Method for testing high-speed rotation performance of micro bearing

Abstract

The application discloses a kind of micro bearing high-speed rotation performance test method, it is related to bearing test technical field, the application first collects the spindle end displacement sequence of test micro bearing, test seat displacement sequence and transient temperature;Displacement sequence is denoised and decomposed based on adaptive local iterative filtering algorithm, and a plurality of intrinsic mode matrix sets are obtained;After the white dimension reduction of the plurality of intrinsic mode matrix set, the decoupling matrix is solved based on improved whale optimization algorithm, and the decoupled steady-state error parameter is calculated;With the product of radial load dynamic reduction and cooling flow rate dynamic increase as constraint condition, combined with decoupled steady-state error parameter, penalty function equation is constructed to solve, and output control vector is output;Finally, according to the control vector, unilateral control is executed, combined with the separated bearing pure dynamic clearance signal calculation equivalent dynamic stiffness, and test results are generated.The application effectively eliminates the bending interference of spindle, and accurately extracts equivalent dynamic stiffness.

Description

Technical Field

[0001] This invention relates to the field of bearing testing technology, and in particular to a method for testing the high-speed rotation performance of miniature bearings. Background Technology

[0002] As a core component in precision machinery and other fields, the performance of miniature bearings under high-speed rotation directly determines the stability and reliability of equipment. Under ultra-high-speed operating conditions, complex vibrations and rapid temperature rises easily occur inside the bearing. To ensure safe operation and detect failure boundaries, precise testing of the rotational performance of miniature bearings under high-speed and extreme conditions is essential. However, in actual high-speed rotational testing environments, the acquired signals not only include pure dynamic clearance signals caused by minute internal bearing vibrations, but also often mix in spindle bending vibrations, motor electromagnetic noise, and signals caused by high-speed friction and rolling. To address the high-frequency intermittent noise generated by the intermittent impact of the ball, and for bearing testing and vibration signal processing, Chinese Patent Application Publication No. CN121296583A discloses a method for suppressing and testing magnetic bearing vibration. This method mainly uses a controller to output a sinusoidal voltage signal to the magnetic levitation bearing and uses a displacement sensor to obtain the displacement error signal of the rotor relative to the center position. It uses a notch filter algorithm to remove the same frequency current in the power amplifier to suppress the current stiffness force at the same speed. At the same time, through offline frequency sweep identification, online compensation signal generation, and offline calibration of compensation current gain, the same frequency displacement stiffness force is canceled. However, when dealing with high-frequency complex miniature bearing tests, the aforementioned technologies and existing conventional testing methods often suffer from extremely uneven distribution of extreme points when faced with signal frequency abrupt changes caused by high-frequency intermittent impacts. This wide range of smooth and abrupt regions easily leads to severe modal aliasing and data divergence, making it impossible to accurately extract pure bearing dynamic signals from multi-source vibrations. Due to the failure to effectively eliminate interference from the macroscopic bending and deflection components of the spindle, the dynamic stiffness calculated by traditional methods is often extremely distorted and cannot truly reflect the mechanical ability of miniature bearings to resist external deformation under extreme thermal expansion conditions. Under extreme testing conditions where miniature bearings operate at ultra-high speeds and temperatures rise sharply, the mechanical clearance inside the bearing will be severely compressed due to thermal expansion, easily leading to thermal seizure. If the test bench control system adopts traditional, crude intervention methods, such as simultaneously executing defensive actions like significantly reducing radial load and increasing coolant flow rate, it will cause severe cross-coupling oscillations in the hydraulic servo system and thermodynamic balance system of the test bench. This will not only cause the test data to become completely invalid but may even directly damage the spindle of the test equipment. Summary of the Invention

[0003] The technical problem solved by this invention is that, in terms of signal processing, existing technologies cannot accurately extract pure bearing dynamic signals from multi-source vibrations when faced with signal frequency changes caused by high-frequency intermittent impacts. Due to the failure to effectively eliminate the interference of macroscopic bending and deflection components of the spindle, the dynamic stiffness calculated by traditional methods is often extremely distorted.

[0004] To solve the above-mentioned technical problems, the present invention provides the following technical solution: a method for testing the high-speed rotation performance of a miniature bearing, comprising the following steps: Step S1: Collect the spindle end displacement sequence, test seat displacement sequence, and transient temperature of the test miniature bearing; Step S2: Based on the adaptive local iterative filtering algorithm, the displacement sequence of the main shaft end and the displacement sequence of the test seat are denoised and decomposed to obtain a set of multi-order intrinsic mode matrices; Step S3: Whiten and reduce the dimensionality of the multi-order intrinsic mode matrix set to obtain the multi-source heterogeneous decoupling matrix, solve the separation matrix based on the improved whale optimization algorithm, and calculate the decoupling steady-state error parameters; Step S4: Using the product of the dynamic reduction of radial load and the dynamic increase of cooling flow rate being zero as a constraint condition, a penalty function equation is constructed in conjunction with the decoupled steady-state error parameter for solution, and the control vector is output. Step S5: Perform unilateral control according to the control vector, and calculate the equivalent dynamic stiffness by combining the bearing's pure dynamic clearance signal to generate the micro-bearing performance test results.

[0005] Preferably, step S1 includes the following sub-steps: Step S101: According to the preset sampling frequency and preset time window, the displacement of the spindle end is collected as the first displacement sequence, and the displacement of the outside of the test seat is collected as the second displacement sequence. Step S102: Collect the transient temperature of the outer ring of the current miniature bearing.

[0006] Preferably, step S2 includes the following sub-steps: Step S201: Extract all the maximum and minimum points and their sampling point numbers in the first displacement sequence to form an initial extreme point number sequence; Step S202: Calculate the distance between the sampling point numbers corresponding to two adjacent in-phase extreme points as the first distance, take half of the first distance as the local extreme value scale, and take the median of all local extreme value scales as the benchmark extreme value scale. Step S203: Calculate the distance between the sampling point numbers corresponding to adjacent maxima and minima as the second distance. If the second distance is greater than or equal to a preset multiple of the benchmark extreme value scale, calculate the pseudo extreme value point number between the sampling point numbers corresponding to adjacent maxima and minima through linear interpolation and rounding operations, and insert the pseudo extreme value point number into the corresponding position in the initial extreme value point number sequence to obtain the first extreme value point number sequence.

[0007] Preferably, step S2 further includes the following sub-steps: Step S204: Based on the difference between adjacent extreme point numbers in the first extreme point number sequence, allocate a filter window width to the sampling point corresponding to each extreme point number, assign filter window width values ​​to the beginning and end endpoint regions, and use the piecewise cubic Hermitian interpolation polynomial algorithm to smoothly fill the assigned filter window width to obtain the initial filter sequence. Step S205: Extract the maximum and minimum points of the initial filter sequence, and use the piecewise cubic Hermitian interpolation polynomial algorithm to fit and generate the upper envelope curve and the lower envelope curve respectively. Average the values ​​of the upper envelope curve and the lower envelope curve at the same sampling point to obtain the de-oscillation smoothing filter sequence. The elements in the deoscillation smoothing filter sequence are used as the standard deviation parameters of the Gaussian filter, and point-by-point convolution operations are performed with the first displacement sequence to obtain the first local mean baseline sequence. Subtract the first local mean baseline sequence from the first displacement sequence to obtain the first-order intrinsic mode sequence, and repeat the above steps with the first local mean baseline sequence as the new sequence to obtain multi-order intrinsic mode sequences. Step S206: Process the second displacement sequence using the same method to obtain the corresponding multi-order intrinsic mode sequence; Step S207: Concatenate the eigenmode sequences of the same order in the first displacement sequence and the second displacement sequence row by row to obtain a set of multi-order eigenmode matrices.

