阅读说明：本技术 一种螺栓轴向应力的非线性超声检测方法 (Nonlinear ultrasonic detection method for axial stress of bolt ) 是由 潘勤学 常梅乐 李双阳 徐晓宇 潘瑞鹏 张云淼 于 2020-04-30 设计创作，主要内容包括：本发明提供一种螺栓轴向应力的非线性超声检测方法,其实施步骤如下：步骤A：基于超声波在各向同性介质中的传播理论,建立二次谐波幅值与基波幅值之间的关系模型,得到相对非线性系数的表达式；步骤B：对螺栓试样进行轴向应力加载实验并进行非线性超声检测,计算出不同应力状态下的相对非线性系数；步骤C：对加载的轴向应力和对应的相对非线性系数进行拟合,确定螺栓轴向应力超声检测系数,最终得到螺栓轴向应力和相对非线性系数的关系式；通过以上步骤,可以实现螺栓轴向应力的非线性超声检测,该方法可以对螺栓的轴向应力进行快速、准确地检测,提高螺栓轴向应力检测技术的准确性和实用性。(The invention provides a nonlinear ultrasonic detection method for axial stress of a bolt, which comprises the following implementation steps: step A: establishing a relation model between the amplitude of the second harmonic and the amplitude of the fundamental wave based on the propagation theory of the ultrasonic wave in the isotropic medium to obtain an expression of a relative nonlinear coefficient; and B: carrying out an axial stress loading experiment on a bolt sample, carrying out nonlinear ultrasonic detection, and calculating relative nonlinear coefficients under different stress states; and C: fitting the loaded axial stress and the corresponding relative nonlinear coefficient, determining the ultrasonic detection coefficient of the axial stress of the bolt, and finally obtaining a relational expression of the axial stress of the bolt and the relative nonlinear coefficient; through the steps, the nonlinear ultrasonic detection of the axial stress of the bolt can be realized, the method can be used for quickly and accurately detecting the axial stress of the bolt, and the accuracy and the practicability of the bolt axial stress detection technology are improved.)

1. The nonlinear ultrasonic detection method for the axial stress of the bolt is characterized by comprising the following implementation steps of:

step A: establishing a relation model between the amplitude of the second harmonic and the amplitude of the fundamental wave based on the propagation theory of the ultrasonic wave in the isotropic medium to obtain an expression of a relative nonlinear coefficient;

and B: carrying out an axial stress loading experiment on a bolt sample, carrying out nonlinear ultrasonic detection, and calculating relative nonlinear coefficients under different stress states;

and C: and fitting the loaded axial stress and the corresponding relative nonlinear coefficient, determining the ultrasonic detection coefficient of the axial stress of the bolt, and finally obtaining a relational expression of the axial stress of the bolt and the relative nonlinear coefficient.

2. The nonlinear ultrasonic detection method for the axial stress of the bolt according to claim 1, characterized in that:

in step a, a relation model between the second harmonic amplitude and the fundamental amplitude is established based on the propagation theory of the ultrasonic wave in the isotropic medium to obtain an expression of the relative nonlinear coefficient, which is specifically performed as follows:

according to the propagation rule of ultrasonic waves in an isotropic medium, one-dimensional wave equation is as follows:

in formula (1):

ρ is the density of the material;

u-displacement in the x direction;

t is the propagation time;

stress in the σ -x direction;

x is the propagation distance of the ultrasonic wave;

the stress versus strain in the x-direction is:

σ＝E·f() (2)

in formula (2):

e-modulus of elasticity of the material;

f () -strain function;

the positive strain in the x-direction is defined as:

substituting formulae (2) and (3) for formula (1):

wherein

Substituting formula (5) for formula (4) to obtain:

in formula (6):

c-ultrasonic wave velocity;

β -second order nonlinear coefficients;

-third order non-linear coefficients;

the equation has no analytic solution, and is solved by adopting a perturbation approximation theory, namely solving parameters to be solved by power series expansion to obtain:

in formula (7):

