Method for constructing overall frequency response function of electromagnetic coupling system of vibration table machine

Abstract

The application discloses a method for constructing a general frequency response function of a vibration table electromechanical coupling system, and comprises the following steps: S1, applying an electric signal to a measuring point on an electromagnetic vibration table, and converting the electric signal into a force signal excitation; S2, obtaining an acceleration signal of the measuring point according to the force signal excitation; and S3, calculating the frequency response of the acceleration signal to the force signal excitation, and obtaining the complete frequency response function of the general vibration table electromechanical coupling system through the relationship between the force signal excitation and the electric signal. The application proposes a method for equivalently converting a spatially distributed electromagnetic exciting force into a concentrated load, can obtain a more accurate general frequency response function, can more accurately predict the results of an actual test, and can better guide the actual test.

Description

Technical Field

[0001] This technology belongs to the field of vibration testing technology, specifically involving a method for constructing the overall frequency response function of an electromagnetic coupling system for a vibration test bench. Background Technology

[0002] The shaking table involves electric field, magnetic field and structural field. Analyzing it requires multi-physics coupled calculations. The computational workload is too large, resulting in low computational efficiency. Moreover, the superposition of multiple physical fields may further amplify the error. Summary of the Invention

[0003] To address the problem of not being able to determine the frequency response function under uniformly distributed loads, this invention proposes an equivalent algorithm for the overall frequency response function matrix of a vibration table-electromagnetic coupling system. It also proposes a method to equate the spatially distributed electromagnetic excitation force to a concentrated load, which can obtain a more accurate overall frequency response function, enable more precise prediction of actual test results, and provide better guidance for actual experiments.

[0004] To solve the above technical problems, the technical solution adopted by the present invention is as follows:

[0005] A method for constructing the overall frequency response function of an electromagnetic coupling system for a vibration table machine, the method comprising the following steps:

[0006] S1, apply an electrical signal to the measuring point on the electromagnetic vibration table, and convert the electrical signal into a force signal for excitation;

[0007] S2, the acceleration signal at the measuring point is obtained based on the force signal excitation;

[0008] S3, calculate the frequency response of the acceleration signal to the force signal excitation, and obtain the overall frequency response function of the complete electromagnetic coupling system of the vibration table machine through the relationship between the force signal excitation and the electrical signal.

[0009] Furthermore, the electromagnetic coupling system of the vibration table includes a moving coil, an excitation coil, an auxiliary motion device, and a controller, which is used to send excitation electrical signals;

[0010] The moving coil includes a moving coil frame and a drive coil, with the moving coil frame and drive coil fixedly connected. The auxiliary motion device includes an air spring and a guide device. The drive coil has a honeycomb grid-shaped hollow structure inside for water cooling.

[0011] Furthermore, step S1 specifically includes:

[0012] S11, after the alternating time-domain current signal is amplified by the power amplifier, it is applied to the inside of the drive coil. The excitation coil is supplied with a constant DC current, which is obtained from Maxwell's equations (1):

[0013]

[0014] Where B represents the magnetic field strength of the approximately uniform magnetic field in the gap, E represents the electric field strength, Q represents the charge, ε0 represents the vacuum permittivity, and Φ B and Φ E These represent magnetic flux and electric flux, respectively; I represents the magnitude of the current flowing through the driving coil; and μ0 represents the free permeability.

[0015] S12, the excitation coil forms an approximately uniform magnetic field in the gap inside the electromagnetic exciter. Force analysis of this strong magnetic field yields the following results:

[0016] F = BIL (2)

[0017] In the formula, I represents the magnitude of the current flowing through the drive coil, L represents the total length of the drive coil, B represents the magnetic field strength of the approximately uniform magnetic field in the gap, and F is the total force on the entire drive coil.

[0018] Furthermore, S3 includes the following: selecting an inner node within the moving coil, converting the response of the electrical signal into an electromagnetic force on the inner node, then calculating the response of the measuring point acceleration to the electromagnetic force excitation of the inner node, and subsequently calculating the frequency response function of the entire moving coil of the vibration table.

