A z-map milling surface simulation method based on elastic-plastic deformation determination

Abstract

The application discloses a kind of Z-map milling surface simulation methods based on elastic-plastic deformation determination, the method is as follows: S1: the geometric model of workpiece and tool is established, and workpiece surface is dispersed into Z-map, determines tool geometric parameter and cutting path;S2: according to tool trajectory, the removal depth of each grid point is calculated, and the surface topography of geometric level is formed;S3: weight function is constructed on the two sides of tool, and the plastic side flow correction amount is calculated;S4: superimposed plastic side flow correction term, obtain the surface height after correction;S5: calculate elastic recovery correction term;S6: the updated Z-map surface is subjected to elastic recovery compensation, and the final surface topography is obtained;S7: establish elastic-plastic residual height analytical model;S8: output the surface height matrix after correction.The application can realize the high-precision, physical consistency prediction of material real removal mechanism and residual surface topography in single-blade straight blade milling cutter ultra-precision milling process.

Description

Technical Field

[0001] This invention belongs to the field of ultra-precision machining and surface morphology modeling technology, and relates to a Z-map surface morphology prediction method, specifically an improved Z-map milling surface morphology simulation method that combines elastoplastic deformation mechanism. Background Technology

[0002] Ultra-precision milling is widely used in the precision manufacturing of optical molds, microstructured functional surfaces, and high-end devices. In this type of machining, single-edged or few-edged tools remove material with extremely small depths of cut and tiny feeds on high-rigidity machine tools. The surface morphology is typically determined by the tool geometry, tool path, dynamic response of the machine tool-fixture-workpiece system, and the elasto-plastic behavior of the material under high stress and high strain rate. Unlike conventional models, when the depth of cut / feed rate is comparable to (or even smaller than) the material grain size, the material exhibits significant local yielding, extrusion displacement, and unloading springback, which have a non-negligible impact on the final residual height, directional texture, and roughness.

[0003] To achieve rapid prediction of surface morphology during process design, parameter optimization, and CAM path generation, the Z-map method, based on geometric mapping, is widely adopted in industry and academia. This type of method discretizes the workpiece into a height array sampled along the normal direction, and performs geometric calculations for material removal by intercepting / updating each grid point based on tool geometry and path. It has advantages such as simplicity, high computational efficiency, and ease of integration with CAM, and has become the mainstream method in macroscopic and conventional simulations. However, the basic assumptions of the traditional Z-map method are "rigid geometric contact between the tool and the workpiece" and "ideal material removal." In ultra-precision and micro-scale cutting scenarios, this assumption faces the following limitations: First, plastic side-flow cannot be represented. When the depth of cut is comparable to the grain size, the material undergoes lateral accumulation (plasticside-flow) under the combined stress state of normal and tangential directions under the extrusion and friction of the cutting edge. This changes the geometric residual relationship between adjacent toolpaths, leading to a systematic deviation of the geometric model in terms of ripple amplitude and peak-valley morphology. Second, elastic recovery is not modeled. After the tool leaves, the release of local stress causes surface micro-springback (elastic recovery), which is more pronounced in tough materials and under conditions of small depth of cut and low undeformed chip thickness. The geometric update does not include this mechanism and often underestimates the residual height.

[0004] Therefore, the technical challenge in this field is to introduce interpretable elastoplastic mechanism corrections while maintaining the high efficiency of Z-map, so as to achieve rapid and reliable prediction of the morphology of microscale cut surfaces.

[0005] Current simulation modeling methods exist for predicting the surface morphology of ultra-precision milled surfaces. These methods can numerically simulate the residual morphology of workpiece surfaces and evaluate roughness under different machining parameters and toolpaths, making them particularly suitable for fields such as optical mold processing, microstructure part manufacturing, and multi-axis ultra-precision machining. The key performance indicators for these simulation models are prediction accuracy and physical consistency, reflecting the model's ability to fit and reproduce the real machined surface under different material and process conditions.

[0006] CN120470798A discloses a method, system, terminal, and storage medium for modeling the surface morphology and predicting the surface roughness of longitudinal-torsional ultrasonic milling based on the Z-map method. This longitudinal-torsional composite ultrasonic milling surface morphology modeling method solves the problem that the traditional Z-map model cannot describe the nonlinear correspondence between the composite vibration trajectory of the tool and the machined surface. By introducing the longitudinal-torsional vibration model and the tool eccentricity correction mechanism into the geometric simulation, the simulation's prediction accuracy and scalability of the real surface texture are improved, thereby enhancing the applicability of the model in ultrasonic-assisted ultra-precision machining scenarios.

