Method for calculating ultrasonic phased array sound field based on non-paraxial approximate multi-gaussian sound beam model

Abstract

The application discloses a kind of based on non-paraxial approximate multivariate Gaussian sound beam model ultrasonic phased array Rayleigh wave field calculation method, the method first solves single array element Rayleigh wave field by establishing non-paraxial approximate multivariate Gaussian sound beam model, then determines phased array transducer parameter to calculate phased array each array element coordinate and the delay required for phased array Rayleigh wave deflection and focusing each array element, finally to single array element Rayleigh wave field is delayed and is added to obtain phased array Rayleigh wave synthesis sound field.The method realizes the fast calculation of phased array Rayleigh wave field under the premise of guaranteeing accuracy, solves the problems, such as low efficiency of traditional Rayleigh wave field calculation method, deviation increases with off-axis distance, etc., has guiding significance to the optimization of ultrasonic testing process and the quantitative evaluation of defect.

Description

Technical Field

[0001] This invention belongs to the field of ultrasonic testing technology, specifically relating to a method for calculating the Rayleigh wave sound field of an ultrasonic phased array based on a non-paraxial approximate multivariate Gaussian acoustic beam model. Background Technology

[0002] Under the influence of factors such as load impact, alternating stress, and thermal stress, defects such as holes, cracks, and pitting will inevitably appear on the shallow surface of metal parts during manufacturing and operation, which will lead to the failure of parts and even production safety accidents over time.

[0003] Ultrasonic Rayleigh waves are highly sensitive to near-surface defects in materials and can avoid echo aliasing. They are widely used in the field of ultrasonic nondestructive testing. Accurate calculation of the acoustic field of Rayleigh wave transducers has important guiding significance for transducer design, testing process optimization, and quantitative evaluation of defects. Currently, Rayleigh wave ultrasonic testing mainly employs the paraxial approximation multivariate Gaussian beam superposition method for sound field calculation, such as in the literature "Duan Xiaomin, Zhao Xinyu, Sun Huafei. Gaussian beam superposition method for sound field of rectangular surface wave probe [J]. Acta Physica Sinica, 2014, 63(01): 216-221" and the point source superposition method, such as in the literature "Lester W. Schmerr Jr., Alexander Sedov. ULTRASONIC BEAM MODELS FOR THE GENERATION OFSURFACE WAVES AND PLATE WAVES WITH ANGLE BEAM TRANSDUCERS [J]. AIP Conference Proceedings, 2011, 1335(1)". However, the above methods suffer from low computational efficiency and the deviation increases with the off-axis distance.

[0004] This invention proposes a method for calculating the Rayleigh wave sound field of an ultrasonic phased array based on a non-paraxial approximation multivariate Gaussian beam model, which can achieve rapid calculation of the Rayleigh wave sound field of the phased array while ensuring accuracy. Summary of the Invention

[0005] To address the issues of poor accuracy and low efficiency in traditional Rayleigh wave sound field calculations, this invention proposes a method for calculating the Rayleigh wave sound field using an ultrasonic phased array based on a non-paraxial multi-element Gaussian sound beam, which offers advantages such as high calculation speed and high accuracy.

[0006] To achieve the above objectives, the present invention provides the following technical solution:

[0007] A method for calculating the Rayleigh wave acoustic field of an ultrasonic phased array based on a non-paraxial approximate multivariate Gaussian acoustic beam model, characterized by comprising:

[0008] Step 1: Establish a non-paraxial approximate multivariate Gaussian acoustic beam model to obtain the Rayleigh wave acoustic field of a single rectangular phased array element.

[0009] Step 2: Determine the basic parameters of the transducer and calculate the coordinates of each element of the phased array transducer and the delay of each element required for deflection.

[0010] Step 3: Based on the delay, the phased array Rayleigh wave sound fields of each array element are superimposed to obtain the phased array Rayleigh wave composite sound field.

