A real-time compensation method for machining errors of a numerical control machine tool

Abstract

The application discloses a real-time compensation method for machining errors of a numerical control machine tool, and comprises the following steps: performing transient physical field tomographic reconstruction based on acoustic ballistic effect, extracting an ultrasonic time-of-flight sequence matrix to output a three-dimensional physical field tensor containing temperature and stress information; performing manifold space topology dimension reduction on the three-dimensional physical field tensor to output a principal component manifold feature vector; constructing a fractional order non-autonomous dynamic error evolution model according to the principal component manifold feature vector and solving the model to separate a low-frequency deviation component vector and a high-frequency deviation component vector and synchronously extract a dynamic fractional order degree parameter; calculating excitation current control instructions according to the high-frequency deviation component vector and the dynamic fractional order degree parameter; and performing macro low-frequency displacement feeding compensation, micro high-frequency displacement reverse offset and physical rheological damping self-adaptive tuning in parallel according to the low-frequency deviation component vector, the high-frequency deviation component vector and the excitation current control instructions, and performing acoustic magnetic closed loop cooperative action.

Description

Technical Field

[0001] This invention relates to the field of CNC machine tool error control technology, specifically a real-time compensation method for CNC machine tool machining errors. Background Technology

[0002] CNC machine tools are the fundamental machining equipment in modern precision manufacturing industries. The spatial positioning accuracy of the tool tip during operation directly determines the final manufacturing quality of the parts. In long-cycle continuous cutting operations, the machine tool spindle and internal mechanical structure are subjected to the combined effects of spindle motor heat generation, bearing friction heat generation, and alternating cutting resistance. This complex thermo-mechanical coupled load causes spatial displacement drift and transient oscillations in the machine tool structure, altering the ideal cutting trajectory between the tool tip and the workpiece, thereby introducing machining errors.

[0003] To mitigate accuracy degradation caused by physical deformation, existing technologies generally employ an error compensation mechanism that combines condition monitoring with servo feedback. In industrial settings, temperature sensors and mechanical sensors are typically placed at key structural points on the spindle and bed to collect physical state data during machine operation. This data is then input into a pre-defined error fitting model to calculate the estimated deviation of the tool tip position. After obtaining the estimated deviation, the CNC system generates a corresponding reverse displacement offset command, which in turn calls the feed servo motors of each axis to drive the lead screws and perform compensation actions, thus offsetting the positional deviation caused by the machine tool's thermodynamic deformation in physical space.

[0004] Existing real-time error compensation systems typically divide the monitoring area into a massive number of discrete spatial voxel nodes when analyzing the temperature and stress physical field state inside the machine tool spindle. The generated global three-dimensional physical field contains extremely large high-dimensional tensor data. Directly inputting this high-dimensional node data without effective feature extraction and dimensionality reduction into the back-end error prediction model for iterative calculation will cause extremely high computational redundancy and system resource consumption. This will cause the controller's mathematical solution time to far exceed the communication cycle of the underlying CNC system, resulting in significant time delays in the issuance of compensation commands. This cannot meet the low-latency input requirements for real-time closed-loop control of transient force-induced deformation in CNC machining processes. Summary of the Invention

[0005] To address the shortcomings of existing technologies, this invention provides a real-time compensation method for machining errors in CNC machine tools. This method solves the technical problem in existing real-time error compensation technologies for CNC machine tools where the high-dimensional tensor data required for analyzing the internal physical field state of the spindle causes significant computational redundancy, resulting in dynamic calculation time exceeding the communication cycle of the underlying CNC system. Consequently, the compensation execution command experiences significant time delay, making it impossible to implement low-delay closed-loop control and precise cross-scale cancellation for high-frequency cutting chatter and transient force-induced deformation.

[0006] To achieve the above objectives, the present invention provides the following technical solution: a real-time compensation method for machining errors in CNC machine tools, comprising the following steps:

[0007] Step S1: Perform transient physical field tomography reconstruction based on acoustic effect, extract the flight time sequence matrix of ultrasonic waves propagating in the spindle rotor and tool holder, and output a three-dimensional physical field tensor containing spatial distribution of temperature and stress information.

[0008] Step S2: Perform manifold space topological dimensionality reduction and state feature extraction on the three-dimensional physical field tensor output in step S1, and output the principal component manifold feature vector.

[0009] Step S3: Based on the principal component manifold eigenvectors output in step S2, perform fractional-order non-autonomous dynamic error evolution and prediction, construct a fractional-order non-autonomous dynamic error evolution model and solve it by discretization, output the three-dimensional spatial position deviation vector sequence of the cutting tip in the continuous time domain, and perform frequency domain decoupling filtering on the three-dimensional spatial position deviation vector sequence of the cutting tip to separate the low-frequency deviation component vector and the high-frequency deviation component vector, and simultaneously extract the dynamic fractional-order parameters;

[0010] Step S4: Obtain the high-frequency deviation component vector separated in step S3 and the extracted dynamic fractional order parameters to perform the ontological mapping of algorithm features and physical constitutive model, calculate the target magnetic induction intensity applied to the magnetorheological fluid, and solve the excitation current control command based on the target magnetic induction intensity.

[0011] Step S5: Based on the low-frequency deviation component vector and high-frequency deviation component vector separated in step S3, and the excitation current control command calculated in step S4, execute in parallel the macroscopic low-frequency displacement feed compensation action, the microscopic high-frequency displacement reverse cancellation action, and the physical rheological damping adaptive tuning and acoustic-magnetic closed-loop coordinated action.

[0012] Preferably, the transient physical field tomography reconstruction based on the acoustic effect described in step S1 specifically includes:

[0013] An ultrasonic beam with a preset deflection angle is emitted into the spindle rotor and the medium inside the tool holder, and the flight time sequence matrix of the ultrasonic beam from the transmitting array element to the receiving array element is extracted.

[0014] Establish an acoustic-elastic-thermo-acoustic coupling physical model of the spindle rotor and the internal medium of the tool holder, as well as an integral model of the ultrasonic beam propagation path.

[0015] The monitoring area inside the spindle rotor and tool holder is discretized into multiple spatial voxels. The flight time series matrix is ​​input into the algebraic reconstruction algorithm to reconstruct the three-dimensional temperature field tensor and the three-dimensional stress field tensor of the spatial voxel at each moment. The three-dimensional temperature field tensor and the three-dimensional stress field tensor are then spliced ​​together according to spatial nodes to output the three-dimensional physical field tensor.