[0008] Preferably, step S3 includes the following sub-steps: Step S301: Concatenate the multi-order intrinsic mode matrix set sequentially to obtain the initial observation matrix; Step S302: Calculate the covariance matrix of the initial observation matrix and perform eigenvalue decomposition. Sort the eigenvalues ​​from largest to smallest, extract the eigenvectors corresponding to the first two eigenvalues, arrange them in rows, and construct a whitening dimensionality reduction matrix. Multiply the whitening dimensionality reduction matrix by the initial observation matrix to obtain the multi-source heterogeneous decoupling matrix.

[0009] Preferably, step S3 further includes the following sub-steps: Step S303: Construct a fitness optimization equation with the goal of maximizing the negative entropy of the separated signal, and convert the maximization of negative entropy into an optimization form that seeks the minimum value; The logistic chaotic mapping equation is used to generate a preset number of initial step size position parameters, and an initial separation matrix after Schmitt orthogonalization is generated. The inverse solution is calculated by the inverse learning equation. The initial step size position parameter and the inverse solution are substituted into the damped Newton iteration equation to calculate the test separation matrix. The test separation matrix is ​​multiplied by the multi-source heterogeneous decoupling matrix to obtain the separation signal. The separation signal is substituted into the fitness optimization equation to calculate the fitness. The preset number parameter with the smallest fitness is selected as the initial population array.

[0010] Preferably, step S3 further includes the following sub-steps: S304, in the iterative optimization process, uses the spiral position update equation combined with the Lévy flight perturbation equation to update the step size parameter and obtain the globally optimal step size parameter; The globally optimal step size parameter is substituted into the damping Newton iteration equation as a damping factor for iterative updating. The Frobenius norm of the difference between the separation matrices generated by two adjacent iterations is calculated and used as the decoupling steady-state error parameter. The iteration stops when the decoupling steady-state error parameter is less than a preset threshold or reaches a preset maximum number of iterations, and the final separation matrix is ​​obtained. S305, multiply the final separation matrix with the multi-source heterogeneous decoupling matrix to obtain the independent source data matrix, calculate the kurtosis value of each row vector in the independent source data matrix, sort the row vectors in descending order of kurtosis value, and extract the row vector with the largest kurtosis value as the bearing pure dynamic clearance signal.

[0011] Preferably, step S4 includes the following sub-steps: Step S401: Construct a first variable and a second variable, wherein the first variable is a normalized radial load dynamic reduction amount, and the second variable is a normalized cooling flow rate dynamic increase amount, and the product of the first variable and the second variable is zero as a hard constraint equation. The hard constraint equation is transformed into a penalty function equation, the mathematical expression of which is: ; in, As the first variable, As the second variable, For penalty parameters, The penalty function equation is... The basic objective equation; The mathematical expression of the basic objective equation is: ; in, Based on the objective equation, As the first variable, As the second variable, and To control energy loss weight, As the weight for temperature tracking error, Transient temperature, For safe temperature, The equivalent cooling constant is reduced for full-scale load. To increase the equivalent cooling constant for full-scale cooling, This is the limit of permissible temperature difference constant.

[0012] Preferably, step S4 further includes the following sub-steps: Step S402: Establish a nonlinear exponential amplification dynamic mapping equation between the penalty parameter and the decoupled steady-state error parameter, and assign values ​​to the penalty parameter in the penalty function equation based on the dynamic mapping equation; Based on the limit penalty characteristic of the penalty function equation on non-zero products when the penalty parameter tends to a maximum value, at least one of the first and second variables is set to zero. The penalty function equation is decoupled into a first one-dimensional optimization sub-equation when the first variable is zero and a second one-dimensional optimization sub-equation when the second variable is zero. Non-negative boundary constraints are set for the first and second variables, and the first and second one-dimensional optimization sub-equations are solved analytically to obtain the corresponding first and second local optimal solutions. The first and second local optimal solutions are substituted back into the penalty function equation for comparison. A set of variables that makes the calculation result of the penalty function equation smaller is selected as the final first and second variables, and inverse normalization is performed to construct a control vector.

[0013] Preferably, step S5 includes: Step S501: The first element of the control vector is used as the first control quantity and the second element is used as the second control quantity, which are then converted into the first analog voltage signal and the second analog voltage signal, respectively. The first analog voltage signal is transmitted to the hydraulic servo valve that controls the radial load, and the second analog voltage signal is transmitted to the proportional regulating valve that controls the cooling flow rate. Step S502: Take the square root of the sum of the squares of all elements in the bearing pure dynamic clearance signal to obtain the equivalent dynamic clearance scalar. The actual radial load scalar is divided by the calculated result of the equivalent dynamic clearance scalar to obtain the equivalent dynamic stiffness, wherein the actual radial load scalar is the difference between the applied base radial load and the first control quantity. Collect the current rotational speed and the current transient temperature, and concatenate the current rotational speed, the equivalent dynamic stiffness, and the current transient temperature into an independent state row vector; Step S503: Concatenate the independent state row vectors row by row in chronological order to obtain the state evolution matrix; The state evolution matrix is ​​used as the performance test result of the miniature bearing. The beneficial effects of this invention are as follows: By introducing a pseudo-extreme point insertion mechanism into the adaptive local iterative filtering algorithm, this invention effectively overcomes the frequency mutation problem caused by high-frequency friction and intermittent ball impacts when micro-bearings operate at high speeds. This mechanism forcibly cuts the large-span smooth region in the index dimension, making the distribution of extreme points compact and uniform. It avoids the modal aliasing and data divergence problems that are easily caused by conventional blind source separation algorithms when processing displacement sequences containing high-frequency intermittent noise, and greatly improves the robustness and decomposition accuracy of the preprocessing of multi-source heterogeneous vibration signals. This invention combines a multi-source heterogeneous decoupling matrix with an improved whale optimization algorithm to construct a fitness optimization system based on maximizing negative entropy. By introducing logistic chaotic mapping, inverse learning equations, and a deep search strategy that alternates between spiral position updates and Lévy flight perturbations, it effectively avoids getting stuck in local dead ends when solving the separation matrix. Based on the non-Gaussian differences of independent components of multi-channel signals, this method successfully extracts the pure dynamic clearance signal of the bearing with high-frequency pulse impact characteristics using the principle of maximizing kurtosis. It also eliminates the interference of low-frequency bending and deflection components of the spindle on stiffness calculation, so that the final calculated equivalent dynamic stiffness can reflect the true mechanical ability of the micro-bearing to resist external deformation under extreme thermal expansion. This invention addresses the risk of thermal seizure and jamming of miniature bearings under ultra-high-speed operation and rapid temperature rise. It introduces the rapidly increasing decoupling steady-state error parameter caused by the rigid contact between the spindle and bearing into the penalty function equation, establishing a nonlinear exponentially amplified dynamic mapping relationship between the decoupling steady-state error and the penalty parameter. Approaching the critical temperature rise point, it can apply an exponentially increasing penalty force. Based on the penalty characteristic, the optimization space is reduced and decoupled. Through analytical solution, a control vector is forced to be output that satisfies the absolute zero product of the dynamic reduction of radial load and the dynamic increase of cooling flow rate. This unilateral defense control strategy eliminates the severe cross-coupling oscillations generated when the hydraulic servo system and thermodynamic balance system of the test bench simultaneously perform unloading and powerful cooling actions. While ensuring that the spindle and test equipment are protected from physical damage, it achieves a safe and accurate exploration of the specific performance evolution law and failure boundary of miniature bearings under extreme operating conditions. Attached Figure Description

[0014] Figure 1 The flowchart illustrates the steps of a method for testing the high-speed rotation performance of a miniature bearing, as provided in one embodiment of the present invention. Detailed Implementation

[0015] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments.

