A method, system, device and medium for online detection of the anti-loosening performance of a toothed strip and nut

Abstract

The application discloses a kind of tooth bar and nut anti-loose performance online detection method, system, equipment and medium, belong to anti-loose performance detection technical field, comprising the following steps: emitting two groups of ultrasonic pulses with different central frequencies to test piece, time alignment is carried out to the modulation wave and tooth bar axial load time course, and load alignment modulation signal is obtained;The load alignment modulation signal is implemented time window by time window load decoupling processing, and decoupling modulation spectrum is formed;Recursive analysis is carried out to the decoupling modulation spectrum, and recursive degree sequence is extracted;The distribution offset trend of the recursive degree sequence in the load space formed by tooth bar axial load time course generates anti-loose performance degradation signal.The application emits two groups of ultrasonic pulses with different central frequencies to test piece, constructs thread contact state proxy quantity using the time-of-flight ratio of two groups of reflected waves, and carries out time bending transformation to modulation wave according to this, and the influence of uneven rhythm of load sampling on analysis is eliminated.

Description

Technical Field

[0001] This invention relates to the field of anti-loosening performance testing technology, specifically to an online testing method, system, equipment, and medium for the anti-loosening performance of threaded rods and nuts. Background Technology

[0002] The degradation of the anti-loosening performance of threaded fasteners is a common safety hazard in engineering structures. Existing ultrasonic testing methods typically emit a single set of ultrasonic pulses to the threaded fasteners and assess the thread contact condition by receiving changes in the amplitude or time of flight of the reflected waves from the thread interface.

[0003] Under actual service conditions, the axial load on the threaded rack is constantly and dynamically changing, and the contact state of the thread interface changes in real time with the load. This results in the reflected wave signal containing both reversible changes caused by the elastic response of the load and irreversible changes caused by the degradation of the anti-loosening performance. Existing methods cannot distinguish between these two types of components, leading to interference signals generated by the elastic hysteresis effect overshadowing the anti-loosening degradation signal under conditions of large load fluctuations.

[0004] For example, under high-frequency alternating loads, the thread interface exhibits different contact states along the load increasing and decreasing paths. In the variation of reflected wave amplitude obtained from a single ultrasonic test, the contribution from elastic hysteresis can be several times the total signal variation, causing the test results to misjudge normal contact hysteresis caused by the load as a degradation of anti-loosening performance, which seriously reduces the accuracy and reliability of the test. Summary of the Invention

[0005] In view of the above-mentioned problems, the present invention is proposed.

[0006] Therefore, the technical problem solved by the present invention is that the existing methods cannot distinguish between the reversible change components caused by the elastic response of the load and the irreversible change components caused by the degradation of the anti-loosening performance, which results in the interference signal generated by the elastic hysteresis effect overwhelming the anti-loosening degradation signal under working conditions with large load fluctuations.

[0007] To solve the above-mentioned technical problems, the present invention provides the following technical solution: an online detection method for the anti-loosening performance of a threaded rod and nut, comprising the following steps: transmitting two sets of ultrasonic pulses with different center frequencies to the test piece, receiving the modulated wave reflected from the thread interface, aligning the modulated wave with the time history of the threaded rod axial load to obtain a load-aligned modulation signal; using the time history of the threaded rod axial load as a guiding condition, performing time-window-by-time load decoupling processing on the load-aligned modulation signal to form a decoupling modulation spectrum; performing recursive analysis on the decoupling modulation spectrum to extract a recursion degree sequence; and generating an anti-loosening performance degradation signal based on the distribution offset trend of the recursion degree sequence in the load space formed by the time history of the threaded rod axial load.

[0008] As a preferred embodiment of the online detection method for the anti-loosening performance of the threaded rod and nut described in this invention, the step of performing the time alignment includes: at each sampling moment of the axial load time history of the threaded rod, calculating the time-of-flight ratio of the reflected waves of the two sets of ultrasonic pulses at the thread interface, using the time-of-flight ratio of the reflected waves as the thread contact state surrogate quantity to form the thread contact state surrogate quantity time history; using the thread contact state surrogate quantity time history as a monotonic variable to perform monotonic mapping construction to generate monotonic mapping information; performing time bending transformation on the modulation wave according to the monotonic mapping information, mapping the modulation wave to the thread contact state surrogate quantity domain, and obtaining the load-aligned modulation signal.

[0009] As a preferred embodiment of the online detection method for the anti-loosening performance of the threaded rod and nut described in this invention, the step of constructing the monotonic mapping includes: dividing the axial load time history of the threaded rod into a load increasing segment and a load decreasing segment; extracting the piecewise cumulative integral of the thread contact state proxy amount time history in the load increasing segment and the load decreasing segment respectively to form an increasing integral curve and a decreasing integral curve; calculating the integral difference between the increasing integral curve and the decreasing integral curve at the same thread contact state proxy amount, and using the integral difference as the contact hysteresis compensation amount; and correcting the mapping parameters of the time bending transformation corresponding to the load decreasing segment through the contact hysteresis compensation amount to form a hysteresis-corrected monotonic mapping.

[0010] Replace the monotonic mapping information with the hysteresis-corrected monotonic mapping.

[0011] As a preferred embodiment of the online detection method for the anti-loosening performance of threaded rods and nuts according to the present invention, the step of performing the load decoupling processing by time window includes: performing a sliding short-time Fourier transform on the load-aligned modulation signal to generate a load-aligned short-time spectrum sequence, the load-aligned short-time spectrum sequence including multiple short-time spectra corresponding to different time windows; resampling the load-aligned modulation signal on the load increasing segment and the load decreasing segment respectively using the hysteresis-corrected monotonic mapping to form an increasing modulation signal sequence and a decreasing modulation signal sequence; performing a sliding short-time Fourier transform on the increasing modulation signal sequence and the decreasing modulation signal sequence respectively to generate an increasing modulation spectrum sequence and a decreasing modulation spectrum sequence; calculating the spectral difference between the increasing modulation spectrum sequence and the decreasing modulation spectrum sequence at the same thread contact state surrogate quantity, and using the spectral difference as the elastic hysteresis residual spectrum; subtracting the elastic hysteresis residual spectrum from the short-time spectrum of the corresponding time window in the load-aligned short-time spectrum sequence to separate the nonlinear modulation components in each time window, forming a decoupled modulation spectrum.