[0016] Preferably, the manifold space topological dimensionality reduction and state feature extraction of the three-dimensional physical field tensor output in step S1, as described in step S2, specifically includes:

[0017] The discretized three-dimensional physical field tensor is flattened to construct a high-dimensional state vector;

[0018] Based on the local linear embedding algorithm, the Euclidean distance between each high-dimensional state vector is calculated, the local neighborhood structure of the high-dimensional state vector is searched in the partially ordered half-lattice topological space, and the reconstruction weight matrix of the high-dimensional state vector is calculated by linearly reconstructing it from the nearest neighbor nodes.

[0019] While keeping the reconstruction weight matrix unchanged, the high-dimensional state vector is projected into the tangent space of the low-dimensional manifold to solve for the optimal embedding coordinate vector, and the optimal embedding coordinate vector is output as the principal component manifold feature vector.

[0020] Preferably, during the fractional-order non-autonomous dynamic error evolution and prediction process in step S3:

[0021] The dynamic model is based on a time-dependent variable-order Caputo fractional derivative operator, and the fractional-order non-autonomous dynamic error evolution model is discretized and solved by a fractional-order prediction-correction numerical algorithm.

[0022] Read the pre-configured servo bandwidth limit parameters of the feed drive units of each axis of the machine tool, and set the servo bandwidth limit parameters to the cutoff frequency of the low-pass filter;

[0023] The three-dimensional spatial position deviation vector sequence of the blade tip is input into a low-pass filter with a set cutoff frequency to filter out high-frequency oscillation signals higher than the cutoff frequency and output low-frequency deviation component vector.

[0024] Subtract the low-frequency deviation component vector at the corresponding moment from the current three-dimensional spatial position deviation vector of the blade tip to separate the high-frequency deviation component vector.

[0025] Preferably, step S3 involves constructing a fractional-order non-autonomous dynamic error evolution model, specifically including:

[0026] The principal component manifold eigenvectors are extracted as external excitation inputs. The internal temperature and stress distribution of the machine tool are dynamically correlated with the tool tip spatial position deviation vector to construct a fractional-order non-autonomous dynamic error evolution model.

[0027] The dynamic equilibrium condition of the fractional-order non-autonomous dynamic error evolution model satisfies the following: the variable-order Caputo fractional derivative of the blade tip three-dimensional spatial position deviation vector with respect to time is equal to the sum of the product of the non-autonomous dynamic state matrix and the blade tip three-dimensional spatial position deviation vector, the nonlinear coupling excitation vector function excited by the principal component manifold eigenvector, and the product of the control input gain matrix and the control vector; the non-autonomous dynamic state matrix is ​​updated in time with the temperature gradient and stress distribution state inside the three-dimensional physical field tensor.

[0028] Preferably, the ontology mapping between the execution algorithm features and the physical constitutive model described in step S4 specifically includes:

[0029] The Bingham plasticity model is introduced to describe the physical rheological behavior of magnetorheological fluids. A reverse adjustment correspondence is established between the dynamic fractional order parameter representing the decay rate of mathematical history memory and the damping characteristics of magnetorheological fluids representing the physical energy dissipation rate.

[0030] The inverse trend of the dynamic fractional order parameter is transformed using the natural exponential function, where the exponent of the natural exponential function is a constant minus the difference between the dynamic fractional order parameter and the exponent. The target magnetic flux density applied to the magnetorheological fluid is calculated by multiplying the natural exponential function, the electromagnetic conversion proportional coefficient extracted from the offline calibration experiment, and the L2 norm of the high-frequency deviation component vector. When the dynamic fractional order parameter decreases and the L2 norm of the high-frequency deviation component vector increases, the target magnetic flux density increases exponentially.

[0031] A linear electromagnetic conversion model between the target magnetic flux density and the excitation current control command is established. The target magnetic flux density is divided by the electromagnetic induction conversion coefficient of the excitation coil to calculate the excitation current control command acting on the excitation coil.

[0032] Preferably, the macroscopic low-frequency displacement feed compensation action described in step S5 specifically includes:

[0033] The low-frequency deviation component vector separated in step S3 is subjected to coordinate inversion and negative operation to generate the macroscopic servo compensation command vector.

[0034] The macro servo compensation command vector is decomposed into three one-dimensional displacement offsets in the machine tool working coordinate system, and the three one-dimensional displacement offsets are written into the zero-point offset address corresponding to the workpiece coordinate system of the machine tool G code, so as to form the coordinate origin offset command.

[0035] The machine tool's native axis feed drive units generate corresponding macroscopic compensation displacements based on the coordinate origin offset command.

[0036] Preferably, the micro-high frequency displacement reverse cancellation action described in step S5 specifically includes:

[0037] The high-frequency deviation component vector separated in step S3 is subjected to a negative operation in coordinate space to generate a micro servo compensation command vector.

[0038] Multiply the micro servo compensation command vector with the electromechanical conversion calibration matrix to calculate the three-dimensional high-frequency drive current vector, and extract the three high-frequency current commands for each axis of the corresponding machine tool working coordinate system.

[0039] The three-channel high-frequency current commands are synchronously output to the three-dimensional magnetostrictive exciter inside the spherical electromagnetic vector micro-motion tool holder. The kinematic vector is synthesized through a spatial flexible hinge mechanism, and the spatial reverse displacement is output at the tool clamping end of the spindle rotor.

[0040] Preferably, the coordinated action of physical rheological damping adaptive tuning and acousto-magnetic closed loop described in step S5 specifically includes:

[0041] The excitation current control command calculated in step S4 is input to the excitation coil assembly arranged around the labyrinth-type dynamic sealing ring cavity to generate a controlled transient magnetic field, so that a chain bundle physical structure is formed inside the magnetorheological fluid, thereby increasing the apparent shear viscosity and dynamic yield stress of the magnetorheological fluid to dissipate cutting chatter energy.

[0042] By increasing the controlled transient magnetic field strength, the bulk elastic modulus of the magnetorheological fluid increases, causing the acoustic impedance parameter of the magnetorheological fluid to adaptively approach the inherent acoustic impedance value of the spindle rotor metal material, thereby reducing the acoustic wave reflection loss of the ultrasonic beam at the solid-liquid interface.

