Aviation aluminum alloy hole milling machining time lag error resolving method based on stress mapping method

Abstract

The invention discloses an aviation aluminum alloy hole milling machining time lag error resolving method based on a stress mapping method. Comprising a deformation control-oriented aviation aluminum alloy component heat treatment numerical simulation and geometric effect prediction method, an aviation aluminum alloy component milling hole machining stress state and numerical matrix transfer method, and a dynamic and time-lag error coupling effect and influence characteristic identification method in aviation aluminum alloy component milling hole machining. On the basis of a dynamic cutting behavior of a spiral milling cutter and milling surface topography research, a space coordinate transformation method is adopted to carry out mathematical characterization on a motion trail of a cutter cutting edge aiming at the time-varying property of an instantaneous contact relationship between the cutter tooth cutting edge of the milling cutter and a milling transition surface. The instantaneous cutting pose of the milling cutter under the action of the cutter tooth error and the milling vibration is solved, the influence of the instantaneous cutting pose of the milling cutter on the dynamic error forming process of the milling surface is illuminated, and the machining process requirement of the aviation transmission system casing is met.

Description

Technical Field

[0001] This invention relates to the field of aerospace aluminum alloy processing technology, specifically to a method for calculating time delay errors in aerospace aluminum alloy milling based on stress mapping. Background Technology

[0002] The lightweight and compact casing, as a major load-bearing and containment component of the heavy helicopter transmission system, has a significant impact on the service performance of the aviation transmission system due to its machining quality. Casing parts are characterized by complex structures, uneven mass distribution, localized weak walls and rigidity, and high dimensional accuracy requirements. Their machining involves numerous processes, and under the coupled effects of positioning and clamping, cutting vibration, and dynamic cutting force thermal loads, the casing structure and rigidity are highly variable. The rebalancing of stiffness fields and residual stresses and machining deformations at each process stage are uncertain, making it difficult to precisely control machining errors. This results in prominent problems such as poor casing machining quality, low machining efficiency, and long machining cycles, making it difficult to achieve the machining process goals for aviation transmission system casings and failing to meet the development and production requirements of aviation models. Summary of the Invention

[0003] The purpose of this invention is to provide a method for calculating the time delay error in milling of aerospace aluminum alloys based on stress mapping, so as to solve the problems mentioned in the background art.

[0004] To achieve the above objectives, the present invention provides the following technical solution: a method for calculating time lag error in milling of aerospace aluminum alloys based on stress mapping, comprising the following steps:

[0005] Step 1: Establish a three-dimensional finite element model of the blank, perform numerical simulation of the temperature field, and combine the nonlinear thermophysical parameters of the blank with the solution quenching process of the blank. Based on the results of the temperature field simulation, introduce the nonlinear mechanical property parameters of the material to obtain the simulation results of the quenching temperature field and thermal stress field of the blank.

[0006] Step 2: Establish a simulation model of blank milling. Based on the thermo-mechanical coupling deformation behavior of the milling process, select the explicit dynamic temperature-displacement coupling type in the analysis step, and set the analysis step duration according to the milling stroke and tool feed rate. Select milling force, milling temperature, element stress and strain in the on-site output and historical output options as required, and obtain the distribution of output parameters and their evolution over time.

[0007] The JC constitutive model is used to describe the elastic-plastic deformation of the blank, and the stress-strain behavior of the blank from deformation to fracture during the cutting process is analyzed.

[0008] The initial temperatures of the tool and the blank are set to the ambient temperature. The thermal stress obtained from the finite element simulation of the heat treatment of the blank is applied layer by layer to the blank unit as the inherent residual stress of the blank to complete the data transfer. Boundary conditions and loads are set according to the milling scheme parameters.

[0009] A temperature-displacement coupling analysis is established. In a predefined field, the field parameters obtained by solving are transferred from the dynamic analysis step to the static analysis step by setting the initial state. The blank boundary conditions and loads are unloaded, and the blank temperature is allowed to drop to room temperature until the stress field stabilizes into the residual stress field.

[0010] Step 3: The workpiece material is aviation aluminum alloy 7050-T7451. The workpiece model after milling is established according to the size of 90×90×20mm. The workpiece is divided into area G and area M. Area G is the range affected by the initial residual stress, and area M is the range affected by the initial residual stress and the machining residual stress.

[0011] A general static analysis step is established for the workpiece deformation problem. The initial residual stress of the workpiece and the residual stress of milling are applied together. The data of initial residual stress and milling residual stress are discretized according to the stress distribution characteristics and mesh size. The relative contribution and dominant role of initial residual stress and milling residual stress on deformation are quantitatively analyzed.

[0012] Calculate the milling surface error to obtain the final milling surface error;

[0013] To achieve prediction of residual stress surface distribution based on milling parameters, residual stress data under different milling parameters are obtained through numerical simulation and preprocessed to ensure data quality.

[0014] An analytical method is used to investigate the influence of residual stress on workpiece deformation. Based on the residual stress equivalent moment method, the residual stress in a specific area of ​​the workpiece is calculated to obtain the equivalent moment. A model is established to evaluate the influence of residual stress on the workpiece surface on the deformation of thin-walled parts. A deformation prediction model based on process parameters is obtained. Combined with the workpiece milling surface contour reconstruction method of residual stress field release, the response characteristics of the constructed surface contour to residual stress release are obtained. Finally, a workpiece machining error calculation model under milling vibration and residual stress is obtained.

[0015] Furthermore, in step three, the workpiece is meshed. The workpiece mesh in regions G and M should be divided into 40 layers in the Z-axis direction, which is equivalent to the number of discretization layers of the initial residual stress. The workpiece mesh in region M is divided into 40 ring structures along the hole-forming radial direction, which is equivalent to the number of discretization layers of the machining residual stress. The global mesh size is set to 1 mm, and the workpiece mesh type is selected as 8-node linear hexahedral element C3D8R. The workpiece is divided into 532,480 elements using the hexahedral structure meshing method.

[0016] Furthermore, in step three, three schemes are set up for quantitative analysis: Scheme one, only the initial residual stress is applied to analyze its influence on the workpiece deformation; Scheme two, only the milling residual stress is applied to study its contribution to the deformation during the processing; Scheme three, both the initial residual stress and the milling residual stress are applied simultaneously to comprehensively examine the deformation characteristics under the combined action of the two.

[0017] Furthermore, in step three, the first part is based on the tool-workpiece contact model. Under the action of tool tooth error and milling vibration, the simulation method of milling surface morphology is used to calculate the logical relationship between the geometric shape and spatial volume between the tool and the blank. The second part uses the geometric structure characteristics of the workpiece as the boundary condition and the initial residual stress and cutting-induced residual stress of the workpiece as the load to solve the workpiece time delay error. The final milling surface error is obtained by superimposing the ideal state machining error and the time delay error.

[0018] Furthermore, in step three, based on the characteristics of the residual stress distribution, a piecewise function is used for fitting, and the function coefficients are determined through an optimization algorithm to ensure fitting accuracy. On this basis, a regression model is constructed with milling parameters as independent variables and piecewise function coefficients as dependent variables to describe the mathematical relationship between the two. Through this model, a quantitative correlation between milling parameters and residual stress distribution is established, thereby enabling the prediction of residual stress distribution.

[0019] Compared with the prior art, the beneficial effects of the present invention are:

[0020] (1) By introducing the spatial coordinate transformation method, the motion trajectory of the cutting edge of the tool is mathematically represented with high precision. It can solve the instantaneous cutting posture of the milling cutter under the combined action of tooth error and milling vibration in real time, reveal the formation mechanism of the dynamic error of the machining surface caused by the instantaneous posture change of the milling cutter, break through the limitation of the existing model in insufficient coverage of milling surface error prediction, and significantly improve the prediction accuracy and adaptability under complex dynamic working conditions.

