Geometric error distribution characteristic identification method for machined surface of efficient face milling cutter

Abstract

The invention relates to the technical field of high-efficiency face milling cutter machining error analysis, and discloses a high-efficiency face milling cutter machined surface geometric error distribution characteristic identification method, a milling experiment is carried out on a numerical control milling machine XK7124, and the instantaneous cutting poses of a face milling cutter and cutter teeth of the face milling cutter are calculated by analyzing the time-frequency characteristics of milling vibration. A milling machining surface morphology is constructed, and a reference plane of a machining surface is identified. On the basis, machining errors are solved, and influence factors of dynamic distribution of the machining errors are analyzed. Through a grey relative correlation analysis method, the influence degree of each factor on the machining error is determined, and the machining error dynamic distribution characteristics of different process schemes are compared. Finally, the invention provides an efficient processing error dynamic distribution characteristic identification method, and the effectiveness of the method is verified through simulation and experiments. The method provides important technical support for improving the milling precision and stability.

Description

Technical Field

[0001] The invention belongs to the technical field of machining error analysis of high-efficiency face milling cutters, 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 cutter is a typical special tool with high processing efficiency, high energy utilization and high processing surface quality. Its processing error is an important indicator for evaluating the geometric parameters and distribution consistency of the processing surface of high-efficiency face milling cutter. The dynamic distribution of the error of the processed surface of high-efficiency face milling cutter directly reflects the change characteristics of the residual processing surface feature points between the teeth constituting the processed surface in time and space during the milling process. It is an important indicator for measuring the quality of the processed surface. This characteristic can be used to reveal the formation process of the processed surface.

[0003] Traditional research on machining errors of high-efficiency face milling cutters mainly focuses on the overall level of geometric parameters of the machined surface and the degree to which they deviate from the design indicators. These studies are often based on static error analysis, ignoring the influence of factors such as cutter tooth error, machining process parameters and milling vibration on the instantaneous cutting behavior of different cutter 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 geometric parameters of the machined surface. They cannot meet the requirements of cutting stability and machining quality during milling of high-efficiency face milling cutters, so it is necessary to study the identification method of the dynamic distribution characteristics of machining errors of 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. Aiming at the high-quality cutting processing requirements of high-efficiency face milling cutters, the present invention studies a dynamic distribution solution model of milling processing errors of high-efficiency face milling cutters. According to the time-frequency characteristic parameters of milling vibration of the milling cutter in different cutting periods, 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 under milling vibration conditions and the diversity of their distribution 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 errors 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 technical problems that the above-mentioned prior art lacks the ability to monitor the dynamic changes of errors during the processing process, cannot capture the real-time changes of errors, does not fully consider the systematic influence of factors such as tooth errors, processing parameters, milling vibrations, etc., and is difficult to provide complete error analysis; has 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 lacks 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 of an efficient face milling cutter comprises the following steps:

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

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

[0010] S3, constructing the milling surface morphology and identifying the reference plane: using the calculated cutting trajectory of the cutter teeth, construct the milling surface morphology 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 dynamic distribution of milling machining 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 influence of each factor on the machining error;

[0013] S6. Identification of dynamic distribution response characteristics of milling machining 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 energy-efficient milling machining errors and the analysis results of response characteristics, an efficient identification method of dynamic distribution characteristics of machining errors is proposed, and 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 =R 1 [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 =T 3 T 2 R 3 R 2 T 1 R 4 [x i y i z i 1] T ;

[0020] [xyz 1] T =T 3 T 2 R 3 R 2 T 1 R 1 [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, T 1 ,T 2 ,T 3 is the translation matrix, R 1 ,R 2 ,R 3 ,R4 is the rotation matrix.

[0022] As a preference, T 1 ,T 2 ,T 3 , R 1 ,R 2 ,R 3 ,R 4 The specific formula is as follows:

[0023]

[0024] Where n is the spindle speed, v is 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 turning radius of any cutter 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 in the negative x-axis direction, y-axis direction and z-axis direction 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 blade tooth coordinate system, θ 1 (t) is the distance between the non-vibration milling cutter coordinate system and the vibration milling cutter coordinate system at x c -oz c The angle of the plane projection, θ 2 (t) is the distance between the non-vibration milling cutter coordinate system and the vibration milling cutter coordinate system at y c -oz c Angle of projection on the plane, Δr i is the i-th 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 iis the x coordinate axis of the i-th tooth i The x axis and the face milling cutter structure coordinate system d The clockwise angle of the axis.

