CN-116773680-B - Ultrasonic phased array Rayleigh wave sound field calculation method based on non-paraxial approximate multi-element Gaussian sound beam model

CN116773680BCN 116773680 BCN116773680 BCN 116773680BCN-116773680-B

Abstract

The invention discloses an ultrasonic phased array Rayleigh wave sound field calculation method based on a non-paraxial approximate multi-element Gaussian sound beam model, which comprises the steps of firstly solving a single-element Rayleigh wave sound field by establishing the non-paraxial approximate multi-element Gaussian sound beam model, and then determining parameters of the phased array transducer to calculate coordinates of each array element of the phased array and delay time of each array element required by deflection and focusing of the phased array Rayleigh waves, and finally carrying out delay superposition on the Rayleigh wave sound fields of the single array element to obtain a synthesized sound field of the phased array Rayleigh waves. The method realizes the rapid calculation of the phased array Rayleigh wave sound field on the premise of ensuring the precision, solves the problems that the traditional Rayleigh wave sound field calculation method is low in efficiency, the deviation is increased along with the increase of the off-axis distance, and the like, and has guiding significance for the optimization of the ultrasonic detection process and the quantitative evaluation of the defects.

Inventors

LIU ZHIPING
LI ZELONG
HU HONGWEI
LI XIONGBING
DONG JINYANG
DING XIA
DING JIE
XU NA
ZHANG ZHIWU

Assignees

长沙理工大学

Dates

Publication Date: 20260508
Application Date: 20230619

Claims (3)

1. An ultrasonic phased array Rayleigh wave sound field calculation method based on a non-paraxial approximate multi-element Gaussian sound beam model is characterized by comprising the following steps: Step one, a non-paraxial approximate multi-element Gaussian sound beam model is established to obtain a Rayleigh wave sound field of a phased array single rectangular array element; The first step is as follows: Step 1, a coordinate system of the surface of the transducer is established, the surface of the transducer is taken as a reference, a central point of the transducer is taken as an origin of coordinates, a coordinate system Oxyz is established, a scanning direction during detection is taken as a Y axis, a central axis of an array element is taken as a Z axis, and an X axis is perpendicular to a Oyz plane, and the surface of an incident point is taken as the surface of the incident point The rectangular area S 2 of the size is a calculated sound source for generating Rayleigh waves, wherein And Respectively rectangular array element long axes and half the length of the minor axis; step 2, calculating sound pressure of the rectangular sound source region S 2 Sound pressure can be expressed as: (1) Wherein, the 、、 Representing the density of the wedge and the longitudinal wave speed of sound and the wave number of the sound beam in the wedge, In order to have a complex gaussian coefficient, Represented as the rayleigh range, Representing any point in the sound field Distance to the transducer center point; By using Instead of To obtain faster calculation speed and perform coordinate transformation Transforming the transducer surface coordinate system into a test block surface coordinate system, wherein For the incident angle when the Rayleigh wave is excited, the coordinates of any point on the upper surface of the tested block can be expressed as It is possible to obtain: (2) Wherein, the , Representing the distance from the array element center to the incident point; step 3, expanding the distance factor in a non-paraxial approximation mode ; Using non-paraxial approximation to develop distance factors to obtain more accurate numerical solutions, distance factors Can be expressed as: (3) Wherein the method comprises the steps of The green function term is expressed as: (4) Step 4, sound pressure based on sound source area And distance factor Performing area integral calculation to obtain the phased array a single rectangular array element Rayleigh wave sound field; sound pressure distribution of projection area sound source based on phased array probe array element on surface of test block Distance factor Obtaining Rayleigh wave velocity vector of rectangular transducer at any point on surface of test block by using angular spectrum method to carry out area ; (5) In the formula, , For the transverse wave and Rayleigh wave numbers in the test block, In order to achieve the density of the test block, For the test block transverse wave sound velocity, Surface integral, distance factor for surface area of test block Represented as any point in the test block Into the surface acoustic source region The deflection angle of the two-point connecting line in the x-axis direction is ; Function of Expressed as: (6) In the middle of , , Respectively representing the Rayleigh wave speed, the longitudinal wave speed and the transverse wave speed of the test block, , , Is a unit vector which is perpendicular to each other, Which represents the angular frequency of the light emitted by the light source, Defined as energy flow, can be expressed as: (7) Substituting the formulas (2) and (4) into the formula (5) to obtain a single rectangular array element Rayleigh wave velocity vector of any point on the surface of the test block, wherein the single rectangular array element Rayleigh wave velocity vector is as follows: (8) In the middle of , ; Calculating Rayleigh wave velocity vectors of all points on the surface of the test block to obtain a Rayleigh wave sound field of a single rectangular array element of the phased array; Step two, basic parameters of the transducer are determined, and coordinates of each array element of the phased array transducer and delay of each array element required by deflection are calculated; And thirdly, superposing phased array Rayleigh wave sound fields of all the array elements according to the time delay to obtain a phased array Rayleigh wave synthesis sound field.
2. The ultrasonic phased array rayleigh wave sound field calculation method based on the non-paraxial approximate multi-element gaussian sound beam model according to claim 1, wherein the step two is specifically as follows: Step 1, determining the center frequency of a transducer, the width of array elements and the center distance; Step 2, calculating the coordinates of each array element of the phased array, wherein the position coordinates of each array element are as follows: (9) In the middle of Is the center of the nth array element (0, 0), Wherein the total number of array elements is N, and the center distance of the array elements is d; Step 3, calculating delay distances of each array element, and when the phased array acoustic beam deflects and focuses at the same time, calculating the distance difference between the acoustic beams radiated by each array element according to a geometric relation to obtain: (10) Wherein N is the excitation array element sequence number n=1, 2..N, d is the array element center-to-center spacing, F represents the focal length of the beam field, and the deflection angle of the acoustic beam is 。
3. The ultrasonic phased array rayleigh wave sound field calculation method based on the non-paraxial approximate multi-element gaussian sound beam model according to claim 2, wherein the step three is specifically as follows: The linear phased array is formed by combining a plurality of array elements, and according to the Huygens principle, the phased array radiation sound field can be obtained by superposing radiation sound pressure values of all the array elements at a target point, and according to a delay rule, the deflection and focusing actions of sound beams are realized by adding a group of delays to all the array elements, and a phase item is introduced for each array element To realize modeling of sound field, wherein In order for the distance to be a difference in distance, To sum up for the phase difference, a composite sound field of the phased array transducer can be obtained according to equation (8) and equation (10): (11) In the middle of Is the Rayleigh wave sound field of the nth phased array single rectangular array element, In order for the distance to be a difference in distance, Is a phase difference.