[0021] (2) By using the instantaneous contact relationship model between the tool and the workpiece under vibration and the corresponding surface morphology calculation method, the ability to predict and control machining errors can be significantly improved. This helps to optimize parameters in the process design stage, avoid ineffective machining and scrap, improve machining efficiency, shorten the development cycle, ensure the machining quality of the casing, and improve the service performance and reliability of the entire aviation transmission system. Attached Figure Description

[0022] Figure 1 This is a schematic diagram of the finite element simulation method for solution quenching of blanks according to the present invention; Figure 2 This is a schematic diagram of the solution quenching process for the blank of the present invention; Figure 3 This is a simplified model diagram of the milling process of the present invention; Figure 4 This is a diagram showing the nonlinear stress-strain evolution of the present invention. Figure 5 This is a flowchart of the three-dimensional milling thermo-mechanical coupling simulation modeling process of the present invention; Figure 6 This is a schematic diagram of the discretization result of the stress field and its loading method in this invention; Figure 7 This is a schematic diagram of the residual stress discretization results of the present invention; Figure 8 This is a schematic diagram of the workpiece mesh generation result of the present invention; Figure 9 This is a schematic diagram illustrating the workpiece boundary condition settings of the present invention; Figure 10 This is a schematic diagram of the machining error calculation method under milling vibration and residual stress according to the present invention; Figure 11 This is a schematic diagram of the residual stress distribution curve prediction method of the present invention; Figure 12 This is a diagram of the calculation model for machining errors of aerospace aluminum alloys under milling vibration and residual stress according to the present invention. Figure 13 This is a three-dimensional geometric model and finite element mesh diagram of the blank of the present invention; Figure 14 This is a diagram showing the stress field changes during the solid solution process of this invention. Figure 15 This is a diagram showing the stress field changes during the quenching process of this invention. Figure 16 This is a diagram illustrating the numerical simulation process of residual stress during milling in this invention. Figure 17 This is a diagram showing the residual stress distribution characteristics of the present invention; Figure 18 This is a diagram showing the residual stress distribution of the surface layer in Schemes 1-4 of the present invention; Figure 19 This is a diagram showing the residual stress distribution of the surface layer in Scheme 5-8 of the present invention; Figure 20 This is a diagram showing the residual stress distribution of the surface layer in Scheme 9-12 of the present invention. Figure 21 These are residual stress distribution diagrams for surface processing in embodiments 13-16 of the present invention; Figure 22 This is a graph showing the variation of residual stress during milling with milling parameters according to the present invention; Figure 23 This is a diagram showing the location of residual stress measurement points during milling in this invention. Figure 24 This is the XRD pattern of the present invention; Figure 25 This is a comparison chart of the measured and simulated values ​​of residual stress on the inner wall of the hole formed in this invention; Figure 26 This is the initial residual stress loading diagram of the present invention; Figure 27 This is a diagram showing the initial residual stress release of the workpiece according to the present invention; Figure 28 This is a diagram showing the deformation of the workpiece structure under the influence of the initial residual stress of the present invention. Figure 29 This is a diagram showing the evolution of deformation under the initial stress field of this invention; Figure 30 This is a distribution diagram of residual stress and deformation in this invention; Figure 31 This is a diagram showing the residual stress loading during the processing of the present invention; Figure 32 This is a diagram showing the release of residual stress during the machining of the workpiece according to the present invention; Figure 33 This is a diagram showing the deformation of the workpiece structure under the influence of residual stress during processing according to the present invention. Figure 34 This is a diagram showing the evolution of deformation under residual stress field during the processing of this invention. Figure 35 The evolution of residual stress and deformation in this invention; Figure 36The initial residual stress and processing residual stress of this invention are applied; Figure 37 This is a diagram of the stress-strain field after the stress field has reached equilibrium according to the present invention. Figure 38 This is a diagram showing the deformation of the workpiece structure under the influence of residual stress according to the present invention. Figure 39 This is a diagram showing the evolution of deformation under the composite stress field of the present invention; Figure 40 This is a diagram showing the evolution of residual stress and deformation field in this invention; Figure 41 This is a diagram showing the influence of residual stress on deformation in various parts of the present invention; Figure 42 This is the main effect diagram of the maximum deformation of the cutting parameters in this invention. Detailed Implementation

[0023] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0024] Please see Figure 1-42 The present invention provides a technical solution: a method for calculating the time delay error in milling of aerospace aluminum alloy based on stress mapping method;

[0025] 1. Numerical Simulation and Geometric Effect Prediction Method for Heat Treatment of Aerospace Aluminum Alloy Components for Deformation Control

[0026] During milling, to achieve the final part shape and size requirements, a portion of the material is removed from the blank. This material removal disrupts the initial equilibrium of the residual stress field. The redistribution of stress occurs alongside workpiece deformation. Therefore, obtaining the inherent stress of the blank before machining analysis is crucial. Stress is inevitably introduced at each stage of the blank's manufacturing process (casting, forging, rolling, and solution quenching), with the stress field generated during heat treatment (solution quenching) having a particularly significant impact on the initial residual stress. This embodiment assumes that the initial residual stress of the blank is primarily generated by the solution quenching process and is influenced by the solution quenching temperature and time.

[0027] For the heat treatment process of the blank studied in this embodiment, a sequential coupled thermal analysis method was used for finite element simulation. Specifically, this included: defining the thermophysical and high-temperature mechanical properties of the material as a function of temperature nonlinearly; determining the specific process parameters and conditions for solution quenching; establishing the finite element model of the blank; and transferring data for the numerical simulation of the temperature and stress fields. For details, see [link to specific methods]. Figure 1 As shown.

[0028] Heat treatment is a crucial method for optimizing the microstructure and properties of aluminum alloys, significantly improving their strength and toughness to meet practical application requirements. Among these processes, solution aging and quenching are particularly critical for improving the mechanical properties of aluminum alloy parts. Different quenching media can lead to differences in material microstructure, thus affecting their performance. Solution quenching processes, such as... Figure 2 As shown.

[0029] like Figure 2 As shown, for the 7050 aluminum alloy blank studied in this embodiment, the high-temperature medium for the solution quenching process is air, the solution aging time is about 10 hours, the cooling medium in the first stage is warm water (60°C), and after holding at the temperature for a period of time, it is air-cooled to room temperature (25°C).

[0030] To construct an accurate finite element simulation model of 7050 aluminum alloy solution quenching, reliable and accurate material parameters of the 7-series aluminum alloy within the quenching temperature range must be obtained. These parameters are the foundation of the finite element simulation, and their accuracy directly determines the reliability and validity of the simulation results. Table 1 shows the thermophysical properties of 7050-T7451 aluminum alloy at different temperatures.

[0031] Tables 2 and 3 show the convective heat transfer coefficients of 7050-T7451 aluminum alloy with water and air at different temperatures.

[0032] Table 1. Nonlinear thermophysical properties of materials

[0033]

[0034] Table 2. Convective heat transfer coefficients of 7050 aluminum alloy with water at different temperatures.

[0035]

[0036] Table 3. Convective heat transfer coefficients of 7050 aluminum alloy with air at different temperatures.

[0037]

[0038] 2. Stress State and Numerical Matrix Transfer Method in Milling of Aerospace Aluminum Alloy Components

[0039] In this embodiment, to further improve the efficiency of milling simulation, a small-sized, short-time-scale sector-shaped workpiece is selected for simulation modeling under the condition that stable cutting force and cutting temperature can be obtained. The workpiece modeling size is as follows: Figure 3As shown. For the cutting tool, without affecting chip flow, the bottom cutting edge of the milling cutter is selected as the simplified tool, retaining the main tool parameters and ignoring tool wear. The established tool model dimensions are: tool diameter 20mm, helix angle 38°, clearance angle 3°, rake angle 7°, and tool height 6mm. The final simplified geometric models of the tool and workpiece are shown below. Figure 3 As shown.

[0040] A milling simulation model of aluminum alloy 7050-T7451 was established based on Abaqus finite element software. According to the thermo-mechanical coupled deformation behavior during milling, an explicit dynamic-temperature-displacement coupling type was selected for the analysis step. The workpiece used hexahedral reduced integral elements C3D8RT, while the tool used tetrahedral elements C3D4T, with the tool mesh size set to 0.2mm. To better capture the distribution of cutting field variables near the cutting surface, a smaller mesh seed was selected for the workpiece, with a mesh size of 0.05mm.

[0041] In the modeling process, the workpiece material is assumed to be an elastoplastic rigid body, and the milling cutter is assumed to be a rigid body. During the cutting process, the material undergoes elastoplastic deformation, after which damage begins to occur until complete fracture. This embodiment uses the JC constitutive model to describe the elastoplastic deformation of the 7050-T7451 aluminum alloy material. The JC constitutive equation is expressed as:

[0042]

[0043] In the formula: σ is the flow stress; A is the initial yield stress of 7050-T7451 aluminum alloy under quasi-static and room temperature conditions; B and n are strain hardening coefficients; ε is the equivalent strain. ( For strain rate, For reference strain rate, this embodiment uses 0.01 s. -1 C is the strain rate hardening coefficient. * =(TT) r ) / (T m -T r ), where T * The term "relative temperature" or "normalized temperature" primarily functions to convert the actual test temperature T into a dimensionless, standardized value. This facilitates the quantification of the relative thermal state of 7050-T7451 aluminum alloy within the range of ambient temperature to melting point. T represents the test temperature. r For ambient temperature, T m ρ is the melting point temperature; the melting point of 7050-T7451 aluminum alloy is 600℃; m is the thermal softening coefficient. Table 4 shows the JC constitutive model parameters for 7050-T7451 aluminum alloy.

