Surface topography prediction method based on ball-end tool model and variable step-size iterative algorithm

Abstract

The present invention relates to a surface topography prediction method based on a ball-end milling cutter model and a variable step-size iterative algorithm. Based on the ball-end milling cutter model, the method uses a dynamic variable time step strategy to accurately divide cutting and non-cutting trajectories, significantly improving simulation efficiency and accuracy. Through multi-coordinate system dynamic modeling and specific functions, the eccentricity of the ball-end milling cutter is compensated, wear is accurately modeled, and combined with dynamic physical coupling, the actual processing state of the ball-end milling cutter is accurately simulated, thereby improving the accuracy and authenticity of the simulation and meeting the high-precision requirements of aerospace parts. At the same time, through modular design, the method accurately simulates complex curved tool paths and can be expanded to surface topography prediction of various difficult-to-process materials by adjusting the evaluation parameter threshold. The method also allows for rapid iteration of process parameters, significantly shortening the process optimization cycle.

Description

Technical Field

[0001] The present invention relates to the technical field of mechanical processing surface quality prediction, and in particular to a method for predicting the surface topography of ball-end cutter milling. Background Art

[0002] In aerospace manufacturing, efficient and precise machining of complex parts such as engine blades and turbine disks is a core technological challenge. The surface quality of these parts directly impacts key issues such as fatigue life, aerodynamic performance, and assembly accuracy. To meet these stringent surface quality requirements, traditional processes rely on extensive trial cutting experiments to adjust parameters, but this approach presents challenges such as high cost, long cycle times, and limited applicability.

[0003] With the advancement of numerical control technology and simulation methods, surface topography prediction based on numerical simulation has become a key means of optimizing processes. However, the particularity of complex surface machining in aerospace has posed higher challenges to surface topography simulation technology.

[0004] When a ball-end milling cutter is machining a curved surface, the cutting edge contact point changes continuously with the ball-end milling cutter posture, resulting in significant dynamic effects such as cutting force and vibration, which increases the complexity of the simulation. At the same time, the surface roughness of aerospace parts usually requires R a ≤0.8μm, requiring the simulation model to have submicron resolution. Traditional Z-MAP methods rely on dense meshing, resulting in an exponential increase in computational complexity, making it difficult to meet real-time engineering requirements.

[0005] Currently, mainstream surface topography simulation methods, while each with their own advantages, all have significant limitations. Solid modeling methods simulate material removal through Boolean operations, but ignore the complex structural characteristics of the dynamic interaction between the ball-end milling cutter and the workpiece. Numerical calculation methods, while highly efficient in solving the ball-end milling cutter trajectory, struggle to extend their consideration of dynamic physical factors, resulting in limited prediction accuracy. Traditional Z-MAP methods, while balancing accuracy and dynamic effects by updating surface heights through discretized grid projections, suffer from computational redundancy in the non-cutting phase due to a fixed time step in high-resolution simulations, leading to low efficiency.

[0006] In recent years, related studies have attempted to optimize the Z-MAP algorithm through linear interpolation, Newton iteration method or point cloud envelope method, but these methods still rely on a constant time step and fail to fundamentally solve the contradiction between efficiency and accuracy. Summary of the Invention

[0007] The purpose of the present invention is to avoid the shortcomings of the existing technology and provide a surface morphology prediction model by using a dynamic simulation strategy, which significantly reduces the computational complexity while ensuring accuracy, and realizes efficient surface morphology prediction under any cutting conditions, so as to meet the urgent needs of efficient and precise manufacturing in aerospace. A surface morphology prediction method based on a ball-end tool model and a variable step-size iterative algorithm is provided.

[0008] To achieve the above object, the technical solution adopted by the present invention is a surface topography prediction method based on a ball-end tool model and a variable step-size iterative algorithm, comprising the following steps:

[0009] Step 1: In the cutting edge geometry model of the ball-end milling cutter, a spatial coordinate system is established to describe the position of the cutting edge of the ball-end milling cutter. The positions of the discrete points of the cutting edges of all the cutting edges of the ball-end milling cutter are determined using the spatial coordinate system, that is, the coordinate expressions of the discrete points of the cutting edges are obtained. At the same time, a normal distribution random quantity function is used in the expression of the discrete points of the cutting edges to characterize the passivation morphology of the actual cutting edge of the ball-end milling cutter during the cutting process.

[0010] Among them, the spatial coordinate system includes the ball end milling cutter coordinate system, the machine tool spindle coordinate system, the workpiece reference coordinate system and the workpiece coordinate system;

[0011] Step 2: Based on the expression of the discrete points of the cutting edge, the motion trajectory of the discrete points of the cutting edge in the spatial coordinate system is described by calculating multiple three-dimensional homogeneous coordinate transformation matrices. Thus, in the workpiece reference coordinate system, the calculation equation of the cutting edge motion trajectory is established to describe the cutting edge motion trajectory;

[0012] Step 3: Divide the cutting edge motion trajectory corresponding to the cutting edge discrete points into a non-cutting trajectory in the non-cutting stage and a cutting trajectory in the cutting stage according to the cutting state, and calculate the time step of the cutting edge discrete points in the non-cutting stage and the cutting stage;

[0013] Step 4: Combining the time step of the discrete points of the cutting edge with the Z-MAP algorithm, and based on the milling program data used to describe the motion state of the ball-end milling cutter, iteratively update the height information of the workpiece machined surface after each cutting edge motion trajectory, that is, obtain the three-dimensional surface morphology of the workpiece machined surface;

[0014] The machining program data includes a tool path file for determining the motion path of discrete points of the cutting edge and cutting process parameters for the motion speed of the discrete points of the cutting edge themselves.

