Variable-depth turning path planning method and system for suppressing thin-wall sleeve ring chatter

Abstract

This invention relates to the field of CNC turning technology, specifically to a method and system for planning variable depth of cut turning paths to suppress chatter in thin-walled ring turning. The method includes: constructing a variable network path model integrating four modes: constant depth of cut, linear gradual change, sinusoidal variable depth of cut, and stiffness feedback adaptive variable depth of cut; generating vibration response using a digital twin of the thin-walled ring-tool system and extracting a risk profile containing a comprehensive chatter risk index and modal risk boundary parameters; optimizing the depth of cut parameters of key nodes using a path value function and a three-layer nested evolutionary game of macro-meso-micro levels; and performing local reconstruction iteration on brittle node groups to obtain a variable depth of cut path that balances agility and robustness. This achieves precise suppression of chatter in thin-walled ring turning, significant improvement in machining stability, and high efficiency.

Description

Technical Field

[0001] This invention relates to the field of CNC turning technology, specifically to a method and system for variable depth of cut turning path planning to suppress chatter in thin-walled rings. Background Technology

[0002] Thin-walled ring-shaped parts are key components in core equipment such as aero-engines and precision machine tool spindles, and their machining accuracy and surface quality directly affect the overall performance of the machine. However, due to the extremely small wall thickness relative to their diameter and weak rigidity, these parts are highly susceptible to chatter during turning. Chatter not only reduces the integrity of the machined surface of the workpiece but also accelerates tool wear and can even lead to chipping, severely restricting machining efficiency and yield. Currently, commonly used chatter suppression methods in industry mainly include conservatively selecting constant low depth of cut and low feed parameters, adding passive dynamic vibration absorbers or active suppression devices, and locally enhancing support stiffness through special fixtures. However, the actual wall thickness of thin-walled rings often varies along the circumference due to design or process variations, and the fixture support positions are discretely distributed, resulting in extremely uneven local dynamic stiffness of the part that evolves in real time as material is removed. A constant depth of cut cannot match this dynamic non-uniform stiffness field: in areas with weak stiffness, a fixed depth of cut may still induce severe chatter; while in areas with sufficient stiffness, an excessively low fixed depth of cut severely sacrifices machining efficiency. Although adaptive adjustment methods based on online vibration monitoring can adjust parameters according to real-time signal feedback, their response lags behind the sudden increase of flutter and they lack the ability to predict the modal evolution during the initial flutter incubation stage. They can only perform passive correction and cannot fundamentally achieve flutter-free processing.

[0003] Furthermore, in exploring the integration of variable depth-of-cut path planning with digital twin technology for the cutting process, existing methods either pre-set regular variable depth-of-cut waveforms such as sine waves and sawtooth waves for open-loop injection, attempting to disrupt the formation conditions of regenerative chatter. However, they fail to intrinsically link the depth-of-cut variation with physical constraints such as the workpiece's wall thickness distribution and clamping boundaries. This can easily introduce new forced vibrations or cause unreasonable fluctuations in material removal rate while suppressing vibrations. In addition, regarding the optimization of all nodes in the turning path, existing plans mostly seek optimization independently at isolated nodes, lacking a multi-level collaborative decision-making mechanism that can take into account the smooth modal transition between adjacent nodes, global stability, and local agile response. This makes it difficult to simultaneously achieve global vibration suppression capability, parameter robustness, and machining efficiency in the turning path of complex thin-walled rings. Summary of the Invention

[0004] To overcome the problems of existing technologies, such as the inability to dynamically adapt the depth of cut based on the local stiffness of thin-walled rings, the lack of quantitative assessment of layered chatter risk, and the lack of multi-node global collaborative optimization, this invention provides a variable depth of cut turning path planning method and system for suppressing chatter in thin-walled rings. This method achieves precise suppression of chatter during thin-walled ring turning, a significant improvement in machining stability, and a balance between high efficiency and high performance.

[0005] The technical solution of this application specifically includes: According to one aspect of this application, a variable depth turning path planning method for suppressing chatter in thin-walled rings is provided, comprising: The surface to be machined on the thin-walled ring is discretized into path nodes. The local static stiffness is characterized by binding the wall thickness and the fixture support position. The cutting depth mode and micro-control parameters are preset to construct a variable network model of the variable cutting depth turning path. The digital twin model is driven to generate time-domain vibration response signals of each path node. Constrained adaptive modal decomposition is performed to obtain a rigid following layer, a semi-stable flutter coupling layer, and an unstable impact layer. Features are extracted to calculate a comprehensive flutter risk index and generate modal risk boundary parameters to form a risk profile. The path value function is constructed using risk profiles to calculate cumulative value and value gradient, identify critical path nodes, and lock the micro-control parameters of the remaining path nodes. A three-layer nested evolutionary game, consisting of a micro-control parameter layer, a meso-mode layer, and a macro-global layer, is executed with critical path nodes as participants. After convergence, the game is spliced ​​together to form a complete variable-cut deep turning path. The complete variable depth turning path is loaded into the digital twin model to calculate the agility index, the brittle node group is marked and local reconstruction iteration is performed to obtain the robust variable depth turning path. The robust variable cutting depth path is compiled into CNC code for the first piece trial cut. The modal level is determined by an online classification model. Dead zone bias is applied to the rigid following layer. The cutting depth parameters are fine-tuned for the semi-stable flutter coupling layer. The protection action is triggered for the unstable impact layer. The process document is then solidified.

[0006] As a further option of the method of the present invention, the local static stiffness characterization method includes: acquiring the wall thickness distribution data and fixture support position of the thin-walled ring, generating path nodes along the tool feed direction, binding a corresponding wall thickness value to each node and calculating the distance from the node to the nearest fixture support point, and calculating the local static stiffness based on the following formula: ;in, Let be the local static stiffness of the i-th node. The elastic modulus of the material. For node wall thickness, The Euclidean distance from the node to the nearest clamp support point is given. The shape factor, The distance decay exponent; The preset cutting depth modes and micro-control parameters include: a preset constant cutting depth mode, a linearly varying cutting depth mode, a sinusoidal variable cutting depth mode, and an adaptive variable cutting depth mode based on adjacent node stiffness feedback; wherein, the sinusoidal variable cutting depth mode is based on... change, For node cutting depth, Based on the cutting depth, For the depth of cut, For spatial frequency, For the initial phase, The coordinates are the arc length of the node; the adaptive variable cutting depth mode adjusts the cutting depth based on the local stiffness changes of the preceding node after being amplified by the gain coefficient, and has a maximum adjustment limit.

[0007] As a further option of the method of the present invention, the step of constructing the variable network model of the variable depth turning path includes: Establish sequential connections between nodes to form the main path; Set conditional branch connections at nodes. If the overall flutter risk index is higher than the preset threshold, or the local stiffness is lower than the preset threshold, branch edges are led out from the corresponding nodes to the conservative cutting depth mode path. A feedback loop connection is constructed to map the vibration monitoring characteristics of subsequent nodes back to the preceding nodes, which is used for online parameter updates of the adaptive variable cut depth mode. The weight of the feedback loop connection is dynamically adjusted by the modal risk boundary parameters in the risk profile.

[0008] As a further option of the method of the present invention, the steps for obtaining the rigid follower layer, the semi-stable flutter coupling layer, and the unstable impact layer include: A digital twin model of the driving thin-walled collar-tool system is used. The digital twin model adopts dynamic cutting force that considers regeneration effect and generates tool tip vibration displacement time history signal with nodal wall thickness and support position as boundaries. Constrained adaptive modal decomposition is performed on the time history signal, with the number of decomposition layers set to 3. Center frequency constraints are introduced in the variational modal decomposition, so that the center frequency of the rigid follower layer is constrained to the principal axis rotation frequency and its low harmonic neighborhood, the center frequency of the semi-stable flutter coupling layer is constrained to the regenerative flutter prediction frequency band, and the center frequency of the unstable impact layer is constrained to the high-frequency broadband region. The three modal components are obtained by iterative solution.

[0009] As a further option of the method of the present invention, the steps of calculating the comprehensive flutter risk index and generating the modal risk boundary parameters include: Calculate the energy proportion of each layer ,in Corresponding sequentially to the rigid follower layer, the semi-stable flutter coupling layer, and the unstable impact layer, For the first The time-domain signal of the layer modal components, For analysis of time windows; Hilbert transform is performed on the modal components of each layer to extract the envelope, and the maximum envelope amplitude is taken. And calculate the coefficient of variation of the envelope as volatility. : ,in and These are the standard deviation and mean of the envelope sequence, respectively, forming a feature vector containing energy proportion, envelope amplitude, and volatility.

[0010] As a further option of the method of the present invention, the calculation method of the comprehensive tremor risk index includes: Calculate the instability contribution coefficient of each layer using the following formula. : ;in, The stiffness attenuation index, This is the volatility amplification factor. For volatility.

[0011] As a further option of the method of the present invention, the calculation of the comprehensive flutter risk index further includes: The comprehensive flutter risk index is obtained by weighting and aggregating the instability contribution coefficients of the three layers. The weight satisfy Furthermore, the weights of the semi-stable flutter coupling layer and the unstable impact layer are greater than the weights of the rigid follower layer.

[0012] As a further option of the method of the present invention, the step of constructing a path value function using a risk profile and calculating the cumulative value and value gradient includes: The instantaneous value of a node is defined as a weighted combination of three factors: cut depth gain, comprehensive flutter risk penalty, and a smoothing term for cut depth changes of adjacent nodes. Establishing paths to accumulate value The recurrence relation: ;in, For the instantaneous value of a node, The feasible region is defined by the modal risk boundary parameters. As a discount factor, For the first The selected cutting depth at each node For the first The cutting depth has been determined at each node. Given the current node's cutting depth as Under the condition of the first The maximum cumulative value from node to endpoint; The cumulative value of each node is solved by recursively working backward from the end node, and the value gradient of the cumulative value with respect to the cutting depth parameter is calculated simultaneously. .

[0013] As a further option of the method of the present invention, the micro-control parameters for calibrating critical path nodes and locking the remaining path nodes include: Nodes that simultaneously meet the following three conditions are: the comprehensive flutter risk index exceeds the preset risk threshold, the value gradient turning point is greater than the gradient significant change threshold, and the arc length with adjacent nodes is greater than the minimum distance. Nodes that do not meet any of the conditions are considered non-critical nodes, and their micro-control parameters are locked to the lowest risk default value or a smooth transition value from the parameters of adjacent critical nodes.