[0011] The method for calculating the Rayleigh wave acoustic field of an ultrasonic phased array based on a non-paraxial approximation multivariate Gaussian acoustic beam model, wherein step one is specifically as follows:

[0012] Step 1: Establish a coordinate system for the transducer surface. Using the transducer surface as a reference and the transducer center point as the origin, establish a coordinate system Oxyz. The scanning direction during detection is the Y-axis, the element center axis is the Z-axis, and the X-axis is perpendicular to the Oyz plane. The rectangular region S2 of size is the computational sound source for generating Rayleigh waves, in which... and These are half the lengths of the major and minor axes of the rectangular array elements, respectively.

[0013] Step 2: Calculate the S2 sound pressure level in the rectangular sound source region. Sound pressure can be expressed as:

[0014] (1)

[0015] in, , , This indicates the density of the wedge, the longitudinal wave velocity, and the wave number of the sound beam within the wedge. For complex Gaussian coefficients, Represented as Rayleigh distance, Represents any point in the sound field The distance to the center point of the transducer.

[0016] use to replace To achieve faster computation speed and perform coordinate transformations. The transducer surface coordinate system is transformed into the test block surface coordinate system, where To determine the angle of incidence when Rayleigh waves are excited, the coordinates of any point on the surface of the test block can be expressed as: We can obtain:

[0017] (2)

[0018] in, , This represents the distance from the center of the array element to the point of incidence.

[0019] Step 3: Expand the distance factor using a non-paraxial approximation. .

[0020] A non-paraxial approximation is used to expand the distance factor to obtain a more accurate numerical solution. The distance factor... It can be represented as:

[0021] (3)

[0022] in The Green's function term is expressed as:

[0023] (4)

[0024] Step 4, based on the sound pressure level in the sound source area and distance factor The Rayleigh wave acoustic field of a single rectangular element of a phased array is obtained by area integral calculation.

[0025] Sound pressure distribution of the sound source based on the projection area of ​​the phased array probe elements on the surface of the test block. and distance factor The Rayleigh wave velocity vector of the rectangular transducer at any point on the surface of the test block is obtained by surface integration using the angular spectrum method. ;

[0026] (5)

[0027] In the formula, , The wavenumbers of the transverse wave and Rayleigh wave in the test block, For the density of the test block, The transverse wave velocity of the test block, Perform area integral and distance factor on the surface area of ​​the test block. Represented as any point in the test block To the surface acoustic source region The distance between the two points, and the angle of deflection of the line connecting the two points along the x-axis. .

[0028] function Represented as:

[0029] (6)

[0030] In the formula , , These represent the Rayleigh wave velocity, longitudinal wave velocity, and transverse wave velocity of the test block, respectively. , , , are mutually perpendicular unit vectors. Represents angular frequency. Defined as energy flow, it can be expressed as:

[0031] (7)

[0032] Substituting equations (2) and (4) into equation (5), we obtain the Rayleigh wave velocity vector of a single rectangular array element at any point on the surface of the test block as follows:

[0033] (8)

[0034] In the formula , .

[0035] The Rayleigh wave velocity vectors at all points on the surface of the test block are calculated to obtain the Rayleigh wave acoustic field of a single rectangular element of the phased array.

[0036] The method for calculating the Rayleigh wave acoustic field of an ultrasonic phased array based on a non-paraxial approximation multivariate Gaussian acoustic beam model, wherein step two is specifically as follows:

[0037] Step 1: Determine the transducer center frequency, array element width, and center spacing.

[0038] Step 2: Calculate the coordinates of each element in the phased array. The position coordinates of each element are as follows:

[0039] (9)

[0040] In the formula For the nth array element center (0, The y-coordinate value of (0, 0) is given, the total number of array elements is N, and the center distance between array elements is d.

[0041] Step 3: Calculate the delay distance of each array element. When the phased array sound beams simultaneously deflect and focus, the distance difference between the radiated sound beams of each array element can be calculated using geometric relationships:

[0042] (10)

[0043] Where n is the excitation array element number n=1,2...N, and d is the center-to-center distance of the array elements. F represents the focal length of the beam field. This is the beam deflection angle.