[0025] As a preferred embodiment, the instantaneous attitude angle θ(t) generated by the vibration during the milling cutter cutting process is c -oz c Projection of the surface and y c -oz c The projections of the surfaces are θ 1 (t) and θ 2 (t), the solution is as follows:

[0026]

[0027] Preferably, the equation in the main cutting edge workpiece coordinate system is:

[0028] l i (x(t),y(t),z(t))=T 3 ·R 4 ·T 2 ·R 3 ·R 2 ·T 1 ·R 1 ·[x i y i z i 1] T ;

[0029] Main cutting edge upper boundary point m 1 The coordinates in the workpiece coordinate system are:

[0030]

[0031] Main cutting edge lower boundary point m 0 The coordinates in the workpiece coordinate system are:

[0032]

[0033] The main cutting edge equation is:

[0034]

[0035] In the workpiece coordinate system, the lower boundary point b of the secondary cutting edge 0 The lower boundary point m of the main cutting edge 0 The coordinates of the secondary cutting edge upper boundary point b are the same. 1 The coordinates in the workpiece coordinate system are:

[0036]

[0037] The secondary cutting edge equation is:

[0038]

[0039] Among them, m 1 b is the intersection point between the current tooth cutting edge and the upper surface of the workpiece, that is, the upper boundary point of the main cutting edge; b 1 b is the intersection of the current tooth cutting edge and the transition surface of the previous tooth, that is, the upper boundary point of the secondary cutting edge; b 0 is the lower boundary point of the secondary cutting edge, b 1 With b 0 The height is the same in the workpiece coordinate system, and this point is also the lower boundary point of the main cutting edge m 0 ;m 2 Select a point on the main cutting edge; b 2 Select a 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.

[0040] As a preferred method, during the milling process, the trajectory equation of any point on the main and auxiliary cutting edges is:

[0041] f(x(t),y(t),z(t))=0 0≤t≤t max ;

[0042] Among them, (x(t), y(t), z(t)) represents the position of the tool in the workpiece coordinate system at time t;

[0043] Combining the main and secondary cutting edge trajectory equations, the milling surface topography equation is obtained as follows:

[0044] G 1 (x(t 1 ),y(t 1 ),z min )=0 0≤t 1 ≤t max ;

[0045] Among them, x(t 1 ),y(t 1 ) indicates that at t 1 The x-axis and y-axis positions of the tool in the workpiece coordinate system at the moment, Z min Indicates the minimum z-axis position where the tool contacts the workpiece during machining.

[0046] As a preference, g -x g y g z g Fit the characteristic points to the reference coordinate system, and obtain the milling error trajectory and its surface equation under the action of cutter tooth error and milling vibration as follows:

[0047] f 1 (x i ,y j ,z ij )=0

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

[0049] 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.

[0050] 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:

[0051]

[0052] 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 face y g o g z g The normal vector, θ xyj is m j The tangent plane and 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 between the positive axis and the j For 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 direction 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 and x g og 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 to the reference plane at time t, and is the machining error in the z-axis direction. 0 is the distance between the reference plane and the xoy plane.

[0053] Preferably, in step S5, the influencing factors of the dynamic distribution of machining errors include process design posture, cutter tooth error, and milling vibration.

[0054] Compared with the prior art, the technical effects and advantages of the present invention are:

[0055] This method for identifying the distribution characteristics of geometric errors of machined surfaces of efficient face milling cutters is based on the dynamic monitoring and analysis of various influencing factors during the machining process. First, by constructing a dynamic distribution solution model for milling machining errors, the model can calculate in real time the machining errors caused by factors such as cutter tooth errors, machining process parameters, and milling vibrations. Secondly, the method uses time-frequency analysis technology to analyze the machining errors in the time domain and frequency domain to identify the dynamic characteristics of the errors. Finally, through experimental verification, the simulation solution results are compared with the actual measurement results to verify the accuracy and effectiveness of the model.

[0056] This method for identifying the distribution characteristics of geometric errors of machined surfaces by efficient face milling cutters can timely monitor the error changes during the machining process by real-time calculation and analysis of machining errors, thereby quickly adjusting machining parameters and improving machining accuracy and stability. Compared with traditional high-precision measurement equipment, this method reduces the reliance on expensive equipment and reduces machining costs, and is particularly suitable for large-scale production environments. Through dynamic monitoring and time-frequency analysis of machining errors, the real-time changes of errors during the machining process can be fully understood, providing a more accurate basis for the optimization of machining technology.