[0044] Table 4. Johnson-Cook material constitutive model parameters for aluminum alloy 7050

[0045]

[0046] The stress-strain behavior of material deformation leading to fracture during the cutting process, such as Figure 4 As shown, stage ac represents the elastoplastic deformation stage of the material. At point c, the material begins to show damage, and the strain at this point is defined as the equivalent damage strain. The state variable ω is related to the equivalent plastic strain. ω is accumulated after each analysis increment step. When the value of ω exceeds 1, the material will begin to fail, and its expression is:

[0047]

[0048] In the formula: ω is the state variable, Δε is the equivalent plastic strain increment, and ε f The failure plastic strain is expressed as shown in equation (3-3):

[0049]

[0050] In the formula: D1~D5 are failure parameters, as shown in Table 5; σ * =σ m / σ represents stress triaxiality; σ m It is the average value of the three normal stresses.

[0051] Table 5. Failure Parameters of 7050 Aluminum Alloy

[0052] <![CDATA[D1]]> <![CDATA[D2]]> <![CDATA[D3]]> <![CDATA[D4]]> <![CDATA[D5]]> 0.059 0.0246 -2.41 -0.1 0.147

[0053] A milling simulation model of aluminum alloy 7050-T7451 was established based on Abaqus finite element software. According to the thermo-mechanical coupling deformation behavior during the milling process, the analysis step selected the dynamic display temperature-displacement coupling type and set the analysis step duration based on the milling stroke and tool feed rate. Milling force, milling temperature, element stress, and strain were selected from the on-site output and historical output options as required, and the distribution of output parameters and their evolution over time were obtained.

[0054] A connector is established in the interaction module to realize the rotation and revolution of the tool in the milling space. The wireframe features are sequentially selected, with the design of the contour point RP-1 on the center axis of the hole and the milling cutter axis, and the connection section type selected as "slot + Cardan". A connector coordinate system is established with RP-1 as the origin and the X-axis pointing in the direction of RP-2. The tool is set as a rigid body; the tool mesh surface and the workpiece cutting layer node set are defined as mesh surface-node contact. The normal and tangential behaviors between the tool and the workpiece are hard contact and frictional behavior, respectively, with a friction coefficient of 0.2. The heat exchange coefficient between the workpiece and the environment is adopted from Table 3, and the ambient temperature is 25℃.

[0055] In the load module, the initial temperatures of the tool and workpiece are set to ambient temperature. The Abaqus subroutine Usdfld is used to apply the thermal stress obtained from the finite element simulation of the workpiece blank's heat treatment as the inherent residual stress of the workpiece layer by layer onto the workpiece elements, completing the data transfer. Boundary conditions and loads are set according to the milling scheme parameters.

[0056] After solving, the mechanical stress field and temperature field introduced by milling are obtained. A new temperature-displacement coupled (transient) analysis step is established. In the predefined field, the field parameters obtained from the solution are transferred from the dynamic analysis step to the static analysis step by setting the initial state. The workpiece boundary conditions and loads are unloaded, and the workpiece temperature is allowed to drop to room temperature until the stress field stabilizes into a residual stress field. Figure 5 The process of thermo-mechanical coupling three-dimensional milling simulation modeling of aluminum alloy 7050-T7451 is shown.

[0057] 3. Coupling effect and influence characteristics of dynamic and time-delay errors in milling of aerospace aluminum alloy components

[0058] Identification method

[0059] Residual stress from machining and initial residual stress are important factors leading to workpiece deformation during machining. To achieve stress field transfer, this embodiment uses a mapping method to establish a machining deformation model based on stress transfer. The basic principle of the mapping method is to map the residual stress from machining, obtained through experimental measurement or numerical simulation, onto the surface elements of the machined surface in the finite element model, and then directly obtain the overall deformation of the workpiece based on the principles of elasticity.

[0060] The mapping method is widely used in solving workpiece machining deformation problems under the influence of initial residual stress. A common application involves using a uniform stress assumption model, discretizing the machining residual stress obtained experimentally or through numerical simulation, and layering it across the entire model. The birth and death element method is then used to remove material, causing machining deformation of the blank. This method does not require consideration of complex physical cutting processes during numerical simulation, yet it effectively simulates various boundary conditions in actual machining, obtaining machining deformation results that closely match actual machining. The modeling process is simple and computationally efficient. This embodiment, based on this method, applies the residual stress field introduced by milling and the initial residual stress field of the blank together to the workpiece, considering the workpiece machining deformation under a combined residual stress field.

[0061] The workpiece material is aerospace-grade aluminum alloy 7050-T7451. A milled workpiece model with dimensions of 90×90×20mm is established. To achieve discretized mapping of residual stress on the workpiece, the workpiece needs to be divided into regions based on the influence range of residual stress. It is known that the initial residual stress is distributed throughout the entire workpiece, while the machining residual stress is concentrated within a radial depth of 200μm in the machined surface layer. Therefore, the workpiece is divided into region G (the influence range of initial residual stress) and region M (the combined influence range of initial residual stress and machining residual stress). The region division results are as follows. Figure 6 As shown.

[0062] Based on the obtained final stress field state of the workpiece after solution quenching and milling, data support is provided for simulating the deformation process of the workpiece under residual stress using the mapping method. To achieve accurate transmission of the residual stress field, the initial residual stress and machining residual stress data are discretized according to the stress field distribution characteristics and workpiece mesh size. The discretization results of the residual stress are as follows: Figure 7 As shown.

[0063] When meshing the workpiece, the meshes in regions G and M should be divided into 40 layers in the Z-axis direction, corresponding to the number of discretization layers for the initial residual stress. The mesh in region M, along the hole-forming radial direction, should be divided into 40 layers in a ring structure, corresponding to the number of discretization layers for the machining residual stress. To simplify calculations, the global mesh size is set to 1 mm. The workpiece mesh type is selected as an 8-node linear hexahedral element C3D8R. Using a hexahedral structure meshing method, the workpiece is divided into 532,480 elements. The workpiece meshing result is as follows: Figure 8 As shown.

[0064] In Abaqus, a general static analysis step was established for the workpiece deformation problem. To ensure sufficient release of residual stress, the analysis step duration was set to 6000 seconds. The workpiece boundary condition setting steps are as follows: A point A is selected on the bottom surface of the workpiece, and its translational degrees of freedom in the X, Y, and Z directions are constrained; a point B is selected through point A, parallel to the Y-axis, and its translational degrees of freedom in the X and Z directions are constrained; finally, a point C on the bottom surface, not collinear with points A and B, is selected to constrain its Z-axis translational degree of freedom. This restricts the rigid displacement of the workpiece while ensuring the free deformation caused by the redistribution of the internal stress field to equilibrium. The workpiece boundary condition setting results are as follows: Figure 9 As shown.

[0065] In Abaqus, the use of subroutines is crucial for achieving complex simulations and customized functions. The mapping between initial residual stress and machining residual stress relies on the Sigini subroutine. The specific steps are as follows: First, write the subroutine code using Fortran. Modify the inp. file, adding the keyword before the analysis step, and select the subroutine in the folder to run when submitting the job. Partial Sigini subroutine code and operation steps are as follows:

[0066] {SUBROUTINE SIGINI(SIGMA,COORDS,NTENS,NCRDS,NOEL,NPT,LAYER

[0067] 1KSPT,LREBAR,NAMES)

[0068] INCLUDE'ABA PARAMINC

[0069] DIMENSION SIGMAINTENS).COORDS(NCRDS)! The SIGMA array stores stress components, and COORDS stores node coordinates. CHARACTERNAMES(2)*80

[0070] REALPARAMETER: PI = acos(-1.0)

[0071] REAL:XYTHETA,THETA MOD,RADIUS

[0072] X-COORDS(1)

[0073] Y = COORDS(2)

[0074] RADUISS = SQRT(X**2 + Y**2)