[0044] The method for calculating the Rayleigh wave acoustic field of an ultrasonic phased array based on a non-paraxial approximation multivariate Gaussian acoustic beam model, wherein step three is specifically as follows:

[0045] A linear phased array is composed of multiple array elements. According to Huygens' principle, the radiated sound field of the phased array can be obtained by superimposing the radiated sound pressure values ​​of each element at the target point. According to the time delay rule, the deflection and focusing behavior of the sound beam can be achieved by adding a set of delays to each element. A phase term is introduced for each element. To achieve the modeling of the sound field, where For distance difference, Given the phase difference, in summary, according to formulas (8) and (10), the synthesized sound field of the phased array transducer can be obtained as follows:

[0046] (11)

[0047] In the formula The Rayleigh wave acoustic field of the nth phased array single rectangular element. For distance difference, This represents the phase difference.

[0048] Compared with the prior art, the present invention has the following beneficial technical effects:

[0049] This invention proposes a method for calculating the Rayleigh wave sound field of an ultrasonic phased array based on a non-paraxial approximation multivariate Gaussian sound beam model. The overall scheme of this invention provides an efficient sound field calculation method for phased array Rayleigh wave sound fields, enabling rapid and high-precision calculation of the phased array Rayleigh wave sound field. It effectively solves the shortcomings of low accuracy and long calculation time in traditional Rayleigh wave sound field calculations, and has guiding significance for the optimization of ultrasonic testing processes and quantitative evaluation of defects. Attached Figure Description

[0050] Figure 1 This is a schematic diagram of the process of the present invention;

[0051] Figure 2 This is a schematic diagram of the coordinate system for a surface wave detection system.

[0052] Figure 3 For deflection angles of 0° and 15°, the amplitude diagrams of particle velocity of Rayleigh waves on a two-dimensional surface are calculated using different methods.

[0053] Figure 4 The Rayleigh wave particle velocity amplitude diagram is shown along the deflection axis when the deflection angle is 15°.

[0054] Figure 5 This is a diagram showing the amplitude of Rayleigh wave particle velocity in the off-axis direction at the focal point when the deflection angle is 15°. Detailed Implementation

[0055] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0056] refer to Figures 1 to 5The present invention discloses a method for calculating the Rayleigh wave sound field of an ultrasonic phased array based on a non-paraxial approximate multivariate Gaussian sound beam.

[0057] The embodiments of this invention take the focused sound field simulation in an aluminum specimen using the phased array Rayleigh wave acoustic beam model established in this paper as an example, and compare the differences in Rayleigh integral method (RSI), paraxial approximation multivariate Gaussian beam superposition method (MGB), and non-paraxial approximation multivariate Gaussian beam ultrasonic phased array Rayleigh wave acoustic field calculation method (NMGB) in terms of Rayleigh wave acoustic field calculation accuracy and calculation efficiency. The specific steps are as follows:

[0058] Step 1: Establish a non-paraxial approximate multivariate Gaussian acoustic beam model to obtain the Rayleigh wave acoustic field of a single rectangular phased array element.

[0059] Step 2: Determine the basic parameters of the transducer and calculate the coordinates of each element of the phased array transducer and the delay of each element required for deflection.

[0060] Step 3: Based on the delay, the phased array Rayleigh wave sound fields of each array element are superimposed to obtain the phased array Rayleigh wave composite sound field.

[0061] The specific process of step one is as follows:

[0062] Step 1, as follows Figure 2 As shown, a transducer surface coordinate system is established. Using the transducer surface as a reference and the transducer center point as the origin, a coordinate system Oxyz is established. The scanning direction during detection is the Y-axis, the element center axis is the Z-axis, and the X-axis is perpendicular to the Oyz plane. The incident point surface... The rectangular region S2 of size is the calculated sound source for generating Rayleigh waves.

[0063] Step 2: Calculate the S2 sound pressure level in the rectangular sound source region. Sound pressure can be expressed as:

[0064] (1)

[0065] Among them, the density of the wedge 1.2 g / cm 3 Longitudinal wave speed The wavenumber of the sound beam in the wedge is 2700 m / s. 3.703 , The complex Gaussian coefficients are given in Table 1. Represented as Rayleigh distance, Represents any point in the sound field The distance to the center point of the transducer.