[0014] As a further option of the method of the present invention, the three-layer nested evolutionary game with critical path nodes as participants, comprising a micro-level control parameter layer, a meso-level model layer, and a macro-level global layer, includes: Define a strategy as a tuple for each key node , The pattern identifier selected from the four depth cutting modes. The vector represents the micro-control parameters for the corresponding mode. The policy feasible region is constrained by the modal risk boundary parameters and the value gradient. The payoff function is the cumulative value of the nodes.

[0015] As a further option of the method of the present invention, the three-layer nested evolutionary game includes: The micro-control parameter layer independently runs particle swarm optimization within each key node at the highest frequency. The particle velocity update introduces a value gradient guiding term, and the optimal micro-control parameters are iteratively solved within the feasible region. The meso-mode layer binds adjacent key nodes into fragments at a moderate frequency, performs cutting-depth mode selection synchronously, adopts an evolutionary strategy and applies modal smoothing constraints, and penalizes mode differences and jumps between adjacent nodes. The macro-level global layer synchronizes all key nodes at the lowest frequency, aiming to maximize the global value function. It dynamically coordinates the strategies of each node through optimal response until Nash equilibrium is reached.

[0016] As a further option of the method of the present invention, the step of forming the complete variable depth of cut turning path includes: Extract the cut depth pattern and micro-control parameters after convergence at each key node; For locked non-critical nodes, a smooth transition is achieved by linear interpolation based on the arc length ratio of the parameters of adjacent critical nodes; By concatenating the parameters of critical nodes and non-critical nodes in the path order, a complete variable depth turning path is generated.

[0017] As a further option of the method of the present invention, the robust variable cut depth path formation step includes: In a digital twin model, short-duration, depth-of-cut pulse perturbations are injected along the path to selected nodes. The vibration response after the perturbation is recorded, and the agility index is calculated. : ;in The recovery time for vibration to return to steady state. For the maximum overshoot, , These are the weighting coefficients; Nodes whose agility index exceeds the allowable upper limit are marked as fragile nodes, and spatially continuous fragile nodes are clustered into fragile node groups. Extract the fragile node group and several adjacent nodes before and after it as the local reconstruction region, return to execute the steps of calculating the cumulative value and value gradient, identifying critical path nodes and the three-layer nested evolutionary game, re-optimize the parameters of the local region until the agility index of all nodes reaches the target, and output the robust variable cutting depth path.

[0018] As a further option of the method of the present invention, the steps of using an online classification model to determine the modal level, performing dead zone bias on the rigid following layer, fine-tuning the shear depth parameters of the semi-stable flutter coupling layer, and triggering protective actions on the unstable impact layer include: The online classification model is trained using modal feature vectors and three-layer labels from the risk profile. It takes the vibration features of the sliding window as real-time input and outputs the probability of each modal level. For nodes identified as rigid follower layers, keep the current cut depth parameters unchanged; For nodes identified as semi-stable flutter coupling layers, according to Calculate the depth of cut fine adjustment amount ,in This is an adjustable gain coefficient; and before performing fine-tuning, it is verified whether the sign of the fine-tuning amount is consistent with the sign of the value gradient calculated in real time. If they are inconsistent, the fine-tuning is abandoned. For nodes identified as unstable impact layers, rapid tool retraction and spindle deceleration protection actions are immediately triggered.

[0019] Another aspect of this application provides a variable depth of cut turning path planning system for suppressing chatter in thin-walled rings, the system comprising: The path discretization and network modeling module is used to discretize the surface of the thin-walled ring to be machined into path nodes, bind the wall thickness and the fixture support position to characterize the local static stiffness, preset the cutting depth mode and micro control parameters, and construct a variable network model of the variable cutting depth turning path. The vibration response analysis and risk filing module is used to drive the digital twin model to generate time-domain vibration response signals of each path node, perform constrained adaptive modal decomposition to obtain a rigid following layer, a semi-stable flutter coupling layer and an unstable impact layer, extract features to calculate a comprehensive flutter risk index and generate modal risk boundary parameters to form a risk file; The value delivery and key node identification module is used to construct a path value function using risk profiles, calculate cumulative value and value gradient, identify key path nodes, and lock the micro-control parameters of other path nodes. The three-layer nested evolutionary game optimization module is used to perform a three-layer nested evolutionary game with key path nodes as participants, consisting of a micro-control parameter layer, a meso-mode layer, and a macro-global layer. After convergence, the game is spliced ​​together to form a complete variable-cut deep turning path. The digital twin verification and brittle reconstruction module is used to load the complete variable depth turning path into the digital twin model to calculate the agility index, mark the brittle node group and perform local reconstruction iteration to obtain a robust variable depth turning path. The online control and process solidification module is used to compile the robust variable cutting depth path into CNC code for the first piece trial cut, use the online classification model to determine the modal level, perform dead zone bias on the rigid following layer, fine-tune the cutting depth parameters on the semi-stable flutter coupling layer, trigger protection actions on the unstable impact layer, and solidify the process file.

[0020] The beneficial effects of this invention are: To address the bottlenecks in existing technologies, such as the inability of constant cutting depth to match the non-uniform local stiffness field of thin-walled rings, the inefficiency of passive vibration suppression methods, and the lag of adaptive adjustment behind the sudden increase in flutter, this paper proposes a new approach. This approach discretizes the surface to be processed into path nodes bound to the wall thickness and support positions to accurately characterize local static stiffness. A variable network model encompassing four cutting depth modes and microscopic control parameters is constructed. This model drives a digital twin to generate a time-domain vibration response, which is then constrained by adaptive modal decomposition into a rigid following layer, a semi-stable flutter coupling layer, and an unstable impact layer. This achieves refined stratification of vibration modes and quantification of a comprehensive flutter risk index. Subsequently, key nodes are calibrated using path value functions and value gradients. A three-layer nested evolutionary game involving microscopic parameters, mesoscopic modes, and macroscopic global parameters is executed to achieve global collaborative optimization of cutting depth modes and parameters. Robust variable cutting depth paths are obtained through digital twin probe perturbation agility verification and iterative local reconstruction of brittle nodes. Finally, a modal classification model is applied online to achieve stratified differentiated control. The implementation examples demonstrate that, compared with the traditional constant depth of cut process, this method improves the roundness of the thin-walled ring's weakest section from 25μm to 8μm, reduces the surface roughness from 1.2μm to 0.6μm, and shortens the single-piece processing time by approximately 18%. It achieves a leap from passive correction to active prediction and full-path optimization suppression of chatter, significantly improving the balance between processing accuracy, surface quality, and production efficiency. Attached Figure Description

[0021] Figure 1 A schematic diagram of the variable depth of cut turning path planning method to suppress chatter in thin-walled rings; Figure 2 S100 flowchart of the variable depth of cut turning path planning method to suppress chatter in thin-walled rings; Figure 3 S200 flowchart of the variable depth of cut turning path planning method to suppress chatter in thin-walled rings; Figure 4S300 flowchart of the variable depth of cut turning path planning method to suppress chatter in thin-walled rings; Figure 5 S400 flowchart of variable depth of cut turning path planning method to suppress chatter of thin-walled rings; Figure 6 S500 flowchart of variable depth of cut turning path planning method to suppress chatter of thin-walled rings; Figure 7 S600 flowchart of the variable depth of cut turning path planning method to suppress chatter in thin-walled rings; Figure 8 , Figure 9 , Figure 10 , Figure 11 and Figure 12 The interface diagram of the variable depth of cut turning path planning system for suppressing chatter in thin-walled rings. Detailed Implementation

[0022] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0023] The theoretical foundation of this invention is based on the dynamics of regenerative chatter during thin-walled rotating workpiece cutting, constrained adaptive modal decomposition theory, path value transfer, and multi-level nested evolutionary game theory. By discretizing the surface to be machined along the feed direction into path nodes bound by wall thickness and support positions, a variable network model containing multiple depth-of-cut modes and micro-control parameters is established. For each node, a digital twin model of the thin-walled collar-tool system is driven to generate a time-domain vibration response, and constrained adaptive modal decomposition is performed. The response is decoupled into three levels: rigid following, semi-stable chatter coupling, and unstable impact. Features such as energy proportion, envelope amplitude, and volatility of each level are extracted. A path value function is then constructed, and the accumulated value and value gradient are obtained through forward accumulation and backward recursion, identifying key path nodes. Using key nodes as game participants, a three-level nested evolutionary game involving micro-parameter layer, meso-mode layer, and macro-global layer is executed. After evolution convergence, a complete variable depth-of-cut turning path is formed. Combining digital twin verification and local reconstruction of brittle nodes, a robust variable depth-of-cut path is finally obtained and fine-tuned and solidified online. The core theoretical conception includes: a single-degree-of-freedom cutting dynamics model for thin-walled rings under regenerative effects, whose general form is a time-delay differential equation jointly described by modal mass, damping, stiffness, and cutting force coefficients, with the regeneration term consisting of the difference between the previous revolution and the current vibration displacement. By decomposing the tool tip vibration displacement into three independent modal components and achieving separation through applying a priori constraints on the center frequency, the dynamic behavior at different time scales can be quantitatively distinguished. Path planning transforms chatter suppression into an optimal control problem that maximizes the cumulative value under risk boundary constraints, and solves it using Bellman recursion. This theoretical framework unifies chatter suppression, depth-of-cut variation, and global path optimization within the same mathematical model, providing a physical and mathematical foundation for practical implementation.

[0024] The specific embodiments of the present invention will be described in detail below.

[0025] Example 1: Please see Figure 1 This invention illustrates a variable depth-of-cut turning path planning method for suppressing chatter in thin-walled rings, provided by an embodiment of the present invention. The method includes: S100: Discretize the surface to be machined into path nodes along the feed direction, binding the wall thickness and support position. Preset four depth-of-cut modes and their micro-control parameters, and construct a variable network model of variable depth-of-cut turning path that includes sequential connection, conditional branching and feedback loop.