[0075] RADIUS=SQRT(X**2+Y**2)-24.97

[0076] IF(ABS(COORDS(3)_LE.10.0AND.RADIUSS GE.26.0)THEN

[0077] IF(ABS(COORDS(3)LE.0.5)THEN

[0078] SIGMA(3)=6.0681

[0079] ELSEIF(ABS(COORDS(3).GE.0.5.AND.ABS(COORDS(3)LE.1.5)THEN

[0080] SIGMA(3)=10.71724

[0081] ELSEIF(ABS(COORDS(3)GE.1.5AND.ABS(COORDS(3)LE.2.5)THEN

[0082] SIGMA(3)=16.28588

[0083] ELSEIF(ABS(COORDS(3).GE.2.5.AND.ABS(COORDS(3)LE.3.5)THEN

[0084] SIGMA(3)=15.44904

[0085] ELSE IF(ABS(COORDS(3).GE.3.5ANDABS(COORDS(3)LE.4.5)THEN

[0086] SIGMA(3)=3.84684

[0087] ELSE IF(ABS(COORDS(3).GE.4.5AND.ABS(COORDS(3)LE.5.5)THEN

[0088] SIGMAI3)=-11.15439

[0089] ELSEIF(ABS(COORDS(3)GE.5.5.AND.ABS(COORDS(3)LE.6.5)THEN

[0090] SIGMA(3)=-17.18794

[0091] ELSE IF(ABS(COORDS(3)GE.6.5.AND.ABS(COORDS(3)LE.7.5)THEN

[0092] SIGMA(3)= -16.27878

[0093] ELSEIF(ABS(COORDS(3).GE.7.5.AND.ABS(COORDS(3)LE.8.5)THEN

[0094] SIGMA(3)= -15.17331

[0095] ELSEIF(ABS(COORDS(3).GE.8.5.AND.ABS(COORDS(3)LE.9.5)THEN

[0096] SIGMA(3)= -13.28266

[0097] ELSEIF(ABS(COORDS(3).GE.9.5.AND.ABS(COORDS(3)LE.10.5)THEN

[0098] SIGMA(3)= -11.12339

[0099] END IF

[0100] ELSE

[0101] IF(RADIUS.LE.0.0S.AND.RADIUS.GE.0.0O)THEN

[0102] SIGMA(3)= -60.38897}

[0103] {**BOUNDARY CONDITIONS

[0104] **Name: BC-1 Type: Displacement / Rotation

[0105] "Boundary

[0106] Set-6, 1, 1

[0107] **Name: BC-2 Type: Displacement / Rotation

[0108] *Boundary

[0109] Set-7, 1, 1

[0110] *INITIAL CONDITIONS, TYPE = STRESS, USER

[0111] **STEP: Step-1

[0112] *Step,name=Step-1,nlgeom=NO,inc=10000

[0113] Static

[0114] 0.01,1,1e-08,0.1

[0115] **BOUNDARY CONDITIONS}

[0116] To systematically evaluate the severity of the influence of initial residual stress in the blank and machining stress on machining deformation, three loading schemes can be designed for comparative analysis: Scheme 1, loading only the initial residual stress in the blank and analyzing its impact on workpiece deformation; Scheme 2, loading only the machining stress field (milling residual stress) and studying its contribution to deformation during machining; Scheme 3, loading both initial residual stress and machining stress simultaneously and comprehensively examining the deformation characteristics under their combined effect. Through simulation results from these three schemes, the relative influence of initial residual stress and machining stress on workpiece deformation can be quantitatively compared, clarifying which stress plays a dominant role in the deformation process.

[0117] This embodiment calculates the milling surface error in two parts: The first part, based on the tool-workpiece contact model, considers tool tooth error and milling vibration, and uses a milling surface morphology simulation method to calculate the logical relationship between the tool and the workpiece's geometry and spatial volume, obtaining the ideal state machining error. The second part uses the workpiece's geometric features as boundary conditions and the initial residual stress of the workpiece and the cutting-induced residual stress as loads to calculate the workpiece time-delay error. The ideal state machining error and the time-delay error are then superimposed to obtain the final milling surface error.

[0118] The residual stress distribution on the surface exhibits similar characteristics, with the following trends: First, the residual stress gradually decreases radially (inwards towards the workpiece) until it reaches the maximum residual compressive stress; then, the residual stress value continues to increase, and the stress state changes from compressive stress to tensile stress; finally, the residual stress gradually decreases until it converges to the residual stress level of the matrix. This process forms a curve distribution resembling a "spoon." This curve can be divided into four characteristic points: surface residual stress, maximum residual compressive stress, maximum residual compressive stress depth, and residual stress influence depth. These four characteristics contain key information about the distribution of residual stress on the surface, such as... Figure 11 As shown.

[0119] By choosing an appropriate function to fit the curve, the most commonly used fitting functions include polynomial, exponential, logarithmic, and sine functions. Polynomial functions are often used to describe the relationship between variables due to their simplicity and flexibility, but too many polynomials not only require more fitting points, but also result in a very large number of constant terms.

[0120] like Figure 11 As shown in this embodiment, the residual stress curve is divided into two curves, with the maximum residual compressive stress characteristic point as the dividing point. The first curve is fitted by a quadratic polynomial function, and the second curve is fitted by a cubic polynomial function.

[0121] The equation for fitting the residual stress curve is:

[0122] σ(h)=a1h 2 +b1h+c1 (0≤h≤DMRS)

[0123] σ(h)=a2h 3 +b2h 2 +c2h+d2 (DMRS≤h≤DRS) (5-1)

[0124] In the formula, σ(h) is the residual stress value; h is the depth from the workpiece surface; a1, b1, c1, a2, b2, c2, d2 are polynomial fitting constants; DMRS is the maximum residual stress depth; and DRS is the residual stress influence depth.

[0125] However, seven coefficients are excessive for fitting the curve. During curve fitting, since c1 is the intercept of the first segment of the curve, it can be represented by the surface residual stress. The first segment of the curve involves fewer data points, and the rate of stress change decreases as it approaches the point of maximum residual compressive stress; therefore, this point is considered a minimum on the curve. Based on these considerations, the following equation is used to fit the curve:

[0126]

[0127] In the formula, SRS is the surface residual stress value, and MRS is the maximum residual stress.

[0128] The second curve shows some variability in different directions. After several attempts, the tangential residual stress curve can be fixed at a2 of 50000 and b2 of -26000; the axial residual stress curve can be fixed at a2 of 25000 and b2 of -17000. At this time, the fitted residual stress curve can be expressed as Equation (5-3).

[0129]

[0130] In the formula, c 2t c 2a It can be represented as:

[0131]

[0132] In the formula, where c 2t d 2t It is the polynomial parameter of the circumferential residual stress, c2a d 2a It is the polynomial parameter of axial residual stress; DMRS t The depth of influence of the maximum circumferential residual stress (subscript t indicates circumferential; subscript a indicates axial).

[0133] To predict the surface distribution of residual stress based on milling parameters, residual stress data under different milling parameters were obtained through numerical simulation. The data was preprocessed to ensure quality. Based on the characteristics of the residual stress distribution, a piecewise function was used for fitting, and the function coefficients were determined through an optimization algorithm to ensure fitting accuracy. On this basis, a regression model was constructed with milling parameters as independent variables and the piecewise function coefficients as dependent variables to describe the mathematical relationship between them. This model establishes a quantitative correlation between milling parameters and residual stress distribution, thereby enabling the prediction of residual stress distribution. This process typically relies on a regression equation to express the relationship between the dependent and independent variables.

[0134] An analytical method was employed to investigate the influence of residual stress on workpiece deformation. The effect of the stress field introduced during milling on part deformation is typically simplified as an equivalent torque effect. The distribution of the equivalent torque on a thin plate under a bidirectional normal stress field (axial and circumferential) is presented. This simplified model provides an intuitive and effective theoretical basis for analyzing part deformation caused by residual stress.

[0135] The core of the residual stress equivalent moment method lies in calculating the equivalent moment of a specific region of a plate (one side of a workpiece) by integrating the residual stress in that region. Then, assuming zero deformation at the central plane of the plate (i.e., the reference point), the distribution of the equivalent moment relative to that reference point can be determined. Since residual stress in different parts of a plate or shell structure may be equivalent to forces of different directions and magnitudes, and these forces have significant directionality, the generated moments may point in different directions, leading to diverse deformation effects. Based on this principle, this embodiment proposes a model for evaluating the influence of surface residual stress on the deformation of thin-walled parts, as shown in equation (5-5).

[0136]

[0137] In the formula, V t and V a The values ​​represent the evaluation results of tangential and axial residual stresses, respectively; S is the integrated surface area of ​​the workpiece; H is the distance between the part surface and the residual stress matrix; and h is the depth from the workpiece surface.

[0138] Regarding the derivation of the deformation equation in the numerical simulation method, formula (5-5) can be approximately equivalent to formula (5-6):

[0139]

[0140] Where Δh is the mesh element size; N is the total number of meshes for the workpiece, h i It is the depth position of the i-th grid cell.

[0141] Based on this, the relationship between the deformation evaluation coefficient V and the deformation amount U is shown in equation (5-7):

[0142] U = a3V t +b3V a +c3 (5-7)

[0143] The values ​​of a3, b3, and c3 are related to the geometric features of the workpiece, and U is the deformation of the workpiece.

[0144] Based on the above conclusions, by combining equations (5-1), (5-3), (5-6), and (5-7), a deformation prediction model based on process parameters can be obtained, as shown in equation (5-8):

[0145] RF2(f z ,a p ,a e )=U (5-8)

[0146] Wherein, RF2 is a deformation prediction function based on process parameters, f z It is the feed per tooth, a p It is the cutting depth, a e It refers to the cutting width.

[0147] Based on the above-mentioned method for reconstructing the surface profile of aluminum alloy milling based on residual stress field release, the response characteristics of the constructed surface profile to residual stress release are obtained, and a calculation model for the machining error of aerospace aluminum alloy under milling vibration and residual stress is obtained, such as... Figure 12 As shown.

