Auxiliary device for ultrasonic flaw detection of TKY pipe joints and its use method

By designing an auxiliary device for ultrasonic flaw detection at TKY tube nodes, the detection operation is simplified, the detection efficiency and accuracy are improved, and the detection complexity and human-reliance problems in the prior art are solved.

CN116337998BActive Publication Date: 2025-09-05ZHONG XING HAI LU GONG CHENG YOU XIAN GONG SI
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Patent Information

Application Number
CN202211689034.7
Authority / Receiving Office
CN · China
Patent Type
Patents(China)
Current Assignee / Owner
Filing Date
2022-12-28
Publication Date
2025-09-05
Estimated Expiration
2042-12-28

AI Technical Summary

Technical Problem

In the prior art, ultrasonic detection of the welds of the TKY structural pipe nodes is difficult, and the detection results depend on the skills and experience of the detectors, and the operation is complex and time-consuming.

Method used

An auxiliary device for ultrasonic flaw detection of TKY tube nodes is designed, including the main frame, protractor, connecting shaft and spring. The ultrasonic probe is fixed by clamp, and the protractor and cantilever pointer are used to indicate the angle between the probe direction and the axis of the branch pipe, and the defect echo is judged in combination with formula calculation and chart.

Benefits of technology

It simplifies the detection operation, improves the detection efficiency, reduces the complexity of shape acquisition and drawing, and improves the accuracy and consistency of the detection results.

✦ Generated by Eureka AI based on patent content.

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Abstract

The present invention relates to the technical field of ultrasonic flaw detection, and more specifically to an auxiliary device for ultrasonic flaw detection of a TKY pipe node and a method for using the auxiliary device. The auxiliary device comprises a main frame, a protractor, a connecting shaft, a retaining spring, and a fixing screw. The main frame comprises a head clamp and a tail cantilever pointer. A total of four screw holes are provided on both sides of the head clamp portion, a connecting hole is provided on the tail cantilever pointer, and a center indicator line is provided at the end of the tail cantilever pointer of the main frame. The main frame has a groove for clamping and fixing an ultrasonic probe, and the ultrasonic probe is clamped by a fixing bolt engaged with the screw hole. The auxiliary device can be manufactured from a variety of materials such as aluminum alloy, copper alloy, steel, and engineering plastics. The device has low consumables, a small size, and a simple structure. The detection personnel can easily master the method of use, eliminating complex operations such as taking shapes and drawing during the detection process, facilitating rapid judgment of defect echoes, and greatly improving detection work efficiency.
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Description

Technical Field

[0001] The present invention relates to the technical field of ultrasonic flaw detection, and in particular to an auxiliary device for ultrasonic flaw detection of a TKY pipe node and a method for using the device. Background Art

[0002] TKY structural pipe nodes are common in engineering fields such as marine equipment construction and building steel structures. Ultrasonic testing is often required for the intersection line welds of important pipe nodes. However, the intersection line welds have complex shapes and large variations in the curvature of the inspection surface. Therefore, manual ultrasonic testing is difficult and requires high skills from the inspectors. The accuracy of the inspection results often depends on the level, experience and proficiency of the inspectors. During the inspection process, in order to determine whether the echo is a defect echo, the inspectors often need to perform some calculations and use shape gauges or plasticine to shape the echoed area and draw a 1:1 weld cross-section diagram for confirmation. The operation is complicated and time-consuming. So far, there is no simple and quick method or device that can effectively help inspectors perform inspection operations and judgments on TKY structural pipe node welds. Summary of the Invention

[0003] In view of the existing deficiencies, the present invention provides an auxiliary device for ultrasonic flaw detection of TKY pipe joints and a method for using the same.

[0004] To achieve the above object, the technical solution adopted by the present invention is:

[0005] An auxiliary device for ultrasonic flaw detection of TKY pipe nodes, comprising a main frame, a protractor, a connecting shaft, a retaining spring, and a fixing screw. The main frame comprises a head fixture and a tail cantilever pointer. A total of four screw holes are provided on both sides of the head fixture portion. The tail cantilever pointer has a connecting hole, and a center indicator line is provided at the end of the tail cantilever pointer of the main frame. The main frame has a groove for clamping and fixing an ultrasonic probe. The ultrasonic probe is clamped by a fixing screw engaged with the screw hole. The cantilever pointer of the main frame indicates the angle between the probe direction and the branch pipe axis on the protractor.

