Milling workpiece surface topography prediction method considering multi-factor influence

Abstract

The invention belongs to the technical field of milling, and discloses a milling workpiece surface topography prediction method considering multi-factor influence, which comprises the following steps: considering a tool rake angle geometric parameter, establishing a milling force model, and calculating a shear force coefficient and a tillage force coefficient; a tool vibration displacement model is established, a generalized RKN4 method is adopted, a second-order motion differential equation of the tool vibration displacement model is directly solved, and the vibration displacement solving speed is increased; establishing a workpiece deformation model, and applying a node division method to workpiece deformation calculation; and establishing a surface topography prediction model, and generating a workpiece surface topography matrix by adopting a Z-map method. According to the milling workpiece surface topography prediction method considering the multi-factor influence, the geometric parameters of the front angle are considered, and accurate prediction of the milling force is achieved; a generalized RKN4 method is adopted, so that the vibration displacement solving efficiency is improved; influences of tool vibration displacement and workpiece deformation on the surface topography are comprehensively considered, and accurate prediction of the surface topography is achieved.

Description

Technical Field

[0001] This invention relates to the field of milling technology, and in particular to a method for predicting the surface morphology of milled workpieces that takes into account the influence of multiple factors. Background Technology

[0002] In the field of end mill side milling technology, especially for the machining of precision parts with high surface quality requirements in aerospace and automotive manufacturing, the industry's need for accurate prediction of surface morphology is increasingly urgent. Currently, it is generally believed that tool geometry parameters, motion trajectory, and the dynamic response of the machining system are key factors affecting surface quality. Regarding tool geometry, researchers have successfully developed numerous static milling force models that consider tool runout, installation errors, and dynamic changes in the thickness of undeformed chips. These models can accurately describe trajectory interference and chip load distribution during multi-tooth cutting. In terms of system dynamics, research has further extended to the mechanism of the effect of tool-workpiece relative vibration on surface micromorphology, and a correlation model between vibration characteristics and cutting forces has been established through experimental measurements and intelligent algorithms such as neural networks. For the machining of thin-walled parts, researchers are dedicated to predicting workpiece deformation, developing stiffness evolution models based on finite element method, birth and death element, and voxelization methods to simulate the impact of workpiece deflection and stress redistribution under cutting forces on the macroscopic geometric errors of the machined surface.

[0003] However, current theoretical modeling methods have key limitations. First, existing methods generally oversimplify the geometry of the cutting edge, which limits the prediction accuracy of the cutting force model. Second, the computational efficiency is limited when solving for displacement. Third, it is difficult to achieve high computational efficiency while accurately predicting workpiece deformation. Fourth, existing models fail to fully integrate the combined effects of tool vibration and workpiece deformation on surface morphology, resulting in insufficient prediction accuracy of surface morphology. Therefore, a new approach is urgently needed to address these problems. Summary of the Invention

[0004] The purpose of this invention is to provide a method for predicting the surface morphology of milled workpieces that considers the influence of multiple factors. It considers the rake angle geometric parameters to achieve accurate prediction of milling force; it adopts the generalized RKN4 method to improve the efficiency of vibration displacement solution; and it comprehensively considers the influence of tool vibration displacement and workpiece deformation on surface morphology to achieve accurate prediction of surface morphology.

[0005] To achieve the above objectives, the present invention provides a method for predicting the surface morphology of milled workpieces considering the influence of multiple factors, comprising the following steps: Step S1: Considering the geometric parameters of the tool rake angle, establish a milling force model to calculate the shear force coefficient and tillage force coefficient; Step S2: Establish the tool vibration displacement model and use the generalized RKN4 method to directly solve its second-order motion differential equations; Step S3: Establish a workpiece deformation model and apply the node partitioning method to workpiece deformation calculation; Step S4: Establish a surface morphology prediction model and use the Z-map method to generate the workpiece surface morphology matrix.

[0006] Preferably, in step S1, considering the geometric parameters of the tool rake angle, a milling force model is established, and the specific process is as follows: Step S11: Establish the end mill coordinate system and determine the tool parameters; The tool parameters of a cylindrical end mill include radius. helix angle and front corner The origin is located at the center of the bottom circle of the cutting tool. The axis is along the feed direction. The axis is perpendicular to axis, The axis is along the tool axis; Step S12: Adjust the spiral cutting edge of the tool The axis is discretized into several infinitesimal elements to establish a milling force model; The spiral edge of the tool The axis is discretized into several infinitesimal elements, and the differential element acting on the k-th cutting edge... Above, axial height and angle position The cutting force is described as the tangential force component. Radial force component and axial force component As shown below: (1); in, , and These represent the shear force coefficients in the tangential, radial, and axial directions, respectively. , and These represent the plowing force coefficients in the tangential, radial, and axial directions, respectively. Represents the axial position of the k-th cutting edge. and angle position The instantaneous uncut thickness; Considering the geometry of the cutting tool, the relationship between the height and angular position of the helical cutting edge is as follows: (2); Substituting formula (2) into formula (1) and integrating along the spiral edge, we get: (3); in, , and These represent the milling forces along the x, y, and z directions, respectively. and These represent the starting angle and ending angle of integration, respectively. This represents the number of cutting teeth.