[0015] Furthermore, the spatial coordinate system described in step 1 specifically includes:

[0016] The center of the ball end mill is the origin O, and the axis of the ball end mill is the Z. T Axis, from the tip of any cutting edge to Z T The axis line direction is X T Axis, thus, the Y axis is determined by the right-hand coordinate system rule. T Axis, establish the ball end milling cutter coordinate system; the ball end milling cutter coordinate system can rotate with the machine tool spindle as the rotation center;

[0017] X based on the ball end milling cutter coordinate systemT Axis and Y T Axis direction, with the machine tool spindle as Z S Axis, the established machine tool spindle coordinate system;

[0018] Based on the coordinate axis origin O of the ball end mill coordinate system, the cutting line direction is X G Axis, ball end mill feed direction is Y G Axis, determine Z using the right-hand coordinate system rule G Axis, established workpiece reference coordinate system;

[0019] The workpiece coordinate system is established based on the coordinate axis direction of the workpiece reference coordinate system and with any vertex on the bottom surface of the workpiece as the origin;

[0020] Furthermore, the spatial coordinate system is used to determine the positions of the discrete points of all cutting edges of the ball-end milling cutter. For any cutting edge j among the N cutting edges in the cutting edge geometry model, the expression of the discrete point L of any cutting edge j is:

[0021] ,

[0022] Where R is the radius of the ball end mill, γ is the helix angle, N is the total number of cutting teeth, E(σ) is the normal distribution random quantity function, θ is the line connecting the discrete points of the cutting edge and the center of the ball end mill, and in the ball end mill coordinate system X T OY T Projection of the plane and X T The angle between the axes.

[0023] Furthermore, the cutting edge motion trajectory calculation equation established in step 2 is the motion trajectory calculation equation for any discrete point L of any cutting edge j among the N cutting edges in the cutting edge geometric model, specifically:

[0024] ,

[0025] Among them, θ is the line connecting the discrete point of the cutting edge and the center of the ball end milling cutter, t is the cutting edge motion time, (x WL ,y WL , z WL ) is the position coordinate of the discrete point L in the workpiece coordinate system;

[0026] M1~M5 are the rotation, eccentric translation, spindle rotation, posture adjustment and feed transformation matrices of the ball end mill respectively. The specific expressions are:

[0027] The rotation matrix M1 is:

[0028] ,

[0029] The eccentric translation matrix M2 is:

[0030] ,

[0031] Where δ is the radial eccentric angle of the ball end mill; the spindle rotation matrix M3 is:

[0032] ,

[0033] Among them, φ0 is the initial phase angle of the cutting edge, ω is the angular velocity of the machine tool spindle;

[0034] The attitude adjustment matrix M4 is:

[0035] ,

[0036] Among them, α is the rake angle of the ball end mill, and β is the side rake angle of the ball end mill;

[0037] The feed transformation matrix M5 is:

[0038] ,

[0039] Among them, f p is the processing line spacing of the ball end mill, f v is the feed rate of the ball end mill, i is any cutting line among the N cutting edges, and (x0, y0, z0) is the initial position coordinate of the center of the ball end mill in the workpiece coordinate system.

[0040] Furthermore, the step three is specifically as follows:

[0041] In any rotation cycle of the ball end mill during the cutting process, for any cutting edge j among the N cutting edges in the cutting edge geometric model, we have:

[0042] Since the initial discrete points of the cutting edge are all at the workpiece grid height W Z Above, there is: Z L >W Z , Z L is the height of any discrete point L of any cutting edge j at time t. At this time, the discrete point of the cutting edge is in the first non-cutting stage. According to the maximum discrete time step Δt, the cutting edge motion trajectory is calculated, and the counting variable of the discrete point of the cutting edge in the first non-cutting stage is recorded as A=A+1 until the discrete point of the cutting edge leaves the first non-cutting stage, that is, Z L ≤W Z ;

[0043] As the cutting edge discrete point leaves the first non-cutting stage, i.e. Z L ≤W ZAt this time, the cutting edge discrete point is in the cutting stage, and the cutting edge discrete point count variable in the cutting stage is recorded as B=B+1, until the cutting edge discrete point leaves the cutting stage, that is, Z appears again. L >W Z ;

[0044] Continuing, the discrete points of the cutting edge leave the cutting stage, that is, Z appears again L >W Z At this time, the discrete points of the cutting edge are in the second non-cutting stage, and the counting variable of the discrete points of the cutting edge in the second non-cutting stage is recorded as C=C+1 until the rotation cycle of the ball end milling cutter ends;

