A bearing cage rotating speed ultrasonic measurement method based on short-time fourier transform

Abstract

The application discloses a bearing cage rotating speed ultrasonic measurement method based on short-time Fourier transform. Firstly, an ultrasonic probe is used to collect ultrasonic pulse signals under different bearing cage rotating speeds, and a sliding window function is used to divide the ultrasonic pulse signals into multiple sub-signals. Secondly, VMD is used to decompose each sub-signal component with the minimum correlation coefficient as the target, and each sub-signal decomposition component is reordered according to the frequency. Then, the short-time fractional Fourier transform of the reordered signal component is carried out with different window lengths to obtain a time-frequency diagram, and the envelope spectrum entropy of the time-frequency distribution is used as the target function to determine the optimal window length. Finally, the time-frequency diagram of the short-time fractional Fourier transform is superimposed under the optimal window length, and the time-frequency ridge is extracted by using the matching compression technology, so that the accurate bearing cage rotating speed is obtained. When there is noise and lubricating oil pollution, the high-precision measurement of the time-varying rotating speed of the cage can be realized without any processing of the bearing.

Description

Technical Field

[0001] This invention relates to the field of bearing cage speed measurement, and in particular to an ultrasonic method for measuring bearing cage speed based on short-time Fourier transform. Background Technology

[0002] As a crucial component of a bearing, the bearing cage's motion stability and reliability are key factors determining bearing performance. Bearing cage speed measurement is a vital indicator for assessing its motion and calculating bearing slippage. Current research on bearing cage speed measurement largely fails to consider the effects of noise and lubricating oil contamination, making it difficult to apply in practical devices. Even the few studies that do consider the impact of lubricating oil contamination require appropriate modifications to the bearing cage to achieve satisfactory speed measurement results; obviously, this will have a certain impact on the original bearing structure and performance, which is unacceptable for many high-end bearings operating in extreme environments.

[0003] To address the aforementioned issues, this invention proposes an ultrasonic measurement method for bearing cage rotational speed based on short-time Fourier transform. This method utilizes the reflected ultrasonic signal emitted by an ultrasonic probe to detect the bearing cage rotational speed. Unlike previous studies, it eliminates the need for any machining of the bearing cage, making it more suitable for practical applications. Furthermore, considering the susceptibility of ultrasonic probe signals to bearing and housing vibrations, and the high demands of time-frequency analysis for time-varying rotational speed signals, a data processing algorithm based on short-time Fourier transform is designed to deeply process the ultrasonic signal, achieving high accuracy in measuring cage rotational speed even under time-varying conditions. Summary of the Invention

[0004] Technical Problem: In view of this, the purpose of the present invention is to provide an ultrasonic measurement method for bearing cage rotation speed based on short-time Fourier transform, which can achieve high-precision measurement of time-varying cage rotation speed without any processing of the bearing in the presence of noise and lubricating oil contamination.

[0005] Technical solution: The present invention provides an ultrasonic measurement method for bearing cage rotational speed based on short-time Fourier transform, comprising:

[0006] Step S1: Use an ultrasonic probe to collect ultrasonic pulse signals at different bearing cage speeds, and use a sliding window function to divide the ultrasonic pulse signals into multiple sub-signals;

[0007] Step S2: Using variational mode decomposition (VMD) to decompose each sub-signal obtained in step S1 with the goal of minimizing the correlation coefficient, and reordering them according to the frequency of the decomposed components of each sub-signal.

[0008] Step S3: Adjust different window lengths to perform short-time fractional Fourier transform on the sorted signal components in step S2 to obtain the time-frequency diagram, and use the minimum of the envelope spectrum entropy of the time-frequency distribution as the objective function to determine the optimal window length;

[0009] Step S4: Under the optimal window length, superimpose the time-frequency graph of the short-time fractional Fourier transform from step S3 to obtain the global time-frequency graph, and use matched compression technology to extract the time-frequency ridge line, thereby obtaining the accurate time-varying speed of the bearing cage.