[0019] Furthermore, S3 specifically includes:

[0020] S31, firstly, the driving coil is divided into n nodes, and the electromagnetic force F is uniformly distributed on the n nodes. According to the distribution law of uniformly distributed body force and finite element theory, the force on each node should be equal. According to equation (2):

[0021] F = f1 + ... + f n (3)

[0022] f1 = ... = f n =F / n (4)

[0023] Where f n This represents the equivalent concentrated force acting on the nth node;

[0024] S32, According to the frequency domain substructure method, each node acting on an equivalent concentrated force is an internal node, denoted as a, and its set is denoted as a. The acceleration response at any measuring point d on the driving coil is denoted as a. d According to the superposition principle of linear systems, we get:

[0025]

[0026] By combining equations (2), (4), and (5), we obtain:

[0027]

[0028] Where I represents the magnitude of the current flowing through the drive coil, B represents the magnetic field strength of the approximately uniform magnetic field in the gap created by the excitation coil, and L represents the total length of the drive coil. Let represent the acceleration frequency response functions measured at point d when the excitation is applied at point 1 and point n, respectively.

[0029] Furthermore, the layers of each coil are fixed together with epoxy resin.

[0030] Beneficial effects

[0031] A method is proposed to equate spatially distributed electromagnetic excitation force to a concentrated load. Through precise analysis and modeling of the shaking table, an accurate frequency response function matrix can be obtained, thereby better predicting actual test results. This approach can facilitate better pre-testing in engineering and provide guidance for actual experiments.

[0032] This paper proposes a novel method for constructing the overall frequency response function of a mechanical electromagnetic coupling system. This method solves the problem of converting between electrical signals and measurement point signals, and addresses the issue that the moving coil is subjected to a uniformly distributed force under electrical signal excitation, thus making it impossible to obtain an accurate overall frequency response function. Attached Figure Description

[0033] The accompanying drawings, which form part of this application, are used to provide a further understanding of this application. The illustrative embodiments of this application and their descriptions are used to explain this application and do not constitute an undue limitation of this application.

[0034] Figure 1 This is a schematic diagram of the geometric model of the vibration table drive coil;

[0035] Figure 2 This is a graph showing the error curve at the inner edge point.

[0036] Figure 3 This is the error curve for the outer edge point. Detailed Implementation

[0037] To enable those skilled in the art to better understand the technical solutions in one or more embodiments of this specification, the technical solutions in one or more embodiments of this specification will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of this specification, and not all of the embodiments. Based on one or more embodiments of this specification, all other embodiments obtained by those skilled in the art without creative effort should fall within the protection scope of this document.

[0038] Specific implementation process:

[0039] This invention proposes a method for constructing the overall frequency response function of an electromagnetic coupling system for a vibration table. In order to solve the problem that the frequency response function cannot be obtained under uniformly distributed load, a method is proposed to convert the spatially distributed electromagnetic excitation force into a concentrated load.

[0040] The overall idea of ​​the load equivalent algorithm is as follows: the electrical signal supplied to the electromagnetic vibration table is converted into a force signal, the acceleration signal of the measuring point is obtained through the excitation of the force signal, the frequency response of the acceleration signal to the force signal is first calculated, and then the complete frequency response function of the electromagnetic vibration table is obtained through the relationship between the force signal and the electrical signal.

[0041] The vibration table mainly consists of a moving coil (including the moving coil frame and the drive coil, which are fixedly connected), an excitation coil, and auxiliary motion devices (air springs and guide devices, etc.). The drive coil has a honeycomb-like hollow structure inside (used for water cooling), and the layers of the coil are fixed and insulated with epoxy resin. The alternating time-domain current signal emitted by the controller is amplified by the power amplifier and then enters the drive coil. At the same time, the excitation coil is energized with a constant DC current, as can be seen from Maxwell's equations (1):

[0042]

[0043] The excitation coil generates an approximately uniform magnetic field within the gap inside the electromagnetic exciter. The alternating current within this uniform magnetic field experiences an alternating electromagnetic force of the same frequency. Force analysis readily reveals the following:

[0044] F = BIL (2)

[0045] In the formula, I represents the magnitude of the current flowing through the drive coil, L represents the total length of the drive coil, B represents the magnetic field strength of the approximately uniform magnetic field in the gap, and F is the total force on the entire drive coil.