[0066] use to replace To achieve faster computation speed and perform coordinate transformations. The transducer surface coordinate system is transformed into the test block surface coordinate system, where the incident angle when Rayleigh waves are excited is... If the angle is 71.63°, then the coordinates of any point on the surface of the test block can be expressed as: We can obtain:

[0067] (2)

[0068] in, , This represents the distance from the center of the array element to the incident point.

[0069] Step 3: Expand the distance factor using a non-paraxial approximation. .

[0070] A non-paraxial approximation is used to expand the distance factor to obtain a more accurate numerical solution. The distance factor... It can be represented as:

[0071] (3)

[0072] in The Green's function term is expressed as:

[0073] (4)

[0074] Step 4, based on the sound pressure level in the sound source area and distance factor The Rayleigh wave acoustic field of a single rectangular element of a phased array is obtained by area integral calculation.

[0075] Sound pressure distribution of the sound source based on the projection area of ​​the phased array probe elements on the surface of the test block. and distance factor The Rayleigh wave velocity vector of the rectangular transducer at any point on the surface of the test block is obtained by surface integration using the angular spectrum method. ;

[0076] (5)

[0077] In the formula, the transverse wave number in the test block It is 1.574 , Rayleigh wave number 3.401 , is the density of the test block 2.7 g / cm 3 transverse wave velocity of the test block It is 3170 m / s; Perform area integral and distance factor on the surface area of ​​the test block. Represented as any point in the test block To the surface acoustic source region The distance between the two points, and the angle of deflection of the line connecting the two points along the x-axis. .

[0078] function Represented as:

[0079] (6)

[0080] In the formula, Rayleigh wave velocity of the test block is... The transverse wave velocity is 2940 m / s. The longitudinal wave velocity is 6350 m / s. It is 3170 m / s. , , , are mutually perpendicular unit vectors. Represents angular frequency. Defined as energy flow, it can be expressed as:

[0081] (7)

[0082] Substituting equations (2) and (4) into equation (5), we obtain the Rayleigh wave velocity vector of a single rectangular array element at any point on the surface of the test block as follows:

[0083] (8)

[0084] In the formula , .

[0085] The Rayleigh wave velocity vectors at all points on the surface of the test block are calculated to obtain the Rayleigh wave acoustic field of a single rectangular element of the phased array.

[0086] The specific process of step two is as follows:

[0087] Step 1: Determine the transducer parameters. The phased array probe has 64 elements, a center frequency of 5MHz, an element width of 0.5mm, and a center-to-center distance of 0.6mm.

[0088] Step 2: Calculate the coordinates of each element in the phased array. The position coordinates of each element are as follows:

[0089] (9)

[0090] In the formula For the nth array element center (0, The y-coordinate value of (,0), the total number of array elements N is 64, and the center distance d of the array elements is 0.6mm.

[0091] Step 3: Calculate the delay distance of each array element. When the phased array sound beams simultaneously deflect and focus, the distance difference between the radiated sound beams of each array element can be calculated using geometric relationships:

[0092] (10)

[0093] Where n is the excitation array element number n=1,2...N, and d is the center-to-center distance of the array elements. The focal length F of the beam field is 150mm, and the beam deflection angle is... .

[0094] The specific process of step three is as follows:

[0095] A linear phased array is composed of multiple array elements. According to Huygens' principle, the radiated sound field of the phased array can be obtained by superimposing the radiated sound pressure values ​​of each element at the target point. According to the time delay rule, the deflection and focusing behavior of the sound beam can be achieved by adding a set of delays to each element. A phase term is introduced for each element. To achieve the modeling of the sound field, where For distance difference, Given the phase difference, in summary, according to formulas (8) and (10), the synthesized sound field of the phased array transducer can be obtained as follows:

[0096] (11)

[0097] In the formula The Rayleigh wave acoustic field of the nth phased array single rectangular element. For distance difference, This represents the phase difference.