[0012] As a preferred embodiment of the online detection method for the anti-loosening performance of threaded rods and nuts according to the present invention, the step of calculating the elastic hysteresis residual spectrum includes: sorting the increasing modulation spectrum sequence and the decreasing modulation spectrum sequence according to the thread contact state proxy quantity to form an increasing ordered spectrum matrix and a decreasing ordered spectrum matrix; performing first-order difference on the increasing ordered spectrum matrix and the decreasing ordered spectrum matrix respectively to extract the increasing modulation spectrum increment and the decreasing modulation spectrum increment; and using the difference between the mean values ​​of the increasing modulation spectrum increment and the decreasing modulation spectrum increment at each thread contact state proxy quantity as the elastic hysteresis residual spectrum.

[0013] As a preferred embodiment of the online detection method for the anti-loosening performance of the threaded rod and nut according to the present invention, the recursive analysis step includes: constructing a two-dimensional load phase plane using the load value and load change rate of the axial load time history of the threaded rod at each detection time as coordinates; dividing the two-dimensional load phase plane into load phase grids according to the equally spaced quantiles of the load value and load change rate; using the spectral amplitude vector of the decoupled modulation spectrum in each time window as the state vector, assigning each state vector to the load phase grid according to the coordinate value of the axial load time history of the threaded rod at the corresponding time; calculating the pairwise Euclidean distance mean of the state vector in each load phase grid, using the reciprocal of the pairwise Euclidean distance mean as the grid recursion density, and arranging all the grid recursion densities into a recursion degree sequence according to the position order of the load phase grids.

[0014] In a preferred embodiment of the online detection method for the anti-loosening performance of the threaded rod and nut described in this invention, the step of calculating the cell recursive density includes: extracting the state vector corresponding to the load increasing segment and the state vector corresponding to the load decreasing segment within each load phase cell; calculating the Euclidean distance mean for the state vector corresponding to the load increasing segment to form an increasing cell distance mean, and calculating the Euclidean distance mean for the state vector corresponding to the load decreasing segment to form a decreasing cell distance mean; using the ratio of the increasing cell distance mean to the decreasing cell distance mean as a hysteresis resolution factor; multiplying the hysteresis resolution factor by the cell recursive density to form the final cell recursive density, and replacing the cell recursive density with the final cell recursive density.

[0015] This invention provides an online testing system for the anti-loosening performance of threaded rods and nuts.

[0016] To solve the above-mentioned technical problems, the present invention provides the following technical solution: an online testing system for the anti-loosening performance of threaded rods and nuts, comprising: an ultrasonic transmitting and receiving module configured to transmit two sets of ultrasonic pulses with different center frequencies to the test piece, and to receive the modulated wave reflected from the thread interface;

[0017] The load synchronization acquisition module is configured to synchronously acquire the time history of the axial load on the toothed rack;

[0018] The time alignment processing module is configured to time-align the modulation wave with the time history of the axial load of the toothed rack to obtain a load-aligned modulation signal.

[0019] The load decoupling processing module is configured to perform time-window-by-time load decoupling processing on the load alignment modulation signal, guided by the axial load time history of the toothed rack, to form a decoupling modulation spectrum;

[0020] The recursive analysis module is configured to perform recursive analysis on the decoupled modulation spectrum and extract the recursion degree sequence.

[0021] The anti-loosening degradation assessment module is configured to generate an anti-loosening performance degradation signal based on the distribution offset trend of the recursion sequence in the load space formed by the axial load time history of the toothed rack.

[0022] The present invention provides a computer device, including a memory and a processor, wherein the memory stores a computer program, characterized in that the processor executes the computer program to implement the steps of the online detection method for the anti-loosening performance of a toothed rod and nut.

[0023] The present invention provides a computer-readable storage medium having a computer program stored thereon, characterized in that, when the computer program is executed by a processor, it implements the steps of the online detection method for the anti-loosening performance of a toothed rack and nut.

[0024] The beneficial effects of this invention are as follows: By transmitting two sets of ultrasonic pulses with different center frequencies to the test piece, the time-of-flight ratio of the two sets of reflected waves is used to construct the thread contact state proxy quantity, and the time bending transformation is applied to the modulated wave accordingly, so as to achieve precise time alignment between the modulated wave and the time history of the axial load of the toothed rack, and eliminate the influence of uneven load sampling rhythm on subsequent analysis.

[0025] The axial load time history of the threaded rod is divided into a load increasing segment and a load decreasing segment. The contact hysteresis compensation is formed by calculating the piecewise cumulative integral difference of the time history of the surrogate quantity of the two thread contact states. Then, a hysteresis correction monotonic mapping is constructed, which enables the load decoupling processing to establish modulation spectrum sequences for the two paths of load increasing and decreasing. The elastic hysteresis residual spectrum is extracted by calculating the spectral difference between the two. The modulation component caused by the nonlinear contact behavior change of the thread interface is separated from the load-aligned modulation signal, forming a decoupling modulation spectrum, which eliminates the interference of the elastic hysteresis effect on the detection results.

[0026] Recursive analysis is performed on the decoupled modulation spectrum. A two-dimensional load phase plane is constructed using the load value and the load change rate. By calculating the mean of the pairwise Euclidean distance of the state vectors in each load phase cell and taking its reciprocal as the cell recursion density, a recursion degree sequence is formed. This allows the weak evolution of the nonlinear modulation behavior of the thread interface caused by the degradation of anti-loosening performance to be quantitatively characterized in the load space in the form of a distribution offset trend, thereby generating an anti-loosening performance degradation signal. Attached Figure Description

[0027] To more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0028] Figure 1 This is a flowchart illustrating an online testing method for the anti-loosening performance of a threaded rod and nut, as provided in one embodiment of the present invention. Detailed Implementation

[0029] To make the above-mentioned objects, features, and advantages of the present invention more apparent and understandable, specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of them. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort should fall within the protection scope of the present invention.

[0030] Example 1, referring to Figure 1 This is one embodiment of the present invention, which provides an online testing method for the anti-loosening performance of threaded rods and nuts, comprising the following steps:

[0031] Two sets of ultrasonic pulses with different center frequencies are emitted to the test piece, and the modulated wave reflected from the thread interface is received. The modulated wave is time-aligned with the time history of the axial load of the toothed rack to obtain a load-aligned modulation signal.

[0032] Using the axial load time history of the toothed rack as a guiding condition, the load alignment modulation signal is subjected to time-window-by-time load decoupling processing to form a decoupling modulation spectrum;

[0033] Recursive analysis is performed on the decoupled modulation spectrum to extract the recursion degree sequence;

[0034] The anti-loosening performance degradation signal is generated by the distribution offset trend of the recursion sequence in the load space formed by the axial load time history of the toothed bar.

[0035] Under actual service conditions, the axial load on the threaded rack is constantly and dynamically changing, and the contact state of the thread interface changes in real time with the load. This results in the reflected wave signal containing both reversible changes caused by the elastic response of the load and irreversible changes caused by the degradation of the anti-loosening performance. Existing methods cannot distinguish between these two types of components, leading to interference signals generated by the elastic hysteresis effect overshadowing the anti-loosening degradation signal under conditions of large load fluctuations.