[0046] Since the moving coil includes both the moving coil frame and the driving coil, the frequency response function includes both the structural response of the moving coil frame and the electromagnetic excitation response of the coil. Therefore, the original frequency response function of the shaking table should be the response of the acceleration at the measuring point to the input signal, i.e., the magnitude of the current or voltage. In actual testing, this frequency response function is relatively easy to obtain; it can also be obtained by calculating multi-physics coupling using the finite element method. However, the original frequency response function obtained either experimentally or through multi-physics coupling is a direct response of the acceleration at the measuring point to the input current or voltage. It lacks a clear internal node, i.e., there is no clear point of application of the force, making it impossible to calculate the cross-point frequency response function and the origin frequency response function.

[0047] Therefore, the main idea is to find a suitable internal node and convert the response of the electrical signal into the electromagnetic force on the internal node instead of directly converting it into the acceleration signal at the measuring point. Then, the response of the measuring point acceleration to the electromagnetic force excitation of the internal node is calculated. In this way, the frequency response function relationship between the electromagnetic field and the structural field is communicated through the electromagnetic force as an intermediary, and then the frequency response function of the entire shaking table moving coil is calculated.

[0048] Analysis of the electromagnetic force experienced by a current-carrying coil under the influence of a magnetic field reveals that the electromagnetic force is equal in magnitude and direction per unit length of the conductor. Without considering the presence of voids within the coil, and assuming the conductor is evenly distributed within it, the electromagnetic force can be considered a uniformly distributed, constant-magnitude, but direction-dependent uniformly distributed body force. Therefore, it is necessary to discretize the system with infinite degrees of freedom and select specific nodes as internal and external nodes. Thus, the finite element method is used to divide the coil and frame into a finite number of elements, thereby discretizing the physical quantities, including the electromagnetic force.

[0049] First, the coil is divided into n nodes, and the electromagnetic force F is distributed across these n nodes. According to the distribution law of uniformly distributed body forces and the finite element theory, the force on each node should be equal. From equation (2), we know that:

[0050] F = f1 + ... + f n (3)

[0051] f1 = ... = f n =F / n (4)

[0052] Equation (3) indicates that the total electromagnetic force F is equivalently concentrated on n nodes, and Equation (4) shows that, according to the law of uniform force distribution, the force on all nodes is equal in magnitude. Where f n This represents the equivalent concentrated force acting on the nth node.

[0053] According to the frequency domain substructure method, all n nodes subjected to concentrated forces are internal nodes, denoted as set a. Now, we want to find the response at point d when an excitation is applied to set a, denoted as the acceleration response at point d, a. d According to the superposition principle of linear systems, we know that:

[0054]

[0055] By combining equations (2), (4), and (5), we can obtain:

[0056]

[0057] In equation (6), I represents the magnitude of the current flowing through the driving coil, B represents the magnetic field strength of the approximately uniform magnetic field in the gap created by the excitation coil, and L represents the total length of the driving coil. Let represent the acceleration frequency response functions measured at point d when the excitation is applied at point 1 and point n, respectively.

[0058] Consider two measuring points: one located at the exact center of the top end face of the shaking table, denoted as the inner edge point, and the other located at the edge of the top end face, denoted as the outer edge point. Simulation calculations revealed that the difference in acceleration response at the measuring points under the action of a concentrated force at 8 points in the middle of the drive coil and under the action of a uniformly distributed body force was minimal. Error results were also calculated for the surface force in the middle of the coil and the concentrated force at 4 points in the middle. The results are shown below. Figure 2 As shown.

[0059] Depend on Figure 2 It can be seen that regardless of whether the measuring point is located on the inner or outer edge, the acceleration signal error exhibits a relatively consistent regularity, which can be summarized as follows:

[0060] The overall trend of the error curve is that it increases with increasing frequency.

[0061] As the number of concentration points increases, the error at the resonance peak decreases. That is, as the number of concentration points increases, the curve becomes flatter, and the overall error and average error become smaller.

[0062] Whether the measuring point is located on the inner or outer edge, it does not affect the pattern of the above error curve, thus eliminating the possibility that the randomness of the measuring point will lead to a biased result.

[0063] When the 8-point concentrated force model is selected, the error at the resonance peak is small, the overall error curve is flat, and the maximum error is less than 1%, which meets the computational accuracy requirements. Therefore, considering both computational accuracy and computational cost, the eight-point concentrated force model is appropriate.

