Tool axis vector optimization domain planning method and system considering workpiece machining flexibility

Abstract

The application belongs to the field of tool axis vector trajectory planning, and particularly discloses a tool axis vector optimization domain planning method and system considering workpiece machining flexibility, which comprises the following steps: establishing a workpiece finite element proxy model, loading cutting force at each tool point to obtain equivalent flexibility of each tool point, and determining a maximum flexibility point; obtaining a maximum cutting force according to a maximum deformation allowed by the workpiece and the equivalent flexibility of the maximum flexibility point, and combining a pre-established cutting force prediction model to obtain a constraint condition; based on the constraint condition and a preset range of machining parameters, performing multi-objective optimization of the maximum flexibility point in coupling with machining parameters to obtain a critical tool axis vector of the maximum flexibility point under critical machining parameters; determining critical tool axis vectors of other tool points under the critical machining parameters to obtain a tool axis vector optimization domain. The application can calculate the tool axis vector optimization domain division within the machining parameter limited range under the influence of force-induced errors and machining efficiency, and provide guidance for tool axis vector trajectory planning.

Description

Technical Field

[0001] This invention belongs to the field of tool axis vector trajectory planning, and more specifically, relates to a tool axis vector optimization domain planning method and system that considers workpiece machining compliance. Background Technology

[0002] Compressor blades, stator and rotor blades, and turbine blades of aero-engines are key thin-walled blade components. In the machining process of these complex thin-walled curved surface parts, the good contact state between the tool and the machined surface is one of the key factors to ensure the machining quality of the parts. Therefore, the optimization of the tool axis vector is crucial.

[0003] Traditional tool axis vector optimization methods often optimize the tool axis vector with fixed machining parameters, without considering the coupling relationship between machining parameters and tool axis vectors. This leads to problems such as a reduced optimization space and difficulty in planning the tool axis vector at certain tool positions during the tool axis vector optimization process. In addition, thin-walled blade parts have thin walls, making them highly susceptible to cutting forces during machining, which can cause tool deformation. Furthermore, the large overlap area and small machinable domain during the machining of thin-walled blades make it difficult to combine force-induced error control with tool axis vector planning. Summary of the Invention

[0004] In view of the above-mentioned defects or improvement needs of the prior art, the present invention provides a tool axis vector optimization domain planning method and system that considers the workpiece machining compliance. Its purpose is to realize tool axis vector optimization domain planning within the machining parameter limit range under the influence of force-induced errors caused by the compliance of the tool and the workpiece.

[0005] To achieve the above objectives, according to a first aspect of the present invention, a tool axis vector optimization domain planning method considering workpiece machining compliance is proposed, comprising the following steps:

[0006] A finite element proxy model of the workpiece is established, and then cutting force is applied at each tool point of the workpiece to obtain the equivalent compliance of each tool point, and then the maximum compliance point is determined.

[0007] Based on the tool cutting process, a cutting force prediction model is established;

[0008] The maximum cutting force is obtained by taking the maximum allowable deformation of the workpiece and the equivalent compliance of the maximum compliance point, and then the constraint conditions are obtained by combining the cutting force prediction model. Based on the constraint conditions and the preset range of machining parameters, the maximum compliance point is subjected to multi-objective optimization coupled with machining parameters to obtain the critical machining parameters and the critical tool axis vector of the maximum compliance point under the critical machining parameters.

[0009] Based on the critical tool axis vector of the maximum compliance point under critical machining parameters, the critical tool axis vectors of other tool positions under critical machining parameters are determined, and the optimization domain planning of the tool axis vector is completed.

[0010] As a further preferred embodiment, the method for determining the equivalent compliance is as follows: For any tool position point, a cutting force is applied to it, and the equivalent compliance of the tool position point is calculated by the ratio of the difference in deformation of the tool position point under different cutting forces to the difference in cutting force; then, the tool position point with the largest equivalent compliance is taken as the maximum compliance point.