[0036] The axial load time history of the threaded rod is divided into a load increasing segment and a load decreasing segment. The contact hysteresis compensation is formed by calculating the piecewise cumulative integral difference of the time history of the surrogate quantity of the two thread contact states. Then, a hysteresis correction monotonic mapping is constructed, which enables the load decoupling processing to establish modulation spectrum sequences for the two paths of load increasing and decreasing. The elastic hysteresis residual spectrum is extracted by calculating the spectral difference between the two. The modulation component caused by the nonlinear contact behavior change of the thread interface is separated from the load-aligned modulation signal, forming a decoupling modulation spectrum, which eliminates the interference of the elastic hysteresis effect on the detection results.

[0037] Recursive analysis is performed on the decoupled modulation spectrum. A two-dimensional load phase plane is constructed using the load value and the load change rate. By calculating the mean of the pairwise Euclidean distance of the state vectors in each load phase cell and taking its reciprocal as the cell recursion density, a recursion degree sequence is formed. This allows the weak evolution of the nonlinear modulation behavior of the thread interface caused by the degradation of anti-loosening performance to be quantitatively characterized in the load space in the form of a distribution offset trend, thereby generating an anti-loosening performance degradation signal.

[0038] Example 2, an embodiment of the present invention, provides an online testing method for the anti-loosening performance of threaded rods and nuts based on the previous embodiment, including the following steps:

[0039] S1. Two sets of ultrasonic pulses with different center frequencies are emitted to the test piece, and the modulated wave reflected from the thread interface is received. The modulated wave is time-aligned with the axial load time history of the toothed bar to obtain a load-aligned modulation signal.

[0040] In this embodiment, a set of M16 threaded rods and nuts fastening pairs are used as test pieces. Two longitudinal wave straight probes with center frequencies of 2MHz and 5MHz are coupled to the end face of the threaded rods. The two probes are alternately excited by a pulse transmitter and receiver at an ultrasonic pulse repetition frequency of 1kHz to collect two reflected wave signals from the thread interface.

[0041] The time alignment steps include S1.1 to S1.3:

[0042] S1.1 At each sampling moment of the axial load time history of the toothed rack, calculate the ratio of the flight time of the reflected waves of the two sets of ultrasonic pulses at the thread interface, and use the ratio of the flight time of the reflected waves as the thread contact state proxy quantity to form the thread contact state proxy quantity time history.

[0043] When extracting the flight time, for the reflected wave signal within each ultrasonic pulse excitation cycle, the time interval between the start time of the transmitted pulse triggering time and the peak time of the reflected wave envelope is calculated to obtain the flight time of the reflected wave of the first group of ultrasonic pulses and the flight time of the reflected wave of the second group of ultrasonic pulses.

[0044] Because the center frequencies of the two sets of ultrasonic pulses are different, their transmission and reflection at the thread interface are sensitive to the contact area and contact pressure to different degrees. The time-of-flight ratio can reflect the true contact state of the thread interface.

[0045] In this embodiment, when the axial load increases from 0 to 80kN, the flight time of the reflected wave from the 2MHz probe decreases from 12.40μs to 11.85μs, and the flight time of the reflected wave from the 5MHz probe decreases from 12.38μs to 11.60μs. The flight time ratio increases monotonically from 1.0016 to 1.0216, showing a good monotonicity that increases monotonically with increasing load.

[0046] S1.2. Using the time history of the thread contact state proxy quantity as a monotonic variable, a monotonic mapping is constructed to generate monotonic mapping information.

[0047] Specifically, the steps for constructing the monotonic mapping include A1 to A4:

[0048] A1. Divide the axial load time history of the toothed rack into a load increasing segment and a load decreasing segment, and extract the piecewise cumulative integral of the time history of the thread contact state proxy quantity in the load increasing segment and the load decreasing segment respectively to form an increasing integral curve and a decreasing integral curve.

[0049] The time history of the axial load on the toothed rack is sampled point by point. When the difference between adjacent sampling points is ≥0, it will be classified into the load increasing segment; otherwise, it will be classified into the load decreasing segment.

[0050] For the time history of the thread contact state surrogate quantity within the load increasing segment, the thread contact state surrogate quantity is arranged in ascending order, and the cumulative integral is calculated with the thread contact state surrogate quantity as the integration variable to form an increasing integral curve.

[0051] In the above test, the load time history had 250 load increment sampling points and 250 load decrement sampling points. The cumulative integral was calculated after arranging the 250 surrogate values ​​in ascending order for the increment segment, resulting in the increment integral curve.

[0052] The cumulative integral is calculated after arranging the 250 agent values ​​of the decreasing segment in ascending order, resulting in the decreasing integral curve.

[0053] A2. Calculate the integral difference between the increasing integral curve and the decreasing integral curve at the same thread contact state, and use the integral difference as the contact hysteresis compensation amount.

[0054] In this step, several surrogate reference values ​​are taken at equal intervals within the range of the monotonic variable. At each reference value, the corresponding integral value is read from the increasing integral curve and the decreasing integral curve respectively by linear interpolation, and the integral difference is calculated. The integral difference is used as the contact hysteresis compensation amount at the surrogate reference value.

[0055] For example, 100 equally spaced proxy reference values ​​are taken, covering the time-of-flight ratio range [1.0016, 1.0216]. The contact hysteresis compensation sequence is calculated.

[0056] The maximum compensation occurs when the contact hysteresis compensation is 1.0108, and the integral difference is 0.0187.

[0057] A3. The mapping parameters of the time curvature transformation corresponding to the load reduction segment are corrected by the contact hysteresis compensation amount to form a hysteresis-corrected monotonic mapping.

[0058] The mapping parameters are: the proxy value corresponding to each sampling moment in the load reduction segment is used as the output coordinate of the time curvature transformation.

[0059] The correction method is as follows: at the corresponding surrogate value, the compensation amount is read from the contact hysteresis compensation amount sequence through linear interpolation, and this compensation amount is additively added to the corresponding surrogate value to obtain the corrected mapped output coordinates. Where α is the compensation coefficient. For agent volume value, This is the amount of compensation.

[0060] Keep the mapping parameters of the load increasing segment unchanged, and replace the mapping parameters of the load decreasing segment with the corrected parameters. The two segments are merged to form a hysteresis-corrected monotonic mapping.

[0061] For example, calculate the compensation coefficient α = 0.93. For 250 sampling times during the load reduction phase, sequentially read the corresponding compensation values ​​and apply corrections to obtain the corrected surrogate quantity sequence. Using the original surrogate quantity... For example, the corrected value is 1.0100 + 0.93 × 0.0187 = 1.0274, which is approximately 0.17% of the original proxy value.

