeling established by the present invention addresses the problem that traditional models do not adequately consider coupling effects. The dynamic coil is modeled equivalently and simplified, the boundary conditions of the dynamic coil are determined, the dynamic model of the dynamic coil is established, and the dynamic coil model is corrected according to the modal test of the dynamic coil; the working point of the magnetic circuit system of the vibration table is determined according to the actual situation of the vibration table, the electromagnetic model of the magnetic circuit system is established, and the electromagnetic model is corrected according to the actual magnetic field distribution of the air gap of the vibration table. The physical nature of the electromagnetic vibration table is analyzed, a mathematical model of electro-magnetic-structural coupling is established, the transmission method between the magnetic field excitation force and the table surface response data is determined, and the electro-magnetic-structural coupling modeling of the vibration table is realized. Based on the establishment of the electro-magnetic-structural coupling model, a complete electric vibration table simulation model is established through control system analysis. The accuracy and effectiveness of the model analysis are improved, providing theoretical support for the research of vibration simulation technology. Summary of the Invention

[0007] The purpose of the present invention is to provide a control system modeling method for an electric vibration table based on electro-magnetic-structural coupling modeling. This method addresses the electro-magnetic-structural coupling effect of the electric vibration table by modeling the dynamic coil equivalently and simplifying it, determining its boundary conditions, establishing a dynamic model of the dynamic coil, and correcting the dynamic coil model based on modal tests of the dynamic coil. Furthermore, the operating point of the magnetic circuit system of the vibration table is determined based on the actual conditions of the vibration table, and an electromagnetic model of the magnetic circuit system is established. This electromagnetic model is corrected based on the actual magnetic field distribution in the air gap of the vibration table. The physical nature of the electromagnetic vibration table is analyzed, a mathematical model of electro-magnetic-structural coupling is established, and the transmission method between the magnetic field excitation force and the table surface response data is determined, thereby achieving electro-magnetic-structural coupling modeling of the vibration table. Based on the electro-magnetic-structural coupling model, a complete electric vibration table simulation model is established through control system analysis.

[0008] The technical solution adopted to achieve the above purpose includes the following steps:

[0009] (1) The present invention takes into account the working principle of the electric vibration table. When the vibration table is working, a direct current with opposite current directions is passed through the upper and lower magnetic field coils, so that the magnet is magnetized and a strong constant magnetic field environment is formed in the annular air gap. The vibration table motion system consists of a driving coil and a table frame, collectively referred to as a moving coil. The moving coil is the most important component of the vibration table, and the vibration performance of the vibration table is determined by it. The moving coil is supported and fixed in the air gap by the upper support springs around the table and the air suspension device, namely the air spring. This part is the elastic support system. The operating frequency of the vibration table is generally determined by the natural frequency of the vibration system composed of the support system and the moving coil. Both types of coils of the electric vibration table will pass a large current and generate a large amount of heat. The conductor will also generate heat due to eddy current loss in the alternating magnetic field of the driving coil, so a cooling system is required. The guide system refers to the guide system ring at the bottom of the moving coil, which is used to ensure the movement direction of the moving parts, reduce lateral movement and torsion during vibration, and avoid friction loss between the moving parts and the magnetic poles. The main components for generating electromagnetic force are the excitation coil and the drive coil. The drive coil of the vibration table is located in a working air gap with high magnetic induction intensity. When the drive signal is generated by the controller and amplified by the power amplifier and loaded onto the drive coil, the vibration table will generate the required vibration waveform.

[0010] During operation, a set DC current is passed through the excitation coil to generate a magnetic field. The magnetization of the magnetic steel guides the distribution of magnetic lines of force, resulting in an extremely strong constant magnetic field in the annular air gap. According to the right-hand rule, the direction of the constant magnetic field is radially inward along the drive coil. When AC current is passed through the drive coil, the energized coil is subjected to the alternating Ampere force in the constant magnetic field, causing the moving coil to vibrate up and down.

[0011] F=Bli=2πrnB I sin(ωt)

[0012] Where F represents the electromagnetic force acting on the electrodynamic shaker, B is the magnetic flux density T in the air gap of the electrodynamic shaker, l represents the effective length of the drive coil wire, I is the drive current amplitude A, r is the drive coil radius, n is the number of turns in the drive coil, and is the alternating current frequency. For a given shaker, the coil radius, number of turns, and air gap magnetic flux density are all constants, so the electromagnetic force F is proportional to the current amplitude I. In the electrodynamic shaker control system, the drive current is controlled to produce different acceleration outputs on the dynamic table surface. The magnetic field in the shaker is generated by the high-current excitation coil. The magnetic circuit system itself has certain asymmetries. The alternating magnetic field generated by the alternating current flowing through the drive coil interacts with the excitation magnetic field, preventing the formation of a constant and uniform magnetic field in the air gap. This results in uneven driving force in the drive coil, indirectly highlighting the necessity of establishing an electromagnetic model for the electrodynamic shaker.

[0013] (2) Establish the theoretical model of the dynamic coil structure according to the given vibration model (such asFigure 1 As shown), after analyzing the vibration environment in which it is located, the simplified vibration theory model of the dynamic coil of the electric vibration table is obtained as follows Figure 2 As shown, the entire system has four degrees of freedom: X1, X2, Y, and Z (not shown). M1 represents the vibration table, the central guide rod, and the frame, while M2 represents the winding excitation coil. K1 represents the equivalent connection stiffness between the vibration table frame and the winding coil, K2 represents the equivalent spring stiffness between the central guide rod and the air spring, and K3 and K4 (not shown) represent the equivalent stiffness of the spring support system surrounding the table. C1 represents the structural damping between the frame and the winding coil, while C2, C3, and C4 (not shown) represent the structural damping of the air spring and U-shaped spring support system.

[0014] According to the simplified model diagram, the following equations can be listed based on the basic knowledge of vibration dynamics:

[0015]

[0016]

[0017] After sorting, we get the system of equations:

[0018]

[0019] Write this equation in matrix form:

[0020]

[0021] Among them are:

[0022]

[0023] For the undamped free vibration differential equation, the damping effect is no longer considered, and the system characteristic equation can be obtained:

[0024]

[0025] Expanding it gives:

[0026]

[0027] The solution is:

[0028]

[0029] It can be seen that the resonant frequency of the moving coil is related to k1, k2, m1, and m2, that is, to its own system stiffness and mass. When the moving coil vibrates longitudinally, its resonant frequency is related to the stiffness of the leaf spring. Theoretically, the natural frequency of the simplified four-degree-of-freedom model of the moving coil is obtained.

[0030] Introducing the modal coordinate q, that is, {x} = [Φ] {q}, decouple the matrix equation and transform it into a diagonal matrix, and substitute it into:

[0031]

[0032] Transpose the natural vibration mode matrix [Φ] T Multiplying the above formula on the left yields:

[0033]

[0034] The mass matrix [M] and the stiffness matrix [K] are both positive definite or semi-positive definite symmetric matrices, so they are diagonalized using orthogonality. The damping matrix satisfies the necessary and sufficient conditions for decoupling: [C][M] -1 [K]=[K][M] -1 [C]

[0035] At this time there are:

[0036]

[0037] In the formula:

[0038] [Mi]=[Φ] T [M][Φ], [Mi] is the diagonalized modal mass matrix;

[0039] [Ci]=[Φ] T [C][Φ], [Ci] is the diagonalized modal damping matrix;

[0040] [Ki]=[Φ] T [K][Φ], [Ki] is the diagonalized modal stiffness matrix;

[0041] The original formula with coupling factors is decoupled into a set of independent n-degree-of-freedom subsystem equations in modal coordinates, which is convenient for analyzing and solving the system equations.