[0010] Step S1 includes:

[0011] Step S101: Acquire ultrasonic pulse signals x(t) at different bearing cage rotation speeds using an ultrasonic probe:

[0012] Align the ultrasonic probe vertically downwards with the center of the bearing, and adjust the distance between the probe and the outer ring surface of the bearing according to the measurement focal length and focusing diameter;

[0013] in,

[0014] The focal length of the ultrasonic probe is calculated as follows:

[0015]

[0016] In the formula: F is the focal length of the ultrasonic probe in water; F1 is the focal length of the ultrasonic probe after considering the refraction between the bearing outer ring surface and the water section; C2 is the propagation speed of the ultrasonic wave in water; C3 is the propagation speed of the ultrasonic wave in the bearing outer ring; H0 is the depth of the ultrasonic probe focal point entering the bearing outer ring.

[0017] The focusing diameter Φ of the ultrasonic probe is calculated as follows:

[0018] Φ=1.025C2F / (fD) (2)

[0019] In the formula: D is the diameter of the ultrasonic probe; f is the center frequency of the ultrasonic probe; adjust the focusing diameter Φ of the ultrasonic probe to be less than or equal to the diameter of the bearing roller; adjust the distance H between the ultrasonic probe and the outer ring surface of the bearing. α satisfy:

[0020]

[0021] Step S102: Divide the ultrasonic pulse signal obtained in step S101 into multiple sub-signals using a sliding window function:

[0022] The time-domain ultrasonic pulse signal x(t) obtained in step S101 is segmented using a sliding window function, and the ultrasonic pulse signal sampling frequency is f. s The total sampling time is t s According to the maximum frequency f of the ultrasonic pulse signal maxDetermine the data segment length L s for:

[0023]

[0024] The time-domain ultrasonic pulse signal x(t) was obtained as a multi-segment sub-signal. t represents time.

[0025] Step S2 includes:

[0026] Step S201: Using VMD to decompose each sub-signal component obtained in step S102 with the objective of minimizing the correlation coefficient:

[0027] Step S2011, the VMD decomposition process is as follows:

[0028] For the ultrasonic pulse multi-segment signal obtained in step S102 The VMD decomposition is performed as follows:

[0029]

[0030] In the formula: x i (t) represents the ultrasonic pulse sub-signal to be decomposed; The signal is a single-component signal obtained after VMD decomposition, k i =1,2,...,Π i ; for The instantaneous amplitude; for Instantaneous phase; Π i Let be the VMD decomposition level of the i-th sub-signal; the constraint variable model expression for VMD decomposition is as follows:

[0031]

[0032] In the formula: and Let represent all modal components and their center frequencies; δ(t) is the Dirac distribution; The '*' represents the derivative with respect to time; the '*' represents the convolution operation. L is a vector 2 Norm; Instantaneous frequency;

[0033] Step S2012, the correlation coefficient calculation process is as follows:

[0034] Based on the sub-signal x obtained in step S102 i (t) and the single-component signal obtained in step S2011 Minimizing the correlation coefficient between them determines the number of VMD decomposition layers Π i The correlation coefficient is calculated as follows:

[0035]

[0036] In the formula: Cov(·) represents the covariance of the variable; Var[·] is the variance of the signal; re(·) is the correlation coefficient of the signal;

[0037] Step S202: Based on the decomposed signals obtained in step S201, reorder them according to the frequency of the components:

[0038] For the sub-signal x in step S201 i (t) Single-component signal obtained after decomposition center frequency Reorder according to frequency.

[0039] Step S3 includes:

[0040] Step S301: Adjust different window lengths to perform short-time fractional Fourier transforms on the sorted signal components from step S202 to obtain the time-frequency diagram.

[0041] For the sorted single-component signals obtained in step S202 Choose a short-time window function g(t), window length B, and sliding step size H = B / 2; divide the original time series signal into N segments, and window each sub-signal. Define the short-time fractional Fourier transform as follows:

[0042]

[0043] In the formula: g(τ-t) is a window function centered at time t; p is the order of the fractional Fourier transform; For signal The p-th order fractional Fourier transform; θ is the p-th order fractional Fourier domain; K p (u,τ) is the kernel function of the p-th order fractional Fourier transform, satisfying:

[0044]

[0045] In the formula: α is the rotation angle of the time-frequency plane, satisfying α=pπ / 2; n is any integer; δ(·) is the unit impulse function; j is the imaginary unit; A α satisfy:

[0046]

[0047] Step S302: Determine the optimal window length by minimizing the envelope spectral entropy of the time-frequency distribution as the objective function.

