Modeling method of electromagnetic ultrasonic time domain signal in bolt

Abstract

This invention discloses a method for modeling electromagnetic ultrasonic time-domain signals in bolts. The method simplifies the bolt into a cylinder and constructs a prediction model of the bolt's time-domain signal based on EMAT in a cylindrical coordinate system. Specifically, it includes the following steps: Step 1, solving for the force source distribution based on EMAT; Step 2, solving for the ultrasonic wave propagation transfer function in the cylindrical rod; Step 3, solving for the EMAT received time-domain signal. This invention is the first to propose a method for modeling electromagnetic ultrasonic time-domain signals in bolts. This method combines EMAT excitation, sound wave propagation, and transducer reception to establish a model for predicting the bolt's time-domain signal. This model can accurately predict the waveform and amplitude information of the electromagnetic ultrasonic time-domain signal in the bolt, providing a new method for predicting bolt time-domain signals.

Description

Technical Field

[0001] This invention relates to a method for modeling time-domain signals of an electromagnetic ultrasonic transducer (EMAT), specifically a method for modeling electromagnetic ultrasonic time-domain signals in a bolt. Background Technology

[0002] The change in axial force of a bolt can be measured by utilizing the change in ultrasonic wave time. When measuring axial force, it is often necessary to select a sound wave with a good signal-to-noise ratio. Based on the given bolt geometry (bolt diameter and length) and the parameters of the electromagnetic ultrasonic transducer coil and magnet, accurately predicting the received signal of EMAT in the bolt helps to quickly identify and select a waveform with a good signal-to-noise ratio for bolt axial force measurement.

[0003] Currently, the method for obtaining the EMAT time-domain signal based on EMAT parameters and bolt size is the finite element method. The finite element method is feature-rich and flexible, but it has high requirements for computer operation and is time-consuming, especially when the bolt size is large or the transducer frequency is high. Summary of the Invention

[0004] To address the above problems, this invention provides a method for modeling electromagnetic ultrasonic time-domain signals in bolts. This method combines EMAT excitation, sound wave propagation, and transducer reception to establish a model for predicting bolt time-domain signals. This model can accurately predict the waveform and amplitude information of electromagnetic ultrasonic time-domain signals in bolts, providing a new method for predicting bolt time-domain signals.

[0005] The objective of this invention is achieved through the following technical solution:

[0006] A method for modeling electromagnetic ultrasonic time-domain signals in bolts simplifies the bolt into a cylinder and constructs a bolt time-domain signal prediction model based on EMAT in cylindrical coordinates. The method includes the following steps:

[0007] Step 1: Solving for force source distribution based on EMAT:

[0008] Step 11: The static magnetic vector potential distribution of the equivalent current of the permanent magnet in the test block is as follows:

[0009]

[0010] in, This is the equivalent current of the permanent magnet. Where is the radius of the permanent magnet. For the model boundary, Depend on Calculations show that , The relative permeability of the test block and These are first-order and zero-order Bessel functions, respectively.

[0011] Steps 1 and 2: In the test block, the dynamic magnetic vector potential distribution generated by the alternating current is as follows:

[0012]

[0013] in, It is the coil current. and It refers to the inner and outer radii of the coil. , It is the imaginary unit. ;

[0014] Step 13: In cylindrical coordinates, the relationship between the magnetic field components generated by the alternating current and the permanent magnet and the magnetic vector potential is as follows:

[0015]

[0016] Step 1.4: Eddy Currents Generated in the Specimen by Alternating Current for:

[0017]

[0018] Step 15, to Directional integral and according to J × B The Lorentz force components in cylindrical coordinates are expressed as follows:

[0019]

[0020] Step 2: Solving for the transfer function of ultrasonic waves propagating in a round rod:

[0021] Step 2.1 The force source excited by EMAT includes a lateral force source. and longitudinal force source The force source can be considered as the superposition of various guided wave modes. Therefore, the boundary conditions of the circular rod based on EMAT satisfy:

[0022]

[0023] in, Let be the shear stress in each mode of the circular rod. Let be the vertical stress in each mode of the circular rod. The amplitude of each modal excitation, Represents a mode;

[0024] Step 22: The amplitude of the guided wave mode is written as:

[0025]

[0026] Steps two and three: The propagation process of the guided wave affects the phase information of the sound wave, as expressed in the following expression:

[0027]

[0028] in, This represents the distance the guided wave propagates, i.e., the length of the cylinder;

[0029] Step Two Four, according to V × B The expression for the EMAT receive transfer function is:

[0030]

[0031] in, yes Directional static magnetic field, yes Direction of static magnetic field, Hehe The expression for the velocity component in the direction is:

[0032]

[0033]

[0034] Step 25: The transfer function of the signal propagating in the cylindrical rod is:

[0035]

[0036] Step 3: Solving for the time-domain signal received by EMAT:

[0037] The transfer functions of the propagating guided wave modes at each frequency point are calculated and then summed over all frequency points. The frequency domain signal is then transformed to the time domain. Finally, the signal received by the transducer is obtained. Represented as:

[0038]

[0039] in, This represents an excitation signal.

