Part machining error modeling and calibration method and system based on multi-source uncertainty

Abstract

The application relates to the technical field of part machining, and discloses a part machining error modeling and calibration method and system based on multi-source uncertainty. The method comprises the following steps: calculating a first machining error component by analyzing three-way cutting force and a workpiece flexibility matrix, and calculating a second machining error component by analyzing three-way cutting force and tool radial flexibility; a multi-source uncertainty error prediction model containing five uncertain calibration coefficients is constructed; after five-axis milling machining is performed on a thin-wall curved surface part, the calibration values of the five uncertain calibration coefficients are calculated; and the calibration values of the five uncertain calibration coefficients are substituted into the multi-source uncertainty error prediction model to obtain machining error prediction values of each type of point. The application eliminates the systematic influence of multiple types of uncertainty on prediction accuracy from the model structure level, realizes multi-dimensional uncertainty coefficient calibration combining a mechanism model and working condition data, greatly shortens single-point prediction time, and makes prediction efficiency meet the engineering application demand.

Description

Technical Field

[0001] This invention relates to the field of parts processing technology, and in particular to a method and system for modeling and calibrating parts processing errors based on multi-source uncertainty. Background Technology

[0002] Mechanism-based analytical modeling and finite element simulation are effective means of predicting machining errors. They often employ forward modeling to quantitatively model and analyze the machining process. Considering the numerous uncertainties and noises in the process system, this paper analyzes the uncertainties in the machining error prediction model, focusing on the source tracing and quantification of uncertainties under single-factor conditions. These uncertainties include those caused by tool / workpiece deformation and springback, uncertainties in the process system, uncertainties in the fitted regression coefficients, and uncertainties in residual stress. However, existing methods only analyze single sources of uncertainty and lack a systematic approach that integrates multiple types of uncertainties into a single prediction model framework.

[0003] To address the unique characteristics of five-axis milling of complex parts, it is necessary to simultaneously consider machining errors at both the workpiece and tool ends. Furthermore, multi-source uncertainties, such as tool wear uncertainty, contact area uncertainty, and process system uncertainty, need to be introduced to improve the prediction model. However, in existing mechanistic models, the single-point calculations for analytical prediction of cutting forces and finite element simulation of workpiece compliance are time-consuming. This presents a fundamental contradiction with the numerous iterative calls required for uncertainty coefficient calibration based on working condition data. While the prediction accuracy of the model is significantly improved after uncertainty calibration, the computational efficiency still cannot meet the demands of rapid response to part machining errors in engineering applications. Summary of the Invention

[0004] The main objective of this invention is to provide a method and system for modeling and calibrating part processing errors based on multi-source uncertainties. Compared with existing prediction methods that only consider single-source uncertainties, this invention eliminates the systematic impact of multiple types of uncertainties on prediction accuracy from the model structure level, realizes multi-dimensional uncertainty coefficient calibration by combining the mechanism model with working condition data, significantly shortens the single-point prediction time, and makes the prediction efficiency meet the needs of engineering applications.

[0005] To achieve the above objectives, this invention provides a method for modeling and calibrating part machining errors based on multi-source uncertainties, comprising the following steps: The first machining error component is calculated by analyzing the triaxial cutting force and the workpiece compliance matrix, and the second machining error component is calculated by analyzing the triaxial cutting force and the tool radial compliance. A multi-source uncertainty error prediction model with five uncertain calibration coefficients is constructed based on the first processing error component and the second processing error component. After performing five-axis milling on the thin-walled curved surface part, the measured values ​​of the machining error at each type value point are measured and the calibration values ​​of the five uncertain calibration coefficients are calculated. Substitute the calibration values ​​of the five uncertain calibration coefficients into the multi-source uncertain error prediction model to obtain the predicted processing error values ​​for each type of value point.

[0006] Optionally, in a first implementation of the first aspect of the present invention, calculating the first machining error component by analyzing the triaxial cutting force and the workpiece compliance matrix, and calculating the second machining error component by analyzing the triaxial cutting force and the tool radial compliance matrix, includes: The analytical triaxial cutting force and the workpiece compliance matrix are multiplied together to obtain the triaxial deformation vector at the shape value point. The first machining error component is obtained by multiplying the three-dimensional deformation vector with the normal vector of the shape value point. The second machining error component is obtained by multiplying the radial component of the analytical triaxial cutting force with the radial compliance of the tool and projecting it onto the normal vector direction of the back profile point.

[0007] Optionally, in a second implementation of the first aspect of the present invention, the radial component of the analytical triaxial cutting force is multiplied by the radial compliance of the tool and then projected onto the normal vector direction of the profile point to obtain the second machining error component, including: The tool axis direction is calculated based on the normal vector direction of the model value point, the tool rake angle, and the tool side tilt angle. The axial component along the tool axis direction is removed from the analytical triaxial cutting force to obtain the tool radial cutting force. Multiply the radial cutting force of the tool by the radial compliance of the tool to obtain the radial deformation vector of the tool. Then, multiply the radial deformation vector of the tool by the normal vector of the shape value point to obtain the second machining error component.

[0008] Optionally, in a third implementation of the first aspect of the present invention, a multi-source uncertainty error prediction model containing five uncertainty calibration coefficients is constructed based on the first processing error component and the second processing error component, including: The first machining error component is superimposed with the second machining error component, and the three components of the analytical triaxial cutting force (x, y, z) are respectively corrected by introducing three multiplicative calibration coefficients of the three cutting contact areas to obtain the superimposed error term. Two wear multiplicative calibration coefficients are introduced for the amplitude coefficient and shape coefficient of the Sigmoid mapping function between tool wear and cutting length, respectively, to obtain the corrected tool wear Sigmoid function term; The modified tool wear Sigmoid function term is added to the superposition error term to obtain a multi-source uncertainty error prediction model containing five uncertainty calibration coefficients.

[0009] Optionally, in the fourth implementation of the first aspect of the present invention, after performing five-axis milling on the thin-walled curved surface part, measuring the measured values ​​of the machining errors at each type value point and calculating the calibration values ​​of the five uncertain calibration coefficients includes: After performing five-axis milling on thin-walled curved parts, a machine measuring device is installed on the end of the machine tool spindle, and the actual coordinates of each type value point are measured sequentially along the normal direction of each type value point. The actual coordinates of each model point are subtracted from the theoretical coordinates of the corresponding model point and then projected onto the normal vector direction of the model point to obtain the measured value of the machining error of each model point. The calibration values ​​of the five uncertain calibration coefficients are calculated based on the measured values ​​of the processing error and the multi-source uncertain error prediction model.

[0010] Optionally, in a fifth implementation of the first aspect of the present invention, calculating the calibration values ​​of the five uncertain calibration coefficients based on the measured values ​​of the processing error and the multi-source uncertain error prediction model includes: Based on the cutting force mechanism model and the physical prior knowledge of tool wear, the initial values ​​of the five uncertain calibration coefficients are set as the initial state of the Markov chain, and the posterior probability density function is constructed by the difference between the measured value of the machining error at each type point and the predicted value of the multi-source uncertain error prediction model. The posterior probability density function is subjected to multidimensional Metropolis-Hastings iterative sampling to obtain the calibration values ​​of the five uncertain calibration coefficients.

[0011] Optionally, in a sixth implementation of the first aspect of the present invention, multidimensional Metropolis-Hastings iterative sampling is performed on the posterior probability density function to obtain the calibration values ​​of the five uncertain calibration coefficients, including: Multidimensional Metropolis-Hastings iterative sampling is performed on the posterior probability density function, and in each iteration, candidate states of the five uncertain calibration coefficients are generated. The candidate states are substituted into the multi-source uncertain error prediction model, and the acceptance rate is calculated by the ratio of the posterior probability corresponding to the candidate state to the current state. Random numbers are sampled from a uniform distribution and compared with the acceptance rate. If the random number is less than the acceptance rate, the current state of the Markov chain is replaced by the candidate state. Otherwise, the current state of the Markov chain remains unchanged. After multiple iterations of sampling, the median of the posterior distribution samples of each uncertain calibration coefficient is taken as the calibration value of the five uncertain calibration coefficients.