[0057] The method for identifying the distribution characteristics of geometric errors on the machined surface of the efficient face milling cutter also has the advantages of strong predictability and adaptability. By analyzing the dynamic distribution characteristics of the error, the development trend of the error can be predicted, providing a basis for preventing machining defects. At the same time, the method can adapt to different machining conditions, provide accurate solutions for error identification under different process schemes, and enhance the flexibility and reliability of the machining process. BRIEF DESCRIPTION OF THE DRAWINGS

[0058] 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; Figure 5 A diagram of a method for extracting feature points of a processed surface according to the present invention; Figure 6 A diagram of a method for constructing an actual reference plane according to 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; Fig. 9 is the spatial distribution diagram of the relative position deviation Δz of the present invention; Fig.10 This is a comparison diagram of the milling surface at different positions along the y-axis of the present invention; Fig.11 It is the spatial distribution diagram of the normal vector inclination angle deviation θxy of the present invention; Fig.12 It is the spatial distribution diagram of the normal vector direction angle deviation θxoz of the present invention; Fig.13 is the spatial distribution diagram of the curvature Δw of the present invention; Fig.14 It is the time domain and frequency domain distribution diagram of the relative position deviation Δz of the present invention; Fig.15 It is the time domain and frequency domain distribution diagram of the normal vector inclination deviation θxy of the present invention; Fig.16 It is the time domain and frequency domain distribution diagram of the normal vector direction angle deviation θxoz of the present invention; Fig.17 It is the time domain distribution diagram of the curvature Δw of the present invention; Fig.18 This is the frequency domain distribution diagram of the relative position deviation Δz of the present invention; Fig.19 It is the frequency domain distribution diagram of the normal vector inclination angle deviation θxy of the present invention; Fig. 20 It is the frequency domain distribution diagram of the normal vector direction angle deviation θxoz of the present invention; Fig.21 It is the frequency domain distribution diagram of the curvature Δw of the present invention; Fig. 22 This is a comparative analysis result diagram of the time-frequency characteristics of the milling machining error along the x-axis direction under the influence of the root mean square value factor of the present invention; Fig.23 This is a comparative analysis result diagram of the time-frequency characteristics of the milling machining error along the x-axis direction under the influence of the kurtosis factor of the present invention; Fig.24 This is a comparative analysis result diagram of the time-frequency characteristics of the milling processing error along the x-axis direction under the influence of the main frequency factor of the present invention; Fig.25 This is a milling surface topography diagram of the present invention; Fig.26 This is the time domain distribution diagram of the relative position deviation Δz of Scheme 1 of the present invention; Fig. 27 This is the time domain distribution diagram of the normal vector inclination angle deviation θxy of Scheme 1 of the present invention; Fig.28 It is the time domain distribution diagram of the normal vector direction angle deviation θxoz of Scheme 1 of the present invention; Fig.29 This is a time domain distribution comparison diagram of the curvature Δw of Scheme 1 of the present invention; Fig.30 This is the time domain distribution diagram of the relative position deviation Δz of Scheme 1 of the present invention; Fig.31 This is the frequency domain distribution diagram of the normal vector inclination angle deviation θxy of Scheme 1 of the present invention; Fig.32 This is the frequency domain distribution diagram of the normal vector direction angle deviation θxoz of Scheme 1 of the present invention; Fig.33 This is a time domain distribution comparison diagram of the curvature Δw of Scheme 1 of the present invention; Fig.34 A diagram of a method for identifying dynamic distribution characteristics of machining errors of a high-efficiency face milling cutter according to the present invention; Fig.35 This is a comparison diagram of the spatial distribution of the relative position deviation Δz of Scheme 1 of the present invention; Fig.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; Fig.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; Fig.38 This is a comparison diagram of the spatial distribution of curvature Δw of Scheme 1 of the present invention; Fig.39 This is a time domain distribution comparison diagram of the relative position deviation Δz of Scheme 1 of the present invention; Fig.40 This is a time domain distribution comparison diagram of the normal vector inclination angle deviation θxy of Scheme 1 of the present invention; Fig.41 This is a time domain distribution comparison diagram of the normal vector direction angle deviation θxoz of Scheme 1 of the present invention; Fig.42 This is a time domain distribution comparison diagram of the curvature Δw of Scheme 1 of the present invention; Fig.43 This is a time-frequency characteristic parameter comparison diagram of the relative position deviation Δz of solution 1 of the present invention; Fig.44 This is a time-frequency characteristic parameter comparison diagram of the normal vector inclination deviation θxy of Scheme 1 of the present invention; Fig.45 This is a time-frequency characteristic parameter comparison diagram of the normal vector direction angle deviation θxoz of Scheme 1 of the present invention; Fig.46 This is a comparison diagram of the time-frequency characteristic parameters of the curvature Δw of solution 1 of the present invention; Fig.47 This is a comparison diagram of the spatial distribution of the relative position deviation Δz of Scheme 2 of the present invention; Fig.48 This is a comparison diagram of the spatial distribution of the normal vector inclination angle deviation θxy of Scheme 2 of the present invention; Fig.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; Fig.50 This is a comparison diagram of the spatial distribution of curvature Δw of Scheme 2 of the present invention; Fig.51 This is a time domain distribution comparison diagram of the relative position deviation Δz of Scheme 2 of the present invention; Fig.52This is a time domain distribution comparison diagram of the normal vector inclination angle deviation θxy of Scheme 2 of the present invention; Fig.53 This is a time domain distribution comparison diagram of the normal vector direction angle deviation θxoz of Scheme 2 of the present invention; Fig.54 This is a time domain distribution comparison diagram of the curvature Δw of Scheme 2 of the present invention; Fig.55 This is a time-frequency characteristic parameter comparison diagram of the relative position deviation Δz of Scheme 2 of the present invention; Fig.56 This is a time-frequency characteristic parameter comparison diagram of the normal vector inclination deviation θxy of Scheme 2 of the present invention; Fig.57 This is a time-frequency characteristic parameter comparison diagram of the normal vector direction angle deviation θxoz of Scheme 2 of the present invention; Fig.58 This is a comparison diagram of the time-frequency characteristic parameters of the curvature Δw of solution 2 of the present invention; Fig.59 The present invention is a flow chart of the method for identifying the geometric error distribution characteristics of a machined surface of a high-efficiency face milling cutter. DETAILED DESCRIPTION

