Identification method of geometric error distribution characteristics of machined surface by high-efficiency face milling cutter

Abstract

The present invention relates to the technical field of efficient face milling cutter machining error analysis, and discloses a method for identifying the geometric error distribution characteristics of the machined surface of an efficient face milling cutter. Milling experiments were carried out on a CNC milling machine XK7124. By analyzing the time-frequency characteristics of milling vibration, the instantaneous cutting posture of the face milling cutter and its teeth was solved, the milling surface morphology was constructed, and the reference plane of the machined surface was identified. On this basis, the machining error was solved, and the influencing factors of the dynamic distribution of the machining error were analyzed. Through the gray relative correlation analysis method, the degree of influence of each factor on the machining error was determined, and the dynamic distribution characteristics of the machining errors of different process schemes were compared. Finally, an efficient method for identifying the dynamic distribution characteristics of machining errors was proposed, and its effectiveness was verified through simulation and experiments. This method provides important technical support for improving milling machining accuracy and stability.

Description

Technical Field

[0001] The invention belongs to the technical field of high-efficiency face milling cutter machining error analysis, and in particular relates to a method for identifying geometric error distribution characteristics of a machined surface of a high-efficiency face milling cutter. Background Art

[0002] High-efficiency face milling cutters are typically specialized tools that offer high machining efficiency, high energy utilization, and high surface quality. Their machining error is a key indicator for evaluating the geometric parameters and distribution consistency of the surface they machine. The dynamic distribution of surface error directly reflects the temporal and spatial variations in the residual surface feature points between the teeth that make up the machined surface during the milling process. This is a key indicator for measuring surface quality and can be used to reveal the surface formation process.

[0003] Traditional research on machining errors with high-efficiency face milling cutters focuses primarily on the overall level of machined surface geometry and the degree to which it deviates from design specifications. These studies, often based on static error analysis, overlook the impact of factors such as tooth error, machining parameters, and milling vibration on the instantaneous cutting behavior of different teeth during the surface formation process, as well as the impact of the dynamic distribution of machining errors on the overall deviation level of the machined surface geometry. This fails to meet the cutting stability and machining quality requirements of high-efficiency face milling cutters, necessitating research on methods for identifying the dynamic distribution characteristics of machining errors with high-efficiency face milling cutters.

[0004] In view of this, we propose a method for identifying the distribution characteristics of geometric errors of machined surfaces of high-efficiency face milling cutters to solve the above problems. In response to the high-quality cutting processing requirements of high-efficiency face milling cutters, the present invention studies a dynamic distribution solution model for milling processing errors of high-efficiency face milling cutters. According to the time-frequency characteristic parameters of milling vibration in different cutting periods of the milling cutter, the instantaneous cutting posture of the milling cutter and the time-frequency characteristics of the dynamic distribution of machining surface errors in different cutting periods under milling vibration conditions are solved, the dynamic cutting behavior of the milling cutter in different cutting periods and its changing characteristics and the formation process of milling surface errors and the diversity of their distribution under milling vibration conditions are revealed, the influencing factors of the time-frequency characteristic parameters of the dynamic distribution of milling processing errors are identified, the influence characteristics of cutting parameters, tooth error and milling vibration on the dynamic distribution of machining errors are revealed, a method for identifying the dynamic distribution characteristics of milling processing errors of high-efficiency face milling cutters is proposed, and experimental verification is carried out. Summary of the Invention

[0005] The present invention aims to solve the following technical problems: the above-mentioned existing technologies lack the ability to monitor the dynamic changes of errors during the processing process, cannot capture the real-time changes of errors, do not fully consider the systematic influence of factors such as tooth errors, processing parameters, milling vibrations, etc., and are difficult to provide complete error analysis; have poor adaptability to error identification under different process conditions, and cannot provide accurate error analysis for different processing conditions; cannot predict the error changes that may occur during the processing, and lack the ability to predict the development trend of errors.

[0006] To achieve the above object, the present invention provides the following technical solutions:

[0007] A method for identifying geometric error distribution characteristics of a machined surface by an efficient face milling cutter comprises the following steps:

[0008] S1. Milling experiment and analysis of milling vibration time-frequency characteristics: A vibration experiment was conducted on a CNC milling machine XK7124 three-axis milling machining center using a face milling cutter in a down-feed mode while cutting 45# steel. The time-frequency characteristics of milling vibration were analyzed using root mean square value, kurtosis, and main frequency characteristic parameters. The milling vibration characteristics at different times were compared to identify the impact of milling vibration on machining errors.

[0009] S2. Calculation of the instantaneous cutting posture of the face milling cutter and its teeth: Establish an instantaneous cutting posture model of the face milling cutter and its teeth, and calculate the instantaneous cutting trajectory of the teeth based on the milling cutter design posture, tooth error, and milling vibration factors;

[0010] S3. Constructing the milling surface topography and identifying the reference plane: Using the calculated tooth cutting trajectory, construct the milling surface topography and identify the reference plane of the machined surface for subsequent error analysis;

[0011] S4. Processing error calculation: According to the processing surface topography and the reference plane, the processing error is calculated, and the relative position vector deviation and geometric shape deviation of the processing error are analyzed;

[0012] S5. Identification of factors affecting the dynamic distribution of milling errors: Analyze the influence of different factors on the dynamic distribution of machining errors and use the grey relative correlation analysis method to identify the degree of influence of each factor on the machining errors;

[0013] S6. Identification of dynamic distribution response characteristics of milling errors: Compare the dynamic distribution characteristics of machining errors of different process solutions and identify the impact of key process variables on the dynamic distribution of machining errors;

[0014] S7. Identification method of dynamic distribution characteristics of milling machining errors and its verification: Based on the identification of influencing factors of dynamic distribution of high-efficiency milling machining errors and the analysis of response characteristics, an efficient identification method of dynamic distribution characteristics of machining errors is proposed. The effectiveness of this method is verified through simulation and experiments.

[0015] Preferably, the milling cutter is the M4003-050-B22-04-6.5 face milling cutter produced by Walter Company, the blade is SDMT1204AZN-D57WKP35G, the blade coating material is TiCN, the cutting edge diameter is 50mm, the number of teeth is 4, the functional length is 40mm, the blade length is 6.5mm, and the main deflection angle is 45°.

[0016] As a preferred method, the conversion equation of any point of adjacent teeth of the milling cutter is:

[0017] [x i+1 y i+1 z i+1 1] T =R1[x i y i z i 1] T ;

[0018] The trajectory equations of any point on the cutting edge of the i-th and i+1-th teeth of the milling cutter are:

[0019] [xyz 1] T =T3T2R3R2T1R4[x i y i z i 1] T ;

[0020] [xyz 1] T =T3T2R3R2T1R1[x i y i z i 1] T ;

[0021] Among them, (x i ,y i ,z i ) is the coordinate of any point on the cutting edge in the tooth coordinate system, T1, T2, T3 are translation matrices, and R1, R2, R3, R4 are rotation matrices.

