A mechanical equipment machining tool feed speed control system

Abstract

The application discloses a mechanical equipment machining tool feed speed control system and belongs to the technical field of machining control. The system comprises a signal acquisition module, a chaotic analysis module, a recursive adjustment module and an optimization control module. The signal acquisition module acquires cutting force signals and tool vibration signals in real time, performs cooperative phase space reconstruction on the cutting force signals and the tool vibration signals, and obtains high-dimensional phase trajectories. The chaotic analysis module calculates the correlation dimension and the Kolmogorov entropy of the high-dimensional phase trajectories, and judges the chaotic degree of a cutting state according to the change rates of the correlation dimension and the Kolmogorov entropy. When the chaotic degree exceeds a set threshold, the recursive adjustment module extracts the recurrence rate of the cutting force signals based on a recurrence plot, and dynamically adjusts a feed speed reference value. Meanwhile, the tool vibration signals are subjected to local mean decomposition, a cutting chatter characteristic vector is constructed, and the cutting chatter characteristic vector is input into an extreme learning machine model to output a chatter risk grade. The optimization control module updates a feed speed control increment by using an adaptive momentum algorithm, fuses speed smoothness constraints, solves an optimal feed speed by using a Lagrange multiplier method, and converts the optimal feed speed into a servo driving instruction output.

Description

Technical Field

[0001] This invention relates to the field of machining control technology, specifically to a feed speed control system for machining tools in mechanical equipment. Background Technology

[0002] In machining, tool feed rate directly affects machining efficiency, surface quality, and tool life. Cutting force signals and tool vibration signals contain rich information about the machining state, and how to utilize these signals to achieve adaptive control of feed rate is a key focus in this field. In existing technologies, some solutions adjust feed rate by setting a fixed threshold or using simple proportional-integral-derivative (PID) control. These methods are effective under stable cutting conditions, but when the cutting process enters a strongly nonlinear state due to abrupt changes in depth of cut, material hardening, or regeneration effects, it is difficult to perceive changes in the system's dynamic characteristics in real time, easily leading to response lag or improper speed adjustment. Another approach introduces time-frequency analysis or power spectrum characteristics of a single signal to determine chatter and suppresses speed based on empirical rules. This method fails to effectively characterize the transition from ordered to chaotic cutting states, lacks sufficient ability to identify early signs of instability, and often lacks smooth optimization in speed adjustment, affecting workpiece surface quality. Furthermore, when using machine learning models to assess chatter risk, some methods rely on manually designed features, which have limited generalization performance under complex operating conditions. Moreover, the control system fails to effectively combine risk assessment with speed planning that meets kinematic constraints, resulting in jumps in command speed or exceeding the dynamic range allowed by the machine tool.

[0003] One problem this solution needs to address is how to extract features describing the nonlinear dynamic state of the system from cutting force and vibration signals, achieve sensitive discrimination of the degree of cutting chaos, and determine the appropriate timing and magnitude for adjusting the feed rate reference accordingly. Another problem is how to predict the risk level based on the fine time-frequency structure of the vibration signal in the presence of chatter risk, and combine this risk information with feed rate constraint optimization to obtain the optimal speed command that both suppresses chatter and meets the requirements of machine tool motion smoothness. Summary of the Invention

[0004] This invention provides a feed speed control system for machining tools in mechanical equipment. It aims to accurately determine the degree of chaos in the cutting process and adaptively adjust the feed speed reference by utilizing cooperative phase space reconstruction and chaotic feature analysis. At the same time, it predicts chatter risk by adaptive decomposition of vibration signals and limit learning machine, and solves the optimal feed speed by combining adaptive momentum optimization and speed smoothing constraints, thereby achieving high-speed and stable control of the machining process.

[0005] The objective of this invention can be achieved through the following technical solutions: A feed rate control system for machining tools in mechanical equipment includes a signal acquisition module, a chaos analysis module, a recursive adjustment module, a chatter risk assessment module, and an optimization control module. The signal acquisition module acquires cutting force signals and tool vibration signals in real time during the machining process, and performs collaborative phase space reconstruction of the two signals to obtain a high-dimensional phase trajectory. By fusing multi-source signals, it fully captures the coupled dynamic characteristics of force and vibration during the cutting process. The chaos analysis module calculates the correlation dimension and Kolmogorov entropy of the high-dimensional phase trajectory, and determines the degree of chaos in the current cutting state based on the rate of change of the correlation dimension and the Kolmogorov entropy, thereby achieving quantitative assessment and early warning of the nonlinear stability of the cutting process. When the degree of chaos exceeds a set threshold, the recursive adjustment module extracts the recursion rate of the cutting force signal based on a recursive graph analysis method. It then dynamically adjusts the baseline value of the feed rate according to this recursion rate to actively suppress further expansion of the chaotic state. Simultaneously, the module uses a sliding window to perform local mean decomposition on the tool vibration signal, obtaining multiple product function components. Based on the instantaneous frequency and amplitude of each product function component, it constructs a chatter feature vector, thereby resolving the complex vibration signal into chatter characterization parameters with clear physical meaning. The chatter risk assessment module inputs the cutting chatter feature vector into an extreme learning machine model and outputs the chatter risk level. Leveraging the advantages of the extreme learning machine—fast training speed and strong generalization ability—it meets the requirements for online real-time assessment. The optimization control module iteratively updates the control increment of the feed rate using an adaptive momentum algorithm based on the chatter risk level and the current feed rate. It then integrates the control increment with the speed smoothing constraint, solves the constraint optimization problem using the Lagrange multiplier method, and obtains the optimal feed rate. This optimal feed rate is converted into servo drive commands and output to the machine tool controller, thereby effectively suppressing cutting chatter while ensuring a smooth transition of the speed curve, improving the surface finish and tool life.

[0006] As a preferred technical solution of the present invention, the specific process of the cooperative phase space reconstruction is as follows: the time delay of the cutting force signal is calculated using the mutual information method, the embedding dimension is calculated using the false nearest neighbor method, and the initial phase space of the cutting force signal is constructed based on the time delay and the embedding dimension; the initial phase space of the tool vibration signal is constructed using the same time delay and embedding dimension; each phase point in the initial phase space of the cutting force signal is longitudinally spliced ​​with the phase point at the corresponding time in the initial phase space of the tool vibration signal to form a high-dimensional phase point, and the high-dimensional phase points at all times are arranged in chronological order to form the high-dimensional phase trajectory, thereby realizing the deep fusion of the dynamic information of the force signal and the vibration signal.