[0016] Example, refer to Figure 1 A method for testing the high-speed rotation performance of miniature bearings is provided, comprising the following steps: Step S1: Collect the spindle end displacement sequence, test seat displacement sequence, and transient temperature of the test miniature bearing; Step S2: Based on the adaptive local iterative filtering algorithm, the displacement sequence of the spindle end and the displacement sequence of the test seat are denoised and decomposed to obtain a set of multi-order intrinsic mode matrices; Step S3: Whiten and reduce the dimensionality of the multi-order intrinsic mode matrix set to obtain the multi-source heterogeneous decoupling matrix. Solve the separation matrix based on the improved whale optimization algorithm and calculate the decoupling steady-state error parameters. Step S4: Using the product of the dynamic reduction of radial load and the dynamic increase of cooling flow rate being zero as a constraint, a penalty function equation is constructed by combining the decoupled steady-state error parameters for solution, and the control vector is output. Step S5: Perform unilateral control based on the control vector, and calculate the equivalent dynamic stiffness by combining the bearing's pure dynamic clearance signal to generate the performance test results of the miniature bearing.

[0017] This invention deeply integrates an adaptive local iterative filtering algorithm, an improved whale-optimized blind source separation algorithm, and a penalty function-based unilateral defense control strategy to construct a complete closed loop from multi-source heterogeneous noise stripping to safety intervention under extreme conditions. It not only overcomes the problem of extreme distortion in stiffness calculation caused by spindle bending and environmental noise in traditional testing, but also achieves oscillation-free safe cooling and unloading under extreme conditions of near-thermal seizure, ensuring accurate and safe exploration of the true performance boundaries of miniature bearings.

[0018] Step S1 includes the following sub-steps: Step S101: According to the preset sampling frequency and preset time window, the displacement of the spindle end is collected as the first displacement sequence, and the displacement of the outside of the test seat is collected as the second displacement sequence. Step S102: Collect the transient temperature of the outer ring of the current miniature bearing.

[0019] In one specific embodiment of the present invention, a basic radial load is applied to the test micro bearing by a non-contact pneumatic loader. After the load is applied, the variable frequency drive motor is started to increase the spindle speed and stabilize it at the speed preset in the test plan. Before conducting high-speed rotation tests on miniature bearings, a one-dimensional measurement coordinate system is established using the detection reference point of the laser displacement sensor, and the initial coordinates of the spindle end and the outside of the test seat in a static state are obtained as the reference zero point. During the high-speed rotation test of the miniature bearing, the continuous displacement of the spindle end and the test seat holding the miniature bearing within a preset time window of 1 second is collected by a laser displacement sensor at a preset sampling frequency of 50000Hz. The displacement scalar is the relative deviation value between the measured coordinate and the reference zero point at the current moment (in micrometers), thereby constructing the first displacement sequence and the second displacement sequence. The current transient temperature is collected by a fiber optic temperature sensor attached to the outer ring of the miniature bearing.

[0020] Step S2 includes the following sub-steps: Step S201: Extract all the maximum and minimum points and their sampling point numbers in the first displacement sequence to form an initial extreme point numbering sequence; Step S202: Calculate the distance between the sampling point numbers corresponding to two adjacent in-phase extreme points as the first distance, take half of the first distance as the local extreme value scale, and take the median of all local extreme value scales as the benchmark extreme value scale. Step S203: Calculate the distance between the sampling point numbers corresponding to adjacent maxima and minima as the second distance. If the second distance is greater than or equal to a preset multiple of the benchmark extreme value scale, calculate pseudo-extreme point numbers between the sampling point numbers corresponding to adjacent maxima and minima through linear interpolation and rounding operations. Insert the pseudo-extreme point numbers into the corresponding positions in the initial extreme point number sequence to obtain the first extreme point number sequence. Calculate the quotient of the second distance divided by the benchmark extreme value scale, round down to obtain the number of pseudo-extreme points to be inserted, perform linear interpolation according to equal intervals, and round the calculated index positions to obtain the pseudo-extreme point numbers.

[0021] In one specific embodiment of the present invention, the displacement sequence data includes not only spindle deflection and bearing pure dynamic clearance, but also high-frequency intermittent noise generated by high-speed friction and intermittent ball impact. This noise can cause serious data divergence in the subsequent blind source separation algorithm. Therefore, it is necessary to preprocess the displacement sequence to remove noise using an adaptive local iterative filtering algorithm. By traversing the first displacement sequence using the difference algorithm, all maximum and minimum points are extracted, and the sampling point numbers of all maximum and minimum points are extracted to form an initial extreme point number sequence. Calculate the distance between two adjacent in-phase extreme points, such as the distance between the sampling point numbers corresponding to two adjacent maximum points, as the first distance; If the second distance is less than a preset multiple, it is determined to be a normal frequency fluctuation, and the extreme point of the original sequence remains unchanged; In conventional adaptive local iterative filtering algorithms, the presence of high-frequency intermittent noise can cause abrupt changes in signal frequency, resulting in an extremely uneven distribution of extrema. This means the second distance becomes larger, forming a wide-ranging, flat region, which can lead to severe mode aliasing. This embodiment avoids mode aliasing by introducing a pseudo-extremum insertion mechanism. The pseudo-extreme point insertion operation forcibly cuts the originally large-span, flat region along the index dimension, making the extreme point index distribution of the first displacement sequence data more compact and uniform; the preset multiple in this embodiment is 3 times.

[0022] In the face of signal frequency drops caused by low-frequency intermittent interference, this invention introduces pseudo-extreme points to identify flat regions with excessively large extreme point spans. By using linear interpolation to force cut along the index dimension, the originally uneven data distribution becomes compact and uniform. This invention eliminates the severe mode mixing phenomenon caused by abnormal low-frequency spans.

[0023] Step S2 also includes the following sub-steps: Step S204: Based on the difference between adjacent extreme point numbers in the first extreme point number sequence, allocate a filter window width to the sampling point corresponding to each extreme point number, assign filter window width values ​​to the beginning and end endpoint regions, and use the piecewise cubic Hermit interpolation polynomial algorithm to smoothly fill the assigned filter window width to obtain the initial filter sequence. Step S205: Extract the maximum and minimum points of the initial filtered sequence, and use the piecewise cubic Hermitian interpolation polynomial algorithm to fit and generate the upper envelope curve and the lower envelope curve respectively. Average the values ​​of the upper envelope curve and the lower envelope curve at the same sampling point to obtain the deoscillation smoothing filtered sequence. The elements in the deoscillation smoothing filter sequence are used as the standard deviation parameters of the Gaussian filter, and point-by-point convolution operation is performed with the first displacement sequence to obtain the first local mean baseline sequence. Subtract the first local mean baseline sequence from the first displacement sequence to obtain the first-order intrinsic mode sequence, and repeat the above steps with the first local mean baseline sequence as the new sequence to obtain multi-order intrinsic mode sequences. Step S206: Process the second displacement sequence using the same method to obtain the corresponding multi-order intrinsic mode sequence; Step S207: Concatenate the eigenmode sequences of the same order in the first displacement sequence and the second displacement sequence row by row to obtain a set of multi-order eigenmode matrices.

