CN101692072A - Calculation method of sound field of circular arc-shaped linear ultrasonic phased array - Google Patents

Abstract

The invention provides a method for calculating the sound field of an arc-shaped linear ultrasonic phased array transducer. It includes beam steering focusing algorithm, sound field calculation method and influence of structural parameters on sound field characteristics. The calculation method uses the angle method to represent the position information of the transducer array element, thereby deriving the beam control focusing algorithm of the arc-shaped linear phased array transducer; the arc array element is approximated as a rectangular array element, and combined with Coordinate transformation, calculating the sound field of circular arc-shaped linear phased array, using Rayleigh integral and non-paraxial approximate multi-Gaussian model to simulate and verify this method, the results are very consistent. Moreover, the invention analyzes the influence of structural parameters on the characteristics of the sound field, and provides a theoretical basis for designing and optimizing the transducer.

Description

Calculation method of arc-shaped linear ultrasonic phased array sound field

1. Technical field

The invention relates to a method for calculating the arc-shaped linear ultrasonic phased array sound field, which provides a theoretical basis for designing and researching array transducers with special shapes.

2. Technical background

In ultrasonic testing, contact measurement methods are generally used. When the surface shape of the object to be measured is non-planar, if a linear phased array transducer is used for detection, the detection sensitivity will be reduced due to contact mismatch, and the defect cannot be accurately located. Under such circumstances, it is necessary to develop array transducers with special shapes to meet complex detection requirements. Due to the rapid development of computer technology, modeling analysis and simulation calculation provide a very effective method for the development and analysis of transducer performance, which can more intuitively reflect the sound field characteristics of the transducer and optimize the structural parameters of the transducer.

The arc-shaped linear phased array transducer is a curved linear phased array transducer with a simple structure. Each array element has the same curvature radius, and the position information of the array elements is easy to express. The linear phased array transducer with irregular surface can be approximated as composed of multiple arc array elements, the difference is that the arc array elements have different curvature radii. Therefore, arc-shaped linear phased array transducers are the basis for researching and designing phased array transducers with complex shapes, and have important research value.

3. Contents of the invention

The purpose of the present invention is to overcome the shortcomings of linear phased array transducers when detecting objects with complex surface shapes, and to provide a sound field calculation method for regular surface linear phased array transducers, which is useful for designing and optimizing transducers. The energy device provides a theoretical reference.

The object of the present invention is achieved like this: it includes the influence of the focusing algorithm of arc-shaped linear ultrasonic phased array beam control, the sound field calculation method and array parameters on the phased array sound field; the arc-shaped linear ultrasonic phased array The focusing algorithm of the beam control adopts the angle method to represent the position information of the array element, thereby deriving the focusing law of the beam control; the sound field calculation method adopts the method of combining the arc array element with a rectangular array element and coordinate transformation, First calculate the sound field of a single arc array element, and then according to Huygens' principle, the sound field of the phased array transducer is equal to the superposition of the sound field of multiple array elements; the influence of the array parameters on the sound field of the phased array is mainly studied The influence of the number of array elements, array element width and array element spacing on the sound field.

4. Description of drawings

Fig. 1 is a structural schematic diagram of an arc-shaped linear phased array transducer;

Fig. 2 is the calculation result of the delay time of the linear array and the arc-shaped linear array at different spatial positions;

Fig. 3 is coordinate system transformation;

Fig. 4 is the geometric shape of a single arc array element;

Fig. 5 is the calculation result of two-dimensional sound field (F=20, θ _s =0°);

Fig. 6 is the calculation result of two-dimensional sound field (F=20, θ _s =5°);

Figure 7 is a diagram of the focused sound field when the number of array elements is different;

Figure 8 is the sound field of the transducer when the array element width is different;

Fig. 9 is transducer deflection focused sound field;

Figure 10 shows the effect of array element height on the sound field.

5. Specific implementation

The present invention is described in more detail below in conjunction with accompanying drawing example:

Combining with Figure 1, it is assumed that the arc-shaped linear phased array is deformed by the linear phased array. According to the principle of equal length, the aperture D of the linear array is equal to the arc length L of the arc-shaped linear array

D＝L＝ _θc /180×π×R (1)

Where R is the radius of curvature, and θ _c is the central angle corresponding to the arc length of the arc-shaped linear array.