[0026] S200: Drives digital twins to generate time-domain vibration responses of each node. Through constrained adaptive modal decomposition, it separates rigid following layer, semi-stable flutter coupling layer and unstable impact layer. It extracts energy proportion, envelope amplitude and volatility, and calculates instability contribution coefficient and comprehensive flutter risk index in combination with local static stiffness. At the same time, it generates modal risk boundary parameters to form node risk profiles.

[0027] S300: Based on the risk profile, a path value function is constructed that integrates flutter risk and material removal efficiency. The cumulative value and value gradient are obtained by forward accumulation and backward recursion. Nodes that meet the requirements of risk exceeding the limit, significant gradient inflection and spacing greater than the minimum arc length are marked as key nodes, and the remaining nodes are locked with micro-control parameters.

[0028] S400: Taking key nodes as game participants, it performs a three-layer nested evolutionary game of micro-parameter layer, meso-mode layer and macro-global layer within the feasible domain limited by modal risk boundary parameters and value gradient. After convergence, it extracts the optimal cutting depth mode and micro-parameters of each key node and splices them with the locked parameters to form a complete variable cutting depth path.

[0029] S500: Load the complete path into the digital twin and inject probe perturbation along the path. Calculate the agility index through vibration response sensitivity to mark brittle node groups. Extract the brittle region and its neighborhood and return value transfer and nested game to perform local reconstruction iteration until the agility of all nodes meets the standard, and output a robust variable-depth path.

[0030] S600: The robust path is compiled into CNC code for the first piece test cut. The cutting force and vibration spectrum are collected online and the modal feature classification model is used to determine the modal level in real time. Dead zone bias is performed on the rigid following layer. The cutting depth is finely adjusted after the value gradient consistency verification of the semi-stable flutter coupling layer. The protection action is triggered for the unstable impact layer. Finally, the verification parameters are solidified into the process document.

[0031] Please refer to Figure 2 It illustrates a flowchart of step S100 in an exemplary variable depth turning path planning method for suppressing chatter in thin-walled rings, the contents of which include: S110: Discretize the surface of the thin-walled ring to be machined into path nodes along the tool feed direction, and bind the wall thickness and fixture support position information of each node to characterize the local static stiffness.

[0032] S120: Four cutting depth modes and their micro-control parameters are preset for path nodes. The four cutting depth modes are constant cutting depth mode, linear gradual cutting depth mode, sinusoidal variable cutting depth mode and adaptive variable cutting depth mode based on stiffness feedback of adjacent nodes. The micro-control parameters include at least cutting depth amplitude, rate of change and frequency.

[0033] S130: Based on sequential connection, conditional branch connection and feedback loop connection, a variable network model for variable cutting depth turning path is constructed, which includes all path nodes.

[0034] In one possible implementation of step S110, the process of discretizing path nodes and binding local static stiffness further includes: S111: Obtain the complete three-dimensional geometric model and wall thickness distribution data of the thin-walled ring. Extract the parametric expression of the surface to be processed through the CAD model of the workpiece, and obtain the actual wall thickness value by dense sampling along the surface using ultrasonic thickness measurement or optical scanning, forming a wall thickness mapping table.

[0035] S112: Determine the support positions and contact envelopes of all fixture components during turning. Fixture supports include chuck jaws, auxiliary support blocks, tailstock centers or special fan-shaped soft jaws, etc. Record the coordinates of each support point in the workpiece coordinate system and the effective support radius to obtain a discrete support position set.

[0036] S113: Generate a path node sequence along the tool feed direction at equal arc length or equal chord length intervals. Let the total number of nodes be N, and the feed arc length position corresponding to the i-th node be... Spatial coordinates are Based on the wall thickness mapping table, assign the wall thickness values ​​corresponding to the node coordinates. Bind to the node; simultaneously calculate the Euclidean distance from the node to the nearest clamp support point. Bind support distance information.

[0037] S114: Calculation of local static stiffness characterization value based on nodal wall thickness and support distance In one possible implementation of this step, the local static stiffness is approximately derived using cantilever beam or thin shell theory, and the expression is: ;in The elastic modulus of the material. The shape factor is related to the boundary conditions. This is the distance decay exponent. The calculated value... Store it in the node data structure.

[0038] This step S120 further includes: S121: Define a constant cut depth mode. In this mode, the cut depth values ​​of all nodes are kept consistent, and the cut depth of node i is... It equals a fixed value, denoted as This method is suitable for sections with high local stiffness and gradual changes. The micro-control parameters are limited to the depth of cut. This parameter is directly used as a decision variable in the optimization process.

[0039] S122: Defines a linearly varying cut depth mode. The node cut depth changes linearly along the path, starting from the initial cut depth. and depth of cut at the endpoint The decision is made that the cutting depth at intermediate nodes is linearly interpolated based on the arc length. Micro-control parameters include the cutting depth amplitude and rate of change.

[0040] S123: Define the sinusoidal variable shear depth mode. The nodal shear depth varies according to the following formula: ;in Based on the cutting depth, For the depth of cut, For spatial frequency, For the initial phase, These are the coordinates of the nodal arc length. Microscopic control parameters include the basic cutting depth. Amplitude Spatial frequency With phase .

[0041] S124: Defines an adaptive variable shear depth mode based on stiffness feedback from adjacent nodes. In this mode, the shear depth of the i-th node is adjusted by feedback from the local stiffness and vibration response characteristics of the preceding node. The recursive relationship is determined by superimposing the stiffness change, scaled by a gain coefficient, onto the shear depth of the previous node. The gain coefficient and the nominal value jointly determine the adjustment range, and a maximum adjustment limit is set to prevent abrupt changes in shear depth. The micro-control parameters include the gain coefficient and the maximum adjustment limit.

[0042] S125: Package the micro-control parameters of the above four modes into a unified data structure. Each node stores the selected mode identifier and the corresponding parameter set. For unselected modes, the parameters can be left blank or set to the default value.

[0043] This step S130, constructing the network model, further includes: S131: Connect all nodes in the form of a unidirectional linked list or forward graph according to the actual feed direction of the turning process to form the main path. Each edge carries the information of the depth of cut change during node transition.

[0044] S132: At any node i, if the overall flutter risk index is higher than the preset threshold, or the local stiffness is lower than the preset threshold, the network model allows branch edges to be drawn from node i, jumping to the preset conservative cutting depth mode path or directly entering the empty cutting and retraction path to avoid high-risk areas.

[0045] S133: Vibration monitoring characteristics of the last or subsequent nodes are mapped back to several preceding nodes via loop connections for online parameter updates in adaptive variable shear depth modes. The weight of the loop connection represents the feedback strength and is dynamically adjusted by the modal risk boundary parameters in the risk profile.

[0046] S134: Serialize and store the above nodes, edges and connection rules to form a variable network model for variable cutting depth turning path, which can be used for subsequent risk calculation and optimization.

[0047] Please refer to Figure 3 It illustrates a flowchart of step S200 in an exemplary variable depth turning path planning method for suppressing chatter in thin-walled rings, the contents of which include: S210: Using the wall thickness and support position of each node as boundary conditions, drive the digital twin model of the thin-walled collar-tool system to generate the time-domain vibration response signal of the corresponding node under the preset cutting depth parameters.

[0048] S220: Performs constrained adaptive modal decomposition on the time-domain vibration response signal, decomposing it into three modal components: a rigid follower layer, a semi-stable flutter coupling layer, and an unstable impact layer.

[0049] S230: Extract the energy proportion, envelope amplitude and volatility characteristics of each layer component to form a feature vector.

[0050] S240: Combine the local static stiffness of the nodes to calculate the instability contribution coefficients of the three layers respectively, and then weight and aggregate the instability contribution coefficients of the three layers to obtain the comprehensive flutter risk index.

[0051] S250: Based on the feature statistical distribution generated by the same node under different cutting depth parameters, determine the modal risk boundary parameters, and encapsulate the comprehensive flutter risk index, three-layer labels, feature vectors and modal risk boundary parameters into the risk profile of the node.

[0052] In one possible implementation of step S210, the construction of the digital twin model and the generation of the response further include: S211: Establish a parametric multibody dynamics digital twin model of the thin-walled collar-tool system. The model includes a finite element mesh of the workpiece, with the wall thickness discretized according to the node binding values, and displacement constraints and contact stiffness applied at the corresponding fixture support positions. The tool system is simplified to a two-degree-of-freedom spring-damped-mass model. The cutting force adopts a dynamic cutting force model considering the regenerative effect, and the dynamic chip thickness is the difference between the instantaneous undeformed chip thickness and the vibration ripple of the previous revolution.

[0053] S212: For the i-th path node, set the local cutting depth to the corresponding value of the cutting depth mode configured for the node, and the boundary conditions correspond to the wall thickness. Distance from support And apply motion loads on the model that match the spindle speed and feed rate.

[0054] S213: Time-domain numerical simulation is performed using the explicit central difference method or the Newmark method, outputting the time history signal of the relative vibration displacement between the tool tip and the workpiece surface. The signal duration is a steady-state interval containing multiple complete rotation cycles, and the sampling frequency is not less than a preset multiple of the highest frequency of interest in the mode.

[0055] In one possible implementation of step S220, the specific execution method of constraint adaptive mode decomposition includes: S221: Set the number of decomposition layers to 3, and introduce center frequency constraints in the variational mode decomposition framework. The rigid follower layer constrains the center frequency in the spindle speed frequency and its low-order harmonic neighborhood; the semi-stable chatter coupling layer constrains the center frequency in the regenerative chatter prediction frequency band, which is determined by the cutting system's natural frequency and the speed-depth stability lobe diagram; the unstable impact layer constrains the center frequency in the high-frequency broadband region, corresponding to the discontinuous impact response between the tool and the workpiece.

[0056] S222: Solve the following constrained variational problem: find three modal functions. , This minimizes the sum of the estimated bandwidths of all modes and satisfies... The bandwidth is determined by the modal analytic signal. The norm squared is defined, and a quadratic penalty term and Lagrange multipliers are introduced. Each mode and its center frequency are iteratively updated using an alternating direction multiplier method. The center frequency is projected into its respective constraint interval after each update.

[0057] S223: After iterative convergence, the time-domain signals of the three modal components are obtained and sequentially labeled as rigid follower layers. Semi-stable flutter coupling layer and unstable impact layer The convergence criterion is that the total modal energy change is less than a preset threshold.

