CN114858920B - Ultrasonic-based generator end part root crack identification method - Google Patents

Ultrasonic-based generator end part root crack identification method Download PDF

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CN114858920B
CN114858920B CN202210538276.XA CN202210538276A CN114858920B CN 114858920 B CN114858920 B CN 114858920B CN 202210538276 A CN202210538276 A CN 202210538276A CN 114858920 B CN114858920 B CN 114858920B
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measuring point
crack
wake
ultrasonic
detection
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CN114858920A (en
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冉毅
苏振
王勇
马军
刘清
张泽岩
何自勇
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Dongfang Electric Machinery Co Ltd DEC
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    • GPHYSICS
    • G01MEASURING; TESTING
    • G01NINVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N29/00Investigating or analysing materials by the use of ultrasonic, sonic or infrasonic waves; Visualisation of the interior of objects by transmitting ultrasonic or sonic waves through the object
    • G01N29/04Analysing solids
    • G01N29/041Analysing solids on the surface of the material, e.g. using Lamb, Rayleigh or shear waves
    • GPHYSICS
    • G01MEASURING; TESTING
    • G01NINVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N29/00Investigating or analysing materials by the use of ultrasonic, sonic or infrasonic waves; Visualisation of the interior of objects by transmitting ultrasonic or sonic waves through the object
    • G01N29/14Investigating or analysing materials by the use of ultrasonic, sonic or infrasonic waves; Visualisation of the interior of objects by transmitting ultrasonic or sonic waves through the object using acoustic emission techniques
    • GPHYSICS
    • G01MEASURING; TESTING
    • G01NINVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N29/00Investigating or analysing materials by the use of ultrasonic, sonic or infrasonic waves; Visualisation of the interior of objects by transmitting ultrasonic or sonic waves through the object
    • G01N29/22Details, e.g. general constructional or apparatus details
    • G01N29/24Probes
    • GPHYSICS
    • G01MEASURING; TESTING
    • G01SRADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S15/00Systems using the reflection or reradiation of acoustic waves, e.g. sonar systems
    • G01S15/02Systems using the reflection or reradiation of acoustic waves, e.g. sonar systems using reflection of acoustic waves
    • G01S15/06Systems determining the position data of a target
    • G01S15/08Systems for measuring distance only
    • GPHYSICS
    • G01MEASURING; TESTING
    • G01NINVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N2291/00Indexing codes associated with group G01N29/00
    • G01N2291/02Indexing codes associated with the analysed material
    • G01N2291/023Solids
    • G01N2291/0234Metals, e.g. steel
    • GPHYSICS
    • G01MEASURING; TESTING
    • G01NINVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N2291/00Indexing codes associated with group G01N29/00
    • G01N2291/26Scanned objects
    • G01N2291/269Various geometry objects
    • G01N2291/2696Wheels, Gears, Bearings
    • YGENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02EREDUCTION OF GREENHOUSE GAS [GHG] EMISSIONS, RELATED TO ENERGY GENERATION, TRANSMISSION OR DISTRIBUTION
    • Y02E10/00Energy generation through renewable energy sources
    • Y02E10/20Hydro energy

Abstract

The invention relates to the technical field of ultrasonic nondestructive testing, in particular to an ultrasonic-based generator end part root crack identification method, which is characterized in that wake signals are extracted by utilizing the difference of echo characteristics under different measuring points, wake indexes are utilized, a wake energy change curve is established, whether the change curve is suddenly changed and stabilized is judged, if yes, the existence of cracks on small teeth is judged, and if no, the absence of the cracks is judged. The identification method can effectively solve the problem that the crack direction is needed to be known in advance for identification, overcomes the limitation that the existing phased array detection is only suitable for large-size crack detection, can well solve the influence of a double-layer structure on crack detection, reduces detection cost, and improves crack detection efficiency and precision.

Description

Ultrasonic-based generator end part root crack identification method
Technical Field
The invention relates to the technical field of ultrasonic nondestructive testing, in particular to an ultrasonic-based generator end part root crack identification method.
