A Smart Milling Method for Surfaces in Industrial Robots to Compensate for Low-Stiffness Vibrations

Abstract

This invention relates to the field of industrial robot milling technology, specifically disclosing a method for intelligent milling of curved surfaces in industrial robots to compensate for low-stiffness vibrations. The method includes: offline construction of a unified stiffness map of a two-body coupling, comprising the robot's stiffness field and the workpiece's dynamic stiffness field, and pre-training a multi-task prediction model; online acquisition of multi-source sensor signals, combined with the unified stiffness map of the two-body coupling, to decouple the two-body vibrations and separate the robot's body vibration component and the workpiece's elastic vibration component. This invention achieves accurate decoupling of the robot's body vibration component and the workpiece's elastic vibration component by offline construction of a unified stiffness map of the two-body coupling, comprising the robot's stiffness field and the workpiece's dynamic stiffness field, and by combining this with online acquisition of multi-source sensor signals during actual milling. By inputting the separated features into the multi-task prediction model, the system can predict the evolution trend of two-body coupled chatter in advance, and then evaluate the contribution of the two-body vibration based on this trend during the control execution phase.

Description

Technical Field

[0001] This invention relates to the field of industrial robot milling technology, and in particular to an intelligent milling method for curved surfaces of industrial robots that compensates for low-stiffness vibrations. Background Technology

[0002] Industrial robots are widely used in surface milling tasks. In this process, the serial joint structure of the industrial robot causes its body to exhibit low stiffness. Simultaneously, the local structure of the thin-walled workpiece being machined also exhibits low stiffness during the material removal stage.

[0003] In actual milling operations, dynamic cutting forces act simultaneously on both the robot and the workpiece, causing them to vibrate. Existing compensation systems typically treat the robot and workpiece as independent objects, making it impossible to separate the vibration components of the robot body from the elastic vibration components of the workpiece in the sensor signals.

[0004] This approach makes it impossible for the system to predict the coupled chattering trend caused by the interaction between the robot and the workpiece, and thus impossible to assign corresponding compensation weights based on the vibration contributions of the robot and the workpiece, respectively. Due to the lack of targeted composite control commands, there are deviations in pose and displacement compensation during the milling process, affecting the final quality of the surface machining. Summary of the Invention

[0005] This invention aims to at least partially solve one of the technical problems in related technologies. Therefore, the objective of this invention is to propose an intelligent milling method for curved surfaces in industrial robots that compensates for low-stiffness vibrations, thereby reducing coupled vibration errors caused by the interaction between the robot and the workpiece.

[0006] To achieve the above objectives, a first aspect of the present invention proposes an intelligent milling method for curved surfaces of industrial robots to compensate for low-stiffness vibrations, comprising: offline construction of a two-body coupled unified stiffness map containing the robot stiffness field and the workpiece dynamic stiffness field, and pre-training a multi-task prediction model; online acquisition of multi-source sensor signals, combined with the two-body coupled unified stiffness map to decouple the two-body vibrations, separating the robot body vibration component and the workpiece elastic vibration component; fusing the separated robot body vibration component and the workpiece elastic vibration component and inputting them into the multi-task prediction model to predict the evolution trend of two-body coupled chatter, including the total vibration peak amplitude and the total vibration peak phase; dynamically evaluating the contribution of the two-body vibrations based on the two-body coupled chatter evolution trend, and assigning corresponding compensation weights to generate a composite control command that includes at least a low-frequency pose correction amount, a high-frequency micro-displacement compensation vector, and a cutting parameter adjustment command; injecting the composite control command into the robot servo system to execute cutting control, and identifying the actual stiffness value online based on real-time cutting feedback to dynamically update the two-body coupled unified stiffness map.

[0007] To achieve the above objectives, a second aspect of the present invention proposes an intelligent surface milling system for industrial robots that compensates for low-stiffness vibrations, comprising: a graph construction and pre-training module for offline construction of a two-body coupled unified stiffness graph containing the robot stiffness field and the workpiece dynamic stiffness field, and pre-training a multi-task prediction model; a signal acquisition and vibration decoupling module for online acquisition of multi-source sensor signals, combining the two-body coupled unified stiffness graph to perform two-body vibration decoupling, separating the robot body vibration component and the workpiece elastic vibration component; and a flutter evolution trend prediction module for predicting the separated robot body vibration component and the workpiece elastic vibration component. The vibration component fusion input is used to predict the evolution trend of two-body coupled flutter, which includes the total peak amplitude and the total peak phase of vibration. The instruction generation module is used to dynamically evaluate the contribution of the two-body vibration based on the evolution trend of the two-body coupled flutter, and assign corresponding compensation weights to generate a composite control instruction that includes at least low-frequency pose correction, high-frequency micro-displacement compensation vector, and cutting parameter adjustment instructions. The cutting control and map update module is used to inject the composite control instruction into the robot servo system to execute cutting control, and to identify the actual stiffness value online based on real-time cutting feedback to dynamically update the two-body coupled unified stiffness map.

[0008] To achieve the above objectives, a third aspect of the present invention provides an electronic device including a memory, a processor, and a computer program stored in the memory. When the computer program is executed by the processor, it implements the above-described intelligent milling method for industrial robot surfaces to compensate for low-stiffness vibrations.

[0009] This invention constructs an offline unified stiffness map of the two-body coupling, encompassing both the robot's stiffness field and the workpiece's dynamic stiffness field. During actual milling, this is combined with online acquisition of multi-source sensor signals to accurately decouple the robot's vibration components from the workpiece's elastic vibration components. The separated features are input into a multi-task prediction model, enabling the system to predict the evolution trend of two-body coupled chatter in advance. Then, during the control execution phase, this trend is used to assess the contribution of the two-body vibration and allocate corresponding compensation weights.

[0010] In real-world machining of complex curved surfaces, this scheme establishes a dynamic closed loop from vibration decoupling to evolution prediction and then to composite control. This enables the robot servo system to output matching low-frequency pose correction and high-frequency micro-displacement compensation vectors based on the real-time dual-body coupling state, reducing the coupling vibration error caused by the interaction between the robot and the workpiece. Attached Figure Description

[0011] Figure 1 This is a flowchart illustrating the intelligent milling method for curved surfaces of industrial robots that compensates for low-stiffness vibrations provided by the present invention. Figure 2This is a schematic diagram illustrating the implementation of the intelligent milling system for curved surfaces of industrial robots that compensates for low-stiffness vibrations provided by this invention. Figure 3 This is a schematic diagram of the structure of the electronic device provided by the present invention. Detailed Implementation

[0012] Embodiments of the present invention are described in detail below, examples of which are illustrated in the accompanying drawings, wherein the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary and intended to explain the present invention, and should not be construed as limiting the present invention.

[0013] The following description, with reference to the accompanying drawings, describes an intelligent milling system, method, and electronic device for industrial robots to compensate for low-stiffness vibrations.

[0014] Example 1: like Figure 1 As shown in the figure, this embodiment provides an intelligent milling method for curved surfaces of industrial robots to compensate for low-stiffness vibrations.

[0015] In the aerospace, rail transportation, and large mold manufacturing industries, the use of industrial robots for milling complex curved surfaces, such as engine blades and high-speed train front skins, has become a trend. However, due to their serial joint structure, industrial robots exhibit significant low stiffness at their ends; simultaneously, thin-walled curved workpieces also fall into the category of low-stiffness bodies during machining. In actual milling operations, these two low-stiffness characteristics interact with each other.

[0016] Specifically, the method provided in this embodiment includes the following steps: Step 1: Offline construction of a unified stiffness map of two-body coupling and model pre-training.

[0017] Specifically, the method in this embodiment first performs a preparatory stage: offline construction of a unified stiffness map of the two-body coupling, which includes the robot's stiffness field and the workpiece's dynamic stiffness field, and pre-training of a multi-task prediction model. The purpose of this step is to provide high-precision physical benchmarks and prior knowledge for online machining, so that the subsequent control system can fully grasp the stiffness state of the two-body system.