[0006] The arc edge on the protractor is engraved with angle lines and the measuring range is 90 degrees. A connecting hole is opened at the origin of the protractor. The connecting shaft is cylindrical with a slightly larger diameter at the lower end. A retaining ring groove is provided at the upper end of the connecting shaft. The connecting shaft is pin-connected with the connecting hole of the main frame and the connecting hole of the protractor. The main frame and the protractor are connected, and the retaining ring is snapped into the retaining ring groove of the connecting shaft.

[0007] A method for using an auxiliary device for ultrasonic flaw detection of a TKY pipe node includes the following steps:

[0008] S1, install the ultrasonic probe in the fixture of the auxiliary device, tighten the fixing screws on both sides to fix the probe to form an assembly;

[0009] S2, use the probe assembly to scan the intersecting line weld on the branch pipe inspection surface. The scanning should be perpendicular to the weld. When a suspicious echo is found, read the sound path value W displayed on the instrument. x At the same time, keep the probe perpendicular to the weld, rotate the protractor so that its 0-degree edge is parallel to the branch pipe busbar at that position, and use this as a reference to read the angle scale value of the protractor that is aligned with the center indicator line of the cantilever pointer end. This is the deflection angle θ of the probe position relative to the branch pipe axis. B ;

[0010] S3, according to θ B Value Check W tI 、 —θ B Relationship curve, judge W x In the primary or secondary wave;

[0011] S4, Check K d , K l —θ B Relationship curve, get K d and K l value, and according to the formula By calculating the corresponding formula in the equation, we can get the depth and horizontal arc length of the suspicious echo, and thus determine whether the suspicious echo is a defect echo;

[0012] S5. When the judgment is indeed difficult or in doubt, a CAD drawing is made to help the judgment. The drawing parameters are obtained from the above-mentioned relationship curve diagram;

[0013] In the operation step S2, mark the space curve formed by the intersection of two cylindrical surfaces and set it as the intersection line. Any point on the line can be regarded as the intersection point of the main and branch busbars. The point has a tangent line t and a normal plane. The following pipeline parameters need to be measured: main pipe outer diameter D1, main pipe wall thickness t1, branch pipe outer diameter D n , branch pipe wall thickness t n , main-branch included angle θ, groove angle φ, dihedral angle ψ: the angle between normal lines n1 and n2, normal lines n1 and n2 are in the normal plane and are tangent to the main and branch pipe surfaces respectively, branch intersection angle Φ: the angle between the plane formed by the branch busbar at the point and the branch axis and the plane formed by the main and branch pipe axes, deflection angle θ A ,θ B : The angles between the normal plane and the main and branch pipe axes or busbars, the curvature radii ρ1, ρ n : The radius of curvature at the point where the normal plane intersects the main and branch pipe cylindrical surfaces respectively; Center distance L: The distance between the centers of the two ellipses formed by the normal plane intersecting the main and branch pipe cylindrical surfaces;

[0014] The intersection line of the outer surface of the pipe can be expressed by the following equations: Assuming the defect is at point M and the coordinates are set to (x0, y0, z0), the following formula at point M can be obtained: set up: Then we can get the calculation formula necessary for drawing parameter charts:

[0015] Formula ①:

[0016] Formula ②:

[0017] Formula③

[0018] In formulas ①, ②, and ③, when Φ = 0 to 90°, use the "-" sign; when Φ = 90 to 180°, use the "+" sign;

[0019] Formula④

[0020] Formula⑤

[0021] Formula ⑥: When locating defects, the sound path, depth and horizontal position are corrected to obtain the critical refraction angle β of the probe at point M. max , and the probe sound path correction coefficient k, horizontal correction coefficient m, and primary wave sound path W for a given refraction angle β tI , primary wave arc length Formula, where β≤β max :

[0022] Formula⑦

[0023] Formula⑧ θ B =0°, k is 1;

[0024] Formula⑨ θ B =0°, m is 1;

[0025] Formula⑩

[0026] formula The wall thickness of the measured pipe is relatively small compared to the diameter. When positioning the ultrasonic surface flaw detection, an approximate calculation method is used to introduce the depth positioning coefficient K. d and horizontal positioning coefficient K l :

[0027]

[0028] Assume the defect sound path is W x , then the following positioning calculation formula is obtained:

[0029] formula Within the primary wave sound range, W x ≤W tI ;

[0030] Within the sound path of the secondary wave, W tI <W x ≤W tII .