[0007] As a further improvement of the present invention, the process of the chaos analysis module calculating the correlation dimension and Kolmogorov entropy and determining the degree of chaos is specifically as follows: Multiple different distance scales are set; for each distance scale, the proportion of points in the high-dimensional phase trajectory whose distance between any two phase points is less than that distance scale is statistically analyzed to obtain the correlation integral; the correlation integral is linearly fitted to the distance scale in a double logarithmic coordinate system, and the fitting slope is used as the correlation dimension; the high-dimensional phase trajectory is divided into multiple trajectory segments of equal length, the maximum Lyapunov exponent between phase points within each trajectory segment is calculated, and the average of the maximum Lyapunov exponents of each trajectory segment is used as the Kolmogorov entropy; the first difference of the correlation dimension within a preset time window before the current sampling time is calculated as the first rate of change, and the first difference of the Kolmogorov entropy is calculated as the second rate of change; when both the first rate of change and the second rate of change are greater than their respective historical moving averages, the degree of chaos is determined to exceed a set threshold. Preferably, the multiple different distance scales are set according to a geometric series, and the ratio of adjacent distance scales is the square root of two, making the estimation of the correlation integral more stable.

[0008] As another preferred embodiment of the present invention, the process by which the recursive adjustment module extracts the recursion rate of the cutting force signal based on the recursion graph analysis and adjusts the feed rate reference value is as follows: the cutting force signal is delayed and embedded on the time axis to obtain a state vector sequence of the recursion graph; the Euclidean distance between any two state vectors in the state vector sequence is calculated, and a recursion matrix is ​​generated according to the relationship between the Euclidean distance and a preset recursion threshold. Each element in the recursion matrix indicates whether the corresponding two state vectors are recursive; the ratio of the number of recursive points to the total number of elements in the recursion matrix is ​​counted as the recursion rate; the current feed rate reference value is multiplied by an adjustment coefficient proportional to the recursion rate to obtain the adjusted feed rate reference value, wherein the minimum value of the adjustment coefficient is one, and the maximum value is a preset upper limit value. The preset recursion threshold can be dynamically determined by multiplying the average Euclidean distance between all state vectors in the state vector sequence by a proportional coefficient to adapt to different cutting conditions.

[0009] In a preferred embodiment of the present invention, the recursive adjustment module performs local mean decomposition on the tool vibration signal and constructs a cutting chatter feature vector as follows: The length and step size of the sliding window are determined, and a segment of the tool vibration signal is extracted at each window position as a local signal; for each local signal, a local mean function and a local envelope function are constructed by detecting its local extreme points; the local mean function is separated from the local signal and divided by the local envelope function to obtain a frequency-modulated signal; this separation process is iterated until the envelope function of the frequency-modulated signal is close to a constant; the product of all local envelope functions in the last iteration is taken as a product function component of the local signal; the product function component is subtracted from the original local signal, and the above process is repeated to extract the next product function component until the remaining signal is a monotonic function; a Hilbert transform is performed on each product function component to calculate its instantaneous frequency and instantaneous amplitude; the variance of the instantaneous frequency and the attenuation rate of the instantaneous amplitude of each product function component are calculated; the variances and attenuation rates of all product function components are concatenated in sequence to form the cutting chatter feature vector. The iterative separation process continues until the envelope function of the frequency modulation signal approaches a constant, provided that the difference between the maximum and minimum values ​​of the envelope function is less than a preset tolerance threshold, thus ensuring decomposition accuracy.

[0010] As a preferred embodiment of the present invention, the extreme learning machine model in the chatter risk assessment module is obtained and applied in the following manner: various chatter samples under different feed rate conditions are pre-collected; a corresponding chatter feature vector is extracted for each sample, and the chatter risk level is manually labeled, whereby the chatter risk level is a continuous numerical value or a discrete level; an extreme learning machine model containing an input layer, a single hidden layer, and an output layer is constructed; the connection weights from the input layer to the hidden layer and the biases of the hidden layer neurons are randomly initialized; the chatter feature vector is used as the input to the input layer; after nonlinear mapping of the hidden layer, the output weights from the hidden layer to the output layer are calculated using the least squares method; during online evaluation, the chatter feature vector constructed at the current moment is input into the trained extreme learning machine model, and the output value of the output layer is calculated through forward propagation, with this output value serving as the chatter risk level.

[0011] As a further optimization of the present invention, the process of the optimization control module iteratively updating the control increment of the feed rate using the adaptive momentum algorithm is as follows: the initial control increment of the feed rate is set to zero, and the gradient at the current moment is set to the partial derivative of the flutter risk level with respect to the feed rate at the previous moment; the exponentially weighted moving average of the gradient at the current moment is calculated as the first moment estimate, and the exponentially weighted moving average of the square of the gradient at the current moment is calculated as the second moment estimate; the first moment estimate and the second moment estimate are corrected for deviation, and the corrected first moment estimate is divided by the square root of the corrected second moment estimate, and then multiplied by a preset learning rate to obtain the update step size for this iteration; the control increment at the previous moment is subtracted from the update step size to obtain the updated control increment of the feed rate, thereby adaptively adjusting the optimization step size to improve the convergence speed and stability.

[0012] In a preferred embodiment of the present invention, the optimization control module integrates the control increment and speed smoothing constraints to solve for the optimal feed rate as follows: An objective function is constructed to minimize the change in feed rate, where the change is the difference between the current feed rate and the previous feed rate minus the square of the control increment; speed smoothing constraints are set, including that the absolute value of the first-order difference of the feed rate does not exceed the maximum acceleration limit, and the absolute value of the second-order difference of the feed rate does not exceed the maximum acceleration limit; the objective function and the speed smoothing constraints are combined into a Lagrange function, and non-negative Lagrange multipliers are introduced to correspond to each inequality constraint; the partial derivative of the Lagrange function with respect to the current feed rate is calculated and set to zero to obtain the optimality condition equation; simultaneously, the optimality condition equation and the complementary relaxation condition equation are solved to obtain the current feed rate that satisfies all constraints as the optimal feed rate, thereby ensuring that the speed change is always within the dynamic permissible range of the machine tool and avoiding excessive impact.

[0013] As another preferred embodiment of the present invention, the step of converting the optimal feed speed into a servo drive command and outputting it is as follows: obtaining the speed loop transfer function model of the machine tool servo drive system, determining the dynamic response delay time from the speed command to the actual speed based on the transfer function model; using the optimal feed speed as the input setpoint of the speed loop, pre-compensating the optimal feed speed through the inverse function of the transfer function model to generate a pre-compensated speed command; encapsulating the pre-compensated speed command into a standard data frame format according to the communication protocol of the machine tool controller; and sending the data frame to the servo driver in the machine tool controller through a fieldbus or analog interface to achieve high-precision speed tracking control.