[0059] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. 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 creative work are within the scope of protection of the present invention.

[0060] A method for identifying the geometric error distribution characteristics of the machined surface of a face milling cutter. The specific process is as follows: Fig.59 As shown in the figure, the specific contents of the method for identifying the geometric error distribution characteristics of the machined surface of the high-efficiency face milling cutter are as follows:

[0061] 1. Experimental plan and analysis of vibration effects

[0062] 1.1 Milling experiment: On the CNC milling machine XK7124 three-axis milling machining center, a face milling cutter was used to perform a vibration experiment on cutting 45 steel in a down-milling feed mode. The milling cutter was the M4003-050-B22-04-6.5 face milling cutter produced by Walter Company, the blade was SDMT1204AZN-D57WKP35G, the blade coating material was TiCN, the cutting edge diameter was 50mm, the number of teeth was 4, the functional length was 40mm, the blade length was 6.5mm, the main deflection angle was 45°, f was the feed per revolution, and the tooth when i was equal to 1 was the tooth that the face milling cutter first cut into the workpiece. The milling parameters and tooth errors are shown in Table 1.

[0063] Table 1 Milling experimental parameters

[0064]

[0065] In Table 1, n is the spindle speed, vf is the feed speed, a p is the nominal cutting depth, ae 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.

[0066] 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 was analyzed and processed to obtain the milling experiment vibration acceleration signal, vibration displacement and cutting force, as shown in Figure 1 As shown. Figure 1 ,The vibration acceleration, vibration displacement and cutting force of the milling experiment were analyzed, ,and the milling vibration and dynamic cutting force mutation moments during the ,feature milling cutter feed process were obtained, as shown in Table 2.

[0067] Table 2 Milling vibration characteristic time

[0068] Mutation Moment <![CDATA[t 1 (s)]]> <![CDATA[t 2 (s)]]> <![CDATA[t 3 (s)]]> <![CDATA[t 4 (s)]]> <![CDATA[t 5 (s)]]> <![CDATA[t 6 (s)]]> Experiment 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

[0069] 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.

[0070] Table 3 Milling period and cutting cycle

[0071]

[0072]

[0073] Depend on Figure 1 As shown in Table 3, the experimental results are tested and analyzed to obtain the machining errors of the positions at different time periods.

[0074] 1.2 Analysis of time-frequency characteristics of milling vibration

[0075] 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.