[0148] 1.1 Numerical Simulation and Geometric Effect Prediction Method for Heat Treatment of Aerospace Aluminum Alloy Components for Deformation Control

[0149] Based on the structure and actual dimensions of the object under study in this embodiment, a three-dimensional solid model of the blank to be heat-treated was established in the finite element analysis software Abaqus. Considering the subsequent milling simulation of the blank, its geometric region was divided. Subsequently, the three-dimensional finite element model of the blank was meshed, using the DC3D8 element type, i.e., an 8-node linear heat transfer hexahedral element, as shown below. Figure 13 As shown.

[0150] Three analysis steps were set sequentially: solution treatment (477℃, analysis time 36000s), cold water quenching (60℃, analysis time 1000s), and air cooling (25℃, analysis time 1000s). In the first analysis step, the initial temperature of the blank node set was set to 25℃, the ambient air temperature was 477℃, and the convective heat transfer coefficient with air was used. In the second analysis step, the ambient temperature was set to 60℃, and the convective heat transfer coefficient with water was used. In the third analysis step, the ambient temperature was set to 25℃, and the convective heat transfer coefficient with air was used.

[0151] Finite element simulation was used to obtain the transient stress field changes of the blank during the solution treatment and quenching stages, such as... Figure 14 As shown.

[0152] like Figure 14 As shown, the stress changes (including σ) at the nodes along the selected path during the solution treatment process are plotted at the center of the blank. x σ y The trends observed in the graph are as follows:

[0153] At a depth of approximately 5 mm, σ x This peak phenomenon may be related to the following factors:

[0154] Stress concentration caused by phase transition: During the phase transition process, the microstructure of the material changes, which may lead to local stress concentration.

[0155] Temperature gradient: During the quenching process, the surface cools faster than the interior, resulting in a temperature difference between the surface and the interior, which in turn causes thermal stress.

[0156] During the solution treatment stage, the surface of the blank cools faster than the interior, resulting in a temperature difference between the surface and the interior, which in turn causes thermal stress. Therefore, the stress values ​​exhibit a symmetrical pattern along the central axis on the selected path.

[0157] Initially, the surface of the blank is subjected to compressive stress, the interior of the blank is subjected to tensile stress, and the core of the blank is subjected to compressive stress. During the stabilization process, the compressive stress on the surface of the blank increases, the tensile stress on the interior of the blank decreases, and the compressive stress on the core of the blank decreases and then turns into tensile stress.

[0158] After the stress distribution stabilizes, the stress on the blank along the path exhibits an "M" shape. This is mainly manifested as compressive stress on the surface of the blank, and tensile stress inside and at the core. Furthermore, the tensile stress inside the blank initially increases and then decreases with distance from the upper end face. The stress field changes during the blank quenching process are as follows: Figure 15 As shown.

[0159] like Figure 3-5As shown, the stress changes (including σ) of the nodes on the selected path at the center of the blank during the quenching process are plotted. x σ y The trends observed in the graph are as follows:

[0160] Similar to the solution treatment stage, the quenching stage generates a temperature gradient due to the inconsistent rates of temperature change between the surface and interior of the blank. This temperature gradient is the primary cause of the stress field during the quenching stage. Therefore, the stress values ​​always exhibit a symmetrical pattern along the central axis along the selected path.

[0161] Initially, the surface of the blank is subjected to tensile stress, while the interior is subjected to compressive stress. As the stress stabilizes, the compressive stress on the surface of the blank increases, while the tensile stress inside the blank decreases.

[0162] After the stress distribution stabilizes, the stress experienced by the blank along the path exhibits a "U" shape. This is mainly manifested as tensile stress on the surface of the blank and compressive stress on the interior and core of the blank.

[0163] 2.1 Stress State and Numerical Matrix Transfer Method in Milling of Aerospace Aluminum Alloy Components

[0164] The processing parameters are set as follows: n = 1500 r / min; v f =1m / min a p =0.3mm; a e =0.5mm. The model was created and the simulation program was run according to the milling residual stress simulation method in Section 3.2. The numerical simulation process of milling residual stress is as follows: Figure 16 As shown.

[0165] Depend on Figure 16 As shown, after milling, some unmilled material remains on the machined surface, consistent with the hypothesis in Section 2.1. Due to the cyclic loading of cutting forces during milling, the residual stress is mainly distributed on the contact surface between the tool and the workpiece. After milling, the residual stress is relatively uniformly distributed on the side profile. The residual stress on the workpiece surface after machining is extracted, and the distribution characteristics of the residual stress on the milled surface are plotted as follows: Figure 17 As shown.

[0166] Figure 17 In the diagram, the Y-axis angle is the angle between the measurement point and the positive X-axis direction. The distribution of machining residual stress along the circumferential path at the same radius position exhibits some differences, with the range between the maximum and minimum values ​​within 5 MPa. In subsequent residual stress statistics, the average value over the same radial distance is taken as the final result for residual stress.

[0167] During milling, the formation of residual stress is closely related to the machining parameters. This is because the feed per tooth (f) during milling... z ), depth of cut (a) p ) and cutting width (a e Parameters such as [parameter 1] directly affect the deformation and heat distribution of materials, leading to different residual stress states. Based on the numerical simulation method for residual stress in milling (section 3.2), the distribution characteristics of surface residual stress under different machining process parameters are analyzed. By comparing the influence of different process parameters on residual stress distribution, it is hoped to reveal the influence mechanism of milling process parameters on residual stress distribution. The settings of the machining process parameters are shown in Table 6.

[0168] Table 6. Simulation parameters for milling machining

[0169]

[0170]

[0171] Based on the numerical simulation process parameters in Table 6, numerical simulation of residual stress was performed, and the surface residual stress distribution of all simulation schemes (1-16) was obtained as follows: Figure 18 , Figure 19 As shown.

[0172] Depend on Figure 18 It can be seen that as the machining allowance increases, the depth of influence of residual machining stress and its maximum compressive stress amplitude also increase. This is mainly attributed to the increase in cutting force caused by the increase in the thickness of the cutting layer.

[0173] Depend on Figure 19 It can be seen that the cutting width has a greater impact on the distribution of residual stress than the cutting depth. The influence of residual stress on the depth and the trend of its maximum compressive stress amplitude mainly depend on the change in cutting width.

[0174] Depend on Figure 20 It can be seen that the cutting width has a greater impact on the distribution of residual stress than the cutting depth. The influence of residual stress on the depth and the trend of its maximum compressive stress amplitude mainly depend on the change in cutting width.

[0175] Depend on Figure 18-21It can be seen that under different milling parameters, the axial residual stress on the hole surface is always compressive stress. The surface residual compressive stress reaches its maximum value in the range of 0–50 μm, and then gradually decreases. It transforms from compressive stress to tensile stress before reaching 100 μm from the surface, where it reaches its maximum value. With increasing distance from the surface, the stress tends to approach the matrix stress value. The radial residual stress on the hole surface is always tensile stress. With increasing distance from the surface, the residual tensile stress decreases and transforms into tensile stress, reaching its maximum compressive stress around 100 μm from the surface. Subsequently, the compressive stress gradually decreases and tends to approach the matrix stress value. The equivalent stress fluctuates with increasing surface depth, but generally shows a slow decreasing trend. To investigate the influence of milling residues on residual stress, the main effect method was used to further analyze the simulation data, obtaining the relationship curve between machining parameters and the maximum residual compressive stress, as shown in the figure. Figure 22 As shown.

[0176] from Figure 22 It can be seen that the maximum residual compressive stress response of the 7050-T7451 aluminum alloy workpiece under different process parameters after milling simulation experiments is as follows: With the increase of feed rate and feed per tooth, the maximum residual compressive stress (DMRS) increases. t and DMRS a The maximum residual compressive stress shows a clear increasing trend; this may be because higher feed rates and feed per tooth lead to increased cutting forces, resulting in larger plastic deformation and a heat-affected zone, thus increasing the maximum residual compressive stress. The effect of different cutting depths on the maximum residual compressive stress is not significant; the residual stress changes little at each cutting depth, and the change in cutting depth has a negligible impact on the maximum residual compressive stress. Dividing the cutting layer into minimal micro-elements along the axial direction, although increasing the cutting depth increases the tool-workpiece contact area, the cutting parameters do not change for each micro-element in that layer. The effect of changes in cutting width on residual stress is more complex, with a peak value for the maximum residual compressive stress within a certain range.

[0177] Experimental verification of residual stress in milling process

[0178] The residual stress on the surface of a workpiece after milling is measured using X-ray diffraction. The relationship between the wavelength λ of the X-rays, the spacing d between the diffracting crystal planes, and the diffraction angle 2θ can be described by Bragg's Law.