[0048] The short-time fractional Fourier transform window length in step S301 is adjusted sequentially to {B1, B2, ..., B... λ}, respectively the single-component signals obtained in step S202 Perform a short-time fractional Fourier transform to calculate the envelope spectral entropy of the resulting time-frequency distribution. Determine the optimal window length based on the principle of minimizing the envelope spectral entropy. The formula for calculating the envelope spectral entropy is as follows:

[0049]

[0050] In the formula: S R (υ) is the envelope spectrum of the time-frequency distribution; γ is the length of the time-frequency distribution data points; pυ is the probability of the random process; λ is the number of windows.

[0051] Step S4 includes:

[0052] Step S401: Under the optimal window length, superimpose the time-frequency plot of the short-time fractional Fourier transform from step S3 to obtain the global time-frequency plot:

[0053] Based on the same sub-signal x obtained under the optimal window length in step S302 i (t) different components Time-frequency plot and time-frequency matrix For time-frequency matrix Adding them together yields the sub-signal x. i The time-frequency plot and time-frequency matrix SR of (t) i ; Further, different sub-signals x i The time-frequency plot and time-frequency matrix SR of (t) i The global time-frequency plot of the ultrasonic pulse signal x(t) is obtained by splicing the data in chronological order.

[0054] Step S402: Extract the time-frequency ridge line using matched compression technology to obtain the accurate time-varying speed of the bearing cage.

[0055] Step S4021: Based on the global time-frequency matrix V obtained in step S401 M Perform instantaneous frequency operator estimation:

[0056]

[0057] In the formula: This is the estimated value of the instantaneous frequency operator; This indicates taking the real part of a complex number; Represents the partial derivative with respect to time;

[0058] Step S4022: Based on the instantaneous frequency operator estimate obtained in step S4021, complete the global time-frequency matrix V. M Compression and reordering:

[0059]

[0060] In the formula: ω d (t) represents the actual value of the instantaneous frequency operator; This represents the conjugate of the fractional Fourier transform window function; This represents the reordered global time-frequency matrix; v represents the frequency.

[0061] Step S4023: Retain the global time-frequency matrix after reordering in step S4022. The component with the smallest intermediate frequency is taken as the time-frequency ridge, and the obtained time-frequency ridge is the accurate time-varying speed of the bearing cage:

[0062]

[0063] In the formula: v min The component with the lowest frequency; β represents the number of bearing rollers; v σ (t) represents the time-varying speed of the bearing cage.

[0064] Beneficial effects: The advantages of this invention are:

[0065] 1. Utilizing the principle that ultrasonic waves emitted by an ultrasonic probe have different reflectivities when they encounter solid and liquid media, the rotational speed of a bearing cage can be measured without any processing of the bearing cage, which has great practical value.

[0066] 2. The VMD-Short Time Fourier Transform algorithm described in this invention can effectively suppress the interference of noise on ultrasonic pulse signals and obtain good time-frequency analysis results under the time-varying operating conditions of bearing cage speed, thereby improving the accuracy of bearing cage speed measurement.

[0067] 3. The method described in this invention fully combines the advantages of ultrasonic probe measurement and VMD-short time Fourier transform algorithm, and can obtain better measurement results when there is noise and lubricating oil contamination. Attached Figure Description

[0068] Figure 1 This is a flowchart illustrating the ultrasonic measurement method for bearing cage rotation speed based on short-time Fourier transform provided in Example 1.

[0069] Figure 2 This is a structural diagram of the ultrasonic probe used in Example 1 for measuring the rotational speed of the bearing cage;

[0070] Figure 3 The measurement principle of the ultrasonic probe provided in Example 1;

[0071] Figure 4 The time-domain and frequency-domain diagrams of the ultrasonic pulse signal provided in Example 1 are shown.

[0072] Figure 5 The above are time-domain diagrams of the ultrasonic pulse sub-signals provided in Example 1, where a is the time-domain diagram of the ultrasonic pulse sub-signals at 100 seconds, b is the time-domain diagram of the ultrasonic pulse sub-signals at 140 seconds, and c is the time-domain diagram of the ultrasonic pulse sub-signals at 180 seconds.