[0018] For example, the offline construction of a two-body coupled unified stiffness map containing the robot stiffness field and the workpiece dynamic stiffness field includes sampling posture points within the robot's workspace and measuring the end effector static stiffness and contact stiffness characteristics under the corresponding postures to construct the robot stiffness field. In practical applications, since the six rotary joints of an industrial robot constitute a highly nonlinear six-dimensional space, using spatially uniform point distribution methods such as Latin hypercube sampling can effectively avoid the dimensional explosion problem caused by full-space grid sampling. At each sampled posture point, by applying an external calibration load and measuring the end effector displacement using a laser tracker, the end effector static stiffness under that posture can be fitted. Simultaneously, a static pressure test is performed on the surface of the force gauge using a standard tool to obtain contact stiffness characteristics, thereby forming robot stiffness field data covering the entire robot workspace.

[0019] Optionally, this embodiment employs the element birth and death technique to simulate the workpiece material removal process, discretizing and calculating the local stiffness matrix and natural frequencies of the workpiece at each machining step to construct the workpiece's dynamic stiffness field. In practical finite element analysis applications, the "element birth and death technique" simulates the physical state after material removal by multiplying the stiffness and mass matrices of the material mesh elements to be milled by a very small attenuation factor, making their mechanical contribution to the overall structure approach zero. By discretizing along a predetermined machining path, the system can solve for the remaining structural stiffness of the workpiece at each machining step (i.e., when the tool passes through a specific position), forming a workpiece dynamic stiffness field that varies with time and space.

[0020] It is also important to note that after acquiring the two independent stiffness fields mentioned above, the system derives the two-body coupling stiffness matrix based on the robot end effector stiffness matrix, the workpiece local stiffness matrix, and the contact stiffness matrix. This two-body coupling stiffness matrix is ​​then quantized and compressed to construct the unified two-body coupling stiffness map. In actual industrial machining, the robot, the tool contact surface, and the workpiece constitute a series-connected flexible mechanical system. According to the principle of series stiffness equivalence, the sum of the compliance (the reciprocal of the stiffness) of these three components constitutes the total compliance of the overall system. Quantizing and compressing the calculated multidimensional matrix data using eight-bit or sixteen-bit methods can significantly reduce the map's memory footprint in the controller and improve the response rate of online retrieval queries.

[0021] Step 2: Online acquisition of multi-source sensor signals and decoupling of dual-body vibration.

[0022] Specifically, during the cutting process, the system acquires multi-source sensor signals online and combines them with the unified stiffness spectrum of the two-body coupling to decouple the two-body vibration, separating the vibration components of the robot body and the elastic vibration components of the workpiece. Existing industrial robot milling systems often can only measure a general vibration or force signal and cannot distinguish the source of vibration, while this step effectively overcomes this technical limitation.

[0023] For example, the online acquisition of multi-source sensor signals, combined with the dual-body coupling unified stiffness map for dual-body vibration decoupling, includes the simultaneous acquisition of 6-dimensional force sensor signals, 3-axis accelerometer signals, and spindle motor current signals as the multi-source sensor signals. The 6-dimensional force sensor is typically installed between the robot's end flange and the electric spindle to obtain the force and torque in three orthogonal directions in space; the 3-axis accelerometer is attached to the spindle housing to obtain high-frequency end-body vibration acceleration; and the spindle motor current signal is read in real time through the driver's internal bus to reflect minute fluctuations in cutting torque.

[0024] Optionally, the system establishes a robot body dynamics model to isolate the inertial and elastic force responses of the robot body from the 6-dimensional force sensor signals, thus decoupling the actual cutting force. In actual operation, the 6-dimensional force sensor measures not only the force of the tool cutting the material, but also the inertial and damping forces generated by the robot's massive mass during acceleration, deceleration, and vibration. To obtain high-fidelity cutting interaction forces, an inverse dynamics model based on the Newton-Euler equations or the Lagrange equations must be established for this isolation. The formula for calculating the actual cutting force is: ;in, This is the actual cutting force. These are measurements taken by a 6D force sensor. This is the equivalent mass matrix of the robot's end effector, reflecting the inertial characteristics of the end effector load; The robot's end effector acceleration was measured by a 3-axis accelerometer. The equivalent damping matrix of the robot's end effector characterizes joint friction and internal energy dissipation. For the robot's end effector speed, This is the robot end effector stiffness matrix, which characterizes the elastic deformation resistance of the joint drivetrain. This represents the displacement of the robot's end effector.

[0025] It is important to note that after decoupling and extracting the actual cutting force, the elastic vibration components of the workpiece are calculated by inverting the actual cutting force based on the workpiece's local stiffness matrix in the dual-body coupled unified stiffness map. Specifically, the system retrieves the workpiece's local stiffness matrix from the map at the current tool position coordinates and derives the workpiece's elastic yielding and oscillating displacement under the actual cutting force using linear or nonlinear constitutive relations. Thus, the macroscopic hybrid sensing signal is successfully decomposed into two independent physical features belonging to the robot body and the workpiece.

[0026] Step 3: Prediction of the evolution trend of two-body coupled flutter.

[0027] Specifically, the system fuses the separated vibration components of the robot body and the elastic vibration components of the workpiece into the multi-task prediction model to predict the evolution trend of dual-body coupled chatter, including the total peak amplitude and phase of the total vibration. Because milling chatter is sudden and destructive, relying solely on post-feedback control often results in chatter marks already appearing on the workpiece surface. Therefore, the prediction stage is the core of achieving intelligent feedforward compensation.

[0028] For example, the multi-task prediction model is a temporal prediction network containing a self-attention mechanism encoder and decoder. The prediction step includes fusing and concatenating the temporal features extracted from the multi-source sensor signals after preprocessing with the inversion features of the workpiece's elastic vibration components to form a feature input matrix. The preprocessing process typically includes Kalman filtering or bandpass filtering to remove power frequency interference and high-frequency electromagnetic noise. Feature fusion and concatenation aligns physical quantities of different dimensions on the same time section, forming a high-dimensional tensor.

[0029] Optionally, the feature input matrix is ​​input into the multi-task prediction model, which outputs in parallel the predicted robot vibration value, the predicted workpiece vibration value, and a risk level characterizing the two-body vibration coupling coefficient within a set sampling period. The self-attention mechanism can autonomously calculate the influence weights of data at different time points in the historical sequence on the future state without relying on a fixed period assumption, which has a significant advantage when dealing with non-stationary time-varying signals such as milling. The output risk level provides a macro-level decision-making basis for subsequent safety strategies.

[0030] It is also important to note that the system extracts the instantaneous phase and amplitude of the predicted robot vibration and the predicted workpiece vibration, and uses a polynomial fitting algorithm to extrapolate the total vibration peak phase and the total vibration peak amplitude. In actual waveform analysis, two separate vibration waveforms may experience constructive interference (phase alignment, vibration amplification) or destructive interference (phase misalignment, vibration cancellation). By extrapolating the peak value of the superimposed waveforms and its corresponding phase, the system can accurately locate the moment of maximum deformation within the next microsecond cycle, which is the basis for accurately implementing anti-phase cancellation control.

[0031] Step 4: Assessment of the contribution of two-body vibration and allocation of control weights.

[0032] Specifically, the contribution of the two-body vibration is dynamically evaluated based on the evolution trend of the two-body coupling flutter, and corresponding compensation weights are assigned to generate a composite control command that includes at least low-frequency pose correction, high-frequency micro-displacement compensation vector, and cutting parameter adjustment command.

[0033] For example, the dynamic evaluation of the dual-body vibration contribution based on the dual-body coupling flutter evolution trend and the allocation of corresponding compensation weights include aggregating the robot vibration amplitude and the workpiece vibration amplitude to construct a total vibration amplitude benchmark; calculating the proportion of the robot vibration amplitude and the workpiece vibration amplitude in the total vibration amplitude benchmark respectively, and generating the robot vibration contribution and the workpiece vibration contribution. In a real physical scenario, if the robot vibration contribution is as high as 80%, it means that the current flutter is mainly caused by the robot's weak posture stiffness; if the workpiece vibration contribution is dominant, it indicates that the current milling position is exactly in the modal resonance region of the workpiece's thin-walled structure.