[0022] Preferably, T1, T2, T3, R1, R2, R3, and R4 are specifically shown in the following formula:

[0023]

[0024]

[0025] Where n is the spindle speed, v f is the feed speed, a p is the nominal cutting depth, a eis the nominal cutting width, l, w, h are the length, width and height of the workpiece respectively, r max is the maximum tooth turning radius, r i is the gyration radius of the i-th tooth, Δz i is the axial error of the face milling cutter teeth, θ(t) is the inclination angle caused by the vibration during the milling cutter cutting process, A x (t), A y (t), A z (t) are the displacements of the milling vibration along the negative x-axis, y-axis and z-axis in the workpiece coordinate system, o-xyz is the workpiece coordinate system, o c -x c y c z c is the vibration-free cutting coordinate system, o b -x b y b z b is the cutting coordinate system under vibration, o d -x d y d z d is the face milling cutter structure coordinate system, o i -x i y i z i is the tooth coordinate system, θ1(t) is the coordinate system of the non-vibration milling cutter and the vibration milling cutter coordinate system at x c -oz c The angle between the plane projection and the vibration milling cutter coordinate system is θ2(t). c -oz c Angle of plane projection, Δr i is the ith tooth turning radius error, Xg is the distance from the initial position of the milling cutter center along the positive direction of the x-axis to the y-axis, θ i is the x coordinate axis of the i-th tooth i Axis and face milling cutter structure coordinate system x d The clockwise angle of the axis.

[0026] As a preferred method, the instantaneous attitude angle θ(t) generated by the vibration during the milling process is at x c -oz c Projection of the surface and y c -oz c The projections of the surfaces are θ1(t) and θ2(t), and the solution is as follows:

[0027] Among them, l d is the total length of the milling cutter.

[0028] Preferably, the equation in the main cutting edge workpiece coordinate system is:

[0029] l i (x(t),y(t),z(t))=T3·R4·T2·R3·R2·T1·R1·[x i y i z i 1] T ;

[0030] The coordinates of the upper boundary point m1 of the main cutting edge in the workpiece coordinate system are:

[0031]

[0032] The coordinates of the lower boundary point m0 ​​of the main cutting edge in the workpiece coordinate system are:

[0033]

[0034] The main cutting edge equation is:

[0035]

[0036] In the workpiece coordinate system, the coordinates of the lower boundary point b0 of the secondary cutting edge are the same as those of the lower boundary point m0 ​​of the main cutting edge. The coordinates of the upper boundary point b1 of the secondary cutting edge in the workpiece coordinate system are:

[0037]

[0038] The equation of the secondary cutting edge is:

[0039]

[0040] Among them, m1 is the intersection of the current tooth cutting edge and the upper surface of the workpiece, that is, the upper boundary point of the main cutting edge; b1 is the intersection of the current tooth cutting edge and the transition surface processed by the previous tooth, that is, the upper boundary point of the secondary cutting edge; b0 is the lower boundary point of the secondary cutting edge, b1 and b0 have the same height in the workpiece coordinate system, and this point is also the lower boundary point m0 ​​of the main cutting edge; m2 is the selected point on the main cutting edge; b2 is the selected point on the secondary cutting edge, Z H is the upper boundary point, G i-1 is the transition surface equation for the i-1th tooth.

[0041] As a preferred method, during the milling process, the trajectory equation of any point on the main and secondary cutting edges is:

[0042] f(x(t),y(t),z(t))=0 0≤t≤t max ;

[0043] Among them, (x(t), y(t), z(t)) represents the position of the tool in the workpiece coordinate system at time t;

[0044] Combining the main and secondary cutting edge trajectory equations, the milling surface topography equation is obtained as follows:

[0045] G1(x(t1),y(t1),z min )=0 0≤t1≤t max ;

[0046] Among them, x(t1), y(t1) represent the x-axis and y-axis positions of the tool in the workpiece coordinate system at time t1, Z min Indicates the minimum z-axis position where the tool contacts the workpiece during machining.

[0047] As a preference, g -x g y g z g Fit the characteristic points to the reference coordinate system to obtain the milling error trajectory and its surface equation under the action of cutter tooth error and milling vibration as follows:

[0048] f1(x i ,y j ,z ij )=0

[0049] G(x i ,y j ,z ij )=0;

[0050] Among them, (x i ,y j ,z ij ) is the coordinate of the i-th feature point in the j-th position in the reference coordinate system.

[0051] Preferably, in step S4, the point-by-point method is used to characterize the relative position vector deviation and geometric shape deviation of the feature points of the machined surface formed by the milling cutter at any cutting moment as follows:

[0052]

[0053] Δz j (t) = z j (t)-z0,

[0054] Where N is the unit normal vector of the reference plane, N j is m j The tangent plane, N jxy N j In x g o g y g Projection on the surface, N yoz For surface y g o g zg The normal vector, θ xyj is m j The tangent plane at x g o g y g Angular error of the surface, θ xozj N j In x g o g y g Projection on the surface and x g The angle with respect to the positive axis. ρ j is point m j The contour curve is projected to x g o g z g The radius of curvature of the surface; z j (t) is the coordinate value along the z-axis of the workpiece coordinate system when G(x, y, z) = 0 at time t, G xoz (t) is the projection of G(x,y,z)=0 on the xoz plane at time t, θ xyj (t) is the time at which m j The tangent plane at x g o g y g Angular error of the surface, θ xozj (t) is the time at which N j In x g o g y g The angle between the projection on the surface and the positive x-axis. j (t) is the time at which point m j The contour curve is projected to x g o g z g Radius of curvature of the surface, ΔW j (t) is the time at which point m j The curvature, Δz j (t) is the distance from the position corresponding to G(x, y, z) = 0 at time t to the reference plane, is the machining error in the z-axis direction, and z0 is the distance between the reference plane and the xoy plane.

[0055] Preferably, in step S5, factors affecting the dynamic distribution of machining errors include process design posture, cutter tooth error, and milling vibration.

[0056] Compared with the prior art, the technical effects and advantages of the present invention are:

[0057] This efficient method for identifying the distribution characteristics of geometric errors in machined surfaces using face milling cutters is based on the dynamic monitoring and analysis of various influencing factors during the machining process. First, a dynamic distribution model for milling errors is constructed. This model can calculate in real time the machining errors caused by factors such as cutter tooth errors, machining parameters, and milling vibrations. Second, the method utilizes time-frequency analysis techniques to analyze the machining errors in both the time and frequency domains to identify their dynamic characteristics. Finally, experimental verification is conducted by comparing the simulation results with actual measurement results to verify the accuracy and effectiveness of the model.

[0058] This high-efficiency method for identifying the distribution characteristics of geometric errors on machined surfaces using face milling cutters calculates and analyzes machining errors in real time, enabling timely monitoring of error changes during the machining process. This allows for rapid adjustment of machining parameters and improves machining accuracy and stability. Compared to traditional high-precision measurement equipment, this method reduces reliance on expensive equipment and reduces machining costs, making it particularly suitable for large-scale production environments. Dynamic monitoring and time-frequency analysis of machining errors provide a comprehensive understanding of real-time error changes during machining, providing a more precise basis for optimizing machining processes.