[0045] Among them, the initial count variable values ​​of A in the cutting edge discrete point count variable in the first non-cutting stage, B in the cutting edge discrete point count variable in the cutting stage, and C in the cutting edge discrete point count variable in the second non-cutting stage are all 0;

[0046] That is, the division of cutting trajectories and non-cutting trajectories of the discrete points of the cutting edges of all N cutting edges is completed;

[0047] Furthermore, let the time step of the first non-cutting stage Δt1 = AΔt; the time step of the cutting stage Δt2 = Δt; the time step of the second non-cutting stage Δt3 = CΔt;

[0048] Then, during the rotation cycle of the ball-end milling cutter with continuous cutting, the time step is dynamically selected according to the positional relationship between the discrete points of the cutting edge and the workpiece grid, specifically:

[0049] If the discrete point of the cutting edge is in the first non-cutting stage, the time step Δt1 is used;

[0050] If the discrete point of the cutting edge is in the cutting stage, the time step Δt2 is used, otherwise the time step Δt of the second non-cutting stage is used. 3；

[0051] Where Δt is the maximum discrete time step of the cutting edge motion trajectory determined based on the target accuracy of the surface topography prediction output result. The specific expression is:

[0052] ,

[0053] Where A c is the workpiece grid accuracy, A c The value of is used to determine the target accuracy of the ball-end milling cutter milling surface topography prediction results; max It is the maximum axial angle of the cutting edge involved in the cutting part; R is the radius of the ball end mill.

[0054] Furthermore, the step 4 is specifically as follows:

[0055] First, initialize the discrete accuracy A of the workpiece's machining surface c , the discrete accuracy of the cutting edge Δθ, the maximum discrete time step Δt of the cutting edge motion trajectory, and the construction of the discrete point cloud of the machined surface;

[0056] Then, according to the actual size or model of the workpiece, the position coordinates of the discrete point cloud in the workpiece coordinate system are determined, and then the discrete point cloud is converted into a point cloud height matrix W Z ;

[0057] Finally, all the discrete points of the cutting edge are traversed, and based on the tool path file and cutting process parameters, the motion trajectory of the discrete points of the cutting edge is calculated according to the determined time step of the discrete points of the cutting edge. The coordinate points in the workpiece reference coordinate system corresponding to the discrete points of the cutting edge in the cutting stage are subjected to the point cloud height matrix W of the workpiece processing surface. Z The updated surface morphology of the workpiece can be predicted.

[0058] Furthermore, it also includes using the arithmetic mean deviation R of the profile a Arithmetic mean height of dough S a Steps to evaluate the accuracy of surface topography predictions.

[0059] Furthermore, the arithmetic mean deviation of the profile R a Arithmetic mean height of dough S a , respectively:

[0060] ,

[0061] ,

[0062] Where Z i is the height value of the sampling grid point, Z mid To calculate the reference surface height value; m and n are the number of grid divisions along the X and Y axes in the workpiece coordinate system respectively.

[0063] The beneficial effects of the present invention are: the present invention uses a dynamic variable time step strategy to accurately divide cutting and non-cutting trajectories, skips the non-cutting area, greatly reduces redundant calculations, and significantly improves simulation efficiency and accuracy; it also uses multi-coordinate system dynamic modeling and specific functions to compensate for the eccentricity of the ball-end milling cutter, accurately models wear, and combines dynamic physical coupling to accurately simulate the actual processing state of the ball-end milling cutter, comprehensively improving the accuracy and authenticity of the simulation, and can meet the high-precision requirements of aerospace parts.

[0064] At the same time, through modular design, this method can flexibly adapt to a variety of processing scenarios. It can not only support the dynamic analysis of the ball-end milling cutter posture of the five-axis machine tool based on a specific coordinate transformation matrix and accurately simulate the tool path of complex curved surfaces, but also expand to the surface morphology prediction of a variety of difficult-to-process materials by adjusting the evaluation parameter threshold; and it can quickly iterate process parameters, helping to significantly shorten the process optimization cycle. BRIEF DESCRIPTION OF THE DRAWINGS

[0065] Figure 1 Establishing a position diagram for the spatial coordinate system of the present invention;

[0066] Figure 2 Schematic diagram of the motion trajectory of discrete points of the cutting edge of the present invention;

[0067] Figure 3 Schematic diagram of the Z-MAP algorithm flow based on the variable time step strategy of the present invention;

[0068] Figure 4 Schematic diagram showing the comparison of simulation time between the improved Z-MAP method of the present invention and the traditional Z-MAP method;

[0069] Figure 5 This is a first schematic diagram comparing the simulated predicted surface topography and the actually measured surface topography under variable roll angles according to the present invention;

[0070] Figure 6 A second schematic diagram comparing the simulated predicted surface topography and the actually measured surface topography under variable roll angles of the present invention;

[0071] Figure 7 A third schematic diagram comparing the simulated predicted surface topography and the actually measured surface topography under variable roll angles of the present invention;

[0072] Figure 8 A fourth schematic diagram comparing the simulated predicted surface topography and the actually measured surface topography under variable roll angles of the present invention;

[0073] Figure 9 Schematic diagram showing the comparison between the simulated predicted roughness and the actual measured roughness under variable roll angles of the present invention.