[0042] (3) Establishment of the dynamic coil finite element model. Since the dynamic coil, connector, table and other components of the vibration table have many geometric elements such as mounting holes, chamfers, and connection holes, these geometric elements have little effect on the dynamic characteristics of the vibration table, but they cause great obstacles to the meshing and model calculation of the model, which not only increases the workload but also reduces the calculation accuracy of the model. Therefore, these geometric elements are selectively cleaned up first.

[0043] (4) Dynamic modal analysis: For an electric vibration table, the dynamic coil structure is the core component of the table body movement, so it is necessary to conduct structural dynamic modeling analysis on it. In the process of studying and analyzing the system, the elastic support system and the magnetic circuit system are approximately regarded as rigid. Therefore, when analyzing the structural model, the dynamic coil structure is mainly used as the main focus, and the elastic support system is converted into the form of boundary conditions to simulate the actual dynamic coil vibration. Unlike the previous dynamic coil simulation method that only retains the degree of freedom of the vibration direction, in order to more realistically simulate the dynamic coil vibration when setting the boundary conditions, a simulated support rigid spring is used to connect the four sides of the table.

[0044] In the actual structure, the dynamic coil is mounted on the rigid base of the vibration table via elastic supports. During vibration, four sets of support springs are evenly distributed around the table at 90° intervals. One end of the steel sheet is fixed to the side of the dynamic coil table and the other end is fixed to the vibration table base. They are mainly used to support the dynamic coil and limit its lateral and torsional movement. A rigid shaft, which is connected to the bottom of the vibration table and is part of the guide system, guides the vertical movement of the dynamic coil and limits the lateral movement of the vibration table. Another part of the elastic support system is the air spring below the rigid shaft. It mainly supports the overall motion mechanism of the vibration table and provides axial support stiffness.

[0045] The model boundary conditions were established based on the actual situation of the dynamic coil. After performing modal analysis using finite element software, the natural frequencies of each order and their corresponding vibration modes were obtained. The axial resonance frequency characteristic parameter of the dynamic coil is defined as the vibration frequency in the axial direction of vibration. It is the main characteristic indicator of the electric vibration table. Its value determines the upper limit of the operating frequency of the vibration table. Therefore, it should be found when studying the vibration characteristics of the electric vibration table. The vibration mode of the overall tensile and compressive deformation of the vibration table along the axial direction is found, and its corresponding frequency is the axial resonance frequency of the dynamic coil. Then, by performing a sweep frequency test on the dynamic coil of the electric vibration table, the frequency response curve of the acceleration of a certain control point on the vibration table surface is obtained, and the peak frequency is observed, verifying the axial resonance frequency of the dynamic coil of the electric vibration table.

[0046] (5) Analysis of the principle of the vibration table magnetic circuit system. There are many types of electric vibration tables. According to the form of magnetic source, they can be divided into excitation type and permanent magnet type. According to the form of magnetic circuit, they can be divided into single magnetic circuit type and dual magnetic circuit type. According to the cooling method, they can be divided into natural cooling, air cooling and water cooling. Each vibration table has its own scope of application. The vibration table studied in this paper is a dual magnetic circuit excitation vibration table. The magnetic field system consists of an excitation coil, a central magnetic pole, upper and lower magnetic steel covers and an annular air gap. In the magnetic field analysis of the electric vibration table, the size and uniformity of the air gap magnetic flux density are key parameters related to various indicators of the vibration table system. The operating frequency range, amplitude, distortion, table surface unevenness, lateral vibration ratio, maximum load, etc. of the vibration table are all affected by the distribution of the air gap magnetic flux density. When the vibration table is working, a constant current in opposite directions is passed through the upper and lower excitation coils, generating a constant magnetic potential, so that the magnetic lines of force form a magnetic circuit through the central magnetic pole and the upper and lower steel covers, thereby forming a magnetic field. Because the upper and lower excitation coils flow in opposite directions, the two magnetic lines of force overlap in the annular air gap, resulting in a stronger magnetic field in the air gap where the drive coil resides. Applying a specific drive current signal to the drive coil in the high-magnetic-induction working air gap causes the moving coil to move up and down due to the electromagnetic force, outputting a corresponding vibration waveform through the tabletop.

[0047] Assuming F is the electromagnetic force vector acting on the driving coil, F can be described in the form of Maxwell stress tensor as shown below:

[0048]

[0049] Where S is a closed surface surrounding the moving circle, n e is the unit normal vector at a point on this surface, and B is the magnetic induction intensity at this point, both of which satisfy Maxwell's equations. In order to facilitate the subsequent solution of the differential equations describing the electric field and magnetic field, the magnetic vector potential A and the magnetic scalar φ are introduced. The magnetic vector potential A is defined as:

[0050]

[0051] Satisfies the Lorentz condition:

[0052]

[0053] Where μ is the magnetic permeability of the medium, ε is the dielectric constant, and the introduced magnetic vector potential satisfies Gauss's flux theorem:

[0054]

[0055] Substitute the magnetic vector potential A and the magnetic scalar φ into Faraday's law of electromagnetic induction Then we can get the following formula:

[0056]

[0057] Where E is the electric field intensity, substitute the magnetic vector potential A and the magnetic scalar φ into Ampere's law. In which H is the magnetic field intensity, J is the conduction current density vector, and D is the electric displacement vector. Combining the above formulas, we can get:

[0058]

[0059] Similarly, substitute the magnetic vector potential A and the magnetic scalar φ into Gauss's law Where ρ is the charge density, the differential equation describing the electric field is:

[0060]

[0061] By solving the above equation with finite element software, the distribution of the electromagnetic field can be obtained, specifically the change of the magnetic induction intensity at a certain point in space over time, so as to solve the overall force condition of the dynamic coil finite element structure.

[0062] (6) Simulation process of the vibration table magnetic circuit system. After comparing multiple finite element software during the calculation process, Ansoft Maxwell software was selected to simulate the magnetic field. Maxwell2D / 3D software is mainly used to analyze analysis modules such as static magnetic field, eddy current field, and transient field. In this software, electromagnetic devices such as permanent magnet equipment and excitation devices can be set to obtain their working characteristics under static, steady-state, and transient working conditions. In this part, a static magnetic field solver is used. It provides analysis of the magnetic field caused by constant current, permanent magnets, and external excitation. It is widely applicable to various types of exciters, motors, and permanent magnets. In this module, physical quantities such as magnetic field force, torque, and inductance can be automatically calculated. In the subsequent part, a transient magnetic field solver is used to solve the precise electromagnetic force, torque, and other physical quantities of the magnetic circuit system at any time under any given time-varying current source excitation. The module is used to simultaneously solve strongly coupled equations such as electric field, magnetic field, and motion. The Ansys electromagnetic field analysis edge element method is used to perform static magnetic field analysis on the magnetic circuit system, and the element part uses Solid117 edge element. In the edge element method, the structural degrees of freedom are related to the element edges and not to the element nodes. This method has good solving capabilities in the simulation of three-dimensional low-frequency static and dynamic electromagnetic fields.