[0007] CN116275220A discloses a method for predicting surface texture in five-axis ball end milling. This method solves the problem that traditional static models cannot accurately reflect the influence of tool posture changes on surface texture in five-axis machining by superimposing spindle vibration and multi-axis attitude errors in a Z-map geometric modeling framework, thus realizing the prediction and visualization of surface texture for complex curved surfaces. However, this method is still mainly based on geometric contact and motion trajectory analysis, and does not consider the plastic flow and elastic rebound effect of workpiece material under high stress-high strain conditions. Therefore, the prediction of residual bulges, lateral accumulation, and elastic recovery morphology generated in micro-scale cutting still has limitations.

[0008] In ultra-precision machining, with the ever-increasing requirements for machining accuracy and surface quality, traditional geometric modeling methods are no longer sufficient to accurately describe the true deformation behavior of materials during micro-scale cutting. Especially under conditions of minute cutting depths and extremely small feed rates, the workpiece material undergoes both elastic deformation and plastic flow simultaneously under the high stress and friction of the tool edge. While traditional Z-map surface morphology prediction methods based on the principle of geometric superposition have advantages such as high computational efficiency and simple modeling, they treat the workpiece as an ideal rigid body and only consider the geometric removal relationship between the tool path and the workpiece surface, failing to reflect the elastoplastic response characteristics of the material during cutting.

[0009] To address the aforementioned issues, it is necessary to introduce modeling of the material's elastoplastic deformation behavior while maintaining the efficient geometric update characteristics of the Z-map model, so that the simulation results can balance computational efficiency and physical accuracy. Summary of the Invention

[0010] The purpose of this invention is to provide a Z-map simulation method for milling surfaces based on elastoplastic deformation determination, enabling high-precision, physically consistent prediction of the actual material removal mechanism and residual surface morphology during ultra-precision milling with a single-flute straight-edged end mill. This overcomes the shortcomings of existing models, such as insufficient simulation accuracy and lack of physical mechanisms at the microscale. Based on the traditional Z-map framework, this invention introduces modeling extensions for plastic lateral flow and elastic recovery. This model can more realistically simulate the generation and evolution of surface morphology in ultra-precision milling, and is particularly suitable for predicting and analyzing residual height distribution and surface roughness in ultra-precision machining.

[0011] The objective of this invention is achieved through the following technical solution:

[0012] A Z-map simulation method for milled surfaces based on elastoplastic deformation determination includes the following steps:

[0013] Step S1: Establish the geometric model of the workpiece and the tool, and discretize the workpiece surface into a two-dimensional regular height matrix Z-map to determine the tool geometric parameters and cutting path;

[0014] Step S2: Perform geometric contact judgment, calculate the removal depth of each mesh point based on the tool path, obtain the initial Z-map update result, and form the surface morphology at the geometric level;

[0015] Step S3: Define the radius of influence of plastic sideflow And construct weight functions on both sides of the tool. , , The distance from the node to the tool contact center is used to simulate the lateral flow and accumulation behavior of the material, and the plastic lateral flow correction is calculated. ;

[0016] Step S4: After each Z-map update, a plastic sideflow correction term is superimposed to simulate material accumulation on both sides of the tool, thereby obtaining the corrected surface height. ;

[0017] Step S5: Based on the material's elastic modulus Cutting stress Calculate the elastic recovery correction term This is used to describe the springback phenomenon of material after the tool leaves the tool;

[0018] Step S6: Apply elastic recovery compensation to the updated Z-map surface to obtain the final surface morphology. ;

[0019] Step S7: Establish an analytical model of the elastic-plastic residual height for the infeed side region. It is used to quantitatively predict surface bulges caused by material deformation, among which The height increase is caused by material buildup on the infeed side and plastic reflow. Brinell hardness of the material radius of the blade tip arc Cutting stress Normal load on the feed side and equivalent modulus related; This is an empirical correction factor;

[0020] Step S8: Output the corrected surface height matrix and perform statistical analysis and visualization of the residual morphology and surface roughness under different cutting parameter combinations.