[0034] Optionally, the system presets a first contribution threshold and a second contribution threshold, with the first contribution threshold being greater than the second contribution threshold. When the robot vibration contribution is greater than the first contribution threshold, the main weight is allocated to the robot body displacement compensation channel. When the robot vibration contribution is less than or equal to the first contribution threshold but greater than the second contribution threshold, the weights are evenly allocated to the robot body displacement compensation channel and the spindle cutting parameter adjustment channel. When the robot vibration contribution is less than or equal to the second contribution threshold, the main weight is allocated to the spindle cutting parameter adjustment channel. This dynamic allocation mechanism based on quantitative numerical interval division ensures that the compensation action is targeted, avoiding compensation failure caused by blindly driving the robot to move when the workpiece structure is weak.

[0035] Step 5: Frequency band-separated dual-loop composite control and hierarchical collaborative vibration suppression.

[0036] Specifically, in order to address the two types of machining errors with different frequency characteristics, namely low-frequency tool deflection and high-frequency chatter, the generation of composite control commands includes at least low-frequency pose correction, high-frequency micro-displacement compensation vector, and cutting parameter adjustment instructions, which is specifically implemented through a frequency band-separated dual-loop composite control architecture.

[0037] For example, the low-frequency pose correction amount, which is mainly used to suppress static deformation, is calculated through a low-frequency constant force compensation loop, using the following formula: in, This refers to the low-frequency pose correction factor for a 6-DOF system, which includes spatial position and attitude. The compensation frequency is typically in the range of [frequency range missing]. The following macroscopic geometric bias; This is the amount of compensation for robot stiffness deformation. This is the workpiece elastic deformation compensation amount. Under constant cutting force, both the robot body and the workpiece will experience slight elastic yielding, commonly known as tool deflection, leading to insufficient depth of cut. This low-frequency correction amount is achieved by superimposing the calculated deformation amount onto the target trajectory, allowing the tool to compress the system back to the theoretical geometric contour.

[0038] Optionally, the high-frequency micro-displacement compensation vector, which is mainly used to suppress dynamic flutter, is calculated through a high-frequency feedforward compensation loop, using the following formula: in, A 3-DOF anti-phase high-frequency micro-displacement compensation vector for controlling the translation of the main shaft; This represents the total peak amplitude of the vibration. ω is the flutter angular frequency, which characterizes the excitation frequency characteristics of the vibration; The current system time. The phase of the total vibration peak. This is the anti-phase offset constant, used to construct a 180-degree phase difference; This represents the equivalent stiffness value along the principal axis of the minimum stiffness of the two-body coupled system.

[0039] The physical essence of this formula is to actively generate a micro-displacement at the tool tip that has the same amplitude and frequency as the currently estimated chatter waveform but is completely opposite in direction. By utilizing the principle of wave interference cancellation, it effectively suppresses the high-frequency chatter caused by cutting force in its initial stage.

[0040] It is also important to note that the logic for issuing the composite control command is triggered based on the following hierarchical collaborative vibration suppression strategy: A first amplitude threshold and a second amplitude threshold are preset, with the first amplitude threshold being less than the second amplitude threshold; when the total vibration peak amplitude is less than the first amplitude threshold, only the high-frequency micro-displacement compensation vector is output to control the robot end effector to perform anti-phase compensation; when the total vibration peak amplitude is greater than or equal to the first amplitude threshold and less than the second amplitude threshold, the high-frequency micro-displacement compensation vector and the spindle speed adjustment command in the cutting parameter adjustment command are issued in parallel to actively disrupt the phase delay condition of regenerative chatter; when the total vibration peak amplitude is greater than or equal to the second amplitude threshold, the feed rate derating command in the cutting parameter adjustment command is forcibly output, and when the dual-body vibration coupling coefficient is greater than a preset coupling safety threshold, a protection command to stop cutting feed and lift the tool is output. This hierarchical strategy prevents the servo system from outputting high-frequency commands exceeding physical limits under extreme operating conditions, which could lead to motor overload and damage.

[0041] Step Six: Injection and execution of control instructions at the underlying level.

[0042] Specifically, the system injects the composite control commands into the robot servo system to execute cutting control. Because high-frequency chatter suppression has high time delay requirements, the traditional method of issuing commands through the robot's upper-level pose interpolation interface has network and interpolation delays of tens of milliseconds, which cannot meet the requirements for inverse phase compensation.

[0043] For example, injecting the composite control command into the robot servo system to execute cutting control includes establishing a direct mapping interface at the control hardware level to convert the high-frequency micro-displacement compensation vector into a dynamic velocity reference; directly bypassing the position control loop of the robot controller, the dynamic velocity reference is injected as a feedforward quantity into the velocity loop input of the servo driver. Industrial AC servo drivers typically contain position loops, velocity loops, and current loops. The position loop has the slowest response, while the velocity and current loops have faster response rates. Directly mapping the compensation quantity into a velocity feedforward signal and injecting it into the velocity loop can reduce the system response delay to the millisecond or even sub-millisecond level.

[0044] Optionally, the low-frequency pose correction amount, after being parsed by the position control loop to generate a conventional velocity command, is algebraically superimposed with the dynamic velocity reference injected into the velocity loop input. This architecture retains the robot's native controller's high-precision interpolation capability for macroscopic spatial trajectories while also providing the system's underlying layer with high-frequency dynamic response capabilities to resist high-frequency vibration interference.

[0045] Step 7: Online stiffness identification, dynamic map update, and system security protection.

[0046] Specifically, in order to cope with the gradual changes in material properties, tool wear and environmental temperature drift caused by long-term processing, the system identifies the actual stiffness value online based on real-time cutting feedback to dynamically update the dual-body coupled unified stiffness map.

[0047] For example, under stable cutting conditions, the actual end-effector displacement offset and end-effector force data are periodically collected to identify the actual static stiffness of the robot. When the identification error exceeds a preset stiffness error threshold, a weighted average function is used to update the corresponding spatial node parameters in the graph. This can calibrate the robot body stiffness drift caused by thermal expansion of the mechanical transmission chain or changes in lubricant viscosity.

[0048] Optionally, the actual local stiffness value is identified by simultaneously acquiring the real cutting force fluctuation characteristics and workpiece vibration inversion displacement. The weight parameters of the neural network representing the dynamic stiffness field of the workpiece are then iteratively updated using a gradient descent algorithm. This ensures that the digital twin model represented by the graph maintains a high degree of consistency with the real physical environment.

[0049] It is also important to note that the method includes a parallel monitoring system-wide safety protection mechanism: independently setting force protection thresholds and amplitude reduction protection thresholds for anomaly monitoring; continuously calculating the rate of change of the derivative of the dual-body vibration coupling coefficient; and when it is determined that the dual-body vibration coupling coefficient is in the divergence range and the growth rate of the total vibration peak amplitude exceeds a preset surge threshold, the system immediately interrupts the regular machining commands and executes the highest priority emergency protection command to stop cutting and lift the tool. This mechanism serves as a reliable safety barrier for the system, preventing equipment damage caused by abnormal working conditions such as tool breakage and fixture loosening.

[0050] Based on the analysis of the above embodiments, existing technologies generally face problems such as poor machining accuracy, severe vibration texture, and easy tool damage when processing complex curved surfaces by industrial robots. This is due to the superposition of low stiffness of the robot body and local low stiffness of the workpiece. Conventional methods often involve passive filtering and speed reduction of the overall mixed signal, lacking decoupling from the physical source of vibration and targeted compensation strategies.

[0051] The technical solution disclosed in this embodiment effectively decouples robot body vibration from workpiece elastic vibration at the industrial application level through deep fusion of offline unified stiffness maps and online multi-source signals. Based on this decoupling result, an attention mechanism is used to predict flutter evolution, and then a dual-loop joint control system of low-frequency correction and high-frequency anti-phase cancellation is implemented at the control layer. This method combines the rigor of physical modeling with the forward-looking nature of artificial intelligence, significantly improving the system's vibration-resistant machining capability and ensuring the surface quality of thin-walled curved parts without changing the robot's mechanical hardware. It also establishes a high-fidelity digital map dynamic self-evolution mechanism, providing a highly reliable and practical solution for intelligent robot flexible milling in high-end manufacturing. Example

[0052] As a further exploration and expansion of the above embodiment one, this embodiment mainly addresses the unavoidable physical phenomenon of tool wear in long-cycle complex surface milling, and provides a closed-loop adaptive solution that does not require additional external detection hardware.