[0043] This invention provides a real-time compensation method for machining errors in CNC machine tools. It has the following beneficial effects:

[0044] 1. This invention utilizes ultrasonic flight time series to invert the three-dimensional temperature and stress field tensors, and combines a local linear embedding algorithm to project the high-dimensional physical field tensor onto the low-dimensional manifold tangent space. It extracts the principal component manifold feature vectors that retain the thermal deformation and force-induced deformation modes, thereby achieving topological dimensionality reduction of the transient physical field state of the machine tool spindle. While retaining the core physical features, it reduces the computational scale of node data, thus providing a low-dimensional state input that meets the real-time control cycle for the non-autonomous dynamic error evolution model.

[0045] 2. This invention constructs a dynamic error evolution model by introducing a time-dependent variable-order fractional derivative operator, which correlates the physical field state with the spatial position of the tool tip. By using a low-pass filter, the spatial position deviation vector sequence is decoupled into low-frequency deviation component vectors and high-frequency deviation component vectors, thus realizing the physical characterization of the viscoelastic relaxation properties and stress history memory effect of the machine tool metal structure. At the frequency domain level, steady-state thermal drift and transient cutting chatter displacement are separated, providing an independent compensation benchmark for the parallel action of macro and micro servo actuators.

[0046] 3. This invention converts low-frequency deviation component vectors into coordinate origin offset commands to drive the feed servo, and simultaneously uses high-frequency deviation component vectors to drive the three-dimensional magnetostrictive exciter to output spatial reverse displacement. Based on the excitation current control command, it adjusts the apparent shear viscosity and dynamic yield stress of the magnetorheological fluid, realizing the parallel execution of steady-state displacement compensation and transient oscillation cancellation. While dissipating cutting chatter energy, it uses the transient magnetic field to change the bulk elastic modulus so that the acoustic impedance of the medium adaptively approaches the acoustic impedance of the spindle, reducing the reflection loss of the front ultrasonic beam. Attached Figure Description

[0047] Figure 1 This is a flowchart of the overall method of the present invention. Detailed Implementation

[0048] The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0049] The overall execution flow of a real-time compensation method for machining errors in CNC machine tools includes the following steps:

[0050] S1, based on transient physical field tomography reconstruction of the acoustic elastic effect, controls the ultrasonic phased array transceiver array to transmit ultrasonic signals to the spindle rotor and tool holder and receive the echoes, extracts the flight time sequence matrix of the ultrasonic waves propagating in the spindle rotor and tool holder, and reconstructs the three-dimensional physical field tensor representing the current temperature gradient and residual stress inside the spindle and tool through the tomography reconstruction algorithm based on the acoustic elastic effect and thermo-acoustic coupling characteristics inside the solid.

[0051] S2, manifold space topology dimensionality reduction and state feature extraction, performs dimensionality reduction on the reconstructed three-dimensional physical field tensor, maps the three-dimensional physical field tensor to a partially ordered half-lattice topological space, and uses a nonlinear manifold mapping algorithm to extract the local linear embedding coordinates of the three-dimensional physical field tensor in the tangent space, outputting the principal component manifold feature vectors to characterize the thermal deformation and force-induced deformation modes of the machine tool.

[0052] S3, Fractional-order non-autonomous dynamic error evolution and prediction: Based on the principal component manifold eigenvectors output in step S2, a variable-order fractional-order non-autonomous dynamic error evolution model is established. Combining the viscoelastic relaxation physical properties of the machine tool metal structure under historical thermal loads and alternating stresses, the fractional-order non-autonomous dynamic error evolution model is solved and predicted. The tool tip three-dimensional spatial position deviation vector of the target period is calculated. The tool tip three-dimensional spatial position deviation vector is decoupled and filtered in the frequency domain to separate the low-frequency deviation component vector characterizing the steady-state thermal drift of the machine tool structure and the high-frequency deviation component vector characterizing the transient deformation caused by cutting force. The current fractional-order parameters in the solution process are extracted.

[0053] S4, the ontological mapping between algorithm features and physical constitutive model, establishes the corresponding mapping relationship between dynamic operator parameters and magnetorheological fluid shear constitutive model, calculates the target magnetic induction intensity applied to magnetorheological fluid based on the current fractional order parameter value and the norm of high frequency deviation component, and solves the corresponding excitation current control command based on the calculated target magnetic induction intensity.

[0054] S5, macro-micro collaborative control and active damping tuning, converts the separated low-frequency deviation component vector into a coordinate origin offset command, which is sent to the machine tool's native coordinate axis feed drive unit to perform steady-state displacement compensation. The high-frequency deviation component vector is inverted to generate a micro servo compensation command, which is sent to the spherical electromagnetic vector micro-motion tool holder inside the spindle to drive the three-dimensional magnetostrictive exciter to perform spatial reverse cancellation action. Simultaneously, the excitation current control command generated in step S4 is output to the excitation coil assembly of the labyrinth-type dynamic sealing ring cavity. By instantaneously changing the apparent viscosity and physical damping coefficient of the magnetorheological fluid in the labyrinth-type dynamic sealing ring cavity, cutting chatter energy is dynamically absorbed and dissipated.

[0055] The transient physical field tomography reconstruction step S1 based on the acoustic effect specifically includes the following sub-steps:

[0056] S101, Construct a three-dimensional spatial coordinate system and define the position vector of any point in the three-dimensional spatial coordinate system. Satisfy the following expression:

[0057]

[0058] In the formula, The position vector of any point in a three-dimensional coordinate system; The coordinate components of the position vector along the horizontal axis in the three-dimensional coordinate system; The coordinate components of the position vector along the vertical axis in the three-dimensional coordinate system; The coordinate components of the position vector along the vertical axis in the three-dimensional coordinate system; The transpose operation represents a vector, arranged in a ring at equal intervals around the spindle stator of a CNC machine tool. Each ultrasonic phased array transceiver element constitutes an ultrasonic phased array transceiver array. By controlling the excitation pulse delay of each ultrasonic phased array transceiver element, an ultrasonic beam with a preset deflection angle is formed. The ultrasonic phased array transceiver array is controlled to emit an ultrasonic beam with a preset deflection angle to the spindle rotor and the medium inside the tool holder according to the set pulse repetition frequency. The actual flight time of the ultrasonic beam from the transmitting element to the receiving element is recorded.