[0074] In the figure: 1. Ball end milling cutter coordinate system; 2. Workpiece reference coordinate system; 3. Machine tool spindle coordinate system; 4. Workpiece coordinate system; 5. Cycle starting point; 6. Cutting depth; 7. First non-cutting phase; 8. Cutting phase; 9. Second non-cutting phase; 10. Cycle end point; DETAILED DESCRIPTION

[0075] 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.

[0076] In order to achieve the above object, the present invention provides the following specific implementation methods:

[0077] Example 1: Figure 1-3 As shown, a surface morphology prediction method based on a ball-end tool model and a variable step-size iterative algorithm includes the following steps:

[0078] S01. In the cutting edge geometry model of the ball-end milling cutter that participates in the cutting part, a spatial coordinate system is established to describe the position of the cutting edge of the ball-end milling cutter, such as Figure 1 As shown in Figure 2, the spatial coordinate system specifically includes:

[0079] The center of the ball end mill is the origin O, and the axis of the ball end mill is the Z. T Axis, from the tip of any cutting edge to Z T The axis line direction is X T Axis, thus, the Y axis is determined by the right-hand coordinate system rule. T Axis, established ball end milling cutter coordinate system 1; ball end milling cutter coordinate system 1 can rotate with the machine tool spindle as the rotation center;

[0080] X based on the ball end mill coordinate system 1 T Axis and Y T Axis direction, with the machine tool spindle as Z S Axis, established machine tool spindle coordinate system 3;

[0081] Based on the coordinate axis origin O of the ball end mill coordinate system, the cutting line direction is X G Axis, ball end mill feed direction is Y G Axis, determine Z using the right-hand coordinate system rule G Axis, established workpiece reference coordinate system 2;

[0082] Based on the coordinate axis direction of the workpiece reference coordinate system 2, the workpiece coordinate system 4 is established with any vertex on the bottom surface of the workpiece as the origin.

[0083] S02. Use the spatial coordinate system to determine the positions of the discrete points of the cutting edges of all the cutting edges of the ball-end milling cutter, that is, obtain the coordinate expressions of the discrete points of the cutting edges. At the same time, use the normal distribution random quantity function in the expression of the discrete points of the cutting edges to characterize the passivation morphology of the actual cutting edges of the ball-end milling cutter during the cutting process, specifically:

[0084] For any cutting edge j among the N cutting edges in the cutting edge geometry model, the expression of the discrete point L of any cutting edge j is:

[0085] ,

[0086] Where R is the radius of the ball end mill, γ is the helix angle, N is the total number of cutting teeth, E(σ) is the normal distribution random quantity function, θ is the line connecting the discrete points of the cutting edge and the center of the ball end mill, and in the ball end mill coordinate system X T OY T Projection of the plane and X T The angle between the axes.

[0087] S03. Based on the expression of the discrete points of the cutting edge, the motion trajectory of the discrete points of the cutting edge in the spatial coordinate system is described by calculating multiple three-dimensional homogeneous coordinate transformation matrices. Thus, in the workpiece reference coordinate system 2, a cutting edge motion trajectory calculation equation for describing the motion trajectory of the cutting edge is established. That is, for any cutting edge j among the N cutting edges in the cutting edge geometric model, the motion trajectory calculation equation of any discrete point L of the cutting edge j is specifically:

[0088] ,

[0089] Among them, θ is the line connecting the discrete point of the cutting edge and the center of the ball end milling cutter, t is the cutting edge motion time, (x WL ,y WL , z WL ) is the position coordinate of the discrete point L in the workpiece coordinate system;

[0090] M1~M5 are the rotation, eccentric translation, spindle rotation, posture adjustment and feed transformation matrices of the ball end mill respectively. The specific expressions are:

[0091] The rotation matrix M1 is:

[0092] ,

[0093] The eccentric translation matrix M2 is:

[0094] ,

[0095] Among them, δ is the radial eccentric angle of the ball end mill;

[0096] The main axis rotation matrix M3 is:

[0097] ,

[0098] Among them, φ0 is the initial phase angle of the cutting edge, ω is the angular velocity of the machine tool spindle;

[0099] The attitude adjustment matrix M4 is:

[0100] ,

[0101] Among them, α is the rake angle of the ball end milling cutter, and β is the side rake angle of the ball end milling cutter;

[0102] The feed transformation matrix M5 is:

[0103] ,

[0104] Among them, f p is the processing line spacing of the ball end mill, f v is the feed rate of the ball end mill, i is any cutting line among the N cutting edges, and (x0, y0, z0) is the initial position coordinate of the center of the ball end mill in the workpiece coordinate system.

