Ultrasonic vibration amplitude measurement platform and measurement method under load condition

By designing an ultrasonic vibration amplitude measurement platform under load conditions and employing multiple measuring surfaces and a loading mechanism, the accurate measurement of ultrasonic vibration amplitude was achieved, solving the problems of amplitude attenuation and fluctuation under load conditions, and improving machining accuracy and tool life.

CN121048726APending Publication Date: 2025-12-02TIANJIN UNIV
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Patent Information

Application Number
CN202511255124.9
Authority / Receiving Office
CN · China
Patent Type
Applications(China)
Current Assignee / Owner
Filing Date
2025-09-04
Publication Date
2025-12-02

AI Technical Summary

Technical Problem

Existing ultrasonic vibration amplitude measurement devices cannot effectively observe the propagation attenuation and amplitude fluctuation of ultrasonic vibration under load conditions, resulting in weakened ultrasonic machining effect and reduced tool life.

Method used

An ultrasonic vibration amplitude measurement platform under load conditions was designed. It adopts a rotatable ultrasonic transducer, multiple vibration measuring surfaces with gradually decreasing outer diameters, a loading mechanism, and an amplitude measurement mechanism. The amplitude is measured at different positions by a vibration meter, and the measurement data is acquired by a data acquisition card.

Benefits of technology

It enables accurate measurement of the amplitude attenuation and fluctuation of ultrasonic vibration at different locations, evaluates amplitude changes under different load conditions, and is suitable for evaluating the vibration characteristics of special machining tools, thereby improving machining accuracy and tool life.

✦ Generated by Eureka AI based on patent content.

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Abstract

The invention discloses an ultrasonic vibration amplitude measuring platform and method under a load condition, and relates to the technical field of ultrasonic vibration auxiliary machining. Although an existing ultrasonic vibration amplitude measurement device can achieve amplitude measurement under the load condition, measurement data are single, and the propagation attenuation condition and the amplitude fluctuation condition of whole ultrasonic vibration cannot be effectively observed. The device comprises a rotatable ultrasonic transducer, a test piece connected with the ultrasonic transducer, a loading mechanism and an amplitude measuring mechanism, wherein the ultrasonic transducer is used for generating ultrasonic vibration; a plurality of vibration measuring surfaces of which the outer diameters are gradually reduced are arranged on the test piece along the propagation direction of ultrasonic vibration; the loading mechanism is used for applying an axial load and a radial load to the test piece; the amplitude measuring mechanism is used for measuring the amplitude of each vibration measuring surface of the test piece. The method is mainly used for evaluating the amplitude attenuation or fluctuation characteristics of the ultrasonic vibration under different load conditions.
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Description

Technical Field

[0001] This invention relates to the field of ultrasonic vibration-assisted processing technology, and in particular to an ultrasonic vibration amplitude measurement platform and method under load conditions. Background Technology

[0002] Ultrasonic vibration-assisted machining (UVAM) involves superimposing high-frequency vibrations (20–40 kHz) into the traditional machining process. Extensive testing and research have shown that UVAM can effectively reduce grinding forces and heat, thereby reducing tool wear and improving machining quality and surface integrity. However, under heavy loads and other machining conditions, the amplitude output of the power ultrasonic transducer often exhibits attenuation and instability. This significantly weakens the ultrasonic effect and machining advantages of ultrasonic machining, and may even reduce tool life.

[0003] While existing ultrasonic vibration amplitude measurement devices can measure amplitude under load conditions, the measurement data is limited and cannot effectively observe the propagation attenuation and amplitude fluctuation of the entire ultrasonic vibration. Summary of the Invention

[0004] In view of this, the present invention provides an ultrasonic vibration amplitude measurement platform and method under load conditions, which can measure the amplitude attenuation or amplitude fluctuation of ultrasonic vibration at different positions along the propagation path.

[0005] To solve the above-mentioned technical problems, the technical solution adopted by the present invention is as follows:

[0006] An ultrasonic vibration amplitude measurement platform under load conditions, comprising:

[0007] A rotatable ultrasonic transducer for generating ultrasonic vibrations;

[0008] The test piece connected to the ultrasonic transducer has multiple vibration measuring surfaces with gradually decreasing outer diameters arranged along the direction of ultrasonic vibration propagation.

