Digital twinning-based chatter prediction method for complex blade type cutter in machining process

Abstract

The invention discloses a digital twinning-based chatter prediction method for a complex blade type cutter in a machining process, and the method comprises the following steps: S1, simulating a milling process of the complex blade type cutter based on a digital twinning model, and obtaining a meshing region CWE of the cutter and a workpiece in the machining process; s2, the rotation period of the cutter and a cutting edge participating in cutting are discretized, meshing information of the cutter and a workpiece in the machining process is extracted, and a chatter stability lobe graph of the complex-edge-type cutter under the given working condition is obtained through calculation in combination with the attribute of a machined material and the dynamic characteristics of the cutter; and S3, comparing the stability lobe diagrams of the cutters with different blade types, and selecting the cutter with the optimal blade type under the given working condition. According to the chatter prediction method for the complex blade type cutter machining process based on digital twinning, on the basis of a digital twinning model, calculation and analysis are conducted by dispersing the cutter rotation period and the blade in combination with the material and cutter characteristics, and a stability lobe graph is drawn.

Description

Technical Field

[0001] The present invention relates to the field of intelligent manufacturing technology, and in particular to a method for predicting chatter in a complex blade-shaped tool machining process based on digital twins. Background Art

[0002] Chatter during machining is a major limiting factor in improving material removal rates, productivity, surface quality, and dimensional accuracy of machined parts. There are two types of vibrations during machining: forced vibration and self-excited vibration. Chatter is self-excited, caused by the interaction between varying chip thickness and cutting forces during the cutting process. It is the most damaging type of vibration to machine tool structure and machined surface quality, and the most difficult to control.

[0003] In machine tool machining, especially for machining of hard materials, tool edge profile significantly influences chatter suppression. Currently, chatter prediction methods for milling processes primarily include analytical, semi-discrete, fully discrete, and numerical methods. Semi-discrete, fully discrete, and numerical methods offer high accuracy but are computationally expensive, and their results are generally used to experimentally validate and compare analytical methods. Initial analytical methods were only applicable to chatter prediction during machining of uniform-pitch end mills and were unable to assess chatter during milling of non-standard edge profiles, such as those with variable pitch or helix angles. However, with years of theoretical research and expansion, these methods have gradually become capable of predicting chatter during machining of these tools. However, currently available chatter prediction methods are still limited to conventional tools with variable helix angles and pitches. Chatter prediction and stability lobe mapping are not possible for tools with arbitrarily variable helix angles along the tool axis, hindering blade design across a wider range of edge profiles. The chatter prediction of complex blade-shaped tool machining process based on digital twin can draw the stability lobe diagram of any blade-shaped tool, and guide the selection of the optimal blade shape of the cutting tool under specific working conditions under the premise of designability. Summary of the Invention

[0004] The purpose of the present invention is to provide a method for predicting vibration in the machining process of complex blade-shaped tools based on digital twins, which can obtain the vibration stability lobe diagram of the complex blade shape under given working conditions, and by comparing the stability lobe diagrams of tools with different blade shapes, realize the optimal blade shape selection and reverse design of the cutting tool under specific working conditions.

[0005] To achieve the above objectives, the present invention provides a method for predicting chatter during machining of complex blade-shaped cutting tools based on digital twins, comprising the following steps:

[0006] S1. Simulate the milling process of complex-edge cutting tools based on the digital twin model to obtain the engagement area (CWE) between the tool and the workpiece during machining.

[0007] S2. Discretize the tool rotation period and the cutting edge involved in the cutting process, extract the meshing information between the tool and the workpiece during the machining process, and calculate the chatter stability lobe diagram of the complex-edge tool under given working conditions by combining the properties of the machined material and the dynamic characteristics of the tool;

[0008] S3. Compare the stability lobe diagrams of different blade-shaped tools and select the optimal blade-shaped tool under given working conditions.

[0009] Preferably, in S1, the milling process of the complex-edge tool is simulated based on the digital twin model to obtain the meshing area CWE between the tool and the workpiece during the machining process. The specific process is:

[0010] First, tri-dexel is used to represent the spatial information of the workpiece. That is, dense lines are used to pass through the workpiece in the x, y, and z directions in space, and each line is represented by a line segment formed by the two points where the line enters and exits the workpiece.