[0059] This method for identifying the distribution characteristics of geometric errors on machined surfaces using a high-efficiency face milling cutter also offers the advantages of high predictability and adaptability. By analyzing the dynamic distribution characteristics of errors, it is possible to predict their development trends, providing a basis for preventing machining defects. Furthermore, this method can adapt to varying machining conditions, providing accurate solutions for error identification under different process scenarios, and enhancing the flexibility and reliability of the machining process. BRIEF DESCRIPTION OF THE DRAWINGS

[0060] Figure 1 This is a milling time period diagram of the high-efficiency face milling cutter of the present invention; Figure 2 The face milling cutter structure of the present invention and its instantaneous cutting posture diagram; Figure 3 It is a processing transition surface diagram of the present invention; Figure 4 The milling surface topography diagrams of positions 1 to 5 of the present invention are as follows; Figure 5 A diagram of a method for extracting feature points from a processed surface according to the present invention; Figure 6 A diagram showing the actual reference plane construction method of the present invention; Figure 7 This is a comparison diagram of the theoretical processing surface and the actual processing surface data of the present invention; Figure 8 The relative position vector diagram of the milling surface of the present invention; Figure 9 is the spatial distribution diagram of the relative position deviation Δz of the present invention; Figure 10 This is a comparison diagram of the milling surface at different positions along the y-axis of the present invention; Figure 11 is the spatial distribution diagram of the normal vector inclination angle deviation θxy of the present invention; Figure 12 is the spatial distribution diagram of the normal vector direction angle deviation θxoz of the present invention; Figure 13is the spatial distribution diagram of the curvature Δw of the present invention; Figure 14 The time domain and frequency domain distribution diagram of the relative position deviation Δz of the present invention; Figure 15 The time domain and frequency domain distribution diagram of the normal vector inclination deviation θxy of the present invention; Figure 16 The time domain and frequency domain distribution diagram of the normal vector direction angle deviation θxoz of the present invention; Figure 17 This is the time domain distribution diagram of the curvature Δw of the present invention; Figure 18 This is the frequency domain distribution diagram of the relative position deviation Δz of the present invention; Figure 19 This is the frequency domain distribution diagram of the normal vector inclination angle deviation θxy of the present invention; Figure 20 This is the frequency domain distribution diagram of the normal vector direction angle deviation θxoz of the present invention; Figure 21 This is the frequency domain distribution diagram of the curvature Δw of the present invention; Figure 22 This is a comparative analysis result of the time-frequency characteristics of the milling error along the x-axis under the influence of the root mean square value factor of the present invention; Figure 23 This is a comparative analysis result of the time-frequency characteristics of the milling error along the x-axis under the influence of the kurtosis factor of the present invention; Figure 24 This is a comparative analysis result of the time-frequency characteristics of the milling error along the x-axis under the influence of the main frequency factor of the present invention; Figure 25 This is a milling surface topography diagram of the present invention; Figure 26 This is the time domain distribution diagram of the relative position deviation Δz of solution 1 of the present invention; Figure 27 This is the time domain distribution diagram of the normal vector inclination angle deviation θxy of solution 1 of the present invention; Figure 28 This is the time domain distribution diagram of the normal vector direction angle deviation θxoz of Scheme 1 of the present invention; Figure 29 This is a comparison diagram of the time domain distribution of curvature Δw of solution 1 of the present invention; Figure 30 This is the time domain distribution diagram of the relative position deviation Δz of solution 1 of the present invention; Figure 31 This is the frequency domain distribution diagram of the normal vector inclination angle deviation θxy of solution 1 of the present invention; Figure 32 This is the frequency domain distribution diagram of the normal vector direction angle deviation θxoz of Scheme 1 of the present invention; Figure 33 This is a comparison diagram of the time domain distribution of curvature Δw of solution 1 of the present invention; Figure 34 This is a diagram of the method for identifying the dynamic distribution characteristics of machining errors of a high-efficiency face milling cutter according to the present invention; Figure 35 This is a comparison diagram of the spatial distribution of the relative position deviation Δz of Scheme 1 of the present invention; Figure 36 This is a comparison diagram of the spatial distribution of the normal vector inclination angle deviation θxy of Scheme 1 of the present invention; Figure 37 This is a comparison diagram of the spatial distribution of the normal vector direction angle deviation θxoz of Scheme 1 of the present invention; Figure 38 This is a comparison diagram of the spatial distribution of curvature Δw of solution 1 of the present invention; Figure 39 This is a time domain distribution comparison diagram of the relative position deviation Δz of Solution 1 of the present invention; Figure 40 This is a time domain distribution comparison diagram of the normal vector inclination angle deviation θxy of solution 1 of the present invention; Figure 41This is a time domain distribution comparison diagram of the normal vector direction angle deviation θxoz of Scheme 1 of the present invention; Figure 42 This is a comparison diagram of the time domain distribution of curvature Δw of solution 1 of the present invention; Figure 43 This is a comparison diagram of the time-frequency characteristic parameters of the relative position deviation Δz of solution 1 of the present invention; Figure 44 This is a comparison diagram of the time-frequency characteristic parameters of the normal vector inclination deviation θxy of solution 1 of the present invention; Figure 45 This is a comparison diagram of the time-frequency characteristic parameters of the normal vector direction angle deviation θxoz of Scheme 1 of the present invention; Figure 46 This is a comparison diagram of the time-frequency characteristic parameters of curvature Δw of solution 1 of the present invention; Figure 47 This is a comparison diagram of the spatial distribution of the relative position deviation Δz of Scheme 2 of the present invention; Figure 48 This is a comparison diagram of the spatial distribution of the normal vector inclination angle deviation θxy of solution 2 of the present invention; Figure 49 This is a comparison diagram of the spatial distribution of the normal vector direction angle deviation θxoz of Scheme 2 of the present invention; Figure 50 This is a comparison diagram of the spatial distribution of curvature Δw of solution 2 of the present invention; Figure 51 This is a time domain distribution comparison diagram of the relative position deviation Δz of Solution 2 of the present invention; Figure 52 This is a time domain distribution comparison diagram of the normal vector inclination angle deviation θxy of solution 2 of the present invention; Figure 53 This is a time domain distribution comparison diagram of the normal vector direction angle deviation θxoz of Scheme 2 of the present invention; Figure 54 This is a comparison diagram of the time domain distribution of curvature Δw of solution 2 of the present invention; Figure 55 This is a comparison diagram of the time-frequency characteristic parameters of the relative position deviation Δz of Solution 2 of the present invention; Figure 56 This is a comparison diagram of the time-frequency characteristic parameters of the normal vector inclination deviation θxy of solution 2 of the present invention; Figure 57 This is a comparison diagram of the time-frequency characteristic parameters of the normal vector direction angle deviation θxoz of solution 2 of the present invention; Figure 58 This is a comparison diagram of the time-frequency characteristic parameters of curvature Δw in solution 2 of the present invention; Figure 59 This is a flow chart of the method for identifying geometric error distribution characteristics of a machined surface by a high-efficiency face milling cutter according to the present invention. DETAILED DESCRIPTION

[0061] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0062] An efficient method for identifying the geometric error distribution characteristics of the machined surface of a face milling cutter. The specific process is as follows Figure 59 As shown in the figure, the specific content of the method for identifying the geometric error distribution characteristics of the machined surface of the high-efficiency face milling cutter is as follows:

[0063] 1. Experimental plan and analysis of vibration effects

[0064] 1.1 Milling Experiment: A vibration experiment was conducted on a CNC milling machine (XK7124) using a face milling cutter with a down-feed feed pattern. The cutter was a Walter M4003-050-B22-04-6.5 face milling cutter with an SDMT1204AZN-D57WKP35G insert coated with TiCN. The cutting edge diameter was 50 mm, the number of teeth was 4, the functional length was 40 mm, the blade length was 6.5 mm, the lead angle was 45°, f was the feed per revolution, and the tooth with i equal to 1 was the first tooth to enter the workpiece. The milling parameters and tooth errors are shown in Table 1.