[0076] Table 4 Time-frequency characteristic parameters of milling vibration in Experiment 1

[0077]

[0078] From Table 4, the root mean square values ​​of milling vibration in the three directions all show the characteristics of being small in the period close to cutting in and cutting out, and large in the middle period. The kurtosis in the x and y directions shows the opposite characteristics, and in the z direction, it shows the characteristics of oscillating and rising from the period close to cutting in to the period close to cutting out. The main frequencies of vibration in the three directions show different change characteristics. Among them, the main frequencies of vibration along the positive direction of the x-axis and the positive direction of the z-axis are relatively high at the beginning, and the main frequencies of vibration along the negative direction of the y-axis are relatively stable.

[0079] 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 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 the cutter teeth cutting into the workpiece each time is concentrated in the negative direction of the y-axis where the surface to be processed is located, and the vibration is significantly greater than 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-in period, 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.

[0080] The root mean square value and kurtosis in the time domain signal of milling vibration acceleration and the main 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 change. Therefore, the above characteristic parameters are used to analyze the time-frequency characteristics of milling vibration.

[0081] 2. Construction of dynamic distribution calculation model for milling errors of efficient face milling cutters

[0082] 2.1 Calculation of the instantaneous cutting posture of the face milling cutter and its teeth

[0083] 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 action of tooth error and milling vibration is as follows: Figure 2 shown.

[0084] 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 -xi y i z i is the tooth coordinate system. n is the spindle speed, v is 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 turning 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 cutting process of the milling cutter, 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. Δr i is the i-th 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 The x axis and the face milling cutter structure coordinate system d The clockwise angle of the axis.

[0085] θ 1 (t) is the distance between the non-vibration milling cutter coordinate system and the vibration milling cutter coordinate system at x c -oz c The angle of the plane projection, θ 2 (t) is the distance between the non-vibration milling cutter coordinate system and the vibration milling cutter coordinate system at y c -oz c The angle of the plane projection.

[0086] Depend on Figure 2 , the conversion equation of any point of adjacent teeth of the milling cutter is:

[0087] [x i+1 y i+1 z i+1 1] T =R 1 [x i y i z i 1] T (1)

[0088] The trajectory equations of any point on the cutting edge of the i-th and i+1-th teeth of the milling cutter are:

[0089] [xyz 1] T =T 3 T 2 R 3 R 2T 1 R 4 [x i y i z i 1] T (2)

[0090] [xyz 1] T =T 3 T 2 R 3 R 2 T 1 R 1 [x i y i z i 1] T (3)

[0091] Among them, (x i ,y i ,z i ) is the coordinate of any point on the cutting edge in the tooth coordinate system, T 1 ,T 2 ,T 3 is the translation matrix, R 1 ,R 2 ,R 3 ,R 4 is the rotation matrix, as shown in equations (4) to (7):

[0092]

[0093] In formula (5), the instantaneous attitude angle θ(t) generated by the vibration of the milling cutter during cutting is c -oz c Projection of the surface and y c -oz c The projections of the surfaces are θ 1 (t) and θ 2 (t), the solution is as follows:

[0094]

[0095] Among them, the milling cutter is affected by vibration during cutting, and the process of machining transition surface formation, such as Figure 3 As shown;

[0096] Figure 3 Medium, m 1 b is the intersection point between the current tooth cutting edge and the upper surface of the workpiece, that is, the upper boundary point of the main cutting edge; b 1 b is the intersection of the current tooth cutting edge and the transition surface of the previous tooth, that is, the upper boundary point of the secondary cutting edge; b 0 is the lower boundary point of the secondary cutting edge, b1 With b 0 The height is the same in the workpiece coordinate system, and this point is also the lower boundary point of the main cutting edge m 0 ;m 2 Select a point on the main cutting edge; b 2 Select a point on the secondary cutting edge.

[0097] The equation in the workpiece coordinate system of the main cutting edge is:

[0098] l i (x(t),y(t),z(t))=T 3 ·R 4 ·T 2 ·R 3 ·R 2 ·T 1 ·R 1 ·[x i y i z i 1] T (9)

[0099] Main cutting edge upper boundary point m 1 The coordinates in the workpiece coordinate system are:

[0100]

[0101] Main cutting edge lower boundary point m 0 The coordinates in the workpiece coordinate system are:

[0102]

[0103] From equations (12) and (13), the main cutting edge equation can be obtained as follows:

[0104]

[0105] Among them, Z H is the upper boundary point, m 1 At the height of the z-axis, Z bo is the lower boundary point m 0 The height on the z-axis.