[0011] Secondly, the NC code is input into the digital twin system, that is, the motion posture of the tool and the spatial information of the workpiece are input into the digital twin system together to obtain the meshing area CWE between the tool and the workpiece during the machining process.

[0012] Preferably, in S2, the calculation process of the chatter stability lobe diagram of the complex-edge tool is:

[0013] Using the CWE information of the meshing area during the machining process, the discrete steps within any single cycle are extracted, and the time rotation angle, helix angle, and tool axis angle of all cutting edge elements in each discrete step are calculated.

[0014] Calculate the cutting force coefficient matrix under each discrete step, perform zero-order processing on the cutting force coefficient matrix within the cycle, and count the cutting times and time lag angles of all cutting edge elements within the cycle;

[0015] The chatter frequency range is set and discretized according to the tool's natural frequency, and the tool response function, tool speed, and critical stable cutting width at all chatter frequencies are calculated based on the CWE information.

[0016] The critical stable cutting width at all chatter frequencies is plotted against the tool speed, i.e., the stability lobe diagram.

[0017] Preferably, S2 includes performing stability analysis based on a stability analytical model of a standard milling cutter, and the specific process is as follows:

[0018] A four-edge standard milling cutter was selected for milling stability analysis. During the milling process of non-thin-walled workpieces, the vibration amplitude of the workpiece is smaller than that of the tool. Therefore, if the workpiece is regarded as a rigid body, the tool has vibration freedom in the x and y directions respectively.

[0019] Assume that the cutting thickness of the jth blade along the normal direction of the blade during milling is h(φ j ), where φ j is the rotation angle of the jth blade at this moment. This rotation angle is decomposed into Δx and Δy in the x and y directions. The expressions of Δx and Δy are as follows:

[0020] Δx=x j -x j-1 (1);

[0021] Δy=y j -y j-1 (2);

[0022] Among them, x j represents the vibration component of the jth blade along the x direction, x j-1 represents the vibration component of the j-1th edge, i.e., the previous edge, along the x direction;

[0023] According to the stability analysis theory, the relationship between the cutting force and cutting thickness along the x and y directions of the tool is expressed as follows:

[0024]

[0025] Where b is the axial cutting depth, It is the dynamic cutting force coefficient matrix, which is responsible for projecting the force exerted on the tool during the cutting process into the x and y directions.

[0026] Expand the dynamic cutting force coefficient matrix [A] in Fourier series and take the zeroth order term to obtain:

[0027] Assuming that there is no coupling between the degrees of freedom of the tool in the x and y directions, the relationship between the vibration displacement and the cutting force in the x-direction frequency domain is:

[0028]

[0029] Among them, ω c is the flutter frequency, FRF x is the frequency response function of the tool in the x-direction. Substitute equation (4) back into equation (3) and process it to zero order to obtain:

[0030]

[0031] Solving equation (5) yields:

[0032]

[0033] Among them, b lim represents the critical stable cutting width, Λ Re represents the real part of Λ, Λ Im represents the imaginary part of Λ, For standard milling cutters, at the selected chatter frequency ω c The critical stable cutting width is then calculated.

[0034] Preferably, S2 includes discretizing all cutting edges of the milling cutter based on the digital twin model of the generalized milling cutter, and the specific process is as follows:

[0035] Extract relevant information of the blade element meshing with the workpiece at any moment, including the tangential direction, normal direction, cutting thickness and tool speed information of the blade element in the workpiece coordinate system;

[0036] By extracting relevant information of all cutting edge elements within a tool rotation cycle, the stability of the current milling working condition is analyzed, and the stability of the five-axis milling process of unequal helix angle ball-end milling cutters or unequal pitch cylindrical milling cutters is predicted.

