Special-shaped milling cutter wear distribution prediction method considering thermal mechanical load

Abstract

The invention discloses a method for predicting wear distribution of a special-shaped milling cutter by considering a thermal mechanical load, which comprises the following steps of: discretizing a cutter, a workpiece model and a numerical control (NC) code, and identifying and calculating the swept volume of the cutter and a cutter-workpiece meshing area in each analysis step; after a tool-workpiece meshing area is obtained, whether the cutting edge infinitesimal participates in cutting of the current simulation step or not is judged; cutting working conditions of all cutting edge infinitesimal elements participating in cutting are extracted, a force thermal field is solved according to the cutting conditions of the cutting edge infinitesimal elements, and the abrasion width of each cutting edge infinitesimal element is calculated; and carrying out continuous processing on the wear width to obtain a wear distribution prediction result. According to the special-shaped milling cutter wear distribution prediction method considering the thermal mechanical load, wear joint prediction can be carried out on cutters in any shapes, complex cutting edge wear distribution can be accurately presented, the method is suitable for five-axis machining, the wear model is high in applicability, and the method has great significance on process optimization.

Description

Technical Field

[0001] The present invention relates to the technical field of machining, and in particular to a method for predicting the wear distribution of a special-shaped milling cutter considering thermo-mechanical loads. Background Art

[0002] Difficult-to-cut materials such as superalloys are widely used in the aviation industry. Due to the characteristics of the materials themselves, tool wear is usually relatively serious during the machining process. Excessive tool wear will directly affect the surface quality of parts and even lead to scrapping. Especially for high-value parts such as integral blisks, not only high surface quality requirements are needed, but also scrapping will cause great losses.

[0003] Therefore, it is very important to analyze and predict tool wear for a specific machining process before actual machining. The predicted wear in advance can help formulate a reasonable tool change plan, help improve tool life, and reduce production costs.

[0004] In milling, to meet the machining requirements of different parts, many cutting tools with complex cutting edges have been designed and widely used, including ball nose cutters with cutting edges not connected to the tip point, end mills with variable pitch and variable helix angle, various special-shaped roughing inserts, etc.

[0005] Currently, for these milling cutters with complex cutting edges, there is no general wear prediction method that can fully consider the geometric shapes of different cutting edges. The current tool wear prediction methods have two problems. One is that the wear distribution on the cutting edge cannot be predicted, and only single indicators such as VB or KT are predicted, which is not conducive to making full use of the machining ability of the tool. The other is that the modeling method is rough, and most do not explicitly model the milling cutter, especially unable to accurately model special-shaped milling cutters with unequal helix angles and cutting edges not connected to the top, which is not conducive to the accurate prediction of wear distribution.

[0006] Therefore, the present invention proposes a general method for predicting the wear distribution of a complex cutting edge milling cutter considering thermo / mechanical loads, which can solve this technical problem. Summary of the Invention

[0007] The object of the present invention is to provide a method for predicting the wear distribution of a special-shaped milling cutter considering thermo-mechanical loads. Compared with traditional finite element simulation, it has the advantages of high simulation efficiency, high simulation freedom, and the ability to jointly predict force-thermal-wear for any machining process and any shaped tool; it is especially suitable for predicting the wear distribution of the cutting edge during the five-axis machining process of tools with complex cutting edge shapes, and is of great significance for complex cutting edge design and process optimization of the five-axis machining process. It is a general method for predicting the wear distribution of the cutting edge of a tool during the milling process.

[0008] To achieve the above object, the present invention provides a method for predicting the wear distribution of a special-shaped milling cutter considering thermo-mechanical loads, comprising the following steps:

[0009] S1. Discretize the cutter, workpiece model and numerical control (NC) code, and in each analysis step, identify and calculate the swept volume of the cutter and the cutter-workpiece engagement area;

[0010] S2. After obtaining the cutter-workpiece engagement area, determine whether the cutting edge element participates in the cutting of the current simulation step;

[0011] S3. Extract the cutting conditions of all cutting edge elements participating in cutting, solve the force and heat fields according to the cutting conditions of the cutting edge elements, and calculate the wear width of each cutting edge element;

[0012] S4. Perform continuity processing on the wear width to obtain the prediction result of the wear distribution.