[0053] In actual milling operations of difficult-to-machine materials such as titanium alloys and high-temperature alloys in the aerospace field, the tool wear evolution rate is relatively fast. The wear of the tool's flank face directly changes the micro-geometry and tribological properties of the tool-workpiece contact interface, thereby causing nonlinear time-varying drift in local contact stiffness. If the system still uses offline calibrated fixed contact stiffness for vibration prediction, significant model distortion and calculation errors will occur.

[0054] Based on the real technical problems encountered in the aforementioned industrial applications, this embodiment proposes the following content.

[0055] Specifically, the method of dynamically updating the dual-body coupled unified stiffness map by identifying the actual stiffness value online based on real-time cutting feedback also includes an adaptive correction mechanism for contact stiffness in response to tool wear evolution. This mechanism aims to objectively reflect the tool wear state by mining the temporal evolution law of the inherent electronic control signals and mechanical signals within the system, and to physically quantify it into stiffness attributes. The specific steps are as follows: Phase 1: Deep feature extraction of multi-source signals and calculation of energy consumption deviation.

[0056] Specifically, the core task of this stage is to extract the high-order harmonic energy characteristics of the spindle motor current signal from the multi-source sensing signals, and to calculate the specific cutting energy deviation, which characterizes the difference in current cutting energy consumption, based on the decoupled actual cutting force and the theoretical material removal rate of the corresponding machining step.

[0057] During actual spindle motor operation, the periodic contact and fracture between the cutting edge and the workpiece material generate resistance torque fluctuations with a very wide frequency distribution. When the tool is in a sharp state, the cutting process is mainly characterized by material shear slip, and the three-phase current waveform of the spindle motor is relatively smooth, mainly concentrated in the fundamental frequency component.

[0058] However, as the wear band on the tool's flank gradually widens, the frictional effect between the flank and the machined surface intensifies exponentially. This strong nonlinear frictional resistance leads to a large number of high-frequency distortion components in the spindle motor's electromagnetic torque. The system extracts high-order harmonic energy characteristics in specific frequency bands from the online-acquired high-frequency spindle motor current signal using a windowed fast Fourier transform algorithm. These high-order harmonic energy characteristics can filter out fundamental frequency fluctuations caused by changes in macroscopic cutting parameters and are highly sensitive to the degree of microscopic deterioration of the friction contact interface.

[0059] Optionally, relying solely on current characteristics is susceptible to interference from power grid fluctuations or internal switching noise in the spindle drive. To further improve the accuracy of the evaluation, the system introduces a cross-validation mechanism from both macroscopic mechanical and thermodynamic perspectives, namely, calculating the deviation of the specific cutting energy. Specific cutting energy refers to the cutting work consumed to remove a unit volume of workpiece material, and it has a stable baseline value under specific materials and cutting parameters. When the tool becomes dull, the proportion of ineffective work done to overcome friction and compression in the cutting force increases significantly, causing the actual specific cutting energy to deviate significantly from the baseline value.

[0060] The system analyzes the theoretical material removal rate of the current machining step based on the machining program generated by computer-aided manufacturing software, and combines it with the actual cutting force obtained by decoupling from the 6-dimensional force sensor. The specific cutting energy deviation is calculated using the following first preset analytical formula: in, The deviation of cutting energy is a positive indicator of the abnormal increase in energy dissipation during the cutting process. The actual cutting force is obtained by decoupling and eliminating inertial forces and damping forces from the robot dynamics model; The current macroscopic real-time spatial feed rate of the tool relative to the workpiece (excluding high-frequency vibration components) characterizes the kinematic state of the tool. This is a benchmark specific cutting energy experimentally determined for the current workpiece material with the tool in a brand-new state. Through the above calculations, the system eliminates the interference of cutting force fluctuations caused by changes in depth of cut or width of cut, and purely isolates the energy efficiency reduction index caused by tool edge degradation.

[0061] The second stage: wear state deduction based on hidden Markov model.

[0062] For example, after acquiring the above dual characteristics, the system inputs the higher harmonic energy characteristics and the specific cutting energy deviation into a preset hidden Markov wear evaluation model, and outputs the flank wear characteristic quantity that characterizes the current tool degradation state.

[0063] In real-world metal cutting environments, directly measuring tool wear using optical equipment such as machine vision or laser tool setters is unreliable because large amounts of cutting fluid, metal chips, and machining mist can severely obscure the measurement optical path. The introduction of a Hidden Markov Wear Assessment Model (HMM) enables the system to infer invisible internal states from noisy observation sequences. Within this model framework, the actual physical wear of the tool is defined as the "hidden state," while the extracted higher harmonic energy characteristics and the deviation from the specific cutting energy constitute a two-dimensional "observation vector."

[0064] During the model initialization phase, the state transition probability matrix and observation probability distribution function of the Hidden Markov Model (HMM) are pre-trained using a large amount of full-lifecycle cutting experimental data. During online cutting, the system continuously receives new observation vector sequences over time. The HMM wear assessment model employs either a forward-backward algorithm or a Viterbi algorithm to dynamically calculate the posterior probability of each wear state within the tool under the current observation sequence. This model effectively smooths short-term signal abrupt changes caused by uneven machining materials (such as hard particles within the material), thus stably and smoothly deriving and outputting the flank wear characteristic quantity. This flank wear characteristic quantity is a continuous real value, objectively quantifying the average width of the wear band on the tool flank, providing a precise physical interface for subsequent stiffness compensation.

[0065] Third stage: Nonlinear time-varying mapping of contact stiffness.

[0066] Specifically, the system constructs a nonlinear contact stiffness degradation function, maps the back face wear characteristics to a time-varying attenuation coefficient, and uses the time-varying attenuation coefficient to perform coefficient attenuation calculation on the initial contact stiffness matrix to generate a dynamic contact stiffness matrix.

[0067] This step is the key technical link connecting the two independent technical fields of "tool wear assessment" and "low-stiffness vibration compensation" in this embodiment. In milling dynamics, the contact stiffness between the tool and the workpiece is mainly determined by the elastic deformation properties of the microscopic contact area of ​​the cutting edge. When the tool is sharp, the radius of the cutting edge arc is extremely small, and the contact mechanism is similar to Hertzian point contact or line contact, resulting in high penetration stiffness into the workpiece material.

[0068] However, as the wear characteristics of the flank face increase, the tool tip becomes blunt, and a large surface contact is formed between the flank face and the workpiece surface. This change in geometry not only alters the actual normal stress distribution in the contact area but also leads to a significant local accumulation of cutting heat in the passivated region, triggering a transient thermal softening effect at the contact interface. Combining these tribological and thermodynamic mechanisms, tool wear causes a significant nonlinear decrease in local contact stiffness.

[0069] To mathematically describe this physical attenuation process in the control system, a nonlinear contact stiffness degradation function is constructed, and the dynamic contact stiffness matrix is ​​generated using the following second pre-defined analytical formula: in, The generated dynamic contact stiffness matrix in the time evolution dimension reflects the interface stiffness properties under the current wear state in real time. The initial contact stiffness matrix is ​​obtained based on a novel tool calibration during the offline construction phase of the unified stiffness map for two-body coupling. It is an exponential function with the natural constant as its base, used to describe the nonlinear decay behavior caused by wear; The wear sensitivity constant of the tool-workpiece material combination is determined by fitting through cutting experiments, which characterizes the sensitivity of stiffness to wear degradation. The wear characteristics of the back face are derived from the Hidden Markov Wear Assessment Model. The initial wear tolerance threshold is set at this value. The physical significance of this threshold is that, in the initial, very slight wear stage of the tool, the micro-strengthening effect of the cutting edge may temporarily increase stiffness or remain unchanged. Only when the wear exceeds this threshold will a significant stiffness decay begin. The time-varying decay coefficient calculated using this formula effectively corrects the initial calibration value, generating a dynamic contact stiffness matrix that conforms to the actual physical state.

