Surface topography prediction method based on ball-end milling cutter micro cutting edge model

Abstract

The invention provides a ball-end milling cutter micro-cutting edge modeling and surface topography prediction method. The method comprises the following steps that 1, a coordinate system is defined, and a ball-end milling cutter mathematical model under the tool coordinate system is constructed; step 2, constructing a mathematical model of the cutting edge of the ball-end milling cutter under a workpiece coordinate system; step 3, constructing mathematical models LC and RC of a left edge and a right edge of the micro cutting edge under the micro-edge coordinate system; fourthly, mathematical models LT and RT of the left edge and the right edge of the micro cutting edge under the tool coordinate system are constructed; 5, defining and calculating a rotation angle theta TC; step 6, constructing a micro cutting edge model of the ball-end milling cutter; step 7, predicting surface topographies under different parameters; and 8, predicting surface topographies with different features. According to the method, the problems of micro cutting edge design modeling and surface topography design prediction are solved, the design controllability of the surface topography of the ball-end milling cutter is improved, a method is provided for precision machining with high surface quality requirements, and meanwhile, a way is provided for design of the micro cutting edge.

Description

Technical Field

[0001] The invention belongs to the technical field of cutting surface quality prediction, and in particular relates to a surface topography prediction method based on a ball-end milling cutter micro-cutting edge model. Background Art

[0002] In traditional cutting processes, ball-end milling cutters are a commonly used tool, widely used for high-precision surface machining. However, the spherical cutting edge of a ball-end milling cutter is prone to irregular surface topography during the cutting process. These irregular topography features can adversely affect the machining quality of the workpiece, especially in applications requiring high-precision surface quality, and cannot achieve the desired machining results. Although previous studies have proposed improving cutting results by changing the tool shape or adjusting process parameters, existing technologies still have shortcomings in precisely controlling the cutting surface topography. In particular, in high-precision surface machining, the cutting edge topography of traditional ball-end milling cutters is often irregular and difficult to fine-tune. Actual machining relies on trial-and-error methods to determine specific cutting parameters, resulting in unsatisfactory performance in predicting and controlling surface topography under different design and machining conditions. Although some technologies have attempted to improve the cutting edge topography and machined surface topography through tool geometry optimization or advanced manufacturing methods (such as laser engraving), these methods are still limited by high costs and complex processes, making them difficult to apply on a large scale.

[0003] The present invention provides a new method to improve the cutting effect and design controllability of the surface topography of a ball-end milling cutter through micro-cutting edge design and precise modeling, so as to improve the machining quality of the workpiece, especially in precision machining with high surface quality requirements. Summary of the Invention

[0004] The purpose of the present invention is to avoid the shortcomings of the existing technology and provide a surface morphology prediction method based on the micro-cutting edge model of a ball-end milling cutter. By establishing a micro-cutting edge model of a ball-end milling cutter, surface morphology prediction is achieved to solve the problem in the existing technology that the ball-end milling cutter cannot accurately control the surface morphology in high-precision surface processing.

[0005] To achieve the above object, the technical solution adopted by the present invention is a surface morphology prediction method based on a ball-end milling cutter micro-cutting edge model, comprising the following steps: Step 1: Define the coordinate system and construct the mathematical model of the ball end mill in the tool coordinate system. Construct the coordinate system required to describe the cutting edge position and motion trajectory of the ball-end milling cutter, including the micro-edge coordinate system, tool coordinate system, spindle coordinate system, workpiece reference coordinate system, and workpiece coordinate system; based on the geometric model of the ball-end milling cutter, construct the mathematical model of the ball-end milling cutter in the tool coordinate system; Step 2: Construct a mathematical model of the ball end milling cutter cutting edge in the workpiece coordinate system. Select a cutting edge of the ball end mill as the reference cutting edge and define a series of coordinate system transformation matrices of the reference cutting edge, including the cutting edge transformation matrix M 1. Tool eccentric translation matrix M 2. Tool rotation matrix M 3. Tool posture adjustment matrix M 4. Feed translation matrix M 5. Multiply the series of coordinate system transformation matrices of the reference cutting edge by the mathematical model of the ball end mill established in step 1 in sequence according to the mapping relationship, and obtain the mathematical model of the cutting edge of the ball end mill in the workpiece coordinate system; Step 3: Construct the mathematical model of the left and right edges of the micro-cutting edge in the micro-blade coordinate system L C and R C , Each micro-cutting edge is divided into a left edge and a right edge, and one of the micro-cutting edges is defined as the reference edge. After coordinate translation transformation, the mathematical model of the left and right edges on the micro-cutting edge in the micro-cutting coordinate system is obtained. L C and R C ; Step 4: Construct the mathematical model of the left and right edges of the micro-cutting edge in the tool coordinate system L T and R T , The mathematical model of the left and right edges of the micro-cutting edge expressed in the micro-edge coordinate system in step 3 is L C and R C Perform coordinate transformation to obtain the mathematical model of the left and right edges on the micro-cutting edge in the tool coordinate system L T and R T ; Step 5: Define and calculate the rotation angle i TC , Define the rotation angle between the micro-blade coordinate system and the tool coordinate system i TC , combined with the mathematical model of the ball end mill described in step 1, calculate the coordinates of the starting point C1 and the end point C2 of the micro cutting edge, and use the vector dot product formula to calculate the rotation angle i TC ; Step 6: Construct the micro-cutting edge model of the ball end mill. The mathematical model of the left and right edges of the micro-cutting edge in the micro-blade coordinate system described in step 3 is LC and R C and the rotation angle described in step 5 i TC The mathematical model of the left and right edges of the micro-cutting edge in the tool coordinate system described in step 4 is introduced L T and R T In the process, the tool coordinate system is mapped to the workpiece coordinate system according to the coordinate transformation relationship, and the mathematical model of the micro-cutting edge in the workpiece coordinate system is obtained. L M , i.e. a micro-cutting edge model of a ball-end milling cutter; Step 7: Predict the surface morphology under different parameters. The number of teeth on the tool N , spindle speed n , feed speed v f , processing line spacing f p , cutting depth a p The established ball-end milling cutter micro-cutting edge model is brought in and the trajectory diagram is calculated and drawn in MATLAB software to obtain the predicted workpiece surface morphology. Step 8: Predict the surface morphology of different features. By changing the tool feed direction and repeating step seven, surface morphologies with different characteristics can be obtained.

