Modeling method for electromagnetic ultrasonic time-domain signal in bolt

Abstract

The invention discloses a bolt electromagnetic ultrasonic time domain signal modeling method, which simplifies a bolt into a cylinder, and constructs a bolt time domain signal model based on EMAT under a cylindrical coordinate system, and specifically comprises the following steps: step 1, solving force source distribution based on EMAT; 2, solving a propagation transfer function of ultrasonic waves in the round bar; and step 3, solving the EMAT receiving time domain signal. According to the bolt electromagnetic ultrasonic time-domain signal modeling method, the bolt electromagnetic ultrasonic time-domain signal modeling method is provided for the first time, the model for predicting the bolt time-domain signal is established by combining EMAT excitation, sound wave propagation and transducer receiving, the model can accurately predict the waveform and amplitude information of the electromagnetic ultrasonic time-domain signal in the bolt, and a new method is provided for predicting the bolt time-domain signal.

Description

Technical Field

[0001] The invention relates to a method for modeling an electromagnetic ultrasonic transducer (EMAT) time domain signal, and in particular to a method for modeling an electromagnetic ultrasonic time domain signal in a bolt. Background Art

[0002] The change in ultrasonic sound can be used to measure the change in bolt axial force. 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 electromagnetic ultrasonic transducer coil and magnet parameters, accurately predicting the EMAT receiving signal in the bolt helps to quickly judge and select a waveform with a good signal-to-noise ratio for bolt axial force measurement.

[0003] Currently, the method to obtain the EMAT time domain signal based on the EMAT parameters and bolt size is the finite element method. The finite element method is comprehensive and flexible, but for the case of large bolt size or high transducer frequency, it has high requirements for computer operation and is time-consuming. Summary of the invention

[0004] In response to the above problems, the present invention provides a method for modeling electromagnetic ultrasonic time domain signals in bolts. The method combines EMAT excitation, sound wave propagation and transducer reception to establish a model for predicting bolt time domain signals. The 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.

[0005] The objective of the present invention is achieved through the following technical solutions:

[0006] A method for modeling electromagnetic ultrasonic time domain signals in bolts is provided. The bolts are simplified into cylinders, and a bolt time domain signal model based on EMAT is constructed in a cylindrical coordinate system for prediction. The method specifically includes the following steps:

[0007] Step 1: Solve the force source distribution based on EMAT:

[0008] Step 1: The static magnetic vector position distribution of the permanent magnet equivalent current in the test block is:

[0009]

[0010] Where, k is the permanent magnet equivalent current, a 1 is the radius of the permanent magnet, b 1 is the model boundary, q i By J 1 (q i b 1 )=0, P 3 (0) = μ r / (μ r q i +qi ), μ r is the relative magnetic permeability J of the test block 1 and J 0 are the first-order and zero-order Bessel functions, respectively;

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

[0012]

[0013] Among them, i 0 is the coil current, r j1 and r j2 is the inner and outer radius of the coil, s 3i =sqrt(q i 2 +jωμ 0 μ r σ), j is an imaginary unit, P 3 (ω)=μ r / (μ r q i +s 3i );

[0014] Step 13: In the cylindrical coordinate system, 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 14: Eddy current J generated by alternating current in the specimen e for:

[0017] J e =-jωσA d

[0018] Step 15: Integrate in the z direction and obtain the Lorentz force components in the cylindrical coordinate system according to J×B, which are expressed as:

[0019] P r (r)=-jωσA d A s q i J 0 (q i r) / A sr

[0020] P z (r)=jωσA d A s q i

[0021] Step 2: Solve the transfer function of ultrasonic wave propagation in the round rod:

[0022] Step 21: The force source stimulated by EMAT includes the lateral force source P r and the longitudinal force source P z , the force source is regarded as the superposition of each guided wave mode. Therefore, the boundary condition of the circular rod based on EMAT satisfies:

[0023]

[0024] in, is the shear stress of each mode in the circular rod, is the vertical stress of each mode in the round bar, C is the amplitude of each mode excitation, and i represents the mode;

[0025] Step 2: The guided wave mode amplitude is written as:

[0026]

[0027] Step 2 and 3: The propagation process of the guided wave affects the phase information of the sound wave, which is expressed as:

[0028]

[0029] Among them, l represents the distance of waveguide propagation, that is, the length of the cylinder;

[0030] Step 24: According to V×B, the expression of EMAT receiving transfer function is obtained as follows:

[0031]

[0032] Among them, B sr is the static magnetic field in the r direction, B sz is the static magnetic field in the z direction, and the velocity components in the r and z directions are expressed as:

[0033] v z (i) =ωkJ 0 (pr)-2ωkpqJ 1 (pa)J 0 (qr) / (J 1 (qa)(q 2 -k 2 ))

[0034] v r (i) =jωpJ 1 (pr)+2jωk 2 pJ 1 (pa)J 1 (qr) / (J 1 (qa)(q 2 -k 2 ))

[0035] Step 25: The transfer function of the signal propagating in the round rod is:

[0036] H(w)=C (i) (w)Φ (i) (w)R(w)

[0037] Step 3: EMAT receives the time domain signal and solves it:

[0038] The sum of the transfer functions of the propagation guided wave modes at each frequency point is calculated, and then the transfer functions at all frequency points are summed to transform the frequency domain signal into the time domain. Finally, the signal r(t) received by the transducer is expressed as:

[0039]

[0040] Where S(w) represents the excitation signal.