[0011] As a further preferred option, the NSGA-III algorithm is used to perform multi-objective optimization of the machining parameters coupled with the maximum compliance point, with the objective functions being to minimize workpiece deformation and maximize cutting efficiency.

[0012] As a further preferred option, the critical tool axis vector of other tool positions under critical machining parameters is determined as follows: for any other tool position, the maximum allowable cutting force of the tool position is obtained based on the maximum allowable deformation of the workpiece and the equivalent compliance of the tool position, and then the constraint conditions of the tool position are obtained by combining the cutting force prediction model; based on the constraint conditions of the tool position and the critical machining parameters, the tool position is optimized in multiple objectives to obtain the critical tool axis vector of the tool position under critical machining parameters.

[0013] As a further preferred approach, the cutting process is solved by differential equivalent solution. Each cutting edge micro-element is regarded as an oblique cutting process, and an oblique cutting model of each micro-element is established. Then, the cutting force prediction model is obtained by integration.

[0014] As a further preferred embodiment, the cutting force prediction model is specifically as follows:

[0015]

[0016] Where Fx, Fy, and Fz represent the triaxial cutting forces obtained by integrating the infinitesimal cutting forces, i.e., the cutting force prediction model; This is represented as the transformation matrix from the tool coordinate system to the tool tip coordinate system. Let z0 be the transformation matrix from the workpiece coordinate system to the tool coordinate system, z0 be the upper limit of the integral of the cutting element; Krc, Ktc, and Kac be the triaxial cutting force coefficients of the tool; dz be the highly discrete element; and h(φ) be the undeformed chip thickness corresponding to the radial hysteresis angle of the tool being φ.

[0017] As a further preferred method, the radial hysteresis angle of the tool is calculated as follows:

[0018]

[0019] Where j represents the j-th cutting edge of the tool, j∈[1~N], and N represents the total number of tool teeth; φ j(z) represents the radial lag angle of the j-th cutting edge relative to the tool tip at height z, where z represents the height of the infinitesimal cutting edge; β is the helix angle of the tool. The radial hysteresis angle is z = 0, and r is the cutting radius corresponding to the micro-element position.

[0020] As a further preferred embodiment, the machining parameters include depth of cut, width of cut, cutting speed, feed rate, rake angle, and yaw angle.

[0021] According to a second aspect of the present invention, a tool axis vector optimization domain planning system considering workpiece machining compliance is provided, comprising a processor for executing the above-described tool axis vector optimization domain planning method considering workpiece machining compliance.

[0022] According to a third aspect of the present invention, a computer-readable storage medium is provided having a computer program stored thereon, which, when executed by a processor, implements the above-described tool axis vector optimization domain planning method considering workpiece machining compliance.

[0023] In summary, compared with the prior art, the above-described technical solutions conceived by this invention mainly possess the following technical advantages:

[0024] 1. This invention considers the coupling relationship between machining parameters and tool axis vectors. It uses the most easily deformable point in the machining tool position as the initial screening target to screen out the critical tool axis vectors for different machining parameters. It then traverses other tool positions to obtain the variable domain range of the tool axis vector for all machining tool positions under the given parameters. This achieves the optimization domain planning of the tool axis vector within the machining parameter limit, taking into account the force-induced error caused by the tool and workpiece compliance. It can provide deformation control guidance for machining errors caused by cutting forces in the workpiece, and is particularly suitable for tool axis vector domain planning in the machining of thin-walled blades.

[0025] 2. The service life of thin-walled blades in aero-engines mainly depends on the magnitude of deformation error and the quality of the blade surface. This invention achieves rapid extraction of equivalent compliance by using the ratio of the difference in different deformations to the difference in cutting force. Then, using the machining deformation performance as an indicator, that is, using the cutting force, the direct influencing factor of deformation error, as the constraint input of deformation error, the tool axis vector within the allowable machining parameter range is planned.