[0006] Furthermore, the micro-blade coordinate system in step 1 is a local coordinate system with the top of the first cutting edge of the micro-cutting edge as the origin. Z C The axis is consistent with the left edge of the first cutting edge; the tool coordinate system is a local coordinate system with the center of the ball end milling cutter as the origin. Z T The axis is consistent with the tool axis and rotates with the rotation center of the machine tool spindle; the spindle coordinate system is a local coordinate system that moves with the machine tool spindle. Z S The axis coincides with the main spindle rotation axis; the working reference coordinate system is a local coordinate system used to express the tool motion posture, and the origin of the coordinate system coincides with the origin of the main spindle coordinate system. X G Axis is intermittent feed direction, Y G The axis is the tool feed direction, which is always consistent with the direction of the workpiece coordinate system and moves synchronously with the tool; the workpiece coordinate system is a global coordinate system with the vertex in the lower left corner of the workpiece as the origin of the coordinate system. The motion trajectory of each discrete point of the tool in three-dimensional space will eventually be mapped to the workpiece coordinate system through transformation, and finally generate the surface morphology after processing.

[0007] In the tool coordinate system, for a certain ball end milling cutter geometry model, the number of tool teeth is N , the tool radius is R (mm), construct a mathematical model of the ball end mill L ( x jL , y jL , z jL ) is expressed as follows:

[0008] Where, i Any point on the blade L Axial position angle (rad); s is the random shrinkage of the discrete points of the tooth (mm); l for O T L exist X T O T Y T Projection in the plane and X T The angle in the positive direction of the axis is obtained by the following formula:

[0009] Where j = 1, 2, 3... N , c is the helix angle of the ball end mill (rad).

[0010] Furthermore, in the step 2, the ball end milling cutter is a four-edge milling cutter with equal tooth pitch, one of the blades is used as the reference blade and is numbered as 1, and the remaining blades are numbered as 2, 3, and 4 in a clockwise direction. The blade transformation matrix of any blade model to the reference blade model is M 1 is:

[0011] Where, f For the j The angle between the numbered cutter tooth and the reference cutter tooth; There is an eccentric distance between the tool coordinate system and the machine tool spindle coordinate system along the tool radius direction e (mm), eccentric angle is d (°), then the eccentric translation matrix M 2 can be expressed as:

[0012] Specify the initial stateO T X T Coordinate axis and O S X S The angle between the coordinate axes is the initial phase angle of the tool, and the tool coordinate system is based on the angular velocity oh (rad / s) rotates counterclockwise around the principal axis coordinate system, and the initial phase is f 0(°), then the tool rotation transformation matrix M 3 is:

[0013] Where, t The time (s) from the initial moment to the current moment in a single feed process; During the machining process, the tool O G Y G Feed in the coordinate axis direction, and rotate the tool coordinate system TCS around O G Y G The coordinate axis rotates, and the angle of rotation is recorded as the machining inclination angle α (°), then turn the tool around O G Z G The coordinate axis rotates, and the rotation angle is the processing angle β (°), the positive and negative signs of the two are determined according to the right-hand screw criterion; therefore, the tool posture adjustment transformation matrix M 4 is:

[0014] In actual plane machining, the spatial motion of the machine tool spindle relative to the workpiece is regarded as uniform linear motion; the starting position coordinates of the tool center in the workpiece coordinate system are ( x 0, y 0, z 0), the processing mode is one-way feeding, feed translation matrix M 5 is:

[0015] Where, f p is the processing line spacing (mm); v f is the feed rate (mm / min); According to the actual mapping relationship of the transformation matrix obtained above and combined with the product order of matrix transformation, the mathematical model of the ball end milling cutter cutting edge in the workpiece coordinate system is given by the following formula:

[0016] Furthermore, in the step 3, in the micro-blade coordinate system, the mathematical model of the left and right edges on the micro-cutting edge is L C and R C Can be expressed as:

[0017]

[0018] Where, L m is the waist length of the micro cutting edge, that is, the distance from the tip to the root of the micro cutting edge (mm); i c is the micro-blade angle (°); Δ m is the discrete point step size (mm); α is the machining inclination angle (°); Furthermore, in the step 4, the mathematical models of the left and right edges of the micro-cutting edge represented in the micro-edge coordinate system in step 3 are L C and R C Perform coordinate transformation to obtain the mathematical model of the left and right edges of the micro-cutting edge in the tool coordinate system L T and R T Respectively expressed as:

[0019]

[0020] Where, L m is the waist length of the micro cutting edge, that is, the distance from the tip to the root of the micro cutting edge (mm); i c is the micro-blade angle (°); Δ m is the discrete point step size (mm); α is the machining inclination angle (°).

[0021] Furthermore, in step 5, the rotation angle between the micro-blade coordinate system and the tool coordinate system is defined as i TC , combined with the mathematical model of the ball end mill mentioned in step 1 L ( x jL, y jL , z jL ), calculate the coordinates of the starting point C1 and the end point C2 of the micro-cutting edge, and use the vector dot product formula to calculate the rotation angle i TC :

[0022] Where, i 1, i 2 are C 1 and C 2 axial position angle (°); l 1, l 2 are O T C 1 and O T C 2 in X T O T Y T Projection in the plane and X T Angle in the positive direction of the axis (rad).

[0023] Furthermore, in step six, the mathematical models of the left and right edges of the micro-cutting edge obtained in step three in the micro-edge coordinate system are L C and R C and the rotation angle obtained in step 5 i TC Substitute the mathematical model of the left and right edges of the micro-cutting edge obtained in step 4 in the tool coordinate system L T and R T In the process, the tool coordinate system is mapped to the workpiece coordinate system according to the coordinate transformation relationship, and the mathematical model of the micro-cutting edge in the workpiece coordinate system is obtained. L M , that is, a ball-end milling cutter micro-cutting edge model is:

[0024]

[0025] Furthermore, the surface morphology with different characteristics obtained in step eight includes three types of surface morphologies: one is a serrated texture processed when the tool feed direction is perpendicular to the shear and stretching direction; the second is below the serrated texture processed when the tool feed direction is parallel to the shear and stretching direction; and the third is a pyramid-shaped texture formed by first processing in a direction parallel to the shear and stretching direction and then processing in a direction perpendicular to the shear and stretching direction.

[0026] The beneficial effects of the present invention are as follows: the present invention provides a surface morphology prediction method based on a ball-end milling cutter micro-cutting edge model, which can deeply explore the influence of different process parameters and micro-cutting edge shapes on the cutting surface morphology-related characteristics and performance through accurate geometric modeling and simulation analysis; by establishing an accurate ball-end milling cutter micro-cutting edge simulation numerical model, the cutting process under different process conditions is effectively simulated, which significantly improves the process optimization efficiency, reduces the number of experiments and costs, accelerates the cutting process verification and improvement, and ensures the processing efficiency and controllability of surface quality; by establishing a ball-end milling cutter micro-cutting edge model (trajectory equation) and using MATLAB software for calculation, the surface morphology of the workpiece material under micro-cutting edge processing is visualized, providing a theoretical basis for subsequent improvement of the processing technology in combination with actual processing experiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0027] Figure 1 is a flow chart of the present invention; Figure 2 Schematic diagram of the ball end milling cutter machining motion coordinate system of the present invention; Figure 3 This is a schematic diagram of the tool eccentricity of the present invention; Figure 4 This is a schematic diagram of tool posture transformation in the present invention; Figure 5 Schematic diagram of the micro-cutting edge model of the present invention; Figure 6 Schematic diagram of the coordinate translation mapping of the micro-cutting edge of the present invention; Figure 7 This is a prediction diagram of the surface morphology of the micro-cutting edge processed under different process parameters of the present invention; Figure 8 Schematic diagram of programming guide rails with three surface textures according to the present invention; Figure 9 This is a comparison diagram of the predicted morphology and the measured morphology of the present invention; Figure 10 This is a comparison chart of the roughness predicted by simulation and the actual measured roughness of the present invention. DETAILED DESCRIPTION

[0028] The principles and features of the present invention are described below with reference to the accompanying drawings. The examples given are only used to explain the present invention and are not used to limit the scope of the present invention.