[0014] The beneficial effects of this invention are: A collaborative phase space reconstruction method is employed, where cutting force signals and tool vibration signals are separately constructed into initial phase spaces and then longitudinally stitched together to form a high-dimensional phase trajectory. This method integrates the dynamic information of the two heterogeneous signals, reflecting the multidimensional state evolution characteristics of the cutting system. Based on this, the correlation dimension and Kolmogorov entropy are calculated, and the degree of chaos is determined by the combined rate of change of both, rather than relying on a single fixed threshold. This allows for timely capture of the tendency for nonlinear enhancement when the cutting state transitions from ordered to chaotic. When the degree of chaos exceeds a set condition, recursion graph analysis is used to extract the recursion rate from the cutting force signal. The feed rate reference value is then dynamically adjusted by multiplying it by an adjustment coefficient proportional to the recursion rate. This allows the feed rate to adjust accordingly based on changes in the deterministic structure of the signal, avoiding tool damage or machining instability caused by maintaining a high feed rate when chaos intensifies. This approach directly correlates nonlinear dynamic indicators with real-time speed reference adjustment, overcoming the shortcomings of traditional methods in responding slowly to unsteady cutting conditions.

[0015] The tool vibration signal is decomposed using a sliding window local mean decomposition to adaptively obtain multiple product function components. The instantaneous frequency and amplitude of each component are calculated using Hilbert transform, and a cutting chatter feature vector is constructed using its instantaneous frequency variance and instantaneous amplitude decay rate. This feature extraction method does not require preset basis functions and can capture the frequency energy distribution and amplitude evolution before and after chatter occurs, providing a physically meaningful input for the Extreme Learning Machine (ELM). The ELM model randomly generates hidden layer parameters and determines the output weights using least squares, resulting in high training efficiency and the ability to quickly output continuous or discrete chatter risk levels. After obtaining the chatter risk level, an adaptive momentum algorithm is used to iteratively update the feed rate control increment. By estimating the gradient moments and correcting for deviations, the increment update maintains momentum inertia in the direction of risk change and can adaptively adjust the step size, reducing oscillations and overshoot during the control process. By integrating the control increment with speed smoothing constraints including maximum acceleration and maximum jerk limits, a constraint optimization objective is constructed. The Lagrange multiplier method is used to solve the objective, ensuring that the obtained optimal feed speed strictly meets the dynamic capabilities of the machine tool drive system and avoids abrupt changes and discontinuities in speed commands. This achieves refined feed control that balances chatter suppression and motion smoothness. Attached Figure Description

[0016] The invention will now be further described with reference to the accompanying drawings.

[0017] Figure 1 This is a flowchart of the feed speed control system for machining tools in mechanical equipment. Figure 2 This is a flowchart of phase space reconstruction and high-dimensional phase trajectory construction of cutting force and tool vibration signal; Figure 3 This is a flowchart of a cutting chatter suppression method based on adaptive feed rate adjustment. Detailed Implementation

[0018] 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, and 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.

[0019] See Figure 1 This invention provides a feed rate control system for machining tools. A signal acquisition module collects cutting force signals and tool vibration signals in real time during the machining process, and reconstructs the phase space of these two signals to obtain a high-dimensional phase trajectory. A chaos analysis module calculates the correlation dimension and Kolmogorov entropy of the high-dimensional phase trajectory, and determines the degree of chaos in the current cutting state based on the rate of change of the correlation dimension and Kolmogorov entropy. A recursive adjustment module extracts the recursion rate of the cutting force signal based on a recursive graph analysis method when the degree of chaos exceeds a set threshold, and dynamically adjusts the baseline value of the feed rate based on the recursion rate. The recursive adjustment module uses a sliding window to... The tool vibration signal undergoes local mean decomposition to obtain multiple product function components. A chatter feature vector is constructed based on the instantaneous frequency and amplitude of each product function component. The chatter risk assessment module inputs the chatter feature vector into an extreme learning machine model and outputs the chatter risk level. The optimization control module iteratively updates the feed rate control increment using an adaptive momentum algorithm based on the chatter risk level and the current feed rate. The control increment is then fused with the speed smoothing constraint, and the constraint optimization problem is solved using the Lagrange multiplier method to obtain the optimal feed rate. Finally, the optimal feed rate is converted into servo drive commands and output to the machine tool controller.

[0020] In specific implementation, please refer to Figure 2 After acquiring cutting force and tool vibration signals, the time delay of the cutting force signal is calculated using the mutual information method. The cutting force signal is discretized at a fixed sampling frequency to obtain a cutting force signal time series, where each value corresponds to the cutting force amplitude at a sampling moment. A delay time variable is set, and the mutual information value of the cutting force signal time series is calculated for different values ​​of the delay time variable. The formula for calculating the mutual information value is:

[0021] in, This indicates the cutting force signal at time [time]. The sampled values, This indicates the cutting force signal at time [time]. The sampled values, For delay time variables, for Marginal probability distribution, for Marginal probability distribution, for and The joint probability distribution, Delay time variable The corresponding mutual information value. The marginal probability distribution and joint probability distribution are obtained by dividing the sampled values ​​of the cutting force signal time series into intervals and performing frequency statistics. The curve of mutual information value changing with the delay time variable is plotted, and the delay time variable corresponding to the first local minimum point on the mutual information value curve is taken as the time delay of the cutting force signal.

[0022] The embedding dimension of the cutting force signal is calculated using the spurious nearest neighbor method. After determining the time delay of the cutting force signal, the embedding dimension is gradually increased from an initial value. At each embedding dimension, the time series of the cutting force signal is reconstructed in phase space using the time delay and the current embedding dimension to obtain a set of phase points. For each phase point, the nearest neighbor is found, and the rate of change of the distance between the phase point and its nearest neighbor is calculated after increasing the embedding dimension by one dimension. When the proportion of phase points whose distance change rate exceeds a preset threshold is lower than a preset proportion threshold, the current embedding dimension is taken as the embedding dimension of the cutting force signal. The preset threshold is typically a constant between 10 and 15, and the preset proportion threshold is 5%.

[0023] The initial phase space of the cutting force signal is constructed based on the calculated time delay and embedding dimension. The length of the cutting force signal time series is... Time delay is denoted as Embedding dimension is denoted as Then the first phase space of the cutting force signal The vectors of each phase point are represented as follows: ,in, For the cutting force signal at time 10:00 The sampled values, The range of values ​​is from arrive All phase point vectors, arranged in time sequence, constitute the initial phase space of the cutting force signal.

[0024] The initial phase space of the tool vibration signal is constructed using the same time delay and embedding dimension as the cutting force signal. The time series length of the tool vibration signal is... Using the same signal as the cutting force and Then the first phase space of the tool vibration signal The vectors of each phase point are represented as follows: ,in For the tool vibration signal at time 10:00 The sampled values, The range of values ​​also starts from... arrive All phase point vectors, arranged in time sequence, constitute the initial phase space of the tool vibration signal.