[0013] Preferably, in S1, the cutter, workpiece model and NC code are discretized by a method of separating and modeling the cutter rotating body and cutting edge based on a grid. Specifically:

[0014] First, establish a low-density volume grid for generating the cutter rotating body to reduce the computational amount in the process of calculating the cutter-workpiece engagement area; then perform high-density sampling on the cutting edge to ensure an accurate representation of the cutting edge geometry.

[0015] Preferably, in S1, the specific steps for identifying the cutter-workpiece engagement area are:

[0016] S11. Characterize the workpiece using a three-dimensional deep voxel (tri-dexel) model, and discretize the cutter rotating body with triangular meshes to achieve fast ray-triangle intersection calculation;

[0017] S12. Directly construct the cutter-workpiece engagement area, called CWE, through the intersection points of the cutter rotating body and the three-dimensional deep voxels of the material removal area. Its effectiveness is guaranteed by the acute angle judgment criterion of the feed direction and the normal vector;

[0018] S13. The final contact area is characterized by mapping a high-density point cloud to the cutter grid surface. For the determination problem of the cutting edge unit in the contact area, the empty sphere determination AEB algorithm is used:

[0019] Generate a double sphere with a preset radius R using the cutting edge element point and its neighboring CWE points. The centers of the two spheres and the cutting edge element point and CWE point form a rhombic plane;

[0020] When there are no other CWE points in the generated sphere, it is determined to be an empty sphere. If there are no CWE points within 2R around the cutting edge element, it is determined to be in a non-cutting state;

[0021] When there is a CWE point, traverse all neighborhood points to generate double spheres. If any empty sphere exists, it is determined that the unit is outside the contact area.

[0022] Preferably, in S2, after discretizing the cutting edge to obtain high-precision cutting edge micro-elements, determine whether the cutting edge micro-element participates in the cutting of the current simulation step. If it participates, calculate the current cutting conditions of the cutting edge micro-element, including the current cutting thickness, cutting width, cutting speed, flank wear width, and the orientation of the cutting edge micro-element, and enter S3; if it does not participate, return to S1 to continue the analysis step.

[0023] Preferably, determine the nominal chip thickness of the cutting edge micro-element through the feed vector, normal vector, and compensation coefficient of each cutting edge unit, and its mathematical expression is:

[0024]

[0025] In the formula, is the feed vector, is the normal vector, k i is the compensation coefficient;

[0026] When the nominal chip thickness is negative, it indicates that the cutting edge unit is located on the rake surface and does not participate in cutting.

[0027] Preferably, in S3, by constructing a synchronous prediction model of cutting force - cutting temperature - cutting edge wear, solve the force and heat fields according to the cutting conditions of the cutting edge micro-element. The specific process is as follows:

[0028] Adopt a hybrid model of finite element dataset + neural network to reconstruct the force and heat loads during the cutting process. For the micro-element cutting conditions output by the geometric modeling part, make a finite element dataset orthogonal to the cutting conditions, and obtain the relationship between the cutting conditions and the force and heat loads in the case of micro-elements.

[0029] Preferably, S3 specifically includes the following steps:

[0030] S31. Specify the cutting speed, instantaneous cutting thickness, and flank wear condition of the cutting edge micro-element in commercial finite element software, and run two-dimensional orthogonal cutting simulation to obtain the cutting temperature field and cutting normal stress field under the specified cutting speed, instantaneous cutting thickness, and flank wear width;

[0031] S32. Extract the average flank temperature and average flank normal stress from the obtained cutting temperature and cutting normal stress fields, that is, the force and heat loads, to drive the wear model;

[0032] S33. Use a forward neural network to fit the finite element data set, construct a prediction model with cutting conditions as the input and force and heat loads as the output, for predicting the force and heat loads of each cutting edge microelement under specific cutting conditions. The predicted force and heat loads are finally input into the wear prediction model to predict the increment of tool wear in each simulation step;

[0033] S34. Apply continuity conditions between different cutting edge microelements to obtain the distribution of wear on the cutting edge.

[0034] Preferably, in S33, the wear prediction model is expressed by the following formula:

[0035]

[0036] In the formula, respectively represent the flank wear widths of the i-th cutting edge microelement at the (N + 1)-th and N-th analysis steps, and the time interval between adjacent analysis steps is Δt;

[0037] where T f , σ r i.e., the force and heat loads predicted by the neural network, respectively represent the average temperature and average normal stress on the flank of the cutting edge microelement, b p , α, γ, v respectively represent the width of the cutting edge microelement, the flank angle of the cutting edge microelement, the rake angle of the cutting edge microelement, and the cutting speed of the cutting edge microelement;

[0038] C1 and C2 are physical parameters related to the wear model, representing the influence of cutting temperature on the wear rate.