[0021] Compared with the prior art, the present invention has the following advantages:

[0022] 1. This invention employs a micro-scale cutting simulation method on ultra-precision machine tools to verify and apply Z-map milling surface morphology modeling that considers elastoplastic deformation effects. Based on the traditional Z-map geometric simulation framework, this method introduces a material elastoplastic deformation mechanism to achieve high-fidelity reproduction of the actual material removal behavior during ultra-precision milling. By establishing a plastic lateral flow model and an elastic recovery correction model in the simulation process, Z-map simulation can simultaneously reflect the geometric and mechanical effects under the tool-workpiece interaction, effectively describing the material compression and springback phenomena on both sides of the tool cutting edge. This results in a surface morphology that more closely approximates actual machining, providing a more physically consistent modeling framework for high-fidelity prediction of micro-scale cutting surface morphology.

[0023] 2. This invention can rapidly obtain the morphology of three-dimensional machined surfaces, including the effects of elastoplastic deformation, without introducing complex finite element solutions. Compared with traditional pure geometric Z-map models, this invention can significantly improve the physical consistency and prediction accuracy of Z-map models for microscale cutting surface morphology without increasing the overall mechanical solution. It can quantitatively analyze the influence of machining parameters, material properties, and tool characteristics on surface residual height and roughness, and is applicable to scenarios such as optical molds, microstructured parts, and multi-axis ultra-precision machining, providing a reliable theoretical basis and simulation tool for ultra-precision machining process optimization and surface quality control.

[0024] 3. This invention can introduce the plastic lateral flow and elastic recovery effect of materials on the basis of traditional Z-map geometric modeling, and realize the serial modeling process of "geometric update - lateral flow accumulation - springback compensation" in the Z-map update stage. It significantly improves the physical realism and prediction accuracy of the model in ultra-precision and micro-scale cutting scenarios, and provides new theoretical basis and simulation tools for the morphology evolution and residual height control of complex machined surfaces.

[0025] 4. This invention is applicable to different tool structures (including straight cutting edges, circular cutting edges, and composite cutting edges) and multi-axis machining paths. It can automatically generate simulation models by inputting tool geometry parameters; it can also generate models based on material properties (material elastic modulus). Brinell hardness of materials Cutting stress It automatically selects the corresponding empirical functions and correction parameters to achieve cross-material simulation prediction; it supports batch calculation of multiple parameters and visualization of simulation results, and can perform sensitivity analysis on the influence of process parameters such as feed rate, depth of cut, and spindle speed on surface morphology; simulation results can be output as Z-map height matrix or point cloud data for subsequent surface roughness calculation, directional texture analysis, and process optimization; it can achieve an approximate description of the elastoplastic deformation of microscale cutting surfaces without introducing full-field finite element calculations, maintaining high computational efficiency; it can be used in conjunction with an ultra-precision machining experimental platform to verify the model accuracy by comparing with measured surface morphologies, and to adjust empirical correction coefficients. Empirical constants , radius of influence of plastic lateral force Perform reverse optimization and calibration. Attached Figure Description

[0026] Figure 1 Simulation flowchart for single-pass Z-map marking of a single-edge straight-edge end mill;

[0027] Figure 2 This is a schematic diagram of the cutting edge of the tool;

[0028] Figure 3 This is a schematic diagram of a single-pass milling trajectory.

[0029] Figure 4 This is a schematic diagram of the region affected by elastic-plastic deformation. Detailed Implementation

[0030] The technical solution of the present invention will be further described below with reference to the accompanying drawings, but it is not limited thereto. Any modifications or equivalent substitutions to the technical solution of the present invention that do not depart from the spirit and scope of the technical solution of the present invention should be covered within the protection scope of the present invention.

[0031] This invention provides a Z-map milling surface simulation method based on elastoplastic deformation determination. First, an initial Z-map height matrix of the workpiece surface is constructed according to tool geometry parameters and cutting path. Then, in each tool feed step, the lateral influence radius is defined, and the accumulation caused by plastic lateral flow is calculated using a weighting function. After geometric removal, an elastic recovery correction term is calculated based on the material's elastic modulus, cutting stress, and feed rate to compensate for springback in the machined area. Finally, combined with an analytical model of the elastoplastic residual height on the infeed side, the surface micro-protrusions and residual morphology are corrected and predicted. Figure 1 As shown, the specific steps are as follows:

[0032] Step S1: Establish the geometric models of the workpiece and the cutting tool, and discretize the workpiece surface into a two-dimensional regular height matrix (Z-map), and determine the tool's geometric parameters (tool tip radius). Tool radius Front corner (etc.) and cutting path.