[0025] Each phase point in the initial phase space of the cutting force signal is longitudinally spliced ​​with the corresponding phase point in the initial phase space of the tool vibration signal at the same time, forming a high-dimensional phase point. For time... The initial phase point vector of the cutting force signal in phase space is The initial phase point vector of the tool vibration signal in phase space is By concatenating the two vectors sequentially, a high-dimensional phase point vector is obtained. For each valid moment All phase points are spliced ​​together, arranging them in chronological order to form a high-dimensional phase trajectory. The dimension of each phase point in the high-dimensional phase trajectory is the sum of the embedding dimension of the cutting force signal and the embedding dimension of the tool vibration signal, i.e. .

[0026] In practice, when setting multiple different distance scales, a distance scale sequence is generated according to a geometric progression. An initial distance scale is determined, and the next distance scale is obtained by multiplying the initial distance scale by the square root of 2. This process iteratively generates the distance scale sequence until its length meets a preset requirement. The ratio of adjacent distance scales is fixed. To ensure that the distance scale is uniformly distributed in the logarithmic coordinate system, the data points are reasonably distributed during double logarithmic linear fitting. The initial distance scale is taken as the minimum distance between any two phase points in the high-dimensional phase trajectory.

[0027] For each distance scale in the distance scale sequence, the proportion of points in the high-dimensional phase trajectory whose distance to any two phase points is less than the distance scale is calculated, yielding the correlation integral corresponding to the distance scale. The high-dimensional phase trajectory is formed by... It consists of _ high-dimensional phase points, with a total number of phase points of _ . From the high-dimensional phase trajectory, take all phase point pairs consisting of two distinct phase points, and calculate the Euclidean distance between the two phase points in each pair. Set the current distance scale to [scale value]. The statistical Euclidean distance is less than The number of phase pairs will make the Euclidean distance less than The number of phase pairs divided by the total number of phase pairs The resulting ratio is the distance scale. The corresponding integral.

[0028] Plot the data points corresponding to each distance scale on a double logarithmic coordinate system, with the logarithm of the distance scale as the x-axis and the logarithm of the correlation integral as the y-axis. Perform linear fitting on the data points using the least squares method; the slope of the fitted line is the correlation dimension. Let the x-axis be... The vertical axis is ,in, Using distance as the scale, Distance scale The corresponding integral, The natural logarithm is given. The slope of the line obtained from the linear fit is... , This refers to the numerical value of the correlation dimension.

[0029] The high-dimensional phase trajectory is divided into multiple trajectory segments of equal length. The length of each trajectory segment is then determined. This makes the total number of phase points of the high-dimensional phase trajectory... Can be measured by trajectory segment length Divisible by, we get A trajectory segment, Within each trajectory segment, starting from the first phase point, adjacent phase points are sequentially selected, and the phase space distance between adjacent phase points is calculated. The maximum Lyapunov exponent of the trajectory segment is then calculated using the evolution trajectory of the phase space distance. For the th... The trajectory segment, with the largest Lyapunov exponent denoted as . , The value is arrive An integer. The arithmetic mean of the maximum Lyapunov exponents of each trajectory segment is used to obtain the Kolmogorov entropy, which is denoted as . The calculation formula is:

[0030] in, For Kolmogorov entropy, The total number of trajectory segments. For the first The maximum Lyapunov index of each trajectory segment Indicates to from arrive of Sum.

[0031] When calculating the first difference of the correlation dimension, first determine the length of the preset time window before the current sampling time. Preset time window length In terms of the number of sampling points, The value is an integer between 100 and 200, determined based on the sampling frequency of the cutting force signal, ensuring that the preset time window covers the duration of at least one complete cutting cycle. Within the preset time window, the time series of the correlation dimension is taken, and the difference between the correlation dimensions of two adjacent moments in the correlation dimension time series is calculated. The absolute value of the difference is taken as the first-order difference value of the correlation dimension. The first-order difference value corresponding to the last term in the first-order difference value sequence is the first rate of change at the current moment.

[0032] When calculating the first difference of Kolmogorov entropy, the time series of Kolmogorov entropy is taken within the same preset time window. The difference between the Kolmogorov entropy at two adjacent moments in the Kolmogorov entropy time series is calculated. The absolute value of the difference is taken as the first difference of Kolmogorov entropy. The first difference value corresponding to the last term in the first difference value sequence is the second rate of change at the current moment.

[0033] When determining whether the degree of chaos exceeds a set threshold, the historical moving average of the correlation dimension and the historical moving average of the Kolmogorov entropy are calculated respectively. The historical moving average of the correlation dimension is the arithmetic mean of the first-order differences of all correlation dimensions within a historical time period twice the length of the preset time window. The historical moving average of the Kolmogorov entropy is the arithmetic mean of the first-order differences of all Kolmogorov entropy within the same historical time period. When the first rate of change is greater than the historical moving average of the correlation dimension, and the second rate of change is greater than the historical moving average of the Kolmogorov entropy, the degree of chaos in the current cutting state is determined to exceed the set threshold.

[0034] In practical implementation, when the degree of chaos exceeds a set threshold, the cutting force signal is delayed and embedded on the time axis to obtain a state vector sequence of the recursive graph. The cutting force signal has a length of... The one-dimensional time series uses the same time delay as in the initial phase space construction process of the aforementioned cutting force signal. and embedding dimension As a delay embedding parameter, the cutting force signal time series is used as the [missing parameter]. Each sampled value is denoted as Then the first The state vectors are represented as follows: ,in, The range of values ​​is arrive Integers. All state vectors are ordered by... The values ​​of are arranged in ascending order to form a state vector sequence, and the total number of state vectors in the state vector sequence is denoted as . , .

[0035] Calculate the Euclidean distance between any two state vectors in the state vector sequence. State vectors and the State vectors Euclidean distance The calculation method is as follows: Calculate The Middle Each component and The Middle The difference between each component is calculated by summing the squares of the differences and taking the arithmetic square root. The value is arrive Integers. and The values ​​are all arrive an integer, and and different.

[0036] A recursion matrix is ​​generated based on the relationship between Euclidean distance and a preset recursion threshold. The preset recursion threshold is determined as follows: first, the average Euclidean distance between all state vectors in the state vector sequence is obtained; then, the sum of the Euclidean distances of all distinct state vector pairs is calculated and divided by the total number of state vector pairs. The average Euclidean distance is obtained. This average Euclidean distance is then multiplied by a scaling factor to obtain a preset recursive threshold. The scaling factor is a constant between 0.1 and 0.2, selected based on the amplitude fluctuation range of the cutting force signal. A larger scaling factor is used when the amplitude fluctuation range of the cutting force signal is large, and a smaller scaling factor is used when the amplitude fluctuation range of the cutting force signal is small.