[0039] Therefore, the present invention adopts the above-mentioned method for predicting the wear distribution of a special-shaped milling cutter considering thermo-mechanical loads, and the beneficial effects are as follows:

[0040] (1) The tool rotating body / cutting edge separation modeling method proposed by the present invention reduces the calculation amount by generating the tool rotating body with a low-density volume mesh, and at the same time ensures the accuracy by performing high-density sampling on the cutting edge. Combining with a specific tool-workpiece engagement area identification method, it can accurately predict the wear distribution on the cutting edge, rather than only predicting a single index, which is beneficial to giving full play to the machining ability of the tool.

[0041] (2) The present invention is particularly suitable for predicting the wear distribution of the cutting edge during the five-axis machining process of tools with complex cutting edge shapes, and is of great significance for complex cutting edge design and process optimization during the five-axis machining process. It is a general method for predicting the wear distribution of the cutting edge of a milling cutter during the milling process.

[0042] (3) The physical parameters in the wear model of the present invention are only related to the tool and workpiece materials and the wear mechanism. After being calibrated by standard experiments, they can be extended to the machining conditions of the same material tool - same material workpiece, greatly improving the applicability of the wear model. Without a large number of parameter calibrations, it can accurately predict the wear distribution along the cutting edge under different milling parameters, and can also consider the force and thermal loads during the machining process to achieve the synchronous simulation of cutting force - cutting temperature - cutting edge wear.

[0043] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Description of the Drawings

[0044] Figure 1 is the overall flowchart of an embodiment of the method for predicting the wear distribution of a special-shaped milling tool considering thermo-mechanical loads according to the present invention;

[0045] Figure 2 is the schematic diagram of the modeling of the separation of the tool rotating body / cutting edge in an embodiment of the method for predicting the wear distribution of a special-shaped milling tool considering thermo-mechanical loads according to the present invention;

[0046] Figure 3 is the schematic diagram of the process of determining whether the cutting edge unit is in the tool-workpiece engagement area in an embodiment of the method for predicting the wear distribution of a special-shaped milling tool considering thermo-mechanical loads according to the present invention;

[0047] Figure 4 is the schematic diagram of the method for analyzing the cutting conditions of the cutting edge micro-element in an embodiment of the method for predicting the wear distribution of a special-shaped milling tool considering thermo-mechanical loads according to the present invention;

[0048] Figure 5 is the relationship diagram between the cutting conditions and the force and thermal loads in an embodiment of the method for predicting the wear distribution of a special-shaped milling tool considering thermo-mechanical loads according to the present invention;

[0049] Figure 6 is the schematic diagram of the process of predicting the increment of tool wear within each simulation step in an embodiment of the method for predicting the wear distribution of a special-shaped milling tool considering thermo-mechanical loads according to the present invention. Detailed Embodiments

[0050] The technical solution of the present invention will be further described below with reference to the accompanying drawings and embodiments.

[0051] Unless otherwise defined, the technical terms or scientific terms used in the present invention shall have the ordinary meanings understood by those of ordinary skill in the field to which the present invention belongs.

[0052] As Figure 1 shown, a method for predicting the wear distribution of a special-shaped milling tool considering thermo-mechanical loads includes the following steps:

[0053] S1. Discretize the tool, workpiece model, and numerical control (NC) code, and in each analysis step, identify and calculate the swept volume of the tool and the tool-workpiece engagement area.

[0054] In this embodiment, to solve the problem of predicting the wear distribution of tools with arbitrary shapes, a geometric modeling method for separating the tool rotating body / cutting edge and a synchronous prediction model of cutting force-cutting temperature-cutting edge wear are proposed.

[0055] Method for separating the tool rotating body / cutting edge modeling: To ensure both calculation efficiency and cutting edge analysis accuracy, discretize the tool, workpiece model, and NC code by using a method based on grid-based separation modeling of the tool rotating body and cutting edge. Specifically:

[0056] First, establish a low-density volume grid for generating the tool rotating body, which is beneficial to reducing the computational amount in the process of calculating the tool-workpiece engagement area; then, perform high-density sampling on the cutting edge to ensure an accurate representation of the cutting edge geometry. This process is as Figure 2 shown.

