A method and system for constructing a milling stability boundary of a numerical control machine tool considering parameter time variation

Abstract

The application discloses a kind of considering parameter time-varying numerical control machine tool milling stability boundary construction method and system, belong to manufacturing industry processing technical field, this method includes numerical control machine tool processing path dynamic performance parameter set construction, obtains the corresponding numerical control machine tool dynamic performance parameter of each coordinate point on processing path, including inherent frequency, modal mass and damping ratio;Stability feature point set screening, stability feature point set is screened based on designed stability proxy index;Stability lobe diagram calculation, the two-dimensional stability lobe diagram corresponding to feature point is calculated using the semi-discrete method of prediction-correction scheme;Processing whole process stability boundary construction, linear interpolation is obtained between a series of two-dimensional stability lobe diagram three-dimensional milling stability boundary.The application can realize the efficient calculation of stability boundary when considering the time-varying characteristics of machine tool dynamic performance parameters.

Description

Technical Field

[0001] This invention belongs to the field of manufacturing processing technology, specifically relating to a method and system for constructing stability boundaries for CNC machine tool milling that considers time-varying parameters. Background Technology

[0002] Five-axis CNC machine tools are specialized machines for machining complex curved surfaces, commonly used in the processing of critical equipment in key fields such as aero-engine blades and marine propellers. Milling is one of the most important machining methods due to its high material removal efficiency and strong machining adaptability. However, due to the regenerative effect in milling, chatter is easily triggered, leading to a decrease in workpiece quality and accelerated tool wear. Therefore, accurately predicting the stable machining zone during the machining process and optimizing cutting parameters accordingly is an important prerequisite for improving machining efficiency and ensuring machining quality.

[0003] Currently, stability lobe diagrams are commonly used in milling stability analysis to describe the machining stability boundary determined by two machining parameters: spindle speed and depth of cut. However, during machining on a five-axis CNC machine tool, the dynamic performance parameters change over time, causing the machining stability boundary to dynamically change with the machining position. Performing stability calculations on a large number of points along the machining path individually would be computationally intensive, making it difficult to meet the computational efficiency requirements of practical engineering applications.

[0004] Therefore, there is an urgent need for a method that, while ensuring the accuracy of stability prediction, fully considers the time-varying characteristics of the dynamic performance parameters of a five-axis CNC machine tool and constructs the stability boundary of the entire machining process. Summary of the Invention

[0005] To solve the above-mentioned technical problems, the present invention adopts the following technical solution:

[0006] A method for constructing stability boundaries in CNC machine tool milling considering time-varying parameters includes:

[0007] The dynamic performance parameter set of CNC machine tool machining path is constructed to obtain the dynamic performance parameters of CNC machine tool corresponding to each coordinate point on the CNC machine tool machining path, including natural frequency, modal mass and damping ratio;

[0008] Stability feature point set selection: The stability feature point set is selected based on the designed stability surrogate index.

[0009] Stability leaflobe diagram calculation: The two-dimensional stability leaflobe diagram corresponding to the feature points is calculated using the semi-discrete method of the prediction-correction scheme.

[0010] The stability boundary for the entire machining process is constructed by linear interpolation between a series of two-dimensional stability lobe diagrams to obtain the three-dimensional milling stability boundary. This invention enables efficient calculation of the stability boundary when considering the time-varying characteristics of machine tool dynamic performance parameters.

[0011] A system for constructing stability boundaries for CNC machine tool milling considering time-varying parameters includes:

[0012] The module for constructing dynamic performance parameters of CNC machine tool machining path obtains the dynamic performance parameters of CNC machine tool corresponding to each coordinate point on the CNC machine tool machining path, including natural frequency, modal mass and damping ratio;

[0013] The stability feature point set filtering module filters out the stability feature point set based on the designed stability surrogate index.

[0014] The stability leaflobe diagram calculation module uses a semi-discrete method based on a prediction-correction scheme to calculate the two-dimensional stability leaflobe diagram corresponding to the feature points.

[0015] A stability boundary construction module for the entire machining process obtains the three-dimensional milling stability boundary through linear interpolation between a series of two-dimensional stability lobe diagrams. This invention enables efficient calculation of the stability boundary when considering the time-varying characteristics of machine tool dynamic performance parameters.

