Method for recognizing instantaneous cutting pose of high-feed milling cutter under vibration action

Abstract

The application discloses a high-feed milling cutter instantaneous cutting position recognition method under vibration, and belongs to the technical field of milling cutter machining. In order to solve the deviation problem of the existing milling cutter instantaneous cutting position solution under vibration, the application constructs a milling cutter coordinate system and a cutter tooth coordinate system, sets a cutter tooth origin coordinate equation in the milling cutter coordinate system and a milling cutter instantaneous cutting edge equation; a milling cutter and cutter tooth instantaneous cutting position solution model under vibration is constructed; surface appearance pictures of a machined workpiece are collected, and a distribution equation of residual feature points of a machining transition surface is constructed; a grid optimization method is used to solve a milling cutter and cutter tooth instantaneous cutting position function; a milling cutter instantaneous cutting position compensation function is constructed; the milling cutter and cutter tooth instantaneous cutting position solution model under vibration is corrected by using the milling cutter instantaneous cutting position compensation function, and the high-feed milling cutter instantaneous cutting position recognition under vibration is completed. The application is used for revealing a milling machining surface formation process and improving the accuracy of a milling machining surface appearance simulation result.

Description

Technical Field

[0001] This invention belongs to the field of milling cutter technology, specifically relating to a method for instantaneous cutting posture recognition of high-feed milling cutters under vibration. Background Technology

[0002] The instantaneous cutting posture of the milling cutter and its teeth directly reflects the variability of its instantaneous cutting behavior and determines the formation process of the milled surface. Existing model methods neglect the influence of milling vibration on the instantaneous cutting posture of the milling cutter, and cannot accurately reveal the instantaneous cutting behavior of the milling cutter and its teeth. Therefore, when calculating the instantaneous cutting posture of the milling cutter, the milling vibration displacement signal measured in the milling experiment is directly introduced. However, since the milling vibration displacement signal used mainly comes from the workpiece near the cutting deformation zone, the end of the machine tool spindle, and the tool holder, it has a large error compared with the actual position offset of the milling cutter and its teeth cutting edge under rotation and feed conditions. The accuracy of the instantaneous cutting posture calculation of the milling cutter and its teeth needs to be improved. Summary of the Invention

[0003] The problem this invention aims to solve is the deviation in the calculation of the instantaneous cutting posture of a milling cutter under vibration. It proposes a method for recognizing the instantaneous cutting posture of a high-feed milling cutter under vibration.

[0004] To achieve the above objectives, the present invention provides the following technical solution:

[0005] A method for instantaneous cutting posture recognition of high-feed milling cutters under vibration includes the following steps:

[0006] S1. Construct the milling cutter coordinate system and the tooth coordinate system, and set the coordinate equation of the origin of the tooth in the milling cutter coordinate system and the instantaneous cutting edge equation of the milling cutter.

[0007] S2. Construct a calculation model of the instantaneous cutting posture of the milling cutter and teeth under vibration;

[0008] S3. Collect surface morphology images of the milled workpiece and construct the distribution equation of residual feature points on the machining transition surface;

[0009] S4. Based on the distribution equation of residual feature points on the machining transition surface constructed in step S3, the instantaneous cutting pose function of the milling cutter and teeth is solved by the mesh optimization method;

[0010] S5. Construct the instantaneous cutting pose compensation function of the milling cutter based on the instantaneous cutting pose function of the milling cutter and the cutting teeth obtained in step S4;

[0011] S6. Using the instantaneous cutting posture compensation function of the milling cutter obtained in step S5, the instantaneous cutting posture solution model of the milling cutter and the cutting teeth under vibration constructed in step S2 is corrected to complete the instantaneous cutting posture recognition of the high feed milling cutter under vibration.

[0012] Furthermore, the specific implementation method of step S2 includes the following steps:

[0013] S2.1. Constructing the milling cutter cutting coordinate system under vibration-free conditions. v -x v y v z v Milling cutter cutting coordinate system under vibration v ′-x v 'y v ′z v Workpiece coordinate system o-xyz;

[0014] S2.2. Based on the dynamic cutting process of the milling cutter under vibration, construct the milling cutter coordinate system transformation matrix A0, the tooth coordinate system transformation matrix B0, the transformation matrix A1 between the milling cutter coordinate system and the milling cutter cutting coordinate system under vibration, the transformation matrix B1 between the milling cutter cutting coordinate system under vibration and the milling cutter cutting coordinate system without vibration, and the milling cutter attitude angle in x... v o v z v The planar projection transformation matrix A2 and the milling cutter posture angle in y v o v z v Planar projection transformation matrix A3;