[0026] 3. This invention establishes a cutting force prediction model with cutting parameters and pose as inputs, realizing the mapping between cutting force and machining parameters and tool pose; combining maximum deformation constraints and machining efficiency constraints, it carries out multi-objective tool axis vector optimization of NSGA-III, searches for critical machining parameters and tool axis vectors at the workpiece's most easily deformable points, obtains the upper and lower bounds of the tool axis vector variation range under determined machining parameters, and finally traverses the tool position points to find all satisfied tool axis vector optimization spaces under this set of machining parameters, providing the maximum machinable domain for the tool axis vector optimization process considering cutting force-induced error deformation in the blade overlap area. Attached Figure Description

[0027] Figure 1 This is a flowchart of the tool axis vector optimization domain planning method considering workpiece machining compliance in an embodiment of the present invention;

[0028] Figure 2 (a) and (b) are schematic diagrams illustrating the principle of equivalent stiffness extraction of the force-induced error proxy model constructed in the embodiments of the present invention.

[0029] Figure 3 This is an appearance diagram of the mesh domain in the finite element model constructed according to an embodiment of the present invention;

[0030] Figure 4 CL1 to CL constructed for embodiments of the present invention 70 Extraction map of the compliance matrix corresponding to the blade position point;

[0031] Figure 5 This is a schematic diagram illustrating the principle of equivalent bevel cutting using a micro-element of the ball end mill's cutting edge in an embodiment of the present invention.

[0032] Figure 6 A schematic diagram illustrating the expansion of the tool axis critical vector selection domain recursive tool position point constructed for an embodiment of the present invention;

[0033] Figure 7 The image shows the training results of the NSGA-III multi-objective optimization model constructed according to an embodiment of the present invention. Detailed Implementation

[0034] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention. Furthermore, the technical features involved in the various embodiments of this invention described below can be combined with each other as long as they do not conflict with each other.

[0035] This invention provides a tool axis vector optimization domain planning method that considers workpiece machining compliance, such as... Figure 1 As shown, it includes the following steps:

[0036] S1. In ABAQUS software, establish a finite element proxy model of the workpiece, apply cutting force to the workpiece according to the tool position file, calculate the deformation slope between different cutting force differences as the equivalent compliance, and use Python secondary development to traverse and obtain the equivalent compliance of each tool position; then determine the maximum compliance point, i.e. the maximum deformation point.

[0037] S2. The cutting process of the tool is solved by differential equivalent solution. Each cutting edge micro-element is regarded as a bevel cutting process, and a bevel cutting model of each micro-element is established. The triaxial cutting force at each tool position point is expressed as a function of the equivalent chip thickness and the triaxial cutting force coefficient. The triaxial cutting force coefficients Krc, Ktc, and Kac of the tool during the finishing process are calibrated to obtain the cutting force prediction model and realize the expansion of the input parameter domain.

[0038] S3. Since the equivalent compliance represents the relationship between deformation and cutting force, the maximum cutting force can be obtained based on the maximum allowable deformation of the workpiece and the equivalent compliance of the maximum compliance point obtained in step S1. Then, combined with the cutting force prediction model from step S2 (i.e., the cutting force predicted by the cutting force prediction model must not exceed the maximum cutting force), a constraint condition is obtained. Based on this constraint condition and the preset machining parameter range, the NSGA-III algorithm is used to couple the machining parameters (depth of cut ap, width of cut ae, cutting speed v, feed rate fz) and tool posture (including rake angle θ) at the maximum compliance point. L Side tilt angle θ T Through multi-objective optimization, the critical tool axis vector of the maximum compliance point under different machining parameters and cutting forces is obtained, and then a set of critical machining parameters is determined to obtain the critical tool axis vector of the maximum compliance point under these machining parameters.

[0039] S4. Based on the maximum compliance point, calculate the critical tool axis vector for the next tool position. At this point, the tool axis vector should be within the upper and lower bounds of the constraint space domain, represented by the tilt angle and yaw angle. Traverse all tool positions, using the critical machining parameters of the maximum compliance point as a benchmark, to divide the tool axis vector domain for the entire tool position. Specifically, for any other tool position, obtain the maximum cutting force of that tool position based on the maximum allowable deformation of the workpiece and the equivalent compliance of that tool position. Then, combine this with the cutting force prediction model to obtain the error constraint conditions for that tool position. Based on the error constraint conditions of that tool position and the critical machining parameters of the maximum compliance point, perform multi-objective optimization of the tool axis vector for that tool position to obtain the tool axis vector planning space for that tool position under the machining parameters.