[0016] The present invention has the following beneficial effects:

[0017] Characterization of time-varying dynamic performance parameters. This invention fully considers the characteristic that dynamic performance parameters change continuously with the machining position during CNC machine tool machining. It establishes a stability analysis method based on the prediction results of dynamic performance parameters throughout the machining process, changing the assumption of fixed dynamic parameters used in traditional stability analysis methods and improving the accuracy of stability prediction.

[0018] (2) Improved efficiency in stability boundary calculation. This invention designs a stability proxy index, which uses the degree of change in machining stability as the criterion. It only needs to perform high-precision stability calculations on the feature positions where the stability changes significantly, without having to solve the stability boundary point by point on all positions on the CNC machine tool machining path. This significantly improves the calculation efficiency while ensuring the accuracy of the analysis.

[0019] (3) This invention fully considers the characteristics of dynamic performance parameters changing continuously with the machining position during CNC machine tool machining, and establishes a stability analysis method based on the prediction results of dynamic performance parameters throughout the machining path, thereby improving the accuracy of stability prediction. By designing a stability proxy index and using the degree of change in machining stability as the criterion, high-precision stability calculations are only required for the feature positions where stability changes significantly, without having to solve the stability leaflet diagram point by point for all positions on the CNC machine tool machining path, thus solving the problem of the huge amount of computation caused by point-by-point calculation. Attached Figure Description

[0020] Figure 1 This is a flowchart of a method for constructing stability boundaries for CNC machine tool milling that considers time-varying parameters, according to the present invention. Detailed Implementation

[0021] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention. Furthermore, the technical features involved in the various embodiments of this invention described below can be combined with each other as long as they do not conflict with each other.

[0022] This invention provides a method for constructing stability boundaries for CNC machine tool milling considering time-varying parameters. It extracts time-varying features of parameters based on a pre-trained CNC machine tool dynamic performance parameter prediction model, selects stability feature points based on stability surrogate indices, calculates the stability lobe diagram corresponding to each feature point, and constructs stability boundaries for the entire machining process.

[0023] like Figure 1 As shown, the method for constructing stability boundaries for CNC machine tool milling considering time-varying parameters according to the present invention includes:

[0024] The dynamic performance parameter set of CNC machine tool machining path is constructed to obtain the dynamic performance parameters of CNC machine tool corresponding to each coordinate point on the CNC machine tool machining path, including natural frequency, modal mass and damping ratio;

[0025] Stability feature point set selection: The stability feature point set is selected based on the designed stability surrogate index.

[0026] Stability leaflobe diagram calculation: The two-dimensional stability leaflobe diagram corresponding to the feature points is calculated using the semi-discrete method of the prediction-correction scheme.

[0027] The stability boundary for the entire machining process is constructed by linear interpolation between a series of two-dimensional stability lobe diagrams to obtain the three-dimensional milling stability boundary. This invention enables efficient calculation of the stability boundary when considering the time-varying characteristics of machine tool dynamic performance parameters.

[0028] The specific steps are as follows:

[0029] Step 1: Constructing the dynamic performance parameter set for CNC machine tool machining paths.

[0030] The tool coordinate data during the milling process is obtained, and the dynamic performance parameter set of the entire machining path is acquired, including natural frequency, modal mass, and damping ratio. The specific implementation is as follows:

[0031] Step 1.1, Construction of Machining Coordinate Point Dataset: From the CNC system data interface (e.g., the FANUC Open CNC System Interface (FOCAS API) in the FANUC CNC system), collect the position coordinate data of each axis of the CNC machine tool machining path at a fixed frequency (usually on the order of 1Hz) to form a machining coordinate point dataset. , ,in For the coordinate points of the machining tool on the CNC machine tool, This represents the total number of coordinate points of the CNC machine tool machining tools collected. , , For the first spindle position along the entire machining path coordinate points, The first The machining coordinates of each CNC machine tool point are defined in the X-axis, Y-axis, Z-axis, and A-axis coordinates of the five-axis CNC machine tool coordinate system.

[0032] Step 1.2, Construction of the dynamic performance parameter set for the entire processing path: Iterate through the processing coordinate point dataset constructed in Step 1.1. All coordinate points Obtain the dynamic performance parameters of the CNC machine tool at the corresponding position. , This forms a dynamic performance parameter set for the entire processing path. , ,in and They are respectively The natural frequencies of the CNC machine tool in the X and Y axes at the location. and They are respectively Modal mass of the CNC machine tool in the X and Y axes at the location. and They are respectively Damping ratio of the CNC machine tool in the X and Y axes at the location; They are respectively The corresponding dynamic performance parameters. In this embodiment, the acquisition of the dynamic performance parameter set for the entire machining path adopts the dynamic performance parameter prediction method for CNC machine tools oriented towards milling machining from Chinese patent application CN122331442A (A method and system for predicting dynamic performance parameters of CNC machine tools for milling machining). This is achieved by using a dataset of machining coordinate points. Each coordinate point in the graph is used as input to the CatBoost prediction model constructed in the prediction method of this patent application, and the corresponding dynamic performance parameters can be predicted.