[0007] Preferably, in calculating the milling force coefficient, the influence of the tool rake angle on the milling force is considered, and the tangential, radial, and axial shear force coefficients are calculated. , and As shown below: (4); in, Represents the shear flow stress on the shear surface; Represents the normal shear angle; Represents the normal friction angle; The representation method is forward-angled; Represents the tilt angle; Represents the chip velocity angle measured on the rake angle face; using the tool rake angle Substitution method forward angle For helical end mills, the tilt angle Equivalent to helix angle Chip velocity angle Equivalent to tilt angle ; Based on the momentum balance analysis of the chip cut by the cutting tip and the normal friction angle The following formula is derived: (5); in, An exponential constant representing the pressure distribution; This represents the coefficient of sliding friction at the tool-chip interface; Normal shear angle As shown below: (6); in, and It is a constant.

[0008] Preferably, the tangential, radial, and axial tillage coefficients are calculated using a slip-line field model. , and As shown below: (7); in, Indicated by point The radius of the circular sector centered on it; Normal shear angle; , and It is the sector angle, determined by geometric and frictional relationships; The value of is negligible, so it is set to zero.

[0009] Preferably, in step S2, a tool vibration displacement model is established, and its second-order motion differential equation is directly solved using the generalized RKN4 method. The specific process is as follows: Step S21: The vibration displacement model is simplified into a two-degree-of-freedom (DOF) spring-mass-damped system, whose motion differential equation is expressed as: (8); in, , , ; and respectively along the cutting tool shaft and The mass of the shaft; and respectively along the cutting tool shaft and Damping coefficient of the shaft; and respectively along the cutting tool shaft and Shaft stiffness; , and Representing the cutting edge shaft and Milling force in the axial direction; , and These represent the tools in shaft and Displacement in the axial direction; The acceleration of the vibration displacement; The velocity of the vibration displacement; Step S22: Use the generalized RKN4 method to directly solve the second-order differential equations of motion; For second-order ordinary differential equations, when applying the generalized fourth-order Runge-Kutta-Nyström method, the intermediate variables at each stage are calculated based on the current time, displacement, velocity, and step size as follows: (9); in, , , and For intermediate iteration variables; Step size; The current time; For displacement; For speed; Iteration function; The update formula for the solution is expressed as: (10); (11); in, Indicates the displacement at the next time point; Indicates the velocity at the next time point; By combining formulas (8) and (11), the vibration displacement of the tool can be obtained.

[0010] Preferably, in step S3, the node partitioning method is applied to the workpiece deformation calculation, and the specific process is as follows: First, a finite element model of the workpiece is established, and the bottom edge of the workpiece is regarded as a fixed end. In the finite element model, the nodes are divided into two categories: retained nodes located on the machined surface and reduced nodes located on the unmachined surface. Then, during the milling process, the deformation calculation of the workpiece at each feed position is performed on the reserved node; Finally, the process of solving the overall workpiece deformation can be simplified by only calculating the retained nodes, reducing the number of calculation nodes from the total number of workpiece nodes to only the nodes in the machining area.