[0009] The loading mechanism is used to apply axial and radial loads to the test piece;

[0010] And an amplitude measuring mechanism, used to measure the amplitude of each vibration measuring surface of the test piece.

[0011] Furthermore, the test piece is provided with a conical structure, the cross-section of which gradually decreases along the ultrasonic vibration propagation path, and multiple vibration measuring rings are nested on the conical structure along its length. The outer diameter of the vibration measuring rings gradually decreases along the ultrasonic vibration propagation path, and the ring surface of each vibration measuring ring is the vibration measuring surface.

[0012] Furthermore, the loading mechanism includes a force gauge, a loading block, and a force gauge moving platform. The force gauge is mounted on the force gauge moving platform and is driven by the force gauge moving platform to move axially or radially. The loading block is rotatably mounted on the force gauge and connected to the test piece, and it can apply a load to the test piece.

[0013] Furthermore, one end of the test piece is connected to an ultrasonic transducer, and the other end extends toward the loading block side. A spline groove is opened on the end face of the test piece. The loading block is a splined hollow shaft, which is inserted into the spline groove of the test piece.

[0014] Furthermore, the amplitude measurement mechanism includes a vibration meter and a vibration meter moving platform. The vibration meter is mounted on the vibration meter moving platform and is driven by the vibration meter moving platform to move axially or radially.

[0015] Furthermore, the ultrasonic transducer is clamped onto the three-jaw chuck of the machine tool and driven to rotate by the three-jaw chuck.

[0016] Furthermore, the ultrasonic transducer is fitted with a conductive slip ring, and the ultrasonic power supply is connected to the outer stator of the conductive slip ring via wires, while the inner rotor of the conductive slip ring is connected to the ultrasonic transducer.

[0017] Furthermore, it also includes a data acquisition card for acquiring data measured by the force gauge and vibration meter.

[0018] Another technical solution adopted in this invention is:

[0019] A method for measuring ultrasonic vibration amplitude under load conditions includes the following steps:

[0020] S1, the vibration meter moving platform drives the vibration meter to move axially and radially so that the laser emitted by the vibration meter is projected onto the front vibration measuring surface of the test piece, while the distance between the vibration meter and the vibration measuring surface is within the amplitude measurement focal length range of the vibration meter.

[0021] S2, The ultrasonic transducer drives the test piece to rotate and generates axial ultrasonic vibration;

[0022] S3, Vibration meter measures the amplitude on the front vibration measuring surface of the test piece when the ultrasonic transducer is in an unloaded state;

[0023] S4, the vibration meter moving platform drives the vibration meter to move axially and radially so that the laser emitted by the vibration meter is projected onto the second vibration measuring surface of the test piece. The ultrasonic transducer drives the test piece to rotate and generate axial ultrasonic vibration. The vibration meter measures the amplitude on the second vibration measuring surface of the test piece when the ultrasonic transducer is in an unloaded state. This step is repeated so that the laser emitted by the vibration meter is projected onto the remaining vibration measuring surfaces in sequence, thereby obtaining the amplitude change of the ultrasonic transducer along the entire axial length in an unloaded state.

[0024] S5, the vibration meter returns to its initial position, and the force measuring instrument moving platform drives the loading block to move axially to apply an axial load to the test piece and the ultrasonic transducer; repeat steps S1 to S4 to obtain the amplitude change of the ultrasonic transducer along its entire axial length under axial load.

[0025] S6, the vibration meter returns to its initial position, and the force measuring instrument moving platform drives the loading block to move radially to apply a radial load to the test piece and the ultrasonic transducer; repeat steps S1 to S4 to obtain the amplitude change of the ultrasonic transducer along its entire axial length under radial load.

[0026] The beneficial effects of this invention compared to the prior art are:

[0027] The test specimen in this application employs a multi-surface vibration measurement design, which can measure the amplitude of ultrasonic vibration at different positions along the propagation path, thereby evaluating the amplitude attenuation or fluctuation characteristics under different load conditions. In other words, the amplitude variation along the entire axial length of the test specimen under axial and radial loads can be directly reflected by the vibration meter. Furthermore, this method is also suitable for evaluating the vibration attenuation or fluctuation characteristics of special machining tools (such as honing tools). Each vibration measurement surface corresponds to the end face of each grinding head in the honing tool. By measuring the amplitude of each grinding head, the grinding accuracy at different positions on the inner surface of a high aspect ratio hard and brittle material workpiece can be determined. Attached Figure Description

[0028] The accompanying drawings, which form part of this application, are provided to further illustrate the invention.