[0059] S102, Establish the acousto-elastic-thermo-acoustic coupling physical model of the spindle rotor and the internal medium of the tool holder. The local sound velocity of the ultrasonic beam propagating in the internal medium of the spindle rotor and the tool holder satisfies the following equation:

[0060]

[0061] In the formula, The local sound velocity of the ultrasonic beam propagating in the medium inside the spindle rotor and tool holder; The transient temperature field distribution inside the spindle rotor and tool holder; The three-dimensional stress tensor field inside the spindle rotor and tool holder; The spindle rotor and tool holder materials at standard initial temperature And the nominal speed of sound under stress-free conditions; The acoustoelastic stress constant of the spindle rotor and tool holder materials; The thermoacoustic temperature constants of the spindle rotor and tool holder materials; This indicates that trace operation is performed on the three-dimensional stress tensor field.

[0062] S103, construct the ultrasonic beam ray propagation path integral model. The flight time of the ultrasonic beam sent by the transmitting element to the receiving element is equal to the line integral of the reciprocal of the local sound velocity at each point along the ray propagation path of the ultrasonic beam. Extract the flight time sequence matrix containing all combinations of ultrasonic phased array transceiver elements.

[0063] S104 discretizes the monitoring area inside the spindle rotor and tool holder into multiple spatial voxels. The flight time series matrix is ​​input into the algebraic reconstruction algorithm. After multiple algebraic iterations, the inverse problem of the path integral model is solved to reconstruct the three-dimensional temperature field tensor and the three-dimensional stress field tensor of the spatial voxel at each moment. The three-dimensional temperature field tensor and the three-dimensional stress field tensor are spliced ​​together according to spatial nodes to output a three-dimensional physical field tensor containing the spatial distribution of temperature and stress information.

[0064] Step S2, which involves topological dimensionality reduction and state feature extraction in manifold space, specifically includes the following sub-steps:

[0065] S201 flattens the discretized global three-dimensional physical field tensor to construct a high-dimensional state vector. The high-dimensional state vector contains physical field grid node information. To meet the computation time requirements of the machine tool real-time control cycle, the Euclidean distance between each high-dimensional state vector is calculated based on the local linear embedding algorithm. The local neighborhood structure of the high-dimensional state vector is searched in the partially ordered half-lattice topological space.

[0066] S202: In the high-dimensional space, establish the nearest neighbor nodes of the high-dimensional state vector, calculate the reconstruction weight matrix of the high-dimensional state vector linearly reconstructed from the nearest neighbor nodes, construct a local linear embedding mapping function in the partially ordered semi-lattice manifold space, keep the reconstruction weight matrix unchanged, project the high-dimensional state vector onto the tangent space of the low-dimensional manifold, and solve for the optimal embedding coordinate vector by minimizing the reconstruction error. The dimension of the optimal embedding coordinate vector is much smaller than the dimension of the high-dimensional state vector.

[0067] S203 outputs the optimal embedded coordinate vector as the principal component manifold feature vector characterizing the internal thermal accumulation and stress concentration state of the machine tool. The principal component manifold feature vector preserves the topological mapping relationship between the thermal deformation mode and the force-induced deformation mode of the machine tool. The principal component manifold feature vector replaces the original voxel-level data collected by the ultrasonic phased array transceiver array as the low-dimensional input feature of the subsequent dynamic error evolution model.

[0068] The fractional-order non-autonomous dynamic error evolution and prediction step S3 specifically includes the following sub-steps:

[0069] S301, Establish the tool tip spatial position deviation vector model in the working coordinate system, and define the time. The three-dimensional spatial position deviation vector of the tool tip in the working coordinate system is composed of three displacement deviation components of the tool tip in the horizontal, vertical and vertical directions of the working coordinate system, arranged in the form of column vectors.

[0070] S302 introduces a variable-order fractional calculus operator to establish a stress relaxation model for machine tool metal structures. Under alternating cutting forces and non-uniform heat flow, the machine tool metal structure exhibits viscoelastic relaxation physical properties and stress history dependence. Traditional integer-order ordinary differential equations cannot accurately characterize the influence of historical stress accumulation on the current deformation state. Therefore, a time-dependent variable-order Caputo fractional derivative operator is used to establish the basis of the dynamic model. Specifically, the variable-order Caputo fractional derivative operator is defined as the integral over the time interval of the product of the first derivative of the state function and the time-decaying power function. The exponent of the time-decaying power function is determined by a dynamic fractional-order parameter, the range of which is set to... The dynamic fractional order parameter is used to characterize the degree of memory decay of the machine tool's metal structure for its historical deformation state.

[0071] S303, based on the variable-order Caputo fractional derivative operator, constructs a fractional-order non-autonomous dynamic error evolution model. The principal component manifold feature vectors output from the front-end sensing and data preprocessing channels are extracted as external excitation inputs. The internal temperature and stress distribution of the machine tool are dynamically correlated with the tool tip spatial position deviation vector, resulting in the following dynamic equations:

[0072]

[0073] In the formula, The three-dimensional spatial position deviation vector with respect to time The variable-order Caputo fractional derivative; The order parameter is a dynamic fractional order that varies over time. For a moment The three-dimensional spatial position deviation vector of the blade tip; The non-autonomous dynamic state matrix that evolves in real time with the three-dimensional physical field tensor; For three-dimensional physical field tensors; Let be the nonlinear coupled excitation vector function excited by the eigenvectors of the principal component manifold; The principal component manifold eigenvectors; To control the input gain matrix; For a moment The control vector applied to the machine tool actuator.

[0074] S304 extracts time-varying physical parameters from the non-autonomous dynamic state matrix. This matrix contains matrix elements characterizing the transient thermal stiffness and transient damping coefficient of the machine tool body. These matrix elements are updated over time with the temperature gradient and stress distribution within the three-dimensional physical field tensor. To solve the three-dimensional spatial position deviation vector in real time, a fractional-order prediction-correction numerical algorithm is used to discretize and solve the fractional-order non-autonomous dynamic error evolution model. Based on the three-dimensional spatial position deviation vector state values ​​at historical moments, the initial displacement deviation at the current time step is estimated. The fractional-order non-autonomous dynamic error evolution model is then used to iteratively correct the initial displacement deviation, ultimately outputting a continuous time domain sequence of the tool tip's three-dimensional spatial position deviation vector. This sequence provides a continuous dynamic prediction benchmark for subsequent frequency domain decoupling and macro-micro coordinated control.