[0011] Preferably, based on the theory of elastic deformation, the deformation equation for a thin-walled workpiece is as follows: (12); in, Represents the global stiffness matrix of the workpiece; Represents the workpiece displacement matrix; Indicates milling force; Based on the node partitioning method, formula (12) is transformed into: (13); in, , , and Let these represent the stiffness submatrices for retained nodes, reduced nodes, and reduced nodes respectively; and define a displacement matrix for each node type. This represents the displacement matrix that preserves the set of nodes. The displacement matrix represents the reduction of the node set; and These represent the milling forces applied to the retained node set and the reduced node set, respectively; During the machining process, milling force It only acts on the machined surface, therefore Set as the zero vector, substituting this vector into formula (12) yields: (14); The reduced stiffness equation for the nodal displacement solution of the milled surface is as follows: (15); Because the material is removed during the machining process, the local stiffness of the workpiece will change. Therefore, the workpiece stiffness matrix is ​​updated at each feed position, that is, the cutting process is simulated by subtracting the stiffness matrix of the corresponding element. Therefore, when the tool feeds to the next feed position, the numerical relationship between the workpiece stiffness matrices of adjacent feed positions is expressed as follows: (16); in, Indicates that the cutting tool has reached the first... Workpiece stiffness matrix at each feed position; Indicates that the cutting tool has reached the first... Stiffness matrix at each feed position; This indicates the number of complete finite element units contained in the volume of material cut between these two adjacent feed positions; Indicates the number of incomplete finite element elements that were removed; The scaling factor describes the ratio of the cutting volume to the total volume between adjacent feed positions; scaling factor Defined as: (17); in, Indicates the volume of material removed; Represents the volume of a single complete unit; The workpiece deformation is solved by combining formulas (14)-(17).

[0012] Preferably, in step S4, a surface morphology prediction model is established, and the specific process is as follows: Step S41: First, establish four coordinate systems to characterize the spatial relationships within the tool-workpiece system: Tool coordinate system ; Workpiece coordinate system ; Tool offset coordinate system ; Principal axis reference coordinate system ; In this system, the axis of the tool offset coordinate system is parallel to the spindle axis; Step S42: Then, based on the establishment of these coordinate systems, the relative position and attitude changes between the tool and the workpiece are systematically characterized. Tool parallel axis offset mark , defined as the distance between the tool axis and the spindle axis at the tool's fixed end; angle Representing a plane The angle between them; In the tool coordinate system, the tool is simplified to a shape with... A cylinder with several cutting edges, all evenly distributed on a nominal cylindrical surface of radius r, then the position angle... Represented as: (18); in, Indicated by the helix angle The resulting angular delay is as follows: (19); Indicates teeth The angular distance between tooth 1 and tooth 1 is shown below: (20); Step S43: The coordinates of the discrete points of the cutting edge in the tool coordinate system are as follows: (twenty one); The position of the tool tip relative to the principal axis coordinate system is determined by coordinate transformation, as shown below: (twenty two); in, , ; Let x be the x-coordinate of point P in the tool coordinate system; Let P be the y-coordinate of point P in the tool coordinate system; Let z be the z-coordinate of point P in the tool coordinate system; Step S44, Main spindle reference coordinate system orbiting at a constant angular velocity The shaft rotates, and moves a distance along the feed direction with each revolution. ; In the workpiece coordinate system The discrete points of the cutting edge are shown below: (twenty three); in, Indicates the tool's rotation around the spindle axis The rotation angle; Let x be the x-coordinate of point P in the workpiece coordinate system; Let P be the y-coordinate of point P in the workpiece coordinate system; Let z be the z-coordinate of point P in the workpiece coordinate system; Let x be the x-coordinate of point P in the principal axis coordinate system; Let P be the y-coordinate of point P in the principal axis coordinate system; Let z be the z-coordinate of point P in the principal axis coordinate system.

[0013] Preferably, based on the obtained positions of the points in the workpiece coordinate system, the Z-map method is used to generate the workpiece surface topography matrix. The specific process is as follows: First, according to the workpiece A specific level of precision on a plane discretizes the workpiece into several uniformly distributed grid points; Secondly, the workpiece corresponding to each grid Axis height is determined by grid number Corresponding two-dimensional matrix elements This indicates that the actual machining process of the cutting teeth on the workpiece is represented by a surface morphology matrix. The continuous update process; Considering tool vibration displacement and workpiece deformation, the actual surface morphology matrix As shown below: (twenty four); in, Indicates the displacement due to tool vibration; Indicates the workpiece deformation error; Finally, the surface morphology matrix It is converted into a three-dimensional surface, which represents the morphological features of the processed surface.

[0014] Therefore, the present invention adopts the above-mentioned method for predicting the surface morphology of milled workpieces that considers the influence of multiple factors, takes into account the rake angle geometric parameters, and realizes accurate prediction of milling force; adopts the generalized RKN4 method to improve the efficiency of vibration displacement solution; and comprehensively considers the influence of tool vibration displacement and workpiece deformation on surface morphology to realize accurate prediction of surface morphology.