[0033] Step S2: Perform geometric contact judgment, calculate the removal depth of each grid point based on the tool path, obtain the initial Z-map update result, and form the surface morphology at the geometric level.

[0034] Step S3: Define the radius of influence of plastic sideflow And construct weight functions on both sides of the tool. Simulate the lateral flow and packing behavior of materials, and calculate the plastic lateral flow correction. .

[0035] In this step, the plastic sideflow modeling module defines the plastic lateral influence radius. And use a Gaussian or exponentially decaying weighting function. Spatial distribution correction is performed on the material accumulation trend on both sides of the cutting tool.

[0036] In this step, the plastic sideflow correction term... Distance from node to tool contact center Attenuation can be achieved in the form of ,in This is the lateral flow deposition coefficient, used to control the amount of deposition.

[0037] Step S4: After each Z-map update, a plastic sideflow correction term is superimposed to simulate material accumulation on both sides of the tool, thereby obtaining the corrected surface height. .

[0038] In this step, the Z-map update process includes a series of steps: "geometric contact judgment—plastic sideflow correction—elastic recovery compensation," forming a hierarchical iterative simulation structure. The Z-map update formula is:

[0039]

[0040] In the formula, The removal depth is the minimum value of the two values ​​calculated in this iteration of geometric contact. This is the theoretical removal depth obtained when the tool geometry intersects with the workpiece surface mesh. This is the surface height value after the previous iteration.

[0041] In this step, the corrected surface height formula is:

[0042] .

[0043] Step S5: Based on the material's elastic modulus Cutting stress and feed rate Calculate the elastic recovery correction term using equal parameters This is used to describe the springback phenomenon of material after the tool leaves the workpiece.

[0044] In this step, the elastic recovery modeling module is based on the material's elastic modulus. Cutting stress Calculation of the coupling relationship and rebound correction term This correction term can be determined through experimental calibration or derivation from elasticity theory.

[0045] In this step, the elastic recovery item It can be represented as ,in It is an empirical constant that can be calibrated experimentally.

[0046] Step S6: Apply elastic recovery compensation to the updated Z-map surface to obtain the final surface morphology. .

[0047] Step S7: Establish an analytical model of the elastic-plastic residual height for the infeed side region. It is used to quantitatively predict surface bulges caused by material deformation. This is the final surface height after elastoplastic deformation correction. This refers to the theoretical surface height formed by geometric removal after cutting. The height increase is caused by material buildup on the infeed side and plastic reflow. .

[0048] In this step, the analytical model of the elastic-plastic residual height on the infeed side considers the normal load on the infeed side. radius of the blade tip arc Brinell hardness of materials and cutting stress Physical quantities, corrected by empirical factors Model biases are corrected for to quickly estimate surface bulge height.

[0049] Step S8: Output the corrected surface height matrix and perform statistical analysis and visualization of the residual morphology and surface roughness under different cutting parameter combinations.

[0050] This invention introduces an elastoplastic deformation correction module based on traditional Z-map geometric modeling, which can simultaneously describe the plastic lateral flow and elastic rebound effects of materials, significantly improving the physical consistency and accuracy of surface morphology prediction. This invention combines the efficiency of geometric modeling with the physical accuracy of mechanical modeling, enabling high-precision surface morphology prediction and process optimization in fields such as optical molds, microelectronic chips, aerospace structural components, and multi-axis ultra-precision machining, and has broad engineering application prospects.

[0051] Example:

[0052] This embodiment focuses on the single-track scratching process of a single-flute straight-edged end mill on a five-axis ultra-precision milling and turning machine, establishing an improved Z-map surface morphology simulation method that incorporates elasto-plastic deformation mechanisms. This method simulates the material deformation and residual morphology evolution of the workpiece surface as the tool moves along a single scratching trajectory, verifying the effectiveness of the proposed plastic lateral flow and elastic recovery modeling mechanism.

[0053] (1) Geometric modeling and Z-map initialization

[0054] Discretize the workpiece surface into dimensions A two-dimensional regular grid, each grid node Corresponding to a height value .

[0055] The simulation area only covers a single inscription path and its two side influence zones to ensure that the calculation is concentrated in the local deformation zone. Input the tool geometry, which is determined by the tool tip radius. Tool radius and front corner The tool surface is defined as a discretized point cloud. A schematic diagram of the single-flute straight-edge end mill used in this embodiment is shown below. Figure 2 As shown. The cutter along Axial direction at constant feed rate Motion. The initial surface is set to a plane, and the initial height matrix is... This represents an ideal smooth surface. As the initial surface height matrix, in this embodiment, the initial surface of the workpiece is set as an ideal smooth plane, therefore the initial height of all mesh nodes is... All values ​​are constant.