[0037] When generating the recursive matrix, construct a matrix of size . The square formation, the first in the square formation Line 1 The elements of a column are denoted as When Euclidean distance When less than or equal to the preset recursion threshold, The value is 1, indicating the first... The state vector and the th state vector Recursively assigning state vectors. When the Euclidean distance... When the value is greater than the preset recursion threshold, A value of 0 indicates the first... The state vector and the th state vector The state vectors are non-recursive. Count the number of recursive points in the recursion matrix; a recursive point is an element in the recursion matrix with a value of 1. Iterate through all elements in the recursion matrix and count the number of elements with a value of 1 to obtain the number of recursive points. The total number of elements in the recursion matrix is... The recursion rate is the ratio of the number of recursive points to the total number of elements in the recursion matrix. The formula for calculating the recursion rate is:

[0038] in, For recursion rate, This represents the number of elements in the recursive matrix that have a value of 1. The total number of state vectors in the state vector sequence. This represents the total number of elements in the recursive matrix.

[0039] The current feed rate baseline value is multiplied by an adjustment coefficient proportional to the recursion rate to obtain the adjusted feed rate baseline value. The adjustment coefficient is calculated as follows: a minimum value of one is set, and a maximum value is set to a preset upper limit. The preset upper limit is a constant between 1.2 and 1.5, and its specific value is determined based on the ratio of the machine tool servo drive system's maximum allowable feed rate to the current baseline speed. Adjustment Coefficient The calculation formula is ,in, The preset upper limit value, This represents the recursion rate. When the recursion rate is 0, the adjustment coefficient takes its minimum value of 1, and the adjusted feed rate baseline is equal to the current feed rate baseline. When the recursion rate is 1, the adjustment coefficient takes its maximum value. The adjusted feed rate base value is equal to the current feed rate base value multiplied by The adjusted feed rate is obtained by multiplying the base value of the feed rate by the adjustment factor.

[0040] In practical implementation, when determining the length of the sliding window and the sliding step size, the length of the sliding window is determined based on the sampling frequency of the tool vibration signal and the duration of the tool's vibration cycle per revolution during the cutting process. The sampling frequency of the tool vibration signal is denoted as... The number of sampling points corresponding to each vibration cycle of the tool is denoted as The length of the sliding window is set to The sliding window is set to an integer multiple of the sliding window length, with the multiple being an integer between 2 and 4, so that the sliding window covers at least two complete tool vibration cycles. The sliding step size is set to an integer value between one-third and one-half of the sliding window length to retain partial overlap between adjacent windows and avoid abrupt changes in the product function components at the window boundaries.

[0041] When extracting a segment of the tool vibration signal as a local signal at each window position, starting from the initial sampling point of the tool vibration signal, the first local signal is extracted according to the sliding window length. Then, the window position is moved according to the sliding step size to extract the next local signal, until the end of the tool vibration signal. The subsequent local mean decomposition process is performed independently for each local signal.

[0042] When extracting the product function component for each local signal, all local extrema are first detected. Local extrema include local maxima and local minima. Local maxima are points where the sampled value is greater than the two adjacent sampled values, and local minima are points where the sampled value is less than the two adjacent sampled values. The upper envelope is constructed using cubic spline interpolation with the local maxima, and the lower envelope is constructed using cubic spline interpolation with the local minima. The values ​​of the upper and lower envelopes at each sampled point are added together and divided by 2 to obtain the local mean function. The local envelope function is obtained by subtracting the values ​​of the upper and lower envelopes at each sampled point, taking the absolute value, and then dividing by 2.

[0043] The difference signal is obtained by subtracting the local mean function from the local signal. The difference signal is then divided by the local envelope function to obtain the frequency-modulated signal. Local extrema are detected again on the frequency-modulated signal, and a new local envelope function is calculated, repeating the separation process. During iteration, the local envelope function corresponding to the frequency-modulated signal obtained in each iteration is monitored. Iteration stops when the difference between the maximum and minimum values ​​of the local envelope function is less than a preset tolerance threshold. The preset tolerance threshold is a constant between 0.001 and 0.01. The specific value of the tolerance threshold is set based on the normalized amplitude of the tool vibration signal. The tool vibration signal undergoes amplitude normalization during the preprocessing stage, normalizing the signal amplitude to between 0 and 1. At this point, the tolerance threshold is set to 0.005 to ensure that the envelope function of the frequency-modulated signal approaches a constant 1 under amplitude normalization conditions when the iteration terminates.

[0044] Multiplying the local envelope functions calculated in each iteration yields a product function component of the local signal. This product function component reflects the amplitude modulation characteristics of a specific frequency component within the local signal. The formula for calculating the product function component is:

[0045] in, For the first The components of the product function at time... The value of , These are the ordinal numbers of the components of the product function. For the first The envelope signals corresponding to the product function components at time t The value of is formed by the product of all local envelope functions in each iteration. For the first The pure frequency modulated signal corresponding to each product function component at time 1 The value of is derived from the frequency-modulated signal obtained in the last iteration. The extracted product function component is subtracted from the original local signal to obtain the residual signal. Using the residual signal as a new local signal, the complete process of local extremum detection, local mean function construction, local envelope function construction, iterative separation, and product function component extraction is repeated to obtain the next product function component. This process continues until the residual signal is a monotonic function. The criterion for a monotonic function is that the number of local extrema of the residual signal is less than or equal to 1, meaning the residual signal no longer exhibits oscillatory characteristics.

[0046] Perform a Hilbert transform on each component of the product function and calculate the instantaneous frequency and instantaneous amplitude. For the ... Each product function component Perform a Hilbert transform to obtain the Hilbert transform result. ,Will and Combined into analytical signals ,in, The imaginary unit is used. Instantaneous amplitude. To analyze the signal The modulus, instantaneous phase To analyze the signal Complex angle, instantaneous frequency instantaneous phase First derivative with respect to time divided by Calculate the instantaneous amplitude and instantaneous frequency at each time point in the product function component sequence.

[0047] To calculate the variance of the instantaneous frequency of each component of the product function, all instantaneous frequency values ​​in the time series of the instantaneous frequency of the product function component are substituted into the variance formula. The variance of the instantaneous frequency reflects the degree of fluctuation of the frequency components of the product function. To calculate the decay rate of the instantaneous amplitude of each component of the product function, an exponential curve is fitted to the instantaneous amplitude time series. The fitting model is as follows: ,in, The initial instantaneous amplitude, For the first The attenuation rate of the instantaneous amplitude of each component of the product function is estimated using the least squares method. The value of the instantaneous amplitude decay rate reflects the rate at which the energy of the product function components is dissipated.