[0037] Preferably, S2 further includes performing a vibration stability analysis of the ball end cutter based on a stability analytical model of a generalized milling cutter, and the specific process is as follows:

[0038] In the digital twin model, a rotation period T is discretized into n parts. The cutting width of each cutting edge element along the tool axis is Δb. The information of all cutting edge elements is calculated once every Δt. After the zero-order processing of the [A] matrix in equation (5), equation (5) can be rewritten as:

[0039]

[0040] in:

[0041]

[0042] Among them, N represents the number of blade elements currently involved in cutting, is the blade helix angle, φ i is the rotation angle of the i-th blade element, θ i is the angle between the i-th blade element and the xy plane;

[0043] Assuming that the frequency response functions of the tool in the x and y directions are identical and not coupled, substitute Equation (6) back into Equation (7) and average the [A] matrix within one tool rotation cycle to obtain:

[0044]

[0045] If the multiple time delays caused by cylindrical milling cutters with unequal pitches or unequal helix angles are taken into account, according to the Floquet stability theory, Equation (9) satisfies the following equation under the critical stability condition:

[0046]

[0047] Assumptions Among them, τ i represents the tooth-passing period of the i-th blade element, that is, the time delay from the current blade to the previous blade;

[0048] Select the vibration frequency ω to be scanned c For each ω c Calculate the corresponding speed Ω respectively. The specific calculation process is:

[0049]

[0050] Where n represents the number of cutting elements involved in cutting during the tool rotation period, Λ Im represents the imaginary part of Λ, Λ Re Represents the real part of Λ, in determining ω c Then the rotation speed is obtained by solving equation (11);

[0051] Then, each ω is calculated by formula (10) c Critical cutting depth b lim , thus obtaining a series of (Ω, b lim ) Click on the right;

[0052] Connect all point pairs to obtain the stability lobe diagram of any blade type milling cutter in the five-axis or three-axis milling process, and complete the stability analysis of tools with different blade types under specific working conditions.

[0053] Therefore, the present invention adopts the above-mentioned digital twin-based chatter prediction method for complex blade tool machining process, and the beneficial effects are as follows:

[0054] (1) The present invention combines the tool rotation period and blade discreteness with the meshing area information obtained by the digital twin model and calculates the material and tool characteristics. It can predict the chatter of any blade type tool during processing with high precision, effectively overcoming the limitations of traditional methods for predicting the chatter of complex blade type tools.

[0055] (2) By drawing the vibration stability lobe diagrams of different blade-shaped tools and conducting comparative analysis, the optimal blade-shaped tool can be accurately selected under given working conditions, which provides a scientific basis for the rational selection of tools in actual processing and helps to improve processing efficiency and quality.

[0056] (3) The method of the present invention can not only predict chatter and guide the selection of cutting edge profiles, but also provide strong support for the reverse design of cutting edge profiles under specific working conditions based on stability lobe diagrams and related calculation analysis, thereby expanding the design space of cutting edge profiles and promoting the development of cutting edge design technology.

[0057] The technical solution of the present invention is further described in detail below through the accompanying drawings and embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0058] Figure 1 This is an overall process framework diagram of an embodiment of a method for predicting chatter in a complex blade tool machining process based on digital twins of the present invention;

[0059] Figure 2 This is a visualization of the process of drawing a stability lobe diagram using discrete CWE information in an embodiment of a digital twin-based method for predicting chatter in a complex blade tool machining process according to the present invention, wherein (a) shows the process of machining a blisk using a ball-end milling cutter, (b) shows the CWE area obtained in the process, and (c) shows the SLD diagram obtained by CWE drawing.

[0060] Figure 3 It is a schematic diagram of a specific calculation process of a stability lobe diagram of a complex-edge-shaped tool according to an embodiment of a method for predicting chatter during machining of a complex-edge-shaped tool based on digital twins of the present invention;

[0061] Figure 4 Schematic diagram of a milling model of a standard milling cutter according to an embodiment of a method for predicting chatter during machining of a complex-edge-shaped tool based on digital twinning of the present invention;

[0062] Figure 5 This is a digital twin model of the milling process of an embodiment of a method for predicting chatter during machining of a complex-edge tool based on digital twins according to the present invention. FIG. (a) shows an enlarged view of the CWE region obtained during the process, where green dots represent cutting elements not currently involved in cutting, and red dots represent cutting elements currently involved in cutting. FIG. (b) shows the dexel representation of the workpiece and the process of obtaining the CWE region by performing Boolean operations on the tool-swept volume and the workpiece.