[0031] Compared with the prior art, the present invention has the following beneficial effects:

[0032] The device of the present invention can be manufactured using a variety of materials such as aluminum alloy, copper alloy, steel, engineering plastics, etc. It has low consumables, small size, and simple structure. It is easy for inspection personnel to master its use, eliminating complex operations such as taking shapes and drawing during the inspection process, facilitating rapid judgment of defect echoes, and greatly improving inspection work efficiency. BRIEF DESCRIPTION OF THE DRAWINGS

[0033] Figure 1 This is a schematic diagram of the auxiliary device structure decomposition of an auxiliary device for ultrasonic flaw detection of TKY pipe joints and a method for using the auxiliary device according to the present invention;

[0034] Figure 2 A schematic diagram of the structure of a pipe node of an auxiliary device for ultrasonic flaw detection of a TKY pipe node and a method of using the same according to the present invention;

[0035] Figure 3 This is a schematic diagram of the three-dimensional structure of an auxiliary device for ultrasonic flaw detection of TKY pipe joints and a method for using the auxiliary device according to the present invention;

[0036] Figure 4 A schematic diagram of the structural parameters of a TKY pipe node according to the present invention, including an auxiliary device for ultrasonic flaw detection of the pipe node and a method for using the device;

[0037] Figure 5 The invention relates to a TKY pipe node ultrasonic flaw detection auxiliary device and its use method. max ,θ A ,θ B —Φ relationship curve diagram;

[0038] Figure 6 The invention relates to an auxiliary device for ultrasonic flaw detection of TKY pipe joints and its use method. B Schematic diagram of the relationship curve;

[0039] Figure 7The invention discloses an auxiliary device for ultrasonic flaw detection of TKY pipe joints and its use method. B Schematic diagram of the relationship curve;

[0040] Figure 8 The invention relates to an auxiliary device for ultrasonic flaw detection of TKY pipe joints and a method for using the same. tI 、 —θ B Schematic diagram of the relationship curve;

[0041] Figure 9 The invention relates to an auxiliary device for ultrasonic flaw detection of TKY pipe joints and a method for using the same. d , K l —θ B Schematic diagram of the relationship curve.

[0042] In the figure: 1. Main frame; 11. Screw hole; 12. Connecting hole; 13. Center indicator line; 2. Protractor; 3. Connecting shaft; 4. Circlip; 5. Fixing screw. DETAILED DESCRIPTION

[0043] The following will be combined with the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the embodiments described are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0044] Example

[0045] like Figure 1 As shown, an auxiliary device for ultrasonic flaw detection of TKY pipe nodes includes a main frame 1, a protractor 2, a connecting shaft 3, a retaining spring 4, and a fixing screw 5. The main frame 1 includes a head fixture and a tail cantilever pointer, a total of four screw holes 11 are set on both sides of the head fixture part, a connecting hole 12 is opened on the tail cantilever pointer, and a center indicator line 13 is set at the end of the tail cantilever pointer of the main frame 1. The main frame 1 has a groove for clamping and fixing the ultrasonic probe. The fixing screw 5 engaged by the screw hole 11 clamps the ultrasonic probe. The cantilever pointer of the main frame 1 indicates the angle between the probe direction and the branch pipe axis on the protractor 2;

[0046] Angle lines are engraved on the arc edge of the protractor 2 and the measuring range is 90 degrees. A connecting hole 21 is opened at the origin of the protractor 2.