[0075] After discretizing and solving the fractional-order non-autonomous dynamic error evolution model, the three-dimensional spatial position deviation vector sequence of the cutting tip in the continuous time domain is obtained. The frequency domain decoupling and filtering of the cutting tip three-dimensional spatial position deviation vector sequence includes the following sub-steps:

[0076] S305 sets the cutoff frequency of the frequency domain separation operator, reads the pre-configured servo bandwidth limit parameters of the feed drive units of each axis of the machine tool, and sets the servo bandwidth limit parameters as the cutoff frequency of the frequency domain separation operator. The cutoff frequency is used at the physical level to divide the steady-state thermal drift frequency band and the cutting force-induced transient deformation frequency band of the machine tool structure, providing a reference limit for the shunting execution of the deviation signal.

[0077] S306 performs low-pass filtering on the tool tip three-dimensional spatial position deviation vector. The tool tip three-dimensional spatial position deviation vector sequence is input into a low-pass filter with a set cutoff frequency for filtering. The low-pass filter filters out high-frequency oscillation signals higher than the cutoff frequency and outputs a low-frequency deviation component vector. The low-frequency deviation component vector represents the slow geometric drift caused by the internal thermal expansion of the machine tool and quasi-static force.

[0078] S307, calculate the high-frequency deviation component vector caused by cutting chatter. Subtract the low-frequency deviation component vector at the corresponding moment from the three-dimensional spatial position deviation vector of the tool tip at the current moment to separate the high-frequency deviation component vector. The high-frequency deviation component vector represents the transient oscillation displacement caused by sudden changes in local hard particles or alternation of high-frequency cutting force.

[0079] S308 synchronously extracts dynamic fractional-order parameters. Within the calculation cycle of solving the output tool tip three-dimensional spatial position deviation vector, it extracts the dynamically updated fractional-order parameters in the fractional-order non-autonomous dynamic error evolution model. It integrates the low-frequency deviation component vector, the high-frequency deviation component vector, and the dynamic fractional-order parameters into a multi-channel compensation control signal group. The multi-channel compensation control signal group is synchronously output to the macro-micro collaborative control module and the physical constitutive tuning module, providing underlying data support for the constitutive mapping from information space to physical space.

[0080] The ontology mapping step S4 between algorithm features and physical constitutive models specifically includes the following sub-steps:

[0081] S401, constructing the physical boundary conditions of the labyrinth-type dynamic seal ring cavity, embedding the labyrinth-type dynamic seal ring cavity between the machine tool spindle stator and the spindle rotor with a built-in spherical electromagnetic vector micro-motion tool holder, injecting magnetorheological fluid into the labyrinth-type dynamic seal ring cavity, so that the fixed reference system of the spindle stator and the rotating coordinate system of the spindle rotor are physically coupled through the magnetorheological fluid. The magnetorheological fluid exhibits Newtonian fluid characteristics in the absence of an external magnetic field, and exhibits plastic mechanical characteristics with a certain shear yield strength after being excited by an external magnetic field. Using an excitation coil set inside the spherical electromagnetic vector micro-motion tool holder, a controlled magnetic field is generated after energization, penetrating the side wall of the spindle rotor and covering the area where the labyrinth-type dynamic seal ring cavity is located.

[0082] S402, establish the shear constitutive equation of the magnetorheological fluid, and introduce the Bingham plasticity model to describe the physical rheological behavior of the magnetorheological fluid. The apparent shear stress of the magnetorheological fluid is equal to the sum of the dynamic yield stress and the viscous shear stress. The magnitude of the dynamic yield stress varies with the target magnetic induction intensity applied to the magnetorheological fluid. The viscous shear stress is obtained by multiplying the reference viscosity of the magnetorheological fluid in the absence of an external magnetic field by the shear strain rate generated by the rotation of the spindle rotor shearing the magnetorheological fluid.

[0083] S403 calibrates the coupling parameters between dynamic yield stress and target magnetic induction intensity. Within the control range of CNC machine tool spindle cutting, the dynamic yield stress is set to be proportional to the target magnetic induction intensity. A specific electromagnetic conversion proportional coefficient is extracted through offline calibration experiments. The electromagnetic conversion proportional coefficient is used to characterize the linear increase in the dynamic yield stress of the magnetorheological fluid by the unit magnetic field intensity increment generated by the excitation coil. The dynamic yield stress determines the physical damping absorption capacity of the labyrinth dynamic sealing ring cavity for the high-frequency cutting chatter of the spindle rotor, thus providing a parameterized calculation benchmark for the subsequent conversion of the magnetic field intensity command issued by the controller into the actual dissipation damping of the mechanical actuator.

[0084] Following the parameterization of the physical model, step S4, the ontology mapping of algorithmic features and physical constitutive models, specifically includes the following isomorphic mapping derivation sub-steps:

[0085] S404 establishes the isomorphic mapping logic between dynamic fractional order parameters and physical rheological relaxation characteristics. In fractional calculus theory, a dynamic fractional order parameter approaching 1 indicates that the computational model exhibits pure elastic mechanical characteristics, corresponding to a weak historical stress memory effect. A gradual decrease in the dynamic fractional order parameter indicates that the computational model exhibits obvious viscous fluid characteristics, corresponding to a strong historical stress memory effect and a high internal energy dissipation rate. An inverse adjustment correspondence is established between the dynamic fractional order parameter and the magnetorheological damping characteristics. When the L2 norm of the high-frequency deviation component vector increases and the dynamic fractional order parameter decreases, a damping enhancement command is sent to the labyrinthine dynamic sealing ring cavity to absorb cutting chatter energy.