[0062] A4. Replace the monotonic mapping information with the hysteresis correction monotonic mapping.

[0063] S1.3. Perform time bending transformation on the modulated wave according to the monotonic mapping information, and map the modulated wave to the thread contact state proxy domain to obtain the load-aligned modulation signal.

[0064] The modulated wave was originally sampled at uniform time intervals. The time curvature transformation replaces the time axis of the modulated wave with the threaded contact state surrogate axis, that is, for each original sampling moment, its corresponding corrected surrogate value is used as the new independent variable coordinate.

[0065] Since the signal is non-uniformly distributed on the original time axis, the transformed signal is a non-uniform sampling sequence on the surrogate quantity axis. Therefore, it is resampled to a uniform grid in the surrogate quantity domain by cubic spline interpolation, forming a load-aligned modulation signal that is uniformly sampled in the surrogate quantity domain.

[0066] Specifically, the original modulated wave signal was acquired at a sampling rate of 1 kHz, with a total of 1000 sampling points, while the load time history was acquired at a sampling rate of 500 Hz, with a total of 500 sampling points. The time axis rhythms of the two are inconsistent. After replacing the time coordinate of the original modulated wave signal with the corresponding corrected surrogate value using a hysteresis-corrected monotonic mapping, a uniform grid (101 grid points) was set at intervals of 0.0002 within the surrogate value range [1.0016, 1.0216]. The modulated wave was resampled to this uniform grid through cubic spline interpolation to obtain the load-aligned modulated signal, with a total of 101 sampling points.

[0067] S2. Using the axial load time history of the toothed rack as a guiding condition, the load alignment modulation signal is subjected to time-window-by-time load decoupling processing to form a decoupling modulation spectrum.

[0068] The steps for performing the time-window-by-time load decoupling process include S2.1 to S2.5:

[0069] S2.1 Perform a sliding short-time Fourier transform on the load-aligned modulation signal to generate a load-aligned short-time spectrum sequence, wherein the load-aligned short-time spectrum sequence includes multiple short-time spectra corresponding to different time windows.

[0070] In this step, a sliding short-time Fourier transform is performed on the load-aligned modulation signal. Specifically, the analysis window function type, window length, and sliding step size are set. Using the Hanning window as the window function, signal segments of length equal to the window length are sequentially truncated along the surrogate axis from the beginning of the load-aligned modulation signal. After applying the window function to each segment, a fast Fourier transform is performed to obtain the short-time spectrum corresponding to that time window.

[0071] The short-time spectra of all time windows are arranged sequentially to form a load-aligned short-time spectrum sequence. The center position of the proxy quantity corresponding to each short-time spectrum is recorded as the center value of the proxy quantity interval covered by that time window.

[0072] In this embodiment, the Hanning window length is set to 16 sampling points, the sliding step size is 1 sampling point, and a total of 86 time windows are generated. The short-time spectrum frequency resolution corresponding to each time window is 1 / (16×0.0002)=312.5rad. −1 The number of spectral points is 8 (taking the positive frequency half spectrum).

[0073] The 86 short-time spectra are arranged as a load-aligned short-time spectrum sequence, and the corresponding agent quantity center position sequence covers the range of [1.0023, 1.0209], which is uniformly distributed with an interval of 0.0002.

[0074] S2.2. The load-aligned modulation signal is resampled in the load increasing segment and the load decreasing segment respectively using the hysteresis-corrected monotonic mapping to form an increasing modulation signal sequence and a decreasing modulation signal sequence.

[0075] Using the hysteresis-corrected monotonic mapping determined in step A4, the load-aligned modulation signal is extracted separately for the load increasing segment and the load decreasing segment. Specifically, the correction surrogate values ​​corresponding to each sampling time of the load increasing segment and the load decreasing segment are read from the hysteresis-corrected monotonic mapping. Using these surrogate values ​​as interpolation nodes, the corresponding signal amplitudes are extracted from the load-aligned modulation signal through cubic spline interpolation, forming the increasing modulation signal sequence and the decreasing modulation signal sequence.

[0076] Specifically, the surrogate values ​​corresponding to 250 sampling times of the load increment segment and the corrected surrogate values ​​corresponding to 250 sampling times of the load decrement segment are read from the hysteresis correction monotonic mapping. The corresponding amplitude is extracted from the load-aligned modulation signal using each surrogate value as an interpolation node. The signal is then resampled to 101 uniform grid points in the range [1.0016, 1.0216] at intervals of 0.0002, resulting in the increment modulation signal sequence and the decrement modulation signal sequence, each with 101 sampling points.

[0077] S2.3 Perform sliding short-time Fourier transform on the incremental modulation signal sequence and the decrementing modulation signal sequence respectively to generate an incremental modulation spectrum sequence and a decrementing modulation spectrum sequence.

[0078] Perform sliding short-time Fourier transforms with the exact same parameters as in step S2.1 on the incrementing modulation signal sequence and the decrementing modulation signal sequence.

[0079] Since the sampling parameters of the incremental modulation signal sequence and the decremental modulation signal sequence are consistent with those of the load-aligned modulation signal, the short-time spectrum sequences generated by the three have the same number of time windows, the same frequency coordinates, and the same surrogate quantity center position sequence.

[0080] In this embodiment, Hanning window sliding short-time Fourier transform is applied to the incremental modulation signal sequence and the decrementing modulation signal sequence respectively, generating 86 short-time spectra for each, forming the incremental modulation spectrum sequence and the decrementing modulation spectrum sequence respectively.

[0081] Taking the 43rd time window as an example, the main frequency amplitude of the increasing modulation spectrum sequence is 0.342, and the main frequency amplitude of the decreasing modulation spectrum sequence is 0.318. There is an observable difference between the two, which initially reflects the contribution of the elastic hysteresis effect at this surrogate quantity.

[0082] S2.4 Calculate the spectral difference between the incremental modulation spectrum sequence and the decremental modulation spectrum sequence at the same thread contact state agent quantity, and use the spectral difference as the elastic hysteresis residual spectrum.

[0083] Specifically, the steps for calculating the elastic hysteresis residual spectrum include B1 to B3:

[0084] B1. Sort the increasing modulation spectrum sequence and the decreasing modulation spectrum sequence according to the thread contact state proxy quantity to form an increasing ordered spectrum matrix and a decreasing ordered spectrum matrix, respectively.

[0085] In this step, the incremental modulation spectrum sequence is sorted from smallest to largest according to the center position of the proxy quantity corresponding to each time window, and the sorted short-time spectra are stacked sequentially to form an incrementally ordered spectrum matrix.