[0063] Figure 6 This is a diagram showing the blade element normal and tangent vector of an embodiment of a method for predicting vibration in a complex blade tool machining process based on digital twinning of the present invention, where (a) is the normal vector and (b) is the tangent vector. DETAILED DESCRIPTION

[0064] The technical solution of the present invention is further described below with reference to the accompanying drawings and embodiments.

[0065] Unless otherwise defined, technical or scientific terms used in the present invention shall have the same meaning as commonly understood by one of ordinary skill in the art to which the present invention belongs.

[0066] like Figure 1As shown in the figure, a chatter prediction method for complex blade-shaped tool machining process based on digital twin is divided into two parts: discretization of simulation machining process information and drawing of stability lobe diagram and blade-shaped modeling guidance, including the following steps:

[0067] S1. In the discretization of the simulated machining process information, the milling process of the complex blade tool is simulated based on the digital twin model to obtain the meshing area CWE between the tool and the workpiece during the machining process. The specific process is as follows:

[0068] First, tri-dexel is used to represent the spatial information of the workpiece. That is, denser lines are used to pass through the workpiece in the x, y, and z directions in space, and each line is represented by a line segment consisting of the two points where the line enters and exits the workpiece.

[0069] Secondly, input the NC code into the digital twin system, that is, input the motion posture of the tool and the spatial information of the workpiece into the digital twin system, and you can get the following: Figure 2 The engagement area CWE between the tool and the workpiece during machining is shown.

[0070] S2. Discretize the tool rotation period and the cutting edge involved in the cutting, extract the meshing information between the tool and the workpiece during the machining process, and combine the properties of the machined material and the dynamic characteristics of the tool to obtain the vibration stability lobe diagram of the complex edge tool under given working conditions, and use it to guide the design of the tool blade. Figure 3 As shown in Figure 2, the calculation process of the chatter stability lobe diagram of a complex edge tool is as follows:

[0071] The CWE information of the meshing area during the machining process is used to extract the discrete steps in any single cycle, and the time rotation angle, helix angle and tool axis angle of all cutting edge elements in each discrete step are calculated.

[0072] The cutting force coefficient matrix of each discrete step is calculated, the cutting force coefficient matrix is processed at zero order within the cycle, and the cutting times and time lag angles of all cutting edge elements within the cycle are counted.

[0073] The chatter frequency range is set and discretized according to the natural frequency of the tool. The tool response function, tool speed and critical stable cutting width at all chatter frequencies are calculated based on the CWE information.

[0074] The critical stable cutting width at all chatter frequencies is plotted against the tool speed, i.e., the chatter stability lobe diagram.

[0075] S2 includes stability analysis based on the stability analytical model of the standard milling cutter. The specific process is as follows:

[0076] Here we select a four-edge standard milling cutter for milling stability analysis, such as Figure 1During the milling process of non-thin-walled workpieces, the vibration amplitude of the workpiece is much smaller than that of the tool. Therefore, if the workpiece is regarded as a rigid body, the tool has vibration freedom in the x and y directions respectively.

[0077] like Figure 4 As shown in the figure, it is assumed that the cutting thickness of the jth edge along the normal direction of the blade during milling is h(φ j ), where φ j is the rotation angle of the jth blade at this moment. This rotation angle is decomposed into Δx and Δy in the x and y directions. The expressions of Δx and Δy are as follows:

[0078] Δx=x j -x j-1 (1);

[0079] Δy=y j -y j-1 (2);

[0080] Among them, x j represents the vibration component of the jth blade along the x direction, x j-1 It represents the vibration component of the j-1th edge, that is, the previous edge along the x direction.