[0098] use Figure 2 In the coordinate system shown, the sound beam at the center of the probe's radiation enters the aluminum block at an incident angle of 71.63°. Ignoring the sound field in the source region, the deflection and focusing sound fields are calculated using different methods under deflection angles of 0° and 15°. The results are as follows: Figure 3 As shown, comparison Figure 3 The three methods yielded the Rayleigh wave sound field distribution, showing good consistency between the proposed method and the RSI method in the calculation results. The proposed method can calculate the deflection and focusing of the sound beam according to the set delay, with the energy mainly concentrated near the turning axis, and the highest energy at the focal point.

[0099] Figure 4 and Figure 5 The figures show the Rayleigh wave particle velocity amplitude along the deflection axis and the Rayleigh wave particle velocity amplitude off-axis at the focal point, obtained using three different Rayleigh wave acoustic field calculation models when the deflection angle is 15°. Figure 4The amplitude of the particle velocity along the central axis shows that the Rayleigh wave particle velocity amplitude is strongest at the focal point and then gradually decreases with increasing distance. Figure 5 It can be seen that the RSI method and the method of the present invention have good consistency in the region near the axis and can represent the phased array Rayleigh wave sound field well. However, as the off-axis distance increases, the MGB method shows a certain degree of deviation from the method of the present invention and the RSI method, and cannot accurately calculate the phased array Rayleigh wave sound field.

[0100] Under the same parameters, when calculating the amplitude field of particle velocity on a two-dimensional surface, the calculation model is simplified using the method of this invention, and the simulation time is 23.4s, which is close to the calculation time of 27.0s of the MGB method, while the calculation time of the RSI method is 2362.2s.

[0101] In summary, the method of the present invention overcomes the off-axis inaccuracy problem of the MGB method, and the calculation results are in good agreement with the RSI method with high accuracy. Moreover, the calculation efficiency of the method of the present invention is much higher than that of the RSI method.

[0102] Table 1 Gaussian superposition coefficients

[0103] n <![CDATA[A i ]]> <![CDATA[B i ]]> 1 -2.9716+8.6187i 4.1869-5.51600i 2 -3.4811+0.9687i 3.8398-10.8000i 3 -1.3982-0.8128i 3.4355-1635820i 4 0.0773-0.3303i 2.4618-27.7130i 5 2.8798+L61090i 5.4699+28.6310i 6 0.1259-0.0957i 1.9833-33.2880i 7 -0.2641-0.6723i 2.9335-22.0150i 8 18.019+7.8291i 6.3036+36.7772i 9 0.0518+0.0182i 1.3046-38.4650i 10 -16.9428-9.938i 6.5889+37.0680i 11 0.3708+5.4522i 5.5518+22.4255i 12 -6.6929+4.0722i 5.4013+16.7326i 13 -9.3638-4.9998i 5.1498+11.1249i 14 15872-15.4212i 4.9665+5.68550i 15 19.0024+3.685i 4.6296+0.30550i

[0104] The scope of protection of this invention is not limited to the above-described embodiments. Any person skilled in the art can make some modifications or alterations to the methods and techniques disclosed above without departing from the scope of the technical solution of this invention, and such modifications and alterations shall still fall within the scope of the technical solution of this invention if they fall within the scope of the claims of this invention and their equivalents.