[0063] The magnetic circuit system of the electrodynamic shaker is constructed based on the dynamic coil model parameters. The basic requirement is that the drive coil of the shaker be positioned precisely within the air gap where the magnetic flux lines of the excitation coil overlap, while also allowing for the dynamic coil to be accommodated within a certain margin. This requires a certain amount of air space. The overall design should ensure a symmetrical structure to ensure a symmetrical distribution of magnetic induction intensity. The magnetic circuit system of the electrodynamic shaker is modeled using SolidWorks software. A plan view of the magnetic circuit system is first drawn, and then a 3D model is obtained by rotating it around the central axis. The model is exported in step format and used in Ansoft Maxwell software for the next step of magnetic field analysis. The magnetic circuit structure consists of magnets, including a central magnet, outer magnetic rings, upper and lower magnetic covers, two excitation coils, and one drive coil. To ensure calculation accuracy, an air space is created in the air gap between the magnets and the excitation coils to insulate the excitation coils and prevent errors caused by current transfer into the magnets.

[0064] (7) Analysis of electromagnetic-structural coupling method. The driving principle of the electric vibration table is that the excitation coil at the lower end of the moving coil is supplied with alternating current, and is subjected to the Ampere force in the air gap magnetic field. Due to the change in the direction of the alternating current, the moving coil vibrates up and down. The magnetic field in the air gap is generated by the upper and lower excitation coils in the magnetic steel, and its size and distribution have been analyzed. Coupled field analysis refers to the consideration of the cross-action and interaction of two or more physical fields during the finite element analysis process. Based on the coupled field analysis of ANSYS Workbench, the electromagnetic field and the vibration environment of the structure are taken into account during the finite element analysis process, and the electromagnetic field and the structure are coupled. Currently, the coupling field is divided into two types according to the order of coupling: direct coupling and sequential coupling. This time, the sequential coupling method is used to manually set many test parameters, such as boundary conditions, load excitation, etc., to achieve transfer coupling under different grids and different analysis environments.

[0065] The coupling process is to first import the electromagnetic model of the electric vibration table with the drive coil into Maxwell 3D software, perform transient electromagnetic field analysis, and obtain the electromagnetic force data of the drive coil under two complete drive alternating current cycles. Then open ANSYS Workbench to set the Transient Structural analysis link, set the boundary conditions for the dynamic coil to perform transient structural analysis, and then couple Maxwell 3D and Transient Structural links. The obtained electromagnetic force data is passed to the structural analysis link as the excitation force to perform vibration response analysis and obtain the electromagnetic-structural coupling vibration response characteristics of the electric vibration table. The coupling flow chart is as follows: Figure 3 shown.

[0066] The electromagnetic-structural coupling analysis is more complex than the single magnetic field coupling method, but it takes into account the influence of the electric vibration table excitation coil on the magnetic circuit system. Therefore, the electromagnetic force load applied to the electric vibration table excitation coil is applied according to the actual electromagnetic force distribution result, which is more in line with the actual situation, making the simulation results more accurate and reducing the error of the simulation experiment in principle.

[0067] (8) Analysis of the influence of table surface uniformity and coil displacement change on electromagnetic force. For electric vibration tables, table surface vibration consistency is one of the indicators to measure its vibration performance. Table surface uniformity refers to the calculation of the ratio of the maximum deviation of the acceleration amplitude of each point on the table surface and the table surface center point to the acceleration amplitude of the table surface center point in the same measurement when the vibration table is unloaded and multiple accelerometers are rigidly connected to the center of the vibration table surface and on the circumference of different diameters. Table surface uniformity N A The calculation formula is as follows:

[0068]

[0069] Because the shaker structure-electromagnetic unidirectional coupling only transmits real-time electromagnetic force data to the shaker drive coil via Maxwell software, and fails to transmit the displacement data of the drive coil during motion back to Maxwell via Ansys Workbench software, it is necessary to analyze the impact of the displacement changes of the shaker drive coil on the electromagnetic force acting on the drive coil. Because the magnetic induction intensity at each point along the height of the working air gap is not uniform, the electromagnetic force exerted on the moving coil varies at different positions under the same drive current, indicating a certain degree of electromagnetic nonlinearity. The electromagnetic force coefficient varies with the position of the drive coil, and this electromagnetic nonlinearity can be measured using the electromagnetic force coefficient-position curve.

[0070] Here the distance between the driving coil and the center position is set to x d , when x d By taking different values, the electromagnetic force of the driving coil at different displacements can be calculated. In order to more conveniently describe the relationship between the axial electromagnetic force and the moving coil's position under different current loads and moving coil positions, the concept of the electromagnetic force coefficient k is introduced here, which is:

[0071]

[0072] Through multiple tests, the relative difference of the electromagnetic force coefficient of the driving coil relative to the central position at different distances from the central position is analyzed under two different current load conditions.

[0073]

[0074] (9) A single-input single-output random vibration and sine frequency sweep control algorithm was established for the vibration table structure-electromagnetic coupling model. In order to meet higher test requirements, the established random vibration and sine control system added a sine control part on the basis of the broadband random vibration control system;

[0075] The establishment of the random vibration control system of this patent adopts the spectrum reproduction method, and the frequency domain signal control of the output signal is performed based on the self-power spectrum control algorithm, so that the response spectrum of the control point and the reference spectrum remain relatively consistent. The process of the control signal is as follows: an acceleration sensor is set at the control point of the specimen, the measured acceleration signal is converted into a voltage signal after passing through a charge amplifier, and then the signal is converted into an analog-to-digital signal, and the power spectrum PSD is calculated after performing an FFT fast Fourier time-domain-frequency domain conversion. The result is compared and corrected with the preset reference spectrum to obtain a new driving spectrum. For the new driving spectrum, it is necessary to add a random phase and then use IFFT transformation to obtain a pseudo-random signal, and then perform time domain randomization to obtain a true random signal. The analog signal obtained by digital-to-analog conversion is output to the power amplifier and then drives the dynamic coil of the vibration table, so that the power spectrum of the controlled point is close to the reference spectrum.

[0076] For a given sinusoidal reference signal or swept frequency reference signal, a sinusoidal amplitude correction algorithm is used for sinusoidal vibration control. A unit white noise excitation spectrum is applied to the drive coil as the initial input signal to obtain the acceleration response of the control point. The model's frequency response function is derived from the output noise model of the frequency response function. A sinusoidal control spectrum with a fixed amplitude is set, and the amplitude spectrum of the drive spectrum is derived from this control spectrum. The time-domain drive signal is constructed based on the frequency range, frequency interval, and their corresponding amplitudes.

[0077] The model output is compared with the control spectrum, and the drive spectrum is corrected through the amplitude correction control algorithm to establish the control system model.