[0058] In one possible implementation of step S230, the extraction of the three-layer feature vectors is specifically implemented as follows: S231: Calculate the energy proportion of each layer. For the k-th layer, where... Corresponding to the rigid following layer, Corresponding to the semi-stable flutter coupling layer, For the corresponding unstable impact layer, the energy percentage is defined as: ;in The selected analysis time window length. This represents the time-domain signal of the corresponding layer modal component.

[0059] S232: Calculate the envelope amplitude for each layer. Perform a Hilbert transform on each layer's modal components to obtain the envelope. Take the maximum amplitude of the envelope within the analysis window. .

[0060] S233: Calculate the volatility of each layer. Volatility reflects the degree of non-stationarity of the modal components and is characterized by the coefficient of variation of the envelope. ,in and These are the standard deviation and mean of the envelope sequence, respectively.

[0061] Will It forms a 9-dimensional feature vector.

[0062] In one possible implementation of step S240, the calculation of the instability contribution coefficient and the comprehensive flutter risk index further includes: S241: Define the instability contribution coefficient of the k-th layer. for: ;in The stiffness attenuation index is calibrated based on the workpiece material and clamping method. This is a volatility amplification factor used to enhance the sensitivity to non-stationary characteristics. The larger the energy proportion and amplitude, the more dominant the mode is and the stronger the vibration, resulting in a higher risk of flutter. The larger the volatility, the more non-stationary impact components the mode has, which also increases the risk. The power term of the local static stiffness reflects the structure's ability to resist deformation; the lower the stiffness, the greater the contribution of equal vibration to instability.

[0063] S242: The comprehensive flutter risk index is obtained by weighted aggregation of the three-layer instability contribution coefficients. : ; where weight satisfy The weights are determined by the analytic hierarchy process (AHP) combined with cutting test sensitivity analysis. Typically, higher weights are given to the semi-stable chatter coupling layer and the unstable impact layer, while lower weights are given to the rigid follower layer. A higher overall chatter risk index indicates a greater probability of unacceptable chatter occurring at node i when cutting with the current depth of cut parameters.

[0064] In one possible implementation of step S250, the process of generating the modal risk boundary parameters is as follows: S251: For the same node, perform small-amplitude perturbation scans on control variables such as the rate of change of cut depth, sinusoidal frequency, and maximum cut depth in a digital twin environment to obtain a series of risk indices and characteristic statistics. Based on the confidence intervals of the statistical results, extract the upper limit of the rate of change of cut depth for the node. Sine frequency adjustment range and maximum cutting depth limit Exceeding these boundaries will cause the overall tremor risk index to rise sharply or directly plunge into an unstable shock layer-dominated state.

[0065] S252: Integrating the tremor risk index The three-layer label, feature vector, and the above modal risk boundary parameters are packaged to form the risk profile of node i, and stored under the corresponding node of the network model.

[0066] Please refer to Figure 4 It illustrates a flowchart of step S300 in an exemplary variable depth turning path planning method for suppressing chatter in thin-walled rings, the contents of which include: S310: Construct a path value function using the risk profiles of each node, and define the instantaneous value of a node and the cumulative value of the path.

[0067] S320: Accumulate the instantaneous value of each node along the forward direction of the network model, and obtain the cumulative value of each node and the value gradient with respect to the cutting depth parameter by recursively correcting it in the reverse direction.

[0068] S330: Based on preset criteria, nodes with a comprehensive flutter risk index exceeding the threshold, significant value gradient turning point, and adjacent node arc length greater than the minimum distance are marked as critical path nodes, and the micro-control parameters of the remaining nodes are locked.

[0069] In one possible implementation of step S310, the path value function is constructed as follows: Define the instantaneous value of node i To mitigate the trade-offs between material removal benefits, chatter risk, and the cost of cut depth variations, the expression is a weighted combination of cut depth benefit terms, risk penalty terms, and adjacent cut depth variation smoothing terms. Based on instantaneous value, the cumulative value along the path from node i to endpoint N is defined. The recurrence relation is: ;in Let i be the policy feasible region, which is constrained by the modal risk boundary parameters, namely, the cutting depth does not exceed the limit, the rate of change does not exceed the limit, and the frequency is within the adjustment range. This is a discount factor used to adjust the importance of long-term returns. This recursive equation is the core expression of path value optimization.

[0070] In one possible implementation of step S320, the forward accumulation and reverse recursion are specifically implemented as follows: S321: Initialize end boundary conditions Starting from the last node N, traverse backwards to the first node. For each node i, within its feasible region... Discretize the depth of cut with a certain step size. The corresponding risk index is obtained by looking up the table, the sum of the instantaneous value and the optimal cumulative value for the next stage is calculated, and the maximum value is used to update the index. And record the corresponding optimal cutting depth. .

[0071] S322: During the reverse recursion process, the value gradient of the cumulative value with respect to the cutting depth parameter is calculated simultaneously. The gradient can be obtained through numerical differencing or automatic differentiation, and is used to guide the direction of subsequent game parameter updates.

[0072] S323: After completing the reverse recursion, perform forward propagation, determine the nominal cutting depth path based on the optimal strategy of each node, and store the value gradient sequence of each node.

[0073] In one possible implementation of step S330, the criteria for identifying critical path nodes are: A node is designated as a critical node only if it meets all three of the following conditions: Condition 1: Comprehensive Tremor Risk Index Greater than the preset risk threshold , Take the highest quantile of the risk values ​​of all nodes or as specified in the process specifications; Condition 2: The magnitude of the value gradient transition Greater than the threshold of significant gradient change This indicates that the optimal cutting depth at this node is highly sensitive to parameter changes; Condition 3: Arc length between the node and its adjacent nodes Greater than the preset minimum spacing This prevents over-optimization caused by excessively dense nodes.

[0074] Nodes that do not meet any of the above conditions are considered non-critical nodes, and their micro-control parameters are directly locked to the lowest default value in the risk profile, or the parameters of the previous critical nodes after a smooth transition are used.

[0075] Please refer to Figure 5 It illustrates a flowchart of step S400 in an exemplary variable depth turning path planning method for suppressing chatter in thin-walled rings, the details of which include: S410: Using the M key path nodes identified by S300 as game participants, construct a strategy space and payoff function for each participant. The strategy includes the selected cutting depth pattern identifier and the corresponding micro-control parameter vector. The payoff function is associated with the path value function.

[0076] S420: Performs evolutionary game of micro-control parameters, independently adjusting micro-control parameters within each key node at the highest frequency to pursue the maximization of local value.

[0077] S430: Performs meso-level evolutionary game, groups adjacent key nodes together at a moderate frequency, synchronously selects and evolves cutting-depth modes, and applies modal smoothing constraints.

[0078] S440: Performs macro-level global evolutionary game, synchronizing all key nodes at the lowest frequency, and using the global value function to coordinate policy conflicts among nodes.

[0079] S450: After the three-layer evolution converges, the cutting depth mode and micro-control parameters of each key node are extracted and sequentially spliced ​​with the locking parameters of non-key nodes to generate a complete variable cutting depth turning path.

[0080] In one possible implementation of step S410, the process of constructing the strategy space and payoff function of the game participants further includes: S411: Define each key node i as an independent player in the game, with the player number corresponding to the node index. Each player's strategy... A binary tuple Composition, in which The selected cutting depth mode is identified, corresponding to four modes: constant cutting depth, linear gradual cutting depth, sinusoidal variable cutting depth, and adaptive variable cutting depth. This represents the vector of micro-control parameters in the corresponding mode.

[0081] S412: Based on the selected mode Determine the micro-control parameter vector The specific dimensions and meanings of [these]. If... If the cutting depth is constant, then It only includes the depth of cut; if That is, a linear gradual change, then Including the starting and ending cutting depths; if That is, a sine wave. This includes the basic cut depth, amplitude, spatial frequency, and phase; if That is, adaptive, then This includes the gain coefficient and maximum adjustment limit. All continuous parameters have reasonable upper and lower limits set.

[0082] S413: Determine the policy feasibility domain for each participant. The feasible region is jointly defined by the modal risk boundary parameters generated by S250 and the value gradient calculated by S320. Specific constraints include: the cut depth amplitude does not exceed the maximum cut depth limit. The rate of change of cutting depth does not exceed the upper limit of the rate of change. If it is a sine wave mode, the spatial frequency must be within the adjustment range. Internally, it is also required that the direction of the value gradient be consistent with the direction of parameter adjustment, that is, the adjustment should not lead to a decrease in the cumulative value.

[0083] S414: Define the revenue function for each participant as the cumulative value of the node. Its calculation follows the recursive relationship established in S310. The payoff of participant i depends not only on its own strategy. Furthermore, the state propagation depends on the strategy choice of the previous participant i-1, forming a Markov game structure. The goal of the game is to find a joint strategy that maximizes the sum of the cumulative values ​​of all key nodes.

[0084] In one possible implementation of step S420, the specific execution method of the micro-control parameter layer evolution includes: S421: Initialize the micro-level population. For each critical node i, within the feasible region... A small swarm of particles is randomly generated within the system, with a particle count of 1. Each particle represents a set of microscopic control parameters. ,model The particle position vector dimension is temporarily fixed within the current meso-level iteration cycle. Consistent.

[0085] S422: For each particle's parameter combination, substitute it into the digital twin local proxy model of node i or directly query the risk profile to obtain the corresponding risk index; combine the cutting depth of adjacent nodes to calculate the instantaneous value. And look up the table forward along the path to obtain The cumulative value is calculated as the particle fitness based on the recursive relationship.

[0086] S423: Each particle records its own historical best position. The entire particle swarm records the globally optimal position. The particle velocity update formula contains three terms: an inertial term that maintains the previous velocity direction, a cognitive term that moves towards its own optimal value, and a social term that moves towards the global optimal value. Furthermore, a fourth term, the value gradient guiding term, is introduced, with its direction along... Step size is affected by coefficient Adjustments are made. After the velocity is updated, the position is updated, and out-of-bounds components are projected back to the feasible region boundary.

[0087] S424: The micro-layer iterates at the highest frequency. When the global optimal fitness does not improve significantly after several consecutive iterations, or when the preset maximum number of iterations is reached, the micro-layer converges and outputs the optimal micro-parameters of node i in the current mode.

[0088] S425: The micro-level evolution of all key nodes can proceed independently and in parallel, with nodes only coupled through deep tangents between preceding and subsequent nodes in the cumulative value function. After each node converges, it uploads the current optimal micro-parameters to the meso-level.