[0033] Step 2, Stability Feature Point Set Selection. Starting from the processing location, traverse all locations along the entire processing path, calculate the stability surrogate index, and select the stability feature point set based on this index. The specific implementation is as follows:

[0034] Step 2.1, Calculate the machining stability boundary: Sequentially extract the dynamic performance parameter set of the entire machining path constructed in Step 1.2. All dynamic performance parameters are defined by the formula:

[0035] ;

[0036] ;

[0037] in, For the excitation frequency, It is the imaginary unit.

[0038] Computer bed in frequency response function in the X-axis direction at the location and frequency response function in the Y-axis direction .

[0039] According to the formula:

[0040] ;

[0041] ;

[0042] ;

[0043] ;

[0044] ;

[0045] For the cutting coefficient matrix Using the zeroth-order approximation, where, , , , for The matrix coefficients, For summation, The summation index is 1, and 1 is the lower bound of the summation. To find the upper bound of the summation, and the number of teeth, For the first The cutting angle of each cutting tooth, To determine the first A rectangular function to determine whether each cutting tooth is in the cutting position. This is the axial cutting force coefficient. This is the radial cutting force coefficient. This represents the axial cutting depth. The diameter of the cutting tool. Main spindle speed Indicates time, These are the zeroth-order approximation coefficients. , for The zeroth-order direction matrix after Fourier expansion. , , , for The matrix coefficients.

[0046] Solve the system of equations:

[0047] ;

[0048] Obtain the characteristic roots ,in, and The coefficients of the characteristic equation, The selected flutter frequency, , The frequency response functions of the machine tool in the X-axis direction and the Y-axis direction are respectively at the excitation frequency of . The value at time.

[0049] According to the formula:

[0050] ;

[0051] ;

[0052] Calculate the critical axial depth of cut and critical spindle speed ,in, and These are the characteristic roots. The real and imaginary parts. As a scan variable, in Within the range, the scan step size is 1Hz, and a total of [number] scans are taken. each flutter frequency , ... ,in and These are the natural frequencies of the CNC machine tool in the X and Y axes, respectively. This indicates taking the minimum value. This indicates taking the maximum value.

[0053] Calculate the corresponding two-dimensional coordinate points of spindle speed and axial depth of cut using the above method. , ... , Given the number of two-dimensional coordinate points, connecting all the two-dimensional coordinate points representing the spindle speed and axial depth of cut yields the machining stability boundary. .in The flutter frequency is , ... Critical spindle speed at that time The flutter frequency is , ... The critical axial depth of cut at that time.

[0054] Step 2.2, calculate the stability surrogate index: when the coordinate point When doing so, the initial machining stability boundary is selected as the reference boundary. According to the formula:

[0055] ;

[0056] calculate All coordinate points Corresponding stability proxy metrics .in, To calculate stability surrogate metrics The summation index used at that time and These are respectively at the processing stability boundary The selected first The critical axial depth of cut and critical spindle speed corresponding to each calculation point For reference boundary above The critical axial cutting depth is selected corresponding to the critical spindle speed. This indicates taking the maximum value. The number of points to calculate for the stability proxy index.

[0057] Define stability change index :

[0058] ;

[0059] when At that time, the current processing stability boundary is used as the new reference boundary.

[0060] Step 2.3, Construct a stability feature point set: This involves processing the coordinate point dataset. After performing steps 2.1 and 2.2 on all coordinate points, select all... The coordinates of the point and the initial coordinates This constitutes a set of stable feature points. ,in with initial coordinates same, for The corresponding coordinates of the points. This represents the total number of stability feature points.

[0061] Step 3: For each feature point in the stability feature point set, the semi-discrete method of the prediction-correction scheme is used to calculate the two-dimensional stability lobe diagram of that feature point in the spindle speed-axial depth of cut plane. The specific implementation is as follows:

[0062] Step 3.1, divide the prediction step time interval and the correction step time interval:

[0063] According to the formula:

[0064] ;

[0065] Calculate the milling time delay period According to the formula:

[0066] ;

[0067] Calculate the idle cycle of the cutter teeth .