[0086] The decreasing modulation spectrum sequences are sorted in the same way according to the surrogate center position from smallest to largest and then stacked to form a decreasing ordered spectrum matrix.

[0087] After sorting, a monotonic correspondence is established between the row indices and surrogate values ​​of the two matrices.

[0088] B2. Perform first-order difference on the increasing ordered spectrum matrix and the decreasing ordered spectrum matrix respectively to extract the increasing modulation spectrum increment and the decreasing modulation spectrum increment.

[0089] A first-order difference is applied to the increasing ordered spectrum matrix along the row direction (i.e. the direction of increasing surrogate quantity), and the difference of the spectrum vector at adjacent surrogate quantities is calculated to obtain the increasing modulation spectrum increment matrix.

[0090] The decreasing ordered spectrum matrix is ​​subjected to first-order difference along the row direction in the same manner to obtain the decreasing modulation spectrum increment matrix.

[0091] By extracting the local variation of the modulation spectrum with the proxy quantity, the difference in the evolution trend of the modulation spectrum between the two loading paths is amplified, making the elastic hysteresis effect more obvious at the modulation spectrum increment level.

[0092] For example, by performing first-order differences along the row directions on the increasing ordered spectrum matrix and the decreasing ordered spectrum matrix (each an 86×8 matrix), we can obtain the increasing modulation spectrum increment matrix and the decreasing modulation spectrum increment matrix (each an 85×8 matrix).

[0093] Taking row 43 (corresponding to the surrogate interval [1.0100, 1.0102]) as an example, the increment of the main frequency component of the increasing modulation spectrum increment matrix is ​​+0.0031, and the increment of the main frequency component of the decreasing modulation spectrum increment matrix is ​​-0.0028. The two have opposite signs and similar magnitudes, indicating that the modulation spectrum evolution directions of the increasing and decreasing paths are opposite within this surrogate interval.

[0094] B3. The difference between the mean values ​​of the incremental modulation spectrum increment and the incremental modulation spectrum increment at each thread contact state proxy quantity is taken as the elastic hysteresis residual spectrum.

[0095] At each surrogate reference position, the mean values ​​of each frequency point in the k-th row of the incremental modulation spectrum increment matrix and the k-th row of the decremental modulation spectrum increment matrix are calculated to obtain the mean vector of the incremental modulation spectrum increment and the mean vector of the decremental modulation spectrum increment. The difference between the two is then calculated, and the difference is used as the elastic hysteresis residual spectrum at that surrogate.

[0096] The elastic hysteresis residual spectrum sequence is formed by sequentially calculating the reference positions of all K−1 surrogate quantities.

[0097] Taking line 43 as an example, the mean vector of the increasing modulation spectrum increment is +0.0031, and the mean vector of the decreasing modulation spectrum increment is −0.0028. By calculating the difference between the two, i.e. 0.0031−(−0.0028)=0.0059, it is shown that the modulation spectrum increment deviation contributed by the elastic hysteresis effect at the surrogate value of 1.0100 is 0.0059, which accounts for about 1.7% of the main frequency amplitude (0.342) in this time window.

[0098] S2.5. Subtract the elastic hysteresis residual spectrum from the short-time spectrum of the corresponding time window in the load-aligned short-time spectrum sequence to separate the nonlinear modulation components within each time window, forming a decoupled modulation spectrum.

[0099] In this step, for the short-time spectrum of each time window in the load-aligned short-time spectrum sequence, at the corresponding surrogate center position, the corresponding elastic hysteresis residual spectrum is read from the elastic hysteresis residual spectrum sequence by linear interpolation, and the nonlinear modulation component is calculated. . For short-time spectrum, It is the elastic hysteresis residual spectrum. This serves as the nonlinear modulation component within the k-th time window. The above subtraction operation is performed sequentially across all K time windows, arranging all short-time spectra to form a decoupled modulation spectrum.

[0100] The contribution of elastic hysteresis effect has been removed from the decoupled modulation spectrum. The spectral amplitude within each time window only reflects the change in nonlinear contact behavior of the thread interface, which is used for recursive analysis to extract the anti-loosening performance degradation signal.

[0101] In this embodiment, taking the 43rd time window as an example, , After decoupling The elastic hysteresis interference component has been removed.

[0102] Comparing the main frequency amplitude sequences of 86 time windows before and after decoupling, it was found that the systematic deviation of the amplitude sequence between the load increasing and decreasing segments after decoupling decreased from the mean difference of 0.024 before decoupling to 0.003, indicating that the elastic hysteresis effect has been separated and the decoupling modulation spectrum can accurately reflect the nonlinear modulation behavior of the thread interface.

[0103] S3. Perform recursive analysis on the decoupled modulation spectrum and extract the recursion degree sequence.

[0104] Specifically, the steps for performing the recursive analysis include S3.1 to S3.4:

[0105] S3.1. Using the load value and load change rate at each detection time of the axial load time history of the toothed rack as coordinates, construct a two-dimensional load phase plane.

[0106] Specifically, the load change rate is obtained by performing a central difference calculation on the time history of the axial load on the rack, i.e. . The load sampling interval, It is the rate of change of load. and They are time t i+1 and t i-1 The load values ​​are calculated. Forward and backward differential processing are applied to the sampling points at both ends. The horizontal axis of the two-dimensional load phase plane represents the load value, and the vertical axis represents the load change rate.

[0107] For example, for a total of 500 sampling points with a sampling interval of 0.002s, the load change rate at each time point is calculated sequentially.

[0108] During the load increase phase, the load change rate is approximately +800 kN / s; during the load decrease phase, the load change rate is approximately -800 kN / s; and near the load reversal point, the load change rate is close to 0.

[0109] 500 phase points A closed elliptical trajectory is formed on the two-dimensional load phase plane, and the trajectory of the load increment segment is located at... The upper half-plane, the trajectory of the load decreasing segment is located in The two planes intersect at the two endpoints (0,0) and (80,0).

[0110] S3.2 Divide the two-dimensional load phase plane into load phase grids according to the equally spaced quantiles of the load value and the load change rate.

[0111] Calculate equally spaced quantiles for the load value sequence and load change rate sequence at all sampling times, according to the preset number of cells. and Divide the two coordinate axes into equally probable intervals to form A rectangular load phase grid.

[0112] Each cell, in its position The row and column indices (m, n) in the grid are used as identifiers, and the cell boundaries are determined by the corresponding quantile thresholds. After the grid is divided, the boundary coordinates of each cell are recorded.