Description

Ultrasonic phased array Rayleigh wave sound field calculation method based on non-paraxial approximate multi-element Gaussian sound beam model Technical Field The invention belongs to the technical field of ultrasonic detection, and particularly relates to an ultrasonic phased array Rayleigh wave sound field calculation method based on a non-paraxial approximate multi-element Gaussian sound beam model. Background Under the influence of factors such as load impact, alternating stress, thermal stress and the like, the shallow surface of the metal part inevitably has defects such as holes, cracks, pitting corrosion and the like in the manufacturing and working processes, and the failure of the part and even production safety accidents are caused along with the time. The ultrasonic Rayleigh wave is very sensitive to near-surface defects of materials, can avoid echo aliasing, is widely applied in the field of ultrasonic nondestructive testing, accurately calculates the sound field of the Rayleigh wave transducer, and has important guiding significance for the design of the transducer, the optimization of the detection process and the quantitative evaluation of the defects. At present, the Rayleigh wave ultrasonic detection mainly adopts a multi-element Gaussian sound beam superposition method with paraxial approximation in sound field calculation, such as documents ' Duan Xiaomin, zhao Xinyu and Sun Huafei ', the Gaussian sound beam superposition method [ J ] of a rectangular surface wave probe sound field, physical school report, 2014, 63 (01): 216-221 ' and a point source superposition method are such as document "Lester W. Schmerr Jr.,Alexander Sedov. ULTRASONIC BEAM MODELS FOR THE GENERATION OF SURFACE WAVES AND PLATE WAVES WITH ANGLE BEAM TRANSDUCERS[J]. AIP Conference Proceedings, 2011, 1335(1)",, but the method has the problems of low calculation efficiency and increased deviation along with the increase of the off-axis distance. The invention provides an ultrasonic phased array Rayleigh wave sound field calculation method based on a non-paraxial approximate multi-element Gaussian sound beam model, which can realize rapid calculation of a phased array Rayleigh wave sound field on the premise of ensuring accuracy. Disclosure of Invention In order to solve the problems of poor calculation precision and low efficiency in the traditional Rayleigh wave sound field calculation, the invention aims to provide an ultrasonic phased array Rayleigh wave sound field calculation method based on non-paraxial multi-element Gaussian sound beams, which has the advantages of high calculation speed and high precision. In order to achieve the above purpose, the present invention provides the following technical solutions: An ultrasonic phased array Rayleigh wave sound field calculation method based on a non-paraxial approximate multi-element Gaussian sound beam model is characterized by comprising the following steps: step one, a non-paraxial approximate multi-element Gaussian sound beam model is established to obtain a Rayleigh wave sound field of a phased array single rectangular array element. Step two, basic parameters of the transducer are determined, and coordinates of each array element of the phased array transducer and delay of each array element required by deflection are calculated. And thirdly, superposing phased array Rayleigh wave sound fields of all the array elements according to the time delay to obtain a phased array Rayleigh wave synthesis sound field. The ultrasonic phased array Rayleigh wave sound field calculation method based on the non-paraxial approximate multi-element Gaussian sound beam model comprises the following specific steps: Step 1, a coordinate system of the surface of the transducer is established, the surface of the transducer is taken as a reference, a central point of the transducer is taken as an origin of coordinates, a coordinate system Oxyz is established, a scanning direction during detection is taken as a Y axis, a central axis of an array element is taken as a Z axis, and an X axis is perpendicular to a Oyz plane, and the surface of an incident point is taken as the surface of the incident point The rectangular area S 2 of the size is a calculated sound source for generating Rayleigh waves, whereinAndRespectively half the length of the long axis and the short axis of the rectangular array element. Step 2, calculating sound pressure of the rectangular sound source region S 2Sound pressure can be expressed as: (1) Wherein, the 、、Representing the density of the wedge and the longitudinal wave speed of sound and the wave number of the sound beam in the wedge,In order to have a complex gaussian coefficient,Represented as the rayleigh range,Representing any point in the sound fieldDistance to the transducer center point. By usingInstead ofTo obtain faster calculation speed and perform coordinate transformationTransforming the transducer surface coordinate system into a test block surfa