[0089] In one possible implementation of step S430, the specific execution method of the mesoscopic model layer evolution includes: S431: Divide all critical nodes into several overlapping segments according to the path order. Each segment contains... A series of key nodes, with overlapping adjacent segments. There are several nodes to ensure the continuity of mode switching. Let the sequence of key nodes be... Then the q-th segment contains the node to .

[0090] S432: The strategy for each segment is determined by the cut depth pattern selection vector of each node within the segment. The composition involves selecting each component from four patterns. The total number of pattern combinations increases exponentially with the fragment length, and a combinatorial optimization method is used for searching.

[0091] S433: For a set of mode choices within fragment q, after fixing the modes of each node, the micro-layer is invoked to execute the complete convergence process, obtaining the optimal micro-parameters and corresponding cumulative node values ​​under this mode combination. Fragment fitness is defined as the sum of the cumulative values ​​of nodes within the fragment minus the mode switching penalty term. The switching penalty term penalizes cases where adjacent node modes are inconsistent, and the penalty amount is proportional to the mode difference.

[0092] S434: Employs an evolutionary strategy to search the pattern combination space. Each iteration generates several candidate pattern combination variants, with mutation methods including: randomly flipping the pattern of a single node, swapping the patterns of adjacent nodes, and inserting conservative pattern fragments. For each variant, a micro-level evaluation of fitness is performed, and tournament selection or truncation selection is used to retain high-quality pattern combinations for the next generation.

[0093] S435: Explicitly incorporate a smoothing term into fitness evaluation: if a mode transition exists within a segment or at a segment boundary, a cost proportional to the transition amplitude is subtracted from the fitness score. The inter-mode dissimilarity matrix is ​​predefined; for example, the dissimilarity between linearly transitioning and sinusoidal modes is small, while the dissimilarity between linearly transitioning and constant-depth modes is large. Smoothing constraints cause the mesoscale to favor mode sequences with gentle modal transitions.

[0094] S436: The meso-level evolves at a moderate frequency. When the improvement in fragment fitness falls below a preset threshold or reaches the maximum number of iterations, the meso-level converges. It outputs the cut depth pattern determined by each node within the current meso-level iteration cycle and propagates it to the micro-level for the next round of fine-tuning.

[0095] In one possible implementation of step S440, the specific execution method of the macro-global layer evolution includes: S441: Define a global value function considering all critical nodes as a whole. for: The first term is the sum of the accumulated value of all critical nodes, and the second term is the global penalty term. This is the penalty coefficient. The global penalty term includes multiple components: excess penalty for violating the modal risk boundary, smoothing penalty for excessively drastic changes in cut depth between adjacent nodes, and efficiency penalty for total material removal falling below process requirements.

[0096] S442: The current patterns and parameters of all key nodes are used as the initial joint strategy for the global game. Each participant holds the current strategy and knows the strategy information of all participants, thus forming a complete information game environment.

[0097] S443: In each round of macro-level iteration, select participant i sequentially or randomly. Given that the current policies of all other participants are fixed, solve for the optimal response policy of participant i. The optimal response policy is defined as: within the feasible region... Within, choose to make the global value function The pattern with the largest increment and micro parameters The solution process requires rapid evaluation using both mesoscopic and microscopic levels.

[0098] S444: To avoid macroscopic oscillations, instead of directly adopting the optimal response's complete replacement strategy, a small update is performed along the value gradient direction. The gradient of the global value function with respect to participant i's policy is calculated, and the update step size is proportional to the gradient magnitude and multiplied by a small learning rate. After the update, the policy is projected into the feasible region.

[0099] S445: Calculate the change in the global value function after each iteration. When the change is lower than the preset tolerance for several consecutive iterations, check whether the current joint strategy is a Nash equilibrium: for each participant i, verify whether its current strategy is indeed the optimal response when the strategies of the other participants are fixed. If yes, the macro-level converges; if not, continue iterating for the participants that have not reached equilibrium. The macro-level has the lowest evolution frequency and is the outermost loop of the three layers.

[0100] S446: After macroscopic convergence, the final cutting depth mode selection and microscopic control parameters of all key nodes are obtained as the global optimization result of the game evolution.

[0101] In one possible implementation of step S450, the process of splicing together to generate a complete variable depth of cut turning path further includes: S451: Extract the final cutting depth pattern identifier of each key node i from the convergence result of the three-layer nested evolutionary game. and the corresponding micro-control parameter vector .

[0102] S452: For non-critical nodes locked in S330, the preset default micro-control parameters are directly extracted from the risk file, or a smooth transition is achieved through linear interpolation based on the parameters of adjacent critical nodes. The smooth transition strategy is as follows: In the sequence of non-critical nodes between two adjacent critical nodes, the cutting depth is linearly interpolated according to the arc length ratio, and the pattern is uniformly adopted from the previous critical node.

[0103] S453: Read the mode and parameters of each node sequentially from node 1 to node N to form a complete path parameter sequence table. Each row in the sequence table records the node index, arc length coordinates, cutting depth mode, cutting depth value, and corresponding micro parameters.

[0104] S454: Converts the path parameter sequence list into a structured data format required for subsequent digital twin verification and CNC compilation, including path node geometry information, tangent curves of each segment, and mode switching markers.

[0105] Please refer to Figure 6 It illustrates a flowchart of step S500 in an exemplary variable depth turning path planning method for suppressing chatter in thin-walled rings, the contents of which include: S510: Load the complete variable depth of cut turning path generated by stitching together S450 into the turning digital twin environment, and simulate the cutting process along the path in sequence.

[0106] S520: At several selected nodes along the path, inject short-term probe disturbances into the digital twin model, collect the vibration response after the disturbance, and calculate the agility index.

[0107] S530: Compare the agility index with the modal characteristics of the corresponding nodes in the risk profile, mark fragile nodes and cluster them into fragile node groups.

[0108] S540: Extract the fragile node group and its adjacent nodes as the local reconstruction region, and return to S300 and S400 for local re-optimization.

[0109] S550: Repeatedly verify and refactor until the agility index of all nodes reaches the target, and output a robust variable depth turning path.

[0110] In one possible implementation of step S510, the loading path and the specific execution method of the digital twin simulation include: S511: Parse all parameters of the complete variable depth path from the path description file. According to the node order, extract the arc length coordinates, depth mode and corresponding micro-control parameters of each node, and reconstruct the depth variation curve along the feed direction in the digital twin environment.

[0111] S512: Configure the initial state of the digital twin model. Set the workpiece spindle speed, feed rate, and tool geometry parameters. Load the workpiece wall thickness distribution and fixture support position into the model according to the actual clamping scheme. At the starting point of the path, position the tool on the surface to be machined, and set the initial depth of cut to the value corresponding to the first node.

[0112] S513: Perform full-path time-domain cutting simulation. Advance the tool position step-by-step along the node sequence, performing cutting simulation at each node according to preset depth of cut and feed parameters. Record the tool tip vibration displacement response corresponding to each node during the simulation and save it as time-series data for subsequent disturbance injection and agility evaluation.

[0113] In one possible implementation of step S520, the specific execution method of probe perturbation injection and agility index calculation includes: S521: In the path node sequence, select several nodes as perturbation injection candidate points at equal intervals or based on areas with high risk indices in the risk profile. Prioritize nodes at the cutting depth mode switching boundary, areas with drastic local stiffness changes, and nodes with risk indices close to the threshold.

[0114] S522: The probe perturbation design is a short-duration, small-amplitude pulse excitation, which is performed by superimposing an amplitude value onto the preset cutting depth during the cutting process at the target node. Duration is The disturbance should be a rectangular pulse or a half-sine pulse. The amplitude of the disturbance should not be too large to avoid altering the nonlinear characteristics of the system, but it should be sufficient to elicit an observable transient response.

[0115] S523: For each selected node, when the steady-state cutting reaches that node, apply probe perturbation according to the design, and continuously record the tool tip vibration response signal for a period of time after the perturbation is applied. At the same time, set up a set of undisturbed control group and collect the steady-state response under the same conditions as the benchmark.

[0116] S524: Agility Index This is used to quantify the ability of node i to recover stability after being disturbed. Starting from the moment the disturbance ends, the decay process of the vibration response signal is analyzed. Two key metrics are extracted: recovery time and recovery time. Defined as the time required for the vibration amplitude envelope to decay from the peak disturbance value to within a preset multiple of the steady-state amplitude; maximum overshoot. The agility index is defined as the ratio of the maximum peak value of the disturbance response to the steady-state amplitude. ;in and These are the weighting coefficients. The lower the value, the stronger the node's ability to recover from disturbances and the better its processing stability.

[0117] S525: Calculate for all injected disturbance nodes Then, the agility index of nodes that were not directly tested was completed by interpolation, forming an agility distribution curve along the entire path.

[0118] In one possible implementation of step S530, the specific execution method of the fragile node labeling and clustering process includes: S531: Read the modal feature vectors and comprehensive tremor risk index from the risk profile. Extract the three-layer energy proportion, envelope amplitude, volatility, and [other parameters] from the risk profiles generated in S250 for each node. The value is an inherent risk attribute of the node.

[0119] S532: Set the allowable upper limit for the agility index. Based on process requirements and historical processing data, determine the allowable upper limit for the agility index. This upper limit can be determined based on the statistical distribution of successful processing cases of similar workpieces, or set by process engineers according to surface quality requirements.

[0120] S533: Node-by-node comparison and labeling of fragile nodes. For each node i, if... If node i is found to be fragile, then node i is marked as a fragile node. Record the index of the fragile node, the amount of agility index exceeding the limit, and the corresponding risk profile information.

[0121] S534: Fragile nodes are clustered to form fragile node groups. Spatially continuous and adjacent fragile nodes are merged into the same fragile node group. The spatial continuity threshold is set to the maximum preset jump distance when the arc length distance between adjacent fragile nodes does not exceed the threshold. If two fragile nodes are separated only by a few non-fragile nodes and the arc length of the interval is short, the intermediate nodes can be included to form a larger coherent reconstruction region. Each fragile node group records the starting node index, the ending node index, and the number of nodes in the group.