[0015]

[0016] in, For a cutting time t, the x0 axis of the milling cutter coordinate system and the x-axis of the tooth coordinate system are... i Angle between axes;

[0017]

[0018] Where, ψ i (t) represents the coordinate system x0 of the milling cutter structure and the coordinate system x of the milling cutter cutting under vibration. v The included angle of the axis;

[0019]

[0020]

[0021] Among them, A x (t) represents the position of the milling cutter at x v Vibration displacement in the direction, A y (t) represents the position of the milling cutter at y v Vibration displacement in the direction, A z (t) represents the milling cutter at z v The vibration displacement in the x direction, δ1(t) is the milling cutter attitude angle δ(t) in the x direction. v o v zv The projection angle of the plane, δ2(t), is the milling cutter attitude angle δ(t) in y v o v z v The projection angle of the plane;

[0022] S2.3. Calculate the cutter attitude angle δ(t) and cutter direction angle δ'(t) to represent the cutter deflection angle caused by vibration. The calculation expression is:

[0023]

[0024]

[0025]

[0026]

[0027] S2.4. Construct the transformation matrix B2 between the milling cutter cutting coordinate system and the workpiece coordinate system under vibration-free conditions. The expression is:

[0028]

[0029] The expression for the trajectory of the origin of the cutting coordinate system in the workpiece coordinate system is as follows:

[0030]

[0031] Then, using the matrix transformation relationship between the graphical coordinate systems, the trajectory equation of any point on the cutter tooth is solved, and the expression is:

[0032] [xyz 1] T =B2B1A3A2A1A0B0[x i y i z i 1] T (16)

[0033] Obtain the origin o of the knife tooth coordinate system i The trajectory in the workpiece coordinate system is:

[0034] o i (x(t),y(t),z(t))=Φ i ·[0 0 0 1] T (17)

[0035] Where, Φ i Let Φ be the transformation matrix. i =B2B1A3A2A1A0B0;

[0036] S2.5. Calculate the effective cutting time of the cutter teeth, the contact angle of the cutter teeth when they cut out of the workpiece, and complete the construction of the instantaneous cutting posture calculation model of the milling cutter and cutter teeth under vibration; using the trajectory equation of the cutting edge of the (i+1)th cutter tooth, the workpiece side elevation equation, and the machining transition surface equation formed by the cutting edge of the (i+1)th cutter tooth and the machining transition surface equation formed by the ith cutter tooth, solve for the entry and exit cutting times of the (i+1)th cutter tooth, expressed as:

[0037]

[0038]

[0039] The cutting time t is any position of the (i+1)th cutting edge during the cutting time period. i+1 for:

[0040]

[0041] Among them, H i+1 (x(t s i+1 ), y(t) s i+1 ), z(t s i+1 H is the cutting edge equation when the (i+1)th cutting edge of the cutting tooth enters the workpiece. i+1 (x(t e i+1 )), y(t e i+1 ), z(t e i+1 )) is the cutting edge equation when the (i+1)th cutting edge cuts the workpiece, G i (x(t e i ), y(t) e i ), z(t e i Let t be the equation of the transition surface formed when the i-th cutting edge of the cutting tooth cuts out in the workpiece coordinate system. s i +1 For the (i+1)th cutting tooth engagement time, t e i+1 This refers to the moment when the (i+1)th cutting tooth makes its cut.

[0042] The expression for the brief time interval Δt corresponding to the i+1th cutter not yet cutting into the workpiece when the i-th cutter tooth has completely cut out of the workpiece is:

[0043] Δt=t e i+1 -t s i(twenty one)

[0044] The expression for the contact angle when the i-th cutting tooth cuts out of the workpiece is:

[0045]

[0046] Furthermore, the specific implementation method of step S3 includes the following steps:

[0047] S3.1. Acquiring surface morphology images of the milled workpiece: Measurements were performed using a Taylor Hobson CCI·MP non-contact interferometer. White light photography was conducted for different cutting strokes, and a 256×256 pixel array was used for surface morphology imaging to obtain surface morphology images of the milled workpiece.