[0086] S405, construct the volumetric mapping equation between the dynamic fractional-order parameters and the target magnetic flux density, extract the real-time updated dynamic fractional-order parameters and high-frequency deviation component vectors, and use the natural exponential function to transform the inverse change trend of the dynamic fractional-order parameters into a positive target magnetic flux density gain, establishing the following volumetric mapping equation:

[0087]

[0088] In the formula, For a moment The target magnetic flux density applied to the magnetorheological fluid; Electromagnetic conversion proportional coefficient extracted for offline calibration experiments; It is an exponential function with the natural constant as its base; Let be the dynamic fractional order parameter that varies with time; The high-frequency deviation component vector at time... According to the ontological mapping equation, when the dynamic fractional order parameter approaches the value of 1, the target magnetic flux density remains at a low baseline state, and the magnetorheological fluid exhibits a low acoustic impedance physical state to facilitate the transmission of ultrasonic beams; when the dynamic fractional order parameter decreases and the L2 norm of the high-frequency deviation component vector increases, the target magnetic flux density increases exponentially.

[0089] S406, Solve the excitation current control command acting on the excitation coil. Based on the law of electromagnetic induction and the inherent physical structure parameters of the excitation coil, establish a linear electromagnetic conversion model between the target magnetic flux density and the excitation current control command. Divide the target magnetic flux density by the electromagnetic induction conversion coefficient of the excitation coil to calculate the time. The excitation current control command applied to the excitation coil is sent to the peripheral drive hardware through the digital-to-analog converter interface. The peripheral drive hardware outputs an excitation current of corresponding amplitude to the excitation coil, thereby realizing the control of the physical damping of the magnetorheological fluid in the labyrinth-type dynamic sealing ring cavity.

[0090] The macro-micro coordinated control and active damping tuning step S5 includes three parallel execution channels at the execution level: macro low-frequency displacement feed compensation, micro high-frequency displacement reverse cancellation, and physical damping adaptive tuning. The specific execution process of macro low-frequency displacement feed compensation includes the following sub-steps:

[0091] S501 extracts the low-frequency deviation component vector and generates the macro servo compensation command vector. It obtains the low-frequency deviation component vector output from the frequency domain decoupling and filtering stage. The low-frequency deviation component vector represents the slow spatial position drift of the CNC machine tool due to structural heat accumulation and quasi-static force. The low-frequency deviation component vector is then subjected to coordinate inversion and negative operation to generate the macro servo compensation command vector.

[0092] S502 decouples the macro servo compensation command vector and converts it into a coordinate origin offset command. It decomposes the macro servo compensation command vector in three-dimensional space into three independent one-dimensional displacement offsets corresponding to the horizontal, vertical, and longitudinal axes in the CNC machine tool's working coordinate system. It calls the coordinate offset register at the CNC's underlying layer. Specifically, it writes the three one-dimensional displacement offsets into the zero-point offset address corresponding to the workpiece coordinate system in the machine tool's G-code. The offset parameters updated after writing to the zero-point offset address constitute the coordinate origin offset command. The coordinate origin offset command enters the machine tool's position control loop.

[0093] S503, each axis feed drive unit performs steady-state displacement compensation, and sends the coordinate origin offset command synchronously to the machine tool's native axis feed drive unit through the internal bus. Each axis feed drive unit drives the servo motor and ball screw mechanism to generate corresponding macroscopic compensation displacement according to the coordinate origin offset command. The macroscopic compensation displacement of the ball screw mechanism is directly superimposed on the current cutting trajectory command, eliminating steady-state thermal deformation and quasi-static geometric error in physical mechanical space.

[0094] The specific execution process of microscopic high-frequency displacement reverse cancellation includes the following sub-steps:

[0095] S504 extracts the high-frequency deviation component vector and generates the micro servo compensation command vector. It obtains the high-frequency deviation component vector separated in the frequency domain decoupling and filtering stage. The high-frequency deviation component vector represents the transient oscillation displacement caused by cutting chatter or sudden changes in local hard points during the cutting process of the CNC machine tool. The high-frequency deviation component vector is subjected to the inverse negative operation in coordinate space to generate the micro servo compensation command vector with the direction completely opposite to that of the high-frequency deviation component vector. The micro servo compensation command vector represents the physical reverse offset displacement required at the cutting point of the tool tip.

[0096] S505 calculates the drive current vector of the three-dimensional magnetostrictive exciter. The spherical electromagnetic vector micro-motion tool holder is installed as a whole on the tool clamping end of the spindle rotor for outputting high-frequency compensation reverse displacement during cutting. The three-dimensional magnetostrictive exciter is fixedly connected inside the spherical electromagnetic vector micro-motion tool holder. The three-dimensional magnetostrictive exciter includes three magnetostrictive material rods orthogonally arranged along the horizontal, vertical and longitudinal axes of the machine tool working coordinate system, and independent micro-drive coils wound around the outside of the three magnetostrictive material rods respectively. Based on the inverse piezoelectric physical properties of the magnetostrictive material, the micro-servo compensation command vector is multiplied by the electromechanical conversion calibration matrix to calculate the three-dimensional high-frequency drive current vector output to the micro-drive coil. The electromechanical conversion calibration matrix integrates the inherent magnetostrictive strain coefficient of the magnetostrictive material rod and the displacement amplification ratio parameters of the external mechanical structure, and extracts the three high-frequency current commands corresponding to the horizontal, vertical and longitudinal axis micro-drive coils respectively from the three-dimensional high-frequency drive current vector.

[0097] S506 drives the spherical electromagnetic vector micro-motion tool holder to perform a spatial reverse cancellation action. It synchronously outputs the calculated three high-frequency current commands to the corresponding micro-drive coil of the three-dimensional magnetostrictive exciter. After the micro-drive coil is energized, it generates a high-frequency alternating magnetic field. The three orthogonally arranged magnetostrictive material rods generate corresponding axial high-frequency expansion and contraction deformations under the action of the high-frequency alternating magnetic field. It controls the spatial flexible hinge mechanism configured inside the spherical electromagnetic vector micro-motion tool holder to perform kinematic vector synthesis of the axial high-frequency expansion and contraction deformations of the three magnetostrictive material rods. It outputs a spatial reverse displacement at the tool clamping end of the spindle rotor. The spatial reverse displacement generated at the tool clamping end acts on the cutting point of the tool tip, canceling the high-frequency transient oscillation error caused by the high-frequency cutting force at the physical and mechanical level.