[0012] Optionally, in the seventh implementation of the first aspect of the present invention, the calibration values ​​of the five uncertain calibration coefficients are substituted into the multi-source uncertain error prediction model to obtain the predicted processing error values ​​for each type of value point, including: The machining parameter feature vectors of each type of value point are input into the Gaussian process regression proxy model of cutting force and the Gaussian process regression proxy model of workpiece compliance, respectively, and the proxy triaxial cutting force and proxy compliance matrix corresponding to each type of value point are calculated. The analytical triaxial cutting force and the workpiece compliance matrix in the multi-source uncertain error prediction model are replaced by the proxy triaxial cutting force and the proxy compliance matrix. The calibration values ​​of the five uncertain calibration coefficients are substituted into the corresponding multiplicative calibration coefficients of the contact area and the wear multiplicative calibration coefficients in the multi-source uncertain error prediction model to obtain the machining error prediction values ​​of each type point.

[0013] Optionally, in the eighth implementation of the first aspect of the present invention, the feature vectors of the machining parameters for each type of value point are respectively input into the Gaussian process regression proxy model of the cutting force and the Gaussian process regression proxy model of the workpiece compliance, and the proxy triaxial cutting force and proxy compliance matrix corresponding to each type of value point are calculated, including: The machining allowance, feed per tooth, cutting speed, rake angle, side rake angle, and surface position parameters of each type value point are used to construct a feature vector of machining parameters; The feature vector of the machining parameters is input into the Gaussian process regression proxy model of the cutting force constructed with the Matern kernel function to calculate the proxy triaxial cutting force corresponding to each type of value point; The compliance input feature vector, composed of the machining allowance and surface position parameters of each type of value point, is input into the workpiece compliance Gaussian process regression surrogate model constructed with the Matern kernel function, and the surrogate compliance matrix corresponding to each type of value point is calculated.

[0014] This invention also provides a part machining error modeling and calibration system based on multi-source uncertainty, comprising: The mechanism modeling module is used to calculate the first machining error component by analyzing the triaxial cutting force and the workpiece compliance matrix, and to calculate the second machining error component by analyzing the triaxial cutting force and the tool radial compliance. The model improvement module is used to construct a multi-source uncertainty error prediction model containing five uncertainty calibration coefficients based on the first processing error component and the second processing error component. The coefficient calibration module is used to measure the measured values ​​of machining errors at various point values ​​and calculate the calibration values ​​of the five uncertain calibration coefficients after five-axis milling of thin-walled curved parts. The error prediction module is used to substitute the calibration values ​​of the five uncertain calibration coefficients into the multi-source uncertain error prediction model to solve for the predicted processing error values ​​of each type of value point.

[0015] In summary, this invention constructs a five-axis milling machining error prediction model framework that considers multi-source uncertainties in the machining process. It establishes a machining error mechanism model that simultaneously considers machining errors at both the workpiece end and the tool end, determines the explicit mapping relationship between machining parameters, surface position, and machining errors, and introduces three multiplicative calibration coefficients for the x, y, and z components of the analytical triaxial cutting force, respectively, and introduces two wear multiplicative calibration coefficients for the amplitude coefficient and shape coefficient of the tool wear Sigmoid function, respectively. By unifying the uncertainties of the cutting contact area and the uncertainties of tool wear into a multi-source uncertainty error prediction model with five uncertainty calibration coefficients, this invention eliminates the systematic impact of multiple types of uncertainties on prediction accuracy from the model structure level compared to existing prediction methods that only consider single-source uncertainties. Regarding coefficient calibration, based on a Bayesian framework, the prior probabilities of the five uncertain calibration coefficients are constructed using the physical prior knowledge of the cutting force mechanism model and the tool wear Sigmoid function. A log-likelihood function is then constructed by combining the measured machining error values. The posterior probability density function is iteratively sampled using a multidimensional Metropolis-Hastings sampling algorithm, and the calibration value is obtained by taking the median of the posterior distribution samples of each coefficient. This achieves multidimensional uncertainty coefficient calibration by combining the mechanism model with working condition data. In terms of prediction efficiency, during MCMC iterative calibration and machining error prediction, the time-consuming analytical model and finite element simulation are replaced by a cutting force Gaussian process regression surrogate model and a workpiece compliance Gaussian process regression surrogate model. This significantly shortens the single-point prediction time, ensuring that the prediction efficiency meets the requirements of engineering applications. Attached Figure Description

[0016] Figure 1 This is a schematic diagram of the steps of a part machining error modeling and calibration method based on multi-source uncertainty in one embodiment of the present invention; Figure 2 This is a schematic diagram of the processing deformation of a thin-walled part in an embodiment of the present invention; Figure 3 This is a schematic diagram showing the decomposition of the total machining error at the workpiece end in an embodiment of the present invention; Figure 4 This is a schematic diagram of the machining error generated at the workpiece end under the action of Fx in an embodiment of the present invention; Figure 5 This is a schematic diagram of the machining error generated at the workpiece end under the action of Fy in an embodiment of the present invention; Figure 6 This is a schematic diagram of the machining error generated at the workpiece end under the action of Fz in an embodiment of the present invention; Figure 7 This is a schematic diagram illustrating the machining deformation and machining error of the cutting tool tip in an embodiment of the present invention. Figure 8This is a schematic diagram of the geometric model of the milling cutter in an embodiment of the present invention; Figure 9 This is a schematic diagram illustrating the relative positional relationships between various coordinate systems, such as the tool coordinate system and the workpiece coordinate system, in an embodiment of the present invention. Figure 10 This is a comparison chart of the predicted cutting force and the measured data in an embodiment of the present invention; Figure 11 This is a flowchart of the workpiece compliance calculation based on finite element simulation technology in an embodiment of the present invention; Figure 12 This is a schematic diagram showing the workpiece geometry and the distribution of the six thin-walled curved surfaces in an embodiment of the present invention; Figure 13 This is a schematic diagram of the surface measurement area and measurement path planning in an embodiment of the present invention; Figure 14 This is a comparison chart of the predicted results and measured results of the pure mechanism model for 18 processing experiments in this embodiment of the invention; Figure 15 This is a schematic diagram of the distribution of surface sample points in an embodiment of the present invention; Figure 16 This is a schematic diagram of the distribution of 200 sets of hyperparameters during the hyperparameter optimization process of Gaussian process regression in an embodiment of the present invention; Figure 17 This is a graph showing the hyperparameter optimization results of the Gaussian process regression in an embodiment of the present invention; Figure 18 This is a comparison chart of theoretical cutting force and predicted cutting force in an embodiment of the present invention; Figure 19 This is a diagram showing the prediction results of the directional compliance proxy model in an embodiment of the present invention; Figure 20 This is a block diagram of a part processing error modeling and calibration system based on multi-source uncertainty in one embodiment of the present invention.

[0017] The realization of the objective, functional features and advantages of the present invention will be further explained in conjunction with the embodiments and with reference to the accompanying drawings. Detailed Implementation

[0018] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0019] Reference Figure 1 This embodiment provides a method for modeling and calibrating part machining errors based on multi-source uncertainties, including: S1, calculate the first machining error component by analyzing the triaxial cutting force and the workpiece compliance matrix, and calculate the second machining error component by analyzing the triaxial cutting force and the tool radial compliance. S2, construct a multi-source uncertainty error prediction model with five uncertainty calibration coefficients based on the first processing error component and the second processing error component; S3, after performing five-axis milling on a thin-walled curved surface part, measure the actual machining error at each type point and calculate the calibration values ​​of five uncertain calibration coefficients; S4. Substitute the calibration values ​​of the five uncertain calibration coefficients into the multi-source uncertain error prediction model to obtain the predicted processing error values ​​for each type of value point.