[0048] S3.2. Perform feature point recognition on the surface morphology image of the milled workpiece obtained in step S3.1:

[0049] First, select A1-A along the positive y-axis of the workpiece coordinate system on the machined surface morphology. p There are a total of p sections, where A1 and A p These are two end faces, representing the results of white light interferometer testing of the milled surface morphology. The distance between any two cross-sections is Δy. jm The expression for the coordinates of the m-th section along the y-axis starting from the origin of the workpiece coordinate system is:

[0050] y m =y0+(m-1)Δy jm (twenty three)

[0051] Δy jm The distance is less than the distance of the smallest detection unit of the white light interferometer, where m is any one of p;

[0052] Select A1-A along the positive x-axis starting from the origin. p Feature points on the cross section, q1-q are selected on each cross section. k There are k feature points in total, where q1, q2, q3, q4, q5, q k and q min The two highest points and the three lowest points on the cross-section are given, with x1, x2, x3, x4, x5, x6, x7, x8, x9, x1, x10, x11, x12, x13, x14, x15, x16, x17, x18, x19, x10, x10, x11, x12, x13 ... k x m The remaining feature points are evenly distributed among the three points, with a spacing of Δx between them. jm Δx jm The selection method is as follows:

[0053] q k and q min q minAll points between q1 and q2 are divided into two intervals, with interval lengths x and x respectively. k -x m and x m –x1, the lengths of the two intervals x k -x m and x m The expression for the least common multiple Δx of –x1 is:

[0054] [Δx]=[x k -x m x m –x1] (24)

[0055] Then we get Δx jm The expression is:

[0056]

[0057] Where M is the largest positive integer not exceeding [Δx];

[0058] Then, starting from the origin of the workpiece coordinate system, the expression for the coordinates of the s-th feature point along the positive x-axis is:

[0059] x s =x1+(s-1)Δx (26)

[0060] s can be any one of k;

[0061] Next, based on the feature point selection method described above, the highest residual feature point, the lowest residual feature point, and the intermediate transition inflection point on the milled surface morphology are selected along the depth of cut. The selected feature points are arranged along the cutting tooth movement trajectory. Using Matlab to fit the surface equation, the expression for the distribution equation P'(x,y) of the residual feature points on the machining transition surface is obtained as follows:

[0062] P'(x,y)=P 00 +P 10 x+P 01 y+P 20 x 2 +P 11 xy+P 02 y 2 +P 30 x 3 +P 21 x 2 y (27).

[0063] +P 12 xy 2 +P 03 y 3 +P 40 x 4 +P31 x 3 y+P 22 x 2 y 2

[0064] +P 13 xy 3 +P 04 y 4 +P 50 x 5 +P 41 x 4 y+P 32 x 3 y 2

[0065] +P 23 x 2 y 3 +P 14 xy 4 +P 05 y 5

[0066] Furthermore, the specific implementation method of step S4 includes the following steps:

[0067] S4.1. Set the expression for the change in the position X of the cutting edge as follows:

[0068] X={c x c y c z ,ω,γ} (28)

[0069] Among them, c x c y c z ω and γ represent the offsets of the origin of the cutter tooth coordinate system in the x, y, and z directions of the workpiece coordinate system, respectively; ω and γ represent the z-direction offsets of the cutter tooth coordinate system, respectively. i The workpiece coordinate system is offset from the z-axis, and the cutter tooth coordinate system is offset from the y-axis. i Offset from the y-axis of the workpiece coordinate system;

[0070] S4.2. Identify the instantaneous pose of the cutting teeth and the milling cutter in the milled surface morphology, divide the instantaneous offset mesh of the cutting teeth, set the size of the discrete mesh of the instantaneous pose of the cutting teeth to be smaller than the time interval when selecting the feature points of the cross section, take the maximum value of the vibration displacement as the upper boundary and the minimum value as the lower boundary, and calculate the number of meshes λ as shown in expressions (29)-(30):

[0071]

[0072] λ=max(λ1,λ2) (30)

[0073] Set the partition offset mesh size as shown in expression (31):

[0074]

[0075] The instantaneous offset of the instantaneous cutting posture of the cutting teeth is set as shown in expression (32):

[0076]

[0077] Different cutting edge pose sequences are formed by setting different displacement increments of the origin of the cutting tooth coordinate system, as well as the increments of the attitude angle and direction angle, as shown in expressions (33)-(37):

[0078] c x (t)={c x (t)(1),c x (t)(2),...,c x (t)(λ)} (33)

[0079] c y (t)={c y (t)(1),c y (t)(2),...,c y (t)(λ)} (34)

[0080] c z (t)={c z (t)(1),c z (t)(2),...,c z (t)(λ)} (35)

[0081] ω(t)={ω(t)(1),ω(t)(2),...,ω(t)(λ)} (36)

[0082] γ(t)={γ(t)(1),γ(t)(2),...,γ(t)(λ)} (37)