[0068] in, The diameter of the cutting tool. The milling time. , Evenly divided into Prediction step time intervals of equal length , ... ,in These are the endpoints of the time intervals for each prediction step. Based on the divided prediction step time intervals, we can obtain... Each correction step time interval .

[0069] Step 3.2, Solve the two-dimensional stability leaflobe diagram: Within the time interval after discretization as described in Step 3.1, calculate the stability critical point using the semi-discrete method of the prediction-correction scheme. The state-space equation of the milling process solved by the semi-discrete method of the prediction-correction scheme is as follows:

[0070] ;

[0071] ;

[0072] ;

[0073] ;

[0074] in, for The position and velocity state vector of the tool at any given moment. for The position and velocity state vector of the tool at any given moment. A constant matrix reflecting the physical properties of CNC machine tools, and It is a periodic coefficient matrix. , They are respectively The cutting teeth in the tool coordinate system shaft and The position coordinates of the axis , They are respectively The cutting teeth in the tool coordinate system shaft and Velocity coordinates in the axial direction , These are the damping ratios of the CNC machine tool in the X and Y axes, respectively. , The modal mass of the CNC machine tool is defined by the X-axis and Y-axis directions, respectively.

[0075] The initial cutting state vector is calculated according to the following formula. :

[0076] ;

[0077] in, for The position and velocity state vector of the tool at any given time.

[0078] make , , ,in, For the first The left endpoint of the prediction step time interval and For the defined intermediate variables, After variable substitution The periodic coefficient matrix at time t, After variable substitution The position and velocity state vector of the tool at time t. Each prediction step time interval Interpolation formula used:

[0079] ;

[0080] in, , For time step, For the first The right endpoint of the prediction step time interval For the first The left endpoint of the prediction step time interval , , They are respectively time, time, Intermediate variables at time The value of .

[0081] According to the integral formula:

[0082] ;

[0083] The results were:

[0084] ;

[0085] ;

[0086] ;

[0087] ;

[0088] ;

[0089] ;

[0090] ;

[0091] ;

[0092] in, It is the identity matrix. , , , , , , These are all defined intermediate variables. , , , , They are respectively time, time, time, time, The position and velocity state vector of the tool at any given moment. for Time coefficient matrix The value of , For matrix The reverse, , , They are respectively time, time, Time coefficient matrix The value of .

[0093] make , ,in, and For the defined intermediate variables, After variable substitution The periodic coefficient matrix at time t, After variable substitution The position and velocity state vector of the tool at time t. Each correction step time interval Interpolation formula used:

[0094] ;

[0095] in, , , They are respectively time, time, Intermediate variables at time The value of .

[0096] According to the integral formula:

[0097] ;

[0098] The results were:

[0099] ;

[0100] ;

[0101] ;

[0102] ;

[0103] ;

[0104] ;

[0105] ;

[0106] ;

[0107] in, for The position and velocity state vector of the tool at any given moment. for Time coefficient matrix The value of , For matrix The reverse, , , , , , , These are all defined intermediate variables. for Time coefficient matrix The value of , The position and velocity state vector of the tool at any given time. From the above relationship, the state transition equation can be derived:

[0108] ;

[0109] ;

[0110] ;

[0111] in and The coefficient matrix of the state transition equation is... , ... , They are respectively , ... , The position and velocity state vector of the tool at any given moment. , ... , They are respectively , ... , The position and velocity state vector of the tool at any given moment. , Intermediate variables In the 2nd and the The values ​​that can be taken in the time interval of each prediction step. , Intermediate variables In the 2nd and the The values ​​that can be taken in the time interval of each prediction step. , , and , , Intermediate variables , , In the 1st and the The values ​​for each correction step time interval, , , and , , Intermediate variables , , In the 1st and the The values ​​of each correction step time interval are determined. The transition matrix is ​​defined. Traverse all points in the two-dimensional plane of spindle speed-axial depth of cut, for The stability critical points can be obtained using the Floquet criterion. Connecting all stability critical points yields a two-dimensional stability lobe diagram. .

[0112] Step 3.3, Construct a two-dimensional stability leaf lobe diagram set: Traverse the stability feature point set constructed in Step 2.3 For all feature points, calculate the corresponding two-dimensional stability leaflobe diagram according to steps 3.1 and 3.2, and construct a set of two-dimensional stability leaflobe diagrams. .in, Stability feature point The corresponding two-dimensional stability lobe diagram.