[0024] In a specific embodiment of the present invention, adaptively allocating the filter window width for the value at each sampling point in the first displacement sequence specifically includes: For the i-th extreme point number in the first extreme point numbering sequence, calculate the... The extreme point number minus the first extreme point number The difference between the extreme point numbers is divided by 2, and the result is used as the filter window width assigned to the sampling point corresponding to the i-th extreme point number. The filter window width of the sampling point represents the instantaneous average half-cycle at the sampling point time, eliminating the non-stationary calculation error caused by frequency change. For the first extreme point number in the first extreme point numbering sequence, for all sampling points between the first sampling point and the first extreme point, this embodiment forcibly allocates the filter window width corresponding to the second extreme point to all sampling points between the first sampling point and the first extreme point; The width of the filter window corresponding to the second-to-last extreme point is forcibly allocated to all sampling points between the last extreme point and the last sampling point; After the endpoint assignment is completed, the piecewise cubic Hermite interpolation polynomial algorithm is used to smoothly fill the remaining middle part of the filter window width to the remaining sampling points, and an initial filter sequence with the same length as the first displacement sequence is obtained. The initial filter sequence is composed of the filter window width corresponding to each sampling point. The values ​​of the upper and lower envelope curves at the same sampling point are added together and divided by 2 to obtain the filter value corresponding to the sampling point. The filter values ​​corresponding to all sampling points constitute the deoscillation smoothing filter sequence. The length of the deoscillation smoothing filter sequence is the same as the length of the first displacement sequence. Each element of the deoscillation smoothing filter sequence is used as a candidate value for the standard deviation parameter of the Gaussian filter. To prevent local over-smoothing or filter failure, upper and lower limits are set for the candidate value of the standard deviation parameter. If the candidate value exceeds the set upper and lower limits, it is forcibly truncated to the corresponding boundary value. Using the standard deviation parameter after upper and lower limit processing, an adaptive Gaussian filter function is constructed. The first displacement sequence is convolved with the adaptive Gaussian filter function pointwise to output the first local mean baseline sequence. Upper and lower limits are set for each value of the first local mean baseline sequence. If the value exceeds the set upper and lower limits, it is forcibly truncated to the corresponding boundary value. The upper limit is set to +50μm and the lower limit is set to -50μm. The first displacement sequence is subtracted element by element from the first local mean baseline sequence after upper and lower limit processing to obtain the first order intrinsic mode sequence. Using the first local mean baseline sequence as a new sequence, repeat the steps of finding extreme points, calculating distance, interpolating envelope, convolution integral and subtraction to obtain the second-order intrinsic mode sequence and the second local mean baseline sequence, and continue to obtain the third-order intrinsic mode sequence and the fourth-order intrinsic mode sequence. The same method was used to obtain the first-order intrinsic mode sequence, the second-order intrinsic mode sequence, the third-order intrinsic mode sequence, and the fourth-order intrinsic mode sequence obtained from the second displacement sequence; The same order eigenmode sequences of the first and second displacement sequences are concatenated row by row to obtain the first order eigenmode matrix, the second order eigenmode matrix, the third order eigenmode matrix and the fourth order eigenmode matrix respectively. The set of multi-order eigenmode matrices includes: first-order eigenmode matrix, second-order eigenmode matrix, third-order eigenmode matrix and fourth-order eigenmode matrix.

[0025] This invention adaptively allocates the filter window width to extreme points using a piecewise cubic Hermitian interpolation polynomial algorithm, binds the filter parameters to the instantaneous average half-cycle depth at the sampling point, and performs point-by-point convolution operations in conjunction with an adaptive Gaussian filter. This eliminates the non-stationary calculation error caused by the fixed filter window during frequency abrupt changes, and significantly improves the smoothness and accuracy of extracting the local mean baseline of multi-order intrinsic mode sequences.

[0026] Step S3 includes the following sub-steps: Step S301: Concatenate the multi-order intrinsic mode matrix set sequentially to obtain the initial observation matrix; Step S302: Calculate the covariance matrix of the initial observation matrix and perform eigenvalue decomposition. Sort the eigenvalues ​​from largest to smallest, extract the eigenvectors corresponding to the first two eigenvalues, arrange them in rows, and construct a whitening dimensionality reduction matrix. The dimensionality reduction here does not simply reduce the feature dimension, but rather decouples and merges the dominant components of the original multi-channel feature dimensions. Through feature vector extraction, two merged feature vectors are obtained that contain the original core physical meaning of the aforementioned multi-dimensional features. Multiply the whitening dimensionality reduction matrix with the initial observation matrix to obtain the multi-source heterogeneous decoupling matrix.

[0027] In one specific embodiment of the present invention, the first-order intrinsic mode matrix, the second-order intrinsic mode matrix, the third-order intrinsic mode matrix, and the fourth-order intrinsic mode matrix are sequentially concatenated downwards to obtain the initial observation matrix (dimension: ,in, (Number of sampling points) The multi-source heterogeneous decoupling matrix is ​​used to eliminate the second-order correlation between multi-channel signals in the initial observation matrix and reduce the computational cost of the optimization equation.

[0028] This invention employs a whitening dimensionality reduction process based on covariance matrix eigenvalue decomposition. By extracting principal component eigenvectors to construct a whitening dimensionality reduction matrix, it effectively eliminates the second-order correlation between multi-channel signals in the initial observation matrix. While preserving the core vibration characteristics, it significantly compresses the data dimension, greatly reducing the computational load and resource consumption of subsequent high-dimensional optimization equations.

[0029] Step S3 also includes the following sub-steps: Step S303: Construct a fitness optimization equation with the goal of maximizing the negative entropy of the separated signal, and convert the maximization of negative entropy into an optimization form that seeks the minimum value; The logistic chaotic mapping equation is used to generate a preset number of initial step size position parameters, and an initial separation matrix after Schmitt orthogonalization is generated. The inverse solution is calculated by the inverse learning equation. The initial step size position parameter and the inverse solution are substituted into the damped Newton iteration equation to calculate the test separation matrix. The test separation matrix is ​​multiplied by the multi-source heterogeneous decoupling matrix to obtain the separation signal. The separation signal is substituted into the fitness optimization equation to calculate the fitness. The preset number parameter with the smallest fitness is selected as the initial population array.

[0030] Step S3 also includes the following sub-steps: S304, in the iterative optimization process, uses the spiral position update equation combined with the Lévy flight perturbation equation to update the step size parameter and obtain the globally optimal step size parameter; The globally optimal step size parameter is substituted into the damping Newton iteration equation as a damping factor for iterative updating. The Frobenius norm of the difference between the separation matrices generated by two adjacent iterations is calculated and used as the decoupling steady-state error parameter. The iteration stops when the decoupling steady-state error parameter is less than a preset threshold or when the preset maximum number of iterations is reached, and the final separation matrix is ​​obtained. S305, multiply the final separation matrix with the multi-source heterogeneous decoupling matrix to obtain the independent source data matrix, calculate the kurtosis value of each row vector in the independent source data matrix, sort the row vectors in descending order of kurtosis value, and extract the row vector with the largest kurtosis value as the bearing pure dynamic clearance signal.