[0065] Table 1 Milling experimental parameters

[0066]

[0067] In Table 1, n is the spindle speed, vf is the feed speed, a p is the nominal cutting depth, a e is the nominal cutting width, Δri is the rotation radius error of the i-th tooth, and Δzi is the axial error of the i-th tooth of the face milling cutter.

[0068] According to Scheme 1 in Table 1, a vibration experiment of cutting 45 steel was carried out on the milling machining center. The obtained vibration data were analyzed and processed to obtain the milling experiment vibration acceleration signal, vibration displacement and cutting force, as shown in the following figure: Figure 1 As shown. Figure 1 ,The vibration acceleration, vibration displacement and cutting force of the milling ,experiment were analyzed. ,The milling vibration and dynamic cutting force mutation moments during the ,feet of the face milling cutter are shown in Table 2.

[0069] Table 2 Milling vibration characteristic time

[0070] Mutation Moment <![CDATA[t1(s)]]> <![CDATA[t2(s)]]> <![CDATA[t3(s)]]> <![CDATA[t4(s)]]> <![CDATA[t5(s)]]> <![CDATA[t6(s)]]> Experimental time 3.3s 7.3s 11.3s 35.3s 39.3s 43.3s Solving time 3.3s 7.25s 11.20s 34.88s 38.83s 42.78s Relative offset 0 0.05 0.10 0.42 0.47 0.52

[0071] From Table 2, the milling vibration and dynamic cutting force mutation moments during the face milling cutter feed process are the moments when the corresponding machining state changes during the face milling cutter processing. Under the influence of vibration, the corresponding machining state change moments are relatively offset, resulting in the relative offset of the milling vibration and dynamic cutting force mutation moments during the face milling cutter feed process. Figure 2 As shown in Table 2, the milling cutter processing time is divided into time periods, and the idling, cutting-in, cutting-in, and cutting-out time periods are obtained, as shown in Table 3.

[0072] Table 3 Milling period and cutting cycle

[0073]

[0074] Depend on Figure 1 As shown in Table 3, the experimental results are tested and analyzed to obtain the processing errors of the positions at different time periods.

[0075] 1.2 Analysis of time-frequency characteristics of milling vibration

[0076] From Table 3, we can obtain the different cutting periods of the milling cutter. Combined with the experimental vibration signal, we can obtain the time-frequency characteristic parameters of the milling vibration of the milling cutter in different cutting periods, as shown in Table 4.

[0077] Table 4 Time-frequency characteristic parameters of milling vibration in Experiment 1

[0078]

[0079]

[0080] Table 4 shows that the RMS values ​​of milling vibration in all three directions exhibit a characteristic of being smaller near the cut-in and cut-out periods, and larger in the intermediate periods. Kurtosis in the x and y directions exhibits the opposite behavior, while in the z direction, it exhibits an oscillating upward trend from the cut-in period to the cut-out period. The dominant vibration frequencies in the three directions exhibit different variations. The dominant frequency along the positive x and z axes initially appears higher, while the dominant frequency along the negative y axis is relatively stable.

[0081] It was also found that the vibration in the negative direction of the y-axis was significantly higher than that in the other two directions. The main reason for this is that when the face milling cutter is milling a workpiece with a cutting depth of 0.4mm and a cutting width of 25mm, the impact of each time the cutter teeth cut into the workpiece is concentrated in the negative direction of the y-axis where the surface to be machined is located, and the vibration is significantly greater than in the other two directions. The main frequency of milling vibration does not completely obey the frequency determined by the milling cutter speed and the number of cutter teeth. In the period close to the cutting point, the main frequency of vibration in the positive direction of the x-axis and the positive direction of the z-axis is twice the frequency determined by the milling cutter speed. Except for this period, the positive direction of the x-axis and the positive direction of the z-axis are equal to the frequency determined by the milling cutter speed. During the entire cutting period, the main frequency of vibration in the negative direction of the y-axis is twice the frequency determined by the milling cutter speed. The reason may be related to the uneven distribution of cutter tooth errors.

[0082] The root mean square value and kurtosis in the time domain signal of milling vibration acceleration, and the dominant frequency in the frequency domain signal, respectively reflect the intensity of milling vibration, the impact component contained in milling vibration, and the frequency of milling vibration changes. Therefore, the above characteristic parameters are used to analyze the time-frequency characteristics of milling vibration.

[0083] 2. Construction of dynamic distribution calculation model for efficient face milling error

[0084] 2.1 Calculation of the instantaneous cutting posture of the face milling cutter and its teeth

[0085] The instantaneous cutting behavior of the face milling cutter and its teeth directly affects the formation process of the machined surface. Among them, the instantaneous cutting posture of the milling cutter under the influence of tooth error and milling vibration is as follows: Figure 2 shown.

[0086] Figure 2 o-xyz is the workpiece coordinate system, o c -x c y c z c is the vibration-free cutting coordinate system, o b -x b y b z b is the cutting coordinate system under vibration, o d -x d y d z d is the face milling cutter structure coordinate system, o i -x i y i z i is the tooth coordinate system. n is the spindle speed, v f is the feed speed, a p is the nominal cutting depth, a e is the nominal cutting width. l, w, h are the length, width, and height of the workpiece respectively. max is the maximum tooth turning radius, r i is the gyration radius of the i-th tooth, Δz i is the axial error of the i-th tooth of the face milling cutter. θ(t) is the inclination angle caused by the vibration during the milling cutter cutting process, A x (t), A y (t), A z (t) are the displacements of the milling vibration in the workpiece coordinate system along the negative x-axis, y-axis, and z-axis directions. i is the ith tooth turning radius error, Xg is the distance from the initial position of the milling cutter center along the positive direction of the x-axis to the y-axis, θ i is the x coordinate axis of the i-th tooth i Axis and face milling cutter structure coordinate system x d The clockwise angle of the axis.

[0087] θ1(t) is the difference between the non-vibration milling cutter coordinate system and the vibration milling cutter coordinate system at x c -oz c The angle between the plane projection and the vibration milling cutter coordinate system is θ2(t). c -oz c The angle of the plane projection.