[0179] 2dsinθ=nλ (n=1,2,3...) (3-4)

[0180] When stress σ exists in a material, the crystal lattice undergoes minute deformation, thereby altering the interplanar spacing d. The diffraction angle 2θ changes accordingly, following Bragg's law. Therefore, the lattice strain ε can be calculated by measuring the change in diffraction angle 2θ, and the residual stress can be calculated using Hooke's law.

[0181] The residual stress distribution characteristics of the workpiece surface after milling were measured using a residual stress analyzer. To improve the accuracy of residual stress measurement, multiple measurements were taken and the average value was used to reduce the influence of measurement error. In the actual test, each measurement point was subjected to three repeated measurements, and the average value of the three measurements was used as the final measurement data for that point. To measure the residual stress on the workpiece surface, the workpiece surface material was etched using an electro-erosion machine. The thickness of each etched layer was controlled at 30 μm, and a total of 6 layers were etched, resulting in data from 7 test points. The measurement points are shown below. Figure 23 As shown.

[0182] The distribution of residual stress on the surface of a material can be accurately obtained using a residual stress analyzer, especially a measurement method based on X-ray diffraction (XRD) technology. Figure 24 The image shown is an example of the XRD pattern obtained from residual stress analysis.

[0183] Figure 24 XRD patterns, measured by variations in lattice spacing within the material's crystal structure, reflect the distribution characteristics of residual stress. The position and shape of diffraction peaks in the XRD pattern are closely related to the stress state within the material. By analyzing the shift and broadening of the diffraction peaks, the magnitude and direction of the residual stress can be calculated. A comparison of measured and simulated residual stress values ​​on the inner wall of the formed hole is shown below. Figure 25 As shown.

[0184] like Figure 25 As shown, the experimentally measured residual stress values ​​are compared with those obtained from the numerical simulation of milling. The results show that the two have a high degree of consistency in stress distribution trends and numerical magnitudes. Especially in high stress concentration areas, the deviation between the simulation results and the measured data is small, indicating that the numerical simulation of milling can capture the formation and evolution mechanism of residual stress during the machining process well. This verifies the reliability of the prediction method. The numerical simulation of milling comprehensively considers the influence of multiple factors such as the initial residual stress of the blank before milling, the clamping load stress, the mechanical load, and the thermal load during milling on the residual stress distribution, and can accurately simulate the stress state under actual machining conditions.

[0185] 3.1 Coupling Effect of Dynamic and Time Delay Errors and Identification Methods for Their Influencing Characteristics in Milling of Aerospace Aluminum Alloy Components

[0186] Numerical simulation analysis of initial residual stress and processing deformation

[0187] A method for constructing a machining deformation solution model based on stress field transfer applies an initial residual stress field to the workpiece, resulting in a workpiece model under the condition of only being loaded with the initial residual stress field, as shown below. Figure 26 As shown.

[0188] The duration of the static analysis step was set to 6000 seconds. After the numerical simulation, the stress field state of the workpiece at four time points—1500 seconds, 3000 seconds, 4500 seconds, and 6000 seconds—was selected as characteristic moments for analyzing the initial residual stress release process. The initial residual stress release of the workpiece is as follows: Figure 27 As shown.

[0189] like Figure 27 As shown, stress release is slow in the initial stage; by 3000 seconds, the material enters a rapid stress release stage; by 4500 seconds, the stress release rate slows down, and the residual stress has partially balanced; finally, by 6000 seconds, the stress field tends to stabilize, and the residual stress reaches a low level. The residual stress gradually decreases over time, and the internal stress of the material redistributes and tends to stabilize. This dynamic process reveals the nonlinear characteristics of residual stress release, which may be related to the creep behavior or microstructural evolution of the material.

[0190] To investigate the impact of stress release on workpiece structural deformation, time points with the same stress redistribution were selected to analyze the deformation evolution of the workpiece. The structural deformation of the workpiece under the influence of initial residual stress was as follows: Figure 28 As shown.

[0191] Depend on Figure 28 It can be seen that under the influence of the solution quenching stress field, the deformation concentration areas of the workpiece mainly occur at the orifice, bottom, and middle of the hole wall, with the orifice diameter increasing at the orifice and bottom and decreasing in the middle of the hole wall. As time progresses and the stress field gradually reaches equilibrium, stress concentration occurs in the middle of the hole wall. The stress field and deformation field exhibit consistent circumferential distribution characteristics; the equivalent stress decreases significantly at locations of concentrated deformation, while the change in equivalent stress value is not significant at locations with smaller deformation. The occurrence of deformation is closely related to changes in stress values. With the release and redistribution of stress, the overall deformation trend of the workpiece exhibits dynamic evolution characteristics, and there is a close interaction between the two.

[0192] To further reveal the influence of the initial residual stress field on workpiece machining deformation, nodes and paths were selected and tracked on the inner wall. By analyzing the deformation data along these selected paths, the quantitative assessment of how residual stress affects stress redistribution and deformation characteristics of the workpiece during machining can be obtained. The selection method of feature points and the evolution of deformation are as follows: Figure 29 As shown.

[0193] Under the influence of only the initial residual stress Figure 29This study examines the deformation of each node on the workpiece along the X, Y, and Z axes over time. The analysis shows that the displacement rate of each node remains stable across the three axes over time, with the deformation magnitude ranking as follows: Y > Z > X. In the X-axis direction, all selected nodes displace in the negative direction, with the displacement increasing as the distance from the neutral surface increases. In the Z-axis direction, all selected nodes displace in the negative Z-axis direction, with the deformation also increasing as the distance from the neutral surface increases. In the Y-axis direction, the deformation is inconsistent: nodes 1-3 displace in the negative Y-axis direction, increasing the hole diameter; nodes 4-5 displace in the positive Y-axis direction, decreasing the hole diameter. Considering the deformation directions across the three axes, the workpiece deforms away from the hole axis at nodes far from the neutral surface and towards the hole axis at nodes near the neutral surface, exhibiting an overall warping away from the axial direction.

[0194] Depend on Figure 30 It can be seen from the curves showing the evolution of strain and stress fields over time during the deformation process at the finite element analysis point that the initial equivalent stress at the hole opening decreases from 14 MPa to 6 MPa within the analysis step. The deformation reaches its maximum of 0.8 μm at this location. During the axial redistribution of residual stress, the residual stress in the middle section (8 mm to 12 mm from the upper end face) of the hole does not change significantly, while the area with the largest change in residual stress is within 4 mm at both ends of the hole opening. Deformation is also concentrated in these two areas. However, the overall deformation cloud diagram shows that the middle section of the hole deforms towards the hole axis, with a maximum deformation of 0.6 μm; while the two ends of the hole deform away from the hole axis. It is worth noting that the deformation at the two ends of the hole is not consistent, with a larger deformation of 0.8 μm at one end and a smaller deformation of 0.6 μm at the other. The overall deformation causes the hole diameter to decrease in the middle section and increase in the diameter at both ends.

[0195] Numerical simulation analysis of machining residual stress and machining deformation

[0196] The method for constructing a machining deformation solution model based on stress field transfer applies an initial residual stress field to the workpiece to obtain a workpiece model under the condition of only being loaded with the initial machining residual stress field, such as... Figure 31 As shown.

[0197] The duration of the static analysis step was set to 6000 seconds. After the numerical simulation, the stress field state of the workpiece at four time points—1500 seconds, 3000 seconds, 4500 seconds, and 6000 seconds—was selected as characteristic moments for analyzing the release process of residual stress during machining. The release of residual stress during workpiece machining is as follows: Figure 32 As shown.

[0198] like Figure 32As shown, stress release is slow in the initial stage; by 3000 seconds, the material enters a rapid stress release stage; by 4500 seconds, the stress release rate slows down, and the residual stress has partially balanced; finally, by 6000 seconds, the stress field tends to stabilize, and the residual stress reaches a low level. The residual stress gradually decreases over time, and the internal stress of the material redistributes and tends to stabilize. This dynamic process reveals the nonlinear characteristics of residual stress release, which may be related to the creep behavior or microstructural evolution of the material.

[0199] To investigate the impact of stress release on workpiece structural deformation, time points with the same stress redistribution were selected to analyze the deformation evolution of the workpiece. The workpiece structural deformation under the influence of machining residual stress was as follows: Figure 33 As shown.

[0200] like Figure 33 As shown, under the influence of only the machining stress field, the deformation concentration areas of the workpiece mainly occur at the hole opening and bottom, with both the hole opening and bottom diameters increasing. As time progresses and the stress field gradually reaches equilibrium, stress concentration still exists at a certain radial depth in the middle of the hole wall. Due to the workpiece's geometric characteristics, the stress field and deformation field exhibit consistent circumferential distribution characteristics; the equivalent stress decreases significantly at locations of concentrated deformation, while the equivalent stress value does not change significantly at locations with smaller deformation. With the release and redistribution of stress, the overall deformation trend of the workpiece continuously adjusts, indicating a close interaction between the two.