[0078] The beneficial effects achieved by the electric vibration table control system modeling method based on electric-magnetic-structural coupling modeling provided by the present invention are: by analyzing the physical nature of the electromagnetic vibration table, a mathematical model of electric-magnetic-structural coupling is established, and the transmission method between the magnetic field excitation force and the table surface response data is determined, the electric-magnetic-structural coupling modeling of the vibration table is realized, and on the basis of the establishment of the electric-magnetic-structural coupling model, a complete electric vibration table simulation model is established through control system analysis, thereby improving the simulation accuracy of the electric vibration table. BRIEF DESCRIPTION OF THE DRAWINGS

[0079] The invention will be further described below with reference to the accompanying drawings:

[0080] Figure 1 It is a moving coil model diagram;

[0081] Figure 2 It is a simplified model of the vibration theory of the electrodynamic shaker;

[0082] Figure 3 It is a coupled flow chart;

[0083] Figure 4 It is a cleanup diagram of the moving coil geometry;

[0084] Figure 5 This is a 1 / 8 dynamic coil model diagram;

[0085] Figure 6 It is the finite element model of the vibration table's dynamic coil and the mesh quality map;

[0086] Figure 7 is a schematic diagram of boundary conditions;

[0087] Figure 8 It is the vibration mode diagram of the moving coil;

[0088] Figure 9 It is a schematic diagram and modeling diagram of the magnetic circuit system of the electric vibration table;

[0089] Figure 10 It is the vector diagram of the current and magnetic field distribution of the magnetic circuit system of the electric vibration table;

[0090] Figure 11 It is a simulated magnetic induction distribution cloud diagram of the magnetic circuit system of the electric vibration table;

[0091] Figure 12 It is a schematic diagram of the locations of the measuring points on the table;

[0092] Figure 13 It is the acceleration response curve of the measuring point;

[0093] Figure 14 This is the relative difference diagram of the electromagnetic force coefficient of the moving coil from the central position;

[0094] Figure 15 is the frequency response function diagram of the model;

[0095] Figure 16 It is a diagram of the windowed superposition process of a true random signal;

[0096] Figure 17 It is a comparison chart between the reference spectrum and the response spectrum of the shaking table model;

[0097] Figure 18 It is a comparison diagram between the response signal after control and the reference signal;

[0098] Figure 19 It is the frequency response function image from 0 to 1024 Hz;

[0099] Figure 20 This is the flow chart of random vibration control in electromagnetic structure coupled vibration system simulation DETAILED DESCRIPTION

[0100] The following, combined with the accompanying drawings and specific embodiments, further details the modeling method for an electrodynamic vibration table control system based on electromagnetic-magnetic-structural coupling modeling, as proposed by the present invention. The advantages and features of the present invention will become more apparent from the following description and claims. It should be noted that the drawings are highly simplified and not accurately scaled, and are intended solely to facilitate and clarify the purpose of illustrating the embodiments of the present invention.

[0101] The present invention provides a modeling method for an electric vibration table control system based on electro-magnetic-structural coupling modeling, comprising:

[0102] (1) Analyze and study the theory of the dynamic structure of the electric vibration table, and establish a theoretical model of the dynamic structure of the vibration table by comprehensively considering the vibration table surface, vibration table frame, and driving coil.

[0103] (2) Based on the theoretical model of the dynamic coil structure of the electric vibration table, the influence of geometric elements on the dynamic characteristics of the vibration table is considered, the geometric elements are cleaned up, the dynamic coil finite element model is established, and the dynamic coil modal analysis is performed.

[0104] (3) Analyze the principle of the magnetic circuit system of the electric vibration table to obtain the distribution of the electromagnetic field, solve the overall stress of the dynamic coil finite element structure, and establish an electromagnetic system simulation model for the electric vibration table.

[0105] (4) Analyze the electromagnetic-magnetic-structural coupling method of the electric vibration table.

[0106] (5) Establish an electro-magnetic-structural unidirectional coupling model of the electric vibration table, and analyze the influence of the model table surface uniformity and coil displacement changes on the electromagnetic force.

[0107] (6) Based on the electric-magnetic-structural coupling model of the electric vibration table, the control system model of the electric vibration table is established by considering the correction of measured data.

[0108] Specifically, in one embodiment, a method for modeling an electrodynamic vibration table control system based on electro-magnetic-structural coupling modeling comprises the following steps:

[0109] (1) A system has four degrees of freedom: X1, X2, Y, and Z. M1 represents the vibration table, the central guide rod, and the frame. M2 represents the winding excitation coil. K1 represents the equivalent connection stiffness between the vibration table frame and the winding coil. K2 represents the equivalent spring stiffness between the intermediate guide rod and the air spring. K3 and K4 represent the equivalent stiffness of the support spring system around the table. C1 is the structural damping between the frame and the winding coil. C2, C3, and C4 (not shown) are the structural damping of the air spring and U-shaped spring support system.

[0110] According to the basic knowledge of vibration dynamics, the following equations can be listed:

[0111]

[0112] Write this equation in matrix form:

[0113]

[0114] Among them are:

[0115]

[0116] For the undamped free vibration differential equation, the damping effect is no longer considered, and the system characteristic equation can be obtained:

[0117]

[0118] Expanding it gives:

[0119]

[0120] The solution is:

[0121]

[0122] It can be seen that the resonant frequency of the moving coil is related to k1, k2, m1, and m2, that is, to its own system stiffness and mass. When the moving coil vibrates longitudinally, its resonant frequency is related to the stiffness of the leaf spring. Theoretically, the natural frequency of the simplified four-degree-of-freedom model of the moving coil is obtained.

[0123] Introducing the modal coordinate q, that is, {x} = [Φ] {q}, decouple the matrix equation and transform it into a diagonal matrix, and substitute it into:

[0124]

[0125] By transposing the natural vibration mode matrix [Φ]T and multiplying it on the left, we can get:

[0126]

[0127] The mass matrix [M] and the stiffness matrix [K] are both positive definite or semi-positive definite symmetric matrices, so they are diagonalized using orthogonality. The damping matrix satisfies the necessary and sufficient conditions for decoupling: [C][M] -1 [K]=[K][M] -1 [C]

[0128] At this time there are:

[0129]

[0130] In the formula:

[0131] [Mi]=[Φ]T [M][Φ], [Mi] is the diagonalized modal mass matrix;

[0132] [Ci]=[Φ] T [C][Φ], [Ci] is the diagonalized modal damping matrix;

[0133] [Ki]=[Φ] T [K][Φ], [Ki] is the diagonalized modal stiffness matrix;

[0134] The original formula with coupling factors is decoupled into a set of independent n-degree-of-freedom subsystem equations in modal coordinates, which is convenient for analyzing and solving the system equations.

[0135] (2) The geometric elements are first cleaned up Figure 4 The red circle shows the main geometric cleaning part of the dynamic coil (the upper picture shows the effect before cleaning, and the lower picture shows the effect after cleaning), including deleting the chamfers of the dynamic coil table screws, filling the round chamfers and straight chamfers of the dynamic coil frame. Since the mounting holes of the dynamic coil in the vibration table are connected by bolts, all the mounting holes are also filled.

[0136] After cleaning the geometry of the vibration table's dynamic coil and sliding table CAD models, the CAD models were imported into Hypermesh for finite element meshing.

[0137] (3) The dynamic coil frame is made of ZL302; the winding is made of 6061 aluminum; the dynamic coil frame and winding are glued together. The basic dimensions of the dynamic coil are: dynamic coil overall height 800mm, winding coil height 300mm, outer diameter 390mm, inner diameter 350mm. The dynamic coil model was simplified using Inspire software, and the screw removal and screw hole filling were completed. This made the subsequent finite element model meshing more efficient and accurate, facilitating dynamic coil modal analysis.

[0138] Table 1 Dynamic coil material properties

[0139]

[0140] In the actual structure, the dynamic coil is mounted on the rigid base of the vibration table via elastic supports. During vibration, four sets of support springs are evenly distributed around the table at 90° intervals. One end of the steel sheet is fixed to the side of the dynamic coil table and the other end is fixed to the vibration table base. They are mainly used to support the dynamic coil and limit its lateral and torsional movement. A rigid shaft, which is connected to the bottom of the vibration table and is part of the guide system, guides the vertical movement of the dynamic coil and limits the lateral movement of the vibration table. Another part of the elastic support system is the air spring below the rigid shaft. It mainly supports the overall motion mechanism of the vibration table and provides axial support stiffness.