Combined with Figure 1, the width of the arc array element and the distance between two adjacent array elements are represented by symbols a _c and d _c respectively, and their corresponding central angles are defined as θ _a and θ _d respectively, which satisfy the following relationship

(N-1)θ _d +θ _a =θ _c (2)

Where N is the number of array elements. The central angle corresponding to the center of the i-th array element is

${\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; =</span>\frac{{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; a</span>}}}{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; d</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 3</span>}<span\; class="notranslate">\; )</span>$

In the Cartesian coordinate system, the center coordinates of the i-th array element are: x _i =Rsinθ _i , z _i =R-Rcosθ _i .

Combined with Figure 1, according to the above conditions, in the xoz plane, the calculation formula for the delay time of each array element is

${\mathrm{<span\; class="notranslate">\; \&tau;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; -</span>\sqrt{{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; f</span>}\mathrm{<span\; class="notranslate">\; sin</span>}\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; R</span>}\mathrm{<span\; class="notranslate">\; sin</span>}\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; f</span>}\mathrm{<span\; class="notranslate">\; cos</span>}\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; R</span>}\mathrm{<span\; class="notranslate">\; cos</span>}\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; R</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; c</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; t</span>}$

$<span\; class="notranslate">\; =</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; -</span>\sqrt{{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="2"\; label="f"\; filenames="H2009101483361E0000012.png,H2009101483361E0000021.png"\; state="\{\{state\}\}">f</figure-callout></span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 2</span>}{\mathrm{<span\; class="notranslate">\; R</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; cos</span>}\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; FR</span>}\mathrm{<span\; class="notranslate">\; cos</span>}{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; FR</span>}\mathrm{<span\; class="notranslate">\; cos</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}<span\; class="notranslate">\; )</span>}{}_{}{}_{}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; c</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; t</span>}$

$<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>\sqrt{\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 2</span>}\frac{{\mathrm{<span\; class="notranslate">\; R</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}{{\mathrm{<span\; class="notranslate">\; f</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; cos</span>}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 2</span>}\frac{\mathrm{<span\; class="notranslate">\; R</span>}}{\mathrm{<span\; class="notranslate">\; f</span>}}\mathrm{<span\; class="notranslate">\; cos</span>}{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 2</span>}\frac{\mathrm{<span\; class="notranslate">\; R</span>}}{\mathrm{<span\; class="notranslate">\; f</span>}}\mathrm{<span\; class="notranslate">\; cos</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; c</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 4</span>}<span\; class="notranslate">\; )</span>$

Where τ _i is the delay time of the i-th array element, F is the focal length, θ _s is the deflection angle, c is the velocity of the ultrasonic wave in the medium, and θ _i is the angle between the center of the i-th array element and the z-axis.

When F>>R, τ _i ≈F/c+t.

Combining with Figure 1, taking the arc-shaped linear phased array transducer composed of 8 arc array elements as an example, according to the above research method, when θ _c =60°, θ _a =4°, θ _d =8° , and when the spatial positions are different, calculate the delay time of each array element of the linear phased array and the arc-shaped linear phased array respectively.

Combined with Figure 2, when the shape and position of the array elements change, the delay time of each array element calculated at a certain point in space is different, and the resulting focusing effect is also different; when the surface shape of the measured object changes, If the traditional linear array transducer is still used for detection, the actual focusing effect will be affected. Therefore, a new focus delay algorithm should be studied according to the surface of the measured object to adapt to different detection requirements.

Since each array element of the arc-shaped linear phased array is not in the same plane, for the convenience of research, when calculating the sound pressure generated by each array element at the spatial point P, the coordinate transformation is used to convert the point P to Calculate in the new coordinate system.

Combined with Fig. 3, after translation and rotation transformation, a new coordinate system (ξ _i o′η _i ) is established. The coordinate origin o' is the center of the i-th array element, and the η _i axis is the central axis of the i-th array element. According to the geometric relationship, the conversion formula of point P in the new coordinate system is

$\left\{\begin{array}{c}{\mathrm{<span\; class="notranslate">\; \&xi;</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; cos</span>}{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; +</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; z</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; z</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; sin</span>}{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}\\ {\mathrm{<span\; class="notranslate">\; \&eta;</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; sin</span>}{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; +</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; z</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; z</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; cos</span>}{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}\end{array}\right.<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 5</span>}<span\; class="notranslate">\; )</span>$

Where ( _xi , zi ₎ is the center coordinate of the i-th array element in the original coordinate system, and (ξ _pi , η _pi ) is the coordinate of point P in the (ξ _i o′η _i ) coordinate system.