[0122] In one possible implementation of step S540, the specific execution method of local reconstruction includes: S541: Determine the extent of the local reconstruction region. For each fragile node group, extend forward. Each node, expanding backwards Each node expands the region as a local reconstruction region. Forward expansion is used to accept the incoming state of the upstream path, while backward expansion is used to smoothly transition to the downstream unmodified path. The number of expanded nodes is adaptively determined based on the gradient of local stiffness changes; more nodes are expanded when stiffness changes drastically.

[0123] S542: Extract the boundary conditions of the local reconstruction region. Record the tangent depth of the previous node in the reconstruction region. With depth of cut mode This serves as the starting constraint for local path planning; it records the expected tangent depth of the next node in the reconstructed region. , as the endpoint constraint.

[0124] S543: Return to S300 to perform local value transfer and key node identification. Treat the nodes in the local reconstruction area as independent sub-networks, and re-execute the risk profile query, path value function construction, and reverse recursion under boundary conditions to identify new key nodes in the local area.

[0125] S544: Return to S400 to execute a local three-layer nested evolutionary game. Using the local key nodes marked in S543 as participants, re-execute the three-layer evolutionary game of micro, meso, and macro levels under boundary patterns and depth constraints. During the evolution, the strategies of the boundary nodes are restricted by the starting point and ending point constraints and cannot be changed arbitrarily.

[0126] S545: Local reconstruction result concatenation. The parameters of the reconstructed region after local game convergence are concatenated with the original path parameters without modification to form the updated complete variable-depth path.

[0127] In one possible implementation of step S550, the specific execution method of iterative verification and convergence determination includes: S551: Reload the complete path updated in S545 into the digital twin, repeat the agility verification process from S510 to S530, and calculate the agility index of all nodes after the update.

[0128] S552: Check the overall path agility compliance. If it still exists... For nodes that are fragile, the S540 local refactoring process is executed again. After each refactoring, the changing trends of the number of fragile nodes and the maximum agility exceedance are recorded.

[0129] S553: ​​Convergence Determination and Iteration Termination. When all nodes along the entire path satisfy... If the iteration terminates, or if the number of brittle nodes does not decrease after two consecutive reconstructions and the improvement in the maximum excess is less than the preset ratio, the process engineer is prompted to intervene and adjust the constraints. After the termination conditions are met, the current path is marked as a robust variable depth path.

[0130] Please refer to Figure 7 It illustrates a flowchart of step S600 in an exemplary variable depth turning path planning method for suppressing chatter in thin-walled rings, the contents of which include: S610: Compile the robust variable depth path into CNC code to prepare for the first piece trial cut.

[0131] S620: Perform the first test cut and simultaneously acquire cutting force and vibration spectrum signals online.

[0132] S630: Utilizes an online classification model to determine the modal level of the current cutting range in real time.

[0133] S640: Implement differentiated control strategies based on modal determination results.

[0134] S650: After processing is completed, the final parameters are fixed into a batch production process document.

[0135] In one possible implementation of step S610, the specific execution method of CNC code compilation includes: S611: Reads the arc length coordinates, depth of cut mode, and depth of cut value sequence of all nodes from the robust variable depth of cut path file. Converts the node indices into continuous toolpath trajectory points.

[0136] S612: Generates corresponding CNC macro instructions or directly generates G-code for each cutting depth mode. The constant cutting depth segment outputs standard G01 or G00 linear interpolation instructions to work with a fixed cutting depth; the linear gradient segment outputs continuously changing cutting depth instructions, achieved through linear interpolation of macro variables by arc length; the sinusoidal variable cutting depth segment outputs a sine function macro program that calculates the target cutting depth in real time with the spindle encoder or feed axis position as the independent variable; the adaptive variable cutting depth segment has a pre-installed online adjustment interface, allowing fine-tuning of macro variables through feedback from external sensors.

[0137] S613: Insert M-code at the mode switching boundary point to trigger the switching of the sampling window or the classification model mode of the online monitoring system. Insert interface instructions for reading external sensor data at the start of the adaptive segment.

[0138] S614: Load the generated G-code into the CNC simulation software, simulate the tool path trajectory, check for sudden changes in depth of cut, overtravel, interference, or syntax errors, and ensure that the code can be executed safely.

[0139] In one possible implementation of step S620, the specific execution method of the first test cut and signal acquisition includes: S621: A three-dimensional force sensor and accelerometer are mounted on the tool holder, and a reference accelerometer is mounted on the workpiece or fixture. The sensor signals are conditioned by a charge amplifier and then connected to a high-speed synchronous data acquisition card. The acquisition card communicates with the CNC system via a digital or analog interface to obtain the spindle phase and feed axis position signals as triggering and positioning references.

[0140] S622: Load the compiled CNC code into the CNC machine tool, and perform the first-piece trial cut according to the spindle speed, feed rate, and cooling conditions set in the process. The data acquisition system is turned on throughout the trial cut.

[0141] S623: Simultaneously records cutting force components and tool tip vibration acceleration in three directions at a preset sampling rate. It also records spindle encoder pulses and feed axis coordinates, precisely aligning the time-domain signals with the physical positions. The acquired data is stored in real-time in a time-series file format and segmented and labeled according to the node arc length.

[0142] In one possible implementation of step S630, the online modal hierarchy determination is specifically performed in the following ways: S631: Deploy the classification model trained on a large amount of digital twin simulation data from S200 to the online monitoring computer. The model input consists of the spectral and statistical characteristics of the vibration signal within a sliding window, and the output consists of the probability predictions for three modes: a rigid follower layer, a semi-stable flutter coupling layer, and an unstable impact layer. The model can employ support vector machines, random forests, or lightweight neural networks. During training, the feature vectors and three-layer labels from the risk profile are used as supervision signals.

[0143] S632: For real-time acquired vibration acceleration signals, a sliding window analysis is performed with a fixed window length and step size. Within each window, spectral features and time-domain statistical features are calculated to construct an input feature vector consistent with the training set.

[0144] S633: Input the feature vector of each window into the classification model to obtain the predicted probabilities of the three modalities. , and The modal label corresponding to the highest probability is taken as the modal determination result for the current cutting range, and the probability value is recorded as a confidence level reference.

[0145] S634: Map the judgment results of each window to the timestamp and node arc length position to form a modal hierarchy labeling sequence distributed along the path, providing a basis for subsequent differentiated control.

[0146] In one possible implementation of step S640, the specific execution method of the differentiated control strategy includes: S641: If the current node is determined to be a rigid following layer, it indicates that the cutting state is stable and the vibration is within a controllable range. In this case, a dead-zone offset strategy is executed: the current depth of cut parameter remains unchanged, and no adjustment commands are output to the control system. Dead-zone offset avoids unnecessary parameter adjustments caused by small random fluctuations, reduces system disturbances, and maintains continuous stability of the machining state.

[0147] S642: If the current node is determined to be a semi-stable flutter coupling layer, it indicates that the system is on the edge of flutter, with a certain risk of instability but still controllable. At this time, fine-tune the tangent depth by referring to the value gradient pre-stored in S320. The fine-tuning amount is determined by the following steps: Read the value gradient value corresponding to the current node. ; Calculate the fine-tuning amount: ;in This is an adjustable gain coefficient, calibrated based on the online response sensitivity. The fine-tuning amount is constrained by the maximum tangent depth limit and the upper limit of the rate of change in the modal risk boundary parameters, and must not exceed these limits.

[0148] S643: Before officially issuing the fine-tuning instruction, the calculated fine-tuning amount is checked for consistency with the sign of the value gradient in real-time reassessment. If the signs are consistent, that is, the gradient direction matches the pre-stored direction, fine-tuning is allowed; if the signs are opposite, it indicates that there is a deviation between the current actual working condition and the digital twin prediction, the adjustment is abandoned and the abnormal event is recorded to prevent misadjustment due to model deviation.

[0149] S644: If the current node is determined to be an unstable impact layer, it indicates that the system has entered a state of severe chatter or impact, posing a risk of tool breakage and workpiece scrap. At this time, a protective action sequence is immediately triggered: a rapid tool retraction command is sent to the CNC system, causing the tool to exit the cutting zone at the fastest safe rate; the spindle speed is simultaneously reduced to a safe range; an audible and visual alarm is issued to notify the operator; and the operating data of this node, the trigger time, and the short-term signal waveforms before and after it are completely recorded in the anomaly log for post-fault analysis.

[0150] S645: After each fine-tuning or protection action, continue to track the modal determination results of subsequent windows and evaluate the control effect. If the mode changes from a semi-stable layer to a rigid follower layer after fine-tuning, record the successful case and fine-tune the gain coefficient as appropriate; if the mode deteriorates to an unstable impact layer after fine-tuning, backtrack to adjust the strategy and mark the reliability of the value gradient of that node.

[0151] In one possible implementation of step S650, the specific execution method of solidifying the process document includes: S651: Compile the actual cutting depth sequence, mode sequence, final judgment modal level of each node and control record after online adjustment during the trial cutting process into a complete processing data archive.

[0152] S652: Compare the robust variable cut depth path parameters output by S500 with the final parameters actually executed node by node to analyze the deviation and its cause. If the deviation originates from online fine-tuning and the fine-tuning effect is positive, then the fine-tuned parameters are used as the optimized recommended values.

[0153] S653: Compiles the final path parameters, spindle speed, feed rate, tool information, clamping scheme, and depth-of-cut mode descriptions for each segment into a standardized process document. The document format can be structured text or a database record, containing management information such as process version number, applicable workpiece batch, and expiration date.

[0154] S654: The measured vibration response data, cutting force data, and modal determination labels of the first test cut are transmitted back to the digital twin model for model parameter calibration and risk file updates, thereby improving the accuracy of path planning for similar workpieces in the future.

[0155] In this embodiment, through the organic combination of S100 to S600, the dynamic adaptation, layered quantization and global game optimization of the cutting depth path to the local stiffness field of the thin-walled ring are realized, which significantly suppresses turning chatter and improves processing efficiency.

[0156] Example 2: This embodiment uses the turning of a thin-walled raceway on the rear axle of a high-pressure turbine in an aero-engine as an example to verify the variable depth-of-cut path planning method provided by this invention. The raceway material is GH4169 nickel-based superalloy, with an outer diameter of 318 mm, a wall thickness that gradually changes from 3.5 mm to 2.0 mm and then back to 3.5 mm along the circumferential direction, and an axial length of 150 mm. The clamping method is a three-jaw chuck on the left end and a fan-shaped soft jaw for auxiliary support on the right end, with significantly weaker rigidity in the suspended area in the middle. The traditional constant depth-of-cut process uses a depth of cut of 0.5 mm, a spindle speed of 800 r / min, and a feed rate of 0.1 mm / r, which frequently results in chatter marks at the thinnest part of the wall, with a pass rate of approximately 72%.