[0048] Arrange the variances of the instantaneous frequencies and the attenuation rates of the instantaneous amplitudes of all product function components in sequential order of the product function component numbers. When arranging, first arrange the variances of the instantaneous frequencies of the first product function component, then arrange the attenuation rates of the instantaneous amplitudes of the first product function component, then the variances of the instantaneous frequencies and the attenuation rates of the instantaneous amplitudes of the second product function component, and so on, until all product function components are arranged. The resulting sequence is the cutting chatter characteristic vector.

[0049] In specific implementation, please refer to Figure 3 Cutting chatter samples under various feed rate conditions were pre-collected. During sample collection, a force gauge and an accelerometer were installed on the machine tool to collect cutting force signals and tool vibration signals, respectively. The feed rate values ​​covered the range of commonly used machining parameters of the machine tool. Multiple feed rate values ​​were selected from the minimum to the maximum allowable feed rate in an arithmetic sequence. The difference between adjacent feed rate values ​​was a fixed step size, which was a constant between 0.5 mm / min and 2 mm / min. Cutting was performed at each feed rate value, and the cutting force signal and tool vibration signal were recorded simultaneously to form a cutting chatter sample. For each cutting chatter sample, the corresponding cutting chatter feature vector was extracted according to the same process as real-time processing. The steps for extracting the cutting chatter feature vector included sliding window division, local mean decomposition to obtain product function components, calculation of the variance of the instantaneous frequency and the attenuation rate of the instantaneous amplitude of the product function components, and sequential concatenation.

[0050] After extracting the chatter feature vectors, each feature vector is manually labeled with its chatter risk level. During manual labeling, operators observe workpiece surface vibrations, machining noise, and tool wear during the cutting process at the machining site, labeling the chatter risk level as either a continuous numerical value or a discrete level. When using continuous numerical labeling, the chatter risk level ranges from 0 to 1, where 0 indicates no chatter risk, 1 indicates chatter has occurred and is severe, and values ​​between 0 and 1 represent different degrees of chatter tendency. When using discrete levels, the chatter risk level is divided into three levels: Level 1 indicates stable cutting, Level 2 indicates a critical chatter state, and Level 3 indicates chatter has occurred. All labeled samples constitute the training dataset.

[0051] Construct an extreme learning machine model consisting of an input layer, a single hidden layer, and an output layer. The number of neurons in the input layer is equal to the dimension of the cutting flutter feature vector, i.e., twice the number of components in the product function. When the number of components in the product function is... At that time, the dimension of the cutting chatter eigenvector is The number of neurons in the input layer is set accordingly. The number of neurons in a single hidden layer is set to an integer value between 2 and 5 times the number of neurons in the input layer. The specific number of neurons in the single hidden layer is selected from a candidate set on the training dataset using cross-validation, yielding the value that minimizes the prediction error on the validation set. The candidate set consists of an arithmetic sequence of integers with a common difference of 10, and its initial value is twice the number of neurons in the input layer. The output layer has 1 neuron and outputs a continuous tremor risk level value. The connection from the input layer to the single hidden layer uses a fully connected structure, with a connection weight between each input layer neuron and each single hidden layer neuron. Each neuron in the single hidden layer has a bias. The connection weights from the input layer to the single hidden layer and the biases of the single hidden layer neurons are randomly initialized. The random initialization method for the connection weights is based on intervals... The bias is randomly selected from a uniform distribution, and the initialization method of the bias is to start from the interval. The value is randomly selected from a uniform distribution.

[0052] The input matrix is ​​constructed by arranging all the chatter feature vectors in the training dataset row by row. Each row of the input matrix corresponds to the chatter feature vector of one sample. The number of rows in the input matrix is ​​equal to the number of samples in the training dataset, and the number of columns in the input matrix is ​​equal to the dimension of the chatter feature vectors. Multiply the input matrix by the connection weight matrix from the input layer to the single hidden layer, and add the bias vector to obtain the hidden layer input matrix. Apply the Sigmoid activation function to each element of the hidden layer input matrix for a non-linear mapping to obtain the hidden layer output matrix. The expression for the Sigmoid activation function is: ,in, This represents an element in the hidden layer input matrix. After calculating the hidden layer output matrix, the hidden layer output matrix and the manually labeled flutter risk level vector are substituted into the least squares method to calculate the output weight vector from a single hidden layer to the output layer. The output weight vector is calculated by solving the least-norm least squares solution of the linear equation system, using regularization constraints. The regularization coefficient is a constant between 0.001 and 0.01.

[0053] After the Extreme Learning Machine (ELM) model is trained, the cutting chatter feature vector constructed at the current time step is used as the input to the input layer. The dimension of the cutting chatter feature vector at the current time step is consistent with that during the training phase, which is... The current flutter feature vector is multiplied by the trained connection weight matrix, a bias vector is added, and then the result is processed through a sigmoid activation function to obtain the hidden layer output vector. The hidden layer output vector is then multiplied by the trained output weight vector, and the output value of the output layer is calculated through forward propagation. This output value is a scalar and is used as the flutter risk level at the current moment.

[0054] During the iterative update of the feed rate control increment using the adaptive momentum algorithm, the initial control increment of the feed rate is set to zero. The control increment of the feed rate is the amount to be adjusted for the feed rate at the current moment, and the initial control increment is... The value is set to 0. The gradient at the current moment is set as the partial derivative of the flutter risk level with respect to the feed rate at the previous moment. The partial derivative of the flutter risk level with respect to the feed rate is approximated by numerical difference. The calculation method is to divide the difference between the flutter risk level at the preset step size before the current moment and the flutter risk level at the previous moment by the preset step size. The preset step size is the minimum resolution value of the feed rate adjustment.

[0055] The exponentially weighted moving average of the gradient at the current time step is calculated as the first-moment estimate. The update formula for the first-moment estimate is:

[0056] in, For the first First-order moment estimation at the next iteration For the first First-order moment estimation at the next iteration For the first The gradient at the next iteration It is the first-order moment attenuation coefficient. The value is set to 0.9, which is determined by the standard configuration of the adaptive momentum algorithm in optimization problems, ensuring that the first-order moment estimate retains about 90% of the historical gradient information.

[0057] The exponentially weighted moving average of the squared gradient at the current time step is calculated as the second-order moment estimate. The second-order moment estimate is updated by calculating... Exponentially weighted moving average, second moment decay coefficient The value is set to 0.999 to ensure that the second-order moment estimate retains most of the information from the historical gradient squares, providing a slow response to changes in the second-order moment of the gradient. When performing bias correction on the first-order moment estimate, [the value is...]. Divide by ,in, express of The power of 1. When correcting for bias in the second-order moment estimate, divide the second-order moment estimate by 1 / 2. ,in express of The power of the power. Bias correction compensates for the estimation error introduced by the approaching zero of the first and second moment estimates during the initial iteration.