[0073] Figure 6 The following are local time-frequency diagrams of the single-component ultrasonic pulse signal provided in Example 1, where a is the time-frequency diagram of the single-component ultrasonic pulse signal at 100 seconds, b is the time-frequency diagram of the single-component ultrasonic pulse signal at 140 seconds, and c is the time-frequency diagram of the single-component ultrasonic pulse signal at 180 seconds.

[0074] Figure 7 This is the global time-frequency diagram of the ultrasonic pulse signal provided in Example 1;

[0075] Figure 8 The ultrasonic pulse signal time-frequency ridge line provided in Example 1, where a is the time-frequency ridge line region and b is the time-frequency ridge line;

[0076] Figure 9 The bearing cage provided in Example 1 has a time-varying rotational speed. Detailed Implementation

[0077] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0078] Example 1

[0079] See Figures 1-9 This embodiment provides an ultrasonic measurement method for bearing cage rotational speed based on short-time Fourier transform. The procedure is as follows: Figure 1 As shown, this embodiment uses a cylindrical roller bearing as an example to verify the algorithm's performance. Figure 2 A structural diagram illustrating the ultrasonic probe for measuring the rotational speed of a bearing cage is shown. The strategy specifically includes the following steps:

[0080] Step S1: Use an ultrasonic probe to collect ultrasonic pulse signals at different bearing cage speeds, and use a sliding window function to divide the ultrasonic pulse signals into multiple sub-signals;

[0081] Specifically, in this embodiment, step S1 includes:

[0082] Step S101: Acquire ultrasonic pulse signals x(t) at different bearing cage rotation speeds using an ultrasonic probe:

[0083] Position the ultrasonic probe vertically downwards, aligned with the center of the bearing. Adjust the distance between the probe and the outer ring surface of the bearing according to the measured focal length and focusing diameter. The ultrasonic probe focal length is calculated as follows:

[0084]

[0085] In the formula: F is the focal length of the ultrasonic probe in water; F1 is the focal length of the ultrasonic probe after considering the refraction between the bearing outer ring surface and the water section; C2 is the propagation speed of the ultrasonic wave in water; C3 is the propagation speed of the ultrasonic wave in the bearing outer ring; H0 is the depth of the ultrasonic probe focal point entering the bearing outer ring; the ultrasonic probe measurement principle is as follows: Figure 3 As shown;

[0086] The focusing diameter Φ of the ultrasonic probe is calculated as follows:

[0087] Φ=1.025C2F / fD (2)

[0088] In the formula: D is the diameter of the ultrasonic probe; f is the center frequency of the ultrasonic probe; adjust the focusing diameter Φ of the ultrasonic probe to be less than or equal to the diameter of the bearing roller; adjust the distance H between the ultrasonic probe and the outer ring surface of the bearing. α satisfy:

[0089]

[0090] In Embodiment 1 of this invention, an Olympus immersion ultrasonic probe was selected, and its specific parameters are shown in Table 1:

[0091] Table 1 Parameters of Olympus Immersion Ultrasonic Probe

[0092]

[0093] Step S102: Divide the ultrasonic pulse signal obtained in step S101 into multiple sub-signals using a sliding window function:

[0094] The time-domain ultrasonic pulse signal x(t) obtained in step S101 is segmented using a sliding window function. The time-domain and frequency-domain plots of the ultrasonic pulse signal are shown below. Figure 4 As shown, the ultrasonic pulse signal sampling frequency is f s =51200Hz, total sampling time is t s =200s, based on the maximum frequency f of the ultrasonic pulse signal max Determine the data segment length L s for:

[0095]

[0096] The time-domain ultrasonic pulse signal x(t) was obtained as a multi-segment sub-signal. The segmented sub-signals are as follows Figure 5 As shown, the time-domain plots of the segmented sub-signals at 100 seconds, 140 seconds, and 180 seconds are displayed respectively.

[0097] Step S2: Using variational mode decomposition (VMD) to decompose each sub-signal obtained in step S1 with the goal of minimizing the correlation coefficient, and reordering them according to the frequency of the decomposed components of each sub-signal.