[0070] Phase 4: Map self-evolution and prediction parameter reconstruction.

[0071] It should be noted that the system eventually updates the dynamic contact stiffness matrix to the contact interface mapping layer of the two-body coupled unified stiffness map to trigger the system to dynamically reconstruct the stiffness input parameters of the multi-task prediction model.

[0072] The unified stiffness map for two-body coupling is divided into a robot body stiffness layer, a workpiece local stiffness layer, and a contact interface mapping layer connecting the two at the underlying software architecture. After the dynamic contact stiffness matrix is ​​generated, the system writes the new stiffness values ​​to a specific memory address in the contact interface mapping layer through an asynchronous update thread, without blocking the underlying hard real-time control cycle, such as the 1ms position loop.

[0073] Once the data at the interface mapping layer is overwritten, the system's internal data dependency mechanism will be triggered. The system will re-invoke the series stiffness equivalent derivation algorithm from Example 1 to recalculate the overall stiffness properties of the entire two-body system. Due to the attenuation of contact stiffness, the overall stiffness of the two-body coupling of the entire system will inevitably decrease. After receiving this reconstructed stiffness input parameter, the multi-task prediction model's internal tensor network will automatically adjust the attention weights on the currently acquired sensor signal. Under the expectation of lower system stiffness, the two-body coupling flutter evolution trend predicted by the multi-task prediction model will manifest as: a decrease in the critical stability boundary of flutter, and the system being more prone to vibration divergence. Based on this updated prediction result, the subsequent instruction generation module will be more inclined to issue feed rate derating instructions earlier or increase the gain amplitude of the high-frequency micro-displacement compensation vector, thereby maintaining cutting stability under more severe physical conditions.

[0074] In general, most existing intelligent milling solutions for industrial robots assume that the parameters of the cutting system remain constant during the machining process, or rely solely on external, high-precision, and expensive sensors for shutdown detection. This not only increases the complexity and hardware cost of the system, but also greatly limits the robot's ability to perform continuous machining operations in complex and harsh environments.

[0075] The overall technical solution of this invention, through Embodiment 1, establishes a basic framework for microsecond-level closed-loop dynamic compensation based on signal decoupling, unified graph, and multi-task prediction, solving the problem of suppressing short-cycle transient low-stiffness chatter. Furthermore, through the electrical / mechanical feature extraction, hidden Markov modeling, and nonlinear stiffness attenuation mapping mechanism introduced in Embodiment 2, it cleverly reuses existing basic sensor signals in the system, successfully establishing an algorithmic model characterizing the physical evolution of long-cycle tool wear. This solution does not rely on external optical or acoustic emission sensors that are susceptible to interference from the cutting environment; instead, it directly quantifies abstract tool wear parameters into stiffness attenuation coefficients that the control system can understand, achieving dynamic self-calibration and self-evolution of the underlying basic data of the graph.

[0076] In summary, this technical solution can consistently provide the controller with high-fidelity physical stiffness mapping throughout the entire lifespan of the tool, from brand new to near its lifespan limit. This effectively eliminates chatter prediction false alarms or compensation over-adjustments caused by wear, objectively extending the effective service life of a single tool. Simultaneously, it maintains good and consistent surface morphology quality in the machining of low-stiffness, thin-walled parts, demonstrating significant application value in promoting the evolution of industrial robots towards truly autonomous, flexible, and highly adaptive intelligent manufacturing equipment.

[0077] Example 3: In actual construction operations in the aerospace field, the target materials for machining typically include materials such as titanium alloys or nickel-based superalloys. These materials exhibit high strength at room temperature but extremely low thermal conductivity. When a robot-driven spindle performs high-speed cutting, a large amount of mechanical dissipation energy is generated in the shear slip zone and the friction zone of the rake face. Due to the inherent thermal conductivity limitations of the materials, this dissipated energy cannot be quickly carried away by the metal chips, thus accumulating in large quantities within the thin-walled workpiece material being cut within a very short time. This heat accumulation inevitably leads to transient physical softening of the workpiece material, i.e., a sharp, nonlinear decrease in the material's elastic modulus as temperature increases.

[0078] In previous technical solutions, stiffness maps built offline were usually based on isothermal physics assumptions, which would lead to severe spatiotemporal distortion of the physical model in the real-world scenario of thermo-coupling mentioned above.

[0079] To address this bottleneck restricting machining accuracy, this embodiment proposes the following: before decoupling the two-body vibration by combining the unified stiffness map of the two-body coupling, it also includes a feedforward correction mechanism for the dynamic stiffness field of the workpiece based on the thermo-coupling effect. The specific implementation steps of this mechanism are detailed below: Specifically, the first implementation step of this mechanism involves non-invasive acquisition of heat source data and assessment of heat generation. The system synchronously extracts the real-time current of the spindle motor and the real-time speed of the spindle from the multi-source sensor signals, and calculates the transient cutting heat generation rate of the current machining step using the following formula: ;in, For transient cutting heat generation rate, The heat conversion coefficient for cutting work. Real-time current of the spindle motor The real-time speed of the main spindle. This is the torque constant of the main spindle motor.

[0080] In real industrial environments, to obtain temperature information in the cutting zone, traditional methods tend to install infrared thermal imagers outside the machining area or embed thermocouple sensors inside the workpiece. However, during intelligent milling of curved surfaces, a large amount of high-pressure coolant must be continuously sprayed to prevent tool burns. The high-pressure coolant and splashing chips can cause severe optical path obstruction and physical interference, making it difficult for external optical temperature sensing devices to perform effective measurements; embedding sensors, on the other hand, would disrupt the original structural continuity of the workpiece.

[0081] The sensorless evaluation technique used in this step directly reads electrical control parameters at high frequency from the underlying bus of the robot control system. The product of the spindle motor's real-time current and its torque constant represents the actual electromagnetic torque output by the spindle to overcome cutting resistance. The product of this torque and the spindle's real-time speed represents the total mechanical power injected into the cutting zone at the current moment. Since metal cutting is essentially a process of intense plastic deformation and friction of the material, a very high proportion of the input total mechanical power is converted into heat energy. The cutting work-to-heat conversion coefficient is used to characterize this physical conversion ratio and the proportion of heat transferred into the workpiece.

[0082] Through the above calculation formula, the system can continuously output the transient cutting heat generation rate, which characterizes the heat source intensity, at a sub-millisecond response frequency without adding any external physical hardware, providing solid and highly anti-interference underlying data support for subsequent heat transfer deduction.

[0083] Optionally, after acquiring the heat source intensity data, the second implementation step of this mechanism involves deduce the dynamic conduction and diffusion process of heat in the spatial structure. The system substitutes the transient cutting heat generation rate and the tool spatial movement vector into a preset differential equation for the heat transfer of the moving heat source to solve and generate the spatial temperature gradient distribution at the current machining point.

[0084] Because the cutting tool is in a continuous 3D spatial motion state during surface milling, the cutting heat is not concentrated at a single static point, but rather forms a moving heat source that changes over time. The tool's spatial movement vector includes the instantaneous feed rate amplitude and spatial direction of the tool in the current machining step. In actual numerical calculation units, the pre-defined heat transfer differential equation for the moving heat source is usually constructed based on Fourier's law of thermal conductivity. When the system uses the transient cutting heat generation rate as the heat flux boundary condition and the tool's spatial movement vector as the kinematic boundary condition into this differential equation, the solution algorithm can deduce the heat dissipation behavior on the workpiece surface and inside.

[0085] For example, at high tool feed rates, the spatial temperature gradient distribution exhibits a comet-like tailing phenomenon, with heat mainly concentrated in the thin layer of the machined surface behind the tool. Conversely, at lower feed rates or when the tool lingers at a corner, heat is conducted hemispherically to deeper regions of the workpiece. The resulting spatial temperature gradient distribution is composed of a 3D temperature scalar field matrix containing the current machining point and its neighboring spatial grid nodes. This matrix objectively and quantitatively reflects the penetration depth and breadth of the thermal physical effects on the workpiece structure.