[0029] Figure 1 This is a schematic diagram of the structure of an ultrasonic vibration amplitude measurement platform under load conditions according to the present invention. Figure 1 .

[0030] Figure 2 This is a schematic diagram of the structure of an ultrasonic vibration amplitude measurement platform under load conditions according to the present invention. Figure 2 .

[0031] Figure 3 This is a schematic diagram of the test piece.

[0032] Figure 4 This is a cross-sectional schematic diagram of an ultrasonic vibration amplitude measurement platform under load conditions according to the present invention.

[0033] Figure 5 This is a schematic diagram of the honing tool.

[0034] Figure 6 for Figure 1 A magnified view of a portion of point A in the middle.

[0035] Figure 7 for Figure 2 A magnified view of a section at point B.

[0036] Figure 8 This is a flowchart for acquiring load data and amplitude data.

[0037] Figure 9 The amplitude attenuation and fluctuation of the test piece under axial load are shown in (a), (b), (c), (d), (e), and (e) respectively.

[0038] Figure 10 The amplitude attenuation and fluctuation of the test piece under radial load are shown in (a), (b), (c), (d), (e), and (e) respectively.

[0039] Explanation of reference numerals in the attached figures:

[0040] 1-Ultrasonic transducer;

[0041] 2-Test piece, 21-Connecting part, 22-Conical structure, 23-Vibration measuring ring, 24-Spline groove;

[0042] 3-Loading mechanism, 31-Force gauge, 32-Top block, 33-Bearing, 34-Loading block, 35-Force gauge moving platform, 351-Machine tool guide rail, 352-Radial guide rail, 353-Support slider;

[0043] 4-Amplitude measuring mechanism, 41-Support frame, 42-Vibration meter, 43-Vibration meter moving platform, 431-First lead screw and nut pair, 432-Second lead screw and nut pair;

[0044] 5-Three-jaw chuck; 6-Conductive slip ring; 7-Charge amplifier; 8-Data acquisition card; 9-Data display screen. Detailed Implementation

[0045] The present invention will be described in detail below with reference to the accompanying drawings and specific embodiments.

[0046] Example 1:

[0047] See Figure 1This embodiment of an ultrasonic vibration amplitude measurement platform under load conditions is mainly used to measure the attenuation or amplitude fluctuation of ultrasonic vibration of a cutting tool under load conditions. The measurement platform is mounted on a machine tool and includes a rotatable ultrasonic transducer 1, a test piece 2 connected to the ultrasonic transducer 1, a loading mechanism 3, and an amplitude measurement mechanism 4. The ultrasonic transducer 1 is clamped onto a three-jaw chuck 5 of the machine tool and driven to rotate by the three-jaw chuck 5. A conductive slip ring 6 is fitted around the ultrasonic transducer 1. The ultrasonic power supply is connected to the outer stator of the conductive slip ring 6 via wires, and the inner rotor of the conductive slip ring 6 is connected to the ultrasonic transducer 1. The ultrasonic transducer 1 is used to generate ultrasonic vibration. One end of the test piece 2 is connected to the ultrasonic transmitting end of the ultrasonic transducer 1, and the other end extends outward. Multiple vibration measuring surfaces with gradually decreasing outer diameters are arranged on the test piece 2 along the propagation direction of the ultrasonic vibration. The loading mechanism 3 is mounted on the machine tool and is used to apply axial and radial loads to the test piece 2. The amplitude measurement mechanism 4 is mounted on the machine tool and is used to measure the amplitude of each vibration measuring surface of the test piece 2. The loading mechanism 3 applies an axial or radial load to the test piece 2. The ultrasonic transducer 1 rotates and generates ultrasonic vibration. The ultrasonic wave gradually propagates from the tail end of the test piece 2 to the tip of the test piece 2. The amplitude measuring mechanism 4 measures the amplitude on each vibration measuring surface of the test piece 2 in sequence.