[0088] Depend on Figure 2 , the conversion equation of any point of adjacent teeth of the milling cutter is:

[0089] [x i+1 y i+1 z i+1 1] T =R1[x i y i z i 1] T (1)

[0090] The trajectory equations of any point on the cutting edge of the i-th and i+1-th teeth of the milling cutter are:

[0091] [xyz 1] T =T3T2R3R2T1R4[x i y i z i 1] T (2)

[0092] [xyz 1] T =T3T2R3R2T1R1[x i y i z i 1] T (3)

[0093] Among them, (x i ,y i ,z i ) is the coordinate of any point on the cutting edge in the tooth coordinate system, T1, T2, T3 are translation matrices, and R1, R2, R3, R4 are rotation matrices, as shown in Equations (4) to (7):

[0094]

[0095] In formula (5), the instantaneous attitude angle θ(t) generated by the vibration during the milling process is c -oz c Projection of the surface and y c -oz c The projections of the surfaces are θ1(t) and θ2(t), and the solution is as follows:

[0096]

[0097] Among them, such as Figure 2 As shown, l d is the total length of the milling cutter. The milling cutter is affected by vibration during cutting and the transition surface is formed during machining, such as Figure 3 As shown;

[0098] Figure 3In the figure, m1 is the intersection of the current tooth cutting edge and the upper surface of the workpiece, that is, the upper boundary point of the main cutting edge; b1 is the intersection of the current tooth cutting edge and the transition surface processed by the previous tooth, that is, the upper boundary point of the secondary cutting edge; b0 is the lower boundary point of the secondary cutting edge, b1 and b0 have the same height in the workpiece coordinate system, and this point is also the lower boundary point m0 ​​of the main cutting edge; m2 is the selected point on the main cutting edge; b2 is the selected point on the secondary cutting edge.

[0099] The equation in the main cutting edge workpiece coordinate system is:

[0100] l i (x(t),y(t),z(t))=T3·R4·T2·R3·R2·T1·R1·[x i y i z i 1] T (9)

[0101] The coordinates of the upper boundary point m1 of the main cutting edge in the workpiece coordinate system are:

[0102]

[0103] The coordinates of the lower boundary point m0 ​​of the main cutting edge in the workpiece coordinate system are:

[0104]

[0105] From equations (12) and (13), the main cutting edge equation can be obtained as follows:

[0106]

[0107] Among them, Z H is the upper boundary point, the height of m1 on the z axis, Z bo is the height of the lower boundary point m0 ​​on the z-axis.

[0108] In the workpiece coordinate system, the coordinates of the lower boundary point b0 of the secondary cutting edge are the same as the coordinates of the lower boundary point m0 ​​of the main cutting edge. The coordinates of the upper boundary point b1 of the secondary cutting edge in the workpiece coordinate system are:

[0109]

[0110] From equations (14) and (15), the secondary cutting edge equation can be obtained as follows:

[0111]

[0112] Among them, G i-1 is the transition surface equation for the i-1th tooth;

[0113] 2.2 Constructing milling surface topography and identifying reference planes

[0114] 1.2.1 Milling surface topography construction method

[0115] From formula (1) to formula (14), the trajectory equation of any point on the primary and secondary cutting edges is obtained:

[0116] f(x(t),y(t),z(t))=0 0≤t≤t max (15)

[0117] Combining the main and secondary cutting edge trajectory equations, the milling surface topography equation is obtained.

[0118] G1(x(t1),y(t1),z min )=0 0≤t1≤t max (16)

[0119] in,

[0120] z min ={z(0),z(1)....,z(t1)} (17)

[0121] Among them, x(t1), y(t1) represent the x-axis and y-axis positions of the tool in the workpiece coordinate system at time t1, Z min It represents the minimum z-axis position where the tool contacts the workpiece at (x(t1), y(t1)) during machining.

[0122] According to the experimental parameters and vibration data of Scheme 1 in Table 1, the milling surface morphology of positions 1 to 5 is obtained through MATLAB simulation, as shown in Figure 4 As shown in FIG, points on the milling surface topography are extracted along the x-axis to obtain the characteristic points of the milling surface, as shown in FIG. Figure 5 shown.

[0123] Figure 5 In, o g -x g y g z g As the reference coordinate system, Figure 3 In this method, the characteristic points are fitted to obtain the milling error trajectory and its surface equation under the action of cutter tooth error and milling vibration.

[0124]

[0125] Among them, (x i ,y j ,z ij ) is the coordinate of the i-th feature point in the j-th position in the reference coordinate system.

[0126] 2.3 Machining reference plane identification

[0127] like Figure 6 In, x i is the distance from the center of the i-th detection area to the y-axis, y j is the distance from the center of the jth detection area to the x-axis, Δx i is the length of the i-th detection area, Δy is the width of the detection area, l ij m It is the mth actual detection line segment (m=1, 2, ..., 5) in the detection area, and is equidistantly distributed along the y direction.

[0128] Vibration displacement l ij m1 With l ij m2 is the z-axis vibration displacement distribution caused by the machining error of the mth actual detection line segment affecting the ijth detection area, and z1 is the actual detection line segment l ij m The lowest point of the machining error distribution, Δz is the distance from the peak point of the machining error distribution to z1, Δz max is the maximum value of Δz; Δz' max is the maximum value of Δz'.

[0129] z gmin =min(l ij m1 (z),l ij m2 (z)) (19)

[0130] z g =z1-z gmin (20)

[0131] Δz′=Δz+z gmin (twenty one)

[0132] Where z g is the reference of the z-axis vibration displacement distribution, z gmin The z-axis vibration displacement distribution from the lowest point to the z g Δz' is the distance from the peak point of machining error distribution to z g distance;

[0133] Depend on Figure 6 And equations (1) to (21) yield that for the actual detection line segment l 11 1 ~l 51 1 The theoretical machining surface is compared with the actual machining surface data, and the error between the theoretical machining surface and the actual machining surface data is obtained by solving the error, such as Figure 7 and shown in Table 5.

[0134] Table 5 Comparison error between theoretical machined surface and actual machined surface data

[0135]

[0136] Depend on Figure 7 According to Table 5, the actual detection line segment l 11 1 ~l 51 1 The theoretical machined surface data is highly similar to the actual machined surface data. The peak error and average error between the theoretical machined surface data and the actual machined surface data are within 30%, which preliminarily verifies the effectiveness of the method.

[0137] 2.4 Processing error calculation

[0138] According to equations (1) to (18), the extracted data is used to generate the machined surface using MATLAB, and the relative position vector diagram of the milling error surface is obtained, as shown in Figure 8 shown.

[0139] Figure 8 In, m j ' is m j In the reference plane x g o g y g The projection point, z0 is the distance between the reference plane and the xoy plane, Δz j are point m j Position error, N is the unit normal vector of the reference plane, N j is m j The tangent plane, N jxy N j In x g o g y g Projection on the surface, N yoz For surface y g o g z g The normal vector, θ xyj is m j The tangent plane at x g o g y g Angular error of the surface, θ xozj N j In x g o g y g Projection on the surface and x g The angle with respect to the positive axis. ρ j is point m j The contour curve is projected to x g o g zg The radius of curvature of the surface.

[0140] The point-by-point method is used to characterize the relative position vector deviation and geometric shape deviation of the feature points of the machined surface formed by the milling cutter at any cutting moment:

[0141]

[0142] Where z j (t) is the coordinate value along the z-axis of the workpiece coordinate system when G(x, y, z) = 0 at time t, G xoz (t) is the projection of G(x, y, z) = 0 on the xoz plane at time t.