[0057] The specific steps for identifying the tool-workpiece engagement area are as follows:

[0058] S11. Use a three-dimensional deep voxel (tri-dexel) model to represent the workpiece, and discretize the tool rotating body with triangular meshes to achieve fast ray-triangle intersection calculations.

[0059] S12. To balance accuracy and flexibility, directly construct the tool-workpiece engagement area, called CWE, through the intersection points of the tool rotating body and the three-dimensional deep voxels of the material removal area. Its effectiveness is guaranteed by the acute angle judgment criterion of the feed direction and the normal vector.

[0060] S13. The final contact area is characterized by mapping a high-density point cloud to the tool grid surface. For the determination problem of cutting edge elements in the contact area, as Figure 3 shown, use the empty ball judgment AEB algorithm:

[0061] Generate a double sphere with a preset radius R using the cutting edge micro-element point and its neighboring CWE points. The two sphere centers and the cutting edge micro-element point and CWE point form a rhombic plane.

[0062] When there are no other CWE points in the generated sphere, it is judged as an empty ball. If there are no CWE points within a range of 2R around the cutting edge micro-element, it is judged as a non-cutting state.

[0063] If there are CWE points, traverse all neighboring points to generate double spheres. If any empty ball exists, it is judged that the unit is outside the contact area. Through experimental verification, when the radius R is set to 1.5 - 2 times the three-dimensional deep voxel spacing, the optimal balance between calculation efficiency and accuracy can be achieved.

[0064] S2. After obtaining the tool-workpiece engagement area, determine whether the infinitesimal cutting edge participates in the cutting in the current simulation step;

[0065] Specifically, as Figure 4 shown, after discretizing the cutting edge to obtain high-precision infinitesimal cutting edges, determine whether the infinitesimal cutting edge participates in the cutting in the current simulation step. If it participates, calculate the current cutting conditions of the infinitesimal cutting edge. The cutting conditions include the current cutting thickness, cutting width, cutting speed, flank wear width, and the orientation of the infinitesimal cutting edge, and enter S3; if it does not participate, return to S1 to continue the analysis step.

[0066] Calculation of the cutting thickness of the infinitesimal cutting edge: Determine the nominal chip thickness of the infinitesimal cutting edge through the feed vector, normal vector, and compensation coefficient of each cutting edge unit. Its mathematical expression is:

[0067]

[0068] In the formula, is the feed vector (the combined vector of the translation vector and the rotation vector, and its modulus represents the feed per tooth), is the normal vector, and k i is the compensation coefficient;

[0069] Since the angle between the feed vector and the normal vector may be an obtuse angle, when the nominal chip thickness is negative, it indicates that the cutting edge unit is located on the relief surface and does not participate in the cutting.

[0070] S3. Extract the cutting conditions of all infinitesimal cutting edges participating in the cutting, solve the force and heat fields according to the cutting conditions of the infinitesimal cutting edges, and calculate the wear width of each infinitesimal cutting edge;

[0071] In this embodiment, by constructing a synchronous prediction model of cutting force-cutting temperature-cutting edge wear, the force and heat fields are solved according to the cutting conditions of the infinitesimal cutting edges. The specific process is as follows:

[0072] Adopt a hybrid model of finite element data set + neural network to reconstruct the force and heat loads during the cutting process. For the infinitesimal cutting conditions output by the geometric modeling part, make a finite element data set orthogonal to the cutting conditions, and obtain the relationship between the infinitesimal cutting conditions and the force and heat loads as Figure 5 shown.

[0073] S3 specifically includes the following steps:

[0074] S31. Specify the cutting speed, instantaneous cutting thickness, and flank wear condition of the cutting edge microelement in commercial finite element software, and run two-dimensional orthogonal cutting simulation to obtain the cutting temperature field and cutting normal stress field under the specified cutting speed, instantaneous cutting thickness, and flank wear width. The cutting speed, instantaneous cutting thickness, and flank wear width are the cutting conditions described above.

[0075] S32. Extract the average flank temperature and average flank normal stress from the obtained cutting temperature and cutting normal stress fields, which are the force-heat loads, and use them to drive the wear model.