[0029] In order to achieve the above object, the present invention provides the following specific implementation methods: Figure 1 As shown, the surface morphology prediction method based on the ball-end milling cutter micro-cutting edge model includes the following steps: Step 1: Define the coordinate system and construct the mathematical model of the ball end mill in the tool coordinate system. Construct the coordinate system required to describe the position and motion trajectory of the ball-end milling cutter cutting edge, including the micro-edge coordinate system, tool coordinate system, spindle coordinate system, workpiece reference coordinate system and workpiece coordinate system, such as Figure 2 As shown in FIG. 1 ; Based on the geometric model of the ball end milling cutter, a mathematical model of the ball end milling cutter is constructed in the tool coordinate system; The micro-blade coordinate system in step 1 is a local coordinate system with the top of the first cutting edge of the micro-cutting edge as the origin. Z C The axis is consistent with the left edge of the first cutting edge; the tool coordinate system is a local coordinate system with the center of the ball end milling cutter as the origin. Z T The axis is consistent with the tool axis and rotates with the rotation center of the machine tool spindle; the spindle coordinate system is a local coordinate system that moves with the machine tool spindle. Z S The axis coincides with the main spindle rotation axis; the working reference coordinate system is a local coordinate system used to express the tool motion posture, and the origin of the coordinate system coincides with the origin of the main spindle coordinate system. X G Axis is intermittent feed direction, Y G The axis is the tool feed direction, which is always consistent with the direction of the workpiece coordinate system and moves synchronously with the tool; the workpiece coordinate system is a global coordinate system with the vertex in the lower left corner of the workpiece as the origin of the coordinate system. The motion trajectory of each discrete point of the tool in three-dimensional space will eventually be mapped to the workpiece coordinate system through transformation, and finally generate the surface morphology after processing.

[0030] In the tool coordinate system, for a certain ball end milling cutter geometry model, the number of tool teeth is N , the tool radius is R (mm), constructing a mathematical model of the ball end mill L ( x jL , y jL , z jL ) is expressed as follows:

[0031] Where, i Any point on the blade L Axial position angle (rad); sis the random shrinkage of the discrete points of the tooth (mm); l for O T L exist X T O T Y T Projection in the plane and X T The angle in the positive direction of the axis is obtained by the following formula:

[0032] Where j = 1, 2, 3... N , c is the helix angle of the ball end mill (rad).

[0033] Step 2: Construct a mathematical model of the ball end milling cutter cutting edge in the workpiece coordinate system. Select a cutting edge of the ball end mill as the reference cutting edge and define a series of coordinate system transformation matrices of the reference cutting edge, including the cutting edge transformation matrix M 1. Tool eccentric translation matrix M 2. Tool rotation matrix M 3. Tool posture adjustment matrix M 4. Feed translation matrix M 5; A series of coordinate system transformation matrices of the reference blade are left-multiplied to the mathematical model of the ball-end milling cutter established in step 1 according to the mapping relationship to obtain the mathematical model of the cutting edge of the ball-end milling cutter in the workpiece coordinate system; in the actual processing process, in the step 2, the ball-end milling cutter is a four-edge milling cutter with equal tooth pitch, one of the blades is used as the reference blade and is numbered as No. 1, and the remaining blades are numbered as No. 2, No. 3, and No. 4 in a clockwise direction. The blade transformation matrix of any blade model to the reference blade model M 1 is:

[0034] Where, f For the j The angle between the numbered cutter tooth and the reference cutter tooth; During the installation process of the tool and the machine tool spindle, there is a radial installation deviation between the tool axis and the machine tool spindle, which causes the tool axis to offset a certain distance from the machine tool spindle axis. This deviation will cause the rotation center of the tool cutting edge to not coincide with the rotation center of the machine tool spindle, causing inconsistency in the cutting thickness of each tooth, and ultimately having a significant impact on the surface morphology of the workpiece. Figure 3 The figure shows the tool eccentricity diagram, tool coordinate system O T - X TY T Z T With the machine tool spindle coordinate system O S - X S Y S Z S There is an eccentric distance along the tool radius e (mm), eccentric angle is d (°), then the eccentric translation matrix M 2 can be expressed as follows:

[0035] As the machining progresses, the tool will rotate, and the initial state is specified. O T X T Coordinate axis and O S X S The angle between the coordinate axes is the initial phase angle of the tool, and the tool coordinate system is based on the angular velocity oh (rad / s) rotates counterclockwise around the principal axis coordinate system, and the initial phase is f 0(°), then the tool rotation transformation matrix M 3 is:

[0036] Where, t The time (s) from the initial moment to the current moment in a single feed process; Figure 4 The figure shows the tool's posture transformation in the working coordinate system. The present invention starts with the machining roll angle and the machining rotation angle to develop the model. O G Y G Feed in the coordinate axis direction, and rotate the tool coordinate system around O G Y G The coordinate axis rotates, and the angle of rotation is recorded as the machining inclination angle α (°), then turn the tool around O G Z G The coordinate axis rotates, and the rotation angle is the processing angle β (°). The positive and negative signs of the two are determined according to the right-hand screw criterion. Therefore, the tool posture adjustment transformation matrix M 4 is:

[0037] In actual plane machining, the spatial motion of the machine tool spindle relative to the workpiece is regarded as uniform linear motion; the starting position coordinates of the tool center in the workpiece coordinate system are ( x 0, y 0, z 0), the processing mode is one-way feeding, feed translation matrix M 5 is:

[0038] Where, f p is the processing line spacing (mm); v f is the feed rate (mm / min); According to the actual mapping relationship of the transformation matrix obtained above and combined with the product order of matrix transformation, the mathematical model of the ball end milling cutter cutting edge in the workpiece coordinate system is given by the following formula:

[0039] Step 3: Construct the mathematical model of the left and right edges of the micro-cutting edge in the micro-blade coordinate system L C and R C , Each micro-cutting edge is divided into a left edge and a right edge, and one of the micro-cutting edges is defined as the reference edge. After coordinate translation transformation, the mathematical model of the left and right edges on the micro-cutting edge in the micro-cutting coordinate system is obtained. L C and R C ; like Figure 5 As shown, each micro-cutting edge is divided into a left edge and a right edge. One of the micro-cutting edges is defined as the reference edge and numbered 1. The remaining micro-cutting edges are numbered 2, 3, and 4 from left to right. Micro-edge coordinate system O C - X C Y C Z C The top of the first micro blade is used as the coordinate origin, where O C Z C The coordinate axis is parallel to the tool axis. O C X CThe coordinate axis is in the micro-tooth plane and parallel to the horizontal direction. Therefore, in the micro-blade coordinate system, the mathematical model of the left and right edges on the micro-cutting edge is L C and R C Can be expressed as:

[0040]

[0041] In the above two formulas, i c Number the micro cutting edge. L m is the waist length of the micro-cutting edge (mm); i c is the micro-blade angle (°); Δ m is the discrete point step size (mm); α is the machining inclination angle (°).

[0042] Step 4: Construct the mathematical model of the left and right edges of the micro-cutting edge in the tool coordinate system L T and R T , according to Figure 6 The transformation relationship between the micro-blade coordinate system and the tool coordinate system is shown in the figure. The mathematical model of the left and right edges of the micro-cutting edge represented in the micro-blade coordinate system in step 3 is L C and R C Perform coordinate transformation to obtain the mathematical model of the left and right edges on the micro-cutting edge in the tool coordinate system L T and R T Respectively expressed as:

[0043]

[0044] Where, L m is the waist length of the micro cutting edge, that is, the distance from the tip to the root of the micro cutting edge (mm); i c is the micro-blade angle (°); Δ m is the discrete point step size (mm); α is the machining inclination angle (°); Step 5: Define and calculate the rotation angle i TC , Define the rotation angle between the micro-blade coordinate system and the tool coordinate system i TC , combined with the mathematical model of the ball end mill described in step 1, calculate the coordinates of the starting point C1 and the end point C2 of the micro cutting edge, and use the vector dot product formula to calculate the rotation angle i TC for:

[0045] Where, i 1, i 2 are C 1 and C 2 axial position angle (°); l 1, l 2 are O T C 1 and O T C 2 in X T O T Y T Projection in the plane and X T Angle in the positive direction of the axis (rad); Step 6: Construct the micro-cutting edge model of the ball end mill. The mathematical model of the left and right edges of the micro-cutting edge obtained in step 3 in the micro-edge coordinate system is L C and R C and the rotation angle obtained in step 5 i TC Substitute the mathematical model of the left and right edges of the micro-cutting edge obtained in step 4 in the tool coordinate system L T and R T In the process, the tool coordinate system is mapped to the workpiece coordinate system according to the coordinate transformation relationship, and the mathematical model of the micro-cutting edge in the workpiece coordinate system is obtained. L M , that is, a ball-end milling cutter micro-cutting edge model is:

[0046]

[0047] Step 7: Predict the surface morphology under different parameters. The number of teeth on the tool N , spindle speed n , feed speed vf , processing line spacing f p , cutting depth a p The established ball-end milling cutter micro-cutting edge model is brought in and the trajectory diagram is calculated and drawn in MATLAB software to obtain the predicted workpiece surface morphology. Step 8: Predict the surface morphology of different features. By changing the tool feed direction and repeating step seven, surface morphologies with different characteristics can be obtained.

[0048] The surface morphologies with different characteristics include three types of surface morphologies: one is the serrated texture processed when the tool feed direction is perpendicular to the shear and stretching direction, referred to as horizontal grain; the second is the serrated texture processed when the tool feed direction is parallel to the shear and stretching direction, referred to as vertical grain; the third is the pyramid-shaped texture formed by first processing in a direction parallel to the shear and stretching direction and then processing in a direction perpendicular to the shear and stretching direction, referred to as cross grain.

[0049] The surface morphology prediction method based on the ball-end milling cutter micro-cutting edge model, in step 1, ① micro-edge coordinate system { O T ; X T , Y T , Z T}(CCS): local coordinate system with the top of the first cutting edge of the micro-cutting edge as the origin, Z C The axis is consistent with the left edge of the first cutting edge; ② Tool coordinate system { O T ; X T , Y T , Z T (TCS): local coordinate system with the center of the ball end mill as the origin. Z T The axis is consistent with the tool axis and rotates with the rotation center of the machine tool spindle. O S ; X S , Y S , Z S}(SCS): local coordinate system with the spindle motion of the random machine tool, Z S The axis coincides with the main spindle rotation axis. ④Working reference coordinate system { O G ;X G , Y G , Z G}(GCS): Local coordinate system used to express tool motion posture. The origin of the coordinate system coincides with the origin of the spindle coordinate system. X G Axis is intermittent feed direction, Y G The axis is the tool feed direction, which is always consistent with the workpiece coordinate system direction and moves synchronously with the tool. O W ; X W , Y W , Z W WCS (Working Coordinate System): The global coordinate system with the lower left corner vertex of the workpiece as the origin of the coordinate system. The motion trajectory of each discrete point of the tool in three-dimensional space is finally mapped into the workpiece coordinate system through transformation, and finally the surface morphology after processing is generated.