[0157] During implementation, N=200 path nodes with equal arc lengths are generated along the feed direction. A wall thickness mapping table is obtained through ultrasonic thickness measurement, and the local static stiffness of each node is calculated based on the fixture support position. The attenuation index p=3, and the shape factor is calibrated using finite element analysis. Four depth-of-cut modes are preset and their parameters are initialized. The digital twin model is constructed using Abaqus and Simulink, and the tool system modal parameters are obtained from hammer impact experiments. Time-domain simulation is performed on each node, with a signal duration of 1.0 s, covering 50 rotation cycles, and a sampling frequency of 20 kHz. After constrained adaptive modal decomposition, three layers of features are extracted, and a comprehensive chatter risk index is calculated.

[0158] The value function weights are set as follows: material removal benefit coefficient 2.0, risk penalty coefficient 3.5, and cutting depth smoothing coefficient 1.2. The discount factor is set to 0.95 to take into account long-term returns. The three-layer nested evolutionary game uses a particle swarm optimization of 20 iterations for the micro-level, 30 iterations for the meso-level with three adjacent nodes bound together, and a macro-level that executes the optimal response dynamic for 20 rounds before each node's strategy reaches Nash equilibrium.

[0159] After the game convergence, in the thinnest section of the wall, the algorithm automatically selects a sinusoidal variable cut depth mode with a basic cut depth of 0.40mm, an amplitude of 0.12mm, and a spatial frequency of 0.5mm. -1 The phase-locking condition of regenerative flutter is disrupted by periodic depth perturbation; a linear gradient mode is adopted in the stiffness transition zone, with the depth of cut increasing at a slope of ±0.15mm. -1 Smooth transition; a constant cutting depth of 0.70 mm is maintained in the stiffness-rich regions at both ends to maximize material removal rate. Table 1 summarizes the cutting depth patterns and micro-parameter configurations for each typical node.

[0160] Table 1. Critical Path Node Cut Depth Allocation Scheme In the robustness verification phase, the complete variable cut depth path is loaded into the digital twin, and 40 injection probes are selected at equal intervals among 200 nodes to perturb the perturbation in the form of a half-sine cut depth pulse with an amplitude of 0.05 mm and a duration of 5 ms.

[0161] The robust path was compiled into CNC code for the first test cut. An online random forest classification model was deployed and trained with three-layer feature vectors, achieving an accuracy of 93.5%. During the entire test cut, only two semi-stable chatter coupling layer fine-tuning events were triggered, with amplitudes of 0.015 mm and 0.018 mm respectively, and the unstable impact layer protection was not triggered. Table 2 summarizes the key indicators of processing quality and efficiency, and Table 3 lists the main statistics of the agility index.

[0162] Table 2 Comparison of Key Indicators of Processing Quality and Efficiency Table 3 Agility Index Full Path Statistics After trial cutting, coordinate measuring machine (CMM) measurements showed that the roundness of the thinnest section decreased from 25.4 μm to 8.2 μm, the surface roughness Ra decreased from 1.22 μm to 0.58 μm, the single-piece machining time was reduced from 186 s to 152 s, the chatter probability decreased from 34% to 2.5%, and the tool flank wear decreased from 48 μm to 31 μm. The agility index met the standard throughout the entire path, with a maximum value of 0.31 after reconstruction, far below the allowable upper limit of 0.50, and no unstable nodes were observed. The results indicate that this method can dynamically match the cutting depth mode and parameters based on local stiffness, and achieve global path optimization through a three-layer nested evolutionary game. It effectively suppresses chatter while significantly improving machining efficiency and surface quality, and is particularly suitable for precision turning of thin-walled rotating parts with non-uniform wall thickness.

[0163] Example 3: A variable depth of cut turning path planning system for suppressing chatter in thin-walled rings, with an interface as shown in Figure 1. Figure 8 , Figure 9 , Figure 10 , Figure 11 and Figure 12 As shown, it contains five interfaces, which are as follows: Overview dashboard interface: Displays the 3D model of thin-walled rings and the risk distribution of path nodes, providing a global overview of the comprehensive risk index, the number of key nodes, and path robustness.

[0164] Risk profile interface: Through a three-layer modal energy proportion histogram, the node distribution and modal risk boundary of rigid follower, semi-stable flutter coupling and unstable impact are quantified.

[0165] Path Value Interface: Presents a three-dimensional surface of cut depth, nodes, and value, marking the cumulative value peak and value gradient inflection points to support optimal path decision-making.

[0166] Nested game interface: Visualizes the three-layer game network structure and evolution convergence state of the micro, meso, and macro levels, and shows the attainment of Nash equilibrium.

[0167] Agility Validation Interface: Fragile node groups are marked by the agility index scatter distribution to verify path robustness and guide local reconstruction iterations.

[0168] The system includes: The path discretization and network modeling module is used to discretize the surface of the thin-walled ring to be machined into path nodes, bind the wall thickness and the fixture support position to characterize the local static stiffness, preset the cutting depth mode and micro control parameters, and construct a variable network model of the variable cutting depth turning path. The vibration response analysis and risk filing module is used to drive the digital twin model to generate time-domain vibration response signals of each path node, perform constrained adaptive modal decomposition to obtain a rigid following layer, a semi-stable flutter coupling layer and an unstable impact layer, extract features to calculate a comprehensive flutter risk index and generate modal risk boundary parameters to form a risk file; The value delivery and key node identification module is used to construct a path value function using risk profiles, calculate cumulative value and value gradient, identify key path nodes, and lock the micro-control parameters of other path nodes. The three-layer nested evolutionary game optimization module is used to perform a three-layer nested evolutionary game with key path nodes as participants, consisting of a micro-control parameter layer, a meso-mode layer, and a macro-global layer. After convergence, the game is spliced ​​together to form a complete variable-cut deep turning path. The digital twin verification and brittle reconstruction module is used to load the complete variable depth turning path into the digital twin model to calculate the agility index, mark the brittle node group and perform local reconstruction iteration to obtain a robust variable depth turning path. The online control and process solidification module is used to compile the robust variable cutting depth path into CNC code for the first piece trial cut, use the online classification model to determine the modal level, perform dead zone bias on the rigid following layer, fine-tune the cutting depth parameters on the semi-stable flutter coupling layer, trigger protection actions on the unstable impact layer, and solidify the process file.

[0169] Those skilled in the art will understand that the embodiments of this application are provided as methods, systems, or computer program products. Therefore, this application takes the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this application takes the form of a computer program product implemented on one or more computer storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer program code. The solutions in the embodiments of this application are implemented using various computer languages, exemplified by the object-oriented programming language Java and the interpreted scripting language JavaScript.

[0170] This application is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this application. It will be understood that each block of the flowchart illustrations and / or block diagrams, as well as combinations of blocks in the flowchart illustrations and / or block diagrams, are implemented by computer program instructions. These computer program instructions are 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, create means for implementing the functions specified in the flowchart illustrations and / or block diagrams.

[0171] These computer program instructions are also stored in a computer-readable storage medium that can direct a computer or other programmed 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 that implement the functions specified in the flowchart or multiple flowcharts and / or block diagram blocks or multiple block diagrams.

[0172] These computer program instructions are also loaded onto a computer or other programming data processing device to cause a series of operational steps to be performed on the computer or other programming device to produce a computer-implemented process, such that the instructions, which execute on the computer or other programming device, provide steps for implementing the functions specified in the flowchart flow or multiple flows and / or the block diagram blocks or multiple blocks.

[0173] Although preferred embodiments of this application 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 the preferred embodiments as well as all changes and modifications falling within the scope of this application.

[0174] Obviously, those skilled in the art can make various modifications and variations to this application without departing from the spirit and scope of this application. Therefore, if such modifications and variations fall within the scope of the claims of this application and their equivalents, this application also intends to include such modifications and variations.

Claims

1. A method for planning a variable depth of cut turning path to suppress chatter in thin-walled rings, characterized in that, include: The surface to be machined on the thin-walled ring is discretized into path nodes. The local static stiffness is characterized by binding the wall thickness and the fixture support position. The cutting depth mode and micro-control parameters are preset to construct a variable network model of the variable cutting depth turning path. The digital twin model is driven to generate time-domain vibration response signals of each path node. Constrained adaptive modal decomposition is performed to obtain a rigid following layer, a semi-stable flutter coupling layer, and an unstable impact layer. Features are extracted to calculate a comprehensive flutter risk index and generate modal risk boundary parameters to form a risk profile. The path value function is constructed using risk profiles to calculate cumulative value and value gradient, identify critical path nodes, and lock the micro-control parameters of the remaining path nodes. A three-layer nested evolutionary game, consisting of a micro-control parameter layer, a meso-mode layer, and a macro-global layer, is executed with critical path nodes as participants. After convergence, the game is spliced ​​together to form a complete variable-cut deep turning path. The complete variable depth turning path is loaded into the digital twin model to calculate the agility index, the brittle node group is marked and local reconstruction iteration is performed to obtain the robust variable depth turning path. The robust variable cutting depth path is compiled into CNC code for the first piece trial cut. The modal level is determined by an online classification model. Dead zone bias is applied to the rigid following layer. The cutting depth parameters are fine-tuned for the semi-stable flutter coupling layer. The protection action is triggered for the unstable impact layer. The process document is then solidified.

2. The variable depth of cut turning path planning method for suppressing chatter in thin-walled rings according to claim 1, characterized in that, The local static stiffness characterization method includes: acquiring the wall thickness distribution data and fixture support position of the thin-walled ring, generating path nodes along the tool feed direction, binding a corresponding wall thickness value to each node and calculating the distance from the node to the nearest fixture support point, and calculating the local static stiffness based on the following formula: ;in, Let be the local static stiffness of the i-th node. The elastic modulus of the material. For node wall thickness, The Euclidean distance from the node to the nearest clamp support point is given. The shape factor, The distance decay exponent; The preset cutting depth modes and micro-control parameters include: a preset constant cutting depth mode, a linearly varying cutting depth mode, a sinusoidal variable cutting depth mode, and an adaptive variable cutting depth mode based on adjacent node stiffness feedback; wherein, the sinusoidal variable cutting depth mode is based on... change, For node cutting depth, Based on the cutting depth, For the depth of cut, For spatial frequency, For the initial phase, The coordinates are the arc length of the node; the adaptive variable cutting depth mode adjusts the cutting depth based on the local stiffness changes of the preceding node after being amplified by the gain coefficient, and has a maximum adjustment limit.