A₁-the fundamental amplitude;

k is the wave number;

omega-angular frequency;

let the coefficient of the second term in equation (7) be the second harmonic amplitude A₂The coefficient of the third term is the third harmonic amplitude A₃By analogy, the nonlinear coefficient can be expressed as:

in the ultrasonic nonlinear response, the amplitude of higher harmonic wave is lower than that of fundamental wave by more than two orders of magnitude, and the amplitude of third harmonic wave is very weak, so that the ultrasonic wave is characterized by only using second harmonic wave, when the excitation frequency is constant, the wave number of ultrasonic wave is also determined, and under the condition of unchanging propagation distance, only the relative nonlinear coefficient β' is obtained, and the property change condition in the material can be characterized, in which the second order relative nonlinear coefficient is

From equation (10), the second-order relative nonlinear coefficient β' and the square A of the fundamental amplitude₁ ²Inversely proportional to the second harmonic amplitude A₂Is in direct proportion; therefore, when the nonlinear ultrasonic method is used for detecting the axial stress of the bolt, only the fundamental wave amplitude and the second harmonic amplitude need to be measured.

3. The nonlinear ultrasonic detection method for the axial stress of the bolt according to claim 1, characterized in that:

in the step B, "performing an axial stress loading experiment on the bolt sample and performing nonlinear ultrasonic detection, and calculating relative nonlinear coefficients in different stress states" includes the following steps: firstly, preparing a bolt sample to be tested, loading axial stresses with different values on the bolt, and respectively naming the applied axial stresses as F₁,F₂,…,F_nThen respectively carrying out nonlinear ultrasonic detection on the bolts in different loaded states to obtain nonlinear response signals, and calculating corresponding relative nonlinear coefficients which are respectively named as β'₁,β′₂,…,β′_n(ii) a The specific steps of the process are as follows:

step B1: preparing a bolt sample to be tested, and determining the elastic limit sigma of the bolt sample to be tested_ECarrying out axial stress loading experiment on the steel plate, setting the interval s of loading stress values, and loading the steel plate to a target stress value F_iWhen it is time to stop loading, F_iRepresenting the axial stress applied by the ith axial stress loading experiment;

step B2: adopting a 'transmitting-receiving' detection method, enabling ultrasonic waves to enter a bolt sample to be detected through a transmitting transducer, and enabling a receiving transducer to receive signals at the other end of the bolt, wherein the central frequency of the receiving transducer is 2 times of that of the transmitting transducer so as to receive second harmonic signals; the transmitting transducer and the end face of the bolt as well as the receiving transducer and the other end face of the bolt are stably coupled by using a coupling agent, the attenuation of ultrasonic waves in the transmission process is reduced to the maximum extent, a stable second harmonic signal can be received, and then the axial stress is F_iThe bolt is subjected to a nonlinear ultrasonic detection experiment to obtain experimental data of a frequency domain signal;

step B3: due to the influence of an experimental system and an experimental environment, the received ultrasonic signals contain signals beyond a target frequency, in order to obtain an ideal frequency domain waveform, a Matlab tool is used for filtering original sampling data, the influence of high-frequency signals is eliminated, a filtered frequency domain signal diagram is obtained, and the fundamental wave amplitude A of the received signals under the stress condition is read_1iAnd the second harmonic amplitude A_2i；

Step B4: according to the formula (10) from A_1iAnd A_2iThe relative nonlinear coefficient is calculated to be β'_i，β′_iRepresenting axial stress F_iRelative non-linear coefficients of time;

and repeating the steps B1-B4, increasing the axial stress applied each time by s compared with the previous time, repeating the experiment for a plurality of times within the elastic limit of the bolt, and calculating to obtain a group of relative nonlinear coefficients.