[0050] In step 2, the ball-end milling cutter typically tilts the cutter axis at a certain angle relative to the normal to the contact surface to achieve more precise and efficient cutting. This is because when the ball-end milling cutter is perpendicular to the workpiece surface, the linear velocity of the tool tip is zero. Chips generated during cutting cannot be effectively discharged and tend to accumulate near the cutter teeth, forming a built-up edge. This built-up edge not only reduces cutting efficiency but can also lead to unstable cutting forces, compromising machining quality.

[0051] In step three, Figure 5 middle C 1 and C 2 are the starting position and the ending position of the micro cutting edge, and these two points are also located on the cutting edge of the ball end cutter. l 1, l The value of 2 can be obtained from the following formula:

[0052] In step 7, the simulation experiment parameters used are: number of tool teeth N is 4, the spindle speed n Feed speed is 1000-5000r / min v f 1000-5000mm / min, processing line spacing f p 0.4mm, helix angle 30 , machining inclination 50 , processing corners 0 , cutting depth a p The spindle speed is 0.3mm. n and feed speed v f There are five sets of data, with 1000 values ​​as intervals, namely: spindle speed n Feed speed: 1000r / min, 2000r / min, 3000r / min, 4000r / min, 5000r / min; v f They are 1000mm / min, 2000mm / min, 3000mm / min, 4000mm / min and 5000mm / min respectively. Therefore, a total of 25 sets of simulation experiments were carried out to obtain 25 predicted morphology images, such as Figure 7 shown.

[0053] In step eight, by changing the tool feed direction, three different surface textures were designed and predicted: the first is a serrated texture (referred to as horizontal grain) produced when the tool feed direction is perpendicular to the shear and stretch directions; the second is a serrated texture (referred to as vertical grain) produced when the tool feed direction is parallel to the shear and stretch directions; and the third is a pyramidal texture (referred to as cross grain) produced by first machining parallel to the shear and stretch directions and then machining perpendicular to the shear and stretch directions. The tool paths for the three surface textures were programmed using NX 2024 software, as shown in the following example. Figure 8 The following are schematic diagrams of guide rail programming for three types of surface textures: (a) is a schematic diagram of a transverse tool rail, (b) is a schematic diagram of a longitudinal tool rail, and (c) is a schematic diagram of a cross-texture tool rail.

[0054] Figure 9 The following figure compares the simulated and measured surface topography for three different surface textures: (a) simulated horizontal stripes, (b) simulated vertical stripes, (c) simulated cross-stripe topography, (d) measured horizontal stripes, (e) measured vertical stripes, and (f) measured cross-stripe topography. Because the microgrooves machined by the micro-cutting edge are narrow, surface data cannot be obtained using a 3D optical profilometer. Therefore, a tool scanner was used to observe their topography to verify the accuracy of the established micro-cutting edge simulation model.

[0055] Figure 10 Comparison of simulated roughness prediction and actual measured roughness. The roughness of the transverse and longitudinal grain surfaces is significantly higher than that of the cross grain surface, and this phenomenon is also reflected in the simulated roughness prediction, indicating that the established micro-cutting edge simulation model is highly accurate.

[0056] The technical solution provided by the present invention has the following application values: (1) Facilitate the study of surface morphology: The establishment of the micro-cutting edge model provides a convenient technical means for the subsequent design and research of different types of surface morphology. Through accurate geometric modeling and simulation analysis, we can deeply explore the influence of different process parameters and micro-cutting edge shapes on the cutting surface morphology-related features and performance, such as the control of surface roughness and texture, and the study of the performance of different texture features related to surface morphology such as adhesion and infiltration, thereby providing a reliable theoretical basis for optimizing surface quality, improving processing accuracy and optimizing related performance.

[0057] (2) By establishing a precise numerical model for simulating the micro-cutting edge of a ball-end cutter, the present invention can obtain the blade motion trajectory without actual testing, reflecting the surface morphology of the workpiece after processing, thereby rapidly optimizing process parameters. This model effectively simulates the cutting process under different process conditions, significantly improving process optimization efficiency, reducing the number of experiments and costs, accelerating cutting process verification and improvement, and ensuring efficient processing and controllable surface quality.

[0058] (3) The present invention establishes a ball-end milling cutter micro-cutting edge model (trajectory equation) and uses MATLAB software for calculation to visualize the surface morphology of the workpiece material processed by the micro-cutting edge, providing a theoretical basis for subsequent improvement of the processing technology in combination with actual processing experiments.