[0064] In summary, the electromagnetic vibration table has a total of 10 nodes, including 8 concentrated force points in the concentrated force model and 2 measuring points on the end face of the vibration table. According to basic matrix knowledge and the naming rules for frequency response functions, the frequency response function matrix of the electromagnetic vibration table will be a 10×10 matrix. If the 8 concentrated force points are named w1-w8 respectively, and the 2 measuring points are named u and v respectively, then the specific frequency response function matrix of the electromagnetic vibration table is as follows:

[0065]

[0066] in,

[0067]

[0068] In the above formula, each element in the matrix is ​​a frequency response function that varies with frequency from point to point. If the sweep interval is 1 Hz, then the overall frequency response function matrix of the electromagnetic vibration table is a three-dimensional matrix of 10×10×1000.

[0069] According to the additivity of linear systems and equation (5), the acceleration responses of measuring points u and v to a unit force applied simultaneously at 8 points should be as follows:

[0070]

[0071]

[0072] According to equation (6), we can see that:

[0073]

[0074]

[0075] Thus, the acceleration response of the input electrical signal to different measuring points can be obtained.

[0076] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Those skilled in the art can make various modifications and adjustments within the technical scope disclosed in the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A method for constructing a general frequency response function of a vibration table electromagnetism coupling system, characterized in that, The method includes the following steps: S1, apply an electrical signal to the measuring point on the electromagnetic vibration table, and convert the electrical signal into a force signal for excitation; S2, the acceleration signal at the measuring point is obtained based on the force signal excitation; S3, calculate the frequency response of the acceleration signal to the force signal excitation, and obtain the overall frequency response function of the complete electromagnetic coupling system of the vibration table machine through the relationship between the force signal excitation and the electrical signal; The electromagnetic coupling system of the vibration table includes a moving coil, an excitation coil, an auxiliary motion device, and a controller, which is used to send excitation electrical signals. The moving coil includes a moving coil frame and a drive coil, the moving coil frame and the drive coil are fixedly connected, the auxiliary motion device includes an air spring and a guide device; the drive coil has a honeycomb grid-shaped hollow structure inside for water cooling. Step S1 is as follows: S11, after the alternating time-domain current signal is amplified by the power amplifier, it is applied to the inside of the drive coil. The excitation coil is supplied with a constant DC current, which is obtained from Maxwell's equations (1): （1） wherein, denotes the magnetic field strength of the gap-approximated uniform magnetic field, denotes the electric field strength, denotes the electric charge quantity, denotes the vacuum permittivity, and denote the magnetic flux and the electric flux, respectively, denotes the current size flowing through the drive coil, denotes the vacuum permeability; S12, the excitation coil forms an approximately uniform magnetic field in the gap inside the electromagnetic exciter. Force analysis of this strong magnetic field yields the following results: （2） wherein, denotes the magnitude of the current flowing through the drive coil, denotes the total length of the drive coil, denotes the magnetic field strength of the approximately uniform magnetic field in the gap, is the total force experienced by the entire drive coil; The S3 includes the following: selecting an inner node within the moving coil, converting the response of the electrical signal into the electromagnetic force on the inner node, then calculating the response of the acceleration at the measuring point to the electromagnetic force excitation of the inner node, and then calculating the frequency response function of the entire moving coil of the shaking table. Specifically, S3 is: S31, firstly, divide the drive coil into n equal nodes, and then apply the electromagnetic force... The force is uniformly distributed across n nodes. According to the distribution law of uniformly distributed body forces and the finite element theory, the force on each node should be equal. According to equation (2): (3) (4) in This represents the equivalent concentrated force acting on the nth node; S32, according to the frequency domain substructure method, each node acting on an equivalent concentrated force is an internal node, denoted as set a, and the acceleration response at any measuring point d on the driving coil is denoted as... According to the superposition principle of linear systems, we get: (5) By combining equations (2), (4), and (5), we obtain: (6) in, This indicates the magnitude of the current flowing through the drive coil. This represents the magnetic field strength created by the excitation coil in the gap, which is approximately a uniform magnetic field. Indicates the total length of the drive coil. , Let represent the acceleration frequency response functions measured at point d when the excitation is applied at point 1 and point n, respectively.

2. The method for constructing the overall frequency response function of the electromagnetic coupling system of the vibration table machine according to claim 1, characterized in that, The layers of each coil are fixed together with epoxy resin.

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