Background
When a large turbine generator is operated, the rotor of the large turbine generator generates a great centrifugal force due to a high linear speed, so that a retaining ring is usually adopted to be hooped on the periphery of small teeth of the rotor with a great compressive stress so as to resist centrifugal stress in high-speed operation. Because the generator rotor is frequently started and stopped and runs under variable working conditions, alternating stress is generated, and fatigue cracks at weak parts of the root parts of the small teeth are extremely easy to induce. In actual operation, because of complete fracture induced by fatigue crack of small teeth of the rotor, metal powder is generated due to mutual collision and grinding with a guard ring, an end slot wedge, a rotating shaft and the like, and turn-to-turn short circuit fault of the rotor is caused. If the small teeth are broken too much, the effective matching area between the guard ring and the lap joint surface of the rotating shaft is reduced, so that the circumferential displacement of the guard ring is caused, and the serious fault of the operation of the unit is induced. Early crack detection of rotor small teeth has become an important aspect of periodic detection.
As the strong sound attenuation effect, the multi-interface reflection phenomenon and the measured material which are introduced by the generator guard ring-small tooth double-layer structure are all made of non-magnetic materials, the conventional nondestructive testing methods in the market at present, including a permeation method, a magnetic powder method and a ray method, are difficult to be applied to the detection of the small teeth of the generator rotor. In addition, after the rotor is extracted from the stator bore, the rotor guard ring is extracted by hot drawing, and rotor small teeth are detected by visual inspection and dye check, so that whether cracks exist or not can be detected, but the method cannot realize in-service detection.
In the prior art, a chinese invention patent document with publication number CN101413924 and publication date 2009, 04 month and 22 is proposed to solve the above-mentioned technical problems, and the technical scheme disclosed in the patent document is as follows: a method and apparatus for detecting cracks in a generator rotor tooth. The method is a method for nondestructively testing a rotor of a high power generator, comprising the steps of: providing a plurality of ultrasonic pulse echo transducers arranged in an array and positioned and arranged to provide a range of different inspection angles for tooth geometry; positioning an array over the rotor teeth; exciting at least one of the plurality of ultrasonic pulse echo transducers to generate a transmit beam to interrogate a wedge angle on the inside of the tooth; and adjusting data acquired from at least one of the plurality of ultrasonic pulse echo transducers to capture reflections from defects within the tooth.
In the prior art, a Chinese patent document with publication number of CN112154323A and publication date of 2020, 12 and 29 is proposed to solve the above technical problems, and the technical scheme disclosed in the patent document is as follows: in the rotor tooth crack inspection method, when an angle of occurrence of a crack with respect to a reference line intersecting a tooth shoulder and orthogonal to a radial direction of the tooth is set to be α, a phased array probe is set in advance at a position of an outer peripheral surface of a retainer ring in a direction estimated to be orthogonal to the angle of occurrence α, and an ultrasonic beam emitted from the phased array probe is subjected to sector scanning, thereby inspecting whether or not a crack is generated in the tooth shoulder.
The following problems occur in the practical use process of the technical scheme of ultrasonic detection:
ultrasonic waves are incident on the guard ring-small tooth double-layer structure and the high attenuation material, so that complex multi-boundary reflection behaviors are shown, and cracks are difficult to accurately identify. The existing ultrasonic phased array detection method needs to know the expansion angle of a crack in advance, and then sector scanning is carried out at the intersection point of the normal vector of the crack and the surface of the generator guard ring, so that qualitative analysis is carried out according to the ultrasonic ranging principle.
Disclosure of Invention
In order to solve the technical problems, the invention provides the ultrasonic-based generator end part root crack identification method, which can effectively solve the problem that crack directions are required to be known in advance for identification, overcomes the limitation that the existing phased array detection is only suitable for large-size crack detection, can well solve the influence of a double-layer structure on crack detection, reduces detection cost, and improves crack detection efficiency and precision.