[0020] In one example, the first machining error component is calculated by analyzing the triaxial cutting force and the workpiece compliance matrix, and the second machining error component is calculated by analyzing the triaxial cutting force and the tool radial compliance matrix, including: The analytical triaxial cutting force and the workpiece compliance matrix are multiplied together to obtain the triaxial deformation vector at the shape value point. The first machining error component is obtained by multiplying the three-dimensional deformation vector with the normal vector of the shape value point. The second machining error component is obtained by multiplying the radial component of the analytical triaxial cutting force with the radial compliance of the tool and then projecting it onto the normal vector direction of the back profile point.

[0021] Figure 2 This figure illustrates the spatial distribution of workpiece and tool deformation during five-axis milling of thin-walled curved parts. The figure shows the workpiece coordinate system (WCS) and the machine coordinate system (MCS). The curved surface is represented in the uv-parameter coordinate system, where u represents the cutting feed direction and v represents the multi-toolpath stepping direction. Point P1 is located in the upper half of the workpiece, in a region with greater flexibility, corresponding to a situation where workpiece deformation is greater than tool deformation. Point P2 is located in the lower half of the workpiece, near the clamping point, in a region with less flexibility, corresponding to a situation where tool deformation is greater than workpiece deformation. The reference numerals in the attached figures include: WCS for workpiece coordinate system, MCS for machine coordinate system, u for surface cutting direction parameter, v for surface stepping direction parameter, P1 for upper workpiece profile point, P2 for lower workpiece profile point, np1 for surface normal vector at point P1, np2 for surface normal vector at point P2, nt1 for tool axis direction at point P1, nt2 for tool axis direction at point P2, F1 for resultant cutting force at point P1, F2 for resultant cutting force at point P2, tool label indicates ball end mill, and workpiece label indicates thin-walled curved surface part.

[0022] Figure 3This figure illustrates the spatial geometric relationship of the triaxial deformation at various shape points on the workpiece end under the combined action of three-directional cutting forces. The figure shows the workpiece coordinate system (WCS) and the machine coordinate system (MCS). The cutting force F acts at shape point P, causing deformation components in the x, y, and z directions. The total deformation vector is ultimately projected onto the normal vector direction np of the shape point to obtain the normal machining error component at the workpiece end. The figure labels include: WCS for workpiece coordinate system, MCS for machine coordinate system, u for surface cutting direction parameter, v for surface step direction parameter, P for shape point, np for surface normal vector direction at shape point, Fx for cutting force component in the x direction, Fy for cutting force component in the y direction, Fz for cutting force component in the z direction, dwx for total deformation in the x direction, dwy for total deformation in the y direction, and dwz for total deformation in the z direction.

[0023] Figure 4 This figure shows the spatial geometric relationship of the deformation components of the workpiece shape point P in the x, y, and z directions under the action of a cutting force Fx in the x direction alone. The reference numerals include: P is the shape point, np is the direction of the surface normal at the shape point, Fx is the cutting force in the x direction, dxx is the deformation component in the x direction under the action of Fx, dyx is the deformation component in the y direction under the action of Fx, and dzx is the deformation component in the z direction under the action of Fx.

[0024] Figure 5 This figure shows the spatial geometric relationship of the deformation components of the workpiece shape point P in the x, y, and z directions under the action of a cutting force Fy in the y direction alone. The reference numerals include: P is the shape point, np is the direction of the surface normal at the shape point, Fy is the cutting force in the y direction, dxy is the deformation component in the x direction under the action of Fy, dyy is the deformation component in the y direction under the action of Fy, and dzy is the deformation component in the z direction under the action of Fy.

[0025] Figure 6 This figure shows the spatial geometric relationship of the deformation components of the workpiece shape point P in the x, y, and z directions under the action of a cutting force Fz in the z direction alone. The reference numerals include: P is the shape point, np is the normal vector direction of the surface at the shape point, Fz is the cutting force in the z direction, dxz is the deformation component in the x direction under the action of Fz, dyz is the deformation component in the y direction under the action of Fz, and dzz is the deformation component in the z direction under the action of Fz.

[0026] In this example, the analytical triaxial cutting force vector at the point of origin is defined within the workpiece coordinate system. ,in , , These are the instantaneous cutting force components corresponding to the three orthogonal directions. The analytical cutting force is obtained based on the cutting force mechanism expression and the cutting contact region determination function, and the calibrated cutting force coefficients are used. MPa MPa MPa is used in the calculation of tangential, radial, and axial micro-element forces, thus establishing a consistent mapping relationship between the triaxial cutting force at the shape point and the undeformed chip thickness, axial discrete element, and tool rotation angle. To obtain the elastic deformation state of the shape point under triaxial load, a workpiece compliance matrix is ​​introduced at the shape point. ,in Indicates the first The first unit force under direction The displacement compliance value generated in each direction, and the workpiece compliance matrix obtained by finite element simulation or analytical compliance calculation, correspond to the spatial position of the shape value point. Based on the above definition, matrix multiplication is used to solve for the three-dimensional deformation vector, written as... ,in The three-dimensional deformation vector of the shape value point. , , The displacement components of the model point along three orthogonal directions are represented respectively. Matrix multiplication formally maps the unit force compliance to the actual cutting force and automatically includes a three-dimensional coupling term in the calculation, forming a comprehensive deformation result consistent with the load direction change. The outward normal vector of the model point is defined as a unit vector. ,in , , Let the direction cosine of the normal vector in the workpiece coordinate system be given. The normal vector is determined by the geometry of the surface to be machined and corresponds one-to-one with the shape value points. The three-dimensional deformation vector is projected onto the direction of the normal vector by the dot product operation to obtain the first machining error component. The dot product operation extracts the normal displacement and directly outputs the normal dimensional error components, thus transforming the "workpiece end deformation" from a three-dimensional displacement domain into a one-dimensional normal error quantity consistent with the definition of machining error. Simultaneously, to obtain the contribution of the tool end to the normal dimensional error, the analytical three-dimensional cutting force vector is decomposed from the workpiece coordinate system to the tool radial direction and the tool axis direction. First, the unit vector in the tool axis direction is determined, and then the tool radial force component is obtained by combining the coordinate system rotation transformation relationship. , This represents the resultant component of the three-dimensional cutting forces in the tool radial direction and reflects the dominant load on the cantilever of a tool with a large aspect ratio. The tool radial compliance is then introduced. ,in This represents the radial displacement compliance of the tool under a unit radial force. The radial compliance of the tool is obtained from cantilever beam theory or finite element simulation and is consistent with the tool material, diameter, and clamping length. The radial deformation of the tool is obtained using a proportional relationship. To convert the radial deformation of the tool into a normal machining error component at the shape point, a geometric projection is performed on the radial deformation direction and the normal vector direction of the shape point. Let the unit vector of the tool radial direction be... The normal machining error component at the tool tip is written as... ,in The direction cosine is used to represent the distance between the radial direction of the tool and the normal vector direction of the model point, and is used to complete the direction consistency conversion, thereby converting "radial elastic offset" into "normal dimensional deviation". At the same model point, the first machining error component With the second machining error component Two error component calculation pathways with clear sources and consistent projections are formed.

[0027] In one example, the radial component of the analytical triaxial cutting force is multiplied by the tool radial compliance and then projected back onto the normal vector direction of the profile point to obtain the second machining error component, which includes: The tool axis direction is calculated based on the normal vector direction of the model value point, the tool rake angle, and the tool side tilt angle. The axial component along the tool axis direction is removed from the analytical triaxial cutting force to obtain the tool radial cutting force. Multiply the radial cutting force of the tool by the radial compliance of the tool to obtain the radial deformation vector of the tool. Then, multiply the radial deformation vector of the tool by the normal vector of the shape value point to obtain the second machining error component.