[0106] In the workpiece coordinate system, the lower boundary point b of the secondary cutting edge 0 The lower boundary point m of the main cutting edge 0 The coordinates of the secondary cutting edge upper boundary point b are the same. 1 The coordinates in the workpiece coordinate system are:

[0107]

[0108] From equations (14) and (15), the secondary cutting edge equation can be obtained as follows:

[0109]

[0110] Among them, G i-1 is the transition surface equation for the i-1th tooth;

[0111] 2.2 Constructing milling surface topography and identifying reference planes

[0112] 1.2.1 Milling surface topography construction method

[0113] From formula (1) to formula (14), we can get the trajectory equation of any point of the main and auxiliary cutting edges:

[0114] f(x(t), y(t), z(t))=0 0≤t≤t max (15)

[0115] Combining the main and secondary cutting edge trajectory equations, the milling surface topography equation is obtained:

[0116] G 1 (x(t 1 ), y(t 1 ), z min )=0 0≤t 1 ≤t max (16)

[0117] in,

[0118] z min ={z(0),z(1)....., z(t 1 )} (17)

[0119] Among them, x(t 1 ),y(t 1 ) indicates that at t 1 At the moment, the x-axis and y-axis positions of the tool in the workpiece coordinate system, Z min Indicates that during the processing, (x(t 1 ),y(t 1 )) position, the minimum z-axis position where the tool contacts the workpiece.

[0120] 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. 1 , points on the milling surface topography are extracted along the x-axis to obtain the feature points of the milling surface, such as Figure 5 shown.

[0121] Figure 5 In, o g -x g y g zg 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.

[0122]

[0123] 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.

[0124] 2.3 Identification of machining reference plane

[0125] 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, It is the mth actual detection line segment (m=1, 2, ..., 5) in the detection area, which is equidistantly distributed along the y direction.

[0126] Vibration displacement is the z-direction vibration displacement distribution caused by the machining error of the mth actual detection line segment affecting the ijth detection area, z 1 is the actual detection line segment The lowest point of the machining error distribution, Δz is the distance from the peak point of the machining error distribution to z 1 The distance, Δz max is the maximum value of Δz; Δz' max is the maximum value of Δz'.

[0127]

[0128] z g =z 1 -z gmin (20)

[0129] Δz′=Δz+z gmin (twenty one)

[0130] In the formula, z g is the reference of the z-axis vibration displacement distribution, gmin The z-axis vibration displacement distribution from the lowest point to z g Δz' is the distance from the peak point of machining error distribution to z g distance;

[0131] Depend on Figure 6And equations (1) to (21) yield that for the actual detection line segment 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 as shown in Table 5.

[0132] Table 5 Comparison error between theoretical machined surface and actual machined surface data

[0133]

[0134] Depend on Figure 7 And Table 5, the actual detection line segment 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% of the actual machined surface data, which preliminarily verifies the effectiveness of the method.

[0135] 2.4 Processing error calculation

[0136] 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.

[0137] Figure 8 Medium, m j ' is m j On the reference plane x g o g y g The projection point, z 0 is the distance between the reference plane and the xoy plane, Δz j are point m j The position error is N, N is the unit normal vector of the reference plane, 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 face y g o g z g The normal vector, θ xyj is m j The tangent plane and 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 xg The angle between the positive axis and the j For point m j The contour curve is projected to x g o g z g The radius of curvature of the surface.

[0138] 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:

[0139]

[0140] In the formula, z j (t) is the coordinate value along the z-axis direction 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.

[0141] In the formula, 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. xoz (t) is the time at which G(x,y,z)=0 at x g o g z g The projection of the surface, θ xyj (t) is the time at which m j The tangent plane and 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.

[0142] 3. Identification of factors affecting dynamic distribution of milling errors

[0143] 3.1 Time-frequency characteristics of milling errors under different factors

[0144] By using equations (1) to (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 distribution of milling surface error is as follows: Figures 9 to 13 The comparative analysis results of the time-frequency characteristics of milling machining 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 21 As shown, it is the time domain distribution diagram of machining error under the action of various factors;

[0145] Depend on Figures 9 to 21 , only the milling surface under the milling cutter process design posture is uniformly distributed, the milling surface under the influence of cutter tooth error presents 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.

[0146] 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 influence of each factor on the dynamic distribution of milling error can be further identified.

[0147] 3.2 Identification of influencing factors of dynamic distribution of machining errors

[0148] The comparative analysis results of the time-frequency characteristics of milling machining errors along the x-axis direction under the influence of various factors are as follows: Figure 22 to Figure 24 As shown, Fig.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, the kurtosis, and the normalized value of the main frequency. Fig.24 At different positions along the x-axis direction, 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.