[0105] S04. During any rotation cycle of the ball end mill during the cutting process, for any cutting edge j among the N cutting edges in the cutting edge geometric model, there is:

[0106] Since the initial discrete points of the cutting edge are all at the workpiece grid height W Z Above, there is: Z L >W Z , Z L is the height of any discrete point L of any cutting edge j at time t. At this time, the discrete point of the cutting edge is in the first non-cutting stage. According to the maximum discrete time step Δt, the cutting edge motion trajectory is calculated, and the counting variable of the discrete point of the cutting edge in the first non-cutting stage is recorded as A=A+1 until the discrete point of the cutting edge leaves the first non-cutting stage, that is, Z L ≤W Z ;

[0107] As the cutting edge discrete point leaves the first non-cutting stage, i.e. Z L ≤W Z At this time, the cutting edge discrete point is in the cutting stage, and the cutting edge discrete point count variable in the cutting stage is recorded as B=B+1, until the cutting edge discrete point leaves the cutting stage, that is, Z appears again. L >W Z ;

[0108] Continuing, the discrete points of the cutting edge leave the cutting stage, that is, Z appears again L >W Z At this time, the discrete points of the cutting edge are in the second non-cutting stage, and the counting variable of the discrete points of the cutting edge in the second non-cutting stage is recorded as C=C+1 until the rotation cycle of the ball end milling cutter ends;

[0109] Among them, the initial count variable values ​​of A in the cutting edge discrete point count variable in the first non-cutting stage, B in the cutting edge discrete point count variable in the cutting stage, and C in the cutting edge discrete point count variable in the second non-cutting stage are all 0;

[0110] That is, the division of the cutting trajectories and non-cutting trajectories of the discrete points of the cutting edges of all N cutting edges is completed.

[0111] S05. According to the target accuracy of the surface topography prediction output result, the maximum discrete time step Δt of the cutting edge motion trajectory is determined. The specific expression is:

[0112] ,

[0113] Where A c is the workpiece grid accuracy, A c The value of is used to determine the target accuracy of the ball-end milling cutter milling surface topography prediction results; max It is the maximum axial angle of the cutting edge involved in the cutting part; R is the radius of the ball end mill.

[0114] S06, let the time step of the first non-cutting stage Δt1 = AΔt; the time step of the cutting stage Δt2 = Δt; the time step of the second non-cutting stage Δt3 = CΔt;

[0115] Then, during the rotation cycle of the ball-end milling cutter with continuous cutting, the time step is dynamically selected according to the positional relationship between the discrete points of the cutting edge and the workpiece grid, specifically:

[0116] If the discrete point of the cutting edge is in the first non-cutting stage, the time step Δt1 is used;

[0117] If the discrete point of the cutting edge is in the cutting stage, the time step Δt2 is used, otherwise the time step Δt3 of the second non-cutting stage is used.

[0118] S07. Initialize the discrete accuracy A of the workpiece's machining surface c , the discrete accuracy of the cutting edge Δθ, the maximum discrete time step Δt of the cutting edge motion trajectory, and the construction of the discrete point cloud of the machined surface are realized.

[0119] S08. Determine the position coordinates of the discrete point cloud in the workpiece coordinate system based on the actual size or model of the workpiece, and then convert the discrete point cloud into a point cloud height matrix W. Z .

[0120] S09, traverse all the discrete points of the cutting edge, calculate the motion trajectory of the discrete points of the cutting edge based on the processing program data and the determined time step of the discrete points of the cutting edge, and perform a point cloud height matrix W on the workpiece processing surface for the coordinate points in the workpiece reference coordinate system corresponding to the discrete points of the cutting edge in the cutting stage. Z The update of , that is, the predicted workpiece processing surface morphology is obtained;

[0121] The machining program data includes a tool path file for determining the motion path of discrete points of the cutting edge and cutting process parameters for the motion speed of the discrete points of the cutting edge themselves.

[0122] S10, using the contour arithmetic mean deviation Ra Arithmetic mean height of dough S a To evaluate the accuracy of surface topography prediction, the arithmetic mean deviation R a Arithmetic mean height of dough S a , respectively:

[0123] ,

[0124] ,

[0125] Where Z i is the height value of the sampling grid point, Z mid To calculate the reference surface height value; m and n are the number of grid divisions along the X and Y axes in the workpiece coordinate system respectively.

[0126] like Figures 1-9 In order to further illustrate the scheme and technical effects of the present invention, the following specific examples are provided:

[0127] A surface topography prediction method based on a ball-end tool model and a variable step-size iterative algorithm comprises the following steps:

[0128] Step 1: Based on the cutting edge geometry model, a spatial coordinate system is constructed to describe the position and motion of the cutting edge, such as Figure 1 As shown, it includes the ball-end milling cutter coordinate system 1, the spindle coordinate system 3, the workpiece reference coordinate system 2, and the workpiece coordinate system 4; wherein, the cutting edge geometric model includes the ball-end milling cutter radius R, the helix angle γ, the number of teeth N, and the normal distribution random quantity function E(σ) is introduced to characterize the blunt morphology of the ball-end milling cutter during the cutting process;

[0129] Accurately describing the position and motion of the cutting edge is the basis for accurate simulation and prediction of the milling process. By establishing the ball end mill coordinate system 1, the spindle coordinate system 3, the workpiece reference coordinate system 2, and the workpiece coordinate system 4, the relative position relationship between the ball end mill, the spindle, and the workpiece can be clearly defined, providing a unified and accurate coordinate framework for subsequent kinematic and dynamic analysis.