[0028] In this example, in solving the error at the shape point of a five-axis machining center, the unit vector of the outward normal vector of the surface at the shape point is used. As a geometric reference, the tool rake angle and tool side tilt angle are introduced as attitude parameters into the process of determining the tool axis direction, making the tool axis direction a unit vector. It is obtained from "the result of the normal vector direction after two attitude rotations", thus making It corresponds one-to-one with the surface geometry of the shape value points and the tool posture, while maintaining the unitized constraints. This yields... Then, for the analytical triaxial cutting force vector at the same type value point... First, the axial force component along the tool axis is obtained through projection. ,in This represents the scalar projection of the three-dimensional cutting force along the tool axis. The axial force vector is expressed as a vector, and then the radial cutting force vector is obtained by removing the axial force vector from the total cutting force vector. The decomposition logic for "removing the axial component along the tool axis and obtaining the radial cutting force" is completed, and the radial cutting force is made consistent with the bending dominant load of the tool cantilever structure. Tool radial compliance is introduced. ,in This represents the radial displacement response coefficient of the tool under a unit radial load, determined by the tool structure parameters. Based on this, the radial deformation vector of the tool is obtained by multiplying the radial cutting force by the radial compliance of the tool. ,in Represents the radial equivalent displacement components of the tool in the three spatial directions and is related to The direction remains consistent. To convert the influence of tool radial deformation on the normal dimension of the model point into directly superimposed error components, the tool radial deformation vector is projected along the direction of the normal vector of the model point and a dot product operation is performed to obtain the second machining error component. ,make Geometrically, it represents the "equivalent deviation of the radial elastic offset of the tool in the normal direction of the curved surface" and ensures that the measurement definition of the second machining error component is consistent with that of the normal error of the shape point and can be combined with the normal error component of the workpiece end under the same projection reference.

[0029] Figure 7 This paper describes the spatial geometric relationship of radial deformation of a ball end mill with a large length-to-diameter ratio as a cantilever beam structure under cutting force, and the calculation process of the normal machining error component at the tool end obtained by projecting the radial deformation of the tool onto the normal vector direction of the shape point. The reference numerals in the figures include: WCS for workpiece coordinate system, MCS for machine coordinate system, u for surface cutting direction parameter, v for surface step direction parameter, P for shape point, np for surface normal vector direction at the shape point, nt for tool axis direction, F for resultant cutting force, Fr for radial cutting force, Fx for cutting force in the x-direction, Fy for cutting force in the y-direction, Fz for cutting force in the z-direction, tool label indicating ball end mill, and workpiece label indicating thin-walled curved surface part.

[0030] Figure 8 This is the standard geometric model of a ball end mill, comprising two parts: the circular arc cutting edge region and the side cutting edge region, as well as the definition of the position parameters of the infinitesimal point Q on the cutting edge. The reference numerals include: ZT is the direction of the tool coordinate system axis, n is the tool rotation direction, D is the tool diameter, H is the total height of the cutting edge, r is the tool radius, OT is the center of the tool bottom surface, XT is the x-axis of the tool coordinate system, YT is the y-axis of the tool coordinate system, φ is the radial position angle of the infinitesimal point Q, ψ0 is the radial angle of the cutting edge at axial position 0, κ is the axial contact angle of the infinitesimal point Q, Q is any infinitesimal point on the cutting edge, dFt is the tangential cutting force, dFr is the radial cutting force, dFa is the axial cutting force, and the cutting edge markings indicate the tool cutting edge curve.

[0031] Figure 9This diagram illustrates the relative positions of the tool coordinate system (TCS), workpiece coordinate system (WCS), and machining feed coordinate system (FCS) during five-axis milling, as well as the spatial geometric relationships of the ball end mill cutting the workpiece along the tool path. The reference numerals include: ZT for the tool coordinate system z-axis, XT for the tool coordinate system x-axis, YT for the tool coordinate system y-axis, OT for the origin of the tool coordinate system, ZW for the workpiece coordinate system z-axis, XW for the workpiece coordinate system x-axis, YW for the workpiece coordinate system y-axis, OW for the origin of the workpiece coordinate system, ZF for the machining feed coordinate system z-axis, XF for the machining feed coordinate system x-axis, YF for the machining feed coordinate system y-axis, OF for the origin of the machining feed coordinate system (i.e., the tool contact point), the ball end mill label indicating the tool used for machining, the workpiece label indicating the thin-walled curved surface to be machined, and the tool path label indicating the machining path curve.

[0032] Figure 10 This is a bar chart comparing the predicted and experimentally measured results of the maximum triaxial cutting force for the three test sets (Experiments 10 to 12) using the calibrated triaxial cutting force coefficients. The labels include: the vertical axis represents the maximum cutting force (in N), the horizontal axis represents the test set experiment number, the red bars represent the model predictions, the green bars represent the experimental measurements, 10-Fx, 10-Fy, and 10-Fz represent the maximum triaxial cutting force for Experiment 10, 11-Fx, 11-Fy, and 11-Fz represent the maximum triaxial cutting force for Experiment 11, and 12-Fx, 12-Fy, and 12-Fz represent the maximum triaxial cutting force for Experiment 12.

[0033] Figure 11 This document presents the complete workflow for calculating the compliance matrix of a thin-walled curved surface part using ABAQUS finite element simulation software combined with the birth and death element technique. The dashed box on the left represents the finite element simulation model establishment stage, and the dashed box on the right represents the execution stage of the birth and death element technique. The attached labels include: 3D modeling of the part is the first step of the workflow; defining material physical properties is the second step; meshing is the hexahedral element mesh generation step (mesh length E1=1mm, height Eh=0.6mm); defining boundary conditions is the fixed constraint setting step; element selection is the step of selecting cutting elements based on the machining strategy; dynamic loading of cutting load & dynamic removal of material are the core execution steps of the birth and death element technique; cutting end is node determination; automatic extraction of node displacement & calculation of node compliance is the step of automatically extracting node deformation and calculating the compliance matrix using Python. The finite element simulation model annotation indicates the workflow box on the left, and the birth and death element technique annotation indicates the workflow box on the right.

[0034] Figure 12This diagram shows the basic geometric dimensions of the workpiece blank used in the thin-walled titanium alloy milling experiment, as well as the distribution of six thin-walled curved surfaces on the rectangular blank. The reference numerals include: Z, Y, and X represent the three axes of the workpiece coordinate system; u represents the surface cutting feed direction; v represents the surface step direction; 0.89 mm represents the wall thickness at the thinnest point of the surface; 5.25 mm represents the total height of the workpiece; 34 mm represents the dimension of the surface along the v direction; 24 mm represents the dimension of the surface along the u direction; 120 mm represents the blank length; 60 mm represents the blank width; 10 mm represents the blank base height; and ① to ⑥ indicate the numbers of the six thin-walled curved surfaces.

[0035] Figure 13 This document describes the distribution of 48 model points on each thin-walled surface and the measurement path planning method during machine measurement. The measurement area ranges from u∈[0.0625, 0.9375] in the u direction and from v∈[0.2, 0.95] in the v direction. The reference numerals include: u is the surface cutting feed direction parameter, v is the surface step direction parameter, u=0.0625 is the left boundary of the measurement area in the u direction, u=0.9375 is the right boundary of the measurement area in the u direction, v=0.95 is the upper boundary of the measurement area in the v direction, v=0.2 is the lower boundary of the measurement area in the v direction, 1 to 48 are the measurement numbers of the 48 model points, and the arrows indicate the measurement path sequence from top to bottom (-v direction) and from right to left (-u direction).

[0036] In one example, a multi-source uncertainty error prediction model with five uncertainty calibration coefficients is constructed based on the first and second processing error components, including: The first machining error component is superimposed with the second machining error component, and the three components of the analytical three-dimensional cutting force (x, y, z) are respectively corrected by multiplicative calibration coefficients of three cutting contact areas to obtain the superimposed error term. Two wear multiplicative calibration coefficients are introduced for the amplitude coefficient and shape coefficient of the Sigmoid mapping function between tool wear and cutting length, respectively, to obtain the corrected tool wear Sigmoid function term; The modified tool wear Sigmoid function term is added to the superposition error term to obtain a multi-source uncertainty error prediction model containing five uncertainty calibration coefficients.