[0083] The arbitrary combination of variables in each sequence represents the cutting edge of the cutting tooth under different poses. The sequence of cutting edges composed of arbitrary pose parameters is shown in expression (38):

[0084] H(x,y,z)={H(1),H(2),...,H(λ 5 )} (38)

[0085] The cutting edge of the cutting tooth is set as a spatial curve, and its shape characteristics are characterized by curvature and deflection. During the effective cutting time of the cutting tooth, the cutting edge equation at any cutting position is shown in expression (39):

[0086] H=H(x(t),y(t),z(t)) (39)

[0087] The curvature deflection at a certain point on the cutting edge equation is calculated using expressions (40)-(42):

[0088]

[0089]

[0090]

[0091] Where ρ is the curvature at any point on the cutting edge; τ is the deflection at any point on the cutting edge; and g is the total curvature.

[0092]

[0093] S4.3. Identify the lowest point formed by the cutting edge in the fitted milled surface. Construct a quadratic surface using the neighboring points of the lowest point to calculate its curvature. Then, match this surface with points in the cutting edge equation that have the same curvature and whose Euclidean distance is less than a minimum threshold. For any lowest point p on the fitted machined transition surface... n A quadratic surface is constructed using its neighboring points, and the surface equation is shown in expression (43):

[0094] p n (U,V)=(U,V,S(U,V)) (43)

[0095] Among them, S(U,V)=a U 2 +bUV+c V 2 The S-axis is the direction of the surface normal vector where the lowest point of the fitted surface is located; U and V are orthogonal to each other and lie on the tangent plane of the lowest point;

[0096] If p n The nearest point p n 1 The coordinates in the local coordinate system (S-UV) are (U n 1 V n 1 ,S n 1 The linear equation system obtained from m neighboring points is shown in expression (44):

[0097]

[0098] S4.4. Solve the linear equation system (44) using the least squares method to obtain the surface equations p of the characteristic points and neighboring points. n(U,V), and then the Gaussian curvature and mean curvature of each point on the surface are obtained;

[0099] S4.5. Assume H1, H2, ... H n and P1, P2, ... P n Let n be the n feature segments around the lowest point of the fitting equation between the cutting edge of the cutting tooth and the surface, and each feature segment has m feature sets. The curvature and torsion feature sets of each feature segment on the cutting edge of the cutting tooth and the fitting surface are represented as follows: (i = 1, 2, ..., n; j = 1, 2, ..., m), the feature points on each feature segment are represented as: h1, h2, ..., h n Correspondingly, the feature set of the corresponding feature segment of the fitted surface is represented as: (i = 1, 2, ..., n; j = 1, 2, ..., m), the feature points on each feature set are represented as: p1, p2, ..., p n ;

[0100] The discrimination is based on the fact that the Euclidean distance between the corresponding feature points of each cutting edge and the fitted surface equation is less than the minimum tolerance range. The Euclidean distance between any two feature points and the minimum tolerance discrimination are shown in expression (45):

[0101]

[0102] Wherein, ρ(h) n ), ρ(p n ) and τ(h n ), τ(p n ) represent the curvature and torsion between any corresponding feature points on the cutting edge and the fitted surface, respectively, and η is the minimum tolerance of the Euclidean distance, which depends on the solution accuracy.

[0103] S4.6. Repeat steps S4.1-S4.5. When the curvature and deflection of the feature points on the corresponding feature segments on the cutting edge and the machining transition surface are matched and the Euclidean distance is within the minimum tolerance range, the tooth position and orientation variables during the entire effective cutting cycle can be calculated.

[0104] Furthermore, the specific implementation method of step S5 includes the following steps:

[0105] S5.1. Based on the structural relationship between the origin of the cutter tooth coordinate system and the origin of the milling cutter coordinate system, the instantaneous pose of the milling cutter and the instantaneous pose of the cutter tooth are as shown in expression (46):

[0106]

[0107] S5.2. By comparing the instantaneous pose parameters obtained through the solution with the pose parameters obtained using vibration displacement, the instantaneous pose deviation of the milling cutter in the current cutting cycle is obtained as shown in expression (47):

[0108]