[0141] The model boundary conditions are established according to the actual situation of the dynamic coil, which is divided into three parts: the upper support spring constraint is symmetrically distributed at intervals of 90° on the table surface, and a total of 16 radial springs are evenly distributed, and their stiffness is K1, which is 3.125×10 6 N / m, and the viscous damping coefficient C1 is 8×10 6 N·S / m; the guide constraint of the guide rod inserted into the bottom of the cylinder in the center of the vibration table constrains the translational and rotational degrees of freedom in the X and Y directions of all the nodes on the inner surface of the cylinder in contact with the guide rod in the model, retaining only the axial translational and rotational degrees of freedom of the dynamic coil; the air spring at the bottom of the dynamic coil and the steel leaf springs around the table provide equivalent axial stiffness. Under the vibration isolation effect of the air spring, the first-order axial natural frequency of the system is generally below 5Hz. At this point, the system can be simplified to a single-degree-of-freedom system with the dynamic coil as the mass block. The natural frequency calculation formula is known according to the known model mass. The axial equivalent stiffness k of the air spring is obtained to be 1.84×105N / m, and the viscous damping coefficient C2 is 1×105N·S / m. The overall application of the dynamic coil boundary conditions is as follows Figure 7 shown.

[0142] The Lanczos method of eigenvalue extraction was applied to solve the problem. After performing modal analysis using finite element software, the natural frequencies of each order and their corresponding vibration modes were obtained. The vibration mode of the overall tensile and compressive deformation of the vibration table along the axial direction was found, and the corresponding frequency was the axial resonance frequency of the dynamic coil. A frequency sweep test was then performed on the dynamic coil of the electric vibration table to obtain the frequency response curve of the acceleration of a certain control point on the vibration table surface. The peak frequency was observed, verifying the axial resonance frequency of the dynamic coil of the electric vibration table. Figure 8 This is the vibration mode diagram of the moving coil.

[0143] From the vibration mode of the moving coil, we can see that the first-order natural frequency of the moving coil is the resonant frequency of the air spring, that is, the moving coil moves upward as a whole, with a resonant frequency of 4.99Hz; the second-order natural frequency is the rotation of the moving coil around the guide shaft, with a frequency of 13.83Hz; the fifth-order is the breathing movement of the moving coil, with a frequency of 379.23Hz; the forty-sixth-order is the overall tensile and compressive deformation of the vibration table along the axial direction, that is, the first-order axial resonant vibration mode of the moving coil, with a frequency of 1726.4Hz. The other order vibration modes are the rotational bending of the ribs, the torsional deformation of the drive coil, and the local complex deformation. After observing the modal vibration mode diagrams of each order of the finite element model, the following conclusions can be drawn:

[0144] 1) The first-order mode of the dynamic coil is a resonant mode caused by the interaction between the dynamic coil and the internal support system of the vibration table, commonly known as the suspension mode. This mode manifests as the dynamic coil's entire translational motion along the Z-axis. The frequency of this modal is primarily determined by the stiffness of the spring unit and the total mass of the dynamic coil. If the mass of the dynamic coil is known, the modal frequency can be adjusted by adjusting the spring stiffness. The first-order mode of the dynamic coil has little effect on its higher-order modes.

[0145] 2) The dynamic coil structure itself is symmetrical, and many modal orders appear in pairs, which are conjugate modes. Their vibration shapes are the same but the phases are different. The 3rd and 4th order vibration shapes are manifested as the movement of the lower end of the center hole driving the overall breathing movement of the dynamic coil, which is affected by the constraint of the center guide rod. The 7th and 8th order vibration shapes are manifested as the reverse bending mode of the entire dynamic coil, where the table and the drive coil bend in opposite directions. Due to the existence of conjugate modes, when the electric vibration table operates near these frequency points, these modes may be excited, resulting in the axis of the drive coil not coinciding with the main vibration direction of the vibration table, and exciting the nonlinearity of the electromagnetic force of the vibration table.

[0146] 3) The 46th order is the elastic tensile-compressive deformation mode of the dynamic coil in the axial direction, also known as the first-order axial expansion and contraction mode. Like the first-order mode, this mode is characterized by relative elastic deformation between the table and the drive coil. This order frequency is a crucial design parameter in the design of an electrodynamic shaker, determining its upper operating frequency limit and significantly influencing its dynamic performance.

[0147] (4) The magnetic circuit system of the electric vibration table is established according to the parameters of the dynamic coil model. The basic requirement is that the vibration table drive coil can be placed exactly in the air gap where the magnetic lines of force of the excitation coil overlap, and at the same time, the dynamic coil can be placed in the case of some space, that is, a part of the air domain must be left. The overall design should ensure a symmetrical structure so that the magnetic induction intensity is also symmetrically distributed. Use Solidworks software to model the magnetic circuit system of the electric vibration table. First, draw a plan view of the magnetic circuit system, and then obtain a 3D model of the magnetic circuit system by rotating it around the central axis. Export the model in step format to Ansoft Maxwell software for the next step of magnetic field analysis. The magnetic circuit structure contains magnets, including a central magnet, an outer magnet ring, and two upper and lower magnet covers, as well as two excitation coils and a driving coil. In order to ensure the accuracy of the calculation, an air domain must be established in the air gap between the magnet and the excitation coil to insulate the excitation coil from the magnet to prevent the current from entering the magnet and causing errors. The resulting schematic diagram and modeling diagram of the magnetic circuit system of the electric vibration table are as follows: Figure 9 shown.

[0148] Ansoft Maxwell software is used to simulate the magnetic field. It can analyze various states such as static magnetic field, eddy current field, transient field, etc., and can obtain physical quantities such as magnetic field force, torque, inductance, etc. The material of the excitation coil is set to copper, which has a relative magnetic permeability of 1 and an electrical conductivity of 59.6×10 6 S / m. The upper and lower excitation coils are defined as 500 turns, and the current excitation surface is set in the XY plane, and the current is 80A per turn. The current directions of the upper and lower excitation coils are set to be opposite, and the direction of the magnetic lines of force is required to be radially inward when passing through the annular air gap. The material of the central magnet and the upper and lower magnet covers is defined as Q235 steel. Set the calculation area Region and boundary conditions. The boundary condition is that the external magnetic lines of force are parallel, that is, AZ=0. The grid division of the magnetic circuit system directly affects the calculation accuracy. The overall magnetic circuit model is divided by hexahedral grid mapping, and the overall grid is uniform.

[0149] After setting the conditions, run the program. An excitation current flows through the excitation coil to generate a magnetic field. The magnet is magnetized by the magnetic field, and the magnetic lines of force pass through the center magnet, then return to the magnet via the upper and lower poles, crossing the air gap to form a stable magnetic circuit. Because the magnetic circuits of both the upper and lower excitation coils pass through the air gap, the magnetic induction intensity at the air gap should be high. As the magnetic lines of force pass through the magnet into the air medium and then from the air medium into the magnet, their distribution changes during this process. The magnetic lines of force in the air region diverge, while the magnetic lines of force are denser near the magnet. Consequently, the magnetic lines of force in the air gap field are non-uniform. Figure 10 This is the vector diagram of the current and magnetic field distribution of the magnetic circuit system of the electric vibration table given by Maxwell software. Figure 11 The magnetic induction distribution cloud diagram of the magnetic circuit system of the electric vibration table is simulated.