Combined with Figure 4, after a single array element undergoes coordinate transformation, according to the chord length formula, the array element width _ac and array element spacing _dc are obtained as

a _c =2Rsin(θ _a /2), d _c =2Rsin(θ _d /2)(6)

When θ _a is very small, sin(θ _a /2)～θ _a /2, a _c ～Rθ _a , that is, a single circular array element can be approximated as a single rectangular array element.

Taking a circular arc-shaped linear phased array with radius of curvature R=20mm and central angle θ _c =60° as an example, when the center frequency of the transducer f ₀ =5MHz, the number of array elements N=8, θ _a =4°, θ _d = 7°, focal length F = 20mm, and deflection angles are θ _s = 5° and θ _s = 0° Two-dimensional sound field map of the instrument.

Combining Figure 5 and Figure 6, the two-dimensional sound field calculation results obtained by using the RSI and NMG models are very consistent.

In order to study the influence of the element spacing d _c of the arc-shaped linear phased array on the sound field characteristics, the array element width a _c is taken as a fixed value, that is, θ _a is constant, and the effect of the array element spacing on the sound pressure is observed by changing the number of array elements N and beam characteristics.

Referring to Fig. 7, taking θ _a = 3° as an example, in the xoz plane, when the beam is focused at (0, 20), as the number of elements N increases, the sound pressure at the focus increases gradually, and the main The lobe width narrows, and the grating lobe gradually disappears. Therefore, the grating lobe can be eliminated and the energy of the main lobe can be enhanced by increasing the number of array elements.

Combining with Figure 8, when the number of array elements is fixed, by increasing the array element width θ _a , observe the influence of array element spacing and array element width on beam characteristics and sound pressure. When N=10, when θ _a takes different values, under the condition that θ _a <θ _d is satisfied, increasing θ _a can not only increase the sound pressure but also change the beam characteristics.

Combined with Fig. 9, when the beam is focused at (5, 0, 20), the energy of the sound field is enhanced after the beam is deflected and focused; the energy of the sound field is also enhanced by increasing the width of the array element.

Through the above analysis, when θ _d <6°, the grating lobes can be basically eliminated; when the number of array elements is fixed, the width of the array elements can be increased to increase the energy of the sound field.

According to the above analysis results, take the arc-shaped linear phased array transducer composed of 10 array elements as an example, change the value of the array element height b, and observe the change of the sound field.

Combined with Figure 10, when b is different, the NMG model is used to calculate the two-dimensional sound field of the transducer; the effect of the height of the array element on the sound field is not obvious, and an appropriate value can be selected from the aspect of processing.

Claims (7)

1. A sound field calculation method of an arc-shaped linear ultrasonic phased array transducer, which comprises a beam control focusing algorithm, a sound field calculation method and the influence of structural parameters on the sound field. It is characterized in that the arc-shaped linear ultrasonic phased array transducer is composed of multiple arc array elements, and the position of each array element is not in the same plane. In order to derive the focusing algorithm for beam control, it is necessary to use A new method to represent the position of the transducer array element; according to Huygens' principle, when calculating the sound field of a circular arc linear phased array transducer, first calculate the sound field of a single arc array element, and then perform the corresponding delay Then superimpose; analyze the structural parameters, including the influence of array element width, array element spacing, array element number and array element height on the sound field. 2. The method according to claim 1, wherein the arc-shaped linear ultrasonic phased array transducer is deformed from a linear ultrasonic phased array transducer. 3. The method according to claim 1, characterized in that: the angle method is used to represent the position of the array element in the array transducer, that is, the radius of curvature of the arc-shaped linear phased array transducer and the center of the array element and Indicated by the included angle of the z-axis. 4. The method according to claim 1, characterized in that: approximate the arc array element to a rectangular array element, and combine the coordinate transformation method to calculate the sound field of a single array element in the newly established coordinate system. 5. The method according to claim 1, characterized in that: when calculating the sound field of a single arc array element, each arc array element is approximated as a rectangular array element, and in combination with the coordinate transformation method, the entire transducer is calculated The distribution of the sound field. 6. The method according to claim 4, wherein a new coordinate system is established with the center of each array element as the origin, and the central axis of the array element is the z-axis, and the coordinates of any point in space are converted to new coordinates calculations within the department. 7. The method according to claim 1, characterized in that: when analyzing the influence of array element width and array element spacing on the sound field of circular arc-shaped linear phased array transducers, the central angle corresponding to these two variables is mainly studied effect on the sound field.

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