[0109] Where Δx0(t) is the milling cutter feed direction deviation, Δy0(t) is the milling cutter width deviation, Δz0(t) is the milling cutter depth deviation, Δω0(t) is the milling cutter attitude angle deviation, and Δγ0(t) are the milling cutter direction angle deviations; A x (t)-δ'(t) are the pose parameters obtained through experiments, respectively; A'x0(t) is the instantaneous position of the milling cutter in the feed direction, A'y0(t) is the instantaneous position of the milling cutter in the width direction, A'y0(t) is the instantaneous position of the milling cutter in the depth direction, ω'0(t) is the milling cutter z-axis offset angle, and γ'0(t) is the milling cutter y-axis angular offset; t s i Let t be the time when the i-th cutting tooth enters the workpiece. e i+2 The time when the (i+2)th cutting tooth makes a cut;

[0110] The instantaneous pose compensation function over time is fitted using the instantaneous deviation curve of the origin of the milling cutter coordinate system, as shown in expression (48):

[0111]

[0112] in, The coefficients of the pose compensation function fitting formula are l = 0, 1, ..., 7, j = 0, 1, 2, 3, 4, and t is the effective time within the milling cutter cutting cycle.

[0113] Furthermore, the specific implementation method of step S6 includes the following steps:

[0114] S6.1. Based on the machining transition surface formed by the adjacent cutting edges of the cutting teeth, the cutting edge trajectory equation of the i-th cutting tooth is set in the workpiece coordinate system o-xyz as shown in expression (49):

[0115]

[0116] S6.2. The equation for the machining transition surface formed by the sweeping of the i-th cutting edge is shown in expression (50):

[0117]

[0118] The (i+1)th cutting edge sweeps to form a machining transition surface and intersects with the machining transition surface formed by the previous cutting edge, as shown in expression (51):

[0119]

[0120] The (i+2)th cutting edge sweeps to form a machining transition surface, and together with the previous cutting edge, forms the final milled surface as shown in expression (52):

[0121]

[0122] S6.3. Substitute the instantaneous cutting pose compensation function of the milling cutter into the pose transformation matrix to form a simulation model of the milling shape after pose compensation;

[0123] The transformation matrix of the milling cutter cutting coordinate system with the introduction of the pose compensation function is shown in expression (53):

[0124]

[0125]

[0126] in, These are the projection angles of the attitude angle offset in the xoz and yoz planes, respectively;

[0127] The transformation matrix of the milling cutter coordinate system under the direction angle offset is set as shown in expression (54):

[0128]

[0129] The pose-compensated transformation matrix is ​​constructed using the matrix after pose compensation and the solved matrix, as shown in expression (55):

[0130] [xyz 1] T =B2B1'A4A'3A2'A1A0B0[x i y i z i 1] T (55)

[0131] S6.4. The pose-compensated transformation matrix Φ' obtained in step S6.3 is... i =B2B1'A4A'3A2'A1A0B0 is re-introduced into the model of the cutting tooth forming the machining transition surface and simulated to obtain new simulation results, thus completing the instantaneous cutting posture recognition of the high feed milling cutter under vibration.

[0132] The beneficial effects of this invention are:

[0133] The present invention describes a method for identifying the instantaneous cutting posture of a high-feed milling cutter under vibration. This method identifies and calculates the instantaneous cutting posture of the milling cutter and its teeth under vibration. Through milling experiments, the surface morphology of the milled surface is obtained, and a method is constructed using the distribution equation of residual feature points on the transition surface. Based on the obtained surface morphology, the instantaneous cutting posture of the teeth is identified, and the cutting posture is calculated using a mesh optimization method. A milling cutter posture compensation function is constructed. A milling morphology simulation model is established, and a correction method for the milling cutter instantaneous cutting posture calculation model under vibration is proposed. The method is verified using simulation and experimental results of the milling surface morphology.

[0134] The present invention describes a method for identifying the instantaneous cutting posture of a high-feed milling cutter under vibration. During the efficient, intermittent cutting process of a high-feed milling cutter, the instantaneous contact relationship between the cutter teeth and the workpiece constantly changes due to the combined effects of various factors such as milling parameters, milling method, cutter tooth error, and milling vibration, resulting in uncertainty in the instantaneous cutting posture of the milling cutter. Based on the milled surface morphology, this invention utilizes a mesh optimization method to solve for the instantaneous cutting posture during the cutting process, thus solving the problem of inaccurate calculation and identification of the instantaneous cutting posture of the cutter teeth and the milling cutter. Furthermore, this invention establishes a compensation function for the instantaneous cutting posture of the milling cutter, which corrects and compensates for existing methods for calculating the instantaneous cutting posture, improving the accuracy of the calculation. This method can be used to reveal the formation process of the milled surface and improve the accuracy of simulation results for the milled surface morphology. Attached Figure Description

[0135] Figure 1 This is a flowchart of the instantaneous cutting posture recognition method for high-feed milling cutters under vibration as described in this invention;

[0136] Figure 2 This is a schematic diagram of the high feed milling cutter, its tooth structure, and its coordinate system as described in this invention;

[0137] Figure 3 This is a schematic diagram of the instantaneous position and coordinate system of the milling cutter and its teeth under vibration as described in this invention;

[0138] Figure 4 This is a schematic diagram of the cutting time period between adjacent cutting teeth as described in this invention;

[0139] Figure 5 This is a graph showing the vibration signal of the milling cutter during the cutting experiment described in this invention.