[0031] In a specific embodiment of the present invention, during the testing of the micro bearing, the vibration data collected not only includes the tiny vibrations inside the bearing, but also the spindle bending vibration, motor electromagnetic noise, and environmental high-frequency noise. It is necessary to decompose the mixed vibration signals into their respective independent pure signals. The multi-source heterogeneous decoupling matrix is ​​regarded as the product of the original real signal and the mixed signal of the environment. In order to approximate the original real signal, it is necessary to solve the inverse matrix of the mixed signal of the environment, that is, the separation matrix. The product of the separation matrix and the multi-source heterogeneous decoupling matrix is ​​the approximate estimate of the original real signal, that is, the separated signal. The bending vibration of the spindle, the impact vibration of the ball hitting the crack, and the white noise of the surrounding environment are generated by completely different physical causes. The signals generated by different causes should be independent of each other. After multiple independent non-Gaussian signals are mixed, the distribution of the mixed signal will approach the Gaussian distribution. Then, the separation of the signal is to maximize the non-Gaussianity. The mathematical index used to measure the non-Gaussianity of the signal is negative entropy. By maximizing negative entropy, the non-Gaussianity of the separated signal is maximized, and thus the original true signal is obtained. An optimization equation based on maximizing negative entropy is constructed, and a damped Newton iteration method is used to update the separation matrix. In this embodiment, an improved whale optimization algorithm is used to dynamically find the optimal step size parameter for each iteration. The mathematical expression for negative entropy is: ; in, For the separation signal The negative entropy value; This represents the operation of calculating the mathematical expectation. It is a standard pure Gaussian random variable (mean 0, variance 1); For the selected nonlinear smoothing function, the logarithmic function of hyperbolic cosine is selected in this embodiment; The improvements to the whale optimization algorithm specifically include: Because the underlying logic of the improved whale optimization algorithm is to find the minimum value of the objective function, in order to maximize negative entropy, this embodiment transforms the negative entropy equation into a fitness optimization equation that seeks to minimize the value. The mathematical expression of the optimization equation is as follows: ; in, For the fitness of individuals in the population, For the separation signal The negative entropy value, The extremely small constant set to prevent the denominator from being zero is taken as a value in this embodiment. ; When the improved whale optimization algorithm finds through iteration When the absolute minimum value is reached, it is equivalent to the separation signal. negative entropy The global maximum value is reached, at which point the signal has the strongest independence, and the pure bearing clearance signal is stripped away; The initial population size is set at 30, and the logistic chaotic mapping equation is used. In the interval 30 pseudo-random initial step size position parameters are generated internally, among which, The branch parameter for the chaotic mapping is set to 4 in this embodiment; A 2x2 random matrix is ​​generated using a Gaussian random function. Then, a Schmitt orthogonalization operation is performed on this initial random matrix to forcibly remove the correlation between its internal column vectors, resulting in an absolutely orthogonal initial separation matrix. ; Using the reverse learning equation ( Calculate the corresponding 30 reverse solutions. Using the pseudo-random initial step size position parameters and the reverse solutions as test compensations, substitute them along with the initial separation matrix into the damped Newton iteration equation for calculation. The mathematical expression of the damped Newton iteration equation is: ; in, To test the separation matrix, These are the initial step size position parameters. The initial separation matrix, To calculate the mathematical expectation, It is a nonlinear hyperbolic tangent function. Let be the derivative of the nonlinear hyperbolic tangent function. This is a multi-source heterogeneous decoupling matrix; This represents a diagonal matrix constructed using vector elements as the main diagonal elements; Obtain the test separation matrix, and use the product of the test separation matrix and the multi-source heterogeneous decoupling matrix as the separation signal. Substitute the parameters into the negative entropy optimization equation to calculate the fitness, and select the 30 parameters with the smallest fitness, i.e. the strongest non-Gaussianity, as the initial population array. In the iterative search for the optimal step size, a spiral position update equation is used to simulate the local depth search, updating the value of each step size parameter. The mathematical expression of the spiral position update equation is: ; in, This indicates the updated step size parameter. This represents the globally optimal step size parameter with the minimum fitness (i.e., the strongest non-Gaussianity) in the current population. This represents the absolute distance between the current step size parameter and the globally optimal step size parameter. is the base of the natural logarithm. The constant representing the shape of the logarithmic spiral is set to 1 in this embodiment. In order to be in A random number that is uniformly distributed within an interval; By using the spiral position update equation, the step size parameter will approach the current optimal solution with a spirally shrinking mathematical trajectory, thus achieving a local depth search of the parameter.

[0032] To prevent the parameter search from getting stuck in a local dead end, the Lévy flight perturbation equation is introduced to perform position perturbation. The mathematical expression of the Lévy flight perturbation equation is as follows: ; in, The new step size parameters after perturbation. These are the step size parameters before the disturbance. Let the fixed constant weights be set to 0.01, and p be the probability constant set to 1.5. Let variables u and v follow normal distributions. , , Based on the standard Gamma function and the probability constant Calculated; Through this mathematical mechanism of alternating long and short step sizes, an absolute scalar value between 0 and 1 is ultimately output as the globally optimal step size parameter. Substituting the globally optimal step size parameter as the damping factor into the damped Newton iteration equation, the mathematical expression of the damped Newton iteration equation is: ; in, For the first The separation matrix generated in the next iteration For the first The separation matrix generated in the next iteration The globally optimal step size parameter. To calculate the mathematical expectation, the specific operation logic in the discrete data processing of this embodiment is as follows: along the time axis, calculate the arithmetic mean of the multi-source heterogeneous decoupling matrix at all discrete sampling points, that is, at all column elements of the matrix; It is a nonlinear hyperbolic tangent function. The derivative of the nonlinear hyperbolic tangent function; This is a multi-source heterogeneous decoupling matrix; Repeat the above iterative calculation, and then... The separation matrix generated in the next iteration With the The separation matrix generated in the next iteration Perform a mathematical subtraction operation and calculate the Frobenius norm of the difference matrix. The Frobenius norm of the difference matrix is ​​used as the decoupling steady-state error parameter. Until the decoupling steady-state error parameter is less than the preset threshold Alternatively, iteration may stop when the preset maximum number of iterations, 200, is reached. The final separation matrix is ​​obtained, which has a dimension of 2 rows and 2 columns. The separation matrix and the multi-source heterogeneous decoupling matrix are multiplied to obtain the independent source data matrix. Since the vibration generated by the internal clearance collision of the micro-bearing is a high-frequency pulse impact signal, its kurtosis value is significantly higher than that of the low-frequency bending and flexural vibration signal of the main shaft. Therefore, the kurtosis value of each row vector in the independent source data matrix is ​​calculated, and the row vector with the largest kurtosis value is extracted as the pure dynamic clearance signal of the bearing, thereby accurately eliminating the bending and flexural deformation component of the main shaft. Under the test conditions of ultra-high speed operation and rapid temperature rise of miniature bearings, when the internal clearance of the bearing is compressed to near zero due to thermal expansion and thermal seizure is about to occur, the spindle and the inner and outer rings of the bearing will physically be rigidly attached. This physical rigid attachment will directly cause the two vibration sources to lose statistical independence in mathematics. The most direct manifestation of this is that the decoupling steady-state error parameter will increase exponentially. In this embodiment, the decoupled steady-state error parameters are transmitted to step S4 to dynamically replace the penalty factor in the internal point penalty function equation, thereby forcibly triggering the unilateral defensive action of the subsequent test bench pneumatic loader or cooling pump to prevent the miniature bearing from being actually damaged during the test.

[0033] The iterative optimization and signal reconstruction design of this invention integrates the logarithmic spiral position update equation and the Lévy flight disturbance mechanism, achieving a dynamic balance between local depth search and global long step size jump, and locking the globally optimal damping factor. Based on this, by utilizing the physical characteristic of significantly high kurtosis values ​​of high-frequency pulse impact signals, the pure bearing dynamic clearance signal is accurately extracted by maximizing the kurtosis value, and the low-frequency bending and deflection components of the spindle are stripped away. The decoupled steady-state error parameters obtained by iterative calculation are transformed into early warning indicators for the imminent rigid contact of the micro-bearing.