[0059] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A surface morphology prediction method based on a ball-end milling cutter micro-cutting edge model, characterized in that: The following steps are involved: Step 1: Define the coordinate system and construct the mathematical model of the ball end mill in the tool coordinate system. Construct the coordinate system required to describe the cutting edge position and motion trajectory of the ball-end milling cutter, including the micro-edge coordinate system, tool coordinate system, spindle coordinate system, workpiece reference coordinate system, and workpiece coordinate system; based on the geometric model of the ball-end milling cutter, construct the mathematical model of the ball-end milling cutter in the tool coordinate system; Step 2: Construct a mathematical model of the ball end milling cutter cutting edge in the workpiece coordinate system. Select a cutting edge of the ball end mill as the reference cutting edge and define a series of coordinate system transformation matrices of the reference cutting edge, including the cutting edge transformation matrix M 1. Tool eccentric translation matrix M 2. Tool rotation matrix M 3. Tool posture adjustment matrix M 4. Feed translation matrix M 5. Multiply the series of coordinate system transformation matrices of the reference cutting edge by the mathematical model of the ball end mill established in step 1 in sequence according to the mapping relationship, and obtain the mathematical model of the cutting edge of the ball end mill in the workpiece coordinate system; Step 3: Construct the mathematical model of the left and right edges of the micro-cutting edge in the micro-blade coordinate system L C and R C , Each micro-cutting edge is divided into a left edge and a right edge, and one of the micro-cutting edges is defined as the reference edge. After coordinate translation transformation, the mathematical model of the left and right edges on the micro-cutting edge in the micro-cutting coordinate system is obtained. L C and R C ; Step 4: Construct the mathematical model of the left and right edges of the micro-cutting edge in the tool coordinate system L T and R T , The mathematical model of the left and right edges of the micro-cutting edge expressed in the micro-edge coordinate system in step 3 is L C and R C Perform coordinate transformation to obtain the mathematical model of the left and right edges on the micro-cutting edge in the tool coordinate system L T and R T ; Step 5: Define and calculate the rotation angle θ TC , Define the rotation angle between the micro-blade coordinate system and the tool coordinate system θ TC , combined with the mathematical model of the ball end mill described in step 1, calculate the coordinates of the starting point C1 and the end point C2 of the micro cutting edge, and use the vector dot product formula to calculate the rotation angle θ TC ; Step 6: Construct the micro-cutting edge model of the ball end mill. The mathematical model of the left and right edges of the micro-cutting edge in the micro-blade coordinate system described in step 3 is L C and R C and the rotation angle described in step 5 θ TC The mathematical model of the left and right edges of the micro-cutting edge in the tool coordinate system described in step 4 is introduced L T and R T In the process, the tool coordinate system is mapped to the workpiece coordinate system according to the coordinate transformation relationship, and the mathematical model of the micro-cutting edge in the workpiece coordinate system is obtained. L M , i.e. a micro-cutting edge model of a ball-end milling cutter; Step 7: Predict the surface morphology under different parameters. The number of teeth on the tool N , spindle speed n , feed speed v f , processing line spacing f p , cutting depth a p The established ball-end milling cutter micro-cutting edge model is brought in and the trajectory diagram is calculated and drawn in MATLAB software to obtain the predicted workpiece surface morphology. Step 8: Predict the surface morphology of different features. By changing the tool feed direction and repeating step seven, surface morphologies with different characteristics can be obtained.

2. The surface morphology prediction method based on the ball-end milling cutter micro-cutting edge model according to claim 1, characterized in that: The micro-blade coordinate system in step 1 is a local coordinate system with the top of the first cutting edge of the micro-cutting edge as the origin. Z C The axis is consistent with the left edge of the first cutting edge; the tool coordinate system is a local coordinate system with the center of the ball end milling cutter as the origin. Z T The axis is consistent with the tool axis and rotates with the rotation center of the machine tool spindle; the spindle coordinate system is a local coordinate system that moves with the machine tool spindle. Z S The axis coincides with the main spindle rotation axis; the working reference coordinate system is a local coordinate system used to express the tool motion posture, and the origin of the coordinate system coincides with the origin of the main spindle coordinate system. X G Axis is intermittent feed direction, Y G The axis is the tool feed direction, which is always consistent with the direction of the workpiece coordinate system and moves synchronously with the tool. The workpiece coordinate system is a global coordinate system with the vertex at the lower left corner of the workpiece as the coordinate system origin. The motion trajectory of each discrete point of the tool in three-dimensional space will eventually be mapped to the workpiece coordinate system through transformation, and the final surface morphology after processing will be generated. In the tool coordinate system, for a certain ball end milling cutter geometry model, the number of tool teeth is N , the tool radius is R (mm), constructing a mathematical model of the ball end mill L ( x jL , y jL , z jL ) is expressed as follows: ， Where, θ Any point on the blade L Axial position angle (rad); σ is the random shrinkage of the discrete points of the tooth (mm); λ for O T L exist X T O T Y T Projection in the plane and X T The angle in the positive direction of the axis is obtained by the following formula: ， Where j = 1, 2, 3... N , γ is the helix angle of the ball end mill (rad).