[0086] Specifically, the third implementation step of this mechanism involves converting temperature field data into a physical bridge of solid mechanical parameters. Based on the spatial temperature gradient distribution and the temperature-stress constitutive relationship of the target workpiece material, the system extracts the absolute temperature peak and calculates the elastic modulus and thermal softening proportional constant.

[0087] In actual material mechanics responses, after a local area of ​​a workpiece is subjected to the aforementioned conducted heat, the molecular thermal motion of its internal crystal structure intensifies, and its ability to resist deformation due to interatomic bonding forces decreases, macroscopically manifested as a decrease in the material's elastic modulus. Since the local stiffness of a workpiece is mainly determined by the geometric characteristics of that region's structure and the material's elastic modulus, extracting the absolute temperature peak in the spatial temperature gradient distribution can pinpoint the critical weak point where the workpiece material experiences the most severe thermal softening. To accurately quantify this thermal softening effect mathematically, the system uses the following formula to calculate the elastic modulus thermal softening proportionality constant: ;in, is the thermal softening ratio constant of the elastic modulus, used to characterize the stiffness ratio factor retained by a material in its current thermal state compared to its room temperature state; The absolute temperature peak value is extracted by traversing the above spatial temperature gradient distribution matrix; The preset ambient temperature within the system; Melting point temperature of the target workpiece material; The thermal softening index is a material index determined by tensile tests on the target workpiece material under different temperature gradients. It is used to describe the nonlinear softening sensitivity of the material as the temperature increases.

[0088] Through rigorous physical mapping of the above calculation formulas, the system transforms abstract thermodynamic temperature field peak data into dimensionless penalty coefficients that can be directly applied to the dynamic stiffness model. The range of the elastic modulus thermal softening proportionality constant is strictly controlled between 0 and 1. When the absolute temperature peak approaches the ambient reference room temperature, the proportionality constant approaches 1, indicating that the material has not softened. When the absolute temperature peak rises sharply, the proportionality constant decreases nonlinearly with the material's thermal softening exponent, objectively characterizing the transient physical compromise characteristics of difficult-to-machine materials under high cutting temperatures.

[0089] The fourth implementation step of this mechanism involves achieving the underlying correction and feedback connection of stiffness field data. The system uses the elastic modulus thermal softening ratio constant as the stiffness mapping weight, performs nonlinear derating reconstruction on the initial workpiece local stiffness matrix in the dual-body coupled unified stiffness map, and generates a thermo-coupled corrected workpiece stiffness matrix, which is then input into the dual-body vibration decoupling stage.

[0090] Before the introduction of this feedforward correction mechanism, the initial local stiffness matrix of the workpiece entering the two-body vibration decoupling stage was calculated based on the room-temperature elastic constants of the material in the embodiment. When encountering strong thermo-mechanical coupling, the actual physical stiffness of the workpiece is much lower than the value recorded in the matrix. Here, the system performs a nonlinear derating reconstruction by deeply embedding the thermal softening proportional constant of the elastic modulus into the matrix through tensor scalar multiplication or by performing a Hadamard product operation based on the sensitivity matrix of the stiffness matrix to the temperature gradient in each direction. This operation reduces the main diagonal and off-diagonal elements of the matrix according to the degree of thermal softening without changing the original dimensional structure of the matrix.

[0091] The resulting thermo-coupled corrected workpiece stiffness matrix is ​​directly input and replaces the static matrix reference originally called by the two-body vibration decoupling algorithm. This step plays a crucial role in practical applications. The core logic of the two-body vibration decoupling algorithm lies in allocating the total displacement offset and force fluctuation measured by the sensors based on the stiffness and impedance capabilities of the robot and the workpiece. Without thermo-correction, when the decoupling algorithm detects a large machining deflection offset, it will mistakenly assume the workpiece still possesses high stiffness, thus misinterpreting a large amount of offset error as vibration deformation of the robot's joints. However, after inputting the thermo-coupled corrected workpiece stiffness matrix, the decoupling algorithm can "sense" that the local workpiece structure has become more flexible due to heat, thus arriving at a conclusion more consistent with physical reality: under the same cutting force, most of the current deflection offset and vibration components are caused by the thermally softened workpiece material.

[0092] Based on the detailed technical solutions described in this embodiment, this method addresses the cross-physical field interference challenge faced by industrial robots in high-speed surface milling by establishing a logically rigorous adaptive processing link. The overall solution extracts the underlying electrical power signal, reconstructs the transient temperature field distribution along the tool's trajectory, and successfully analyzes the stiffness attenuation characteristics caused by heat accumulation during cutting based on the material's own mechanical constitutive relations. This series of physical variable mapping mechanisms enables the entire control system to possess thermo-mechanical coupling feedforward sensing capabilities.

[0093] Ultimately, by reconstructing the stiffness map through derating, this scheme effectively prevented decoupling misjudgments caused by the isothermal assumption of the physical model, providing a data foundation with extremely high physical fidelity for subsequent multi-task prediction models and anti-phase high-frequency micro-displacement compensation. This not only avoids the control system issuing over-adjustment compensation commands based on incorrect stiffness benchmarks, but also effectively prevents the danger of artificial vibration caused by erroneous compensation, ensuring that industrial robots maintain excellent vibration control accuracy and surface machining quality even under extreme cutting thermodynamic conditions when machining aerospace-grade thin-walled easily deformable materials.

[0094] Example 4: This embodiment provides an intelligent milling system for curved surfaces of industrial robots that compensates for low-stiffness vibrations.

[0095] In industrial robot milling operations, the robot's serial joint structure inherently results in low stiffness. Similarly, thin-walled curved workpieces, common in aerospace and large mold industries, exhibit low stiffness in their local structures during material removal. During actual machining, dynamic cutting forces simultaneously induce complex coupled vibrations between the robot and the workpiece. Existing industrial control systems typically treat the robot and workpiece as static, independent objects, relying on a single feedback mechanism. This fails to effectively separate the vibration components of the robot and the elastic vibration components of the workpiece from the mixed sensor signals. This technological limitation prevents the system from predicting the coupled chattering trend caused by their interaction, making it difficult to allocate corresponding compensation weights based on the respective vibration contributions of the robot and workpiece. Consequently, deviations in pose and displacement compensation during milling lead to decreased surface machining quality and surface chatter marks.

[0096] like Figure 2 As shown, to address the technical challenges encountered in practical applications and achieve precise vibration decoupling and dynamic composite control, this embodiment constructs an intelligent milling system deeply integrated with specific industrial hardware and the underlying control system. This intelligent milling system for industrial robots that compensates for low-stiffness vibrations includes: a graph construction and pre-training module, a signal acquisition and vibration decoupling module, a chatter evolution trend prediction module, an instruction generation module, and a cutting control and graph update module.

[0097] The system in this embodiment specifically includes the following: Specifically, the stiffness map construction and pre-training module is used to offline construct a unified stiffness map of a two-body coupled system, including the robot's stiffness field and the workpiece's dynamic stiffness field, and to pre-train a multi-task prediction model. In industrial deployments, this module typically runs on an industrial-grade edge computing server equipped with a high-performance graphics processing unit (GPU). During the offline construction phase, the system interacts with external large-scale measurement equipment (such as a laser tracker) to guide the industrial robot through representative posture points within its workspace, apply calibration forces, and measure minute deformations. This digitizes the nonlinear flexibility space of the robot, composed of multiple connected rotary joints, and establishes the robot's stiffness field.

[0098] Simultaneously, this module imports the workpiece's 3D geometric model generated by a computer-aided design (CAD) system. Utilizing its internal finite element analysis engine, it simulates the material removal process under different machining steps, calculating and storing the workpiece's dynamic stiffness field, which changes dynamically with the machining process. Subsequently, the module performs matrix inverse operations and coupling equivalence on these two data sets, generating a unified stiffness map of two-body coupling covering global machining characteristics. This map is quantized, compressed, and stored in high-frequency dynamic random access memory (DRAM). Furthermore, this module uses historical milling experiment datasets to train the neural network weights of a multi-task prediction model, providing prior knowledge for online prediction.