[0047] like Figure 1As shown, in this embodiment, the main frame 1 includes two parts: a head clamp and a tail cantilever pointer. A total of four screw holes 11 are set on both sides of the head clamp part, a connecting hole 12 is opened on the tail cantilever pointer, and a center indicator line 13 is set at the end. The function of the clamp is to clamp and fix the ultrasonic probe, and the function of the cantilever pointer is to indicate the angle between the probe direction and the branch axis on the protractor 2; the arc edge on the protractor 2 is engraved with an angle line, the angle range is 90 degrees, and a connecting hole 21 is opened at the origin. The function of the protractor 2 is to provide the angle value; the connecting shaft 3 is a cylinder with a slightly larger diameter at the lower end, and a retaining ring groove 31 is provided at the upper end. The function of the connecting shaft 3 is to connect the main frame 1 and the protractor 2 through the connecting hole 12 of the main frame 1 and the connecting hole 21 of the protractor 2, and to enable the protractor 2 to rotate; the function of the retaining ring 4 is to fit into the retaining ring groove 31 of the connecting shaft 3 to prevent the connecting shaft 3 from falling off; the function of the fixing screw 5 is to be screwed in through the screw hole 11 of the main frame 1 to fix the ultrasonic probe.

[0048] like Figure 1-9 As shown, a method for using an auxiliary device for ultrasonic flaw detection of TKY pipe nodes includes the following steps:

[0049] S1, install the ultrasonic probe in the fixture of the auxiliary device, tighten the fixing screws 5 on both sides to fix the probe to form an assembly;

[0050] S2, use the probe assembly to scan the intersecting line weld on the branch pipe inspection surface. The scanning should be perpendicular to the weld. When a suspicious echo is found, read the sound path value W displayed on the instrument. x At the same time, keep the probe perpendicular to the weld and rotate the protractor 2 so that its 0-degree edge is parallel to the branch pipe busbar at that position. Based on this, read the angle scale value of the protractor 2 aligned with the center indicator line 13 of the cantilever pointer end. This is the deflection angle θ of the probe position relative to the branch pipe axis. B ;

[0051] S3, according to θ B Value Check W tI 、 —θ B Relationship curve, judge W x In the primary or secondary wave;

[0052] S4, Check K d , K l —θ B Relationship curve, get K d and K l value, and according to the formula By calculating the corresponding formula in the equation, we can get the depth and horizontal arc length of the suspicious echo, and thus determine whether the suspicious echo is a defect echo;

[0053] S5. When there are difficulties or doubts in judgment, make a CAD drawing to help judge. The drawing parameters are obtained from the above-mentioned relationship curve diagram.

[0054] In this embodiment, if Figure 4 As shown, the first step is to draw the data required for the parameter chart, which involves the relevant calculation formula. The formula is based on the following theoretical basis:

[0055] The weld of a pipe joint is geometrically a spatial curve formed by the intersection of two cylindrical surfaces, called the intersection line. Any point on the line can be regarded as the intersection point of the main and branch pipe busbars. This point has a tangent line t and a normal plane (normal lines n1 and n2 are in the plane and are tangent to the main and branch pipe surfaces respectively). The normal plane intersects the main and branch pipe cylindrical surfaces to form two ellipses (not marked). The relevant parameters of the pipe joint are as follows:

[0056] Main pipe outer diameter D1 Main pipe wall thickness t1

[0057] Branch pipe outer diameter D n Branch pipe wall thickness t n

[0058] Main and branch pipe angle θ Bevel angle φ

[0059] Dihedral angle ψ: the angle between normals n1 and n2

[0060] Branch intersection angle Φ: The angle between the plane formed by the branch busbar at the point and the branch axis and the plane formed by the main and branch axis

[0061] deflection angle θ A ,θ B : The curvature radius of the angle between the normal plane and the main and branch pipe axes (or generatrix) ρ1, ρ n : The radius of curvature at the point where the normal plane intersects the cylindrical surfaces of the main and branch pipes respectively; The distance between the centers of the two ellipses formed by the normal plane intersecting the cylindrical surfaces of the main and branch pipes; After establishing the spatial coordinate system shown in the figure above, the intersection line of the outer surface of the pipe can be expressed by the following equations:

[0062]

[0063] Assuming the defect is at point M and the coordinates are set to (x0, y0, z0), the following formula at point M can be obtained:

[0064]

[0065] set up: Then we can get the calculation formula necessary for drawing parameter charts:

[0066] Formula ①:

[0067] Formula ②:

[0068] Formula③

[0069] Note: In the above formula, when Φ = 0 ~ 90°, take the “-” sign; when Φ = 90 ~ 180°, take the “+” sign.