[0130] Step 2: Describe the motion trajectory of the discrete points of the cutting edge in the spatial coordinate system through multiple three-dimensional homogeneous coordinate transformation matrices. Combined with the radial eccentricity distance e, radial eccentricity angle δ, rake angle α, rake angle β of the ball end mill and the angular velocity ω of the machine tool spindle, construct an equation to realize the calculation of the motion trajectory of the cutting edge in the workpiece coordinate system.

[0131] Accurately calculating the motion trajectory of the cutting edge is crucial for predicting machining results and optimizing machining processes. By describing the motion trajectory of discrete points on the cutting edge using multiple three-dimensional homogeneous coordinate transformation matrices, and taking into account the various motion states and posture parameters of the ball-end milling cutter, the cutting process can be more realistically reflected.

[0132] Step 3: Determine the maximum discrete time step of the cutting edge motion trajectory based on the target accuracy of the surface topography prediction output result; then calculate the division position and duration of the cutting trajectory and non-cutting trajectory of each discrete point of the cutting edge within any ball end mill rotation cycle during the cutting process. Then, traverse each discrete point of the cutting edge and calculate the division position and duration of its cutting trajectory and non-cutting trajectory;

[0133] While meeting the output accuracy requirements, the amount of calculation is reasonably controlled to avoid the problems of insufficient accuracy or waste of computing resources that may be caused by a fixed step size. By dynamically adjusting the step size, detailed calculations are performed in the cutting stage to ensure accuracy, and a larger step size is used in the non-cutting stage to improve efficiency, thus balancing accuracy and computing efficiency.

[0134] Step 4: Combine the time step of the discrete points of the cutting edge with the Z-MAP algorithm to obtain an improved Z-MAP algorithm; generate a three-dimensional surface topography by updating the coordinate information of the workpiece processing surface in real time, and use the arithmetic mean deviation of the profile R a Arithmetic mean height of dough S a Evaluate the accuracy of surface topography predictions;

[0135] Using the arithmetic mean deviation R a Arithmetic mean height of dough S a Evaluating simulation accuracy can quantify the degree of agreement between simulation results and actual measurement results, which helps optimize machining processes, predict machining surface quality in advance, and improve the accuracy and reliability of workpiece machining.

[0136] The above steps 1 to 4 are connected in series to obtain the time step of the discrete point of the cutting edge and the Z-MAP algorithm process as follows: Figure 3 As shown;

[0137] The following is a verification explanation based on the specific example 1:

[0138] Specific example 1: This is a ball end milling cutter plane milling experiment. The workpiece material is TC4. The ball end milling cutter has 4 teeth, a diameter of 8 mm, and a helix angle γ of 20°. The spindle speed n is 4000 r / min, and the feed speed f is 1000 mm / min. Figure 2 The cutting depth 6 shown is a p The thickness of the workpiece is 0.3 mm, the rake angle α is 60°, and the side rake angle β is 0°. After the workpiece is processed, the NPFLEX 3D optical profiler of BRUKER is used to measure its 3D surface morphology. The test lens is 2.5 times and the reflectivity is 0.1%~100%.

[0139] According to the above selected process parameters, the output size is determined to be 1.2mm×1.2mm×2.3mm based on the principle of sufficient output of three-dimensional surface morphology features. Based on this target output size, the discrete accuracy A of the workpiece machining surface is adopted. c =50 to A c =200, a total of 16 groups of accuracy levels, such as Figure 2 As shown, by determining the cycle starting point 5 and the cycle ending point 10, the division of the first non-cutting stage 7, the cutting stage 8 and the second non-cutting stage 9 is completed, and the time step of each stage is calculated respectively, and finally the three-dimensional surface morphology is calculated and output;

[0140] The method provided by the present invention is compared with the traditional Z-MAP method in terms of the improvement effect of the total simulation time; the total simulation time of the two methods is compared. Figure 4 As shown in the figure, under the same grid accuracy conditions, the simulation efficiency of the improved Z-MAP method based on the variable time step strategy is generally improved by more than 3 times compared with the traditional Z-MAP method;

[0141] Specific Example 2: Based on the process parameters and experimental settings selected in Specific Example 1, a single-factor experiment was conducted in which only the tilt angle β was changed from 0° to 330°, and the three-dimensional surface morphology was calculated and output respectively;

[0142] The comparison between some output results and measured results is shown in the following figure: Figure 5-8 shown; in Figure 5 In are respectively the simulated predicted surface morphology and the actual measured surface morphology when the roll angle β=0°; Figure 6 In the figure, the simulated predicted surface morphology and the actual measured surface morphology are respectively when the roll angle β=30°; Figure 7 In the figure, the simulated predicted surface morphology and the actual measured surface morphology are respectively when the roll angle β=60°; Figure 8 The figures in the figure are the simulated predicted surface morphology and the actual measured surface morphology when the roll angle β=90°.

[0143] In order to quantitatively evaluate the accuracy of the method provided by the present invention, the arithmetic mean deviation of the contours R was calculated for each group. a Arithmetic mean height of dough S a The comparison between the calculated results and the measured values ​​is shown in the following figure: Figure 9 As shown in the figure, it further illustrates that the improved Z-MAP method based on the variable time step strategy not only achieves a significant improvement in simulation efficiency, but also ensures prediction accuracy.