[0040] More preferably, in step S2, the tool is a ball-end tool. The ball-end tool is divided into micro-elements based on its height. The angled cutting model for each micro-element, i.e., the calculation method for the micro-element cutting force, is as follows:

[0041]

[0042] Where dFx, dFy, and dFz are the infinitesimal cutting forces in the workpiece coordinate system, and dF t dF r dF a This represents the tangential, radial, and axial infinitesimal cutting forces in the tool tip coordinate system. This is represented as the transformation matrix from the tool coordinate system to the tool tip coordinate system. It is represented as the transformation matrix from the workpiece coordinate system to the tool coordinate system, where dz is the highly discrete infinitesimal element, φ is the radial hysteresis angle, and h is the undeformed chip thickness.

[0043] The radial hysteresis angle φ is calculated using the following formula:

[0044]

[0045] Where j represents the cutting edge with the j-th tooth number of the tool, j∈[1~N]; N represents the number of tool teeth; z represents the height of the infinitesimal cutting edge; and β is the helix angle of the ball end mill. Let θ be the hysteresis angle when z equals zero, and r be the cutting radius corresponding to the position of the infinitesimal element.

[0046] Therefore, the cutting force prediction model is the equivalent integral of the above-mentioned oblique cutting model, and the cutting force calculation method of the cutting force prediction model is as follows:

[0047]

[0048] Where Fx, Fy, and Fz represent the cutting force model obtained by integrating the infinitesimal cutting force, and z0 is the upper limit of the integration of the infinitesimal cutting element, which represents the depth of cut.

[0049] More preferably, in step S3, when using the NSGA-III algorithm for multi-objective optimization, the objective optimization functions are minimizing workpiece deformation and maximizing cutting efficiency, and the critical machining parameters of the tool position point are optimized.

[0050] More preferably, in step S4, the tool axis vector range is found by traversing all tool positions to define the range of the tilt angle and the forward tilt angle, thus forming a tool axis vector constraint domain.

[0051] The following are specific examples:

[0052] A tool axis vector optimization domain planning method considering the machining compliance of thin-walled blades includes the following steps:

[0053] Step 1: Determine the range of input parameters in the thin-walled blade manufacturing process.

[0054] Based on the machining parameters in the actual machining process of thin-walled blades, the optimization range of machining parameters is determined. Here, the optimization range of parameters is limited according to the model of a compressor blade and its machining process, including depth of cut (0.1-0.3mm), width of cut (0.2-0.6mm), cutting speed (40-80m / s), feed (0.04-0.08mm), rake angle (25-45°), and side rake angle (25-45°). The workpiece material Ti6Al4V and its corresponding property parameters are determined. The cutting tool is a SECO tool, specifically model JS532040G3B.0Z2-NXT, with a diameter of 4mm and a total length of 63mm. Based on the actual machining process optimization range, the next step is to determine the corresponding machining parameter tool axis vector optimization domain.

[0055] Step 2: Establish a finite element proxy model of the workpiece.

[0056] The principle of extracting equivalent stiffness, such as Figure 2 As shown, a cutting force in the workpiece coordinate system is applied at the tool position corresponding to the tool path, and the deformation produced by the force F is observed. Changing the cutting force of different magnitudes will produce different deformations. The deformation is proportional to the magnitude of the force. Based on the difference between the slope and the deformation, the deformation slope of the workpiece is extracted and regarded as the equivalent stiffness.