[0150] The vector diagram of the current and magnetic field distribution in the magnetic circuit system of the electric vibration table shows that the current is primarily distributed in the excitation coil and in opposite directions. The magnetic field is perpendicular and inward in the annular air gap. The magnetic induction cloud distribution shows that the air gap is colored light green, corresponding to a magnetic induction intensity of approximately 1.34 T. The magnetic lines of force are densely distributed at both ends of the central magnetic pole, and the magnetic field is stronger in the central air gap due to the combined effect of the magnetic fields of the upper and lower coils. For an electric vibration table, the radius and number of turns of the excitation coil are fixed. To increase the magnetic induction intensity in the air gap, the DC current supplied can be adjusted.

[0151] (5) In order to analyze the vibration consistency of the simulated vibration table system, 8 response measurement points were selected on the table based on the results of fixed-frequency test simulation at multiple frequency points. Their positions and coordinates are shown in the figure. All nodes are located on distribution circles of different diameters.

[0152] The acceleration response curve images of each measuring point on the table are as follows: Figure 13shown.

[0153] The acceleration output curves at each measuring point on the table are generally consistent, forming a sinusoidal curve after the system stabilizes. However, as the frequency increases, the peak values ​​of the vibration acceleration at different measuring points on the table begin to deviate, and the table surface begins to exhibit vibration non-uniformity. The simulation results show that the maximum uniformity of the vibration table surface is approximately 4.62%, demonstrating the practicality of the surface uniformity of the established electrodynamic vibration table structure-electromagnetic coupling model.

[0154] Through multiple tests, the relative difference of the electromagnetic force coefficient of the driving coil relative to the central position at different distances from the central position is analyzed under two different current load conditions. Its image is Figure 14 As shown in the figure, it can be observed that the electromagnetic force coefficient shows a nonlinear distribution as the position of the moving coil changes. The current load has little effect on it, and the relative difference does not exceed 3% in general.

[0155] (6) Calculate the frequency response function. For the input signal X(t) and the output signal Y(t), the corresponding frequency domain signals are obtained by Fourier transform, which are expressed as X(ω) and Y(ω) respectively, and satisfy the relationship:

[0156] Y(ω)=H(ω)X(ω)

[0157] Where H(ω) is the frequency response function of the constructed model, which is determined by the properties of the vibration table magnetic circuit system and the vibration table dynamic coil, boundary conditions, etc. The primary goal in random vibration control tests is to achieve power spectrum balance at the controlled point. The characteristics of the response signal reflect the structural characteristics of the entire system. In the actual frequency response calculation process, the measured input and output signals will inevitably be interfered by noise, so a reasonable frequency response function estimation method should be selected to improve the effect of vibration control. The output noise model is adopted. Assuming that only the output signal has noise interference, N is used to represent the output noise. At this time, the relationship between N and the input signal X and the output signal Y is:

[0158] Y=HX+N

[0159] Multiply both ends of the above equation by X H , we can find the mathematical expectation of both ends:

[0160] S yx =HS xx +S nx

[0161] Among them S yx Represents the cross power spectrum density of the input signal and the output signal, S xx Represents the autopower spectral density of the input signal, S nxrepresents the cross power spectral density of the input signal and the output noise. Assuming that the output noise and the input signal are uncorrelated, then S nx =0, we can deduce:

[0162]

[0163] Where H is the frequency response function calculated using the output noise model. For the vibration table model, the unit white noise excitation spectrum is used as the input signal. Since the analysis range is 0 to 2000 Hz, the sampling frequency f is set according to the sampling theorem. s The frequency response of the control point acceleration is 5000Hz, the time interval dt of the time domain signal is 0.0002s, and there are 1024 sampling points, totaling 0.2048s. After obtaining the time domain response of the control point acceleration, an FFT transform is performed on it. The cross-power spectrum of the input and output signals and the auto-power spectrum of the input signal are calculated, and then the frequency response function of the model is calculated. The figure below shows the frequency response function of the vibration table structure-electromagnetic unidirectional coupling model from 0 to 2500Hz. The image shows that the output noise model used is effective and can well reflect the frequency response characteristics of the constructed model.

[0164] The spectrum control of the spectrum reproduction type used in random vibration control only cares about the amplitude characteristics of the frequency domain signal, so the autopower spectrum relationship of the input and output signals is used in the calculation:

[0165] S y (ω)=|H(ω)| 2 S x (ω)

[0166] The goal of the random vibration control system is to make the response signal power spectrum of the controlled point as similar as possible to the reference spectrum, that is, to make the difference between the two within the tolerance range. Therefore, the most ideal state is S y (ω)=S r (ω), the driving spectrum should satisfy the following requirements:

[0167]

[0168] Before performing random vibration control on the vibration table, the corresponding reference spectrum is set according to the test specification conditions. The control goal is to make the power spectrum of the control point consistent with the reference spectrum, which can be obtained:

[0169] S y (ω)=S r (ω)=|H(ω)| 2 S x (ω)

[0170] From the above formula, we can get the product of the driving spectrum and the square of the frequency response function of the controlled system as the reference spectrum. Therefore, the random vibration control process is as follows: Modify the driving spectrum S x(ω) to compensate for the transmission ratio H of the controlled system, their product and the reference spectrum S r The difference of (ω) is within a certain tolerance range. Since the transmission ratio H of the controlled system cannot be known in advance before the test control, in order to calculate the transmission ratio of the controlled system, we can first assume that the transmission ratio H of the controlled system is 1. Then, the reference spectrum PSD is used as the driving signal to make the vibration table vibrate, and the vibration signal PSD spectrum S of the test control point is obtained. y (ω), then we can use the known S of the controlled system r (ω) and the test output signal S y1 (ω) Calculate the transmission ratio H1:

[0171]

[0172] After obtaining the transmission ratio H1 of the controlled system, the new driving spectrum PSD, namely S x1 (ω):

[0173]

[0174] After the new driving spectrum PSD excites the vibration table to generate vibration, the new S y2 (ω), from which the new transmission ratio H2 can be calculated. However, due to the nonlinearity and time-varying nature of the vibration table control system, the transmission ratio obtained in each calculation process cannot be exactly the same. Therefore, it is necessary to make corrections through repeated iterations to meet the requirements and satisfy the equilibrium state. The algorithm used in this simulation is the auto-power spectrum control method, and its equilibrium formula is as follows:

[0175]

[0176] Among them S r is the reference spectrum set, G dd,i is the power spectrum of the control point of the ith time, D d,i is the i-th driving spectrum, D d,i+1 is the driving spectrum of the i+1th time. Set the control reference spectrum S r , the control point sets the auto power spectrum shape in the frequency range of 20 ~ 2000Hz. The auto spectrum shape consists of a rising spectrum in the range of 20 ~ 100Hz, a flat spectrum in the range of 100 ~ 1000Hz, and a falling spectrum in the range of 1000 ~ 2000Hz. The slope of the rising spectrum is k = +3dB / oct, the slope of the falling spectrum is k = -3dB / oct, and the value of the flat spectrum is 0.02g 2 / Hz.