[0015] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0016] Figure 1 This is a diagram of the milling force model of the present invention; Figure 2 This is a model diagram of the slide wire field of the present invention; Figure 3 These are milled surface diagrams under the influence of vibration according to the present invention; wherein, (a) is the ideal milling process; and (b) is the milling process considering the influence of vibration. Figure 4 This is a diagram showing the workpiece deformation and workpiece structure division of the present invention; wherein, (a) is during processing; (b) is after processing; and (c) is the node division. Figure 5This is a geometric modeling diagram of the tool runout of the present invention; wherein, (a) is a three-dimensional view; and (b) is a top view; Figure 6 This is a tool trajectory diagram that takes into account tool runout in this invention; Figure 7 This invention uses the Z-map method to predict the surface morphology of a workpiece. Detailed Implementation

[0017] The technical solution of the present invention will be further described below with reference to the accompanying drawings and embodiments.

[0018] This invention provides a method for predicting the surface morphology of milled workpieces considering the influence of multiple factors, comprising the following steps: Step S1: Considering the geometric parameters of the tool rake angle, establish a milling force model to calculate the shear force coefficient and tillage force coefficient; Step S2: Establish the tool vibration displacement model and use the generalized RKN4 method to directly solve its second-order motion differential equation to improve the speed of vibration displacement solution. Step S3: Establish a workpiece deformation model and apply the node partitioning method to workpiece deformation calculation; Step S4: Establish a surface morphology prediction model and use the Z-map method to generate the workpiece surface morphology matrix.

[0019] Example Step S1: Considering the geometric parameters of the tool rake angle, establish a milling force model to calculate the shear force coefficient and tillage force coefficient.

[0020] Step S11: Establish the end mill coordinate system and determine the tool parameters.

[0021] like Figure 1 As shown, the tool parameters of a cylindrical end mill include radius. helix angle and front corner The origin is located at the center of the bottom circle of the tool. The axis is along the feed direction. The axis is perpendicular to axis, The axis is along the tool axis.

[0022] Step S12: Adjust the spiral cutting edge of the tool The axis is discretized into several infinitesimal elements to establish a milling force model.

[0023] To establish a milling force model, the helical cutting edge of the tool... The axis is discretized into several infinitesimal elements, and the differential element acting on the k-th cutting edge ( On the axial height and angle position The cutting force is described as the tangential force component. Radial force component and axial force component As shown below: (1); in, , and These represent the shear force coefficients in the tangential, radial, and axial directions, respectively. , and These represent the plowing force coefficients in the tangential, radial, and axial directions, respectively. Represents the axial position of the k-th cutting edge. and angle position The instantaneous uncut thickness.

[0024] Considering the geometry of the cutting tool, the relationship between the height and angular position of the helical cutting edge is as follows: (2); Substituting formula (2) into formula (1) and integrating along the spiral edge, we get: (3); in, , and These represent the milling forces along the x, y, and z directions, respectively. and These represent the starting angle and ending angle of integration, respectively. This represents the number of cutting teeth.

[0025] Step S13: In the process of calculating the milling force coefficient, the influence of the tool rake angle on the milling force is considered, and the tangential, radial, and axial shear force coefficients are calculated. , and As shown below: (4); in, Represents the shear flow stress on the shear surface; Represents the normal shear angle; Represents the normal friction angle; The representation method is forward-angled; Represents the tilt angle; This represents the chip velocity angle measured on the front face.

[0026] In this invention, the rake angle of the cutting tool is used. Substitution method forward angle For helical end mills, the tilt angle Equivalent to helix angle Chip velocity angle Approximately equal to the angle of inclination This enables accurate prediction of milling force.

[0027] Based on the momentum balance analysis of the chip cut by the cutting tip and the normal friction angle The following formula is derived: (5); in, The exponential constant representing the pressure distribution (usually taken as 3); This represents the coefficient of sliding friction at the tool-chip interface. Normal shear angle. As shown below: (6); in, Take 0.785; Take 0.5.

[0028] Step S14, as follows Figure 2 As shown, the tillage coefficients in the tangential, radial, and axial directions are calculated using a slip-line field model. , and As shown below: (7); in, Indicated by point The radius of the circular sector centered on it; Normal shear angle; , and It is the sector angle, determined through geometric and frictional relationships; generally The value of is negligible, so it is set to zero.

[0029] Step S2: Establish the tool vibration displacement model and use the generalized RKN4 method to directly solve its second-order motion differential equations to improve the speed of vibration displacement solution.

[0030] Step S21, as follows Figure 3 As shown, the vibration displacement model is simplified to a two-degree-of-freedom (DOF) spring-mass-damped system, whose motion differential equation is expressed as: (8); in, , , ; and respectively along the cutting tool shaft and The mass of the shaft; and respectively along the cutting tool shaft and Damping coefficient of the shaft; and respectively along the cutting tool shaft and Shaft stiffness; , and Representing the cutting edge shaft and Milling force in the axial direction; , and These represent the tools in shaft and Displacement in the axial direction; The acceleration of the vibration displacement; The velocity is the vibration displacement.