[0070] Formula④

[0071] Formula⑤

[0072] Formula ⑥: Ultrasonic curved surface flaw detection is different from flat surface flaw detection. When locating defects, it is necessary to correct the sound path, depth and horizontal position. According to the principle of curved surface flaw detection, the critical refraction angle β of the probe at point M can be obtained. max , and the probe sound path correction coefficient k, horizontal correction coefficient m, and primary wave sound path W for a given refraction angle β tI , primary wave arc length Formula, where β≤β max :

[0073] Formula⑦

[0074] Formula⑧ θ B =0°, k is 1;

[0075] Formula⑨ θ B =0°, m is 1;

[0076] Formula⑩

[0077] formula For structural pipes, most of the pipe wall thickness is relatively small relative to the diameter value. Therefore, when ultrasonic surface flaw detection is performed, an approximate calculation method is often used. At this time, the depth positioning coefficient K can be introduced. d and horizontal positioning coefficient K l :

[0078]

[0079] Assume the defect sound path is W x , then the following positioning calculation formula is obtained:

[0080] formula Within the primary wave sound range, W x ≤W tI ;

[0081] Within the sound path of the secondary wave, W tI <W x ≤W tII .

[0082] Step 2: Draw a parameter chart

[0083] By using commonly used Excel spreadsheet software and inputting corresponding formulas, you can quickly and easily calculate various required parameters, and then use its chart function to automatically draw various curves. You can also use CAD software to draw composite curves according to functional requirements.

[0084] The following examples illustrate various composite curves drawn using CAD software:

[0085] Main pipe specifications (D1×t1): 325×20mm

[0086] Branch pipe specifications (D n ×t n ): 219×10mm

[0087] Main branch pipe angle (θ): 35°

[0088] Angle of the oblique probe (β): 70°

[0089] like Figure 5 As shown, it is β max ,θ A ,θ B —Φ relationship curve diagram.

[0090] Main functions: It is the basis for dividing the weld into detection sections; determining the main detection probes used in each section; obtaining the θ of different positions on the intersecting weld A ,θ B Corresponding value.

[0091] like Figure 6 As shown, ψ, φ—θ B Relationship curve

[0092] Main function: Get the ψ value at different positions, and then get the groove angle φ value according to a certain rule, which is a necessary value for drawing the local weld section.

[0093] Regarding the φ value, it should be measured before assembly as much as possible, or obtained from a reference line drawn in advance; or it can be obtained according to construction regulations; if there are no regulations, it can be calculated according to general engineering rules.

[0094] like Figure 7 As shown, L—θ B Relationship curve

[0095] Main function: To obtain the center distance of the main and branch pipe ellipses intercepted by the normal plane at a certain point on the weld, which is a necessary value when making the weld cross-section diagram.

[0096] like Figure 8 As shown, W is plotted according to the probe refraction angle β. tI 、 —θ B Relationship curve

[0097] Main function: Obtain the primary wave acoustic path length and arc length of any point under fixed β, which helps to determine defects and locate them.

[0098] like Figure 9 As shown, K is plotted according to the probe refraction angle β. d , K l —θ B Relationship curve

[0099] Main function: Get the positioning coefficient of any point under fixed β, and then get the positioning data through simple calculation.

[0100] Obviously, the above embodiments of the present invention are merely examples for clearly illustrating the present invention, and are not limitations on the implementation methods of the present invention. For ordinary technicians in the relevant field, other different forms of changes or modifications can be made based on the above description. It is impossible to list all the implementation methods here. Any obvious changes or modifications derived from the technical solution of the present invention are still within the scope of protection of the present invention.

Claims

1. An auxiliary device for ultrasonic flaw detection of TKY pipe joints, comprising a main frame (1), a protractor (2), a connecting shaft (3), a retaining spring (4), and a fixing screw (5), characterized in that: The main frame (1) includes a head clamp and a tail cantilever pointer, a total of four screw holes (11) are set on both sides of the head clamp part, a connecting hole (12) is opened on the tail cantilever pointer, and a center indicator line (13) is set at the end of the tail cantilever pointer of the main frame (1), the main frame (1) has a groove for clamping and fixing the ultrasonic probe, and the ultrasonic probe is clamped by a fixing screw (5) engaged with the screw hole (11), and the cantilever pointer of the main frame (1) indicates the angle value between the probe direction and the branch pipe axis on the protractor (2); The arc edge of the protractor (2) is engraved with an angle line and has a measuring range of 90 degrees. A connecting hole (21) is opened at the origin of the protractor (2); the connecting shaft (3) is cylindrical with a slightly larger diameter at the lower end. A retaining ring groove (31) is provided at the upper end of the connecting shaft (3). The connecting shaft (3) is pin-connected with the connecting hole (12) of the main frame (1) and the connecting hole (21) of the protractor (2). The main frame (1) and the protractor (2) are connected, and the retaining ring (4) is inserted into the retaining ring groove (31) of the connecting shaft (3).