[0081] According to Altintas' stability analysis theory, the relationship between the cutting force along the x and y directions and the cutting thickness is expressed as follows:

[0082]

[0083] Where b is the axial cutting depth, is the dynamic cutting force coefficient matrix, which is responsible for projecting the force exerted on the tool during the cutting process into the x and y directions;

[0084] Expand the dynamic cutting force coefficient matrix [A] in Fourier series and take the zeroth order term to obtain:

[0085]

[0086] Assuming that there is no coupling between the degrees of freedom in the x and y directions of the tool, taking the x direction as an example, the relationship between the vibration displacement and the cutting force in the x direction frequency domain is:

[0087]

[0088] Among them, ω c is the flutter frequency, FRF x is the frequency response function of the tool in the x direction. Substituting equation (4) back into equation (3) and performing zero-order processing, we can obtain:

[0089]

[0090] Solving equation (5) yields:

[0091]

[0092] Among them, b lim represents the critical stable cutting width, Λ Re represents the real part of Λ, Λ Im represents the imaginary part of Λ, For standard milling cutters, at the selected chatter frequency ω c The critical stable cutting width can then be calculated.

[0093] S2 includes Figure 5 The digital twin model of the generalized milling cutter shown discretizes all the cutting edges of the milling cutter. The specific process is as follows:

[0094] Extract the microelement of the cutting edge that is engaged with the workpiece at any moment (e.g. Figure 5 The relevant information of the tool edge element (shown as a red dot) includes the tangential direction, normal direction, cutting thickness and tool speed of the tool edge element in the workpiece coordinate system.

[0095] By extracting relevant information of all blade elements within a tool rotation cycle, the stability of the current milling working condition can be analyzed, thereby realizing the stability prediction of the five-axis milling process of unequal helix angle ball-end milling cutters or unequal pitch cylindrical milling cutters.

[0096] S2 also includes a chatter stability analysis of ball-end cutters based on a generalized milling cutter stability analytical model. The specific process is as follows:

[0097] Altintas calculates the dynamic cutting force coefficient matrix based on the current meshing area and processes it using either the zero-order method or the multi-frequency method. However, in complex five-axis milling conditions with ball-end cutters, the meshing area between the tool and the workpiece changes constantly during the tool rotation cycle. Therefore, assuming the meshing area remains constant, calculating the dynamic cutting force coefficient matrix over a single tool rotation cycle is not accurate.

[0098] Therefore, this embodiment not only realizes a more accurate calculation of the dynamic cutting force coefficient matrix by extracting the state information of the blade element at each moment, but also takes into account the multiple time delays caused by unequal pitch cylindrical milling cutters or unequal helix angle cylindrical milling cutters, thereby realizing the stability prediction of the five-axis milling process for unequal helix angle ball-end milling cutters or unequal pitch cylindrical milling cutters while improving the prediction accuracy.

[0099] In the digital twin model, a rotation period T is discretized into n parts. The cutting width of each blade element along the tool axis is Δb. The information of all cutting edge elements is calculated once every Δt. After the zero-order processing of the [A] matrix in equation (5), equation (5) can be rewritten as:

[0100]

[0101] in:

[0102]

[0103] Among them, N represents the number of blade elements currently involved in cutting, is the blade helix angle, φ i is the rotation angle of the i-th blade element, θ i is the angle between the i-th blade element and the xy plane (e.g. Figure 3 shown).

[0104] Assuming that the frequency response functions of the tool in the x and y directions are identical and not coupled, substitute Equation (6) back into Equation (7) and average the [A] matrix within one tool rotation cycle to obtain:

[0105]

[0106] If the multiple time delays caused by cylindrical milling cutters with unequal pitches or unequal helix angles are taken into account, according to the Floquet stability theory, Equation (9) satisfies the following equation under the critical stability condition:

[0107]

[0108] Assumptions Among them, τ i It represents the tooth-passing period of the i-th blade element, that is, the time delay from the current blade to the previous blade.