[0144] In summary, the present invention has significantly improved both simulation efficiency and accuracy, and the algorithm has strong universality and supports expansion of complex working conditions. From the specific example 1, it can be seen that under the same grid accuracy conditions, the simulation efficiency of this method is generally improved by more than 3 times compared with the traditional Z-MAP method; the specific example 2 shows that this method not only achieves a significant improvement in simulation efficiency, but also calculates the arithmetic mean deviation R of the contour. a Arithmetic mean height of dough S a The results are compared with the measured values ​​to ensure the prediction accuracy, which provides strong support for surface morphology prediction and process parameter optimization in cutting of complex aerospace parts.

[0145] 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 topography prediction method based on a ball-end tool model and a variable step-size iterative algorithm, characterized in that: The following steps are involved: Step 1: In the cutting edge geometry model of the ball-end milling cutter, a spatial coordinate system is established to describe the position of the cutting edge of the ball-end milling cutter. The positions of the discrete points of the cutting edges of all the cutting edges of the ball-end milling cutter are determined using the spatial coordinate system, that is, the coordinate expressions of the discrete points of the cutting edges are obtained. At the same time, a normal distribution random quantity function is used in the expression of the discrete points of the cutting edges to characterize the passivation morphology of the actual cutting edge of the ball-end milling cutter during the cutting process. Among them, the spatial coordinate system includes the ball end milling cutter coordinate system, the machine tool spindle coordinate system, the workpiece reference coordinate system and the workpiece coordinate system; Step 2: Based on the expression of the discrete points of the cutting edge, the motion trajectory of the discrete points of the cutting edge in the spatial coordinate system is described by calculating multiple three-dimensional homogeneous coordinate transformation matrices. Thus, in the workpiece reference coordinate system, the calculation equation of the cutting edge motion trajectory is established to describe the cutting edge motion trajectory; Step 3: Divide the cutting edge motion trajectory corresponding to the cutting edge discrete points into a non-cutting trajectory in the non-cutting stage and a cutting trajectory in the cutting stage according to the cutting state, and calculate the time step of the cutting edge discrete points in the non-cutting stage and the cutting stage; Step 4: Combining the time step of the discrete points of the cutting edge with the Z-MAP algorithm, and based on the milling program data used to describe the motion state of the ball-end milling cutter, iteratively update the height information of the workpiece machined surface after each cutting edge motion trajectory, that is, obtain the three-dimensional surface morphology of the workpiece machined surface; The machining program data includes a tool path file for determining the motion path of discrete points of the cutting edge and cutting process parameters for the motion speed of the discrete points of the cutting edge themselves.

2. The surface topography prediction method based on a ball-end tool model and a variable step-size iterative algorithm according to claim 1, characterized in that: The spatial coordinate system described in step 1 specifically includes: The center of the ball end mill is the origin O, and the axis of the ball end mill is the Z. T Axis, from the tip of any cutting edge to Z T The axis line direction is X T Axis, thus, the Y axis is determined by the right-hand coordinate system rule. T Axis, establish the ball end milling cutter coordinate system; the ball end milling cutter coordinate system can rotate with the machine tool spindle as the rotation center; X based on the ball end milling cutter coordinate system T Axis and Y T Axis direction, with the machine tool spindle as Z S Axis, the established machine tool spindle coordinate system; Based on the coordinate axis origin O of the ball end mill coordinate system, the cutting line direction is X G Axis, ball end mill feed direction is Y G Axis, determine Z using the right-hand coordinate system rule G Axis, established workpiece reference coordinate system; The workpiece coordinate system is established based on the coordinate axis direction of the workpiece reference coordinate system and with any vertex on the bottom surface of the workpiece as the origin; Furthermore, the spatial coordinate system is used to determine the positions of the discrete points of all cutting edges of the ball-end milling cutter. For any cutting edge j among the N cutting edges in the cutting edge geometry model, the expression of the discrete point L of any cutting edge j is: ， Where R is the radius of the ball end mill, γ is the helix angle, N is the total number of cutting teeth, E(σ) is the normal distribution random quantity function, and θ is the line connecting the discrete points of the cutting edge and the center of the ball end mill in the ball end mill coordinate system X. T OY T Projection of the plane and X T The angle between the axes.

3. The surface topography prediction method based on a ball-end tool model and a variable step-size iterative algorithm according to claim 1, characterized in that: The cutting edge motion trajectory calculation equation established in step 2 is the motion trajectory calculation equation for any discrete point L of any cutting edge j among the N cutting edges in the cutting edge geometric model, specifically: ， Where θ is the line connecting the discrete point of the cutting edge and the center of the ball end milling cutter in the ball end milling cutter coordinate system X T OY T Projection of the plane and X T The angle between the axes, t is the cutting edge motion time, (x WL ,y WL , z WL ) is the position coordinate of the discrete point L in the workpiece coordinate system; M1~M5 are the rotation, eccentric translation, spindle rotation, posture adjustment and feed transformation matrices of the ball end mill respectively. The specific expressions are: The rotation matrix M1 is: ， The eccentric translation matrix M2 is: ， Among them, δ is the radial eccentric angle of the ball end mill; The main axis rotation matrix M3 is: ， Among them, φ0 is the initial phase angle of the cutting edge, ω is the angular velocity of the machine tool spindle; The pose adjustment matrix M4 is: ， Among them, α is the rake angle of the ball end milling cutter, and β is the side rake angle of the ball end milling cutter; The feed transformation matrix M5 is: ， Among them, f p is the machining line spacing of the ball end mill, f v is the feed rate of the ball end mill, i is any cutting line among the N cutting edges, and (x0, y0, z0) is the initial position coordinate of the center of the ball end mill in the workpiece coordinate system.