[0140] Figure 6 The graph shows the position and attitude offset curves caused by milling vibration in this invention, where (a) is the origin deviation of the coordinate system, (b) is the attitude angle offset, and (c) is the direction angle offset.

[0141] Figure 7This is a schematic diagram of the measurement site and workpiece sampling points of the white light interferometer of the present invention, wherein (a) is a picture of the milling morphology detection site, and (b) is a schematic diagram of the sampling of the detection points;

[0142] Figure 8 The image shows the surface topography detection results of the sampling points in this invention, where (a) is the first sampling point, (b) is the second sampling point, (c) is the third sampling point, (d) is the fourth sampling point, and (e) is the fifth sampling point.

[0143] Figure 9 This is a schematic diagram of the surface morphology feature recognition method of the present invention; Figure 10 This is a schematic diagram of the cross-sectional feature point recognition method of the present invention; Figure 11 This is a graph showing the fitting results of the milled surface in this invention;

[0144] Figure 12 This is a comparison curve of the fitting curves of the milled surface and the cross-section at the same position as the experimental results, where (a) is A. a -A a Section ', (b) is A m -A m Section ' at point (c) is A m -A m 'section at point;

[0145] Figure 13 This is a diagram illustrating the instantaneous pose recognition of the milling cutter and teeth based on the surface morphology of the machined surface, as described in this invention.

[0146] Figure 14 The diagram shows the experimental and computational comparison of the trajectory of the origin of the knife tooth coordinate system along the y-direction, as well as the deviation curve. (a) is a comparison diagram of vibration results, (b) is a comparison diagram of computational results, and (c) is a comparison diagram of deviation results.

[0147] Figure 15 The diagram shows the experimental and computational comparison of the trajectory of the origin of the knife tooth coordinate system along the z-direction, as well as the deviation curve. (a) is a comparison diagram of vibration results, (b) is a comparison diagram of computational results, and (c) is a comparison diagram of deviation results.

[0148] Figure 16 The diagram shows the experimental and calculated attitude angles of the knife tooth coordinate system of the present invention, as well as the deviation curves. (a) is a comparison diagram of vibration results, (b) is a comparison diagram of calculation results, and (c) is a comparison diagram of deviation results.

[0149] Figure 17 The diagram shows the comparison of experimental and calculated directions of the knife tooth coordinate system of the present invention, as well as the deviation curve. (a) is a comparison diagram of vibration results, (b) is a comparison diagram of calculated results, and (c) is a comparison diagram of deviation results.

[0150] Figure 18The milling cutter coordinate system position and attitude deviation curve for the 15th cycle of this invention is shown, where (a) is the x-direction deviation, (b) is the y-direction deviation, (c) is the z-direction deviation, (d) is the attitude angle offset, and (e) is the direction angle offset.

[0151] Figure 19 The curves showing the position and attitude deviations of the milling cutter coordinate system in the 30th cycle of this invention are shown, where (a) is the deviation in the x-direction, (b) is the deviation in the y-direction, (c) is the deviation in the z-direction, (d) is the attitude angle offset, and (e) is the direction angle offset.

[0152] Figure 20 The milling cutter coordinate system position and attitude deviation curve for the 45th cycle of this invention is shown, where (a) is the x-direction deviation, (b) is the y-direction deviation, (c) is the z-direction deviation, (d) is the attitude angle offset, and (e) is the direction angle offset.

[0153] Figure 21 The curves showing the position and attitude deviations of the milling cutter coordinate system in the 60th cycle of this invention are shown, where (a) is the deviation in the x-direction, (b) is the deviation in the y-direction, (c) is the deviation in the z-direction, (d) is the attitude angle offset, and (e) is the direction angle offset.

[0154] Figure 22 The milling cutter coordinate system position and attitude deviation curve for the 75th cycle of this invention is shown, where (a) is the x-direction deviation, (b) is the y-direction deviation, (c) is the z-direction deviation, (d) is the attitude angle offset, and (e) is the direction angle offset.