[0034] Step S4 includes the following sub-steps: Step S401: Construct a first variable and a second variable, where the first variable is the normalized radial load dynamic reduction amount and the second variable is the normalized cooling flow rate dynamic increase amount. Set the product of the first variable and the second variable to zero as the hard constraint equation. The hard constraint equation is transformed into a penalty function equation, and the mathematical expression of the penalty function equation is: ; in, As the first variable, As the second variable, For penalty parameters, The penalty function equation is... The basic objective equation; The mathematical expression for the basic objective equation is: ; in, Based on the objective equation, As the first variable, As the second variable, and To control energy loss weight, As the weight for temperature tracking error, Transient temperature, For safe temperature, The equivalent cooling constant is reduced for full-scale load. To increase the equivalent cooling constant for full-scale cooling, This is the limit permissible temperature difference constant (30℃ in this embodiment), which is the maximum temperature range allowed for the miniature bearing to go from a safe temperature to the critical point of bearing seizure and failure.

[0035] This invention constructs a basic objective equation and a hard constraint equation, accurately quantifies and balances the control energy consumption cost and temperature tracking priority of radial unloading and increasing cooling flow rate. At the same time, it cleverly transforms the hard constraint with a product of zero into an external penalty function, which enforces the mutual exclusivity of unloading and cooling actions from the bottom layer of the mathematical equation, laying a mathematical foundation for avoiding cross-coupling oscillations in the test bench servo system.

[0036] Step S4 also includes the following sub-steps: Step S402: Establish a nonlinear exponential amplification dynamic mapping equation between the penalty parameter and the decoupled steady-state error parameter, and assign values ​​to the penalty parameter in the penalty function equation based on the dynamic mapping equation. Based on the limit penalty characteristic of the penalty function equation for non-zero products when the penalty parameter tends to a maximum value, at least one of the first and second variables is set to zero. The penalty function equation is decoupled into a first one-dimensional optimization sub-equation when the first variable is zero and a second one-dimensional optimization sub-equation when the second variable is zero. Non-negative boundary constraints are set for the first and second variables, and the first and second one-dimensional optimization sub-equations are solved analytically to obtain the corresponding first and second local optimal solutions. The first and second local optimal solutions are substituted back into the penalty function equation for comparison. A set of variables that results in a smaller penalty function equation is selected as the final first and second variables, and inverse normalization is performed to construct a control vector. If the penalty function equations corresponding to the two sets of variables are equal, the variable combination that performs the dynamic increase in cooling flow rate is selected first according to the preset safety priority to construct the control vector. In one specific embodiment of the present invention, under extreme test conditions of ultra-high-speed operation and rapid temperature rise of the micro-bearing, the mechanical clearance inside the bearing will be severely compressed due to the thermal expansion of the metal components. When the clearance is compressed to near zero, the micro-bearing will be about to thermally seize. In order to save the test bearing, there are two intervention methods: the first is to quickly reduce the externally applied radial load to reduce frictional heat generation, and the second is to significantly increase the flow rate of external cooling lubricating oil to forcibly cool it down. If the two actions of load reduction and cooling are performed simultaneously under such extreme critical conditions, the hydraulic servo system and thermodynamic balance system of the test bench will generate severe cross-coupled oscillations, leading to test data failure or even damage to the spindle. Construct a first variable and a second variable, where the first variable represents the normalized proportion of the dynamic reduction of radial load (in Newtons); and the second variable represents the normalized proportion of the dynamic increase of cooling flow rate (in liters per minute). The product of the first variable and the second variable being 0 is taken as a hard constraint equation, which forces that one of the two variables must be 0 in the final solution; Since hard constraint equations with products equal to zero are extremely difficult to solve directly, this embodiment uses an external penalty function algorithm to transform the problem into a penalty problem with boundary constraints. Specifically, a penalty function equation is constructed, and the basic objective equation in the penalty function equation is used to balance control energy consumption and temperature deviation. This embodiment , This indicates that the energy cost of increasing coolant is greater than the cost of unloading. This indicates that under extreme operating conditions such as thermal seizure, cooling takes priority over saving energy. , This information originates from the factory parameters of the test bench. and This represents the mechanical control energy cost incurred in implementing load reduction and increased cooling. This represents temperature-induced tracking error elimination, where This indicates the current transient temperature collected in step S1. Distance from preset safe target temperature (In this embodiment, the temperature is set to 120 degrees Celsius) the difference, while This represents the temperature that is expected to decrease after control is applied. By seeking the minimum value of this basic objective equation, we can find the most energy-efficient and most effective control combination for cooling. This is an external product penalty term, used to force the algorithm to seek solutions in the direction where the product is 0; Meanwhile, to ensure that the calculated control quantity has practical physical meaning, non-negative boundary constraints are set for the first and second variables, i.e., mandatory limits are imposed. and The first and second variables are input into the sequential quadratic programming algorithm. The sequential quadratic programming algorithm has the ability to handle inequality boundary constraints at its underlying level. During the rapid iterative optimization process of the algorithm, the optimization is performed by combining the set non-negative boundary constraints and the constructed penalty function equation. By establishing penalty parameters The dynamic mapping equation for the decoupled steady-state error parameter assigns a penalty parameter value, and the mathematical expression of the dynamic mapping equation is: ; in, For penalty parameters, To decouple steady-state error parameters; The dynamic mapping equation employs a nonlinear exponential amplification equation because, under normal overtemperature conditions, i.e., only step S1... Under conditions exceeding the limit, the spindle and bearing vibrate independently, and the algorithm converges normally and quickly. Iteration stops when the decoupling steady-state error parameter is less than a preset threshold. At this point, the transmitted decoupling steady-state error parameter is extremely small, and the penalty parameter... When the temperature approaches 100, relying solely on the temperature tracking term in the basic objective equation for stable and routine cooling adjustment, when the internal clearance of the micro-bearing contracts sharply, causing rigid contact, the physical rigid coupling causes the two signals to lose statistical independence, the blind source separation algorithm cannot converge mathematically, and the iteration will continue until the maximum number of iterations is forcibly stopped. At this time, the transmitted decoupling steady-state error parameter will remain at a very large abnormal jump value. Driven by an infinitely large penalty parameter, anything that makes the product... Non-zero solutions will cause the value of the penalty function equation to tend to infinity. Therefore, the global optimal solution of this penalty function equation exists in... or On the coordinate axis boundaries, this embodiment performs dimensionality reduction based on the aforementioned limit penalty characteristic: forced... At this point, the product penalty term in the penalty function equation is naturally eliminated, and the original equation collapses into a function that only relates to... The first one-dimensional optimality equation, combined with Perform analytical calculations to obtain the first local optimum; Similarly, injunction The original equation collapses into a equation about The second one-dimensional optimization equation is used to obtain the second local optimal solution. The two local optimal solutions are then substituted back into the penalty function equation for numerical comparison. The variable combination corresponding to the scenario that makes the penalty function value smaller is selected as the final first and second variables.

[0037] Finally, step S4 outputs a 2-row, 1-column one-dimensional column vector to the subsequent step S5 as the control vector. The two elements of the control vector are the calculated compensation control values ​​of the first and second variables, respectively. Due to the algorithm's mandatory constraints, at least one of the first and second variable compensation control quantities has a value of 0. This control vector containing the absolute 0 value is directly sent to the programmable logic controller of the test machine, ensuring that at least one of the servo valve and the proportional valve remains stationary. When there is an abnormal temperature rise during the test process that requires cooling, only the other valve is allowed to perform dynamic compensation.

[0038] This invention establishes a nonlinear exponentially amplified dynamic mapping equation between the penalty parameter and the decoupling steady-state error parameter. When the temperature is normally over-temperature, it is adjusted smoothly. However, once the bearing clearance shrinks sharply and causes rigid contact, the decoupling steady-state error increases sharply, the penalty parameter soars exponentially and provides an infinite penalty. This extreme penalty drives the sequential quadratic programming algorithm to output an absolutely non-negative one-sided solution at high speed, thus preventing the test equipment from getting stuck due to thermal bearing failure.