The invention is realized by adopting the following technical scheme:
an ultrasonic-based generator end part root crack identification method is characterized by comprising the following steps of: the method comprises the following steps:
S 1 marking five detection measuring points on the outer surface of the guard ring according to the guard ring-small tooth structure, wherein the five detection measuring points comprise a measuring point 1, a measuring point 2, a measuring point 3, a measuring point 4 and a measuring point 5, the central positions of the ultrasonic probe are respectively the measuring point 1 and the measuring point 5 when the circular wall of the outer ring of the ultrasonic probe is tangent to the side wall of the small tooth, the measuring point 3 is opposite to the center of the small tooth, and the measuring points 2 and 4 are respectively arranged at the measuring points1 with the measuring point 3 and 5 with the measuring point 3; the ultrasonic probe is respectively arranged at a measuring point 2 or a measuring point 4, a plurality of echoes are found through echo signals, and the ultrasonic probe is respectively provided with: a faying surface echo, a crack end point echo, a shoulder echo, a wake wave and a bottom wave;
S 2 scanning the ultrasonic probe back and forth between the measuring point 1 and the measuring point 5 for a plurality of times, extracting a wake wave signal, obtaining a wake wave energy change curve, judging whether the wake wave energy change curve is suddenly changed and stabilized, if so, judging that the small teeth have cracks, and if not, judging that the small teeth have no cracks.
Said step S 2 The obtained wake energy change curve is specifically: obtaining a wake energy change curve by using wake indexes, wherein the wake indexes are specifically as follows:
Figure BDA0003647370770000021
a and b are respectively the initial time and the end time of wake signal interception; u (t) is an ultrasonic echo signal.
Said step S 2 The judging method of (3) further comprises the following steps: if the wake wave energy change curve suddenly becomes larger or smaller and is stabilized, the situation that a crack exists at the tooth root of the small tooth below the detection point on the side where the curve becomes larger is judged.
When judging which detection point below the small tooth root has a crack, placing an ultrasonic probe at the detection point, and calculating the crack endpoint depth by using the crack endpoint echo.
The method for calculating the crack endpoint depth comprises the following steps:
Figure BDA0003647370770000031
wherein c 1 And c 2 Sound velocity of guard ring and small teeth respectively, deltaT 1 And DeltaT 2 The time difference of ultrasonic wave propagation in the guard ring and the small teeth, respectively.
Compared with the prior art, the invention has the beneficial effects that:
1. aiming at the problem that the root crack is difficult to identify under the guard ring-small tooth double-layer structure, the small tooth crack is detected by utilizing the change degree of the characteristic wave signal energy obtained by an ultrasonic pulse reflection method, more specifically, the difference of echo characteristics under different measuring points is utilized, the wake wave signal is extracted, the wake wave index is utilized, a wake wave energy change curve is established, the influence of the double-layer structure on crack detection can be well solved, and the crack detection efficiency and precision are improved.
The method does not need to know the crack propagation direction before detection, overcomes the limitation that the existing phased array detection is only suitable for large-size crack detection, and reduces the detection cost.
2. According to the invention, through the crack endpoint echo, the calculated relative error of the crack endpoint depth is less than 3%, so that the engineering measurement requirement is met.
Drawings
The invention will be described in further detail with reference to the drawings and detailed description, wherein:
FIG. 1 is a schematic flow chart of the present invention;
FIG. 2 is a schematic diagram of the arrangement of detection points in the present invention;
FIG. 3 is a schematic diagram of echo signals at a crack height of 4 mm;
FIG. 4 is a schematic diagram of echo signals at a crack height of 6 mm;
FIG. 5 is a schematic diagram of echo signals at a crack height of 8 mm;
FIG. 6 is a schematic diagram of echo signals at full break of a small tooth;
FIG. 7 is a schematic representation of a wake index curve without a crack;
FIG. 8 is a schematic representation of a wake index curve with a crack height of 4 mm;
FIG. 9 is a schematic representation of a wake index curve with a crack height of 6 mm;
FIG. 10 is a schematic representation of a wake index curve with a crack height of 8 mm;
FIG. 11 is a schematic representation of a wake index curve at full break;
the marks in the figure:
1. the ultrasonic probe comprises a guard ring, 2, small teeth, 3, crack end points, 4, small tooth shoulders, 5, small tooth bottom surfaces, 6, an ultrasonic probe, a, measuring points 1, b, 2, c, 3, d, 4, e and 5.