[0143] Where Δz j (t) is the distance from the position corresponding to G(x, y, z) = 0 to the reference plane at time t, and is the machining error in the z-axis direction, G xoz (t) is the time when G(x,y,z)=0 at x g o g z g Projection of the surface, θ xyj (t) is the time at which m j The tangent plane at x g o g y g Angular error of the surface, θ xozj (t) is the time at which N j In x g o g y g The angle between the projection on the surface and the positive x-axis. j (t) is the time at which point m j The contour curve is projected to x g o g z g Radius of curvature of the surface, ΔW j (t) is the time at which point m j curvature.

[0144] 3. Identification of factors affecting the dynamic distribution of milling errors

[0145] 3.1 Time-frequency characteristics of milling errors under different factors

[0146] By using formula (1) to formula (23), combined with scheme 1 in Table 1, the machining error is solved and the milling surface error under the action of various factors is obtained. The milling surface error distribution is as follows: Figures 9 to 13 The comparative analysis results of the time-frequency characteristics of milling errors along the x-axis under the influence of various factors are shown in Figure 2. Figures 14 to 17 As shown. Figures 18 to 21As shown, this is the time domain distribution diagram of machining error under the influence of various factors;

[0147] Depend on Figures 9 to 21 , only the milling surface under the milling cutter process design posture shows a uniform distribution, the milling surface under the influence of cutter tooth error shows a relatively regular periodic change, and the milling surface under the influence of milling vibration shows a change characteristic that is significantly different from the above two types of surfaces. Figures 9 to 17 ,There are obvious differences in the time-frequency distribution curves of the relative position vector deviation and shape deviation of the milling surface under the action of various factors.

[0148] The results show that the milling cutter process design posture, cutter tooth error, and milling vibration have different influence characteristics on the milling surface formation. By utilizing the differences in the influence of the above factors, the degree of influence of each factor on the dynamic distribution of milling errors can be further identified.

[0149] 3.2 Identification of factors affecting the dynamic distribution of machining errors

[0150] The comparative analysis results of the time-frequency characteristics of milling errors along the x-axis under the influence of various factors are as follows: Figures 22 to 24 As shown, Figure 24 In the figure, the scale 0.00~1.00 is the processing error index Δy, θ xz ,θ xoz , the root mean square value of Δw, kurtosis, and the normalized value of the main frequency. Figure 24 At different positions along the x-axis, the time-frequency characteristic parameters of the milling error under the milling cutter process design posture are all 0, indicating that the initial posture and cutting parameters determined by the milling cutter process design scheme make the cutting posture of each cutter tooth consistent and stable, and will not directly cause dynamic changes in the milling error.

[0151] The time-frequency characteristic parameters of milling machining error under the combined effects of milling vibration and multiple factors show different variation characteristics along the nominal cutting depth direction of the milling cutter, indicating that milling vibration changes the instantaneous cutting posture of the milling cutter and cutter teeth, making the distribution of the characteristic points of the maximum residual height of the machined surface between the cutter teeth unstable, thereby causing changes in the distribution characteristics of the milling machining error; and the superposition of the influence characteristics of the cutter tooth error will change the time-frequency characteristics of the milling machining error under the action of milling vibration.

[0152] 3.3 Relative correlation analysis of dynamic distribution of machining errors

[0153] In order to quantitatively identify the influence of various factors on the dynamic distribution of milling errors, an improved grey relative correlation analysis method is used to calculate the relative correlation between process design posture, cutter tooth error, milling error under milling vibration, and milling error under the combined effect of multiple factors, as shown in Table 6.

[0154] Table 6 Identification results of factors affecting dynamic distribution of milling errors

[0155]

[0156] It can be seen from Table 6 that the relative position deviation Δz, the normal vector inclination deviation θxy, the normal vector direction angle deviation θxoz and the curvature Δw are the machining error indicators, and γ(Δz), γ(θxy), γ(θxoz) and γ(Δw) are the correlations between the machining error indicators and the process design posture, tool tooth error and milling vibration.

[0157] Among them, the correlation between process design posture, cutter tooth error, milling vibration and dynamic distribution of milling machining error is greater than 0.50, which is a strong correlation and positive correlation, indicating that the above factors have a great influence on milling machining error.

[0158] The above analysis results show that, constrained by the initial design position of the milling cutter, the overall level of milling error remains similar to the designed surface, but the stability and consistency of its dynamic distribution cannot be guaranteed. The cutting parameters not only constrain the distribution of milling error by matching the designed milling cutter position, but also cause changes in the dynamic distribution of milling error through cutter tooth errors and milling vibration excitation.

[0159] 4. Identification of dynamic distribution response characteristics of milling errors

[0160] 4.1 Comparison of dynamic distribution characteristics of milling errors under different process schemes

[0161] According to equations (1) to (23) and the parameters of scheme 2 in Table 1, the corresponding machined surface morphology is obtained, as follows: Figure 25 As shown, the machining error is solved to obtain the milling surface under the action of comprehensive factors, and the time-frequency distribution of the milling surface error is solved, as shown in Figures 26 to 33 shown; with Figures 26 to 29 and Figures 30 to 33 By comparison, it is found that different processing schemes have different effects on the time-frequency characteristics of the dynamic distribution of milling errors, but the degree of influence on the time-frequency characteristics of the dynamic distribution of milling errors cannot be quantitatively identified.

[0162] The comparison of the calculation results of the dynamic distribution of milling errors along the x-axis direction under the two experimental schemes is shown in Table 7.

[0163] Table 7 Variation range of time-frequency characteristic parameters of machining errors in two experimental schemes

[0164]

[0165] It was also found that, with the exception of the RMS value of curvature, all other RMS values ​​for Scheme 1 were smaller than those for Scheme 2. With the exception of kurtosis, all other RMS values ​​for Scheme 1 were smaller than those for Scheme 2. The main frequency changes for Schemes 1 and 2 were not significantly different, indicating that the milling error variation and impact of Scheme 1 were lower than those for Scheme 2, and its dynamic distribution of machining errors was superior to that of Scheme 1. The results of calculating the characteristic parameters of milling errors in the time and frequency domains can be used to evaluate energy-efficient milling process solutions.

[0166] 4.2 Comparison of identification results of factors affecting the dynamic distribution of milling processing errors for different process schemes The relative correlation identification results of factors affecting the dynamic distribution of milling processing errors along the x-axis direction of the two experimental schemes are compared, as shown in Table 8.

[0167] Table 8 Correlation of factors affecting milling errors in two experimental schemes

[0168]

[0169] Table 8 shows that, compared with Scheme 2, the milling cutter design posture in Scheme 1 has a slightly stronger effect on the normal vector orientation angle deviation and curvature change, while its effect on the normal vector inclination angle deviation and relative position deviation change remains unchanged. This result indicates that Scheme 1 can, to a certain extent, enhance the constraint effect of the milling cutter design posture on the milled surface, thereby increasing the approximation of the milled surface to a plane.

[0170] Compared with Scheme 2, in Scheme 1, the tooth error has a stronger influence on the normal vector inclination deviation, normal vector orientation angle deviation, and curvature change, while its influence on relative position deviation is weakened. However, milling vibration has a stronger influence on relative position deviation and normal vector orientation angle deviation. This result shows that under the constraints of the milling cutter's designed position, the cutter speed and feed per tooth cause changes in the dynamic distribution of milling errors through the excitation of tooth error and milling vibration.