[0113] Step 4: Construct the stability boundary for the entire machining process. Linear interpolation is performed between the two-dimensional stability lobe diagrams corresponding to two adjacent stability feature points to generate a three-dimensional stability lobe diagram that continuously varies with the machining position, thus constructing the three-dimensional milling stability boundary. According to the stability boundary of three-dimensional milling The stability of the milling machining scheme can be determined, and the specific implementation is as follows:

[0114] Based on the set of two-dimensional stability lobe diagrams constructed in step 3.3, a linear interpolation method is used between the two-dimensional stability lobe diagrams corresponding to adjacent stability feature points to obtain the three-dimensional milling stability boundary of the entire CNC machine tool machining process, which is oriented towards the position coordinates of the CNC machine tool machining path, radial cutting depth, and spindle speed. .lie in The parameter points below are the stable milling machining parameter points.

[0115] The present invention further provides a system for constructing stability boundaries for CNC machine tool milling considering time-varying parameters, comprising:

[0116] The module for constructing dynamic performance parameters of CNC machine tool machining path obtains the dynamic performance parameters of CNC machine tool corresponding to each coordinate point on the CNC machine tool machining path, including natural frequency, modal mass and damping ratio;

[0117] The stability feature point set filtering module filters out the stability feature point set based on the designed stability surrogate index.

[0118] The stability leaflobe diagram calculation module uses a semi-discrete method based on a prediction-correction scheme to calculate the two-dimensional stability leaflobe diagram corresponding to the feature points.

[0119] A stability boundary construction module for the entire machining process obtains the three-dimensional milling stability boundary through linear interpolation between a series of two-dimensional stability lobe diagrams. This invention enables efficient calculation of the stability boundary when considering the time-varying characteristics of machine tool dynamic performance parameters.

[0120] 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 (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code. The embodiments of the present invention can be implemented using various computer languages.

[0121] This invention is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart illustrations and / or block diagrams. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0122] 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.

[0123] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0124] Although preferred embodiments of the invention have been described, those skilled in the art, upon learning the basic inventive concept, can make other changes and modifications to these embodiments. Therefore, the appended claims are intended to be interpreted as including both the preferred embodiments and all changes and modifications falling within the scope of the invention.

[0125] Obviously, those skilled in the art can make various modifications and variations to this invention without departing from its spirit and scope. Therefore, if these modifications and variations fall within the scope of the claims and their equivalents, this invention also intends to include these modifications and variations. The above descriptions are merely embodiments of this invention and do not limit its scope. Any equivalent structural or procedural transformations made using the description and drawings of this invention, or direct or indirect applications in other related system fields, are similarly included within the protection scope of this invention. Contents not described in detail in this specification are prior art known to those skilled in the art.

Claims

1. A method for constructing stability boundaries in CNC machine tool milling considering time-varying parameters, characterized in that, include: The dynamic performance parameter set of CNC machine tool machining path is constructed to obtain the dynamic performance parameters of CNC machine tool corresponding to each coordinate point on the CNC machine tool machining path, including natural frequency, modal mass and damping ratio; Stability feature point set selection: The stability feature point set is selected based on the designed stability surrogate index. Stability leaflobe diagram calculation: The two-dimensional stability leaflobe diagram corresponding to the feature points is calculated using the semi-discrete method of the prediction-correction scheme. The stability boundary of the entire machining process is constructed by linear interpolation between a series of two-dimensional stability lobe diagrams to obtain the three-dimensional milling stability boundary; the present invention can achieve efficient calculation of the stability boundary when considering the time-varying characteristics of the dynamic performance parameters of the machine tool.

2. The method for constructing stability boundaries for CNC machine tool milling considering time-varying parameters according to claim 1, characterized in that, The construction of the dynamic performance parameter set for the CNC machine tool machining path includes: Construction of machining coordinate point dataset: Collect the position coordinate data of each axis of the CNC machine tool machining path from the CNC system data interface at a fixed frequency to form a machining coordinate point dataset; Construction of dynamic performance parameter set for the entire machining path: Iterate through all coordinate points in the machining coordinate point dataset, obtain the dynamic performance parameters of the CNC machine tool at the corresponding positions, and form a dynamic performance parameter set for the entire machining path.