[0037] In this example, the first and second machining error components at the model value point are used as the deterministic error backbone and superimposed to form the reference error expression. Therefore, at the same model value point, the workpiece end normal error component and the tool end normal error component are added to obtain the basic form of the superimposed error term, and this basic form still maintains the geometric meaning of "the dimensional deviation after the displacement is projected along the normal vector direction of the model value point". At the same time, in order to incorporate the component-by-component influence of factors such as dynamic deviation of the cutting contact area, deformation springback and vibration on the analytical value of the cutting force into the same prediction model, three multiplicative calibration coefficients are introduced into the three components of the analytical three-dimensional cutting force and component-by-component correction is performed to make the original analytical three-dimensional cutting force vector Calibrated to F before entering each step of the error calculation chain. ,in , , Corresponding to the three-dimensional cutting forces in , , The multiplicative calibration coefficient of the directional contact area is used to absorb the directional deviation caused by the inconsistency between theoretical and actual contact, so that the workpiece end compliance response and tool end compliance response driven by the cutting force are uniformly calibrated at the load input level. Based on the calibrated three-dimensional cutting force vector, the workpiece end error path uses the workpiece compliance matrix as the basis. As a mapping from load to displacement and along the direction of the normal vector of the shape point. Projection, forming a superimposed item at the workpiece end. Furthermore, the radial compliance coefficient of the tool is used in the error path at the tool tip. Characterizes the radial deformation capability of the tool cantilever, and is achieved by removing the radial deformation along the tool axis from F. The axial component is used to obtain the radial component, that is, with The radial load vector of the tool is characterized, and then this radial load vector is converted into radial deformation using the tool radial compliance coefficient and projected along the normal vector direction of the shape value point to form the tool end superposition term. ] Thus, at the same model point, the superimposed error term after component-wise multiplicative calibration of the three-dimensional cutting force is obtained. The superimposed error term merges the workpiece end error and the tool end error under the same normal projection reference, and also incorporates the uncertainty of the cutting contact area. , , The load input layer is embedded with three parameters. To embed tool wear uncertainty into the error prediction model in a calibrable manner, a sigmoid mapping function between tool wear amount and cutting length is introduced while maintaining its functional structure, so that the tool wear error term is written as... ,in This is the amplitude coefficient and is used to characterize the upper limit of the magnitude of the wear error term. It is a shape factor and is used to adjust the steepness of the wear curve. This is a wear-driving variable related to the cutting length and used to characterize the evolution of wear as machining accumulates. To enable the Sigmoid mapping function to adapt to the differences in wear magnitude drift and evolution rate caused by different materials, working conditions, and tool batches, two wear multiplicative calibration coefficients are introduced for the amplitude coefficient and shape coefficient, respectively, and multiplicative corrections are performed. Revised to ,in This is a multiplicative calibration factor for the amplitude and is used to scale and calibrate the overall amplitude of the wear error term. The shape multiplicative calibration coefficient is used to scale and calibrate the wear evolution curve shape, thus the corrected tool wear Sigmoid function term is expressed as follows: The modified tool wear Sigmoid function term is added to the superimposed error term after component-wise multiplicative calibration of the cutting area to obtain the expression for the multi-source uncertainty error prediction model containing five uncertainty calibration coefficients. And make the model fully express as: ; in Used to characterize residual components of the wear term that are not captured by the Sigmoid principal term. Used to characterize the additional effects of process system uncertainties and other uncertainties on errors, , , , , The five uncertain calibration coefficients are respectively responsible for the functional division of triaxial load component calibration in the contact area and wear Sigmoid amplitude and shape calibration.

[0038] In one example, after performing five-axis milling on a thin-walled curved surface part, the measured machining error values ​​at each type value point are measured, and the calibration values ​​of five uncertain calibration coefficients are calculated, including: After performing five-axis milling on thin-walled curved parts, a machine measuring device is installed on the end of the machine tool spindle, and the actual coordinates of each type value point are measured sequentially along the normal direction of each type value point. The actual coordinates of each model point are subtracted from the theoretical coordinates of the corresponding model point and then projected onto the normal vector direction of the model point to obtain the measured value of the machining error of each model point. The calibration values ​​of five uncertain calibration coefficients are calculated based on the measured values ​​of processing errors and the multi-source uncertain error prediction model.

[0039] In this example, the in-machine measuring device is installed on the machine tool spindle end, and coordinate system alignment and probe calibration are completed to ensure that the spatial orientation of the measuring device is consistent with the machine tool coordinate system. Based on the spatial distribution sequence of the model points in the CNC program, the spindle is controlled to drive the probe to approach the workpiece surface point by point along the normal vector direction corresponding to each model point and perform contact testing. During the contact testing process, the actual spatial coordinate vector of each model point is recorded. ,in , , These represent the measured coordinate components of the model value point in the machine tool coordinate system, and simultaneously read the theoretical coordinate vector of the model value point. The theoretical coordinates are provided by the original design surface model or CNC tool position file and correspond one-to-one with the shape value points. After obtaining the measured coordinates and theoretical coordinates, the spatial deviation vector is obtained by calculating the coordinate difference. ,in The geometric offset of the type value point in three-dimensional space is represented by the spatial offset vector along the normal vector of the type value point. To ensure that the geometric offset is consistent with the definition of the normal error in the error prediction model, the spatial offset vector is aligned with the unit vector of the type value point normal vector. By projecting and performing a dot product operation, the measured values ​​of the machining error at the model value point are obtained. The dot product result geometrically represents the dimensional deviation of the actual machined surface relative to the theoretical surface along the normal direction. Therefore, the measured value of the machining error and the wheel output of the error prediction model are related. They are completely consistent in definition and can be directly used for parameter identification. The above measurement and projection process is repeated at multiple model value points to form a set of measured error data. subscript This indicates different model value point numbers, and simultaneously calculates the output value of the multi-source uncertainty error prediction model for the corresponding model value point based on the cutting parameters, tool posture, and cutting length variables under the same machining state. The predicted value consists of five uncertain calibration coefficients. The model expression is given. To solve for the calibration values ​​of the five uncertain calibration coefficients, a parameter identification problem based on the deviation between measured and predicted errors is constructed, and the least squares criterion is used to establish the objective function. The objective function is expressed as the sum of squared residuals at each type of error point, i.e., by minimizing... To achieve parameter estimation, the residual term... This represents the difference between the measured error and the model prediction error, reflecting the degree of deviation between the model and the actual processing state. By iteratively optimizing the five uncertain calibration coefficients and minimizing the sum of squared residuals, calibration values ​​for the five uncertain calibration coefficients are obtained, making the model output statistically approximate the measured processing error distribution.

[0040] In one example, calibration values ​​for five uncertain calibration coefficients are calculated based on measured machining errors and a multi-source uncertain error prediction model, including: Based on the cutting force mechanism model and the physical prior knowledge of tool wear, the initial values ​​of the five uncertain calibration coefficients are set as the initial state of the Markov chain, and the posterior probability density function is constructed by the difference between the measured value of the machining error at each type point and the predicted value of the multi-source uncertain error prediction model. Multidimensional Metropolis-Hastings iterative sampling of the posterior probability density function yields calibration values ​​for five uncertain calibration coefficients.