[0171] 5. Identification method and verification of dynamic distribution characteristics of milling machining errors

[0172] 5.1 Identification method of dynamic distribution characteristics of machining errors of high-efficiency face milling cutters

[0173] Based on the results of identification of factors affecting dynamic distribution of errors in high energy efficiency milling and analysis of response characteristics, a method for identifying dynamic distribution characteristics of milling errors is proposed, such as Figure 34 shown.

[0174] Figure 34 , A is the set of milling cutter processing parameters, B is the set of milling cutter structural parameters, C is the set of displacements along different directions of milling vibration, D is the milling cutter posture angle under milling vibration, M is the set of machining error index distribution curves, M a is the distribution curve of machining error index under the milling process scheme, Ma0 is the distribution curve of machining error index determined by process design posture, γ(M a , M a0 ) is M a0 With M a0 [γ0] is the minimum value of γ(Mk,Mk0) allowed by the design. N is the set of time-frequency characteristic parameters of the machining error index distribution curve, N b is the time-frequency characteristic parameter of the machining error index distribution curve under the milling process scheme, N b0 It is the time-frequency characteristic parameter of the optimal milling error index distribution curve that can be achieved under the influence of five factors: cutting parameters, milling cutter design posture, milling cutter structure parameters, cutter tooth error and milling vibration. ΔN is the N allowed by the design. b and N b0 The relative error of M a01 is the best machining error index distribution curve that can be achieved under the milling process scheme, γ(M a , M a01 ) is M a With M a01 ) is the correlation degree, [γ1] is the γ(M a ,M a01 ) is the minimum value of .

[0175] This method uses the changing characteristics of the relationship between tooth error and the instantaneous cutting behavior of adjacent teeth under the action of milling vibration to reveal the dynamic formation process of the milling surface; adopts the relative position vector deviation and geometric shape deviation solution model of the milling surface to quantitatively characterize the diversity of the dynamic distribution of milling errors; uses the time-frequency characteristic analysis method and relative correlation to identify the influence characteristics of key process variables on the dynamic distribution of milling errors, and evaluates the milling process plan accordingly.

[0176] 5.2 Comparison between dynamic distribution calculation and experimental results of milling machining error: Based on the parameters of Scheme 1 and 2 in Table 1, the simulation results of Scheme 1 and Scheme 2 are used to obtain the machining error and its time-frequency characteristics. Comparison with the experimental results shows that Figures 35 to 58 As shown in Figure 2, the simulation results of Schemes 1 and 2 are approximately the same as the experimental results in terms of the spatial distribution, time domain distribution, and time-frequency distribution of the machining error.

[0177] 5.3 Experimental verification of dynamic distribution of milling errors

[0178] In order to further verify the correctness of the milling error solution model and the dynamic distribution characteristic identification method, the similarity between the simulation solution results and the experimental solution results in the machining error distribution is quantitatively characterized. To this end, the relative error results of the machining error distribution between the simulation solution results and the experimental solution results are shown in Tables 9 to 11.

[0179] Table 9 Relative error analysis of machining error spatial distribution

[0180]

[0181]

[0182] Table 10 Relative error analysis of machining error time domain distribution

[0183]

[0184] Table 11 Relative error analysis of time-frequency characteristic parameters of machining error

[0185]

[0186] It can be seen from the table that for schemes 1 and 2, corresponding to the detection area, the relative errors of the spatial distribution of machining errors between the simulation solution results and the experimental solution results are both above 80% and within (-10%, 10%). Along the x-axis direction, corresponding to the detection position, the relative errors of the time domain and time-frequency distribution of machining errors between the simulation solution results and the experimental solution results are both above 80% and within (-10%, 10%). Therefore, it is concluded that the spatial distribution, time domain distribution and time-frequency distribution of machining errors between the simulation solution results and the experimental solution results are highly similar, which verifies the effectiveness of the milling machining error solution model and the dynamic distribution characteristic identification method.

[0187] Existing research on the milling errors of high-efficiency face milling cutters focuses on the overall level of the geometric parameters of the machined surface and the degree to which it deviates from the design indicators, and obtains the overall level of the geometric parameters of the machined surface through experiments; existing models ignore the influence of tooth error and milling vibration on the instantaneous cutting behavior of different teeth during the milling surface formation process of high-efficiency face milling cutters, and the influence of the dynamic distribution of machining errors on the overall deviation level of the geometric parameters of the machined surface, and are insufficient in revealing the formation mechanism of the dynamic distribution of machining errors.

[0188] Based on the milling errors of high-efficiency face milling cutters, the present invention constructs a dynamic distribution solution model for the milling errors of high-efficiency face milling cutters, and proposes a method for solving the position, size and shape levels of the machining errors; reveals the influencing factors of the dynamic distribution of milling errors, identifies the influencing factors and quantifies the influence of the influencing factors on the dynamic distribution of milling errors; studies the response characteristics of the dynamic distribution of high-efficiency milling errors and proposes a method for identifying the dynamic distribution characteristics of milling errors. The theoretical model solution is verified by the experimental results, and the deviation of the position, size and shape level indicators of the machining errors is within 20%.

Claims

1. A method for identifying geometric error distribution characteristics of a machined surface by an efficient face milling cutter, characterized in that: The following steps are involved: S1. Milling experiment and analysis of milling vibration time-frequency characteristics: A vibration experiment was conducted on a CNC milling machine XK7124 three-axis milling machining center using a face milling cutter in a down-feed mode while cutting 45# steel. The time-frequency characteristics of milling vibration were analyzed using root mean square value, kurtosis, and main frequency characteristic parameters. The milling vibration characteristics at different times were compared to identify the impact of milling vibration on machining errors. S2. Calculation of the instantaneous cutting posture of the face milling cutter and its teeth: Establish an instantaneous cutting posture model of the face milling cutter and its teeth, and calculate the instantaneous cutting trajectory of the teeth based on the milling cutter design posture, tooth error, and milling vibration factors; Among them, the conversion equation of any point of adjacent teeth of the milling cutter is: [x i+1 y i+1 z i+1 1] T =R1[x i y i z i 1] T ; The trajectory equations of any point on the cutting edge of the i-th and i+1-th teeth of the milling cutter are: [x y z 1] T =T3T2R3R2T1R4[x i y i z i 1] T ; [x y z 1] T =T3T2R3R2T1R1[x i y i z i 1] T ; Among them, (x i ,y i ,z i ) is the coordinate of any point on the cutting edge in the tooth coordinate system, T1, T2, T3 are translation matrices, and R1, R2, R3, R4 are rotation matrices; The equation in the main cutting edge workpiece coordinate system is: l i (x(t),y(t),z(t))=T3·R4·T2·R3·R2·T1·R1·[x i y i z i 1] T ; The coordinates of the upper boundary point m1 of the main cutting edge in the workpiece coordinate system are: The coordinates of the lower boundary point m0 ​​of the main cutting edge in the workpiece coordinate system are: The main cutting edge equation is: In the workpiece coordinate system, the coordinates of the lower boundary point b0 of the secondary cutting edge are the same as those of the lower boundary point m0 ​​of the main cutting edge. The coordinates of the upper boundary point b1 of the secondary cutting edge in the workpiece coordinate system are: The equation of the secondary cutting edge is: Among them, m1 is the intersection of the current tooth cutting edge and the upper surface of the workpiece, that is, the upper boundary point of the main cutting edge; b1 is the intersection of the current tooth cutting edge and the transition surface processed by the previous tooth, that is, the upper boundary point of the secondary cutting edge; b0 is the lower boundary point of the secondary cutting edge, b1 and b0 have the same height in the workpiece coordinate system, and this point is also the lower boundary point m0 ​​of the main cutting edge; m2 is the selected point on the main cutting edge; b2 is the selected point on the secondary cutting edge, Z H is the upper boundary point, G i-1 is the transition surface equation for the i-1th tooth; S3. Constructing the milling surface topography and identifying the reference plane: Using the calculated tooth cutting trajectory, construct the milling surface topography and identify the reference plane of the machined surface for subsequent error analysis; S4. Processing error calculation: According to the processing surface topography and the reference plane, the processing error is calculated, and the relative position vector deviation and geometric shape deviation of the processing error are analyzed; S5. Identification of factors affecting the dynamic distribution of milling errors: Analyze the influence of different factors on the dynamic distribution of machining errors and use the grey relative correlation analysis method to identify the degree of influence of each factor on the machining errors; S6. Identification of dynamic distribution response characteristics of milling errors: Compare the dynamic distribution characteristics of machining errors of different process solutions and identify the impact of key process variables on the dynamic distribution of machining errors; S7. Identification method of dynamic distribution characteristics of milling machining errors and its verification: Based on the identification of influencing factors of dynamic distribution of high-efficiency milling machining errors and the analysis of response characteristics, an efficient identification method of dynamic distribution characteristics of machining errors is proposed. The effectiveness of this method is verified through simulation and experiments.