Claims

1. A method for calculating the Rayleigh wave acoustic field of an ultrasonic phased array based on a non-paraxial approximation multivariate Gaussian acoustic beam model, characterized in that, The method includes the following steps: Step 1: Establish a non-paraxial approximate multivariate Gaussian acoustic beam model to obtain the Rayleigh wave acoustic field of a single rectangular phased array element; Step one is as follows: Step 1: Establish a coordinate system for the transducer surface. Using the transducer surface as a reference and the transducer center point as the origin, establish a coordinate system Oxyz. The scanning direction during detection is the Y-axis, the element center axis is the Z-axis, and the X-axis is perpendicular to the Oyz plane. The rectangular region S2 of size is the computational sound source for generating Rayleigh waves, in which... and These are half the lengths of the major and minor axes of the rectangular array elements, respectively. Step 2: Calculate the S2 sound pressure level in the rectangular sound source region. Sound pressure can be expressed as: （1） in, , , This indicates the density of the wedge, the longitudinal wave velocity, and the wave number of the sound beam within the wedge. For complex Gaussian coefficients, Represented as Rayleigh distance, Represents any point in the sound field Distance to the center point of the transducer; use to replace To achieve faster computation speed and perform coordinate transformations. The transducer surface coordinate system is transformed into the test block surface coordinate system, where To determine the angle of incidence when Rayleigh waves are excited, the coordinates of any point on the surface of the test block can be expressed as: We can obtain: （2） in, , This represents the distance from the center of the array element to the point of incidence. Step 3: Expand the distance factor using a non-paraxial approximation. ; A non-paraxial approximation is used to expand the distance factor to obtain a more accurate numerical solution. The distance factor... It can be represented as: (3) in The Green's function term is expressed as: （4） Step 4, based on the sound pressure level in the sound source area and distance factor The Rayleigh wave acoustic field of a single rectangular element of a phased array is obtained by area integral calculation. Sound pressure distribution of the sound source based on the projection area of ​​the phased array probe elements on the surface of the test block. and distance factor The Rayleigh wave velocity vector of the rectangular transducer at any point on the surface of the test block is obtained by surface integration using the angular spectrum method. ; （5） In the formula, , The wavenumbers of the transverse wave and Rayleigh wave in the test block, For the density of the test block, The transverse wave velocity of the test block. Perform area integral and distance factor on the surface area of ​​the test block. Represented as any point in the test block To the surface acoustic source region The distance between the two points, and the angle of deflection of the line connecting the two points along the x-axis are... ; function Represented as: （6） In the formula , , These represent the Rayleigh wave velocity, longitudinal wave velocity, and transverse wave velocity of the test block, respectively. , , , are mutually perpendicular unit vectors. Represents angular frequency. Defined as energy flow, it can be expressed as: （7） Substituting equations (2) and (4) into equation (5), we obtain the Rayleigh wave velocity vector of a single rectangular array element at any point on the surface of the test block as follows: （8） In the formula , ; Calculate the Rayleigh wave velocity vectors at all points on the surface of the test block to obtain the Rayleigh wave acoustic field of a single rectangular element of the phased array; Step 2: Determine the basic parameters of the transducer and calculate the coordinates of each element of the phased array transducer and the delay of each element required for deflection. Step 3: Based on the delay, the phased array Rayleigh wave sound fields of each array element are superimposed to obtain the phased array Rayleigh wave composite sound field.

2. The method for calculating the Rayleigh wave acoustic field of an ultrasonic phased array based on a non-paraxial approximate multivariate Gaussian acoustic beam model according to claim 1, characterized in that, Step two specifically involves: Step 1: Determine the transducer center frequency, element width, and center spacing; Step 2, calculate the coordinates of each element in the phased array; the position coordinates of each element are: （9） In the formula For the nth array element center (0, The y-coordinate value of (,0), the total number of array elements is N, and the center distance of the array elements is d; Step 3: Calculate the delay distance of each array element. When the phased array sound beams simultaneously deflect and focus, the distance difference between the radiated sound beams of each array element can be calculated using geometric relationships: （10） Where n is the excitation array element number n=1,2...N, and d is the center-to-center distance of the array elements. F represents the focal length of the beam field, and the beam deflection angle is... .

3. The method for calculating the Rayleigh wave acoustic field of an ultrasonic phased array based on a non-paraxial approximation multivariate Gaussian acoustic beam model according to claim 2, characterized in that, Step three specifically involves: A linear phased array is composed of multiple array elements. According to Huygens' principle, the radiated sound field of a phased array can be obtained by superimposing the radiated sound pressure values ​​of each array element at the target point. According to the delay rule, the deflection and focusing behavior of the sound beam can be achieved by adding a set of delays to each array element. A phase term is introduced for each array element. To achieve the modeling of the sound field, where For distance difference, Given the phase difference, in summary, according to formulas (8) and (10), the synthesized sound field of the phased array transducer can be obtained as follows: （11） In the formula The Rayleigh wave acoustic field of the nth phased array single rectangular element. For distance difference, This represents the phase difference.

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