[0201] To further reveal the influence of residual stress fields on workpiece deformation during machining, nodes and paths were selected and tracked on the inner wall. By analyzing the deformation data along these selected paths, the quantitative assessment of how residual stress affects stress redistribution and deformation characteristics of the workpiece during machining can be obtained. The selection method of feature points and the evolution of deformation are as follows: Figure 34 As shown.

[0202] Under the influence of only the initial residual stress Figure 34This study examines the deformation of each workpiece node along the X, Y, and Z axes over time. The analysis shows that the displacement rate of each node remains stable across the three axes over time, with the deformation magnitude ranking as follows: Z > X > Y. In the X-axis direction, all selected nodes displace in the negative direction, with the displacement increasing with distance from the neutral surface. Similarly, in the Y-axis direction, the same nodes displace in the negative direction, again with greater displacement from distance from the neutral surface. This deformation increases the hole diameter, with the increase in diameter increasing more significantly from the neutral surface, especially at the hole opening, where the deformation is significantly higher than at other nodes, exhibiting a sharp drop. In the Z-axis direction, all selected nodes displace in the positive Z-axis direction, with greater deformation from distance from the neutral surface. Considering the deformation directions across all three axes, nodes far from the neutral surface deform away from the hole axis, while nodes near the neutral surface deform towards the hole axis, resulting in an overall warping away from the axial direction.

[0203] like Figure 35 Based on the curves showing the evolution of strain and stress fields over time during the deformation process at the finite element analysis point, it can be seen that the initial equivalent stress at the hole opening decreases from 58 MPa to 25 MPa within 6000 s. The deformation reaches its maximum of 3.4 μm at this location. During the axial redistribution of residual stress, the residual stress in the middle section (5 mm to 15 mm from the upper end face) shows little change, while the area with the largest change in residual stress is within 4 mm of both ends of the hole opening. Deformation is also concentrated in these two areas. However, the overall deformation cloud diagram shows that the middle section of the hole deforms towards the hole axis, with a maximum deformation of 0.6 μm; while the two ends of the hole deform away from the hole axis. The overall deformation results in a smaller hole diameter in the middle section and a larger hole diameter at both ends.

[0204] Numerical simulation analysis of multiple stress field superposition and processing deformation

[0205] The method for constructing a machining deformation solution model based on stress field transfer applies an initial residual stress field to the workpiece to obtain a workpiece model under the condition of only being loaded with the initial machining residual stress field, such as... Figure 36 As shown.

[0206] The duration of the static analysis step was set to 6000 seconds. After the numerical simulation, the stress field state of the workpiece at four time points—1500 seconds, 3000 seconds, 4500 seconds, and 6000 seconds—was selected as characteristic moments for analyzing the release process of its initial residual stress and machining residual stress. The release of machining residual stress in the workpiece is as follows: Figure 37 As shown.

[0207] like Figure 37As shown, stress release is slow in the initial stage; by 3000 seconds, the material enters a rapid stress release stage; by 4500 seconds, the stress release rate slows down, and the residual stress has partially balanced; finally, by 6000 seconds, the stress field tends to stabilize, and the residual stress reaches a low level. The residual stress gradually decreases over time, and the internal stress of the material redistributes and tends to stabilize. This dynamic process reveals the nonlinear characteristics of residual stress release, which may be related to the creep behavior or microstructural evolution of the material.

[0208] To investigate the impact of stress release on workpiece structural deformation, time points with the same stress redistribution were selected to analyze the deformation evolution of the workpiece. The workpiece structural deformation under the influence of initial residual stress and machining residual stress was as follows: Figure 38 As shown.

[0209] like Figure 38 As shown, under the influence of a combined stress field, the deformation concentration areas of the workpiece mainly occur at the orifice and bottom of the hole, with both the orifice and bottom diameters increasing. As time progresses and the stress field gradually reaches equilibrium, stress concentration occurs in the middle of the hole wall. Due to the workpiece's geometric characteristics, the stress field and deformation field exhibit consistent circumferential distribution characteristics; the equivalent stress decreases significantly at locations of concentrated deformation, while the change in equivalent stress value is not significant at locations with smaller deformation. With the release and redistribution of stress, the overall deformation trend of the workpiece continuously adjusts, indicating a close interaction between the two.

[0210] To further reveal the influence of residual stress fields on workpiece machining deformation, nodes and paths were selected and tracked on the inner wall. By analyzing the deformation data along these selected paths, the quantitative assessment of how residual stress affects stress redistribution and deformation characteristics of the workpiece during machining can be obtained. The selection method of feature points and the evolution of deformation are as follows: Figure 39 As shown.

[0211] Under the simultaneous influence of residual stress from solution quenching and stress from machining Figure 39This study examines the deformation of each node on the workpiece along the X, Y, and Z axes over time. The analysis shows that the deformation magnitude is Z > X > Y. The displacement rates of each node along the three workpiece coordinate axes are not consistent. The deformation along the X-axis is relatively small in the initial stage (0s–3000s), gradually increasing in the later stage, showing significant differences between nodes. Points 1–2 displace in the negative X-axis direction, while Points 3–5 displace in the positive X-axis direction, possibly related to the tensile and compressive characteristics of the initial residual stress. The deformation along the Y-axis increases slowly in the initial stage, with a relatively stable deformation rate throughout the deformation process, reflecting the uniformity of stress release in this direction. Except for Point 1, all nodes displace in the negative Y-axis direction, resulting in a significant increase in the hole diameter at the orifice location. The deformation rate along the Z-axis gradually increases over time, with all nodes displacing in the positive Z-axis direction. Overall, these results indicate that the residual stress release process has significant directionality and time dependence. The analysis of the deformation changes of each point over time during the residual stress field release process reveals the dynamic characteristics of workpiece deformation.

[0212] According to finite element analysis, the curves showing the evolution of strain and stress fields at the borehole location over time during machining deformation reveal that the initial equivalent stress decreased from 58 MPa to 26 MPa within 6000 seconds. The deformation at this location reached its maximum value of 3.6 μm. In the axial redistribution of residual stress, the residual stress change was relatively small in the middle section (5 mm to 15 mm) of the upper end face of the borehole, while the residual stress change was more significant within a 4 mm range at both ends of the borehole. Deformation was also mainly concentrated in these two areas. From the overall deformation contour plot, the deformation in the middle section of the borehole towards the borehole axis was the largest, reaching 3.7 μm, while the two ends of the borehole deformed away from the borehole axis. The overall deformation resulted in a decrease in the borehole diameter in the middle section and an increase in the borehole diameter at both ends.

[0213] Deformation evolution mechanism during processing in composite stress fields

[0214] The above analysis shows that under the influence of only the initial residual stress field, the workpiece exhibits a "W"-shaped deformation, with a maximum deformation of 1 μm at the orifice. Under the influence of only the machining residual stress field, the workpiece exhibits a "U"-shaped deformation, with a maximum deformation of 3.2 μm at the orifice. Considering the combined effects of the solution quenching stress field and the machining mechanical stress field, the deformation shape of the workpiece is significantly affected by the initial residual stress, resulting in a "W"-shaped deformation with a maximum deformation of 3.6 μm at the orifice. Specific deformation details are as follows: Figure 41 As shown. In summary, the stress field of machining causes greater deformation in the hole, but the final shape is affected by solution quenching.

[0215] To investigate the contributions of the solution quenching stress field and the machining stress field to the deformation at different locations on the hole surface, the deformation was statistically analyzed as shown in Table 7.

[0216] Table 7. Contribution of residual stress to deformation in each part

[0217]

[0218] This embodiment shows that at the hole opening, the initial residual stress and the machining residual stress contribute 24% and 76% to the workpiece deformation, respectively; at the middle of the hole, the initial residual stress and the machining residual stress contribute 60% and 40% to the workpiece deformation, respectively. Therefore, compared with the initial residual stress, the machining stress field contributes more significantly to the overall deformation of the hole.

[0219] Furthermore, to investigate the corresponding characteristics of workpiece deformation caused by milling with different milling parameters on the comprehensive stress field, the residual stress of the milled surface obtained from the simulation experiment with variable milling parameters was applied to region M of the workpiece. During the milling experiment, the same batch of sheet metal was used as the blank, thus assuming that the residual stress field after solution quenching of materials from the same batch was the same. The same value of the solution quenching stress field was applied to region G, and the relationship between the residual stress field and the workpiece deformation caused by the redistribution of state stress was analyzed. Combining the relationship between milling parameters and residual stress, the relationship between milling parameters and the maximum deformation can be indirectly obtained, such as... Figure 42 As shown.