[0040] Compared with the prior art, the present invention has the following advantages:

[0041] (1) A bolt electromagnetic ultrasonic time-domain signal modeling method was proposed for the first time;

[0042] (2) Accurate time-domain signals can be obtained based on transducer parameters and bolt geometry;

[0043] (3) Compared with the finite element method, this method is less time-consuming and more convenient. Attached Figure Description

[0044] Figure 1The EMAT model is in cylindrical coordinates.

[0045] Figure 2 A flowchart of a method for modeling electromagnetic ultrasonic time-domain signals in bolts;

[0046] Figure 3 For the EMAT stimulus model;

[0047] Figure 4 For the sound wave transfer function model;

[0048] Figure 5 For the received signal model;

[0049] Figure 6 As an excitation signal;

[0050] Figure 7 The results are from experimental and model calculations. Detailed Implementation

[0051] The technical solution of the present invention will be further described below with reference to the accompanying drawings, but it is not limited thereto. Any modifications or equivalent substitutions to the technical solution of the present invention that do not depart from the spirit and scope of the technical solution of the present invention should be covered within the protection scope of the present invention.

[0052] This invention provides a method for modeling electromagnetic ultrasonic time-domain signals in bolts. The method simplifies the bolt into a cylinder, and the EMAT model in cylindrical coordinates is as follows: Figure 1 As shown. Figure 2 As shown, the solution steps of the model include three parts: solving the force source distribution based on EMAT, solving the transfer function of ultrasonic wave propagation in the round rod, and solving the time-domain signal received by EMAT.

[0053] I. EMAT Incentives

[0054] This invention only considers the Lorentz force mechanism during the EMAT transduction process. The goal of modeling during electromagnetic ultrasonic emission is to derive the force source distribution of the Lorentz force. Cylindrical waveguide electromagnetic ultrasonic signal measurement typically uses helical coils and cylindrical permanent magnet structures, such as... Figure 1 As shown. The EMAT force source distribution calculation process is as follows. Figure 3 As shown. The key physical quantity expressions and calculation processes in the model are as follows:

[0055] The static magnetic vector potential distribution of the equivalent current of the permanent magnet in the test block is as follows:

[0056] (1)

[0057] in, This is the equivalent current of the permanent magnet. The saturation magnetic induction intensity of the permanent magnet; Where is the radius of the permanent magnet. For the model boundary, Depend on Calculations show that and These are first-order and zero-order Bessel functions, respectively. , denoted as ρ, where ρ is the relative permeability of the test block.

[0058] In the test block, the dynamic magnetic vector potential distribution generated by the alternating current is as follows:

[0059] (2)

[0060] in, It is the coil current. and It refers to the inner and outer radii of the coil. , It is the imaginary unit. In cylindrical coordinates, the relationship between the magnetic field components generated by the alternating current and the permanent magnet and the magnetic vector potential is as follows:

[0061] (3)

[0062] Eddy currents generated in the specimen by alternating current for:

[0063] (4)

[0064] right Directional integral and according to J × B The Lorentz force components in cylindrical coordinates are expressed as follows:

[0065] (5)

[0066] II. Signal Propagation

[0067] In the electromagnetic ultrasound propagation process, the modeling objective is to derive the sound wave transfer function. The transfer function calculation includes calculating the amplitude of the guided wave modes, the phase change caused by signal propagation, and the ultrasonic signal reception transfer function. The specific calculation process is as follows: Figure 4 As shown, the key physical quantity expressions are as follows:

[0068] The force source excited by the transducer includes transverse and longitudinal force source The force source can be considered as the superposition of various guided wave modes. Therefore, the boundary conditions of the circular rod based on EMAT satisfy:

[0069] (6)

[0070] Among them, the shear stress of each mode in the circular rod and vertical stress for:

[0071] (7)

[0072] (8)

[0073] The amplitude of each modal excitation, Represents mode, Represents the radius of the cylinder. , , For wave number, This refers to the longitudinal wave velocity of ultrasound. Let be the transverse wave velocity. According to equation (6), the amplitude of the guided wave mode can be written as:

[0074] (9)

[0075] The propagation process of the guided wave affects the phase information of the sound wave, as expressed by:

[0076] (10)

[0077] in, This represents the distance the guided wave propagates, i.e., the length of the cylinder. According to... V × B The expression for the EMAT receive transfer function is:

[0078] (11)

[0079] in, yes Direction of static magnetic field, yes Direction of static magnetic field, and The expression for the velocity component in the direction is:

[0080] (12)

[0081] (13)

[0082] Therefore, the transfer function for signal propagation in the rod is:

[0083] (14)

[0084] III. Transducer Received Signal

[0085] Calculate the sum of the transfer functions of the propagating guided wave modes at each frequency point, then sum the transfer functions over all frequency points, transform the frequency domain signal to the time domain, and finally, as shown... Figure 5 As shown, the signal received by the transducer Represented as:

[0086] (15)

[0087] in, This represents an excitation signal. Example

[0088] In this embodiment, the EMAT includes a helical coil and a cylindrical permanent magnet, and... Figure 1 The parameters are consistent, with the helical coil having an inner diameter of 0.5 mm, an outer diameter of 6.5 mm, and a lift-off distance of 0.4 mm; the permanent magnet having a radius of 10 mm, a height of 15 mm, and a lift-off distance of 1.5 mm. The cylindrical specimen being tested has a diameter of 30 mm and a length of 255 mm. The RETIC5000 is used to transmit and receive ultrasonic waves, with the excitation signal as follows: Figure 6 As shown, the experimentally obtained signal and the ultrasonic signal calculated by the model are as follows: Figure 7 As shown, the signal waveforms and relative amplitudes obtained from the experiment and the model calculations are almost identical.

Claims

1. A method for modeling electromagnetic ultrasonic time-domain signals in bolts, characterized in that... The method simplifies the bolt into a cylinder and constructs a time-domain signal model for the bolt based on EMAT in cylindrical coordinates. Specifically, it includes the following steps: Step 1: Solving for force source distribution based on EMAT: Step 11: The static magnetic vector potential distribution of the equivalent current of the permanent magnet in the test block is as follows: in, This is the equivalent current of the permanent magnet. Where is the radius of the permanent magnet. For the model boundary, Depend on Calculations show that , Let be the relative permeability of the test block. and These are first-order and zero-order Bessel functions, respectively. Steps 1 and 2: In the test block, the dynamic magnetic vector potential distribution generated by the alternating current is as follows: in, It is the coil current. and It refers to the inner and outer radii of the coil. , It is the imaginary unit. ; Step 13: In cylindrical coordinates, the relationship between the magnetic field components generated by the alternating current and the permanent magnet and the magnetic vector potential is as follows: Step 1.4: Eddy Currents Generated in the Specimen by Alternating Current for: Step 15, to Directional integral and according to J × B The Lorentz force components in cylindrical coordinates are expressed as follows: Step 2: Solving for the transfer function of ultrasonic waves propagating in a round rod: Step 2.1 The force source excited by EMAT includes a lateral force source. and longitudinal force source The force source is considered as the superposition of various guided wave modes. Therefore, the boundary conditions for the circular rod based on EMAT satisfy: in, Let be the shear stress in each mode of the circular rod. Let be the vertical stress in each mode of the circular rod. The amplitude of each modal excitation, Represents a mode; Step 22: The amplitude of the guided wave mode is written as: Steps two and three: The propagation process of the guided wave affects the phase information of the sound wave, as expressed in the following expression: in, This represents the distance the guided wave propagates, i.e., the length of the cylinder; Step Two Four, according to V × B The expression for the EMAT receive transfer function is: in, yes Direction of static magnetic field, yes Direction of static magnetic field, and The expression for the velocity component in the direction is: Step 25: The transfer function of the signal propagating in the cylindrical rod is: Step 3: Solving for the time-domain signal received by EMAT: The transfer functions of the propagating guided wave modes at each frequency point are calculated and then summed over all frequency points. The frequency domain signal is then transformed to the time domain. Finally, the signal received by the transducer is obtained. Represented as: in, This represents an excitation signal.

2. The method for modeling electromagnetic ultrasonic time-domain signals in bolts according to claim 1, characterized in that... Shear stress in each mode of the circular rod and vertical stress for: in, Represents the radius of the cylinder. , , For wave number, This refers to the longitudinal wave velocity of ultrasound. The speed of sound for transverse waves.

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