[0098] Specifically, in this embodiment, step S2 includes:

[0099] Step S201: Using VMD to decompose each sub-signal component obtained in step S102 with the goal of minimizing the correlation coefficient: (1) The VMD decomposition process is as follows:

[0100] For the ultrasonic pulse multi-segment signal obtained in step S102 The VMD decomposition is performed as follows:

[0101]

[0102] In the formula: x i (t) represents the ultrasonic pulse sub-signal to be decomposed; This is the single-component signal obtained after VMD decomposition. for The instantaneous amplitude; for The instantaneous phase of ; Π is the VMD decomposition level of the i-th sub-signal; the constraint variable model expression of VMD decomposition is as follows:

[0103]

[0104] In the formula: and Let represent all modal components and their center frequencies; δ(t) is the Dirac distribution; The '*' represents the derivative with respect to time; the '*' represents the convolution operation. L is a vector 2 Norm; (2) The correlation coefficient is calculated as follows: (1) It is the instantaneous frequency; (2) The correlation coefficient is calculated as follows:

[0105] Based on the sub-signal x obtained in step S102 i (t) and the single-component signal obtained in step S2011 Minimizing the correlation coefficient between them determines the number of VMD decomposition layers Π i The correlation coefficient is calculated as follows:

[0106]

[0107] In the formula: Cov(·) represents the covariance of the variable; Var[·] is the variance of the signal; re(·) is the correlation coefficient of the signal;

[0108] Based on the principle of minimizing the correlation coefficient, the number of VMD grading layers is determined to be Π. i =5.

[0109] Step S202: Based on the decomposed signals obtained in step S201, reorder them according to the frequency of the components:

[0110] For the sub-signal x in step S201 i (t) Single-component signal obtained after decomposition center frequency Reorder according to frequency;

[0111] Step S3: Adjust different window lengths to perform short-time fractional Fourier transform on the sorted signal components in step S2 to obtain the time-frequency diagram, and use the minimum of the envelope spectrum entropy of the time-frequency distribution as the objective function to determine the optimal window length;

[0112] Specifically, in this embodiment, step S3 includes:

[0113] Step S301: Adjust different window lengths to perform short-time fractional Fourier transforms on the sorted signal components from step S202 to obtain the time-frequency diagram.

[0114] For the sorted single-component signals obtained in step S202 Choose a short-time window function g(t), window length B, and sliding step size H = B / 2; divide the original time series signal into N segments, and window each sub-signal. Define the short-time fractional Fourier transform as follows:

[0115]

[0116] In the formula: g(τ-t) is a window function centered at time t; p is the order of the fractional Fourier transform; For signal The p-th order fractional Fourier transform; θ is the p-th order fractional Fourier domain; K p (u,τ) is the kernel function of the p-th order fractional Fourier transform, satisfying:

[0117]

[0118] In the formula: α is the rotation angle of the time-frequency plane, satisfying α=pπ / 2; n is any integer; δ(·) is the unit impulse function; j is the imaginary unit; A α satisfy:

[0119]

[0120] Step S302: Determine the optimal window length by minimizing the envelope spectral entropy of the time-frequency distribution as the objective function.

[0121] The short-time fractional Fourier transform window length in step S301 is adjusted sequentially to {B1, B2, ..., B λ}, respectively the single-component signals obtained in step S202 Perform a short-time fractional Fourier transform to calculate the envelope spectral entropy of the resulting time-frequency distribution. Determine the optimal window length based on the principle of minimizing the envelope spectral entropy. The formula for calculating the envelope spectral entropy is as follows:

[0122]

[0123] In the formula: S R (υ) represents the envelope spectrum of the time-frequency distribution; γ represents the length of the time-frequency distribution data points; p υ Let be the probability of the random process; λ be the window number.

[0124] Based on the optimal window length, a short-time Fourier transform is performed on the single-component signal obtained in step S202 to obtain the local time-frequency diagram, as shown below. Figure 6 As shown.

[0125] Step S4: Under the optimal window length, superimpose the time-frequency graph of the short-time fractional Fourier transform from step S3 to obtain the global time-frequency graph, and use matched compression technology to extract the time-frequency ridges to obtain the accurate time-varying speed of the bearing cage.