[0048] Obviously, the test piece 2 in this embodiment adopts a multi-surface vibration measurement design, which can measure the amplitude of ultrasonic vibration at different positions along the propagation path, thereby evaluating the amplitude attenuation or fluctuation characteristics under different load conditions. In other words, the amplitude change along the entire axial length of the test piece 2 under axial and radial loads can be directly reflected by the vibration meter 42. Furthermore, this method is also suitable for evaluating special machining tools (such as…). Figure 5 The vibration attenuation or fluctuation characteristics of the honing tool in the honing tool are measured. Each vibration measuring surface is equivalent to the end face of each grinding head in the honing tool. By measuring the amplitude of each grinding head, the grinding accuracy at different positions on the inner surface of a workpiece with a large aspect ratio and hard and brittle material can be determined.

[0049] See Figure 1 and Figure 6 The loading mechanism 3 in this embodiment includes a force gauge 31, a top block 32, a bearing 33, a loading block 34, and a force gauge moving platform 35. The force gauge 31 is fixedly mounted on the force gauge moving platform 35 and is driven by the force gauge moving platform 35 to move axially or radially. The force gauge moving platform 35 is composed of a machine tool guide rail 351, a radial guide rail 352, and a support slider 353. The radial guide rail 352 is slidably engaged with the machine tool guide rail 351, and the support slider 353 is slidably engaged with the radial guide rail 352. The force gauge 31 is mounted on the support slider 353. The bearing 33 is mounted inside the top block 32 and is mounted on the force gauge 31 via the top block 32. One end of the loading block 34 is fixedly connected to the inner ring of the bearing 33, and the other end is connected to the end of the test piece 2 away from the ultrasonic transducer 1.

[0050] When the loading mechanism 3 applies an axial load to the test piece 2, the driving radial guide rail 352 moves along the machine tool guide rail 351 toward the test piece 2. The loading block 34 moves toward the test piece 2 along the radial guide rail 352 via the support slider 353 and the force gauge 31. The loading block 34 applies an axial load to the test piece 2. The distance the radial guide rail 352 moves is adjusted according to the magnitude of the axial load measured by the force gauge 31, thereby adjusting the magnitude of the axial load. When the loading mechanism 3 applies a radial load to the test piece 2, the driving support slider 353 moves along the radial guide rail 352. The loading block 34 moves along the support slider 353 via the force gauge 31. The loading block 34 applies a radial load to the test piece 2. The distance the radial guide rail 352 moves is adjusted according to the magnitude of the radial load measured by the force gauge 31, thereby adjusting the magnitude of the radial load.

[0051] See Figure 3 In this embodiment, one end of the test piece 2 is provided with a connecting part 21 that connects to the ultrasonic transmitting end of the ultrasonic transducer 1. The remaining part of the test piece 2 is a conical structure 22. The cross-section of the conical structure 22 gradually decreases along the ultrasonic vibration propagation path, and multiple vibration measuring rings 23 are nested on the conical structure 22 along its length. The outer diameter of the vibration measuring rings 23 gradually decreases along the ultrasonic vibration propagation path, and the ring surface of each vibration measuring ring 23 is a vibration measuring surface. In addition, a spline groove 24 is opened at the outwardly extending end of the test piece 2. The loading block 34 is a spline hollow shaft that mates with the spline groove 24. The loading block 34 is inserted into the spline groove 24 of the test piece 2. In this way, when the ultrasonic transducer 1 drives the test piece 2 to rotate, the outwardly extending end of the test piece 2 can be supported by the loading block 34 and the top block 32.

[0052] See Figure 1 and Figure 7The amplitude measuring mechanism 4 in this embodiment includes a support frame 41, a vibration meter 42, and a vibration meter moving platform 43. The vibration meter moving platform 43 is mounted on the support frame 41, and the vibration meter 42 is mounted on the vibration meter moving platform 43 and is driven by the vibration meter moving platform 43 to move axially or radially. The vibration meter moving platform 43 is formed by two lead screw and nut pairs perpendicularly intersecting each other. Specifically, the two lead screw and nut pairs are respectively designated as a first lead screw and nut pair 431 and a second lead screw and nut pair 432. The first lead screw and nut pair 431 is mounted on the support frame 41, and the driving direction of the first lead screw and nut pair is the axial direction of the test piece 2. The second lead screw and nut pair 432 is mounted on the nut of the first lead screw and nut pair 431, and the driving direction of the second lead screw and nut pair 432 is the radial direction of the test piece 2. When the vibration meter 42 is measuring the amplitude of a certain measuring surface, the second lead screw and nut pair 432 drives the vibration meter 42 to move radially, so that the laser of the vibration meter 42 is projected onto the corresponding measuring surface; then the first lead screw and nut pair 431 drives the vibration meter 42 to move axially, so that the distance between the vibration meter 42 and the measured surface is within the amplitude measurement focal length range of the vibration meter 42. This achieves the measurement of the amplitude of the measuring surface of the test piece 2.