[0056] (2) Geometric contact judgment

[0057] Tool marking trajectory as follows Figure 3 As shown, the geometric relationship between the tool point cloud and the workpiece surface is determined in real time during the tool's movement along the engraving trajectory. When the tool point cloud... When the coordinates are lower than the current height of the workpiece node, the point is considered to be cut.

[0058] The Z-map update formula is:

[0059]

[0060] By gradually advancing the tool path, the preliminary geometric residual morphology after single-track engraving is obtained.

[0061] (3) Plastic lateral flow correction

[0062] Because the depth of cut is extremely small and the strain rate in the cutting zone is high during single-pass scribing, the workpiece material undergoes significant plastic lateral flow along the normal-tangential direction under the pressure and friction of the tool edge. For example... Figure 4 As shown, to simulate this effect, the present invention defines lateral influence radii on both sides of the inscribed trajectory. The material packing distribution is described using a Gaussian weighting function:

[0063]

[0064] in: The lateral packing coefficient reflects the plastic flow strength of the material. The distance from the node to the center of the tool contact; The lateral influence radius is defined; after each geometry update, the lateral flow correction is superimposed on the corresponding region to obtain the corrected height.

[0065]

[0066] This correction reflects the accumulation of material on both sides of the cutting edge due to plastic extrusion.

[0067] (4) Flexible recovery compensation

[0068] After the cutting tool leaves the cutting area, the workpiece material elastically rebounds due to stress release.

[0069] According to the theory of elasticity, the amount of recovery can be approximately expressed as:

[0070]

[0071] in: The elastic modulus of the material; This refers to the cutting stress during the scribing process; It is an empirical constant that can be calibrated experimentally.

[0072] The updated surface height is:

[0073]

[0074] This compensation term effectively describes the bulging effect caused by surface micro-rebound after unloading.

[0075] (5) Elastic-plastic residual height model on the infeed side

[0076] During single-pass engraving, the main deformation is concentrated in the area on the infeed side.

[0077] To quantitatively describe the local bulge in this region, this invention establishes an analytical model of the elastoplastic residual height:

[0078]

[0079] in: This is the normal load on the infeed side; The Brinell hardness of the material; This is an empirical correction factor.

[0080] This model is used to quickly estimate the height of the infeed side bulge caused by elastoplastic deformation and reflects the combined influence of material properties, cutting load and tool geometry on the surface residual morphology.

Claims

1. A method of Z-map milling surface simulation based on elastic-plastic deformation criterion, characterized in that The method comprises the following steps: Step S1: establishing a geometric model of a workpiece and a tool, discretizing a workpiece surface into a two-dimensional regular height matrix Z-map, determining tool geometric parameters and a cutting path; Step S2: performing geometric contact judgment, calculating the removal depth of each grid point according to the tool trajectory, obtaining an initial Z-map update result, and forming a surface topography in the geometric level; Step S3: define the plastic side flow influence radius and build weight functions on both sides of the tool simulate the side flow and accumulation behavior of the material and calculate the plastic side flow correction where: , , is the distance of the node to the tool contact center, is the side flow accumulation coefficient; Step S4: After each Z-map update, superimpose a plastic side flow correction term to achieve simulation of material accumulation on both sides of the tool, thus obtaining the corrected surface height ; Step S5: Calculate the elastic modulus of the material according to the cutting force , the cutting stress , and the elastic recovery correction term , which is used to describe the springback phenomenon of the material after the tool leaves. Step S6: Apply elastic recovery compensation to the updated Z-map surface to obtain the final surface topography ; Step S7: output the surface height matrix corrected in step S6 The residual topography and surface roughness under different cutting parameter combinations are statistically analyzed and visualized.

2. The method of claim 1, wherein In the step S4, the Z-map update formula is: wherein is the surface height value from the current iteration of the geometric contact calculation, is the height value from the intersection of the tool geometry with the workpiece surface mesh, is the surface height value from the previous iteration.

3. The method of claim 1, wherein In the step S4, the corrected surface height formula is: In the formula, is the surface height value obtained for the current iteration of the geometric contact calculation.

4. The method of claim 1, wherein In the step S5, the elastic recovery correction term is expressed as where is an empirical constant.

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