[0098] After the microscopic high-frequency displacement reversal compensation is completed, the physical rheological damping adaptive tuning and acousto-magnetic closed-loop collaborative execution process is carried out in parallel, specifically including the following sub-steps:

[0099] S507 executes the physical rheological damping adaptive tuning action, synchronously receiving the excitation current control command generated in the body mapping step of algorithm features and physical constitutive model, and inputting the excitation current control command to the excitation coil inside the spherical electromagnetic vector micro-motion tool holder. The excitation leakage magnetic field generated after the excitation coil is energized penetrates the spindle rotor sidewall and excites a controlled transient magnetic field inside the labyrinth-type dynamic seal ring cavity. The magnetic field lines of the controlled transient magnetic field penetrate the magnetorheological fluid filled in the labyrinth-type dynamic seal ring cavity. Under the action of the controlled transient magnetic field, the magnetic particles inside the magnetorheological fluid are oriented along the direction of the magnetic field lines to form a chain physical structure. The chain physical structure instantly increases the apparent shear viscosity and dynamic yield stress of the magnetorheological fluid. The increase in apparent shear viscosity and dynamic yield stress constructs a highly dissipative physical damping boundary between the machine tool spindle stator and spindle rotor. The physical damping boundary absorbs and dissipates a large amount of high-frequency cutting chatter energy transmitted by the spindle rotor through fluid shear friction.

[0100] S508 establishes an acoustic-magnetic closed-loop collaborative mechanism between the sensing and execution modules. While the magnetorheological fluid (MRF) alters its apparent shear viscosity and dynamic yield stress, its bulk modulus and internal density distribution change synchronously. According to acoustic physics laws, the acoustic impedance parameter of the medium increases significantly with increasing bulk modulus. When cutting chatter intensifies and the dynamic fractional-order parameter decreases, the controlled transient magnetic field strength increases, causing the MRF to exhibit viscoplastic hardening characteristics, transitioning from a liquid to a solid-like state. This leads to a sharp increase in the MRF's bulk modulus, which in turn causes a significant increase in the MRF's acoustic impedance parameter. The adaptive approach of the acoustic impedance value of the main shaft rotor metal material is used. The magnetorheological fluid in the labyrinthine dynamic sealing ring cavity acts as the transmission coupling layer for ultrasonic beam transmission and reception in the transient physical field tomography reconstruction step. The adaptive approach matching of the medium acoustic impedance parameters significantly reduces the acoustic wave reflection loss of the ultrasonic beam at the solid-liquid interface and improves the energy transmittance of the ultrasonic beam into the main shaft rotor. The improvement of energy transmittance inversely optimizes the signal-to-noise ratio of the ultrasonic phased array transceiver array under severe flutter conditions. This step utilizes the physical state change of the compensation execution end to achieve passive gain improvement of the quality of the front-end ultrasonic sensing signal.

[0101] For the low-level code writing of the digital-to-analog conversion communication protocol between the machine tool main control module and the peripheral execution hardware, the high-frequency filtering circuit design of the ultrasonic phased array transceiver array, and the electrical wiring of the excitation coil power amplifier drive circuit, those skilled in the art can use general industrial fieldbus standard protocols, commercial high-frequency data acquisition cards, and commercial programmable DC power supply modules for specific implementation. The configuration rules of industrial fieldbus standard protocols, the debugging instructions of commercial high-frequency data acquisition cards, and the electrical connection topology of commercial programmable DC power supply modules are well-known technologies in this field and will not be elaborated here.

[0102] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A real-time compensation method for machining errors in CNC machine tools, characterized in that, Includes the following steps: Step S1: Perform transient physical field tomography reconstruction based on acoustic effect, extract the flight time sequence matrix of ultrasonic waves propagating in the spindle rotor and tool holder, and output a three-dimensional physical field tensor containing spatial distribution of temperature and stress information. Step S2: Perform manifold space topological dimensionality reduction and state feature extraction on the three-dimensional physical field tensor output in step S1, and output principal component manifold feature vectors. Step S3: Based on the principal component manifold feature vector output in step S2, perform fractional-order non-autonomous dynamic error evolution and prediction, construct a fractional-order non-autonomous dynamic error evolution model and solve it by discretization, output the three-dimensional spatial position deviation vector sequence of the cutting tip in the continuous time domain, and perform frequency domain decoupling filtering on the three-dimensional spatial position deviation vector sequence of the cutting tip to separate the low-frequency deviation component vector and the high-frequency deviation component vector, and simultaneously extract the dynamic fractional-order parameters; Step S4: Obtain the high-frequency deviation component vector separated in step S3 and the extracted dynamic fractional order parameters to perform the ontological mapping of the algorithm features and physical constitutive model, calculate the target magnetic induction intensity applied to the magnetorheological fluid, and solve the excitation current control command based on the target magnetic induction intensity. Step S5: Based on the low-frequency deviation component vector and the high-frequency deviation component vector separated in step S3, and the excitation current control command calculated in step S4, perform macroscopic low-frequency displacement feed compensation action, microscopic high-frequency displacement reverse cancellation action, and physical rheological damping adaptive tuning and acoustic-magnetic closed-loop coordinated action in parallel.

2. The real-time compensation method for machining errors in CNC machine tools according to claim 1, characterized in that, The step S1 of performing transient physical field tomography reconstruction based on the acoustic effect specifically includes: An ultrasonic beam with a preset deflection angle is emitted into the spindle rotor and the medium inside the tool holder, and the flight time sequence matrix of the ultrasonic beam from the transmitting array element to the receiving array element is extracted. Establish an acoustic-elastic-thermo-acoustic coupling physical model of the spindle rotor and the internal medium of the tool holder, as well as an integral model of the ultrasonic beam propagation path. The monitoring area inside the spindle rotor and tool holder is discretized into multiple spatial voxels. The flight time series matrix is ​​input into an algebraic reconstruction algorithm to reconstruct the three-dimensional temperature field tensor and the three-dimensional stress field tensor of the spatial voxel at each moment. The three-dimensional temperature field tensor and the three-dimensional stress field tensor are then concatenated and combined according to spatial nodes to output the three-dimensional physical field tensor.