2. The method for identifying geometric error distribution characteristics of a machined surface of a high-efficiency face milling cutter according to claim 1, characterized in that: The milling cutter is a M4003-050-B22-04-6.5 face milling cutter produced by Walter Company, the blade is SDMT1204AZN-D57WKP35G, the blade coating material is TiCN, the cutting edge diameter is 50mm, the number of teeth is 4, the functional length is 40mm, the blade length is 6.5mm, and the main deflection angle is 45°.

3. The method for identifying geometric error distribution characteristics of a machined surface of a high-efficiency face milling cutter according to claim 1, characterized in that: T1, T2, T3, R1, R2, R3, R4 are shown in the following formula: Where n is the spindle speed, v f is the feed speed, a p is the nominal cutting depth, a e is the nominal cutting width, l, w, h are the length, width and height of the workpiece respectively, r max is the maximum tooth turning radius, r i is the gyration radius of the i-th tooth, Δz i is the axial error of the face milling cutter teeth, θ(t) is the inclination angle caused by the vibration during the milling cutter cutting process, A x (t), A y (t), A z (t) are the displacements of the milling vibration along the negative x-axis, y-axis and z-axis in the workpiece coordinate system, o-xyz is the workpiece coordinate system, o c -x c y c z c is the vibration-free cutting coordinate system, o b -x b y b z b is the cutting coordinate system under vibration, o d -x d y d z d is the face milling cutter structure coordinate system, o i -x i y i z i is the tooth coordinate system, θ1(t) is the coordinate system of the non-vibration milling cutter and the vibration milling cutter coordinate system at x c -oz c The angle between the plane projection and the vibration milling cutter coordinate system is θ2(t). c -oz c Angle of plane projection, Δr i is the ith tooth turning radius error, Xg is the distance from the initial position of the milling cutter center along the positive direction of the x-axis to the y-axis, θ i is the x coordinate axis of the i-th tooth i Axis and face milling cutter structure coordinate system x d The clockwise angle of the axis.

4. The method for identifying geometric error distribution characteristics of a machined surface of a high-efficiency face milling cutter according to claim 3, characterized in that: The instantaneous attitude angle θ(t) generated by the vibration during the milling process is at x c -oz c Projection of the surface and y c -oz c The projections of the surfaces are θ1(t) and θ2(t), and the solution is as follows: Among them, l d is the total length of the milling cutter.

5. The method for identifying geometric error distribution characteristics of a machined surface of a high-efficiency face milling cutter according to claim 1, characterized in that: During the milling process, the trajectory equation of any point on the main and secondary cutting edges is: f(x(t),y(t),z(t))=0 0≤t≤t max ; Among them, (x(t), y(t), z(t)) represents the position of the tool in the workpiece coordinate system at time t; Combining the main and secondary cutting edge trajectory equations, the milling surface topography equation is obtained as follows: G1(x(t1),y(t1),z min )=0 0≤t1≤t max ; Among them, x(t1), y(t1) represent the x-axis and y-axis positions of the tool in the workpiece coordinate system at time t1, Z min Indicates the minimum z-axis position where the tool contacts the workpiece during machining.

6. The method for identifying geometric error distribution characteristics of a machined surface of a high-efficiency face milling cutter according to claim 5, characterized in that: with o g -x g y g z g Fit the characteristic points to the reference coordinate system to obtain the milling error trajectory and its surface equation under the action of cutter tooth error and milling vibration as follows: f1(x i ,y j ,z ij )=0 G(x i ,y j ,z ij )=0; Among them, (x i ,y j ,z ij ) is the coordinate of the i-th feature point in the j-th position in the reference coordinate system.

7. The method for identifying geometric error distribution characteristics of a machined surface of a high-efficiency face milling cutter according to claim 1, characterized in that: In step S4, the point-by-point method is used to characterize the relative position vector deviation and geometric shape deviation of the feature points of the machined surface formed by the milling cutter at any cutting moment as follows: Δz j (t)=z j (t)-z0, Where N is the unit normal vector of the reference plane, N j is m j The tangent plane, N jxy N j In x g o g y g Projection on the surface, N yoz For surface y g o g z g The normal vector, θ xyj is m j The tangent plane at x g o g y g Angular error of the surface, θ xozj N j In x g o g y g The angle between the projection on the surface and the positive x-axis, ρ j is point m j The contour curve is projected to x g o g z g The radius of curvature of the surface; z j (t) is the coordinate value along the z-axis of the workpiece coordinate system when G(x, y, z) = 0 at time t, G xoz (t) is the projection of G(x,y,z)=0 on the xoz plane at time t, θ xyj (t) is the time at which m j The tangent plane at x g o g y g Angular error of the surface, θ xozj (t) is the time at which N j In x g o g y g The angle between the projection on the surface and the positive x-axis, ρ j (t) is the time at which point m j The contour curve is projected to x g o g z g Radius of curvature of the surface, ΔW j (t) is the time at which point m j The curvature, Δz j (t) is the distance from the position corresponding to G(x, y, z) = 0 at time t to the reference plane, is the machining error in the z-axis direction, and z0 is the distance between the reference plane and the xoy plane.

8. The method for identifying geometric error distribution characteristics of a machined surface of a high-efficiency face milling cutter according to claim 1, characterized in that: In step S5, the factors affecting the dynamic distribution of machining errors include process design posture, cutter tooth error, and milling vibration.

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