[0031] Step S22: Use the generalized Runge-Kutta-Nyström (RKN4) method to directly solve the second-order motion differential equations, thereby improving the speed of solving for vibration displacement.

[0032] For second-order ordinary differential equations, when applying the generalized fourth-order Runge-Kutta-Nyström method, the intermediate variables at each stage are calculated based on the current time, displacement, velocity, and step size as follows: (9); in, , , and For intermediate iteration variables; Step size; The current time; For displacement; For speed; This is an iterative function.

[0033] The update formula for the solution is expressed as: (10); (11); in, Indicates the displacement at the next time point; This indicates the speed at the next time point.

[0034] By combining formulas (8) and (11), the vibration displacement of the tool can be obtained.

[0035] Step S3: Establish a workpiece deformation model and apply the node partitioning method to workpiece deformation calculation.

[0036] like Figure 4 As shown in (a) above, during machining, thin-walled parts deform under cutting forces due to their low stiffness. Figure 4 As shown in (b), the elastic recovery of the workpiece after processing causes a deviation between the final surface and the ideal surface.

[0037] Therefore, the node partitioning method is applied to workpiece deformation calculation. The specific process is as follows: First, a finite element model of the workpiece is established, with the bottom edge of the workpiece considered as a fixed end. In the finite element model, nodes are divided into two categories: retained nodes located on the machined surface and reduced nodes located on the unmachined surface.

[0038] Then, during the milling process, the deformation calculation of the workpiece at each feed position is performed on the reserved node.

[0039] Finally, by calculating only the retained nodes, the solution process for the overall workpiece deformation can be simplified, reducing the number of calculation nodes from the total number of workpiece nodes to only the nodes in the machining area, such as... Figure 4 As shown in (c).

[0040] According to the theory of elastic deformation, the deformation equation for a thin-walled workpiece is as follows: (12); in, Represents the global stiffness matrix of the workpiece; Represents the workpiece displacement matrix; This indicates the milling force.

[0041] Based on the node partitioning method, formula (12) is transformed into: (13); in, , , and Let these represent the stiffness submatrices for retained nodes, reduced nodes, and reduced nodes respectively; and define a displacement matrix for each node type. This represents the displacement matrix that preserves the set of nodes. The displacement matrix represents the reduction of the node set; and These represent the milling forces applied to the retained node set and the reduced node set, respectively.

[0042] During the machining process, milling force It only acts on the machined surface, therefore Set as the zero vector, substituting this vector into formula (12) yields: (14); The reduced stiffness equation for the nodal displacement solution of the milled surface is as follows: (15); Due to material removal during machining, the local stiffness of the workpiece changes, necessitating an update of the workpiece stiffness matrix at each feed position. To simplify this process, the cutting process is simulated by subtracting the corresponding element stiffness matrix. Therefore, when the tool moves to the next feed position, the numerical relationship between the workpiece stiffness matrices at adjacent feed positions is expressed as follows: (16); in, Indicates that the cutting tool has reached the first... Workpiece stiffness matrix at each feed position; Indicates that the cutting tool has reached the first... Stiffness matrix at each feed position; This indicates the number of complete finite element units contained in the volume of material cut between these two adjacent feed positions; Indicates the number of incomplete finite element elements that were removed; This represents the scaling factor, describing the ratio of the cutting volume to the total volume between adjacent feed positions. Scaling factor Defined as: (17); in, Indicates the volume of material removed; This represents the volume of a single complete unit.

[0043] The workpiece deformation is solved by combining formulas (14)-(17).

[0044] Step S4: Establish a surface morphology prediction model and use the Z-map method to generate the workpiece surface morphology matrix.

[0045] Step S41: First, establish four coordinate systems to characterize the spatial relationships within the tool-workpiece system: Tool coordinate system ; Workpiece coordinate system ; Tool offset coordinate system ; Principal axis reference coordinate system ; In this system, the axis of the tool offset coordinate system is parallel to the axis of the spindle.

[0046] Step S42: Then, based on the establishment of these coordinate systems, the relative position and attitude changes between the tool and the workpiece are systematically characterized.

[0047] like Figure 5 As shown, the tool's parallel axis offset (labeled as...) Angle is defined as the distance between the tool axis and the spindle axis at the fixed end of the tool. Representing a plane The angle between them. Due to tool runout, the actual trajectory of the cutting edge deviates from the theoretical trajectory, affecting the cutting area, such as... Figure 6 As shown.