4. The nonlinear ultrasonic detection method for the axial stress of the bolt according to claim 1, characterized in that:

in the step C, the loaded axial stress and the corresponding relative nonlinear coefficient are fitted, the bolt axial stress ultrasonic detection coefficient is determined, and finally the relation between the bolt axial stress and the relative nonlinear coefficient is obtained, which includes the following steps: axial stress F of bolt₁,F₂,…,F_nAnd calculating the resulting relative non-linearity coefficient of β'₁,β′₂,…,β′_nOne-to-one correspondence, with β'₁,β′₂,…,β′_nAs independent variable, with F₁,F₂,…,F_nTaking the relation curve of the relative nonlinear coefficient β 'and the bolt axial stress F as a dependent variable, and carrying out linear fitting to obtain the relation curve of the relative nonlinear coefficient β' and the bolt axial stress F, wherein the specific steps of the process are as follows:

step C1, carrying out linear fitting on axial stress F applied in the experiment and a corresponding relative nonlinear coefficient β 'by using a Matlab tool, wherein β' is used as an independent variable, and F is used as a dependent variable to obtain ultrasonic detection coefficients a and b;

and C2, substituting the ultrasonic detection coefficient into a linear equation to obtain a relation between the bolt axial stress F and the relative nonlinear coefficient β':

F＝aβ′+b (11)。

A technical field

The invention provides a nonlinear ultrasonic detection method for axial stress of a bolt, and relates to the technical field of bolt fastener detection.

Second, background Art

The bolt is used as a common fastener, is widely applied to the industrial fields of aerospace, railway traffic, ship turbines, armored vehicles, civil manufacturing and the like due to the advantages of good connection performance, simplicity in disassembly and low cost, and is used for ensuring good connection performance or sealing effect. The bolt is required to maintain sufficient strength and rigidity in the service process so as to meet the requirement of stability of the whole structure. However, the bolt is inevitably subjected to the action of axial force in the working process, and the overall performance of the bolt is degraded along with the accumulation of time, so that the service performance and the service life of the bolt are greatly influenced. In extreme cases, even sudden bolt breakage can occur, resulting in significant personnel safety accidents and property damage. Therefore, it is necessary to detect the axial force applied to the bolt.

Since the propagation process of ultrasonic waves can directly reflect the internal characteristics of the material, the ultrasonic detection technology becomes one of the main methods for evaluating the material performance. The traditional ultrasonic detection method is used for evaluating the stress of a material through the relation between the sound velocity and the stress, however, when the stress changes by 100MPa, the sound velocity only changes by 0.01%, and therefore, the stress borne by the material is not accurate enough to be reflected through the change of the wave velocity. The nonlinear ultrasonic detection technology is a new method for nondestructive detection, can accurately represent the change of the microstructure of the solid material, and is widely researched in recent years. The change of the material microstructure is mostly caused by dislocation and slippage, and when ultrasonic waves propagate in the material, the ultrasonic waves and the micro defects act to generate nonlinear response, so that the waveform is distorted, and higher harmonics are generated.

The invention provides a nonlinear ultrasonic detection method for axial stress of a bolt, which has better universality and innovativeness and can realize accurate and rapid detection of the axial stress of the bolt.

Third, the invention

1. Objects of the invention

The invention aims to provide a nonlinear ultrasonic detection method for axial stress of a bolt, which is used for quickly and accurately detecting the axial stress of the bolt and improving the accuracy and the practicability of a bolt axial stress detection technology.

2. Technical scheme

The invention provides a nonlinear ultrasonic detection method for axial stress of a bolt, which comprises the following implementation steps:

step A: establishing a relation model between the amplitude of the second harmonic and the amplitude of the fundamental wave based on the propagation theory of the ultrasonic wave in the isotropic medium to obtain an expression of a relative nonlinear coefficient;

and B: carrying out an axial stress loading experiment on a bolt sample, carrying out nonlinear ultrasonic detection, and calculating relative nonlinear coefficients under different stress states;

and C: fitting the loaded axial stress and the corresponding relative nonlinear coefficient, determining the ultrasonic detection coefficient of the axial stress of the bolt, and finally obtaining a relational expression of the axial stress of the bolt and the relative nonlinear coefficient;

through the steps, the nonlinear ultrasonic detection of the axial stress of the bolt can be realized, the method can be used for quickly and accurately detecting the axial stress of the bolt, and the accuracy and the practicability of the bolt axial stress detection technology are improved.