[0220] according to Figure 42 It can be seen that there is a significant correlation between cutting parameters and maximum deformation. The increase in feed rate (from 0.8 to 1.4 m / min) corresponds to a significant increase in maximum deformation. Lower feed rates result in a smoother cutting process, reducing cutting forces and thus minimizing material deformation; while higher feed rates may lead to greater cutting forces and heat, increasing material deformation. As the feed per tooth increases from 0.15 mm / z to 0.19 mm / z, the maximum deformation also gradually increases, indicating that higher feed rates increase the amount of material cut per pass and may enhance the mechanical extrusion effect, thereby increasing stress and deformation. Relatively speaking, the depth of cut has a smaller impact on the maximum deformation; the deformation at each level does not change significantly, indicating that changes in the depth of cut do not significantly alter the deformation characteristics under these experimental conditions. The effect of the cutting width fluctuates; the deformation reaches its peak at the highest level (2 mm / min) and then decreases slightly, possibly indicating that an excessively large cutting width leads to reduced cutting efficiency and instability. Feed rate and feed per tooth are the main factors affecting the maximum deformation, showing a significant positive correlation, which provides an important basis for parameter optimization in subsequent milling experiments of aerospace aluminum alloys.

[0221] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A stress mapping method-based method for solving the time lag error in the milling of an aviation aluminum alloy, characterized in that, The method comprises the following steps: Step one, a three-dimensional finite element model of the blank is established, a temperature field numerical simulation is carried out, and the simulation results of the quenching temperature field and the thermal stress field of the blank are obtained by combining the nonlinear thermal physical parameters of the blank with the blank solid solution quenching process, based on the results of the temperature field simulation, and introducing the nonlinear force physical parameters of the material; Step two, a blank milling simulation model is established, the thermal-mechanical coupling deformation behavior in the milling process is analyzed, the explicit dynamic temperature-displacement coupling type is selected, the analysis step time is set according to the milling stroke and the tool feed speed, the milling force, the milling temperature, the element stress and the strain are selected in the field output and the historical output options according to the demand, and the distribution of the output parameters and the evolution of the output parameters with time are obtained respectively; The J-C constitutive model is used to describe the elastic-plastic deformation of the blank, and the stress-strain behavior of the blank deformation to fracture in the cutting process is analyzed; The initial temperature of the tool and the blank is set as the environmental temperature, the thermal stress obtained by the blank heat treatment finite element simulation is applied on the blank element layer by layer as the inherent residual stress of the blank, the data transmission is completed, the boundary conditions and the load are set according to the milling scheme parameters; The temperature-displacement coupling is established for analysis, the field parameters obtained by solving are transmitted from the dynamic analysis step to the static analysis step in the pre-defined field by setting the initial state, the blank boundary conditions and the load are unloaded, the blank temperature is lowered to room temperature, and the stress field is stabilized as the residual stress field; Step three, the workpiece material is aviation aluminum alloy 7050-T7451, a workpiece model after milling is established according to the size of 90*90*20mm, the workpiece is divided into G area and M area, the G area is the initial residual stress influence range, and the M area is the initial residual stress and the machining residual stress common influence range; A general static analysis step is established for the workpiece deformation problem, the initial residual stress and the milling residual stress are loaded together, the initial residual stress and the milling residual stress data are discretized according to the stress distribution characteristics and the grid size, and the relative contribution and the dominant role of the initial residual stress and the milling residual stress to the deformation are quantitatively analyzed; The milling surface error is calculated, and the final milling surface error is obtained; In order to realize the residual stress surface layer distribution prediction based on the milling parameters, the residual stress data under different milling parameters are obtained by numerical simulation method, and the data are preprocessed to ensure the data quality; An analytical method is used to explore the influence of residual stress on the workpiece deformation, the equivalent moment of the workpiece in a specific area is calculated based on the residual stress equivalent moment method, a model for evaluating the influence of the workpiece surface residual stress on the deformation of the thin-walled part is established, a deformation prediction model based on the process parameters is obtained, the response characteristics of the surface profile construction to the residual stress release are obtained by combining the workpiece milling hole processing surface profile reconstruction method, and then the workpiece machining error solving model under the action of milling vibration and residual stress is obtained.

2. The method according to claim 1, wherein the method is characterized in that: In step two, the J-C constitutive equation is represented as: wherein σ is the flow stress; A is the initial yield stress of the blank under quasi-static and room temperature conditions; B, n are the strain hardening coefficients; ε is the equivalent strain, C is the strain rate hardening coefficient; T is the experimental temperature; T*m is T raised to the power of m; m is the softening exponent, T * = (T - T r ) / (T m - T r ), is the dimensionless temperature; for the strain rate, for the reference strain rate.

3. The method of claim 1, wherein the method is a stress mapping method for solving the milling time lag error of the aviation aluminum alloy. In step two, the stress-strain definition of the blank deformation to fracture in the cutting process is equivalent damage strain, and the state variable expression is: where ω is the state variable, Δε is the equivalent plastic strain increment, ε f is the failed plasticity; where D1-D5 are failure parameters, σ * = σ m / σ is the stress triaxiality; σ m is the average of the three normal stresses.

4. The method of claim 1, wherein the method is a stress mapping method for solving the milling time lag error of an aircraft aluminum alloy. In step three, the workpiece is meshed, and the workpiece mesh in the G region and the M region should be equivalent to the initial residual stress discretization layer in the Z-axis direction, which is divided into 40 layers; the workpiece mesh in the M region is equivalent to the machining residual stress discretization layer along the hole radial direction, which is divided into 40 layers of annular structure; the global mesh size is set to 1 mm, the workpiece mesh type is selected as 8-node linear hexahedral element C3D8R, and the workpiece is divided into 532480 units by adopting the hexahedral structure mesh division method.

5. The method of claim 1, wherein the method is a stress mapping method based method for solving the milling time lag error of the aviation aluminum alloy. In step three, three sets of schemes are set for quantitative analysis, scheme one, only the initial residual stress is loaded, and the influence of the initial residual stress on the deformation of the workpiece is analyzed; scheme two, only the milling machining residual stress is loaded, and the contribution of the machining residual stress to the deformation is studied; scheme three, the initial residual stress and the milling machining residual stress are loaded at the same time, and the deformation characteristics under the combined action of the two are comprehensively investigated.

6. The method of claim 1, wherein the method is a stress mapping method for milling of an aluminum alloy in an aircraft. In step three, the first part is based on the tool-workpiece contact model, under the action of the tool tooth error and the milling vibration, the milling machining surface topography simulation method is adopted to calculate the logical relationship between the geometry and the space body between the tool and the blank, the second part takes the geometric structure characteristics of the workpiece as the boundary condition, takes the initial residual stress of the workpiece and the cutting induced residual stress as the load, and solves the time lag error of the workpiece, and the final milling machining surface error is obtained by superimposing the ideal state machining error and the time lag error.

7. The method of claim 1, wherein the method is a stress mapping based method for solving the time lag error in milling of an aluminum alloy in an aircraft.

8. In step three, according to the characteristics of the residual stress distribution, a segmented function is used for fitting, and the function coefficients are determined through an optimization algorithm to ensure the fitting accuracy, and on this basis, a regression model is constructed with the milling parameters as the independent variable and the segmented function coefficients as the dependent variable, to describe the mathematical relationship between the two, through the model, the quantitative correlation between the milling parameters and the residual stress distribution is established, and the prediction of the residual stress distribution is realized.

8. The method of claim 1, wherein, The formula of the model for evaluating the influence of the workpiece surface residual stress on the deformation of the thin-walled part is: wherein V t and V a respectively represent the evaluation results of tangential and axial residual stress; S is the integrated surface area of the workpiece; H is the distance between the surface of the workpiece and the residual stress matrix; h is the depth from the surface layer of the workpiece.

9. The method of claim 8, wherein the method is a stress mapping method for milling of an aluminum alloy in an aircraft, and wherein the method further comprises: For the derivation of the deformation equation of the numerical simulation method, the formula of the model for evaluating the influence of the workpiece surface residual stress on the deformation of the thin-walled part is approximately equivalent to the following formula: Wherein, Ah is the grid unit size; N is the total number of workpiece grid division, h i is the depth position of the i-th grid unit; σ t is the circumferential normal stress; σ a is the axial normal stress.

10. The method for calculating the time delay error in milling aerospace aluminum alloys based on stress mapping according to claim 9, characterized in that, deformation The relationship formula between the evaluation coefficient V and the deformation U is: U = a3V t + b3V a + c3: Wherein, the values of a3, b3 and c3 are related to the geometric characteristics of the workpiece, and U is the deformation of the workpiece; The formula of the deformation prediction model based on process parameters is: RF2(f z ,a p ,a e ) = U; wherein RF2 is a deformation prediction function based on process parameters, f z is the feed per tooth, a p is the cutting depth of cut, a e is the cutting width of cut.

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