[0057] The surrogate model was built using ABAQUS software. The workpiece has a unique shape, with varying cross-sectional dimensions and equivalent compliance at different locations. The surrogate model assigns material properties to the workpiece; in this example, the thin-walled blade is made of Ti6Al4V with a density of 4430 kg / m³. 3 It has a Poisson's ratio of 0.34, an elastic modulus of 104.5 GPa, and a Young's modulus of 895 MPa.

[0058] Using Python secondary development, the cutting force data at tool positions is cyclically loaded. In this embodiment, 70 analysis steps are used to load the cutting force at 70 tool positions along the toolpath trajectory, and a mesh is generated. Figure 3 As shown, a total of 4452 grids were divided. The grids were refined at the blade tip, with the specific grid size being approximately 1mm × 1mm × 1mm.

[0059] After submitting the job, the post-processing result file (ODB file) is processed to extract the deformation generated at the tool position during the application of the corresponding cutting force, and all tool positions are traversed. The cutting force is changed to calculate the equivalent compliance, and the compliance matrix image extracted from the tool positions is used as follows: Figure 4 As shown.

[0060] Step 3: Perform cutting force modeling and coefficient calibration.

[0061] like Figure 5 As shown, each height micro-element of the ball end mill is divided, and the model on each height micro-element of the ball end mill is equivalent to the micro-element oblique angle cutting model. The cutting force prediction model is the equivalent integral of the oblique angle cutting model.

[0062] Step 4: Construct tool axis vector programming based on the NSGA-III model.

[0063] The optimization of the tool axis vector involves multi-parameter, multi-objective optimization solutions, including depth of cut ap, width of cut ae, cutting speed v, feed rate fz, and rake angle θ. L Side tilt angle θ T In this multi-objective programming problem, the objectives are conflicting, and multiple objectives cannot be merged into a single unified objective for solution. Therefore, the NSGA-III multi-objective optimization model is constructed to perform multi-objective optimization at the point where the compliance value is maximized at the cutting edge. For example... Figure 6 As shown, when the machining parameters have a critical tool axis vector or a critical vector range at the point of maximum workpiece compliance (CL1) (represented here by the critical tool axis vector), then at other compliance value points (CL2, CL3, ..., CL...), n There will be a larger range of tool axis vector optimization. By setting the constraint function in the NSGA-III model, non-occupied target search can be performed on the depth of cut ap, width of cut ae, cutting speed v, and feed fz within the range of all optimization machining parameters. The constraint conditions in the NSGA-III model are as follows.

[0064]

[0065]

[0066] Where f1 is the deformation error optimization objective function based on the equivalent compliance model, represents the parameter set of machining parameters for the critical state of the tool axis, f represents the cutting force prediction model function, represents the cutting force value corresponding to the corresponding machining parameters, error represents the maximum allowable error of the thin-walled blade, and k1 represents the compliance value of the maximum compliance point among all tool positions. f2 represents the optimization objective function constrained by machining efficiency.

[0067] Multi-objective optimization is performed, with M = 6 (number of processing parameters and target domains), 400 iterations, 20 cross parameters, and 20 mutation parameters. The final training results are as follows. Figure 7As shown. The machining parameter values ​​considering the constraint functions f1 and f2 are selected according to requirements. These machining parameters are the critical machining parameters for the maximum compliance point. When all maximum compliance points satisfy these parameters, other points also satisfy them. Using the maximum allowable deformation error of each tool position point as the boundary, a traversal loop is performed on all tool positions to obtain the tool axis vector planning range for all tool positions under these machining parameters. This achieves the partitioning of the tool axis vector domain corresponding to the machining parameters. When the selection of machining parameters changes in the multi-objective optimization model, re-traversing the tool positions yields the new domain.