The step a of establishing a relationship model between the second harmonic amplitude and the fundamental amplitude based on the propagation theory of the ultrasonic wave in the isotropic medium to obtain an expression of the relative nonlinear coefficient includes:

according to the propagation rule of ultrasonic waves in an isotropic medium, one-dimensional wave equation is as follows:

in formula (1):

ρ is the density of the material;

u-displacement in the x direction;

t is the propagation time;

stress in the σ -x direction;

x is the propagation distance of the ultrasonic wave;

the stress versus strain in the x-direction is:

σ＝E·f() (2)

in formula (2):

e-modulus of elasticity of the material;

f () -strain function;

the positive strain in the x-direction is defined as:

substituting formulae (2) and (3) for formula (1):

wherein

Substituting formula (5) for formula (4) to obtain:

in formula (6):

c-ultrasonic wave velocity;

β -second order nonlinear coefficients;

-third order non-linear coefficients;

the equation has no general analytic solution, and is generally solved by adopting a perturbation approximation theory, namely solving by performing power series expansion on solved parameters to obtain:

in formula (7):

A₁-the fundamental amplitude;

k is the wave number;

omega-angular frequency;

let the coefficient of the second term in equation (7) be the second harmonic amplitude A₂The coefficient of the third term is the third harmonic amplitude A₃By analogy, the nonlinear coefficient can be expressed as:

in the ultrasonic nonlinear response, the amplitude of higher harmonic is generally lower than that of fundamental wave by more than two orders of magnitude, the amplitude of third harmonic is quite weak, so that the ultrasonic wave is generally characterized by only using second harmonic, when the excitation frequency is fixed, the wave number of the ultrasonic wave is also determined, and under the condition of unchanging propagation distance, the property change condition in the material can be characterized by only obtaining a relative nonlinear coefficient (namely β'), wherein the second-order relative nonlinear coefficient is

From equation (10), the second-order relative nonlinear coefficient β' and the square A of the fundamental amplitude₁ ²Inversely proportional to the second harmonic amplitude A₂Is in direct proportion; therefore, when the nonlinear ultrasonic method is used for detecting the axial stress of the bolt, only the fundamental wave amplitude and the second harmonic amplitude need to be measured.

And B, performing an axial stress loading experiment on the bolt sample and performing nonlinear ultrasonic detection to calculate relative nonlinear coefficients under different stress states, wherein the method comprises the following steps: firstly, preparing a bolt sample to be tested, carrying out axial stress loading on the bolt with different numerical values, and applying an applied shaftThe directional stresses are respectively named as F₁,F₂,…,F_nThen respectively carrying out nonlinear ultrasonic detection on the bolts in different loaded states to obtain nonlinear response signals, and calculating corresponding relative nonlinear coefficients which are respectively named as β'₁,β′₂,…,β′_n(ii) a The specific steps of the process are as follows:

step B1: preparing a bolt sample to be tested, and setting the elasticity limit (i.e. sigma) of the bolt sample to be tested_E) Carrying out axial stress loading experiment on the steel plate, setting the interval (i.e. s) of loading stress values, and loading the steel plate to a target stress value F_i(F_iAxial stress applied by the ith axial stress loading experiment is shown), the loading is stopped;

step B2: adopting a 'transmitting-receiving' detection method, enabling ultrasonic waves to enter a bolt sample to be detected through a transmitting transducer, and enabling a receiving transducer to receive signals at the other end of the bolt, wherein the central frequency of the receiving transducer is 2 times of that of the transmitting transducer so as to receive second harmonic signals; the transmitting transducer and the end face of the bolt, the receiving transducer and the other end face of the bolt are stably coupled by using a coupling agent, so that the attenuation of ultrasonic waves in the propagation process is reduced to the maximum extent, a stable second harmonic signal can be received, and then a nonlinear ultrasonic detection experiment is performed on the bolt with axial stress of Fi to obtain experimental data of frequency domain signals;

step B3: due to the influence of an experimental system and an experimental environment, a received ultrasonic signal contains signals beyond a target frequency, in order to obtain an ideal frequency domain waveform, a Matlab tool is used for filtering original sampling data, the influence of a high-frequency signal is eliminated, a filtered frequency domain signal diagram is obtained, and the fundamental wave amplitude (namely A) of the received signal under the stress condition is read_1i) And the second harmonic amplitude (i.e. A)_2i)；