[0155] Figure 23 This is a schematic diagram of the instantaneous pose of adjacent cutting teeth and their machining transition surface according to the present invention;

[0156] Figure 24 The image shows the simulation results of the milling topography before cutting pose compensation according to the present invention, where (a) is the first sampling point, (b) is the second sampling point, (c) is the third sampling point, (d) is the fourth sampling point, and (e) is the fifth sampling point. Figure 25 The image shows the simulation results of the milling topography after cutting pose compensation according to the present invention, where (a) is the first sampling point, (b) is the second sampling point, (c) is the third sampling point, (d) is the fourth sampling point, and (e) is the fifth sampling point. Figure 26 The figures shown are simulation and experimental results of the shape before and after pose compensation of the present invention, where (a) is the experimental result figure, (b) is the simulation figure before pose compensation, and (c) is the simulation figure after pose compensation. Figure 27 The images show a comparison of the simulated and experimental cross-sections of the first sampling point before and after pose compensation in this invention, where (a) is the simulation image before compensation and (b) is the simulation image after compensation. Figure 28The image shows a comparison of the simulated and experimental cross-sections of the second sampling point before and after pose compensation, where (a) is the simulation image before compensation and (b) is the simulation image after compensation. Figure 29 The figures show a comparison of the simulated and experimental cross-sections of the third sampling point before and after pose compensation in this invention, where (a) is the simulation figure before compensation and (b) is the simulation figure after compensation. Figure 30 The image shows a comparison of the simulated and experimental cross-sections of the fourth sampling point before and after pose compensation, where (a) is the simulation image before compensation and (b) is the simulation image after compensation. Figure 31 The images show a comparison of the simulated and experimental cross-sections of the fifth sampling point before and after pose compensation, where (a) is the simulation image before compensation and (b) is the simulation image after compensation. Detailed Implementation

[0157] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. It should be understood that the specific embodiments described herein are only for explaining the invention and are not intended to limit the invention; that is, the described specific embodiments are merely a part of the embodiments of the invention, and not all of them. The components of the specific embodiments of the invention described and shown in the accompanying drawings can generally be arranged and designed in various different configurations, and the invention may also have other embodiments.

[0158] Therefore, the following detailed description of specific embodiments of the invention provided in the accompanying drawings is not intended to limit the scope of the claimed invention, but merely to illustrate selected specific embodiments of the invention. All other specific embodiments obtained by those skilled in the art based on these specific embodiments without inventive effort are within the scope of protection of this invention.

[0159] To further understand the invention's content, features, and effects, the following specific embodiments are provided, along with accompanying drawings. Figure 1 - Appendix Figure 31 Detailed explanation is as follows: Specific implementation method one:

[0161] A method for instantaneous cutting posture recognition of high-feed milling cutters under vibration includes the following steps:

[0162] S1. Construct the milling cutter coordinate system and the tooth coordinate system, and set the coordinate equation of the origin of the tooth in the milling cutter coordinate system and the instantaneous cutting edge equation of the milling cutter.

[0163] Furthermore, such as Figure 2As shown, the milling cutter coordinate system is set as o0-x0y0z0. The origin o0 of the milling cutter coordinate system is the intersection of the central axis of the milling cutter and the plane containing the lowest point of the cutter tooth. The projection point of the tip of the tooth with the largest radial error onto the lowest plane of the milling cutter is connected to the origin to form the x0 axis direction. The z0 axis direction is the direction of the central axis of the milling cutter. The y0 axis is determined according to the Cartesian coordinate system principle. i -x i y i z i Let z be the coordinate system of the cutting edge. i The axial direction is the point of the cutter tip near the center axis of the milling cutter, passing through the cutter teeth and parallel to the z0 axis of the milling cutter coordinate system. i The origin of the coordinate system is the intersection of the downward projection and the plane containing the lowest point of the cutting tooth. i The straight line passing through the inner tip of the cutting tooth and perpendicular to the mounting plane of the cutting tooth is taken as x. i The y-axis direction is determined according to the principles of the Cartesian coordinate system. i Axial direction; r max r is the maximum radius of rotation of the milling cutter tip; i Let θ be the radius of rotation of the i-th cutter tip of the milling cutter, i = 1, 2, 3; i Let α be the angle between the i-th and (i+1)-th cutting teeth; α0 is the installation angle of the cutting teeth; Δz i Δr is the axial error between the i-th cutter tooth and the (i+1)-th cutter tooth. i The radial error between the i-th cutting tooth and the (i+1)-th cutting tooth. e represents any point on the cutting edge of the cutting tooth; e m Let R0 be the midpoint of the cutting edge of the cutting tooth. m Point at y i o i z i The radius of the circumcircle in the plane, o z For e m The center point of the external circle; at x i o i y i On the plane, s0 is the midpoint e of the cutting edge of the cutting tooth. m to y i The distance between the axes, s1 is the midpoint e of the cutter teeth. m The distance to the back of the blade, s2 is e m The center point of the circumcircle o z To x i o i z i Distance between planes; For the straight line o z e and o z o i In x i o i z iAngle on a plane From the tip of the knife to o z With o z e m In y i o i z i The included angle on the plane; R1 is the angle of the cutting edge at x i o i y i The circumcircle of the arc containing the plane, β is o i 'e and o i 'e m In x i o i y i The angle between the planes, β0 is o i 'o i with o i 'e m In x i o i y i Angle on a plane; η i Let be the angle between the line connecting the origin of the cutter tooth coordinate system and the origin of the milling cutter coordinate system and the line connecting the two cutter tips.