[0126] Specifically, in this embodiment, step S4 includes:

[0127] Step S401: Under the optimal window length, superimpose the time-frequency plot of the short-time fractional Fourier transform from step S3 to obtain the global time-frequency plot:

[0128] Based on the same sub-signal x obtained under the optimal window length in step S302 i (t) different components Time-frequency plot and time-frequency matrix Where k i =1 i ,2 i ,....Π i And i = 1, 2, ..., L s For the time-frequency matrix Adding them together yields the sub-signal x. i The time-frequency plot and time-frequency matrix SR of (t) i ; Further, different sub-signals x i The time-frequency plot and time-frequency matrix SR of (t) i The global time-frequency plot of the ultrasonic pulse signal x(t) is obtained by splicing the data in chronological order; the global time-frequency plot is shown below. Figure 7 As shown.

[0129] Step S402: Extract the time-frequency ridge line using matched compression technology to obtain the accurate time-varying speed of the bearing cage.

[0130] (1) Based on the global time-frequency matrix V obtained in step S401 M Perform instantaneous frequency operator estimation:

[0131]

[0132] In the formula: This is the estimated value of the instantaneous frequency operator; This indicates taking the real part of a complex number; Represents the partial derivative with respect to time;

[0133] (2) Based on the instantaneous frequency operator estimate obtained in step (1), complete the global time-frequency matrix V. M Compression and reordering:

[0134]

[0135] In the formula: ω d (t) represents the actual value of the instantaneous frequency operator; This represents the conjugate of the fractional Fourier transform window function; This represents the reordered global time-frequency matrix; v represents the frequency.

[0136] (3) Retain the global time-frequency matrix after reordering in step (2). The component with the smallest intermediate frequency is taken as the time-frequency ridge, and the obtained time-frequency ridge is the accurate time-varying speed of the bearing cage:

[0137]

[0138] In the formula: v min The component with the lowest frequency; β represents the number of bearing rollers; v σ (t) represents the time-varying speed of the bearing cage.

[0139] Time-frequency ridges, such as Figure 8 As shown, the time-varying rotational speed of the bearing cage measured by the ultrasonic probe is as follows: Figure 9 As shown.

[0140] Any aspects of this invention not described in detail are well-known to those skilled in the art.

[0141] The preferred embodiments of the present invention have been described in detail above. It should be understood that those skilled in the art can make numerous modifications and variations based on the concept of the present invention without creative effort. Therefore, all technical solutions that can be obtained by those skilled in the art based on the concept of the present invention through logical analysis, reasoning, or limited experimentation on the basis of existing technology should be within the scope of protection defined by the claims.

Claims

1. A short-time Fourier transform based ultrasonic measurement method for determining the rotational speed of a bearing cage in water, characterized in that The method comprises: Step S1, collecting ultrasonic pulse signals under different bearing cage rotating speeds in water by using an ultrasonic probe, and dividing the ultrasonic pulse signals into multiple sub-signals by using a sliding window function; Step S2, decomposing each sub-signal obtained in step S1 by using a variational mode decomposition (VMD) with the minimum correlation coefficient as the target, and reordering the decomposed components according to the frequency of each sub-signal; Step S3, adjusting different window lengths to sequentially perform short-time fractional Fourier transform on the reordered signal components in step S2 to obtain time-frequency diagrams, and determining the optimal window length by taking the minimum envelope spectrum entropy of the time-frequency distribution as the objective function; Step S4, stacking the time-frequency diagrams obtained by the short-time fractional Fourier transform in step S3 under the optimal window length to obtain a global time-frequency diagram, extracting a time-frequency ridge by using a matching compression technique, and then obtaining an accurate bearing cage time-varying rotating speed.