Step B4: according to the formula (10) from A_1iAnd A_2iThe relative nonlinear coefficient is calculated to be β'_i(β′_iRepresenting axial stress F_iRelative non-linear coefficients of time);

and repeating the steps B1-B4, increasing the axial stress applied each time by s compared with the previous time, repeating the experiment for a plurality of times within the elastic limit of the bolt, and calculating to obtain a group of relative nonlinear coefficients.

And C, fitting the loaded axial stress and the corresponding relative nonlinear coefficient, determining the ultrasonic detection coefficient of the axial stress of the bolt, and finally obtaining a relation between the axial stress of the bolt and the relative nonlinear coefficient, wherein the method comprises the following steps: axial stress F of bolt₁，F₂，…，F_nAnd calculating the resulting relative non-linearity coefficient of β'₁，β′₂，…，β′_nOne-to-one correspondence, with β'₁，β′₂，…，β′_nAs independent variable, with F₁，F₂，…，F_nTaking the relation curve of the relative nonlinear coefficient β 'and the bolt axial stress F as a dependent variable, and carrying out linear fitting to obtain the relation curve of the relative nonlinear coefficient β' and the bolt axial stress F, wherein the specific steps of the process are as follows:

step C1, carrying out linear fitting on the axial stress F applied in the experiment and a corresponding relative nonlinear coefficient β 'by using a Matlab tool, wherein β' is used as an independent variable, and F is used as a dependent variable to obtain an ultrasonic detection coefficient (namely a, b);

and C2, substituting the ultrasonic detection coefficient into a linear equation to obtain a relation between the bolt axial stress F and the relative nonlinear coefficient β':

F＝aβ′+b (11)

3. advantages and effects

Compared with the traditional ultrasonic detection method, the invention has the advantages that: the nonlinear characteristic is introduced into the bolt axial stress detection, and the ultrasonic nonlinear response is more sensitive to the stress than the sound velocity, so that the measurement of the ultrasonic wave propagation time is avoided, and the accuracy of the bolt axial stress detection is greatly improved; by introducing a relative nonlinear coefficient, only the amplitude corresponding to the corresponding frequency of the response signal needs to be measured, so that the measurement process is simplified, and the adaptability of the detection model is improved; filtering out signals beyond the target frequency to obtain ideal second harmonic signals, as shown in fig. 3; fitting the relative nonlinear coefficient obtained by the experiment with the corresponding axial stress, wherein the relative nonlinear coefficient and the corresponding axial stress are approximately in a linear relation. The ultrasonic nonlinear response is sensitive to stress, the axial stress of the bolt can be effectively represented by a relative nonlinear coefficient, and the rapid and accurate detection of the axial stress of the bolt can be realized by using a nonlinear ultrasonic detection method; the method is scientific, good in practicability and wide in popularization and application value.

Description of the drawings

FIG. 1 is a flow chart of the method of the present invention;

figure 2 is a schematic view of an ultrasonic transducer coupled to a bolt,

the numbers in the figure illustrate the following: 1 represents a transmitting transducer, 2 represents a bolt sample to be tested, 3 represents a nut, and 4 represents a receiving transducer;

fig. 3 is a frequency domain waveform before and after filtering.

Detailed description of the preferred embodiments

The invention provides a nonlinear ultrasonic detection method for axial stress of a bolt, and aims to accurately and quickly measure the axial stress of the bolt. The existing ultrasonic measurement method is mainly based on the principle of acoustic elasticity, the stress is judged according to the change of the sound velocity, however, when the stress changes 100MPa, the sound velocity only changes by 0.01%, and therefore, the stress borne by the material is not accurate enough to be reflected through the change of the wave velocity. Based on the shortcomings of the existing methods, the axial stress of the bolt is detected from the perspective of nonlinear response. The invention is further described with reference to the following description and embodiments in conjunction with the accompanying drawings.