[0053] See Figure 8 This embodiment also includes a charge amplifier 7, a data acquisition card 8, and a data display screen 9. The data receiving end of the charge amplifier 7 is connected to the data output end of the force measuring instrument 31, the data output end of the charge amplifier 7 is connected to the data receiving end of the data acquisition card 8, and the data output end of the data acquisition card 8 is connected to the data receiving end of the data display screen 9. The data output end of the vibration meter 42 is connected to the data receiving end of the data display screen 9. The magnitude of the load and the amplitude of the vibration on the test piece 2 can be directly obtained from the data displayed on the data display screen 9.

[0054] Example 2:

[0055] This embodiment provides a method for measuring ultrasonic vibration amplitude under load conditions, including the following measurement steps:

[0056] S1, the second lead screw and nut pair 432 drives the vibration meter 42 to move radially, so that the laser of the vibration meter 42 passes through the bearing 33 and the hollow spline shaft and is projected onto the front vibration measuring surface of the test piece 2; the first lead screw and nut pair 431 drives the vibration meter 42 to move axially, so that the distance between the vibration meter 42 and the measured surface is within the amplitude measurement focal length range of the vibration meter 42.

[0057] S2, turn on the ultrasonic power supply, the sinusoidal electrical signal is connected from the ultrasonic power supply to the conductive slip ring 6, and then through the conductive slip ring 6 to the ultrasonic transducer 1, thereby generating axial ultrasonic vibration.

[0058] S3, Vibration meter 42 measures the amplitude on the front vibration measuring surface of the test piece 2 when the ultrasonic transducer 1 is in an unloaded state.

[0059] S4, adjust the radial position of the vibration meter 42 by moving the vibration meter platform 43 to ensure that the laser of the vibration meter 42 can be aligned with the second vibration measuring surface of the test piece 2 within the required focal length range, turn on the ultrasonic power supply, and the vibration meter 42 measures the amplitude on the second vibration measuring surface of the test piece 2 when the ultrasonic transducer 1 is in an unloaded state.

[0060] S5. Repeat step 4 until the vibration meter 42 measures and records the amplitude on all vibration measurement surfaces, thereby obtaining the amplitude change of the ultrasonic transducer 1 along its entire axial length under no-load conditions.

[0061] S6, the vibration meter 42 returns to the initial position, and the force measuring instrument moving platform 35 drives the loading block 34 to move axially to apply an axial load to the test piece 2 and the ultrasonic transducer 1; repeat steps S2 to S5 to obtain the amplitude change of the ultrasonic transducer 1 along its entire axial length under axial load.

[0062] S7, the vibration meter 42 returns to the initial position, and the force measuring instrument moving platform 35 drives the loading block 34 to move radially to apply a radial load to the test piece 2 and the ultrasonic transducer 1; repeat steps S2 to S5 to obtain the amplitude change of the ultrasonic transducer 1 along its entire axial length under radial load.

[0063] like Figure 9 The figures show a comparison of the amplitude changes along the entire axial length of the test specimen under different axial loads and under zero load. These five figures demonstrate that the amplitude of the test specimen changes under axial load, and that amplitude fluctuations exist. Figure 10 The figures show a comparison of the amplitude changes along the entire axial length of the test specimen under different radial loads and under zero load. These five figures demonstrate that the amplitude of the test specimen changes under radial load, and that amplitude fluctuations exist.

[0064] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions created by the present invention, and are not intended to limit the scope of protection of the present invention. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions created by the present invention without departing from the essence and scope of the technical solutions created by the present invention.