[0041] In this example, the reasonable range and initial estimate of the parameters are determined by combining the physical prior knowledge provided by the cutting force mechanism model and the tool wear evolution law, and the initial values ​​of the five uncertain calibration coefficients are used to construct the initial state of the Markov chain. ,in These correspond to the multiplicative calibration coefficients of the three components of the analytical triaxial cutting force. These correspond to the multiplicative calibration coefficients of the amplitude coefficient and shape coefficient in the wear sigmoid function, respectively. The initial values ​​should satisfy fundamental constraints such as no sign reversal during cutting force scaling and no non-physical divergence in the wear term amplitude, thus ensuring the Markov chain starts within the physically feasible region. The measured machining error values ​​at each type point are then obtained. Then, the predicted values ​​of the corresponding type points are calculated using a multi-source uncertainty error prediction model containing five uncertain calibration coefficients. And construct a parameter vector based on the difference between the measured and predicted values. The posterior probability density function is expressed as follows, where the posterior density function is expressed as follows: By combining the likelihood term with the prior term, both the "degree of matching between model prediction and measured error" and the "physical feasibility of parameters" are simultaneously included in the probability weight calculation. When entering the multidimensional Metropolis-Hastings iteration stage, at the... In the next iteration, the current state of the Markov chain is known to be... Each component is sampled tentatively according to the conditional sampling structure to form candidate vectors. Then, according to the acceptance rate formula Calculate the probability that a candidate state is accepted, where Then sample from a uniform distribution And and When comparing, Accept the new state and make Otherwise, maintain the original state. By iteratively forming a Markov chain sample sequence that conforms to the posterior distribution, and finally after reaching the preset number of iterations and removing the initial samples, the calibration values ​​of the five uncertain calibration coefficients can be obtained by statistically summarizing the remaining samples.

[0042] Figure 14 This is a comparison curve of the pure mechanistic model predictions and experimental measurements of the machining errors at various points on thin-walled curved surfaces under 18 different working conditions. The figure labels include: the vertical axis represents the machining error (unit: μm), the horizontal axis represents the point number (0 to 864), the green curve represents the experimental measurement value, the red curve represents the mechanistic model prediction value, surfaces 1 to 18 are labeled with the corresponding surface intervals for the 18 machining experiments, and the vertical dashed lines are the boundaries between the surfaces.

[0043] Figure 15 In the simulation experiment design for the cutting force proxy model, the gridded distribution method and point numbering rules of the sample points on the curved surface are shown. The left figure is a schematic diagram of the grid under the uv parameter coordinate system, and the right figure is the corresponding point numbering distribution. The attached figures include: u is the surface cutting feed direction parameter, v is the surface step direction parameter, i is the row index of u direction (i=1 to m), j is the column index of v direction (j=1 to n), m=8 is the number of points in u direction, n=6 is the number of points in v direction, Pi,j is the model value point in the i-th row and j-th column, and 1 to 48 are the sequential numbers of the 48 model value points.

[0044] In one example, multidimensional Metropolis-Hastings iterative sampling of the posterior probability density function yields calibration values ​​for five uncertain calibration coefficients, including: Multidimensional Metropolis-Hastings iterative sampling is performed on the posterior probability density function, and five candidate states with uncertain calibration coefficients are generated in each iteration. The candidate states are substituted into the multi-source uncertain error prediction model, and the acceptance rate is calculated by the ratio of the posterior probability corresponding to the candidate state to that of the current state. Random numbers are sampled from a uniform distribution and compared with the acceptance rate. If the random number is less than the acceptance rate, the current state of the Markov chain is replaced by a candidate state. Otherwise, the current state of the Markov chain is kept unchanged. After multiple iterations of sampling, the median of the posterior distribution samples of each uncertain calibration coefficient is taken as the calibration value of the five uncertain calibration coefficients.

[0045] In this example, the five uncertain calibration coefficients are constructed into the Markov chain state vector and in the... In the next iteration, it is denoted as Subsequently, in the same iteration, five candidate states with uncertain calibration coefficients are generated according to the candidate generation mechanism and denoted as... The generation of candidate states can employ conditional sampling to allow each component to obtain trial values ​​given the remaining components, thereby making it easier for the candidate states to fall within the physically feasible region and increasing the effective sampling ratio. After obtaining the candidate states, they are substituted into the multi-source uncertainty error prediction model, and the prediction error set corresponding to the measured processing error values ​​of each type of value point is calculated to form the posterior probability density function value of the candidate state. Simultaneously, the current state is also substituted into the multi-source uncertainty error prediction model, and the posterior probability density function value under the current state is calculated. Based on this, the acceptance rate is calculated according to the acceptance rate formula of the sampling algorithm. ,in Depend on This approach unifies the principles that "the smaller the difference between the measured error and the predicted error, the greater the likelihood" and "the more the parameters conform to the physical prior, the greater the prior probability" into the posterior probability calculation. After calculating the acceptance rate, random numbers are sampled from a uniform distribution and denoted as... Then compare the random number with the acceptance rate. The Markov chain accepts a candidate state and replaces the current state of the Markov chain with the candidate state, thereby making... and make Synchronously update to candidate values, and when When a candidate state is rejected and the current state of the Markov chain is kept unchanged, the state of the Markov chain is thus made to... This allows for a higher frequency of access to high posterior regions during the iteration process, resulting in a sample sequence that is statistically consistent with the target posterior distribution. As the number of iterations increases and after discarding the sample segments used to eliminate the influence of the initial state in the early stages, the posterior distribution samples of each uncertain calibration coefficient obtained in subsequent iterations are statistically summarized, and the median of each uncertain calibration coefficient sample sequence is taken as the calibration value of that uncertain calibration coefficient, resulting in a set of calibration values ​​for five uncertain calibration coefficients.

[0046] In one example, the calibration values ​​of five uncertain calibration coefficients are substituted into the multi-source uncertain error prediction model to obtain the predicted processing error values ​​for each type of value point, including: The machining parameter feature vectors of each type of value point are input into the Gaussian process regression proxy model of cutting force and the Gaussian process regression proxy model of workpiece compliance, respectively, and the proxy triaxial cutting force and proxy compliance matrix corresponding to each type of value point are calculated. The analytical triaxial cutting force and workpiece compliance matrix in the multi-source uncertain error prediction model are replaced by surrogate triaxial cutting force and surrogate compliance matrix. The calibration values ​​of the five uncertain calibration coefficients are substituted into the corresponding multiplicative calibration coefficients of the contact area and wear multiplicative calibration coefficients in the multi-source uncertain error prediction model to obtain the predicted machining error values ​​of each type point.

[0047] In this example, a machining parameter feature vector is constructed for each form point, ensuring that the meaning of the machining parameter feature vector is consistent with the variable meaning used in the cutting force mechanism calculation stage. This ensures that the machining parameter feature vector covers feature components such as tool attitude, feed rate, spindle speed, depth of cut, width of cut, cutting position, and geometric quantities related to the spatial position of the form point. Then, the machining parameter feature vectors for each form point are input into the cutting force Gaussian process regression surrogate model and the workpiece compliance Gaussian process regression surrogate model, respectively. This outputs the surrogate three-dimensional cutting force components corresponding to the form point from the cutting force surrogate model side. The proxy flexibility matrix corresponding to the type value point is output on the flexibility proxy model side. The surrogate triaxial cutting force is used to characterize the triaxial load result that should be obtained from the analytical cutting force calculation under the same machining parameter eigenvector conditions, and the surrogate compliance matrix is ​​used to characterize the directional coupling compliance relationship that should be obtained from the finite element compliance solution under the same machining parameter eigenvector conditions. The surrogate triaxial cutting force and the surrogate compliance matrix replace the analytical triaxial cutting force and the workpiece compliance matrix in the multi-source uncertainty error prediction model, and the calibration values ​​of the five uncertainty calibration coefficients are substituted into the multiplicative calibration coefficients of the cutting contact area and the wear multiplicative calibration coefficients, respectively, so that the triaxial cutting force entry first follows... Complete the component-by-component multiplicative correction, while the wear parameter input is according to... The amplitude coefficients will be completed, and for each model point, the three-dimensional cutting force, compliance matrix, and tool axis unit vector will be generated. Type value point normal vector unit vector With the radial compliance coefficient of the tool The common input error prediction solution link is used to solve the model point processing error prediction value under the same normal projection reference according to the overall model expression. The contribution of elastic deformation at the workpiece end to the normal error is characterized by the Sigmoid term. and the models that are retained , The items are synthesized to obtain the predicted machining error value for each model value point. Since the cutting force Gaussian process regression surrogate model and the workpiece compliance Gaussian process regression surrogate model are directly driven by the feature vector of the machining parameters and output load and compliance results with the same semantics as the analytical solution, the multi-source uncertainty error prediction model completes the accelerated solution of "surrogate quantity replacing analytical quantity" while keeping the formula structure unchanged. In addition, the calibration values ​​of the five uncertainty calibration coefficients take effect simultaneously at the force inlet and wear inlet, so that the prediction results have the advantages of mechanism consistency, parameter calibrability and computational efficiency.