[0048] In the tool coordinate system, the tool is simplified to a shape with... A cylinder with several cutting edges, all evenly distributed on a nominal cylindrical surface of radius r, then the position angle... Represented as: (18); in, Indicated by the helix angle The resulting angular delay is as follows: (19); Indicates teeth The angular distance between tooth 1 and tooth 1 is shown below: (20); Step S43: The coordinates of the discrete points of the cutting edge in the tool coordinate system are as follows: (twenty one); The position of the tool tip relative to the principal axis coordinate system is determined by coordinate transformation, as shown below: (twenty two); in, , ; Let x be the x-coordinate of point P in the tool coordinate system; Let P be the y-coordinate of point P in the tool coordinate system; Let P be the z-coordinate of point P in the tool coordinate system.

[0049] Step S44, Main spindle reference coordinate system orbiting at a constant angular velocity The shaft rotates, and moves a distance along the feed direction with each revolution. In the workpiece coordinate system The discrete points of the cutting edge are shown below: (twenty three); in, Indicates the tool's rotation around the spindle axis The rotation angle; Let x be the x-coordinate of point P in the workpiece coordinate system; Let P be the y-coordinate of point P in the workpiece coordinate system; Let z be the z-coordinate of point P in the workpiece coordinate system; Let x be the x-coordinate of point P in the principal axis coordinate system; Let P be the y-coordinate of point P in the principal axis coordinate system; Let z be the z-coordinate of point P in the principal axis coordinate system.

[0050] After obtaining the positions of the points in the workpiece coordinate system through the above steps, the Z-map method is finally used to generate the workpiece surface topography matrix. The three-dimensional surface topography generated by the Z-map method can be summarized into the following three implementation steps: First, according to the workpiece A specific level of precision on a plane discretizes the workpiece into several uniformly distributed grid points.

[0051] Secondly, the workpiece corresponding to each grid The axis height can be represented by the two-dimensional matrix element corresponding to the grid number.

[0052] For example, a grid point is numbered as Then the workpiece The axis height can be determined by the surface topography matrix element. The actual machining process of the cutting teeth on the workpiece can be approximated as a surface morphology matrix. The continuous update process. During the cutting process, discrete points from the cutting edge at different time points may fall into the same workpiece mesh. At this point, selection... The point with the lowest coordinate value is used as the terrain record point for that grid, such as... Figure 7 As shown. Considering tool vibration displacement and workpiece deformation, the actual surface topography matrix is... As shown below: (twenty four); in, Indicates the displacement due to tool vibration; This indicates the workpiece deformation error.

[0053] Finally, the surface morphology matrix It is converted into a three-dimensional surface, which represents the morphological features of the processed surface.

[0054] Therefore, the present invention adopts the above-mentioned method for predicting the surface morphology of milled workpieces that considers the influence of multiple factors, takes into account the rake angle geometric parameters, and realizes accurate prediction of milling force; adopts the generalized RKN4 method to improve the efficiency of vibration displacement solution; and comprehensively considers the influence of tool vibration displacement and workpiece deformation on surface morphology to realize accurate prediction of surface morphology.

[0055] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit them. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the technical solutions of the present invention, and these modifications or equivalent substitutions cannot cause the modified technical solutions to deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. A method for predicting the surface morphology of milled workpieces considering the influence of multiple factors, characterized in that, Includes the following steps: Step S1: Considering the geometric parameters of the tool rake angle, establish a milling force model to calculate the shear force coefficient and tillage force coefficient; Step S2: Establish the tool vibration displacement model and use the generalized RKN4 method to directly solve its second-order motion differential equations; Step S3: Establish a workpiece deformation model and apply the node partitioning method to workpiece deformation calculation; Step S4: Establish a surface morphology prediction model and use the Z-map method to generate the workpiece surface morphology matrix.