[0149] The time-frequency characteristic parameters of milling machining error under the combined effects of milling vibration and multiple factors show different changing 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 the 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.

[0150] 3.3 Relative correlation analysis of dynamic distribution of machining errors

[0151] In order to quantitatively identify the influence of various factors on the dynamic distribution of milling processing errors, the improved grey relative correlation analysis method is used to solve the relative correlation between process design posture, cutter tooth error, milling processing error under milling vibration and milling processing error under the comprehensive effect of multiple factors, as shown in Table 6.

[0152] Table 6 Identification results of factors affecting dynamic distribution of milling errors

[0153]

[0154]

[0155] 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.

[0156] 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 the milling machining error.

[0157] The above analysis results show that, constrained by the initial process design posture of the milling cutter, the overall level of milling machining error remains similar to the process design machining surface, but the stability and consistency of its dynamic distribution cannot be guaranteed. The cutting parameters not only constrain the distribution of milling machining errors by matching the design posture of the milling cutter, but also cause changes in the dynamic distribution of milling machining errors through tooth errors and milling vibration excitation.

[0158] 4. Identification of dynamic distribution response characteristics of milling machining errors

[0159] 4.1 Comparison of dynamic distribution characteristics of milling errors of different process schemes

[0160] According to equations (1) to (23) and the parameters of scheme 2 in Table 1, the corresponding machined surface morphology is obtained, as Fig.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 Figure 26 to Figure 33 shown; Figure 26 to Figure 29 and Figure 30 to Figure 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.

[0161] The calculation results of the dynamic distribution of milling machining error along the x-axis direction under the two experimental schemes are compared, as shown in Table 7.

[0162] Table 7 Variation range of time-frequency characteristic parameters of machining errors in two experimental schemes

[0163]

[0164] At the same time, it is found that, except for the root mean square value of curvature, the root mean square values ​​of other indicators of Scheme 1 are all smaller than those of Scheme 2; except for the kurtosis, the kurtosis of other indicators of Scheme 1 are all smaller than those of Scheme 2, and there is little difference in the change of main frequency between Scheme 1 and Scheme 2, indicating that the change intensity and impact degree of milling error of Scheme 1 are lower than those of Scheme 2, and its dynamic distribution of machining error is better than that of Scheme 1. The solution results of the characteristic parameters of milling error in time domain and frequency domain can be used to evaluate high-efficiency milling process schemes.

[0165] 4.2 Comparison of identification results of influencing factors of dynamic distribution of milling machining error for different process schemes The relative correlation identification results of influencing factors of dynamic distribution of milling machining error along the x-axis direction of the two experimental schemes are compared, as shown in Table 8.

[0166] Table 8 Correlation of factors affecting milling errors of two experimental schemes

[0167]

[0168]

[0169] From Table 8, compared with Scheme 2, the milling cutter design posture in Scheme 1 has a slightly stronger influence on the normal vector direction angle deviation and curvature change, and has no significant change on the normal vector inclination angle deviation and relative position deviation change. This result shows that the adoption of Scheme 1 can enhance the constraint effect of the milling cutter design posture on the milling surface to a certain extent, thereby increasing the approximation degree between the milling surface and the plane.

[0170] Compared with Scheme 2, the influence of the cutter tooth error on the normal vector inclination angle deviation, normal vector direction angle deviation and curvature change in Scheme 1 is enhanced, and the influence on the relative position deviation is weakened, while the milling vibration has an enhanced influence on the relative position deviation and the normal vector direction angle deviation. This result shows that the milling cutter speed and feed per tooth under the constraints of the milling cutter design posture cause the change of the dynamic distribution of the milling machining error through the cutter tooth error and milling vibration excitation.

[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 efficient face milling cutters

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

[0174] Fig.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 of milling vibration along different directions, D is the milling cutter posture angle under milling vibration, M is the set of processing error index distribution curves, M a is the machining error index distribution curve under the milling process scheme, M a0 is the distribution curve of machining error index determined by process design posture, γ(M a , M a0 ) is M a0 With M a0 The correlation degree, [γ 0 ] 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 conditions, γ(M a , M a01 ) is M a With M a01 )’s correlation, [γ 1 ] is the γ(M a ,M a01 ) is the minimum value of .

[0175] This method uses the changing characteristics of the relationship between the instantaneous cutting behavior of adjacent teeth under the action of tooth error and milling vibration to reveal the dynamic formation process of the milling surface; uses 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 judges the milling process plan accordingly.