Detailed Description
Example 1
As a basic embodiment of the invention, the invention comprises an ultrasonic-based generator tip root crack identification method comprising the steps of:
S 1 according to the structure of the guard ring 1 and the small teeth 2, five detection measuring points are marked on the outer surface of the guard ring 1, wherein the five detection measuring points comprise a measuring point 1a, a measuring point 2b, a measuring point 3c, a measuring point 4d and a measuring point 5e. When the circular wall of the outer ring of the ultrasonic probe 6 is tangent to the side wall of the small tooth 2, the central positions of the ultrasonic probe 6 are respectively a measuring point 1a and a measuring point 5e, a measuring point 3c is opposite to the center of the small tooth 2, and a measuring point 2b and a measuring point 4d are respectively arranged between the measuring points 1a and 3c and between the measuring point 5e and 3 c. The ultrasonic probe 6 is respectively arranged at the measuring point 2b or the measuring point 4d, a plurality of echoes are found through echo signals, and the receiving time sequence is as follows: lap surface echo, crack end point echo, shoulder echo, wake and bottom wave.
S 2 Scanning the ultrasonic probe 6 back and forth between the measuring points 1a and 5e for a plurality of times, extracting wake signals, obtaining a wake energy change curve, judging whether the change curve is suddenly changed and stabilized, if so, judging that the small teeth 2 have cracks, and if not, judging that the small teeth have no cracks.
Example 2
As a preferred embodiment of the invention, the invention comprises an ultrasonic-based generator end root crack identification method, comprising the following steps:
S 1 according to the structure of the guard ring 1 and the small teeth 2, five detection measuring points are marked on the outer surface of the guard ring 1, wherein the five detection measuring points comprise a measuring point 1a, a measuring point 2b, a measuring point 3c, a measuring point 4d and a measuring point 5e. When the circular wall of the outer ring of the ultrasonic probe 6 is tangent to the side wall of the small tooth 2, the central positions of the ultrasonic probe 6 are respectively a measuring point 1a and a measuring point 5e, a measuring point 3c is opposite to the center of the small tooth 2, and a measuring point 2b and a measuring point 4d are respectively arranged between the measuring points 1a and 3c and between the measuring point 5e and 3 c. The ultrasonic probe 6 is respectively arranged at the measuring point 2b or the measuring point 4d by echoThe signal finds a plurality of echoes, which are respectively in the order of receiving time: lap surface echo, crack end point echo, shoulder echo, wake and bottom wave.
S 2 Scanning the ultrasonic probe 6 back and forth between the measuring points 1a and 5e for a plurality of times, extracting wake signals, and obtaining a wake energy change curve by using wake indexes. Wherein, the wake index specifically is:
Figure BDA0003647370770000051
a and b are respectively the initial time and the end time of wake signal interception; u (t) is an ultrasonic echo signal.
Judging whether the change curve is suddenly changed and stabilized, if so, judging that the small teeth 2 have cracks, and if not, judging that the small teeth have no cracks. More specifically, if the wake energy change curve suddenly increases or decreases and stabilizes, it is determined that a crack exists at the root of the small tooth 2 below the detection point on the side where the curve increases.
Example 3
As the best mode of the invention, the invention comprises an ultrasonic-based generator end part root crack identification method, and referring to figure 1 of the specification, the method comprises the following steps:
S 1 according to the structure of the guard ring 1 and the small teeth 2, five detection points are marked on the outer surface of the guard ring 1.
For the small tooth 2 structure, five detection measuring points are designed, the positions of the detection measuring points change along with the size of the probe, and specifically the detection measuring points can comprise a measuring point 1a, a measuring point 2b, a measuring point 3c, a measuring point 4d and a measuring point 5e. The small tooth 2 comprises a small tooth shoulder 4 and a small tooth bottom surface 5, wherein the small tooth 2 is provided with a crack, and a crack end point 3 is formed. More specifically, referring to fig. 2 of the specification, when the circular wall of the outer ring of the ultrasonic probe 6 is tangent to the side wall of the small tooth 2, the center position of the ultrasonic probe 6 is respectively a measuring point 1a and a measuring point 5e, a measuring point 3c is opposite to the center of the small tooth 2, a measuring point 2b is between the measuring point 1a and the measuring point 3c, and a measuring point 4d is between the measuring point 5e and the measuring point 3 c.