4. The surface topography prediction method based on a ball-end tool model and a variable step-size iterative algorithm according to claim 1, characterized in that: The step three is specifically as follows: In any rotation cycle of the ball end mill during the cutting process, for any cutting edge j among the N cutting edges in the cutting edge geometric model, we have: Since the initial discrete points of the cutting edge are all in the workpiece grid height matrix W Z Above, there is: Z L >W Z , Z L is the height of any discrete point L of any cutting edge j at time t. At this time, the discrete point of the cutting edge is in the first non-cutting stage. According to the maximum discrete time step Δt, the cutting edge motion trajectory is calculated, and the counting variable of the discrete point of the cutting edge in the first non-cutting stage is recorded as A=A+1 until the discrete point of the cutting edge leaves the first non-cutting stage, that is, Z L ≤W Z ; As the cutting edge discrete point leaves the first non-cutting stage, i.e. Z L ≤W Z At this time, the cutting edge discrete point is in the cutting stage, and the cutting edge discrete point count variable in the cutting stage is recorded as B=B+1, until the cutting edge discrete point leaves the cutting stage, that is, Z appears again. L >W Z ; Continuing, the discrete points of the cutting edge leave the cutting stage, that is, Z appears again L >W Z At this time, the discrete points of the cutting edge are in the second non-cutting stage, and the counting variable of the discrete points of the cutting edge in the second non-cutting stage is recorded as C=C+1 until the rotation cycle of the ball end milling cutter ends; Among them, the initial count variable values ​​of A in the cutting edge discrete point count variable in the first non-cutting stage, B in the cutting edge discrete point count variable in the cutting stage, and C in the cutting edge discrete point count variable in the second non-cutting stage are all 0; That is, the division of cutting trajectories and non-cutting trajectories of the discrete points of the cutting edges of all N cutting edges is completed; Furthermore, let the time step of the first non-cutting stage Δt1 = AΔt; the time step of the cutting stage Δt2 = Δt; the time step of the second non-cutting stage Δt3 = CΔt; Then, during the rotation cycle of the ball-end milling cutter with continuous cutting, the time step is dynamically selected according to the positional relationship between the discrete points of the cutting edge and the workpiece grid, specifically: If the discrete point of the cutting edge is in the first non-cutting stage, the time step Δt1 is used; If the discrete point of the cutting edge is in the cutting stage, the time step Δt2 is used; otherwise, the time step Δt of the second non-cutting stage is used. 3； Where Δt is the maximum discrete time step of the cutting edge motion trajectory determined based on the target accuracy of the surface topography prediction output result. The specific expression is: ， Where A c is the workpiece grid accuracy, A c The value of is used to determine the target accuracy of the ball-end milling cutter milling surface topography prediction results; max It is the maximum axial angle of the cutting edge involved in the cutting part; R is the radius of the ball end mill.

5. The surface topography prediction method based on a ball-end tool model and a variable step-size iterative algorithm according to claim 1, characterized in that: The step 4 is specifically as follows: First, initialize the discrete accuracy A of the workpiece's machining surface c , the discrete accuracy of the cutting edge Δθ, the maximum discrete time step Δt of the cutting edge motion trajectory, and the construction of the discrete point cloud of the machined surface; Then, according to the actual size or model of the workpiece, the position coordinates of the discrete point cloud in the workpiece coordinate system are determined, and then the discrete point cloud is converted into the workpiece grid height matrix W Z ; Finally, all the discrete points of the cutting edge are traversed, and based on the tool path file and cutting process parameters, the motion trajectory of the discrete points of the cutting edge is calculated according to the determined time step of the discrete points of the cutting edge. The coordinate points in the workpiece reference coordinate system corresponding to the discrete points of the cutting edge in the cutting stage are subjected to the point cloud height matrix W of the workpiece processing surface. Z The updated surface morphology of the workpiece can be predicted.

6. The surface topography prediction method based on a ball-end tool model and a variable step-size iterative algorithm according to any one of claims 1 to 5, characterized in that: It also includes the use of the profile arithmetic mean deviation R a Arithmetic mean height of dough S a Steps to evaluate the accuracy of surface topography predictions.

7. The surface topography prediction method based on a ball-end tool model and a variable step-size iterative algorithm according to claim 6, characterized in that: The arithmetic mean deviation of the profile R a Arithmetic mean height of dough S a , respectively: ， ， Where Z i is the height value of the sampling grid point, Z mid To calculate the reference surface height value; m and n are the number of grid divisions along the X and Y axes in the workpiece coordinate system respectively.

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