[0048] Figure 16This figure shows the distribution of 200 initial hyperparameters in three-dimensional logarithmic space when using a grid search strategy to optimize the hyperparameters of a Gaussian process regression model. The figure labels include: lnσn (logarithmic noise variance, ordinate), l (length coefficient, abscissa), lnσf (logarithmic Gaussian process variance, depth coordinate), red, green, and blue dots representing hyperparameter sampling points under different initial value groups, and the three-dimensional grid distribution demonstrating the uniform coverage of the parameter space by Latin hypercube sampling.

[0049] Figure 17 This figure shows the convergence curve of the root mean square error (RMSE) during 200 hyperparameter optimization iterations for Gaussian process regression surrogate modeling of the Fy cutting force component, as well as the final optimal hyperparameter combination. The figure labels include: ordinate for RMSE (root mean square error), abscissa for the number of iterations (0 to 200), the RMSE curve representing the convergence of RMSE with the number of iterations, and the optimal hyperparameters labeled as r=3 / 2, sf=0.43, l=23.31, sn=0.01. Red dots mark the minimum RMSE convergence points corresponding to the optimal hyperparameters.

[0050] Figure 18 This is a scatter plot comparing the predicted and theoretical values ​​of the Gaussian process regression cutting force surrogate model on the training and test datasets to verify the prediction accuracy of the surrogate model. The labels include: the vertical axis represents the predicted value (in N), the horizontal axis represents the theoretical value (in N), the black solid line is the reference line (predicted value equals theoretical value), the red dashed line is the upper deviation line, the black dashed line is the lower deviation line, the blue solid dots are the sample points in the training dataset, and the green solid dots are the sample points in the test dataset.

[0051] Figure 19 This figure illustrates the distribution of the predicted compliance (cyy) values ​​for each type point under four different machining allowances (0.10 mm, 0.16 mm, 0.22 mm, and 0.28 mm) using a Gaussian process regression surrogate model for workpiece compliance. It reflects the spatial distribution characteristics of compliance as a function of the type point location and machining allowance. The figure labels include: the vertical axis represents compliance (unit: μm / N), the horizontal axis represents the point number (numbers 1 to 48 for each allowance), the red solid dots represent the surrogate model predicted compliance values ​​for each type point, and the blue vertical dashed lines represent the boundaries between the four machining allowances. The allowance levels for the four data segments are labeled for 0.10 mm, 0.16 mm, 0.22 mm, and 0.28 mm.

[0052] In one example, the feature vectors of the machining parameters for each type of value point are input into the Gaussian process regression surrogate model for cutting force and the Gaussian process regression surrogate model for workpiece compliance, respectively, to calculate the surrogate triaxial cutting force and surrogate compliance matrix corresponding to each type of value point, including: The machining allowance, feed per tooth, cutting speed, rake angle, side rake angle, and surface position parameters of each type value point are used to construct a feature vector of machining parameters; The feature vector of the machining parameters is input into the Gaussian process regression surrogate model of the cutting force constructed with the Matern kernel function, and the surrogate triaxial cutting force corresponding to each type of value point is calculated. The compliance input feature vector, composed of the machining allowance and surface position parameters of each type of value point, is input into the workpiece compliance Gaussian process regression surrogate model constructed with the Matern kernel function, and the surrogate compliance matrix corresponding to each type of value point is calculated.

[0053] In this example, the machining allowance at the form point, feed per tooth, cutting speed, tool rake angle, tool side rake angle, and surface position parameters are combined into an input vector. ,in for The system uses a multidimensional input vector to simultaneously characterize the combined effects of factors such as material removal intensity, tool orientation, and point geometry on the cutting response. The feature vector of machining parameters is input into the Gaussian process regression surrogate model of the cutting force, and the standard expression form of Gaussian process regression is used. Establish a mapping relationship from input to output, where This represents the observations output by the proxy model. Represents a mapping function. Represents the weight vector. Represent the Gaussian noise term and satisfy the following conditions: Meanwhile, the mapping function is treated as a Gaussian process. This allows us to describe the correlation between samples using the mean function and the covariance function. To ensure the covariance structure can adapt to the smoothness and local variation characteristics of engineering data, the Matern kernel function is chosen as the covariance function and written as follows: ,in For signal variance, For smoothing parameters, For length scale, For sample distance, For gamma function, The second type of modified Bessel function is used, so that the similarity between input feature vectors is determined by the kernel function and drives the surrogate prediction output. The three identical cutting force components are used as surrogate outputs to form three regression output channels, thus ensuring similarity between the input vectors. At that time, they obtained agents respectively ,acting With Agent This ensures that the three-dimensional output and the analytical three-dimensional cutting force components remain consistent in meaning and scale. Simultaneously, to construct a Gaussian process regression surrogate model for workpiece compliance, a compliance input feature vector is established for compliance prediction, highlighting the factors most sensitive to changes in structural stiffness. Therefore, the machining allowance and surface position parameters of each shape point are combined into a compliance input vector and input into a Gaussian process regression model that also uses the Matern kernel function as the covariance function. This yields the surrogate compliance matrix corresponding to the shape point without finite element analysis. Since the compliance matrix contains directional coupling elements, the independent elements of the compliance matrix are used as regression outputs, and matrix reconstruction is performed at the output end to obtain a surrogate compliance matrix with the same dimension and clear physical meaning as the original compliance matrix. This allows each shape point to directly obtain the surrogate three-dimensional cutting force and the surrogate compliance matrix from the input vector.

[0054] Reference Figure 20 This embodiment provides a part machining error modeling and calibration system based on multi-source uncertainty, including: Mechanism modeling module 1 is used to calculate the first machining error component by analyzing the triaxial cutting force and the workpiece compliance matrix, and to calculate the second machining error component by analyzing the triaxial cutting force and the tool radial compliance. Model improvement module 2 is used to construct a multi-source uncertainty error prediction model with five uncertainty calibration coefficients based on the first processing error component and the second processing error component; The coefficient calibration module 3 is used to measure the actual machining error of each type point and calculate the calibration value of five uncertain calibration coefficients after five-axis milling of thin-walled curved parts. Error prediction module 4 is used to substitute the calibration values ​​of the five uncertain calibration coefficients into the multi-source uncertain error prediction model to solve for the predicted processing error values ​​of each type of value point.

[0055] In this embodiment, the specific implementation of each unit in the above system embodiment is described in the above method embodiment, and will not be repeated here.

[0056] It should be noted that, in this document, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, system, article, or method that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, system, article, or method. Unless otherwise specified, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, system, article, or method that includes that element.

[0057] The above description is merely a preferred embodiment of the present invention and does not limit the patent scope of the present invention. Any equivalent structural or procedural transformations made based on the content of the present invention's specification and drawings, or direct or indirect applications in other related technical fields, are similarly included within the patent protection scope of the present invention.