[0068] Those skilled in the art will readily understand that the above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A tool axis vector optimization domain planning method considering workpiece machining compliance, characterized in that, Includes the following steps: A finite element proxy model of the workpiece is established, and then cutting force is applied at each tool point of the workpiece to obtain the equivalent compliance of each tool point, and then the maximum compliance point is determined. Based on the tool cutting process, a cutting force prediction model is established; The maximum cutting force is obtained by taking the maximum allowable deformation of the workpiece and the equivalent compliance of the maximum compliance point, and then the constraint conditions are obtained by combining the cutting force prediction model. Based on the constraints and the preset range of machining parameters, the maximum compliance point is optimized by coupling the machining parameters in a multi-objective manner to obtain the critical machining parameters and the critical tool axis vector of the maximum compliance point under the critical machining parameters. Based on the critical tool axis vector of the maximum compliance point under critical machining parameters, the critical tool axis vectors of other tool positions under critical machining parameters are determined, and the optimization domain planning of the tool axis vector is completed.

2. The tool axis vector optimization domain planning method considering workpiece machining compliance as described in claim 1, characterized in that, The method for determining the equivalent compliance is as follows: For any tool position, a cutting force is applied to it, and the equivalent compliance of the tool position is calculated by the ratio of the difference in deformation of the tool position under different cutting forces to the difference in cutting force; then the tool position with the largest equivalent compliance is taken as the maximum compliance point.

3. The tool axis vector optimization domain planning method considering workpiece machining compliance as described in claim 1, characterized in that, The NSGA-III algorithm is used to perform multi-objective optimization of machining parameters coupled with the maximum compliance point. The objective functions are to minimize workpiece deformation and maximize cutting efficiency.

4. The tool axis vector optimization domain planning method considering workpiece machining compliance as described in claim 1, characterized in that, To determine the critical tool axis vector of other tool positions under critical machining parameters, specifically: for any other tool position, obtain the maximum allowable cutting force of the tool position based on the maximum allowable deformation of the workpiece and the equivalent compliance of the tool position, and then obtain the constraint conditions of the tool position by combining the cutting force prediction model; based on the constraint conditions of the tool position and the critical machining parameters, perform multi-objective optimization on the tool position to obtain the critical tool axis vector of the tool position under critical machining parameters.

5. The tool axis vector optimization domain planning method considering workpiece machining compliance as described in claim 1, characterized in that, The cutting process is solved by differential equivalent solution. Each cutting edge micro-element is regarded as a bevel cutting process. Bevel cutting model of each micro-element is established, and then the cutting force prediction model is obtained by integration.

6. The tool axis vector optimization domain planning method considering workpiece machining compliance as described in claim 5, characterized in that, The cutting force prediction model is specifically as follows: Where Fx, Fy, and Fz represent the triaxial cutting forces obtained by integrating the infinitesimal cutting forces, i.e., the cutting force prediction model; This is represented as the transformation matrix from the tool coordinate system to the tool tip coordinate system. Let z0 be the transformation matrix from the workpiece coordinate system to the tool coordinate system, z0 be the upper limit of the integral of the cutting element; Krc, Ktc, and Kac be the triaxial cutting force coefficients of the tool; dz be the highly discrete element; and h(φ) be the undeformed chip thickness corresponding to the radial hysteresis angle of the tool being φ.

7. The tool axis vector optimization domain planning method considering workpiece machining compliance as described in claim 6, characterized in that, The calculation method for the radial hysteresis angle of the cutting tool is as follows: Where j represents the j-th cutting edge of the tool, j∈[1~N], and N represents the total number of tool teeth; φ j (z) represents the radial lag angle of the j-th cutting edge relative to the tool tip at height z, where z represents the height of the infinitesimal cutting edge; β is the helix angle of the tool. The radial hysteresis angle is z = 0, and r is the cutting radius corresponding to the micro-element position.

8. The tool axis vector optimization domain planning method considering workpiece machining compliance as described in any one of claims 1-7, characterized in that, The machining parameters include depth of cut, width of cut, cutting speed, feed rate, rake angle, and yaw angle.

9. A tool axis vector optimization domain planning system considering workpiece machining compliance, characterized in that, Includes a processor for executing the tool axis vector optimization domain planning method considering workpiece machining compliance as described in any one of claims 1-8.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements the tool axis vector optimization domain planning method that considers the workpiece machining compliance as described in any one of claims 1-8.

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