3. The real-time compensation method for machining errors of CNC machine tools according to claim 1, characterized in that, Step S2, which involves performing manifold space topological dimensionality reduction and state feature extraction on the three-dimensional physical field tensor output in step S1, specifically includes: The discretized three-dimensional physical field tensor is flattened to construct a high-dimensional state vector; Based on the local linear embedding algorithm, the Euclidean distance between each of the high-dimensional state vectors is calculated, the local neighborhood structure of the high-dimensional state vectors is searched in the partially ordered half-lattice topological space, and the reconstruction weight matrix of the high-dimensional state vectors linearly reconstructed by the nearest neighbor nodes is calculated. While keeping the reconstructed weight matrix unchanged, the high-dimensional state vector is projected into the tangent space of the low-dimensional manifold to solve for the optimal embedding coordinate vector, and the optimal embedding coordinate vector is output as the principal component manifold feature vector.

4. The real-time compensation method for machining errors of CNC machine tools according to claim 1, characterized in that, During the fractional-order non-autonomous dynamic error evolution and prediction process in step S3: The dynamic model is based on a time-dependent variable-order Caputo fractional derivative operator, and the fractional-order non-autonomous dynamic error evolution model is discretized and solved by a fractional-order prediction-correction numerical algorithm. Read the pre-configured servo bandwidth limit parameters of the feed drive units of each axis of the machine tool, and set the servo bandwidth limit parameters as the cutoff frequency of the low-pass filter; The three-dimensional spatial position deviation vector sequence of the blade tip is input into a low-pass filter with a set cutoff frequency to filter out high-frequency oscillation signals higher than the cutoff frequency and output the low-frequency deviation component vector. The high-frequency deviation component vector is separated by subtracting the low-frequency deviation component vector from the current three-dimensional spatial position deviation vector of the blade tip.

5. The real-time compensation method for machining errors in CNC machine tools according to claim 4, characterized in that, Step S3 involves constructing the fractional-order non-autonomous dynamic error evolution model, specifically including: The principal component manifold feature vector is extracted as an external excitation input term. The internal temperature and stress distribution of the machine tool are dynamically correlated with the tool tip spatial position deviation vector to construct a fractional-order non-autonomous dynamic error evolution model. The fractional-order non-autonomous dynamic error evolution model includes a non-autonomous dynamic state matrix, which is updated over time as the temperature gradient and stress distribution within the three-dimensional physical field tensor change.

6. The real-time compensation method for machining errors in CNC machine tools according to claim 1, characterized in that, The ontology mapping between the execution algorithm features and the physical constitutive model described in step S4 specifically includes: The Bingham plasticity model is introduced to describe the physical rheological behavior of the magnetorheological fluid, and an inverse adjustment correspondence is established between the dynamic fractional order parameter representing the decay rate of mathematical history memory and the damping characteristic of the magnetorheological fluid representing the physical energy dissipation rate. Construct a volumetric mapping equation between the dynamic fractional order parameter and the target magnetic flux density, and convert the inverse change trend of the dynamic fractional order parameter into a positive target magnetic flux density gain based on the volumetric mapping equation. A linear electromagnetic conversion model between the target magnetic induction intensity and the excitation current control command is established. The target magnetic induction intensity is divided by the electromagnetic induction conversion coefficient of the excitation coil to calculate the excitation current control command acting on the excitation coil.

7. The real-time compensation method for machining errors of CNC machine tools according to claim 6, characterized in that, The construction of the ontological mapping equation between the dynamic fractional order parameters and the target magnetic induction intensity specifically includes: Extract the dynamically updated fractional order parameters and the high-frequency deviation component vector in real time, use the natural exponential function to transform the reverse change trend of the dynamically fractional order parameters, combine the electromagnetic conversion ratio coefficient extracted from the offline calibration experiment and the L2 norm of the high-frequency deviation component vector, and calculate the target magnetic induction intensity applied to the magnetorheological fluid through the body mapping equation. When the dynamic fractional order parameter decreases and the L2 norm of the high-frequency deviation component vector increases, the target magnetic induction intensity increases exponentially.

8. The real-time compensation method for machining errors of CNC machine tools according to claim 1, characterized in that, The macroscopic low-frequency displacement feed compensation action described in step S5 specifically includes: The low-frequency deviation component vector separated in step S3 is subjected to coordinate inversion and negation to generate a macroscopic servo compensation command vector. The macro servo compensation command vector is decomposed into three one-dimensional displacement offsets in the machine tool working coordinate system, and the three one-dimensional displacement offsets are written into the zero-point offset address corresponding to the workpiece coordinate system of the machine tool G code, so as to form the coordinate origin offset command. The machine tool's native axis feed drive units generate corresponding macroscopic compensation displacements based on the coordinate origin offset command.

9. The real-time compensation method for machining errors of CNC machine tools according to claim 1, characterized in that, The execution of the micro-high frequency displacement reverse cancellation action described in step S5 specifically includes: The high-frequency deviation component vector separated in step S3 is subjected to a coordinate space inverse negative operation to generate a micro servo compensation command vector. The micro servo compensation command vector is multiplied by the electromechanical conversion calibration matrix to calculate the three-dimensional high-frequency drive current vector, and the three high-frequency current commands of each axis of the corresponding machine tool working coordinate system are extracted. The three high-frequency current commands are synchronously output to the three-dimensional magnetostrictive exciter inside the spherical electromagnetic vector micro-motion tool holder. Kinematic vector synthesis is performed through a spatial flexible hinge mechanism, and spatial reverse displacement is output at the tool clamping end of the spindle rotor.

10. A real-time compensation method for machining errors in CNC machine tools according to claim 1, characterized in that, The execution of the physical rheological damping adaptive tuning and acousto-magnetic closed-loop coordinated action described in step S5 specifically includes: The excitation current control command calculated in step S4 is input to the excitation coil assembly arranged around the labyrinth-type dynamic sealing ring cavity to generate a controlled transient magnetic field, so that a chain bundle physical structure is formed inside the magnetorheological fluid, thereby increasing the apparent shear viscosity and dynamic yield stress of the magnetorheological fluid to dissipate cutting chatter energy. The increase in the controlled transient magnetic field strength causes the bulk elastic modulus of the magnetorheological fluid to rise, which in turn causes the medium acoustic impedance parameter of the magnetorheological fluid to adaptively approach the inherent acoustic impedance value of the main shaft rotor metal material, thereby reducing the acoustic wave reflection loss of the ultrasonic beam at the solid-liquid interface.

Images