2. The method for predicting the surface morphology of a milled workpiece considering the influence of multiple factors according to claim 1, characterized in that, In step S1, considering the tool rake angle geometry parameters, a milling force model is established, and the specific process is as follows: Step S11: Establish the end mill coordinate system and determine the tool parameters; The tool parameters of a cylindrical end mill include radius. helix angle and front corner The origin is located at the center of the bottom circle of the cutting tool. The axis is along the feed direction. The axis is perpendicular to axis, The axis is along the tool axis; Step S12: Adjust the spiral cutting edge of the tool The axis is discretized into several infinitesimal elements to establish a milling force model; The spiral edge of the tool The axis is discretized into several infinitesimal elements, and the differential element acting on the k-th cutting edge... Above, axial height and angle position The cutting force is described as the tangential force component. Radial force component and axial force component As shown below: （1）； in, , and These represent the shear force coefficients in the tangential, radial, and axial directions, respectively. , and These represent the plowing force coefficients in the tangential, radial, and axial directions, respectively. Represents the axial position of the k-th cutting edge. and angle position The instantaneous uncut thickness; Considering the geometry of the cutting tool, the relationship between the height and angular position of the helical cutting edge is as follows: （2）； Substituting formula (2) into formula (1) and integrating along the spiral edge, we get: （3）； in, , and These represent the milling forces along the x, y, and z directions, respectively. and These represent the starting angle and ending angle of integration, respectively. This represents the number of cutting teeth.

3. The method for predicting the surface morphology of a milled workpiece considering the influence of multiple factors according to claim 2, characterized in that, In calculating the milling force coefficient, the influence of the tool rake angle on the milling force is considered, and the tangential, radial, and axial shear force coefficients are calculated. , and As shown below: （4）； in, Represents the shear flow stress on the shear surface; Represents the normal shear angle; Represents the normal friction angle; The representation method is forward-facing; Represents the tilt angle; Represents the chip velocity angle measured on the rake angle face; using the tool rake angle Substitution method forward angle For helical end mills, the tilt angle Equivalent to helix angle Chip velocity angle Equivalent to tilt angle ; Based on the momentum balance analysis of the chip cut by the cutting tip and the normal friction angle The following formula is derived: （5）； in, An exponential constant representing the pressure distribution; This represents the coefficient of sliding friction at the tool-chip interface; Normal shear angle As shown below: （6）； in, and It is a constant.

4. The method for predicting the surface morphology of a milled workpiece considering the influence of multiple factors according to claim 2, characterized in that, The tangential, radial, and axial tillage coefficients were calculated using a slip-line field model. , and As shown below: （7）； in, Indicated by point The radius of the circular sector centered on it; Normal shear angle; , and It is the angle of the sector field, determined by geometric and frictional relationships; The value of is negligible, so it is set to zero.

5. The method for predicting the surface morphology of a milled workpiece considering the influence of multiple factors according to claim 1, characterized in that, In step S2, a tool vibration displacement model is established, and its second-order motion differential equation is directly solved using the generalized RKN4 method. The specific process is as follows: Step S21: The vibration displacement model is simplified into a two-degree-of-freedom (DOF) spring-mass-damped system, whose motion differential equation is expressed as: （8）； in, , , ; and respectively along the cutting tool shaft and The mass of the shaft; and respectively along the cutting tool shaft and Damping coefficient of the shaft; and respectively along the cutting tool shaft and Shaft stiffness; , and Representing the cutting edge shaft and Milling force in the axial direction; , and These represent the tools in shaft and Displacement in the axial direction; The acceleration of the vibration displacement; The velocity of the vibration displacement; Step S22: Use the generalized RKN4 method to directly solve the second-order motion differential equations; For second-order ordinary differential equations, when applying the generalized fourth-order Runge-Kutta-Nyström method, the intermediate variables at each stage are calculated based on the current time, displacement, velocity, and step size as follows: （9）； in, , , and For intermediate iteration variables; Step size; The current time; For displacement; For speed; Iteration function; The update formula for the solution is expressed as: （10）； （11）； in, Indicates the displacement at the next time point; Indicates the velocity at the next time point; By combining formulas (8) and (11), the vibration displacement of the tool can be obtained.

6. The method for predicting the surface morphology of a milled workpiece considering the influence of multiple factors according to claim 1, characterized in that, In step S3, the node partitioning method is applied to the workpiece deformation calculation. The specific process is as follows: First, a finite element model of the workpiece is established, and the bottom edge of the workpiece is regarded as a fixed end. In the finite element model, the nodes are divided into two categories: retained nodes located on the machined surface and reduced nodes located on the unmachined surface. Then, during the milling process, the deformation calculation of the workpiece at each feed position is performed on the reserved node; Finally, the process of solving the overall workpiece deformation can be simplified by only calculating the retained nodes, reducing the number of calculation nodes from the total number of workpiece nodes to only the nodes in the machining area.