3. The method for constructing stability boundaries for CNC machine tool milling considering time-varying parameters according to claim 1, characterized in that, The stability feature point set selection includes: Calculate the machining stability boundary: Extract the dynamic performance parameters from the dynamic performance parameter set of the entire machining path in sequence, calculate the frequency response function at the corresponding position, and calculate the machining stability boundary at the corresponding position based on the cutting coefficient matrix; Calculate the stability surrogate index: Using the initial processing stability boundary as the reference boundary, calculate the stability surrogate index corresponding to each coordinate point; Construct a stability feature point set: Select the coordinate points when the stability surrogate index exceeds the preset threshold and the initial coordinate points to form a stability feature point set.

4. The method for constructing stability boundaries for CNC machine tool milling considering time-varying parameters according to claim 1, characterized in that, The stability lobe diagram calculation includes: Divide the prediction step time interval and the correction step time interval: Based on the milling time delay period and the cutter tooth idle period, the milling time is evenly divided into multiple prediction step time intervals of equal length, and the correction step time interval is obtained from this. Solving the two-dimensional stability leaflobe diagram: The stability critical points are calculated using a semi-discrete method with a prediction-correction scheme within the time interval after discretization. Connecting all the stability critical points yields the two-dimensional stability leaflobe diagram. Construct a set of two-dimensional stability leaf lobe diagrams: Traverse all feature points in the stability feature point set, calculate the corresponding two-dimensional stability leaf lobe diagrams, and construct a set of two-dimensional stability leaf lobe diagrams.

5. The method for constructing stability boundaries for CNC machine tool milling considering time-varying parameters according to claim 1, characterized in that, The construction of the stability boundary for the entire processing process includes: Linear interpolation is performed between the two-dimensional stability lobe diagrams corresponding to two adjacent stability feature points to generate a three-dimensional stability lobe diagram that continuously changes with the machining position, thus constructing a three-dimensional milling stability boundary.

6. The method for constructing stability boundaries for CNC machine tool milling considering time-varying parameters according to claim 1, characterized in that, The stability proxy index is calculated based on the degree of change of the processing stability boundary. When the stability proxy index exceeds a preset threshold, the current processing stability boundary is used as the new reference boundary.

7. The method for constructing stability boundaries for CNC machine tool milling considering time-varying parameters according to claim 1, characterized in that, The semi-discrete method of the prediction-correction scheme includes: approximating the state vector using an interpolation formula in the prediction step time interval, approximating the state vector using an interpolation formula in the correction step time interval, deriving the state transition equation based on the integral formula, and obtaining the stability critical point by traversing all points in the two-dimensional plane of spindle speed-axial depth of cut and applying the Floquet criterion to the transition matrix corresponding to the state transition equation.

8. The method for constructing stability boundaries for CNC machine tool milling considering time-varying parameters according to claim 1, characterized in that, The stability proxy index is calculated as follows: select multiple calculation points on the machining stability boundary, and calculate the maximum absolute value of the difference between the critical axial depth of cut at each calculation point and the critical axial depth of cut at the corresponding critical spindle speed on the reference boundary, which is used as the stability proxy index.

9. The method for constructing stability boundaries for CNC machine tool milling considering time-varying parameters according to claim 1, characterized in that, The CNC machine tool is a five-axis CNC machine tool, and each coordinate point on the machining path of the CNC machine tool includes X-axis mechanical coordinates, Y-axis mechanical coordinates, Z-axis mechanical coordinates and A-axis mechanical coordinates; the dynamic performance parameters include natural frequencies, modal masses and damping ratios in the X-axis and Y-axis directions.

10. A system for constructing stability boundaries for CNC machine tool milling considering time-varying parameters, characterized in that, include: The module for constructing dynamic performance parameters of CNC machine tool machining path obtains the dynamic performance parameters of CNC machine tool corresponding to each coordinate point on the CNC machine tool machining path, including natural frequency, modal mass and damping ratio; The stability feature point set filtering module filters out the stability feature point set based on the designed stability surrogate index. The stability leaflobe diagram calculation module uses a semi-discrete method based on a prediction-correction scheme to calculate the two-dimensional stability leaflobe diagram corresponding to the feature points. The stability boundary construction module for the entire machining process obtains the three-dimensional milling stability boundary through linear interpolation between a series of two-dimensional stability lobe diagrams; this invention can achieve efficient calculation of the stability boundary when considering the time-varying characteristics of the machine tool's dynamic performance parameters.

Images