2. A method for using the auxiliary device for ultrasonic flaw detection of TKY tube joints according to claim 1, characterized in that: The following steps are included: S1, install the ultrasonic probe in the fixture of the auxiliary device, tighten the fixing screws (5) on both sides to fix the probe to form an assembly; S2, use the probe assembly to scan the intersecting line weld on the branch pipe inspection surface. The scanning should be perpendicular to the weld. When a suspicious echo is found, read the sound path value W displayed on the instrument. x At the same time, keep the probe perpendicular to the weld, rotate the protractor (2) so that its 0 degree edge is parallel to the branch pipe busbar at that position, and use this as a reference to read the angle scale value of the protractor (2) aligned with the center indicator line (13) of the cantilever pointer end. This is the deflection angle θ of the probe position relative to the branch pipe axis. B ; S3, according to θ B Value Check W tI 、 —θ B Relationship curve, judge W x In the primary or secondary wave; S4, Check K d , K l —θ B Relationship curve, get K d and K l value, and according to the formula By calculating the corresponding formula in the equation, we can get the depth and horizontal arc length of the suspicious echo, and thus determine whether the suspicious echo is a defect echo; S5. When the judgment is indeed difficult or in doubt, a CAD drawing is made to help the judgment. The drawing parameters are obtained from the above-mentioned relationship curve diagram; In the operation step S2, mark the space curve formed by the intersection of two cylindrical surfaces and set it as the intersection line. Any point on the line can be regarded as the intersection point of the main and branch busbars. The point has a tangent line t and a normal plane. The following pipeline parameters need to be measured: main pipe outer diameter D1, main pipe wall thickness t1, branch pipe outer diameter D n , branch pipe wall thickness t n , main-branch included angle θ, groove angle φ, dihedral angle ψ: the angle between normal lines n1 and n2, normal lines n1 and n2 are in the normal plane and are tangent to the main and branch pipe surfaces respectively, branch intersection angle Φ: the angle between the plane formed by the branch busbar at the point and the branch axis and the plane formed by the main and branch pipe axes, deflection angle θ A ,θ B : The angles between the normal plane and the main and branch pipe axes or busbars, the curvature radii ρ1, ρ n : The radius of curvature at the point where the normal plane intersects the main and branch pipe cylindrical surfaces respectively; Center distance L: The distance between the centers of the two ellipses formed by the normal plane intersecting the main and branch pipe cylindrical surfaces; The intersection line of the outer surface of the pipe can be expressed by the following equations: Assuming the defect is at point M and the coordinates are set to (x0, y0, z0), the following formula at point M can be obtained: set up: Then we can get the calculation formula necessary for drawing parameter charts: Official 1 Formula 2 Formula 3 In formulas ①, ②, and ③, when Φ = 0 to 90°, use the "-" sign; when Φ = 90 to 180°, use the "+" sign; Formula 4 Official ⑤ Formula ⑥ When locating defects, the sound path, depth and horizontal position are corrected to obtain the critical refraction angle β of the probe at point M. max , and the probe sound path correction coefficient k, horizontal correction coefficient m, and primary wave sound path W for a given refraction angle β tI , primary wave arc length Formula, where β≤β max : Formula ⑦ Formula⑧ θ B =0°, k is 1; Formula⑨ θ B =0°, m is 1; Official 10 The wall thickness of the measured pipe is relatively small compared to the diameter. When positioning the ultrasonic surface flaw detection, an approximate calculation method is used to introduce the depth positioning coefficient K. d and horizontal positioning coefficient K l : Assume the defect sound path is W x , then the following positioning calculation formula is obtained:

Citation Information

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