3. The surface morphology prediction method based on the ball-end milling cutter micro-cutting edge model according to claim 1, characterized in that: In the step 2, the ball end mill is a four-edge milling cutter with equal tooth pitch. One of the blades is used as the reference blade and is numbered as 1. The remaining blades are numbered as 2, 3, and 4 in a clockwise direction. The blade transformation matrix of any blade model to the reference blade model is M 1 is: ， Where, φ For the j The angle between the numbered cutter tooth and the reference cutter tooth; There is an eccentric distance between the tool coordinate system and the machine tool spindle coordinate system along the tool radius direction e (mm), eccentric angle is δ , then the eccentric translation matrix M 2 can be expressed as: ， Specify the initial state O T X T Coordinate axis and O S X S The angle between the coordinate axes is the initial phase angle of the tool, and the tool coordinate system is based on the angular velocity ω (rad / s) rotates counterclockwise around the principal axis coordinate system, and the initial phase is φ 0, then the tool rotation transformation matrix M 3 is: ， Where, t The time (s) from the initial moment to the current moment in a single feed process; During the machining process, the tool O G Y G Feed in the coordinate axis direction, and rotate the tool coordinate system TCS around O G Y G The coordinate axis rotates, and the angle of rotation is recorded as the machining inclination angle α , and then move the tool around O G Z G The coordinate axis rotates, and the rotation angle is the processing angle β , the positive and negative signs of the two are determined according to the right-hand screw criterion; therefore, the tool posture adjustment transformation matrix M 4 is: ， In plane machining, the spatial motion of the machine tool spindle relative to the workpiece is regarded as uniform linear motion; the starting position coordinates of the tool center in the workpiece coordinate system are ( x 0, y 0, z 0), the processing mode is one-way feeding, feed translation matrix M 5 is: Where, f p is the processing line spacing (mm); v f is the feed rate (mm / min); According to the actual mapping relationship of the transformation matrix obtained above and combined with the product order of matrix transformation, the mathematical model of the ball end milling cutter cutting edge in the workpiece coordinate system is given by the following formula: 。 4. The surface morphology prediction method based on the ball-end milling cutter micro-cutting edge model according to claim 1, characterized in that: In the step 3, in the micro-blade coordinate system, the mathematical model of the left and right edges on the micro-cutting edge is L C and R C Can be expressed as: ， ， Where, L m is the waist length of the micro cutting edge, that is, the distance from the tip to the root of the micro cutting edge (mm); θ c is the micro-blade angle; Δ m is the discrete point step size (mm); α is the machining inclination angle.

5. The surface morphology prediction method based on the ball end milling cutter micro-cutting edge model according to claim 1, characterized in that: In the fourth step, the mathematical model of the left and right edges of the micro-cutting edge represented in the micro-edge coordinate system in step three is L C and R C Perform coordinate transformation to obtain the mathematical model of the left and right edges of the micro-cutting edge in the tool coordinate system L T and R T Respectively expressed as: ， ， Where, L m is the waist length of the micro cutting edge, that is, the distance from the tip to the root of the micro cutting edge (mm); θ c is the micro-blade angle; Δ m is the discrete point step size (mm); α is the machining inclination angle.

6. The surface morphology prediction method based on the ball end milling cutter micro-cutting edge model according to claim 1, characterized in that: In step 5, the rotation angle between the micro-blade coordinate system and the tool coordinate system is defined. θ TC , combined with the mathematical model of the ball end mill mentioned in step 1 L ( x jL , y jL , z jL ), calculate the coordinates of the starting point C1 and the end point C2 of the micro-cutting edge, and use the vector dot product formula to calculate the rotation angle θ TC : ， Where, θ 1, θ 2 are C 1 and C 2 axial position angle; λ 1, λ 2 are O T C 1 and O T C 2 in X T O T Y T Projection in the plane and X T Angle in the positive direction of the axis.

7. The surface morphology prediction method based on the ball end mill micro-cutting edge model according to claim 1, characterized in that: In the step 6, the mathematical model of the left and right edges of the micro-cutting edge in the micro-edge coordinate system obtained in step 3 is L C and R C and the rotation angle obtained in step 5 θ TC Substitute the mathematical model of the left and right edges of the micro-cutting edge obtained in step 4 in the tool coordinate system L T and R T In the process, the tool coordinate system is mapped to the workpiece coordinate system according to the coordinate transformation relationship, and the mathematical model of the micro-cutting edge in the workpiece coordinate system is obtained. L M , that is, a ball-end milling cutter micro-cutting edge model is: ， 。 8. The surface topography prediction method based on the ball-end milling cutter micro-cutting edge model according to claim 1, characterized in that: The surface morphologies with different characteristics obtained in step eight include three types of surface morphologies: one is a serrated texture processed when the tool feed direction is perpendicular to the shear and stretching direction; the second is a serrated texture processed below the shear and stretching direction; and the third is a pyramid-shaped texture formed by first processing in a direction parallel to the shear and stretching direction and then processing in a direction perpendicular to the shear and stretching direction.

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