3. The variable depth of cut turning path planning method for suppressing chatter in thin-walled rings according to claim 1, characterized in that, The steps for constructing the variable network model for the variable depth turning path include: Establish sequential connections between nodes to form the main path; Set conditional branch connections at nodes. When the comprehensive flutter risk index is higher than the preset threshold, or the local stiffness is lower than the preset threshold, branch edges are led out from the corresponding nodes to the conservative cutting depth mode path. A feedback loop connection is constructed to map the vibration monitoring characteristics of subsequent nodes back to the preceding nodes, which is used for online parameter updates of the adaptive variable cut depth mode. The weight of the feedback loop connection is dynamically adjusted by the modal risk boundary parameters in the risk profile.

4. The variable depth of cut turning path planning method for suppressing chatter in thin-walled rings according to claim 1, characterized in that, The steps for obtaining the rigid follower layer, the semi-stable flutter coupling layer, and the unstable impact layer include: A digital twin model of the driving thin-walled collar-tool system is used. The digital twin model adopts dynamic cutting force that considers regeneration effect and generates tool tip vibration displacement time history signal with nodal wall thickness and support position as boundaries. Constrained adaptive modal decomposition is performed on the time history signal, with the number of decomposition layers set to 3. Center frequency constraints are introduced in the variational modal decomposition, so that the center frequency of the rigid follower layer is constrained to the principal axis rotation frequency and its low harmonic neighborhood, the center frequency of the semi-stable flutter coupling layer is constrained to the regenerative flutter prediction frequency band, and the center frequency of the unstable impact layer is constrained to the high-frequency broadband region. The three modal components are obtained by iterative solution.

5. The variable depth of cut turning path planning method for suppressing chatter in thin-walled rings according to claim 4, characterized in that, The steps for calculating the comprehensive flutter risk index and generating the modal risk boundary parameters include: Calculate the energy proportion of each layer ,in Corresponding sequentially to the rigid follower layer, the semi-stable flutter coupling layer, and the unstable impact layer, For the first The time-domain signal of the layer modal components, For analysis of time windows; Hilbert transform is performed on the modal components of each layer to extract the envelope, and the maximum envelope amplitude is taken. And calculate the coefficient of variation of the envelope as volatility. : ,in and These are the standard deviation and mean of the envelope sequence, respectively, forming a feature vector containing energy proportion, envelope amplitude, and volatility.

6. The variable depth of cut turning path planning method for suppressing chatter in thin-walled rings according to claim 5, characterized in that, The calculation method for the comprehensive tremor risk index includes: Calculate the instability contribution coefficient of each layer using the following formula. : ;in, The stiffness attenuation index, This is the volatility amplification factor. For volatility.

7. The variable depth of cut turning path planning method for suppressing chatter in thin-walled rings according to claim 6, characterized in that, The calculation of the comprehensive tremor risk index also includes: The comprehensive flutter risk index is obtained by weighting and aggregating the instability contribution coefficients of the three layers. The weight satisfy Furthermore, the weights of the semi-stable flutter coupling layer and the unstable impact layer are greater than the weights of the rigid follower layer.

8. The variable depth of cut turning path planning method for suppressing chatter in thin-walled rings according to claim 1, characterized in that, The process of constructing a path value function using risk profiles and calculating cumulative value and value gradient includes: The instantaneous value of a node is defined as a weighted combination of three factors: cut depth gain, comprehensive flutter risk penalty, and a smoothing term for cut depth changes of adjacent nodes. Establishing paths to accumulate value The recurrence relation: ;in, For the instantaneous value of a node, The feasible region is defined by the modal risk boundary parameters. As a discount factor, For the first The selected cutting depth at each node For the first The cutting depth has been determined at each node. Given the current node's cutting depth as Under the condition of the first The maximum cumulative value from node to endpoint; The cumulative value of each node is solved by recursively working backward from the end node, and the value gradient of the cumulative value with respect to the cutting depth parameter is calculated simultaneously. .

9. The variable depth of cut turning path planning method for suppressing chatter in thin-walled rings according to claim 8, characterized in that, The micro-control parameters for identifying critical path nodes and locking the remaining path nodes include: Nodes that simultaneously meet the following three conditions are: the comprehensive flutter risk index exceeds the preset risk threshold, the value gradient turning point is greater than the gradient significant change threshold, and the arc length with adjacent nodes is greater than the minimum distance. Nodes that do not meet any of the conditions are considered non-critical nodes, and their micro-control parameters are locked to the lowest risk default value or a smooth transition value from the parameters of adjacent critical nodes.

10. The variable depth of cut turning path planning method for suppressing chatter in thin-walled rings according to claim 1, characterized in that, The three-layer nested evolutionary game, in which critical path nodes are the participants, involves a micro-level control parameter layer, a meso-level model layer, and a macro-level global layer, and includes: Define a strategy as a tuple for each key node , The pattern identifier selected from the four depth cutting modes. The vector represents the micro-control parameters for the corresponding mode. The policy feasible region is constrained by the modal risk boundary parameters and the value gradient. The payoff function is the cumulative value of the nodes.

11. The variable depth of cut turning path planning method for suppressing chatter in thin-walled rings according to claim 10, characterized in that, The three-layer nested evolutionary game includes: The micro-control parameter layer independently runs particle swarm optimization within each key node at the highest frequency. The particle velocity update introduces a value gradient guiding term, and the optimal micro-control parameters are iteratively solved within the feasible region. The meso-mode layer binds adjacent key nodes into fragments at a moderate frequency, performs cutting-depth mode selection synchronously, adopts an evolutionary strategy and applies modal smoothing constraints, and penalizes mode differences and jumps between adjacent nodes. The macro-level global layer synchronizes all key nodes at the lowest frequency, aiming to maximize the global value function. It dynamically coordinates the strategies of each node through optimal response until Nash equilibrium is reached.

12. The variable depth of cut turning path planning method for suppressing chatter in thin-walled rings according to claim 11, characterized in that, The steps for forming the complete variable depth of cut turning path include: Extract the cut depth pattern and micro-control parameters after convergence at each key node; For locked non-critical nodes, a smooth transition is achieved by linear interpolation based on the arc length ratio of the parameters of adjacent critical nodes; By concatenating the parameters of critical nodes and non-critical nodes in the path order, a complete variable depth turning path is generated.

13. The variable depth of cut turning path planning method for suppressing chatter in thin-walled rings according to claim 1, characterized in that, The robust variable cut depth path formation step includes: In a digital twin model, short-duration, depth-of-cut pulse perturbations are injected along the path to selected nodes. The vibration response after the perturbation is recorded, and the agility index is calculated. : ;in The recovery time for vibration to return to steady state. For the maximum overshoot, , These are the weighting coefficients; Nodes whose agility index exceeds the allowable upper limit are marked as fragile nodes, and spatially continuous fragile nodes are clustered into fragile node groups. Extract the fragile node group and several adjacent nodes before and after it as the local reconstruction region, return to execute the steps of calculating the cumulative value and value gradient, identifying critical path nodes and the three-layer nested evolutionary game, re-optimize the parameters of the local region until the agility index of all nodes reaches the target, and output the robust variable cutting depth path.

14. The variable depth of cut turning path planning method for suppressing chatter in thin-walled rings according to claim 1, characterized in that, The process of using an online classification model to determine the modal level, applying dead-zone bias to the rigid following layer, fine-tuning the shear depth parameters of the semi-stable flutter coupling layer, and triggering protective actions for the unstable impact layer includes: The online classification model is trained using modal feature vectors and three-layer labels from the risk profile. It takes the vibration features of the sliding window as real-time input and outputs the probability of each modal level. For nodes identified as rigid follower layers, keep the current cut depth parameters unchanged; For nodes identified as semi-stable flutter coupling layers, according to Calculate the depth of cut fine adjustment amount ,in This is an adjustable gain coefficient; and before performing fine-tuning, it is verified whether the sign of the fine-tuning amount is consistent with the sign of the value gradient calculated in real time. If they are inconsistent, the fine-tuning is abandoned. For nodes identified as unstable impact layers, rapid tool retraction and spindle deceleration protection actions are immediately triggered.

15. The variable depth of cut turning path planning system for suppressing chatter in thin-walled rings according to any one of claims 1-14, characterized in that, The system includes: The path discretization and network modeling module is used to discretize the surface of the thin-walled ring to be machined into path nodes, bind the wall thickness and the fixture support position to characterize the local static stiffness, preset the cutting depth mode and micro control parameters, and construct a variable network model of the variable cutting depth turning path. The vibration response analysis and risk filing module is used to drive the digital twin model to generate time-domain vibration response signals of each path node, perform constrained adaptive modal decomposition to obtain a rigid following layer, a semi-stable flutter coupling layer and an unstable impact layer, extract features to calculate a comprehensive flutter risk index and generate modal risk boundary parameters to form a risk file; The value delivery and key node identification module is used to construct a path value function using risk profiles, calculate cumulative value and value gradient, identify key path nodes, and lock the micro-control parameters of other path nodes. The three-layer nested evolutionary game optimization module is used to perform a three-layer nested evolutionary game with key path nodes as participants, consisting of a micro-control parameter layer, a meso-mode layer, and a macro-global layer. After convergence, the game is spliced ​​together to form a complete variable-cut deep turning path. The digital twin verification and brittle reconstruction module is used to load the complete variable depth turning path into the digital twin model to calculate the agility index, mark the brittle node group and perform local reconstruction iteration to obtain a robust variable depth turning path. The online control and process solidification module is used to compile the robust variable cutting depth path into CNC code for the first piece trial cut, use the online classification model to determine the modal level, perform dead zone bias on the rigid following layer, fine-tune the cutting depth parameters on the semi-stable flutter coupling layer, trigger protection actions on the unstable impact layer, and solidify the process file.

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