[0099] Specifically, the signal acquisition and vibration decoupling module is used to acquire multi-source sensor signals online and, combined with the aforementioned unified stiffness map of the two-body coupling, decouple the two-body vibrations, separating the vibration components of the robot body and the elastic vibration components of the workpiece. In actual physical equipment, signal acquisition relies on a network of multiple physical sensors installed at the robot's end effector. Typically, a high-frequency, wide-range 6-dimensional force sensor is integrated between the robot's 6th-axis flange and the high-speed electric spindle; a 3-axis piezoelectric accelerometer is rigidly attached to the metal surface of the electric spindle's housing; simultaneously, it communicates with the spindle servo driver via an industrial Ethernet bus (such as EtherCAT) to read the spindle motor current signal at a sampling rate higher than 10kHz. These three components together constitute the real-time input multi-source sensor signal.

[0100] This module runs in a real-time operating system (RTOS). First, based on a robot dynamics parameter identification algorithm, it extracts the inertial forces caused by robot acceleration and deceleration, as well as the damping forces caused by joint friction, from the 6-dimensional force signal to obtain the pure actual cutting force. Then, the module queries the unified stiffness map of the two-body coupling in the memory of the industrial edge computing server in real time to obtain the local stiffness of the workpiece corresponding to the current tool position, and uses the measured actual cutting force to perform inverse dynamics inversion. Through this physical model-driven calculation process, the system successfully and precisely decouples the macroscopic, mixed mechanical vibration physical quantities into two independent data streams belonging to the robot body vibration component and the workpiece elastic vibration component.

[0101] Specifically, the chatter evolution trend prediction module is used to fuse the separated robot body vibration components and the workpiece elastic vibration components into the multi-task prediction model to predict the evolution trend of the two-body coupled chatter, including the total peak amplitude and phase of the total vibration. To meet the stringent requirements of CNC machining for extremely low latency, the core algorithm of this module is typically deployed in hardware on a Field Programmable Gate Array (FPGA) accelerator card. After decoupling, the two vibration components undergo timing alignment and tensor concatenation, and are then directly fed into the multi-task prediction model deployed within the FPGA as a feature matrix. The multi-task prediction model utilizes a self-attention mechanism to analyze the correlation between data features within the current microsecond-level time window and historical timing features, and outputs prediction results for the state in the next few control cycles in parallel.

[0102] In particular, through a fitting algorithm, this module can accurately extrapolate the upcoming total vibration peak amplitude and the phase of the total vibration peak after the superposition of the two vibration waveforms. This allows the system to grasp the evolution trend of the system before flutter damages the surface quality of the workpiece, transforming it from traditional passive hysteresis feedback to active feedforward sensing.

[0103] Specifically, the instruction generation module is used to dynamically evaluate the contribution of the two-body coupling flutter based on the evolution trend of the two-body coupling flutter, and allocate corresponding compensation weights to generate a composite control instruction that includes at least low-frequency pose correction, high-frequency micro-displacement compensation vector, and cutting parameter adjustment instructions. This module mainly relies on the central processing unit (CPU) of the industrial controller to perform logical operations. The system calculates the energy ratio occupied by the robot side and the workpiece side, i.e., the contribution of the two-body vibration, based on the total peak vibration amplitude returned by the prediction module. According to this contribution, the system dynamically allocates weights. For example, if the evaluation result shows that the current vibration energy is mainly caused by the local stiffness weakness of the workpiece, the system assigns a higher weight to the cutting parameter adjustment (such as changing the spindle speed to avoid the resonance zone); if it is caused by the weakness of the robot posture, a higher weight is assigned to micro-displacement compensation.

[0104] After comprehensive evaluation, this module outputs composite control commands. Among them, the low-frequency pose correction is mainly used to offset the macroscopic static tool deflection deformation caused by cutting force (usually between 0 and 5 Hz), which belongs to the spatial 6-DOF compensation including position and angle; the high-frequency micro-displacement compensation vector is an anti-phase translational command generated based on the phase of the total vibration peak, used to offset high-frequency dynamic chatter (usually above 50 Hz) in three-dimensional space through the wave interference cancellation principle; the cutting parameter adjustment command is used to change the cutting state from the energy input source.

[0105] Specifically, the cutting control and graph update module is used to inject the composite control commands into the robot servo system to execute cutting control, and to dynamically update the dual-body coupled unified stiffness graph by identifying the actual stiffness value online based on real-time cutting feedback. In the actual control link execution, to ensure that the high-frequency micro-displacement compensation vector can be executed with high fidelity and low latency, this module enables a dedicated feedforward mapping channel in the robot's underlying servo driver firmware. Conventional low-frequency pose corrections are input to the position control loop of each joint through the standard robot controller trajectory planner; while the high-frequency micro-displacement compensation vector is converted into a dynamic velocity feedforward command, directly bypassing the position loop and injected into the speed control loop input of each joint servo motor via a high-speed bus. The two are algebraically superimposed at the speed loop point to drive the motor output torque.

[0106] Meanwhile, the module continuously performs posterior error analysis on the model using actual force and displacement offset data collected during online stable cutting. When it detects that the local physical stiffness deviates from the initial value due to tool wear or material thermal softening during the actual machining process, the module silently updates the corresponding node parameters in the two-body coupled unified stiffness map in the background using algorithms such as gradient descent, ensuring that the physical reference of the entire control system has the dynamic evolution capability of adaptive correction as the machining process progresses.

[0107] In summary, the system disclosed in this embodiment tightly integrates offline spectrum construction with online multi-source signal decoupling, achieving precise intervention at the physical level in the coupled vibration mechanism of low-stiffness robots and thin-walled workpieces. Through front-end feature separation, mid-end chatter trend prediction, and back-end dual-loop frequency band split-cutting control, the system enables the robot servo mechanism to output matching compensation commands based on the real-time dual-body coupling state. This not only effectively reduces the coupled vibration error caused by the interaction between the robot and the workpiece, significantly improving the surface morphology and dimensional accuracy of complex curved surfaces, but also endows the equipment system with the ability to self-evolve and update, demonstrating significant industrial application value in the high-end manufacturing field.

[0108] Example 5: Corresponding to the above embodiments, the present invention also proposes an electronic device.

[0109] like Figure 3 The diagram shows a structural schematic of an electronic device according to the present invention. The electronic device 100 includes a processor 101 and a memory 103. The processor 101 and the memory 103 are connected, for example, via a bus 102. Optionally, the electronic device 100 may further include a transceiver 104. It should be noted that in practical applications, the transceiver 104 is not limited to one unit, and the structure of this electronic device 100 does not constitute a limitation on the embodiments of the present invention.

[0110] Processor 101 may be a CPU, a general-purpose processor, a DSP, an ASIC, an FPGA, or other programmable logic device, transistor logic device, hardware component, or any combination thereof. It may implement or execute the various exemplary logic blocks, modules, and circuits described in connection with this disclosure. Processor 101 may also be a combination that implements computational functions, such as including one or more microprocessor combinations, a combination of a DSP and a microprocessor, etc.

[0111] Bus 102 may include a pathway for transmitting information between the aforementioned components. Bus 102 may be a PCI bus or an EISA bus, etc. Bus 102 may be divided into an address bus, a data bus, a control bus, etc. For ease of representation, Figure 3 The bus is represented by a single thick line, but this does not mean that there is only one bus or one type of bus.

[0112] The memory 103 stores a computer program corresponding to the intelligent milling method for curved surfaces of an industrial robot that compensates for low-stiffness vibration according to the above embodiments of the present invention. This computer program is executed under the control of the processor 101. The processor 101 executes the computer program stored in the memory 103 to implement the content shown in the aforementioned method embodiments.

[0113] Among them, electronic devices 100 include, but are not limited to: mobile terminals such as laptops and PADs (tablet computers) and fixed terminals such as desktop computers. Figure 3 The electronic device 100 shown is merely an example and should not be construed as limiting the functionality and scope of the embodiments of the present invention.

[0114] Although embodiments of the present invention have been shown and described above, it is understood that the above embodiments are exemplary and should not be construed as limiting the present invention. Those skilled in the art can make changes, modifications, substitutions and variations to the above embodiments within the scope of the present invention.