Claims

1. An ultrasonic vibration amplitude measurement platform under load conditions, characterized in that, include: A rotatable ultrasonic transducer for generating ultrasonic vibrations; The test piece connected to the ultrasonic transducer has multiple vibration measuring surfaces with gradually decreasing outer diameters arranged along the direction of ultrasonic vibration propagation. The loading mechanism is used to apply axial and radial loads to the test piece; And an amplitude measuring mechanism, used to measure the amplitude of each vibration measuring surface of the test piece.

2. The ultrasonic vibration amplitude measurement platform under load conditions according to claim 1, characterized in that, The test piece has a conical structure with a cross-section that gradually decreases along the ultrasonic vibration propagation path. Multiple vibration measuring rings are nested on the conical structure along its length. The outer diameter of the vibration measuring rings gradually decreases along the ultrasonic vibration propagation path, and the ring surface of each vibration measuring ring is the vibration measuring surface.

3. The ultrasonic vibration amplitude measurement platform under load conditions according to claim 1, characterized in that, The loading mechanism includes a force gauge, a loading block, and a force gauge moving platform. The force gauge is mounted on the force gauge moving platform and is driven by the force gauge moving platform to move axially or radially. The loading block is rotatably mounted on the force gauge and connected to the test piece, and it can apply a load to the test piece.

4. The ultrasonic vibration amplitude measurement platform under load conditions according to claim 3, characterized in that, One end of the test piece is connected to an ultrasonic transducer, and the other end extends toward the loading block. A spline groove is opened on the end face of the test piece. The loading block is a splined hollow shaft, which is inserted into the spline groove of the test piece.

5. The ultrasonic vibration amplitude measurement platform under load conditions according to claim 3, characterized in that, The amplitude measurement mechanism includes a vibration meter and a vibration meter moving platform. The vibration meter is mounted on the vibration meter moving platform and is driven by the vibration meter moving platform to move axially or radially.

6. The ultrasonic vibration amplitude measurement platform under load conditions according to claim 1, characterized in that, The ultrasonic transducer is clamped onto the three-jaw chuck of the machine tool and driven to rotate by the three-jaw chuck.

7. The ultrasonic vibration amplitude measurement platform under load conditions according to claim 1, characterized in that, The ultrasonic transducer is fitted with a conductive slip ring. The ultrasonic power supply is connected to the outer stator of the conductive slip ring via wires, and the inner rotor of the conductive slip ring is connected to the ultrasonic transducer.

8. The ultrasonic vibration amplitude measurement platform under load conditions according to claim 1, characterized in that, It also includes a data acquisition card, used to collect data measured by the force gauge and vibration meter.

9. A method for measuring ultrasonic vibration amplitude under load conditions, characterized in that, This is achieved using the ultrasonic vibration amplitude measurement platform under load conditions described in claim 5. Includes the following steps: S1, the vibration meter moving platform drives the vibration meter to move axially and radially so that the laser emitted by the vibration meter is projected onto the front vibration measuring surface of the test piece, while the distance between the vibration meter and the vibration measuring surface is within the amplitude measurement focal length range of the vibration meter. S2, The ultrasonic transducer drives the test piece to rotate and generates axial ultrasonic vibration; S3, Vibration meter measures the amplitude on the front vibration measuring surface of the test piece when the ultrasonic transducer is in an unloaded state; S4, the vibration meter moving platform drives the vibration meter to move axially and radially so that the laser emitted by the vibration meter is projected onto the second vibration measuring surface of the test piece. The ultrasonic transducer drives the test piece to rotate and generate axial ultrasonic vibration. The vibration meter measures the amplitude on the second vibration measuring surface of the test piece when the ultrasonic transducer is in an unloaded state. This step is repeated so that the laser emitted by the vibration meter is projected onto the remaining vibration measuring surfaces in sequence, thereby obtaining the amplitude change of the ultrasonic transducer along the entire axial length in an unloaded state. S5, the vibration meter returns to its initial position, and the force measuring instrument moving platform drives the loading block to move axially to apply an axial load to the test piece and the ultrasonic transducer; repeat steps S1 to S4 to obtain the amplitude change of the ultrasonic transducer along its entire axial length under axial load. S6, the vibration meter returns to its initial position, and the force measuring instrument moving platform drives the loading block to move radially to apply a radial load to the test piece and the ultrasonic transducer; repeat steps S1 to S4 to obtain the amplitude change of the ultrasonic transducer along its entire axial length under radial load.