[0039] Step S5 includes: Step S501: The first element of the control vector is used as the first control quantity, and the second element is used as the second control quantity, which are then converted into the first analog voltage signal and the second analog voltage signal, respectively. A first analog voltage signal is transmitted to a hydraulic servo valve that controls the radial load, and a second analog voltage signal is transmitted to a proportional control valve that controls the cooling flow rate, so that one of the hydraulic servo valve and the proportional control valve remains stationary while the other performs dynamic compensation. Step S502: Take the square root of the sum of the squares of all elements in the bearing pure dynamic clearance signal to obtain the equivalent dynamic clearance scalar. The equivalent dynamic stiffness is obtained by dividing the actual radial load scalar by the calculated equivalent dynamic clearance scalar, where the actual radial load scalar is the difference between the applied base radial load and the first control quantity. Collect the current rotational speed and current transient temperature, and concatenate the current rotational speed, equivalent dynamic stiffness, and current transient temperature into an independent state row vector; Step S503: In the cyclic test of increasing the base speed in multiple steps, the independent state row vectors obtained in each cycle are spliced ​​together row by row in chronological order to obtain the state evolution matrix. The state evolution matrix is ​​used as the test result of the miniature bearing performance.

[0040] In one specific embodiment of the present invention, the current rotational speed and the current transient temperature of the outer ring of the bearing are collected in real time. Traditional stiffness calculations are often severely distorted due to interference from spindle bending deformation. In this embodiment, the bearing pure dynamic clearance signal is called, which has eliminated the bending and deflection components of the spindle. The root mean square calculation equation is used to reduce the dimension of the bearing pure dynamic clearance signal and calculate the equivalent dynamic clearance scalar. Equivalent dynamic stiffness represents the true mechanical ability of a miniature bearing to resist external deformation under extreme thermal expansion conditions; Throughout the entire testing process, the test machine will increase the base speed stepwise multiple times according to the preset program and execute the above test steps in a loop. The 1-row, 3-column independent state row vectors extracted in each loop will be concatenated row by row in chronological order to obtain the state evolution matrix. By analyzing the state evolution matrix, we can obtain the specific performance evolution law and failure boundary test results of miniature bearings under extreme working conditions.

[0041] The generated unilateral control vector is converted into an analog voltage to directly drive the hardware valve, thus implementing the unilateral defense action at the physical level. By performing root mean square dimension reduction on the purified bearing dynamic clearance signal and combining it with the actual radial load scalar, the true equivalent dynamic stiffness that eliminates the interference of spindle bending is calculated. The state evolution matrix obtained by step-by-step cyclic splicing realizes the visualization of the ability of the micro-bearing to resist external deformation under extreme thermal expansion state, and describes the performance evolution law and failure boundary of the micro-bearing.

[0042] This invention effectively overcomes the frequency mutation problem caused by high-frequency friction and intermittent ball impacts during high-speed operation of micro-bearings by introducing a pseudo-extreme point insertion mechanism into the adaptive local iterative filtering algorithm. This mechanism forcibly cuts the large-span smooth region in the index dimension, making the distribution of extreme points compact and uniform. It avoids the modal mixing phenomenon and data divergence problem that conventional blind source separation algorithms are prone to cause when processing displacement sequences containing high-frequency intermittent noise, and greatly improves the robustness and decomposition accuracy of the preprocessing of multi-source heterogeneous vibration signals. This invention combines a multi-source heterogeneous decoupling matrix with an improved whale optimization algorithm to construct a fitness optimization system based on maximizing negative entropy. By introducing logistic chaotic mapping, inverse learning equations, and a deep search strategy that alternates between spiral position updates and Lévy flight perturbations, it effectively avoids getting stuck in local dead ends when solving the separation matrix. Based on the non-Gaussian differences of independent components of multi-channel signals, this method successfully extracts the pure dynamic clearance signal of the bearing with high-frequency pulse impact characteristics using the principle of maximizing kurtosis. It also eliminates the interference of low-frequency bending and deflection components of the spindle on stiffness calculation, so that the final calculated equivalent dynamic stiffness can reflect the true mechanical ability of the micro-bearing to resist external deformation under extreme thermal expansion. This invention addresses the risk of thermal seizure and jamming of miniature bearings under ultra-high-speed operation and rapid temperature rise. It introduces the rapidly increasing decoupling steady-state error parameter caused by the rigid contact between the spindle and bearing into the penalty function equation, establishing a nonlinear exponentially amplified dynamic mapping relationship between the decoupling steady-state error and the penalty parameter. Approaching the critical temperature rise point, it can apply an exponentially increasing penalty force. Based on the penalty characteristic, the optimization space is reduced and decoupled. Through analytical solution, a control vector is forced to be output that satisfies the absolute zero product of the dynamic reduction of radial load and the dynamic increase of cooling flow rate. This unilateral defense control strategy eliminates the severe cross-coupling oscillations generated when the hydraulic servo system and thermodynamic balance system of the test bench simultaneously perform unloading and powerful cooling actions. While ensuring that the spindle and test equipment are protected from physical damage, it achieves a safe and accurate exploration of the specific performance evolution law and failure boundary of miniature bearings under extreme operating conditions.

[0043] Those skilled in the art will understand that embodiments of the present invention can be provided as methods, systems, or computer program products. Therefore, the present invention can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention can take the form of a computer program product implemented on one or more computer-usable storage media containing computer-usable program code. The storage medium can be implemented by any type of volatile or non-volatile storage device or a combination thereof, such as Static Random Access Memory (SRAM), Electrically Erasable Programmable Read-Only Memory (EEPROM), Erasable Programmable Read Only Memory (EPROM), Programmable Read-Only Memory (PROM), Read-Only Memory (ROM), magnetic storage, flash memory, magnetic disk, or optical disk. These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0044] It should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended 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 protection scope of the present invention.

Claims

1. A method for testing the high-speed rotational performance of a miniature bearing, characterized in that, Includes the following steps: Step S1: Collect the spindle end displacement sequence, test seat displacement sequence, and transient temperature of the test miniature bearing; Step S2: Based on the adaptive local iterative filtering algorithm, the displacement sequence of the main shaft end and the displacement sequence of the test seat are denoised and decomposed to obtain a set of multi-order intrinsic mode matrices; Step S3: Whiten and reduce the dimensionality of the multi-order intrinsic mode matrix set to obtain the multi-source heterogeneous decoupling matrix, solve the separation matrix based on the improved whale optimization algorithm, and calculate the decoupling steady-state error parameters; Step S4: Using the product of the dynamic reduction of radial load and the dynamic increase of cooling flow rate being zero as a constraint condition, a penalty function equation is constructed in conjunction with the decoupled steady-state error parameter for solution, and the control vector is output. Step S5: Perform unilateral control according to the control vector, and calculate the equivalent dynamic stiffness by combining the bearing's pure dynamic clearance signal to generate the micro-bearing performance test results.

2. The method for testing the high-speed rotational performance of miniature bearings as described in claim 1, characterized in that, Step S1 includes the following sub-steps: Step S101: According to the preset sampling frequency and preset time window, the displacement of the spindle end is collected as the first displacement sequence, and the displacement of the outside of the test seat is collected as the second displacement sequence. Step S102: Collect the transient temperature of the outer ring of the current miniature bearing.