[0109] Finally, select the vibration frequency ω to be scanned c range (generally near the natural frequency of the system), for each ω c Calculate the corresponding speed Ω respectively. The specific calculation process is:

[0110]

[0111] Where n represents the number of cutting elements involved in cutting during the tool rotation period, Λ Im represents the imaginary part of Λ, Λ Re Represents the real part of Λ, in determining ω c Then the rotation speed is obtained by solving equation (11);

[0112] Then, each ω can be calculated by formula (10) cCritical cutting depth b lim , thus obtaining a series of (Ω, b lim )Click right.

[0113] By connecting all the point pairs, the stability lobe diagram of any blade type milling cutter in the five-axis or three-axis milling process can be obtained, so that the stability analysis of tools with different blade types under specific working conditions can be completed, thereby guiding the design of tool blade types.

[0114] S3. Compare the stability lobe diagrams of different blade-shaped tools and select the optimal blade-shaped tool under given working conditions.

[0115] Therefore, the present invention adopts the above-mentioned digital twin-based chatter prediction method for the complex blade tool processing process. By simulating the milling process based on the digital twin model, the meshing area information is obtained, the discretized tool rotation cycle and blade are calculated and analyzed in combination with the material and tool characteristics, the stability lobe diagram is drawn and the lobe diagrams of different blade tools are compared, thereby realizing the prediction of chatter in the processing process of any blade tool under high precision, providing an effective method for the optimal blade selection and reverse design of cutting tools under specific working conditions, expanding the scope of tool blade selection and design, and overcoming the limitations of traditional chatter prediction methods in the application of complex blade tools.

[0116] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention rather than to limit the same. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that they can still modify or replace the technical solutions of the present invention with equivalents, and these modifications or equivalent replacements cannot cause the modified technical solutions to deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. A chatter prediction method for complex blade tool machining process based on digital twin, characterized by: The following steps are involved: S1. Simulate the milling process of complex-edge cutting tools based on the digital twin model to obtain the engagement area (CWE) between the tool and the workpiece during machining. S2. Discretize the tool rotation period and the cutting edge involved in the cutting process, extract the meshing information between the tool and the workpiece during the machining process, and calculate the chatter stability lobe diagram of the complex-edge tool under given working conditions by combining the properties of the machined material and the dynamic characteristics of the tool; S3. Compare the stability lobe diagrams of different blade-shaped tools and select the optimal blade-shaped tool under given working conditions.

2. The method for predicting chatter during machining of complex-edge tool based on digital twin according to claim 1, characterized in that: In S1, the milling process of the complex-edge tool is simulated based on the digital twin model to obtain the engagement area (CWE) between the tool and the workpiece during the machining process. The specific process is as follows: First, tri-dexel is used to represent the spatial information of the workpiece. That is, dense lines are used to pass through the workpiece in the x, y, and z directions in space, and each line is represented by a line segment formed by the two points where the line enters and exits the workpiece. Secondly, the NC code is input into the digital twin system, that is, the motion posture of the tool and the spatial information of the workpiece are input into the digital twin system together to obtain the meshing area CWE between the tool and the workpiece during the machining process.

3. The method for predicting chatter during machining of complex-edge tool based on digital twin according to claim 2, characterized in that: In S2, the calculation process of the chatter stability lobe diagram of the complex edge tool is: Using the CWE information of the meshing area during the machining process, the discrete steps within any single cycle are extracted, and the time rotation angle, helix angle, and tool axis angle of all cutting edge elements in each discrete step are calculated. Calculate the cutting force coefficient matrix under each discrete step, perform zero-order processing on the cutting force coefficient matrix within the cycle, and count the cutting times and time lag angles of all cutting edge elements within the cycle; The chatter frequency range is set and discretized according to the tool's natural frequency, and the tool response function, tool speed, and critical stable cutting width at all chatter frequencies are calculated based on the CWE information. The critical stable cutting width at all chatter frequencies is plotted against the tool speed, i.e., the stability lobe diagram.