The embodiment of the invention takes a bolt which is made of 45 steel, has the performance grade of 8.8, has the nominal diameter of M20 and has the length of 120mm as an example, and explains the method of the invention.

In order to achieve the purpose, the technical scheme adopted by the method is 'a nonlinear ultrasonic detection method for axial stress of the bolt'.

The invention relates to a nonlinear ultrasonic detection method for axial stress of a bolt, which has a flow chart shown in figure 1 and comprises the following specific steps:

step A: establishing a relation model between the amplitude of the second harmonic and the amplitude of the fundamental wave based on the propagation theory of the ultrasonic wave in the isotropic medium to obtain an expression of a relative nonlinear coefficient;

and B: carrying out an axial stress loading experiment on a bolt sample, carrying out nonlinear ultrasonic detection, and calculating relative nonlinear coefficients under different stress states;

and C: and fitting the loaded axial stress and the corresponding relative nonlinear coefficient, determining the ultrasonic detection coefficient of the axial stress of the bolt, and finally obtaining a relational expression of the axial stress of the bolt and the relative nonlinear coefficient.

Through the steps, the nonlinear ultrasonic detection of the axial stress of the bolt can be realized, the method can be used for quickly and accurately detecting the axial stress of the bolt, and the accuracy and the practicability of the bolt axial stress detection technology are improved.

The step a of establishing a relationship model between the second harmonic amplitude and the fundamental amplitude based on the propagation theory of the ultrasonic wave in the isotropic medium to obtain an expression of the relative nonlinear coefficient includes:

according to the propagation rule of ultrasonic waves in an isotropic medium, one-dimensional wave equation is as follows:

in formula (12):

ρ is the density of the material;

u-displacement in the x direction;

t is the propagation time;

stress in the σ -x direction;

x is the propagation distance of the ultrasonic wave.

The stress versus strain in the x-direction is:

σ＝E·f() (13)

in formula (13):

e-modulus of elasticity of the material;

f () -strain function.

The positive strain in the x-direction is defined as:

substituting formulae (13) and (14) for formula (12):

wherein

Formula (16) is substituted for formula (15) to obtain:

in formula (17):

c-ultrasonic wave velocity;

β -second order nonlinear coefficients;

-third order non-linear coefficients.

The equation has no general analytic solution, and is generally solved by adopting a perturbation approximation theory, namely solving by performing power series expansion on solved parameters to obtain:

in formula (18):

A₁-the fundamental amplitude;

k is the wave number;

omega-angular frequency.

Let the coefficient of the second term in equation (18) be the second harmonic amplitude A₂The coefficient of the third term is the third harmonic amplitude A₃By analogy, the nonlinear coefficient can be expressed as:

when the excitation frequency is fixed, the wave number of the ultrasonic wave is determined, and under the condition that the propagation distance is not changed, a relative nonlinear coefficient (namely β') is obtained to represent the property change condition in the material, wherein the second-order relative nonlinear coefficient is

From equation (21), the second-order relative nonlinear coefficient β' and the square A of the fundamental amplitude₁ ²Inversely proportional to the second harmonic amplitude A₂Is in direct proportion. Therefore, when the nonlinear ultrasonic method is used for detecting the axial stress of the bolt, only the fundamental wave amplitude and the second harmonic amplitude need to be measured.

And B, performing an axial stress loading experiment on the bolt sample and performing nonlinear ultrasonic detection to calculate relative nonlinear coefficients under different stress states, wherein the method comprises the following steps: firstly, preparing a bolt sample to be tested, wherein the material is 45 steel, the performance grade is 8.8 grade, the nominal diameter is M20, the length is 120mm, carrying out axial stress loading on the bolt with different values, and the applied axial stress is respectively named as F₁,F₂,…,F_nThen respectively carrying out nonlinear ultrasonic detection on the bolts in different loaded states to obtain nonlinear response signals, and calculating corresponding relative nonlinear coefficients which are respectively named as β'₁,β′₂,…,β′_n. The specific steps of the process are as follows:

step B1: fixing a bolt to be tested on a special clamp of an electronic tensile testing machine, performing an axial stress loading experiment on the bolt within the elastic limit of the bolt by using the electronic tensile testing machine, setting the interval of loading stress values to be 50MPa, and firstly loading the bolt to a target stress value of 50 MPa;

step B2: as shown in fig. 2, by using a "transmit-receive" detection method, ultrasonic transducers are respectively fixed at the centers of two end faces of a bolt to be detected, ultrasonic waves enter a bolt sample 2 to be detected through a transmitting transducer 1, and a receiving transducer 3 receives signals at the other end of the bolt, wherein the center frequency of the receiving transducer is 2 times of the center frequency of the transmitting transducer so as to receive second harmonic signals, in this embodiment, the center frequency of the transmitting transducer is 2.5MHz, and the center frequency of the receiving transducer is 5 MHz; the transmitting transducer 1 and the end face of the bolt, the receiving transducer 4 and the other end face of the bolt are stably coupled by using a coupling agent, the attenuation of ultrasonic waves in the transmission process is reduced to the maximum extent, stable second harmonic signals can be received, then a voltage signal is applied to the transmitting transducer by using a nonlinear ultrasonic tester, the transmitting transducer receives the voltage signal and converts the voltage signal into an ultrasonic signal, the ultrasonic signal is transmitted in the bolt to be tested, and the receiving transducer receives the ultrasonic signal and transmits the ultrasonic signal to the nonlinear ultrasonic tester;

step B3: due to the influence of an experimental system and an experimental environment, the received ultrasonic signal contains signals beyond a target frequency, in order to obtain an ideal frequency domain waveform, a Matlab tool is used for filtering derived original sampling data, the influence of a high-frequency signal is eliminated, a filtered frequency domain signal diagram is obtained, and as shown in fig. 3, the fundamental wave amplitude and the second harmonic amplitude of the received signal under the stress condition are read;

step B4: calculating the relative nonlinear coefficient under the stress condition according to a formula (21) by the fundamental wave amplitude and the second harmonic amplitude obtained in the last step;

and (4) repeating the steps B1-B4, increasing the axial stress loaded in each tensile experiment by 50MPa compared with the axial stress loaded in the previous tensile experiment, and performing ten experiments to obtain a group of relative nonlinear coefficients.

In step B2, the oscilloscope and the computer are both connected to the nonlinear ultrasonic tester, the oscilloscope is used to display the received time domain waveform, and the computer is used to store the original sampling data.

And C, fitting the loaded axial stress and the corresponding relative nonlinear coefficient, determining the ultrasonic detection coefficient of the axial stress of the bolt, and finally obtaining a relation between the axial stress of the bolt and the relative nonlinear coefficient, wherein the method comprises the following steps: the axial stress F of the bolt in the step B is measured₁，F₂，…，F₁₀And calculating the resulting relative non-linearity coefficient of β'₁，β′₂，…，β′₁₀One-to-one correspondence, with β'₁，β′₂，…，β′₁₀As independent variable, with F₁，F₂，…，F₁₀And performing linear fitting to obtain a relation curve of the relative nonlinear coefficient β' and the bolt axial stress F as dependent variables, wherein the process comprises the following specific steps:

step C1: in the step B, ten groups of corresponding data of relative nonlinear coefficients and axial stress are obtained through calculation, and a Matlab tool is used for measuring the axial stress F applied in the experiment₁，F₂，…，F₁₀And corresponding relative non-linearity coefficient β'₁，β′₂，…，β′₁₀Performing linear fitting, wherein β' is used as an independent variable and F is used as a dependent variable, and obtaining the ultrasonic detection coefficients (namely a, b) of the bolt sample;

and C2, substituting the ultrasonic detection coefficient into a linear equation to obtain a relation between the bolt axial stress F and the relative nonlinear coefficient β':

F＝aβ′+b (22)

wherein, the ultrasonic detection coefficients a and b of the bolt sample are known, and the evaluation of the axial stress of the bolt can be realized according to the relative nonlinear coefficient β' obtained in the nonlinear ultrasonic detection.