[0113] In this embodiment, the following is set , A total of 5 × 4 = 20 load phase grid cells were divided. The quantiles of the load value sequence were calculated into 5 equal parts, and the load value boundary points were obtained as {0, 16, 32, 48, 64, 80} kN; the quantiles of the load change rate sequence were calculated into 4 equal parts, and the load change rate boundary points were obtained as {−800, −267, +267, +800} kN / s.

[0114] Since the equidistant quantile division ensures equal probability, the number of phase points in each cell is approximately 500 / (5×4)=25.

[0115] S3.3. Using the spectral amplitude vector of the decoupled modulation spectrum in each time window as the state vector, each state vector is assigned to the load phase grid according to the coordinate value of the rack axial load time history at the corresponding time.

[0116] The spectral amplitude vector of each time window k in the decoupled modulation spectrum is used as the state vector. For each state vector, according to the correspondence between the surrogate window and the original time recorded by the hysteresis correction monotonic mapping in step S1, the original sampling time corresponding to the center surrogate of the time window is determined, the load phase coordinates at that time are read, and it is determined which load phase cell (m,n) divided in step S3.2 falls into the coordinates. The state vector is then assigned to that cell.

[0117] The above allocation operation is performed sequentially for all K time windows, forming a set of state vectors within each load phase cell.

[0118] Specifically, the decoupled modulation spectrum contains 86 time windows, each with an 8-dimensional state vector. The corresponding original time is searched sequentially for each of the 86 time windows, and the load phase coordinates are read and assigned to 20 cells.

[0119] Taking the 43rd time window as an example, the coordinate falls into cell (3,3), and the state vector is [0.3241,0.1823,0.0941,0.0512,0.0324,0.0218,0.0153,0.0097]. T It was assigned to cell (3,3).

[0120] S3.4 Calculate the mean of pairwise Euclidean distances for the state vectors within each load phase cell, and use the reciprocal of the mean of pairwise Euclidean distances as the cell recursion density. Arrange all cell recursion densities into a recursion degree sequence according to the positional order of the load phase cells.

[0121] For each load phase cell, calculate the Euclidean distance between all pairs of state vectors in the set. Take the mean of all pairwise Euclidean distances as the mean of the pairwise Euclidean distances of the cell, and use the reciprocal of the mean of the pairwise Euclidean distances as the cell recursion density.

[0122] The mean of pairwise Euclidean distance is calculated as follows: Let there be P state vectors within a lattice cell, then... ;

[0123] It is the mean of pairwise Euclidean distances. and These are the i-th and j-th state vectors, respectively. It is the Euclidean norm.

[0124] When the state vectors within a lattice cell are highly clustered, the mean of the pairwise Euclidean distance is small, and the lattice recursion density is large; conversely, it indicates that the nonlinear modulation behavior has undergone an irreversible change.

[0125] After the cell recursion density is calculated, hysteresis correction is performed through steps C1 to C4. Finally, the final recursion densities of all cells are arranged in order of cell position to form a recursion degree sequence.

[0126] The steps for calculating the recursive density of the lattice cells include C1 to C4:

[0127] C1. Within each load phase cell, extract the state vector corresponding to the load increasing segment and the state vector corresponding to the load decreasing segment.

[0128] In this step, for the set of state vectors within each load phase cell (m,n), the state vectors within the set are divided into two subsets based on the sign of the load change rate at the original sampling time corresponding to each state vector. These are the state vector subsets corresponding to the load increasing segment and the state vector subsets corresponding to the load decreasing segment.

[0129] Record the number of state vectors contained in each of the two subsets. and When the number of state vectors in any subset is less than 2, the cell is marked as a hysteresis-discriminable cell. The hysteresis resolution factor is set to 1 by default, and no hysteresis correction is performed on the cell recursive density.

[0130] For example, the load change rate range of cell (3,3) is [+267,+800] kN / s. The load change rates at the times corresponding to the four state vectors falling into this cell are all positive. Therefore, the subset of state vectors corresponding to the load increase segment... Includes all four state vectors, and the subset of state vectors corresponding to the load reduction segment. If the set is empty, the cell is marked as a hysteresis-resolved unusable cell, and the hysteresis resolution factor is 1.

[0131] The load change rate of lattice cell (3,2) spans positive and negative [−267,+267] kN / s, falling within the 5 state vectors of that lattice cell. It contains 3 (corresponding to the load increment segment). It contains two subsets (corresponding to the load decrease segment), both of which meet the minimum sample requirements and can be used to calculate the hysteresis resolution factor.

[0132] C2. Calculate the mean of pairwise Euclidean distances for the state vectors corresponding to the load increasing segment to form the mean of increasing lattice distances, and calculate the mean of pairwise Euclidean distances for the state vectors corresponding to the load decreasing segment to form the mean of decreasing lattice distances.

[0133] For each load phase cell (m,n) capable of hysteresis resolution, calculate the mean pairwise Euclidean distance within the subset. For the state vector subset corresponding to the load increment segment... Inside Calculate all The mean of the increasing lattice distances is obtained by taking the average of the pairwise Euclidean distances.

[0134] The mean distance of decreasing cells is obtained by calculating in the same way.

[0135] In the above test, in cell (3,2) Given 3 state vectors, calculate For the pairwise Euclidean distances {0.0298, 0.0315, 0.0284}, the mean of the increasing lattice distance is 0.0299;

[0136] Given two state vectors, we calculate one pair of Euclidean distances and obtain a decreasing lattice distance with a mean value of 0.0351.

[0137] C3. The ratio of the average incremental cell distance to the average incremental cell distance is used as the hysteresis resolution factor.

[0138] In this step, for each load phase cell (m,n) that can be hysteresis-resolved, the ratio of the average distance of the increasing cell to the average distance of the decreasing cell is used as the hysteresis resolution factor for that cell.

[0139] Under the same load amplitude, the ratio of the degree of aggregation of the nonlinear modulation state vector corresponding to the increasing path to that of the decreasing path.

[0140] When the ratio of the means is less than 1, it indicates that the state vectors of the ascending path are more clustered than those of the descending path, and the cell recursion density is overestimated on the ascending path; when the ratio of the means is greater than 1, it indicates that the state vectors of the descending path are more clustered than those of the ascending path, and the cell recursion density is overestimated on the descending path.

[0141] By multiplying the cell recursive density by a hysteresis resolution factor, the influence of the difference in the aggregation degree of the two loading paths on the cell recursive density evaluation can be eliminated, making the recursive density more accurately reflect the true repeatability of the nonlinear modulation behavior of the thread interface.

[0142] The hysteresis resolution factor of lattice (3,2) is 0.0299 / 0.0351=0.852, indicating that the state vector of the decreasing path is more clustered than that of the increasing path. The recursive density of the lattice needs to be multiplied by 0.852 for correction.