[0058] The update step size for this iteration is obtained by dividing the corrected first-order moment estimate by the square root of the corrected second-order moment estimate and then multiplying by the preset learning rate. The preset learning rate is a constant between 0.001 and 0.01, and its specific value is determined based on the range of feed rate variation. When the feed rate variation ranges from 0 to 100 mm / min, the learning rate is set to 0.005. The updated control increment is obtained by subtracting the update step size from the control increment of the previous time step. Each iteration uses the gradient of the current time step to update the first-order moment estimate, the second-order moment estimate, and the control increment. After multiple iterations, the control increment converges.

[0059] In solving the constrained optimization problem using the Lagrange multiplier method, the objective function is constructed to minimize the change in feed rate. The change in feed rate is defined as the difference between the current feed rate and the previous feed rate, minus the square of the control increment. The expression for the objective function is: ,in The feed rate at the current moment. The feed rate at the previous moment. This is the control increment of the feed rate obtained after iterative updates using the adaptive momentum algorithm.

[0060] Set velocity smoothing constraints. The first velocity smoothing constraint is that the absolute value of the first-order difference of the feed rate does not exceed the maximum acceleration limit, and the constraint expression is as follows: ,in, This represents the maximum allowable acceleration value for the machine tool servo drive system. This refers to the system's control sampling period. Determined by the technical specifications of the machine tool servo drive system, it is usually expressed in millimeters per second squared. The second speed smoothing constraint condition is that the absolute value of the second-order difference of the feed rate does not exceed the maximum jerk limit, and the constraint expression is: ,in, The maximum allowable jerk value for the machine tool servo drive system is determined by the upper limit of the torque change rate of the machine tool drive motor. Both inequality constraints are rearranged into standard forms less than or equal to zero. The objective function and velocity smoothing constraint are combined into a Lagrange function. Non-negative Lagrange multipliers are introduced to correspond to each inequality constraint, with the first Lagrange multiplier... Corresponding to the maximum acceleration constraint, the second Lagrange multiplier This corresponds to the maximum jerk constraint. The expression for the Lagrange function is: The feed rate of the Lagrange function with respect to the current time. Find the partial derivatives and set them to zero to obtain the optimality condition equations. Simultaneously, formulate the complementary relaxation condition equations, which state that the product of the Lagrange multiplier and the corresponding inequality constraint is zero. Solve the system of equations consisting of the optimality condition equations and the complementary relaxation condition equations, with variables including... , and The solution process employs an iterative method. First, it assumes that the two Lagrange multipliers are zero, and then solves the unconstrained problem to obtain... The trial value is used to determine whether it satisfies both inequality constraints. If neither inequality constraint is satisfied, the corresponding Lagrange multiplier is set to a positive value, and the modified system of equations is solved again until a system that satisfies all constraints is found. , as the optimal feed rate.

[0061] When obtaining the speed loop transfer function model of a machine tool servo drive system, the speed loop transfer function model is obtained by fitting the frequency response data of the speed loop obtained through experimental identification. The speed loop transfer function model is in the form of a first-order inertial element connected in series with a pure time-delay element, and the transfer function is... ,in, For velocity loop gain, The velocity loop time constant, For the pure time delay of the velocity loop, For the Laplace operator. The pure time delay of the velocity loop. This refers to the dynamic response delay time from the speed command to the actual speed.

[0062] The optimal feed rate is used as the input setpoint for the speed loop. Pre-compensation is performed on the optimal feed rate using the inverse function of the transfer function model to generate a pre-compensated speed command. The inverse function of the transfer function model is implemented through an approximation method, combining the inverse function of the first-order inertial element with phase lead compensation for the pure time-delay element. The pre-compensation calculation formula is as follows: ,in, For the first The pre-compensated speed command for each sampling period For the first The optimal feed rate for each sampling period For the first The optimal feed rate for each sampling period The sampling period is The velocity loop time constant, This is the velocity loop gain. (The calculated value is...) Amplitude limiting is applied, with the limiting range between zero and the maximum command value allowed by the machine tool servo drive system.

[0063] The pre-compensated speed command is encapsulated into a standard data frame format according to the machine tool controller's communication protocol. The standard data frame format includes a frame header, address field, data field, check field, and frame trailer. The data field contains the value of the pre-compensated speed command, encoded in binary or ASCII. The check field uses a cyclic redundancy check (CRC) code to verify the contents of the address and data fields, obtaining a check value. The encapsulated data frame is then sent to the servo drive in the machine tool controller via a fieldbus interface or analog interface. When using a fieldbus interface, the data frame is sent bit-by-bit to the physical transmission medium according to the bus protocol. When using an analog interface, the pre-compensated speed command value is converted into a corresponding analog voltage signal, ranging from 0 to 10 volts, linearly corresponding to zero to the maximum feed speed, and output to the analog input port of the servo drive via a digital-to-analog converter.

[0064] The foregoing has provided a detailed description of one embodiment of the present invention, but this description is merely a preferred embodiment and should not be construed as limiting the scope of the invention. All equivalent variations and modifications made within the scope of the claims of this invention should still fall within the patent coverage of this invention.

Claims

1. A feed speed control system for machining tools in mechanical equipment, characterized in that, Includes the following steps: The signal acquisition module acquires cutting force signals and tool vibration signals in real time during the machining process, and performs collaborative phase space reconstruction of the two signals to obtain a high-dimensional phase trajectory; The chaos analysis module calculates the correlation dimension and Kolmogorov entropy of the high-dimensional phase trajectory, and determines the degree of chaos of the current cutting state based on the rate of change of the correlation dimension and the Kolmogorov entropy. The recursive adjustment module, when the degree of chaos exceeds a set threshold, extracts the recursion rate of the cutting force signal based on the recursion graph analysis method, and dynamically adjusts the reference value of the feed rate according to the recursion rate. The recursive adjustment module uses a sliding window to perform local mean decomposition on the tool vibration signal to obtain multiple product function components. Based on the instantaneous frequency and instantaneous amplitude of each product function component, a cutting chatter feature vector is constructed. The chatter risk assessment module inputs the cutting chatter feature vector into the extreme learning machine model and outputs the chatter risk level; The optimized control module uses an adaptive momentum algorithm to iteratively update the control increment of the feed rate based on the flutter risk level and the current feed rate. The control increment and speed smoothing constraint are fused together, and the constraint optimization problem is solved by the Lagrange multiplier method to obtain the optimal feed rate. The optimal feed rate is then converted into a servo drive command and output to the machine tool controller.