[0041] Compared with the prior art, the present invention has the following advantages:

[0042] (1) A bolt electromagnetic ultrasonic time domain signal modeling method was proposed for the first time;

[0043] (2) Accurate time domain signals can be obtained based on transducer parameters and bolt geometry;

[0044] (3) Compared with the finite element method, this method is time-saving and more convenient. BRIEF DESCRIPTION OF THE DRAWINGS

[0045] Figure 1 It is the EMAT model in cylindrical coordinate system;

[0046] Figure 2 Flow chart of the method for modeling electromagnetic ultrasonic time domain signals in bolts;

[0047] Figure 3 It is the EMAT incentive model;

[0048] Figure 4 is the acoustic wave transfer function model;

[0049] Figure 5 is the received signal model;

[0050] Figure 6 is the incentive signal;

[0051] Figure 7 Results are calculated for both experiments and models. DETAILED DESCRIPTION

[0052] The technical solution of the present invention is further described below in conjunction with the accompanying drawings, but is not limited thereto. Any modification or equivalent replacement of the technical solution of the present invention without departing from the spirit and scope of the technical solution of the present invention should be included in the protection scope of the present invention.

[0053] The present invention provides a method for modeling electromagnetic ultrasonic time domain signals in bolts. The method simplifies the bolt into a cylinder. The EMAT model in the cylindrical coordinate system is as follows: Figure 1 As shown. Figure 2 As shown in the figure, the solution steps of the model include three parts: solution of force source distribution based on EMAT, solution of transfer function of ultrasonic wave propagation in round rod and solution of EMAT receiving time domain signal.

[0054] 1. EMAT incentives

[0055] The present invention only considers the Lorentz force mechanism in the EMAT transduction process. In the electromagnetic ultrasonic transmission process, the goal of modeling is to derive the force source distribution of the Lorentz force. Cylindrical waveguide electromagnetic ultrasonic signal measurement usually uses a spiral coil and a cylindrical permanent magnet structure, such as Figure 1 The calculation process of EMAT force source distribution is shown in Figure 3 The key physical quantity expressions and calculation processes in the model are as follows:

[0056] The static magnetic vector potential distribution of the permanent magnet equivalent current in the test block is:

[0057]

[0058] Where k = B r / μ 0 is the permanent magnet equivalent current, B r is the saturation magnetic induction intensity of the permanent magnet; a 1 is the radius of the permanent magnet, b 1 is the model boundary, q i By J 1 (q i b 1 )=0, J 1 and J 0 are the first-order and zero-order Bessel functions, P 3 (0) = μ r / (μ r q i +q i ), μ r is the relative magnetic permeability of the test block.

[0059] In the test block, the dynamic magnetic vector potential distribution generated by the alternating current is:

[0060]

[0061] Among them, i 0 is the coil current, r j1 and r j2 is the inner and outer radius of the coil, s 3i =sqrt(q i 2 +jωμ 0 μ r σ), j is an imaginary unit, P 3 (ω)=μ r / (μ r q i +s 3i ). In the cylindrical coordinate system, the relationship between the magnetic field components generated by the alternating current and the permanent magnet and the magnetic vector potential is as follows:

[0062]

[0063] The eddy current J generated by the alternating current in the specimen e for:

[0064] J e =-jωσA d (4)

[0065] Integrate in the z direction and obtain the Lorentz force components in the cylindrical coordinate system according to J×B:

[0066]

[0067] 2. Signal Propagation

[0068] In the process of electromagnetic ultrasonic propagation, the modeling goal is to derive the acoustic wave transfer function. The transfer function calculation includes the calculation of the guided wave mode amplitude, the phase change caused by signal propagation, and the ultrasonic signal receiving transfer function calculation. The specific calculation process is as follows: Figure 4 As shown, the key physical quantity expressions are as follows:

[0069] The force source excited by the transducer includes the lateral P r and the longitudinal force source P z , the force source can be regarded as the superposition of each guided wave mode. Therefore, the boundary condition of the circular rod based on EMAT satisfies:

[0070]

[0071] The shear stress of each mode in the rod is and vertical stress for:

[0072]

[0073]

[0074] C is the amplitude of each mode excitation, i represents the mode, a represents the radius of the cylinder, k is the wave number, cl is the ultrasonic longitudinal wave velocity, and cs is the transverse wave velocity. According to formula (6), the guided wave modal amplitude can be written as:

[0075]

[0076] The propagation process of guided waves affects the phase information of the sound wave, which is expressed as:

[0077]

[0078] Where l represents the distance of waveguide propagation, that is, the length of the cylinder. According to V×B, the expression of the EMAT receiving transfer function is:

[0079]

[0080] Among them, B sr is the static magnetic field in the r direction, B sz is the static magnetic field in the z direction, and the velocity components in the r and z directions are expressed as:

[0081]

[0082]

[0083] Therefore, the transfer function of the signal propagating in the round rod is:

[0084] H(w)=C (i) (w)Φ (i) (w)R(w) (14)

[0085] 3. Transducer receiving signal

[0086] Calculate the sum of the transfer functions of the propagation guided wave mode at each frequency point, then sum the transfer functions at all frequency points, transform the frequency domain signal to the time domain, and finally, Figure 5 As shown, the signal r(t) received by the transducer is expressed as:

[0087]

[0088] Where S(w) represents the excitation signal.

[0089] Example:

[0090] In this embodiment, the EMAT comprises a spiral coil and a cylindrical permanent magnet. Figure 1The inner diameter of the spiral coil is 0.5 mm, the outer diameter is 6.5 mm, the lift-off distance is 0.4 mm, the radius of the permanent magnet is 10 mm, the height is 15 mm, and the lift-off distance is 1.5 mm. The diameter of the cylindrical specimen to be tested is 30 mm and the length is 255 mm. RETIC5000 is used to transmit and receive ultrasonic waves. The excitation signal is as follows: Figure 6 As shown in the figure, the experimental signal and the ultrasonic signal calculated by the model are as follows Figure 7 The signal waveform and relative amplitude obtained from the experiment and the model calculation are almost the same.

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 bolt time domain signal model based on EMAT for prediction in a cylindrical coordinate system, which specifically includes the following steps: Step 1: Solve the force source distribution based on EMAT: Step 1: The static magnetic vector position distribution of the permanent magnet equivalent current in the test block is: Among them, k is the permanent magnet equivalent current, a1 is the permanent magnet radius, b1 is the model boundary, q i By J1(q i b1)=0, P3(0)=μ r / (μ r q i +q i ), μ r J1 and J0 are the first-order and zero-order Bessel functions of the relative magnetic permeability of the test block, respectively; Step 1 and 2: In the test block, the dynamic magnetic vector potential distribution generated by the alternating current is: Where i0 is the coil current, r j1 and r j2 is the inner and outer radius of the coil, s 3i =sqrt(q i 2 +jωμ0μ r σ), j is an imaginary unit, P3(ω)=μ r / (μ r q i +s 3i ); Step 13: In the cylindrical coordinate system, 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 14: Eddy current J generated by alternating current in the specimen e for: J e =-jωσA d Step 15: Integrate in the z direction and obtain the Lorentz force components in the cylindrical coordinate system according to J×B, which are expressed as: P r (r)=-jωσA d A s q i J0(q i r) / A sr P z (r)=jωσA d A s q i Step 2: Solve the transfer function of ultrasonic wave propagation in the round rod: Step 21: The force source stimulated by EMAT includes the lateral force source P r and the longitudinal force source P z , the force source is regarded as the superposition of each guided wave mode. Therefore, the boundary condition of the circular rod based on EMAT satisfies: in, is the shear stress of each mode in the circular rod, is the vertical stress of each mode in the round bar, C is the amplitude of each mode excitation, and i represents the mode; Step 2: The guided wave mode amplitude is written as: Step 2 and 3: The propagation process of the guided wave affects the phase information of the sound wave, which is expressed as: Among them, l represents the distance of waveguide propagation, that is, the length of the cylinder; Step 24: According to V×B, the expression of EMAT receiving transfer function is obtained as follows: Among them, B sr is the static magnetic field in the r direction, B sz is the static magnetic field in the z direction, and the velocity components in the r and z directions are expressed as: v z (i) =ωkJ0(pr)-2ωkpqJ1(pa)J0(qr) / (J1(qa)(q 2 -k 2 )) v r (i) =jωpJ1(pr)+2jωk 2 pJ1(pa)J1(qr) / (J1(qa)(q 2 -k 2 )) Step 25: The transfer function of the signal propagating in the round rod is: H(w)=C (i) (w)Φ (i) (w)R(w) Step 3: EMAT receives the time domain signal and solves it: The sum of the transfer functions of the propagation guided wave modes at each frequency point is calculated, and then the transfer functions at all frequency points are summed to transform the frequency domain signal into the time domain. Finally, the signal r(t) received by the transducer is expressed as: Where S(w) represents the excitation signal.

2. The method for modeling electromagnetic ultrasonic time domain signals in bolts according to claim 1, characterized in that The shear stress in each mode of the circular rod and vertical stress for: Where a represents the radius of the cylinder, k is the wave number, cl is the ultrasonic longitudinal wave speed, and cs is the transverse wave speed.

3. The method for modeling electromagnetic ultrasonic time domain signals in bolts according to claim 1, characterized in that The guided wave mode amplitude is written as:

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