The ultrasonic probe 6 is respectively arranged at the measuring point 2b or the measuring point 4d, a plurality of echoes are found through echo signals, and the receiving time sequence is as follows: lap surface echo, crack end point echo, shoulder echo, wake and bottom wave.
More specifically, this example identifies five types of small teeth 2 whose crack heights are 0, 4mm, 6mm, 8mm and full fracture. The identified device can comprise a guard ring 1, small teeth 2, a small tooth supporting seat and a base from top to bottom, and is pressed by bolts. When the ultrasonic probe 6 is respectively arranged at the measuring point 2b or the measuring point 4d through the couplant, a series of echo signals are obtained, and the echo is confirmed to be respectively a lap face echo, a crack endpoint echo, a shoulder echo, a wake wave and a bottom wave through the functional relationship of time, speed and path referring to the accompanying figures 3-6 of the specification.
S 2 Scanning the ultrasonic probe 6 back and forth between the measuring point 1a and the measuring point 5e for a plurality of times, extracting wake signals, and retracing the wake signals for a plurality of times, wherein the wake signals are obvious on the side with the crack, and the wake is not on the side without the crack, so that the wake index is constructed based on the difference:
Figure BDA0003647370770000061
a and b are respectively the initial time and the end time of wake signal interception, us; u (t) is an ultrasonic echo signal, V.
And scanning again and again for a plurality of times, and obtaining a wake energy change curve by using the wake index to obtain the change trend of the wake index curve, wherein the change trend is shown in figures 7-11 of the specification.
Judging whether the change curve is suddenly changed and stabilized, if so, judging that the small teeth 2 have cracks, and if not, judging that the small teeth have no cracks. Specifically, after the crack is determined, if the wake wave energy change curve suddenly becomes larger or smaller and stabilizes, the crack is determined at the root of the small tooth 2 below the detection point on the side where the curve becomes larger. Namely, when the ultrasonic probe 6 moves to the side with the crack through the wake energy change curve, the wake energy change curve is suddenly increased and fluctuates up and down at a certain value; similarly, when moving to the crack-free side, the wake energy profile tapers off and fluctuates up and down at a certain value. Thus, if the wake index curve suddenly increases and stabilizes at a certain value, the root of the small tooth 2 on this side is cracked. More specifically, after judging that there is a crack, it can be judged whether there is a sudden increase at the side of the measurement point 2b, if yes, it is judged that there is a crack under the measurement point 2b, and if not, it is judged that there is a crack under the measurement point 4 d.
S 3 Based on step S 2 When judging which detection point has a crack at the tooth root of the small tooth 2 below, the ultrasonic probe 6 is placed at the detection point. For example, if it is determined that there is a crack under the measurement point 2b, the ultrasonic probe 6 is placed at the measurement point 2b, and if it is determined that there is a crack under the measurement point 4d, the ultrasonic probe 6 is placed at the measurement point 4 d. And calculating the depth of the crack endpoint 3 by using the echo of the crack endpoint and an ultrasonic ranging principle. For example, if there is a crack at the measurement point 2b, the echo signal of the measurement point 2b is observed, and the ultrasonic ranging principle is used:
Figure BDA0003647370770000062
wherein c 1 And c 2 Sound velocity, Δt, of the grommet 1 and the pinion 2, respectively 1 And DeltaT 2 The time difference of propagation of the ultrasonic wave in the grommet 1 and the small tooth 2, respectively.
In this embodiment, the grommet 1 has a thickness of about 42.9mm. The sound velocity of the shroud ring 1 was 5524.56 m.s -1 The sound velocity of the small teeth 2 was 5872.7 m.s -1 . The longitudinal wave straight probe with the nominal center frequency of 3.5MHz is adopted to carry out retrace inspection among five measuring points, then different types of small teeth 2 are replaced, and through the wake indexes, five types of wake index change curves are finally obtained, so that the existence and the generation position of cracks can be identified.