[0177] Set up the control spectrum r After that, the driving spectrum S d It can be obtained by the following formula:

[0178] Sd =|H(ω) -1 | 2 S r

[0179] After obtaining the driving spectrum, the signal amplitude spectrum is obtained by the Cooley-Tukey method:

[0180]

[0181] Where N represents the length of the sampling sequence, and Δt is the sampling interval. Since the autospectral density only contains amplitude information and lacks phase information, the time series obtained by directly performing an inverse FFT transform on the amplitude spectrum cannot form a pseudo-random signal. Therefore, a random phase must be added for calculation. A uniformly distributed random phase is generally used in random vibration control. The specific process of time domain randomization is as follows:

[0182] 1) Random delay and reversal

[0183] A pseudo-random vibration signal sequence consisting of N points is connected end to end, and a random point is used as the starting point. Power spectrum analysis is performed on N points in either sequential or reverse order. Since the random vibrations studied are stationary and undergo various states, random delays, reversals, and arbitrary starting points in the middle do not affect the size of the final spectrum. This method generates 2N time series (starting from N points, in either sequential or reverse order), yielding a near-true random signal. Given the inherent principle that the statistical properties of random vibrations cannot be precisely predicted, the fact that each frame of this signal sampled identically to the spectral distribution does not meet this principle, necessitating further correction.

[0184] 2) Windowing and superposition process

[0185] Windowing data after truncation produces two effects in random vibration signal acquisition and analysis theory: first, the continuous spectrum in the frequency domain is discretized with a time interval of df = 1 / T; second, power leakage occurs. The process of generating a truly random signal is the inverse of the above process, and after windowing and extension, the characteristics of a continuous spectrum can be obtained. A half-sine window is typically used for windowing in the time-domain randomization process of vibration control, namely:

[0186]

[0187] Each half-sine window is delayed by T / 2. The specific windowing and superposition process is as follows: Figure 16 shown.

[0188] The adoption of the windowing method ensures the continuity of the signal, but it also reduces the signal frequency resolution to a certain extent. If the control error requirement of ±3dB is not met, the driving spectrum iterative correction formula of the self-power spectrum control method is Make corrections.

[0189] The figure below shows the control effect of the vibration table model. The control point is a point on the table surface. The control effect shows that the control result meets the error range of the reference spectrum, achieving random vibration control of the model.

[0190] For sinusoidal vibration control, a unit white noise excitation spectrum is applied to the drive coil as the initial input signal to obtain the acceleration response at the control point. The model's frequency response function is then derived from the output noise model of the frequency response function. The figure below shows the frequency response function from 0 to 1280 Hz.

[0191] Assume that the sinusoidal signal expression returned at this time in sinusoidal control is:

[0192] V=Asin(ωt+φ)

[0193] Then the square value of the sinusoidal signal is calculated by the RMS method, and the trigonometric function induction formula can be obtained:

[0194]

[0195] From this formula, we can see that the square of the signal contains two parts: one part is the DC constant The other part is a cosine component with twice the original frequency. This signal is passed through a digital low-pass filter to remove the AC component, leaving only the DC constant. This DC constant is the average power of the sinusoidal signal, denoted as P. The amplitude of this sinusoidal signal is then:

[0196]

[0197] Traditional sinusoidal control algorithms modify the amplitude of the sine wave to meet the reference value requirements. This modification is accomplished by continuously adjusting the current flowing into the drive coil. At each frequency point, the amplitude of the next drive signal is determined by comparing the calculated amplitude with the designed control signal reference value. The equalization formula is as follows:

[0198]

[0199] Where A i is the current driving signal, A i+1 is the next drive signal; E is the ratio of the reference control signal amplitude to the response signal amplitude; k is the compression factor, an integer ranging from 1 to 8, with smaller values ​​indicating faster correction. This algorithm is used for sinusoidal vibration control.

[0200] Figure 18The comparison diagram of the response signal after control and the reference signal shows that the acceleration amplitude of the response signal of the controlled point is very close to that of the control signal, and the maximum relative error is about 18.31%. Therefore, it is feasible to use this method to perform sinusoidal vibration control of the vibration table.

[0201] Anything not described in detail in this specification belongs to the prior art known to those skilled in the art. It will be apparent to those skilled in the art that the present invention is not limited to the details of the exemplary embodiments described above and that the present invention can be implemented in other specific forms without departing from the spirit or essential characteristics of the invention. Therefore, the embodiments should be considered in all respects as illustrative and non-restrictive, and the scope of the invention is defined by the appended claims rather than the foregoing description, and it is intended that all variations within the meaning and scope of equivalents of the claims be encompassed within the present invention.

Claims

1. A modeling method for an electric vibration table control system based on electro-magnetic-structural coupling modeling, characterized in that: The steps include: S1. Analyze the structure theory of the dynamic coil of the electric vibration table, comprehensively consider the vibration table surface, vibration table frame and driving coil, and establish the theoretical model of the dynamic coil structure of the vibration table; S2. Based on the theoretical model of the dynamic coil structure of the electric vibration table obtained in step S1, considering the influence of geometric elements on the dynamic characteristics of the vibration table, cleaning the geometric elements, establishing a finite element model of the dynamic coil, and performing dynamic coil modal analysis; S3. Analyze the principle of the magnetic circuit system of the electric vibration table, obtain the distribution of the electromagnetic field, solve the overall force of the dynamic coil finite element structure, and establish an electromagnetic system simulation model for the electric vibration table; S4. Analysis of the electro-magnetic-structural coupling method for the electrodynamic shaker; S5. Establish an electro-magnetic-structural unidirectional coupling model of an electrodynamic vibration table and analyze the effects of the model table surface uniformity and coil displacement changes on the electromagnetic force; S6. Based on the electric-magnetic-structural coupling model of the electric vibration table, the control system model of the electric vibration table is established by considering the correction of measured data.

2. The method for modeling an electric vibration table control system based on electro-magnetic-structural coupling modeling according to claim 1, characterized in that: The step S1 comprises: S1-1. Analyze the working principle of the electric vibration table; S1-2. According to the structural characteristics of the electric vibration table, the vibration environment in which it is located is analyzed to obtain a simplified theoretical model of the dynamic coil vibration of the electric vibration table, and the model is described by the modal mass matrix, modal damping matrix, and modal stiffness matrix.

3. The method for modeling an electric vibration table control system based on electro-magnetic-structural coupling modeling according to claim 2, wherein: The step S2 comprises: S2-1. Analyze the geometric elements of the mounting holes, chamfers, and connection holes of the electric vibration table's moving coil, connector, and table components, and perform geometric cleaning. S2-2. Import the CAD model of the electric vibration table into Hypermesh for finite element meshing. Due to the symmetry of the electric vibration table structure, the vibration table geometric model is divided into 1 / 8 models for meshing. S2-3. Structural dynamics modeling and analysis of the dynamic coil structure of the vibration table: Simplify the dynamic coil model using Inspire software, remove the screws, fill the screw holes, and perform dynamic coil modal analysis using finite element model meshing.