[0143] Hysteresis resolution factors were calculated for all 20 lattice cells. The values ​​for the lattice cells in the middle of the load ranged from 0.85 to 0.95, indicating that the elastic hysteresis effect has a relatively symmetrical impact on the modulation behavior of the two paths under moderate load levels.

[0144] Cells near the load reversal point are marked as unusable due to insufficient samples, and the hysteresis resolution factor is set to 1.

[0145] C4. Multiply the hysteresis resolution factor by the cell recursion density to form the final recursion density, and replace the cell recursion density with the final recursion density.

[0146] In the above test, the initial cell recursion density of cell (3,2) is 31.45, and the final cell recursion density is 0.852 × 31.45 = 26.80;

[0147] The lattice cell (3,3) is unusable due to hysteresis resolution, and the final lattice cell recursion density is 1 × 32.05 = 32.05.

[0148] After correcting all 20 cells, the final cell recursion density is arranged in positional order to form a recursion degree sequence of 20 elements with a value range of [18.3, 38.6]. The cell with the middle of the load and the middle rate of change has the highest recursion density, while the cell with the lowest recursion density is near the load endpoint. This is consistent with the physical expectation that the repeatability of the thread contact state is optimal under moderate cyclic load.

[0149] S4. Generate a signal for deterioration of anti-loosening performance by analyzing the distribution offset trend of the recursion sequence in the load space formed by the axial load time history of the toothed rack.

[0150] Specifically, the entire detection process is divided into several continuous detection periods according to time. Steps S2 to S3 are repeated for the load alignment modulation signal in each detection period to obtain the recursion sequence corresponding to that period.

[0151] Using the recursion degree sequence under the initial healthy state as a benchmark, the difference between the recursion degree sequence and the benchmark sequence at each grid cell position in the load space is calculated for each subsequent time period, forming the recursion degree offset sequence.

[0152] The sum of the absolute values ​​of each element in the recursion offset sequence is used as an index of anti-loosening performance degradation, thus forming an anti-loosening performance degradation signal.

[0153] When the anti-loosening performance remains normal, the recursion sequence of each time period is close to the benchmark, and the anti-loosening performance degradation index remains at a low level.

[0154] When the anti-loosening performance deteriorates, the irreversible change in the nonlinear modulation behavior of the thread interface causes a systematic shift in the recursion distribution in the load space, increasing the anti-loosening performance degradation index, thereby enabling quantitative characterization and online monitoring of the anti-loosening performance degradation.

[0155] Specifically, the anti-loosening performance of M16 fasteners under 0 to 5000 cycles of load was monitored online, with each 500 cycles divided into a testing period, for a total of 10 periods. Based on the recursion sequence of the first period (0 to 500 cycles), the recursion offset sequence and degradation index were calculated sequentially for each period.

[0156] The results showed that during periods 1 to 4, the anti-loosening performance degradation index remained at a low level of [2.1, 3.8], indicating that the thread contact state was stable and the anti-loosening performance did not degrade significantly.

[0157] During period 5 (2500 cycles), the anti-loosening performance degradation index was 7.3, which increased by 89% compared to the previous period. The recursion degree offset sequence showed that the recursion density of the grid cells in the middle of the load (grid cells (3,2) to (3,3)) decreased, indicating that the nonlinear modulation behavior of the thread interface under medium load conditions has undergone irreversible changes.

[0158] During periods 6 to 10, the anti-loosening performance degradation index continued to increase monotonically to 31.6, and the anti-loosening performance degradation signal showed an upward trend, which was consistent with the results of the torque attenuation measurement conducted simultaneously.

[0159] Example 3 is an embodiment of the present invention, which provides an online testing system for the anti-loosening performance of threaded rods and nuts, comprising:

[0160] The ultrasonic transmitter and receiver module is configured to transmit two sets of ultrasonic pulses with different center frequencies to the test piece and receive the modulated wave reflected from the threaded interface.

[0161] The load synchronization acquisition module is configured to synchronously acquire the time history of the axial load on the toothed rack;

[0162] The time alignment processing module is configured to time-align the modulation wave with the time history of the axial load of the toothed rack to obtain a load-aligned modulation signal.

[0163] The load decoupling processing module is configured to perform time-window-by-time load decoupling processing on the load alignment modulation signal, guided by the axial load time history of the toothed rack, to form a decoupling modulation spectrum;

[0164] The recursive analysis module is configured to perform recursive analysis on the decoupled modulation spectrum and extract the recursion degree sequence.

[0165] The anti-loosening degradation assessment module is configured to generate an anti-loosening performance degradation signal based on the distribution offset trend of the recursion sequence in the load space formed by the axial load time history of the toothed rack.

[0166] This embodiment also provides an electronic device applicable to an online testing method for the anti-loosening performance of a threaded rod and nut, comprising: a memory and a processor; the memory is used to store computer-executable instructions, and the processor is used to execute the computer-executable instructions to realize the online testing method for the anti-loosening performance of a threaded rod and nut as proposed in the above embodiment.

[0167] This embodiment also provides a storage medium storing a computer program, which, when executed by a processor, implements an online detection method for the anti-loosening performance of a toothed rod and nut as proposed in the above embodiment.

[0168] The storage medium proposed in this embodiment and the online detection method for the anti-loosening performance of a toothed bar and nut proposed in the above embodiments belong to the same inventive concept. Technical details not described in detail in this embodiment can be found in the above embodiments, and this embodiment has the same beneficial effects as the above embodiments.

[0169] Based on the above description of the implementation methods, those skilled in the art can clearly understand that the present invention can be implemented using software and necessary general-purpose hardware, and of course, it can also be implemented using hardware, but in many cases the former is a better implementation method. Based on this understanding, the technical solution of the present invention, or the part that contributes to the prior art, can be embodied in the form of a software product. This computer software product can be stored in a computer-readable storage medium, such as a computer floppy disk, read-only memory (ROM), random access memory (RAM), flash memory, hard disk, or optical disk, etc., including several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute the methods of the various embodiments of the present invention.

[0170] It should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit it. 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 of the present invention without departing from the spirit and scope of the technical solutions of the present invention, and all such modifications or substitutions should be covered within the scope of the claims of the present invention.

Claims

1. An online testing method for the anti-loosening performance of a threaded rod and nut, characterized in that, Includes the following steps: Two sets of ultrasonic pulses with different center frequencies are emitted to the test piece, and the modulated wave reflected from the thread interface is received. The modulated wave is time-aligned with the time history of the axial load of the toothed rack to obtain a load-aligned modulation signal. Using the axial load time history of the toothed rack as a guiding condition, the load alignment modulation signal is subjected to time-window-by-time load decoupling processing to form a decoupling modulation spectrum; Recursive analysis is performed on the decoupled modulation spectrum to extract the recursion degree sequence; The anti-loosening performance degradation signal is generated by the distribution offset trend of the recursion sequence in the load space formed by the axial load time history of the toothed bar.