2. The method according to claim 1, characterized in that, The step S1 comprises: Step S101, collecting ultrasonic pulse signals x(t) under different bearing cage rotating speeds by using an ultrasonic probe: Aligning the ultrasonic probe vertically downward to the bearing center, adjusting the distance between the probe and the surface of the bearing outer ring according to the measurement focal length and the focusing diameter; Wherein, The measurement focal length of the ultrasonic probe is calculated as follows: In the formula, F is the focal length value of the ultrasonic probe in water; F1 is the focal length value of the ultrasonic probe after considering the refraction of the bearing outer ring surface and the water cross section; C2 is the propagation speed of ultrasonic waves in water; C3 is the propagation speed of ultrasonic waves in the bearing outer ring; H0 is the depth of the ultrasonic probe focus point into the bearing outer ring; The focusing diameter Φ of the ultrasonic probe is calculated as follows: Φ = 1.025C2F / (fD) (2) where: D is the diameter of the ultrasonic probe; f is the center frequency of the ultrasonic probe; the focusing diameter Φ of the ultrasonic probe is adjusted to be less than or equal to the diameter of the bearing roller; the distance H between the ultrasonic probe and the surface of the bearing outer ring is adjusted α satisfies: Step S102, dividing the ultrasonic pulse signals obtained in step S101 into multiple sub-signals by using a sliding window function: The time-domain ultrasonic pulse signal x(t) obtained in step S101 is cut and divided by using a sliding window function, the ultrasonic pulse signal sampling frequency is f s , the total sampling time is t s , and the data segment length L s is determined according to the maximum frequency f max of the ultrasonic pulse signal, and is: The time-domain ultrasonic pulse signal x(t) is obtained as t is time.

3. A short-time Fourier transform based ultrasonic measurement method of the rotational speed of a bearing cage in water according to claim 2, characterized in that, The step S2 comprises: Step S201, decomposing each sub-signal component obtained in step S102 by using VMD with the minimum correlation coefficient as the target: Step S2011, the VMD decomposition process is as follows: The ultrasound pulse multi-segment sub-signals obtained in step S102 are subjected to a VMD decomposition as follows: The VMD decomposition is performed as follows: wherein: x i (t) is the ultrasonic pulse sub-signal to be decomposed; is the single component signal obtained after VMD decomposition, k i = 1, 2,..., Π i ; is the instantaneous amplitude of ; is the instantaneous phase of the single component signal ; Π i is the number of VMD decomposition layers of the i-th sub-signal; the constraint variable model expression of VMD decomposition is as follows: where: and are all modal components and their center frequencies, respectively; δ'(t) is a Dirac distribution; is the derivative with respect to time; * is the convolution operation; is the L 2 norm of a vector; Step S2012, the correlation coefficient calculation process is as follows: The sub-signal x obtained according to step S102 i (t) and the single-component signal obtained in step S2011 The number of VMD decomposition layers Π is determined by minimizing the correlation coefficient between i The correlation coefficient calculation process is as follows: In the formula, Cov(·) represents the covariance of the variable; Var[·] is the variance of the signal; re(·) is the correlation coefficient of the signal; Step S202, reordering the decomposed signals based on step S201 according to the frequency of the components: The sub-signals x i (t) single component signals obtained after decomposition center frequency of the sub-signals x reordering according to the frequency height.

4. The ultrasonic measurement method of claim 3, wherein, The step S3 comprises: Step S301, adjusting different window lengths to sequentially perform short-time fractional Fourier transform on the reordered signal components in step S202 to obtain time-frequency diagrams: For the sorted single-component signals obtained in step S202 A short-time window function g(t), a window length B, and a sliding step H=B / 2 are selected; the original time series signal is divided into N segments, and each segment of the signal is processed by windowing; and the short-time fractional Fourier transform is defined as follows: where: g(τ-t) is a window function centered at time t; τ is an integration variable with respect to time; p is the order of the fractional Fourier transform; is the pth order fractional Fourier transform of the signal ; θ is the pth order fractional Fourier domain; K p (θ,τ) is the kernel function of the pth order fractional Fourier transform, satisfying: In the formula, a is a rotation angle of a time-frequency plane, a satisfies a = pπ / 2; n is an arbitrary integer; δ(·) is a unit impulse function; j is an imaginary unit; A α satisfies: Step S302, determining the optimal window length by taking the minimum envelope spectrum entropy of the time-frequency distribution as the objective function: The short-time fractional Fourier transform window length in step S301 is adjusted sequentially to {B1, B2, ..., B... λ }, respectively the single-component signals obtained in step S202 Perform a short-time fractional Fourier transform to calculate the envelope spectral entropy of the resulting time-frequency distribution. Determine the optimal window length based on the principle of minimizing the envelope spectral entropy. The formula for calculating the envelope spectral entropy is as follows: where: S R (u) is the envelope spectrum of the time-frequency distribution; γ is the length of the time-frequency distribution data point; p υ is the probability of the random process; λ is the number of windows.

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