Claims

1. A method for intelligent milling of curved surfaces using an industrial robot to compensate for low-stiffness vibrations, characterized in that, include: Offline construction of a two-body coupled unified stiffness map containing the robot stiffness field and the workpiece dynamic stiffness field, and pre-training of a multi-task prediction model; Multi-source sensor signals are acquired online, and the two-body vibration is decoupled by combining the dual-body coupled unified stiffness map to separate the robot body vibration component and the workpiece elastic vibration component. The separated robot body vibration component and the workpiece elastic vibration component are fused and input into the multi-task prediction model to predict the evolution trend of dual-body coupled chatter, including the total vibration peak amplitude and the total vibration peak phase. Based on the dual-body coupled chatter evolution trend, the contribution of dual-body vibration is dynamically evaluated, and corresponding compensation weights are assigned to generate a composite control command that includes at least low-frequency pose correction, high-frequency micro-displacement compensation vector, and cutting parameter adjustment instructions. The composite control command is injected into the robot servo system to execute cutting control, and the actual stiffness value is identified online based on real-time cutting feedback to dynamically update the dual-body coupled unified stiffness map.

2. The method according to claim 1, characterized in that, The offline construction of a two-body coupled unified stiffness map, comprising the robot stiffness field and the workpiece dynamic stiffness field, includes: sampling attitude points within the robot's workspace and measuring the end-effector static stiffness and contact stiffness characteristics under the corresponding attitudes to construct the robot stiffness field; simulating the workpiece material removal process using the element birth and death technique, discretizing and calculating the workpiece's local stiffness matrix and natural frequency under each processing step to construct the workpiece dynamic stiffness field; deriving the two-body coupled stiffness matrix based on the robot end-effector stiffness matrix, the workpiece local stiffness matrix, and the contact stiffness matrix, and quantizing and compressing the two-body coupled stiffness matrix to construct the two-body coupled unified stiffness map.

3. The method according to claim 1, characterized in that, The online acquisition of multi-source sensor signals, combined with the unified stiffness map of the dual-body coupling, for dual-body vibration decoupling includes: simultaneously acquiring 6-dimensional force sensor signals, 3-axis accelerometer signals, and spindle motor current signals as the multi-source sensor signals; establishing a robot body dynamics model; separating the inertial and elastic force responses of the robot body from the 6-dimensional force sensor signals to decouple the actual cutting force; the calculation formula for the actual cutting force is: ;in, This is the actual cutting force. These are measurements taken by a 6D force sensor. The equivalent mass matrix of the robot's end effector. The robot's end effector acceleration was measured by a 3-axis accelerometer. Here is the equivalent damping matrix of the robot's end effector. For the robot's end effector speed, Here is the stiffness matrix of the robot's end effector. The displacement of the robot's end effector is given; based on the workpiece's local stiffness matrix in the dual-body coupled unified stiffness map, the elastic vibration component of the workpiece is calculated by inversion from the actual cutting force.

4. The method according to claim 1, characterized in that, The multi-task prediction model is a temporal prediction network containing a self-attention mechanism encoder and decoder. The prediction steps include: preprocessing and extracting the temporal features of the multi-source sensor signals, and performing feature fusion and splicing with the inversion features of the workpiece elastic vibration components to form a feature input matrix; inputting the feature input matrix into the multi-task prediction model, and outputting in parallel the robot vibration prediction value, the workpiece vibration prediction value, and the risk level characterizing the two-body vibration coupling coefficient within a set sampling period; extracting the instantaneous phase and instantaneous amplitude of the robot vibration prediction value and the workpiece vibration prediction value, and using a polynomial fitting algorithm to extrapolate the total vibration peak phase and the total vibration peak amplitude.

5. The method according to claim 1, characterized in that, The dynamic evaluation of the dual-body vibration contribution based on the dual-body coupling flutter evolution trend and the allocation of corresponding compensation weights include: constructing a total vibration amplitude benchmark by aggregating the robot vibration amplitude and the workpiece vibration amplitude; calculating the proportion of the robot vibration amplitude and the workpiece vibration amplitude in the total vibration amplitude benchmark, respectively, to generate the robot vibration contribution and the workpiece vibration contribution; presetting a first contribution threshold and a second contribution threshold, wherein the first contribution threshold is greater than the second contribution threshold; when the robot vibration contribution is greater than the first contribution threshold, allocating the main weight to the robot body displacement compensation channel; when the robot vibration contribution is less than or equal to the first contribution threshold but greater than the second contribution threshold, evenly allocating weights to the robot body displacement compensation channel and the spindle cutting parameter adjustment channel; when the robot vibration contribution is less than or equal to the second contribution threshold, allocating the main weight to the spindle cutting parameter adjustment channel.

6. The method according to claim 1, characterized in that, The generation of the composite control command, which includes at least a low-frequency pose correction amount, a high-frequency micro-displacement compensation vector, and a cutting parameter adjustment command, is specifically implemented through a frequency-band separated dual-loop composite control architecture. This includes: calculating the low-frequency pose correction amount, primarily to suppress static deformation, through a low-frequency constant force compensation loop, using the following formula: in, This is the low-frequency pose correction amount. This is the amount of compensation for robot stiffness deformation. The elastic deformation compensation amount of the workpiece; the high-frequency micro-displacement compensation vector with opposite phase, mainly suppressing dynamic chatter, is calculated through a high-frequency feedforward compensation loop, and the formula is: in, This is a high-frequency micro-displacement compensation vector. This represents the total peak amplitude of the vibration. The flutter angular frequency, The current system time. The phase of the total vibration peak. It is the anti-phase offset constant. This represents the equivalent stiffness value along the principal axis of the minimum stiffness of the two-body coupled system.

7. The method according to claim 6, characterized in that, The logic for issuing the composite control command is triggered based on the following hierarchical collaborative vibration suppression strategy: a first amplitude threshold and a second amplitude threshold are preset, and the first amplitude threshold is less than the second amplitude threshold; when the total vibration peak amplitude is less than the first amplitude threshold, only the high-frequency micro-displacement compensation vector is output to control the robot end effector to perform anti-phase compensation; when the total vibration peak amplitude is greater than or equal to the first amplitude threshold and less than the second amplitude threshold, the high-frequency micro-displacement compensation vector and the spindle speed adjustment command in the cutting parameter adjustment command are issued in parallel; when the total vibration peak amplitude is greater than or equal to the second amplitude threshold, the feed rate derating command in the cutting parameter adjustment command is forcibly output, and when the dual-body vibration coupling coefficient is greater than a preset coupling safety threshold, a protection command to stop cutting feed and lift the tool is output.

8. The method according to claim 1, characterized in that, The step of injecting the composite control command into the robot servo system to execute cutting control includes: establishing a direct mapping interface at the control hardware layer to convert the high-frequency micro-displacement compensation vector into a dynamic velocity reference; directly bypassing the position control loop of the robot controller and injecting the dynamic velocity reference as a feedforward quantity into the velocity loop input of the servo driver; after the low-frequency pose correction quantity is parsed by the position control loop to generate a conventional velocity command, it is algebraically superimposed with the dynamic velocity reference injected into the velocity loop input.

9. The method according to claim 1, characterized in that, The method of dynamically updating the dual-body coupled unified stiffness map by identifying the actual stiffness value online based on real-time cutting feedback includes: under stable cutting conditions, periodically collecting actual end displacement offset and end force data to identify the actual robot static stiffness; when the identification error exceeds a preset stiffness error threshold, using a weighted average function to update the corresponding spatial node parameters in the map; simultaneously collecting real cutting force fluctuation characteristics and workpiece vibration inversion displacement to identify the actual local stiffness value; and iteratively updating the neural network weight parameters characterizing the workpiece dynamic stiffness field through a gradient descent algorithm.

10. The method according to claim 1, characterized in that, The method also includes a system-wide safety protection mechanism with parallel monitoring: independently setting force protection thresholds and amplitude deceleration protection thresholds for anomaly monitoring; continuously calculating the rate of change of the derivative of the dual-body vibration coupling coefficient; when it is determined that the dual-body vibration coupling coefficient is in the divergence range and the growth rate of the total vibration peak amplitude exceeds the preset surge threshold, the system immediately interrupts the regular machining command and executes the highest priority emergency protection command to stop cutting and lift the tool.

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