4. The method for modeling an electric vibration table control system based on electro-magnetic-structural coupling modeling according to claim 2, wherein: The step S3 comprises: S3-1. Conduct principle analysis of the magnetic circuit system of the electric vibration table. Conduct model analysis based on the characteristics of the magnetic field system of the dual-magnetic circuit excitation vibration table, which consists of the excitation coil, center magnetic pole, upper and lower magnetic steel covers, and annular air gap. S3-2. Assuming F is the electromagnetic force vector acting on the driving coil, F is described in the form of Maxwell stress tensor as shown below: Where S is a closed surface surrounding the moving circle, n e is the unit normal vector at a point on this surface, and B is the magnetic induction intensity at this point, both of which satisfy Maxwell's equations. Introducing the magnetic vector potential A and the magnetic scalar φ, the magnetic vector potential A is defined as: Satisfies the Lorentz condition: Where μ is the magnetic permeability of the medium, ε is the dielectric constant, and the introduced magnetic vector potential satisfies Gauss's flux theorem: Substitute the magnetic vector potential A and the magnetic scalar φ into Faraday's law of electromagnetic induction Then we get the following formula: Where E is the electric field intensity, substitute the magnetic vector potential A and the magnetic scalar φ into Ampere's law. In which H is the magnetic field intensity, J is the conduction current density vector, and D is the electric displacement vector, combining the above formulas yields: Similarly, substitute the magnetic vector potential A and the magnetic scalar φ into Gauss's law Where ρ is the charge density, the differential equation describing the electric field is: The distribution of the electromagnetic field is obtained by solving the above equation with finite element software, specifically the change of the magnetic induction intensity at a certain point in space over time, so as to solve the overall force condition of the dynamic coil finite element structure; S3-3. We used Ansoft Maxwell software to simulate the magnetic field. Based on the dynamic coil model parameters, we established the magnetic circuit system for the electric vibration table. This ensured that the vibration table drive coil was located precisely in the air gap where the magnetic field lines of the excitation coil overlapped. This also ensured that there was enough space for the dynamic coil to fit within. This meant that a portion of the air domain was required. The overall design ensured a symmetrical structure, resulting in a symmetrical distribution of magnetic induction intensity. S3-4. Use SolidWorks software to model the magnetic circuit system of the electric vibration table. First, draw a plan view of the magnetic circuit system, and then obtain a 3D model of the magnetic circuit system by rotating it around the central axis. Export the model in step format to Ansoft Maxwell software for the next step of magnetic field analysis. S3-5. Use Ansoft Maxwell software to simulate the magnetic field, analyze the static magnetic field, eddy current field, transient field and other states, and obtain physical quantities such as magnetic field force, torque, and inductance. After the conditions are set, run the program, and an excitation current is passed through the excitation coil to generate a magnetic field. The magnet is magnetized under the action of the magnetic field, and the magnetic lines of force pass through the center magnet, then return to the magnet through the upper and lower magnetic poles, and pass through the air gap to form a stable magnetic circuit.

5. The method for modeling an electric vibration table control system based on electro-magnetic-structural coupling modeling according to claim 4, characterized in that: The step S4 comprises: S4-1. Coupled field analysis based on ANSYS Workbench takes into account the vibration environment of the electromagnetic field and the structure during the finite element analysis process. A sequential coupling method is used to set boundary conditions and load excitations to achieve transfer coupling under different grids and different analysis environments to couple the electromagnetic field and the structure. S4-2. Import the electromagnetic model of the electric vibration table with the drive coil into Maxwell 3D software for transient electromagnetic field analysis. Obtain the electromagnetic force data of the drive coil under two complete drive alternating current cycles. Then, open ANSYS Workbench to set up the transient structural analysis link. Set boundary conditions for the dynamic coil to perform transient structural analysis. Then, couple Maxwell 3D and the transient structural link. Transfer the obtained electromagnetic force data to the structural analysis link as the excitation force for vibration response analysis.

6. The method for modeling an electric vibration table control system based on electro-magnetic-structural coupling modeling according to claim 5, characterized in that: The step S5 comprises: S5-1. Establishing an electromagnetic-magnetic-structural coupling model: Perform a transient magnetic field analysis on the magnetic field model with the drive coil added in the Maxwell magnetic field analysis. Then, import the analyzed electromagnetic force into the Ansys Workbench transient structural analysis with the boundary conditions already loaded to analyze the vibration response. S5-2. Analyze the uniformity of the model surface. The surface uniformity refers to the calculation of the ratio of the maximum deviation of the acceleration amplitude between each point on the surface and the center point of the surface to the acceleration amplitude at the center point of the surface when the vibration table is unloaded and multiple accelerometers are rigidly connected to the center of the vibration table and on the circumference of different diameters in the same measurement; the surface uniformity N A The calculation formula is as follows: Where A is the acceleration amplitude of the center point of the worktable in the same measurement, ΔA max It is the absolute value of the maximum deviation of the acceleration amplitude of each point on the worktable relative to the acceleration amplitude of the center point of the worktable in the same measurement; S5-3. Analyze the effect of model coil displacement changes on electromagnetic force. Because the shaker structure-electromagnetic unidirectional coupling only transmits real-time electromagnetic force data to the shaker drive coil via Maxwell software, the displacement data of the drive coil during movement cannot be transmitted back to Maxwell software via Ansysworkbench software. Analyze the effect of the shaker drive coil displacement changes on the electromagnetic force acting on the drive coil. The electromagnetic nonlinearity caused by the uneven magnetic induction intensity at each point along the height direction of the working air gap is measured by the electromagnetic force coefficient-position curve; The distance between the driving coil and the center position is set to x d , when x d When different values ​​are taken, the electromagnetic force of the driving coil at different displacements can be calculated; the concept of electromagnetic force coefficient k is introduced, which is: Through multiple tests, the relative difference of the electromagnetic force coefficient of the driving coil relative to the central position at different distances from the central position is analyzed under two different current load conditions.

7. The method for modeling an electric vibration table control system based on electro-magnetic-structural coupling modeling according to claim 6, characterized in that: The step S6 comprises: S6-1. Based on the vibration table structure-electromagnetic coupling model, a single-input single-output random vibration and sine frequency sweep control algorithm was established. To meet higher test requirements, the established random vibration and sine control system added a sine control part on the basis of the broadband random vibration control system; S6-2. The random vibration control system is established by using spectrum reproduction and performing frequency domain signal control on the output signal based on the self-power spectrum control algorithm, so that the response spectrum of the control point and the reference spectrum remain relatively consistent; The control signal goes through the following process: an acceleration sensor is set at the control point of the specimen, the measured acceleration signal is converted into a voltage signal after passing through a charge amplifier, and then the signal is converted into a digital signal, and the power spectrum PSD is calculated after FFT fast Fourier time domain-frequency domain conversion. The result is compared and corrected with the preset reference spectrum to obtain a new driving spectrum; for the new driving spectrum, a random phase needs to be added and then a pseudo-random signal is obtained through IFFT transformation, and then a true random signal is obtained through time domain randomization; the analog signal obtained after digital-to-analog conversion is output to the power amplifier and then drives the dynamic coil of the vibration table, so that the power spectrum of the controlled point is close to the reference spectrum. S6-3. For a given sinusoidal reference signal or a swept frequency reference signal, a sinusoidal amplitude correction algorithm is used to perform sinusoidal vibration control. A unit white noise excitation spectrum is loaded onto the drive coil as the initial input signal to obtain the acceleration response of the control point. The frequency response function of the model is obtained from the output noise model of the frequency response function. A sinusoidal control spectrum with a fixed amplitude is set to obtain the amplitude spectrum of the drive spectrum from this control spectrum. A time-domain drive signal is constructed based on the frequency range and frequency interval and their corresponding amplitudes. S6-4. Compare the model output with the control spectrum, and modify the drive spectrum through the amplitude correction control algorithm to establish the control system model.

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