If cracks are observed to be generated on the tooth root of the small tooth 2 below the measuring point 2b, the ultrasonic signals of the measuring point 2b are collected. And finding out the echo of the crack end point, and calculating the depth of the crack end point 3. The actual crack end point 3 depth is obtained through a digital caliper. The results of the actual depth and calculated depth measurements of the crack end point 3 are shown in the table below.
Figure BDA0003647370770000071
Based on an ultrasonic pulse reflection method, whether the generator rotor small tooth 2 has cracks or not can be judged through a wake wave index; and the calculated relative error of the depth of the crack end point 3 is less than 3% through the echo of the crack end point, so that the engineering measurement requirement is met.
In view of the foregoing, it will be appreciated by those skilled in the art that, after reading the present specification, various other modifications can be made in accordance with the technical scheme and concepts of the present invention without the need for creative mental efforts, and the modifications are within the scope of the present invention.

Claims (5)

1. An ultrasonic-based generator end part root crack identification method is characterized by comprising the following steps of: the method comprises the following steps:
S 1 marking five detection measuring points on the outer surface of the guard ring (1) according to the guard ring (1) -small tooth (2) structure, wherein the five detection measuring points comprise a measuring point 1 (a), a measuring point 2 (b), a measuring point 3 (c), a measuring point 4 (d) and a measuring point 5 (e), when the circular wall of the outer ring of the ultrasonic probe (6) is tangential to the side wall of the small tooth (2), the central positions of the ultrasonic probe (6) are respectively the measuring point 1 (a) and the measuring point 5 (e), the measuring point 3 (c) is opposite to the center of the small tooth (2), and the measuring point 2 (b) and the measuring point 4 (d) are respectively arranged between the measuring point 1 (a) and the measuring point 3 (c) and between the measuring point 5 (e) and the measuring point 3 (c); the ultrasonic probe (6) is respectively arranged at the measuring point 2 (b) or the measuring point 4 (d), a plurality of echoes are found through echo signals, and the receiving time sequence is as follows: a faying surface echo, a crack end point echo, a shoulder echo, a wake wave and a bottom wave;
S 2 scanning the ultrasonic probe (6) back and forth between the measuring point 1 (a) and the measuring point 5 (e) for a plurality of times, extracting a wake wave signal, obtaining a wake wave energy change curve, judging whether the wake wave energy change curve is suddenly changed and stabilized, if so, judging that the small teeth (2) have cracks, and if not, judging that the small teeth have no cracks.
2. The ultrasonic-based generator tip root crack identification method of claim 1, wherein: the steps are as followsS 2 The obtained wake energy change curve is specifically: obtaining a wake energy change curve by using wake indexes, wherein the wake indexes are specifically as follows:
Figure FDA0003647370760000011
a and b are respectively the initial time and the end time of wake signal interception; u (t) is an ultrasonic echo signal.
3. The ultrasonic-based generator tip root crack identification method according to claim 1 or 2, characterized by: said step S 2 The judging method of (3) further comprises the following steps: if the wake wave energy change curve suddenly becomes larger or smaller and is stabilized, the crack exists at the tooth root of the small tooth (2) below the detection point on the side of the curve enlargement.
4. A method of ultrasonic-based generator tip root crack identification as set forth in claim 3, wherein: when judging which detection point is below the small tooth (2) root, placing an ultrasonic probe (6) at the detection point, and calculating the depth of the crack endpoint (3) by utilizing the echo of the crack endpoint.
5. The ultrasonic-based generator tip root crack identification method of claim 4, wherein: the method for calculating the depth of the crack endpoint (3) comprises the following steps:
Figure FDA0003647370760000012
wherein c 1 And c 2 Sound velocity of the guard ring (1) and the small teeth (2), delta T 1 And DeltaT 2 The time difference of the ultrasonic wave propagating in the guard ring (1) and the small teeth (2) is respectively.
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