[0176] 5.2 Comparison between dynamic distribution of milling machining error and experimental results: Based on the parameters of Scheme 1 and Scheme 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. Compared with the experimental results, we can get 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 machining error solution model and the dynamic distribution characteristic identification method, the similarity between the simulation solution results and the experimental solution results in machining error distribution is quantitatively characterized. To this end, the results of the relative error 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 results of the relative errors of the spatial distribution of machining errors between the simulation solution results and the experimental solution results both meet more than 80% and are within (-10%, 10%). Along the x-axis direction, corresponding to the detection position, the results of the relative errors of the time domain and time-frequency distribution of machining errors between the simulation solution results and the experimental solution results both meet more than 80% and are 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 studies on the milling errors of high-efficiency face milling cutters focus on the overall level of the geometric parameters of the machined surface and the degree to which they deviate from the design indicators, and obtain the overall level of the geometric parameters of the machined surface through experiments; existing models ignore the influence of tooth errors and milling vibrations 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] The present invention constructs a dynamic distribution solution model for the milling processing error of an efficient face milling cutter based on the milling processing error of an efficient face milling cutter, and proposes a method for solving the position, size and shape level of the processing error; reveals the influencing factors of the dynamic distribution of the milling processing error, identifies the influencing factors and quantifies the influence of the influencing factors on the dynamic distribution of the milling processing error; studies the response characteristics of the dynamic distribution of the high-efficiency milling processing error, and proposes a method for identifying the dynamic distribution characteristics of the milling processing error. The theoretical model solution is verified by the experimental results solution, and the deviation of the position, size and shape level indicators of the processing error is within 20%.

Claims

1. A method for identifying the geometric error distribution characteristics of a machined surface of an efficient face milling cutter, characterized in that: The following steps are involved: S1. Milling experiment and analysis of milling vibration time-frequency characteristics: On the CNC milling machine XK7124 three-axis milling machining center, a face milling cutter was used to perform a vibration experiment on cutting 45 steel in a down-milling feed mode. The root mean square value, kurtosis and main frequency characteristic parameters were used to analyze the time-frequency characteristics of milling vibration, and the milling vibration characteristics at different times were compared to identify the influence of milling vibration on machining errors. S2. Calculation of instantaneous cutting posture of face milling cutter and its teeth: Establish the instantaneous cutting posture model of face milling cutter and its teeth, and calculate the instantaneous cutting trajectory of teeth through the designed posture of milling cutter, tooth error and milling vibration factors; S3, constructing the milling surface morphology and identifying the reference plane: using the calculated cutting trajectory of the cutter teeth, construct the milling surface morphology 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 dynamic distribution of milling machining 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 influence of each factor on the machining error; S6. Identification of dynamic distribution response characteristics of milling machining 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 energy-efficient milling machining errors and the analysis results of response characteristics, an efficient identification method of dynamic distribution characteristics of machining errors is proposed, and 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: 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.

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: T1, T2, T3, R1, R2, R3, R4 are specifically shown in the following formula: Where n is the spindle speed, v is 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 turning radius of any cutter 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 in the negative x-axis direction, y-axis direction and z-axis direction 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 cutter tooth coordinate system, θ1(t) is the difference between the non-vibration milling cutter coordinate system and the vibrating milling cutter coordinate system at x c -oz c The angle between the plane projection and the vibration milling cutter coordinate system in y c -oz c Angle of projection on the plane, Δr i is the i-th 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 The x axis and the face milling cutter structure coordinate system d The clockwise angle of the axis.

5. The method for identifying geometric error distribution characteristics of a machined surface of a high-efficiency face milling cutter according to claim 4, characterized in that: The instantaneous attitude angle θ(t) generated by the vibration during the milling cutter cutting 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:

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: The equation in the workpiece coordinate system of the main cutting edge 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, and the coordinates of the upper boundary point b1 of the secondary cutting edge in the workpiece coordinate system are: The secondary cutting edge equation 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.

7. The method for identifying geometric error distribution characteristics of a machined surface of a high-efficiency face milling cutter according to claim 6, characterized in that: During the milling process, the trajectory equation of any point on the main and auxiliary 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.

8. The method for identifying geometric error distribution characteristics of a machined surface of a high-efficiency face milling cutter according to claim 7, characterized in that: with o g -x g y g z g Fit the characteristic points to the reference coordinate system, and 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.

9. 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: 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 face y g o g z g The normal vector, θ xyj is m j The tangent plane and 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 For 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 direction 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 and 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.

10. 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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