[0076] S33. Use a forward neural network to fit the finite element data set, construct a prediction model with the cutting conditions as the input and the force-heat loads as the output, and use it to predict the force-heat loads of each cutting edge microelement under specific cutting conditions. The predicted force-heat loads are finally input into the wear prediction model to predict the increment of tool wear in each simulation step. The above process is as Figure 6 shown.

[0077] The wear prediction model is expressed by the following formula:

[0078]

[0079] In the formula, respectively represent the flank wear widths of the i-th cutting edge microelement at the (N + 1)-th and N-th analysis steps, and the time interval between adjacent analysis steps is Δt;

[0080] where T f , σ r are the force-heat loads predicted by the neural network, representing the average temperature and average normal stress of the flank of the cutting edge microelement respectively. b p , α, γ, v represent the width of the cutting edge microelement, the flank angle of the cutting edge microelement, the rake angle of the cutting edge microelement, and the cutting speed of the cutting edge microelement respectively. These quantities are all Figure 4 part of the cutting conditions in and can be calculated by the analysis program.

[0081] C1 and C2 are physical parameters related to the wear model, representing the influence of cutting temperature on the wear rate. Theoretically, these parameters are only related to the tool-workpiece materials and wear mechanisms, so they can be extended to the machining conditions of the same material tool - same material workpiece only after standard experiment calibration, greatly improving the applicability of the wear model.

[0082] S34. Apply continuity conditions between different cutting edge microelements to obtain the distribution of wear on the cutting edge.

[0083] The present physical modeling and wear prediction method can accurately predict the wear distribution along the cutting edge under different milling parameters without a large number of parameter calibrations. At the same time, it can also consider the force and heat loads during the machining process to achieve synchronous simulation of cutting force - cutting temperature - cutting edge wear.

[0084] S4. After completing all analysis steps, perform continuity processing on the wear width to obtain the wear distribution prediction result.

[0085] Therefore, the present invention adopts the above-mentioned method for predicting the wear distribution of a special-shaped milling cutter considering thermo-mechanical loads, which is applicable to predicting the wear distribution of the cutting edge of a cutter with a complex cutting edge shape during five-axis machining, and is of great significance for complex cutting edge design and process optimization in the five-axis machining process. It is a general method for predicting the wear distribution of the cutting edge of a cutter during the milling process.

[0086] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit them. Although the present invention has been described in detail with reference to the preferred embodiments, those of ordinary skill in the art should understand that they can still modify or equivalently replace the technical solutions of the present invention, and these modifications or equivalent replacements cannot make the modified technical solutions deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. A method for predicting the wear distribution of a special-shaped milling cutter considering thermo-mechanical loads, characterized in that, It includes the following steps: S1. Discretize the tool, workpiece model and numerical control (NC) code. In each analysis step, identify and calculate the swept volume of the tool and the tool-workpiece engagement area; S2. After obtaining the tool-workpiece engagement area, determine whether the infinitesimal cutting edge participates in the cutting of the current simulation step; S3. Extract the cutting conditions of all infinitesimal cutting edges participating in cutting. Solve the force and heat fields according to the cutting conditions of the infinitesimal cutting edges, and calculate the wear width of each infinitesimal cutting edge; S4. Perform continuity processing on the wear width to obtain the prediction result of the wear distribution.

2. A method for predicting the wear distribution of a special-shaped milling cutter considering thermo-mechanical loads according to claim 1, characterized in that, In S1, the tool, workpiece model and NC code are discretized by the method of separating the revolving body of the tool and the cutting edge based on grids. Specifically: First, establish a low-density volume grid to generate the revolving body of the tool, reducing the computational amount in the process of calculating the tool-workpiece engagement area. Then, perform high-density sampling on the cutting edge to ensure the accurate representation of the cutting edge geometry.