7. The method for predicting the surface morphology of a milled workpiece considering the influence of multiple factors according to claim 6, characterized in that, According to the theory of elastic deformation, the deformation equation for a thin-walled workpiece is as follows: （12）； in, Represents the global stiffness matrix of the workpiece; Represents the workpiece displacement matrix; Indicates milling force; Based on the node partitioning method, formula (12) is transformed into: （13）； in, , , and Let these represent the stiffness submatrices for retained nodes, reduced nodes, and reduced nodes respectively; and define a displacement matrix for each node type. This represents the displacement matrix that preserves the set of nodes. The displacement matrix represents the reduction of the node set; and These represent the milling forces applied to the retained node set and the reduced node set, respectively; During the machining process, milling force It only acts on the machined surface, therefore Set as the zero vector, substituting this vector into formula (12) yields: （14）； The reduced stiffness equation for the nodal displacement solution of the milled surface is as follows: （15）； Because the material is removed during the machining process, the local stiffness of the workpiece will change. Therefore, the workpiece stiffness matrix is ​​updated at each feed position, that is, the cutting process is simulated by subtracting the stiffness matrix of the corresponding element. Therefore, when the tool feeds to the next feed position, the numerical relationship between the workpiece stiffness matrices of adjacent feed positions is expressed as follows: （16）； in, Indicates that the cutting tool has reached the first... Workpiece stiffness matrix at each feed position; Indicates that the cutting tool has reached the first... Stiffness matrix at each feed position; This indicates the number of complete finite element units contained in the volume of material cut between these two adjacent feed positions; Indicates the number of incomplete finite element elements that were removed; The scaling factor describes the ratio of the cutting volume to the total volume between adjacent feed positions; scaling factor Defined as: （17）； in, Indicates the volume of material removed; Represents the volume of a single complete unit; The workpiece deformation is solved by combining formulas (14)-(17).

8. The method for predicting the surface morphology of a milled workpiece considering the influence of multiple factors according to claim 1, characterized in that, In step S4, a surface morphology prediction model is established, and the specific process is as follows: Step S41: First, establish four coordinate systems to characterize the spatial relationships within the tool-workpiece system: Tool coordinate system ; Workpiece coordinate system ; Tool offset coordinate system ; Principal axis reference coordinate system ; In this system, the axis of the tool offset coordinate system is parallel to the spindle axis; Step S42: Then, based on the establishment of these coordinate systems, the relative position and attitude changes between the tool and the workpiece are systematically characterized. Tool parallel axis offset mark , defined as the distance between the tool axis and the spindle axis at the fixed end of the tool; angle Representing a plane The angle between them; In the tool coordinate system, the tool is simplified to a shape with... A cylinder with several cutting edges, all evenly distributed on a nominal cylindrical surface of radius r, then the position angle... Represented as: （18）； in, Indicated by the helix angle The resulting angular delay is as follows: （19）； Indicates teeth The angular distance between tooth 1 and tooth 1 is shown below: （20）； Step S43: The coordinates of the discrete points of the cutting edge in the tool coordinate system are as follows: （21）； The position of the tool tip relative to the principal axis coordinate system is determined by coordinate transformation, as shown below: （22）； in, , ; Let x be the x-coordinate of point P in the tool coordinate system; Let P be the y-coordinate of point P in the tool coordinate system; Let z be the z-coordinate of point P in the tool coordinate system; Step S44, Main spindle reference coordinate system orbiting at a constant angular velocity The shaft rotates, and moves a distance along the feed direction with each revolution. ; In the workpiece coordinate system The discrete points of the cutting edge are shown below: （23）； in, Indicates the tool's rotation around the spindle axis The rotation angle; Let x be the x-coordinate of point P in the workpiece coordinate system; Let P be the y-coordinate of point P in the workpiece coordinate system; Let z be the z-coordinate of point P in the workpiece coordinate system; Let x be the x-coordinate of point P in the principal axis coordinate system; Let P be the y-coordinate of point P in the principal axis coordinate system; Let z be the z-coordinate of point P in the principal axis coordinate system.

9. The method for predicting the surface morphology of a milled workpiece considering the influence of multiple factors according to claim 8, characterized in that, Based on the obtained positions of the points in the workpiece coordinate system, the Z-map method is used to generate the workpiece surface topography matrix. The specific process is as follows: First, according to the workpiece A specific level of precision on a plane discretizes the workpiece into several uniformly distributed grid points; Secondly, the workpiece corresponding to each grid Axis height is determined by grid number Corresponding two-dimensional matrix elements This indicates that the actual machining process of the cutting teeth on the workpiece is represented by a surface morphology matrix. The continuous update process; Considering tool vibration displacement and workpiece deformation, the actual surface morphology matrix As shown below: （24）； in, Indicates the displacement due to tool vibration; Indicates the workpiece deformation error; Finally, the surface morphology matrix It is converted into a three-dimensional surface, which represents the morphological features of the processed surface.

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