4. The method for predicting chatter during machining of complex-edge tool based on digital twin according to claim 3, characterized in that: S2 includes stability analysis based on the stability analytical model of the standard milling cutter. The specific process is as follows: A four-edge standard milling cutter was selected for milling stability analysis. During the milling process of non-thin-walled workpieces, the vibration amplitude of the workpiece is smaller than that of the tool. Therefore, if the workpiece is regarded as a rigid body, the tool has vibration freedom in the x and y directions respectively. Assume that the cutting thickness of the jth blade along the normal direction of the blade during milling is h(φ j ), where φ j is the rotation angle of the jth blade at this moment. This rotation angle is decomposed into Δx and Δy in the x and y directions. The expressions of Δx and Δy are as follows: Δx=x j -x j-1 (1); Δy=y j -y j-1 (2); Among them, x j represents the vibration component of the jth blade along the x direction, x j-1 represents the vibration component of the j-1th edge, i.e., the previous edge, along the x direction; According to the stability analysis theory, the relationship between the cutting force and cutting thickness along the x and y directions of the tool is expressed as follows: Where b is the axial cutting depth, is the dynamic cutting force coefficient matrix, which is responsible for projecting the force exerted on the tool during the cutting process into the x and y directions; Expand the dynamic cutting force coefficient matrix [A] in Fourier series and take the zeroth order term to obtain: Assuming that there is no coupling between the degrees of freedom of the tool in the x and y directions, the relationship between the vibration displacement and the cutting force in the x-direction frequency domain is: Among them, ω c is the flutter frequency, FRF x is the frequency response function of the tool in the x-direction. Substitute equation (4) back into equation (3) and process it to zero order to obtain: Solving equation (5) yields: Among them, b lim represents the critical stable cutting width, Λ Re represents the real part of Λ, Λ Im represents the imaginary part of Λ, For standard milling cutters, at the selected chatter frequency ω c The critical stable cutting width is then calculated.

5. The method for predicting chatter during machining of complex-edge tool based on digital twin according to claim 4, characterized in that: S2 involves discretizing all the cutting edges of the milling cutter based on the digital twin model of the generalized milling cutter. The specific process is as follows: Extract relevant information of the blade element meshing with the workpiece at any moment, including the tangential direction, normal direction, cutting thickness and tool speed information of the blade element in the workpiece coordinate system; By extracting relevant information of all cutting edge elements within a tool rotation cycle, the stability of the current milling working condition is analyzed, and the stability of the five-axis milling process of unequal helix angle ball-end milling cutters or unequal pitch cylindrical milling cutters is predicted.

6. The method for predicting chatter during machining of complex-edge tool based on digital twin according to claim 5, characterized in that: S2 also includes a ball-end cutter chatter stability analysis based on a generalized milling cutter stability analytical model. The specific process is as follows: In the digital twin model, a rotation period T is discretized into n parts. The cutting width of each cutting edge element along the tool axis is Δb. The information of all cutting edge elements is calculated once every Δt. After the zero-order processing of the [A] matrix in equation (5), equation (5) can be rewritten as: in: Among them, N represents the number of blade elements currently involved in cutting, is the blade helix angle, φ i is the rotation angle of the i-th blade element, θ i is the angle between the i-th blade element and the xy plane; Assuming that the frequency response functions of the tool in the x and y directions are identical and not coupled, substitute Equation (6) back into Equation (7) and average the [A] matrix within one tool rotation cycle to obtain: If the multiple time delays caused by cylindrical milling cutters with unequal pitches or unequal helix angles are taken into account, according to the Floquet stability theory, Equation (9) satisfies the following equation under the critical stability condition: τ i represents the tooth-passing period of the i-th blade element, that is, the time delay from the current blade to the previous blade; Select the vibration frequency ω to be scanned c For every ω c Calculate the corresponding speed Ω respectively. The specific calculation process is: Where n represents the number of cutting elements involved in cutting during the tool rotation period, Λ Im represents the imaginary part of Λ, Λ Re Represents the real part of Λ, in determining ω c Then the rotation speed is obtained by solving equation (11); Then, each ω is calculated by formula (10) c Critical cutting depth b lim , thus obtaining a series of (Ω, b lim ) Click on the right; Connect all point pairs to obtain the stability lobe diagram of any blade type milling cutter in the five-axis or three-axis milling process, and complete the stability analysis of tools with different blade types under specific working conditions.

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