3. The method for testing the high-speed rotational performance of miniature bearings as described in claim 2, characterized in that, Step S2 includes the following sub-steps: Step S201: Extract all the maximum and minimum points and their sampling point numbers in the first displacement sequence to form an initial extreme point number sequence; Step S202: Calculate the distance between the sampling point numbers corresponding to two adjacent in-phase extreme points as the first distance, take half of the first distance as the local extreme value scale, and take the median of all local extreme value scales as the benchmark extreme value scale. Step S203: Calculate the distance between the sampling point numbers corresponding to adjacent maxima and minima as the second distance. If the second distance is greater than or equal to a preset multiple of the benchmark extreme value scale, calculate the pseudo extreme value point number between the sampling point numbers corresponding to adjacent maxima and minima through linear interpolation and rounding operations, and insert the pseudo extreme value point number into the corresponding position in the initial extreme value point number sequence to obtain the first extreme value point number sequence.

4. The method for testing the high-speed rotational performance of miniature bearings as described in claim 3, characterized in that, Step S2 further includes the following sub-steps: Step S204: Based on the difference between adjacent extreme point numbers in the first extreme point number sequence, allocate a filter window width to the sampling point corresponding to each extreme point number, assign filter window width values ​​to the beginning and end endpoint regions, and use the piecewise cubic Hermitian interpolation polynomial algorithm to smoothly fill the assigned filter window width to obtain the initial filter sequence. Step S205: Extract the maximum and minimum points of the initial filter sequence, and use the piecewise cubic Hermitian interpolation polynomial algorithm to fit and generate the upper envelope curve and the lower envelope curve respectively. Average the values ​​of the upper envelope curve and the lower envelope curve at the same sampling point to obtain the de-oscillation smoothing filter sequence. The elements in the deoscillation smoothing filter sequence are used as the standard deviation parameters of the Gaussian filter, and point-by-point convolution operations are performed with the first displacement sequence to obtain the first local mean baseline sequence. Subtract the first local mean baseline sequence from the first displacement sequence to obtain the first-order intrinsic mode sequence, and repeat the above steps with the first local mean baseline sequence as the new sequence to obtain multi-order intrinsic mode sequences. Step S206: Process the second displacement sequence using the same method to obtain the corresponding multi-order intrinsic mode sequence; Step S207: Concatenate the eigenmode sequences of the same order in the first displacement sequence and the second displacement sequence row by row to obtain a set of multi-order eigenmode matrices.

5. The method for testing the high-speed rotational performance of miniature bearings as described in claim 4, characterized in that, Step S3 includes the following sub-steps: Step S301: Concatenate the multi-order intrinsic mode matrix set sequentially to obtain the initial observation matrix; Step S302: Calculate the covariance matrix of the initial observation matrix and perform eigenvalue decomposition. Sort the eigenvalues ​​from largest to smallest, extract the eigenvectors corresponding to the first two eigenvalues, arrange them in rows, and construct a whitening dimensionality reduction matrix. Multiply the whitening dimensionality reduction matrix by the initial observation matrix to obtain the multi-source heterogeneous decoupling matrix.

6. The method for testing the high-speed rotational performance of miniature bearings as described in claim 5, characterized in that, Step S3 further includes the following sub-steps: Step S303: Construct a fitness optimization equation with the goal of maximizing the negative entropy of the separated signal, and convert the maximization of negative entropy into an optimization form that seeks the minimum value; The logistic chaotic mapping equation is used to generate a preset number of initial step size position parameters, and an initial separation matrix after Schmitt orthogonalization is generated. The inverse solution is calculated by the inverse learning equation. The initial step size position parameter and the inverse solution are substituted into the damped Newton iteration equation to calculate the test separation matrix. The test separation matrix is ​​multiplied by the multi-source heterogeneous decoupling matrix to obtain the separation signal. The separation signal is substituted into the fitness optimization equation to calculate the fitness. The preset number parameter with the smallest fitness is selected as the initial population array.

7. The method for testing the high-speed rotational performance of miniature bearings as described in claim 6, characterized in that, Step S3 further includes the following sub-steps: S304, in the iterative optimization process, uses the spiral position update equation combined with the Lévy flight perturbation equation to update the step size parameter and obtain the globally optimal step size parameter; The globally optimal step size parameter is substituted into the damping Newton iteration equation as a damping factor for iterative updating. The Frobenius norm of the difference between the separation matrices generated by two adjacent iterations is calculated and used as the decoupling steady-state error parameter. The iteration stops when the decoupling steady-state error parameter is less than a preset threshold or reaches a preset maximum number of iterations, and the final separation matrix is ​​obtained. S305, multiply the final separation matrix with the multi-source heterogeneous decoupling matrix to obtain the independent source data matrix, calculate the kurtosis value of each row vector in the independent source data matrix, sort the row vectors in descending order of kurtosis value, and extract the row vector with the largest kurtosis value as the bearing pure dynamic clearance signal.

8. The method for testing the high-speed rotational performance of miniature bearings as described in claim 4, characterized in that, Step S4 includes the following sub-steps: Step S401: Construct a first variable and a second variable, wherein the first variable is a normalized radial load dynamic reduction amount, and the second variable is a normalized cooling flow rate dynamic increase amount, and the product of the first variable and the second variable is zero as a hard constraint equation. The hard constraint equation is transformed into a penalty function equation, the mathematical expression of which is: ； in, As the first variable, As the second variable, For penalty parameters, The penalty function equation is... The basic objective equation; The mathematical expression of the basic objective equation is: ； in, Based on the objective equation, As the first variable, As the second variable, and To control energy loss weight, As the weight for temperature tracking error, Transient temperature, For safe temperature, The equivalent cooling constant is reduced for full-scale load. To increase the equivalent cooling constant for full-scale cooling, This is the limit of permissible temperature difference constant.

9. The method for testing the high-speed rotational performance of miniature bearings as described in claim 8, characterized in that, Step S4 further includes the following sub-steps: Step S402: Establish a nonlinear exponential amplification dynamic mapping equation between the penalty parameter and the decoupled steady-state error parameter, and assign values ​​to the penalty parameter in the penalty function equation based on the dynamic mapping equation; Based on the limit penalty characteristic of the penalty function equation on non-zero products when the penalty parameter tends to the maximum value, at least one of the first variable and the second variable is set to zero, and the penalty function equation is decoupled into a first one-dimensional optimization sub-equation when the first variable is zero, and a second one-dimensional optimization sub-equation when the second variable is zero. Non-negative boundary constraints are set for the first and second variables. The first and second one-dimensional optimization sub-equations are solved analytically to obtain the corresponding first and second local optimal solutions. The first and second local optimal solutions are substituted back into the penalty function equation for comparison. A set of variables that makes the calculation result of the penalty function equation smaller is selected as the final first and second variables, and inverse normalization is performed to construct the control vector.

10. The method for testing the high-speed rotational performance of miniature bearings as described in claim 9, characterized in that, Step S5 includes: Step S501: The first element of the control vector is used as the first control quantity and the second element is used as the second control quantity, which are then converted into the first analog voltage signal and the second analog voltage signal, respectively. The first analog voltage signal is transmitted to the hydraulic servo valve that controls the radial load, and the second analog voltage signal is transmitted to the proportional regulating valve that controls the cooling flow rate. Step S502: Take the square root of the sum of the squares of all elements in the bearing pure dynamic clearance signal to obtain the equivalent dynamic clearance scalar. The actual radial load scalar is divided by the calculated result of the equivalent dynamic clearance scalar to obtain the equivalent dynamic stiffness, wherein the actual radial load scalar is the difference between the applied base radial load and the first control quantity. Collect the current rotational speed and the current transient temperature, and concatenate the current rotational speed, the equivalent dynamic stiffness, and the current transient temperature into an independent state row vector; Step S503: Concatenate the independent state row vectors row by row in chronological order to obtain the state evolution matrix; The state evolution matrix is ​​used as the performance test result of the miniature bearing.

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