3. A method for predicting the wear distribution of a special-shaped milling cutter considering thermo-mechanical loads according to claim 2, characterized in that In S1, the specific steps for identifying the tool-workpiece engagement area are as follows: S11. Use a three-dimensional deep voxel (tri-dexel) model to represent the workpiece. The revolving body of the tool is discretized by triangular meshes to achieve fast ray-triangle intersection calculation; S12. Directly construct the tool-workpiece engagement area, called CWE, through the intersection points of the revolving body of the tool and the three-dimensional deep voxels of the material removal area. Its effectiveness is guaranteed by the acute angle judgment criterion of the feed direction and the normal vector; S13. The final contact area is characterized by mapping to the tool grid surface through a high-density point cloud. For the determination problem of the cutting edge unit in the contact area, the empty sphere determination AEB algorithm is used: Generate a double sphere with a preset radius R using the infinitesimal cutting edge point and its neighboring CWE points. The two sphere centers and the infinitesimal cutting edge point and CWE point form a rhombic plane; When there are no other CWE points in the generated sphere, it is determined as an empty sphere. If there are no CWE points within 2R around the infinitesimal cutting edge, it is determined as a non-cutting state; If there are CWE points, generate double spheres for all neighboring points. If any empty sphere exists, it is determined that the unit is outside the contact area.

4. A method for predicting the wear distribution of a special-shaped milling cutter considering thermo-mechanical loads according to claim 3, characterized in that In S2, after discretizing the cutting edge to obtain high-precision infinitesimal cutting edges, determine whether the infinitesimal cutting edge participates in the cutting of the current simulation step. If it participates, calculate the current cutting conditions of the infinitesimal cutting edge. The cutting conditions include the current cutting thickness, cutting width, cutting speed, flank wear width and the orientation of the infinitesimal cutting edge, and enter S3; If it does not participate, return to S1 to continue the analysis step.

5. A method for predicting the wear distribution of a special-shaped milling cutter considering thermo-mechanical loads according to claim 4, characterized in that Determine the nominal chip thickness of the infinitesimal cutting edge through the feed vector, normal vector and compensation coefficient of each cutting edge unit. Its mathematical expression is: In the formula, is the feed vector, is the normal vector, and k i is the compensation coefficient; When the nominal chip thickness is negative, it indicates that the cutting edge unit is located on the relief surface and does not participate in cutting.

6. A method for predicting the wear distribution of a special-shaped milling cutter considering thermo-mechanical loads according to claim 5, characterized in that In S3, by constructing a synchronous prediction model of cutting force-cutting temperature-cutting edge wear, solve the force and heat fields according to the cutting conditions of the infinitesimal cutting edges. The specific process is as follows: A hybrid model of finite element data set + neural network is used to reconstruct the force and heat loads during the cutting process. For the micro-cutting conditions output by the geometric modeling part, a finite element data set with orthogonal cutting conditions is made to obtain the relationship between the cutting conditions and the force and heat loads in the micro-element case.

7. A method for predicting the wear distribution of a special-shaped milling cutter considering thermo-mechanical loads according to claim 6, characterized in that S3 specifically includes the following steps: S31. Specify the cutting speed, instantaneous cutting thickness, and flank wear condition of the cutting edge micro-element in the commercial finite element software, and run the two-dimensional orthogonal cutting simulation to obtain the cutting temperature field and cutting normal stress field at the specified cutting speed, instantaneous cutting thickness, and flank wear width; S32. Extract the average flank temperature and average flank normal stress from the obtained cutting temperature and cutting normal stress fields, that is, the force and heat loads, to drive the wear model; S33. Use a forward neural network to fit the finite element data set, construct a prediction model with cutting conditions as the input and force and heat loads as the output, to predict the force and heat loads of each cutting edge micro-element under specific cutting conditions. The predicted force and heat loads are finally input into the wear prediction model to predict the increment of tool wear in each simulation step; S34. Apply continuity conditions between different cutting edge micro-elements to obtain the distribution of wear on the cutting edge.

8. A method for predicting the wear distribution of a special-shaped milling cutter considering thermo-mechanical loads according to claim 7, characterized in that In S33, the wear prediction model is expressed by the following formula: In the formula, respectively represent the flank wear widths of the i-th cutting edge micro-element at the (N + 1)-th and N-th analysis steps, and the time interval between adjacent analysis steps is Δt; where T f , σ r i.e., the thermo-mechanical load predicted by the neural network, representing the average temperature and average normal stress on the flank face of the cutting-edge micro-element, respectively, b p , α, γ, v represent the width of the cutting-edge micro-element, the flank angle of the cutting-edge micro-element, the rake angle of the cutting-edge micro-element, and the cutting speed of the cutting-edge micro-element, respectively; C1 and C2 are physical parameters related to the wear model, representing the influence of cutting temperature on the wear rate.

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