Claims

1. A method for modeling and calibrating part machining errors based on multi-source uncertainty, characterized in that, include: The first machining error component is calculated by analyzing the triaxial cutting force and the workpiece compliance matrix, and the second machining error component is calculated by analyzing the triaxial cutting force and the tool radial compliance. A multi-source uncertainty error prediction model with five uncertain calibration coefficients is constructed based on the first processing error component and the second processing error component. After performing five-axis milling on the thin-walled curved surface part, the measured values ​​of the machining error at each type value point are measured and the calibration values ​​of the five uncertain calibration coefficients are calculated. Substitute the calibration values ​​of the five uncertain calibration coefficients into the multi-source uncertain error prediction model to obtain the predicted processing error values ​​for each type of value point.

2. The method for modeling and calibrating part machining errors based on multi-source uncertainty according to claim 1, characterized in that, The first machining error component is calculated by analyzing the triaxial cutting force and the workpiece compliance matrix, and the second machining error component is calculated by analyzing the triaxial cutting force and the tool radial compliance matrix, including: The analytical triaxial cutting force and the workpiece compliance matrix are multiplied together to obtain the triaxial deformation vector at the shape value point. The first machining error component is obtained by multiplying the three-dimensional deformation vector with the normal vector of the shape value point. The second machining error component is obtained by multiplying the radial component of the analytical triaxial cutting force with the radial compliance of the tool and projecting it onto the normal vector direction of the back profile point.

3. The method for modeling and calibrating part machining errors based on multi-source uncertainty according to claim 2, characterized in that, The second machining error component is obtained by multiplying the radial component of the analytical triaxial cutting force by the tool radial compliance and projecting it back along the normal vector direction of the model value point, including: The tool axis direction is calculated based on the normal vector direction of the model value point, the tool rake angle, and the tool side tilt angle. The axial component along the tool axis direction is removed from the analytical triaxial cutting force to obtain the tool radial cutting force. Multiply the radial cutting force of the tool by the radial compliance of the tool to obtain the radial deformation vector of the tool. Then, multiply the radial deformation vector of the tool by the normal vector of the shape value point to obtain the second machining error component.

4. The method for modeling and calibrating part machining errors based on multi-source uncertainty according to claim 1, characterized in that, A multi-source uncertainty error prediction model with five uncertainty calibration coefficients is constructed based on the first processing error component and the second processing error component, including: The first machining error component is superimposed with the second machining error component, and the three components of the analytical triaxial cutting force (x, y, z) are respectively corrected by introducing three multiplicative calibration coefficients of the three cutting contact areas to obtain the superimposed error term. Two wear multiplicative calibration coefficients are introduced for the amplitude coefficient and shape coefficient of the Sigmoid mapping function between tool wear and cutting length, respectively, to obtain the corrected tool wear Sigmoid function term; The modified tool wear Sigmoid function term is added to the superposition error term to obtain a multi-source uncertainty error prediction model containing five uncertainty calibration coefficients.

5. The method for modeling and calibrating part machining errors based on multi-source uncertainty according to claim 4, characterized in that, After performing five-axis milling on a thin-walled curved surface part, the measured values ​​of machining errors at each type value point are measured, and the calibration values ​​of the five uncertain calibration coefficients are calculated, including: After performing five-axis milling on thin-walled curved parts, a machine measuring device is installed on the end of the machine tool spindle, and the actual coordinates of each type value point are measured sequentially along the normal direction of each type value point. The actual coordinates of each model point are subtracted from the theoretical coordinates of the corresponding model point and then projected onto the normal vector direction of the model point to obtain the measured value of the machining error of each model point. The calibration values ​​of the five uncertain calibration coefficients are calculated based on the measured values ​​of the processing error and the multi-source uncertain error prediction model.

6. The method for modeling and calibrating part machining errors based on multi-source uncertainty according to claim 5, characterized in that, The calibration values ​​of the five uncertain calibration coefficients are calculated based on the measured values ​​of the processing errors and the multi-source uncertain error prediction model, including: Based on the cutting force mechanism model and the physical prior knowledge of tool wear, the initial values ​​of the five uncertain calibration coefficients are set as the initial state of the Markov chain, and the posterior probability density function is constructed by the difference between the measured value of the machining error at each type point and the predicted value of the multi-source uncertain error prediction model. The posterior probability density function is subjected to multidimensional Metropolis-Hastings iterative sampling to obtain the calibration values ​​of the five uncertain calibration coefficients.

7. The method for modeling and calibrating part machining errors based on multi-source uncertainty according to claim 6, characterized in that, Multidimensional Metropolis-Hastings iterative sampling is performed on the posterior probability density function to obtain the calibration values ​​of the five uncertain calibration coefficients, including: Multidimensional Metropolis-Hastings iterative sampling is performed on the posterior probability density function, and in each iteration, candidate states of the five uncertain calibration coefficients are generated. The candidate states are substituted into the multi-source uncertain error prediction model, and the acceptance rate is calculated by the ratio of the posterior probability corresponding to the candidate state to the current state. Random numbers are sampled from a uniform distribution and compared with the acceptance rate. If the random number is less than the acceptance rate, the current state of the Markov chain is replaced by the candidate state. Otherwise, the current state of the Markov chain remains unchanged. After multiple iterations of sampling, the median of the posterior distribution samples of each uncertain calibration coefficient is taken as the calibration value of the five uncertain calibration coefficients.

8. The method for modeling and calibrating part machining errors based on multi-source uncertainty according to claim 7, characterized in that, Substituting the calibration values ​​of the five uncertain calibration coefficients into the multi-source uncertain error prediction model, the predicted processing error values ​​for each type of value point are obtained, including: The machining parameter feature vectors of each type of value point are input into the Gaussian process regression proxy model of cutting force and the Gaussian process regression proxy model of workpiece compliance, respectively, and the proxy triaxial cutting force and proxy compliance matrix corresponding to each type of value point are calculated. The analytical triaxial cutting force and the workpiece compliance matrix in the multi-source uncertain error prediction model are replaced by the proxy triaxial cutting force and the proxy compliance matrix. The calibration values ​​of the five uncertain calibration coefficients are substituted into the corresponding multiplicative calibration coefficients of the contact area and the wear multiplicative calibration coefficients in the multi-source uncertain error prediction model to obtain the machining error prediction values ​​of each type point.

9. The method for modeling and calibrating part machining errors based on multi-source uncertainty according to claim 8, characterized in that, The eigenvectors of the machining parameters for each type of value point are input into the Gaussian process regression surrogate model for cutting force and the Gaussian process regression surrogate model for workpiece compliance, respectively, to calculate the surrogate triaxial cutting force and surrogate compliance matrix corresponding to each type of value point, including: The machining allowance, feed per tooth, cutting speed, rake angle, side rake angle, and surface position parameters of each type value point are used to construct a feature vector of machining parameters; The feature vector of the machining parameters is input into the Gaussian process regression proxy model of the cutting force constructed with the Matern kernel function to calculate the proxy triaxial cutting force corresponding to each type of value point; The compliance input feature vector, composed of the machining allowance and surface position parameters of each type of value point, is input into the workpiece compliance Gaussian process regression surrogate model constructed with the Matern kernel function, and the surrogate compliance matrix corresponding to each type of value point is calculated.

10. A part machining error modeling and calibration system based on multi-source uncertainty, characterized in that, The steps for implementing the part machining error modeling and calibration method based on multi-source uncertainty as described in any one of claims 1 to 9 include: The mechanism modeling module is used to calculate the first machining error component by analyzing the triaxial cutting force and the workpiece compliance matrix, and to calculate the second machining error component by analyzing the triaxial cutting force and the tool radial compliance. The model improvement module is used to construct a multi-source uncertainty error prediction model containing five uncertainty calibration coefficients based on the first processing error component and the second processing error component. The coefficient calibration module is used to measure the measured values ​​of machining errors at various point values ​​and calculate the calibration values ​​of the five uncertain calibration coefficients after five-axis milling of thin-walled curved parts. The error prediction module is used to substitute the calibration values ​​of the five uncertain calibration coefficients into the multi-source uncertain error prediction model to solve for the predicted processing error values ​​of each type of value point.

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