2. The mechanical equipment machining tool feed speed control system according to claim 1, characterized in that, The specific steps for acquiring cutting force signals and tool vibration signals in real time during the machining process, and then performing collaborative phase space reconstruction of the two signals to obtain a high-dimensional phase trajectory are as follows: The time delay of the cutting force signal is calculated using the mutual information method, and the embedding dimension is calculated using the false nearest neighbor method. The initial phase space of the cutting force signal is constructed based on the time delay and the embedding dimension. The initial phase space of the tool vibration signal is constructed using the same time delay and embedding dimension; Each phase point in the initial phase space of the cutting force signal is longitudinally spliced ​​with the corresponding phase point in the initial phase space of the tool vibration signal to form a high-dimensional phase point at each moment. Arrange all the high-dimensional phase points at all times in chronological order to form the high-dimensional phase trajectory.

3. The mechanical equipment machining tool feed speed control system according to claim 1, characterized in that, The specific steps for calculating the correlation dimension and Kolmogorov entropy of the high-dimensional phase trajectory, and determining the degree of chaos of the current cutting state based on the rate of change of the correlation dimension and the Kolmogorov entropy, are as follows: Multiple different distance scales are set up. For each distance scale, the proportion of points in the high-dimensional phase trajectory whose distance between any two phase points is less than that distance scale is counted, and the correlation integral under that distance scale is obtained. The correlation integral and the distance scale are linearly fitted in a double logarithmic coordinate system, and the slope obtained from the fitting is used as the correlation dimension. The high-dimensional phase trajectory is divided into multiple trajectory segments of equal length. The maximum Lyapunov exponent between phase points in each trajectory segment is calculated. The average value of the maximum Lyapunov exponent between the trajectory segments is taken as the Kolmogorov entropy. The first difference of the correlation dimension within a preset time window before the current sampling time is calculated as the first rate of change, and the first difference of the Kolmogorov entropy is calculated as the second rate of change. When both the first rate of change and the second rate of change are greater than their respective historical moving averages, the degree of chaos is determined to exceed a set threshold.

4. The mechanical equipment machining tool feed speed control system according to claim 3, characterized in that, The multiple different distance scales are set according to a geometric series, and the ratio of adjacent distance scales is the square root of 2.

5. A mechanical equipment machining tool feed speed control system according to claim 1, characterized in that, The specific steps for dynamically adjusting the reference value of the feed rate based on the recursion rate to extract the recursion rate of the cutting force signal according to the recursion graph analysis method when the degree of chaos exceeds a set threshold are as follows: The cutting force signal is delayed and embedded on the time axis to obtain the state vector sequence of the recursive graph; Calculate the Euclidean distance between any two state vectors in the state vector sequence, and generate a recursion matrix based on the relationship between the Euclidean distance and a preset recursion threshold. Each element in the recursion matrix indicates whether the corresponding two state vectors are recursively processed. The number of recursive points in the recursion matrix is ​​counted, and the ratio of the number of recursive points to the total number of elements in the recursion matrix is ​​taken as the recursion rate. The current feed rate baseline value is multiplied by an adjustment coefficient proportional to the recursion rate to obtain the adjusted feed rate baseline value, wherein the minimum value of the adjustment coefficient is one and the maximum value is a preset upper limit value.

6. A mechanical equipment machining tool feed speed control system according to claim 5, characterized in that, The preset recursion threshold is dynamically determined by multiplying the average Euclidean distance between all state vectors in the state vector sequence by a scaling factor.

7. A mechanical equipment machining tool feed speed control system according to claim 1, characterized in that, The specific steps for using a sliding window to perform local mean decomposition on the tool vibration signal to obtain multiple product function components, and constructing a cutting chatter feature vector based on the instantaneous frequency and instantaneous amplitude of each product function component are as follows: Determine the length and sliding step of the sliding window, and extract a segment of the tool vibration signal as a local signal at each window position; For each local signal, a local mean function and a local envelope function are constructed by detecting its local extreme points. After separating the local mean function from the local signal, it is divided by the local envelope function to obtain the frequency-modulated signal. This separation process is iterated until the envelope function of the frequency-modulated signal is close to a constant. The product of all local envelope functions in the last iteration is taken as a product function component of the local signal. After subtracting the product function component from the original local signal, repeat the above process to extract the next product function component until the remaining signal is a monotonic function; Perform a Hilbert transform on each component of the product function and calculate its instantaneous frequency and instantaneous amplitude; Calculate the variance of the instantaneous frequency and the attenuation rate of the instantaneous amplitude of each product function component, and concatenate the variances and attenuation rates of all product function components in sequence to form the cutting chatter feature vector.

8. A mechanical equipment machining tool feed speed control system according to claim 7, characterized in that, The iterative separation process continues until the envelope function of the frequency modulation signal approaches a constant. The condition for this is that the difference between the maximum and minimum values ​​of the envelope function is less than a preset tolerance threshold.

9. A mechanical equipment machining tool feed speed control system according to claim 1, characterized in that, The specific steps for inputting the cutting chatter feature vector into the extreme learning machine model and outputting the chatter risk level are as follows: Cutting chatter samples under various feed rate conditions are collected in advance. For each sample, the corresponding cutting chatter feature vector is extracted, and the chatter risk level is manually labeled. The chatter risk level is either a continuous value or a discrete level. An extreme learning machine model containing an input layer, a single hidden layer, and an output layer is constructed. The connection weights from the input layer to the hidden layer and the biases of the hidden layer neurons are randomly initialized. The cutting flutter feature vector is used as the input of the input layer. After nonlinear mapping of the hidden layer, the output weights from the hidden layer to the output layer are calculated by the least squares method. The cutting chatter feature vector constructed at the current moment is input into the trained extreme learning machine model, and the output value of the output layer is calculated through forward propagation. This output value is used as the chatter risk level.

10. A mechanical equipment machining tool feed speed control system according to claim 1, characterized in that, The specific steps for iteratively updating the control increment of the feed rate using the adaptive momentum algorithm based on the flutter risk level and the current feed rate are as follows: The initial control increment of the feed rate is set to zero, and the gradient at the current moment is set to the partial derivative of the flutter risk level with respect to the feed rate at the previous moment. Calculate the exponentially weighted moving average of the gradient at the current time as the first moment estimate, and calculate the exponentially weighted moving average of the squared gradient at the current time as the second moment estimate; The first-order moment estimate and the second-order moment estimate are biased and corrected. The corrected first-order moment estimate is divided by the square root of the corrected second-order moment estimate and then multiplied by the preset learning rate to obtain the update step size for this iteration. The updated feed rate control increment is obtained by subtracting the update step size from the control increment of the previous moment.

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