2. The online testing method for the anti-loosening performance of a threaded rod and nut as described in claim 1, characterized in that, The steps for performing the time alignment include: At each sampling moment of the axial load time history of the toothed bar, the time-of-flight ratio of the reflected waves of the two sets of ultrasonic pulses at the thread interface is calculated, and the time-of-flight ratio of the reflected waves is used as the thread contact state proxy quantity to form the thread contact state proxy quantity time history. Monotonic mapping is constructed using the time history of the thread contact state proxy quantity as a monotonic variable to generate monotonic mapping information; The modulation wave is subjected to time bending transformation based on the monotonic mapping information, and the modulation wave is mapped to the thread contact state proxy domain to obtain the load-aligned modulation signal.

3. The online testing method for the anti-loosening performance of the threaded rod and nut as described in claim 2, characterized in that, The steps for constructing the monotonic map include: The axial load time history of the toothed rack is divided into a load increasing segment and a load decreasing segment. The piecewise cumulative integral of the time history of the thread contact state proxy quantity in the load increasing segment and the load decreasing segment is extracted respectively to form the increasing integral curve and the decreasing integral curve. Calculate the integral difference between the increasing integral curve and the decreasing integral curve at the same thread contact state surcharge, and use the integral difference as the contact hysteresis compensation amount. The contact hysteresis compensation amount is used to correct the mapping parameters of the time curvature transformation corresponding to the load reduction segment, forming a hysteresis-corrected monotonic mapping. Replace the monotonic mapping information with the hysteresis-corrected monotonic mapping.

4. The online testing method for the anti-loosening performance of the threaded rod and nut as described in claim 3, characterized in that, The steps for performing the time-window-by-time load decoupling process include: The load-aligned modulation signal is subjected to a sliding short-time Fourier transform to generate a load-aligned short-time spectrum sequence, which includes multiple short-time spectra corresponding to different time windows. The load-aligned modulation signal is resampled in the load increasing segment and the load decreasing segment using the hysteresis-corrected monotonic mapping to form an increasing modulation signal sequence and a decreasing modulation signal sequence, respectively. Perform sliding short-time Fourier transform on the incremental modulation signal sequence and the decrementing modulation signal sequence respectively to generate an incremental modulation spectrum sequence and a decrementing modulation spectrum sequence; The spectral difference between the increasing modulation spectrum sequence and the decreasing modulation spectrum sequence is calculated at the same thread contact state surrogate quantity, and the spectral difference is used as the elastic hysteresis residual spectrum. The elastic hysteresis residual spectrum is subtracted from the short-time spectrum of the corresponding time window in the load-aligned short-time spectrum sequence to separate the nonlinear modulation components within each time window, forming a decoupled modulation spectrum.

5. The online testing method for the anti-loosening performance of the threaded rod and nut as described in claim 4, characterized in that, The steps for calculating the elastic hysteresis residual spectrum include: The increasing modulation spectrum sequence and the decreasing modulation spectrum sequence are sorted according to the thread contact state proxy quantity to form an increasing ordered spectrum matrix and a decreasing ordered spectrum matrix, respectively. First-order difference is applied to the increasing ordered spectrum matrix and the decreasing ordered spectrum matrix respectively to extract the increasing modulation spectrum increment and the decreasing modulation spectrum increment; The difference between the mean values ​​of the incremental modulation spectrum increment and the decremental modulation spectrum increment at each thread contact state surrogate quantity is used as the elastic hysteresis residual spectrum.

6. The online testing method for the anti-loosening performance of a threaded rod and nut as described in claim 5, characterized in that, The steps for performing the recursive analysis include: A two-dimensional load phase plane is constructed using the load value and load change rate at each detection time of the axial load time history of the toothed rack as coordinates; The two-dimensional load phase plane is divided into load phase grid cells according to the equally spaced quantiles of the load value and the load change rate; Using the spectral amplitude vector of the decoupled modulation spectrum in each time window as the state vector, each state vector is assigned to the load phase grid according to the coordinate value of the rack axial load time history at the corresponding time. For each load phase cell, calculate the mean of the pairwise Euclidean distances of the state vectors. Use the reciprocal of the mean of the pairwise Euclidean distances as the cell recursion density. Arrange all cell recursion densities into a recursion degree sequence according to the positional order of the load phase cells.

7. The online testing method for the anti-loosening performance of a threaded rod and nut as described in claim 6, characterized in that, The steps for performing the lattice recursive density calculation include: Within each load phase cell, the state vector corresponding to the load increasing segment and the state vector corresponding to the load decreasing segment are extracted respectively. For the state vector corresponding to the load increasing segment, calculate the mean of pairwise Euclidean distance to form the mean of increasing lattice distance; for the state vector corresponding to the load decreasing segment, calculate the mean of pairwise Euclidean distance to form the mean of decreasing lattice distance. The ratio of the average incremental cell distance to the average incremental cell distance is used as the hysteresis resolution factor. The final lattice recursion density is formed by multiplying the hysteresis resolution factor by the lattice recursion density, and then the final lattice recursion density replaces the lattice recursion density.

8. An online testing system for the anti-loosening performance of a threaded rod and nut, employing the online testing method for the anti-loosening performance of a threaded rod and nut as described in any one of claims 1 to 7, characterized in that, include: The ultrasonic transmitter and receiver module is configured to transmit two sets of ultrasonic pulses with different center frequencies to the test piece and receive the modulated wave reflected from the threaded interface. The load synchronization acquisition module is configured to synchronously acquire the time history of the axial load on the toothed rack; The time alignment processing module is configured to time-align the modulation wave with the time history of the axial load of the toothed rack to obtain a load-aligned modulation signal. The load decoupling processing module is configured to perform time-window-by-time load decoupling processing on the load alignment modulation signal, guided by the axial load time history of the toothed rack, to form a decoupling modulation spectrum; The recursive analysis module is configured to perform recursive analysis on the decoupled modulation spectrum and extract the recursion degree sequence. The anti-loosening degradation assessment module is configured to generate an anti-loosening performance degradation signal based on the distribution offset trend of the recursion sequence in the load space formed by the axial load time history of the toothed rack.

9. A computer device comprising a memory and a processor, wherein the memory stores a computer program, characterized in that, When the processor executes the computer program, it implements the steps of the online detection method for the anti-loosening performance of the toothed rod and nut according to any one of claims 1 to 7.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements the steps of the online detection method for the anti-loosening performance of the toothed rod and nut according to any one of claims 1 to 7.

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