[0164] Then, within the milling cutter coordinate system, the expression for the coordinates of the origin of the tooth coordinate system is:

[0165]

[0166]

[0167] Milling cutter cutting edge equation h(x) i ,y i ,z i The expression for ) is:

[0168]

[0169] in,

[0170]

[0171] s0=R1-R1cosβ0 (5)

[0172] β0=arcsin(s1 / 2R1) (6)

[0173] S2. Construct a calculation model of the instantaneous cutting posture of the milling cutter and teeth under vibration;

[0174] Furthermore, the specific implementation method of step S2 includes the following steps:

[0175] S2.1. Constructing the milling cutter cutting coordinate system under vibration-free conditions. v-x v y v z v Milling cutter cutting coordinate system under vibration v ′-x v 'y v ′z v Workpiece coordinate system o-xyz;

[0176] Furthermore, o i -x i y i z i Let z be the coordinate system of the milling cutter teeth. i The axis is a line parallel to the tip of the cutter and the lowest point of the cutting edge within the plane where the cutter teeth meet; x i The x-axis is a line parallel to the two cutting edge points within the cutting edge mating plane; o0-x0y0z0 is a milling cutter coordinate system without vibration influence, where the origin o0 is the intersection of the milling cutter's central axis and the plane containing the lowest point of the cutting edge, the x0 axis is the projection of the high-efficiency milling cutter's cutting edge with the largest radial error onto the plane of the lowest point of the cutting edge in the axial direction, and the z0 axis is the milling cutter's central axis pointing towards the tool holder; o v -x v y v z v This is the coordinate system for milling cutter cutting under vibration-free conditions, with the origin at o. v x is the intersection of the center axis of the high-efficiency milling cutter and the machined surface. v Axis through o v The point is parallel to x, y v Axis through o v The point is parallel to y, z v Axis through o v The point is parallel to z; o v ′-x v 'y v ′z v Let ′ be the coordinate system for milling cutter cutting under vibration, and point o v ′ and x v ′、y v ′、z v The '-axis is the origin of the vibration-free cutting coordinate system for high-efficiency milling cutters. v With x v y v z v The offset of the axis; o-xyz is the workpiece coordinate system, the x-axis is the milling feed direction, the y-axis is the milling width direction, the z-axis is the milling depth direction, and O is the intersection of the three axes;

[0177] L is the length of the workpiece, W is the width of the workpiece, H is the height of the workpiece, and v is the height of the workpiece. f n is the feed rate of the high-efficiency end mill, and a is the rotational speed of the high-efficiency end mill. p For the depth of cut, a eψ is the cutting width, t is the cutting time, and ψ is the cutting time. i (t) represents the intersection of the milling cutter structural coordinate system x0 axis and the milling cutter cutting coordinate system x under vibration at time t. v The angle between the ′ axis, For a cutting time t, the x0 axis of the milling cutter structure coordinate system and the x0 axis of the cutter tooth coordinate system are... i Angle between axes, θ d The contact angle is the line connecting the projection point of the cutter tip onto the lowest plane of the milling cutter and the origin of the milling cutter's cutting coordinate system, and the x-axis of the milling cutter's cutting coordinate system. v The included angle of the axis, δ(t) is the cutter attitude angle, δ′(t) is the cutter direction angle, δ1(t) is the cutter attitude angle δ(t) in x v o v z v The projection angle of the plane, δ2(t), is the milling cutter attitude angle δ(t) in y v o v z v The projection angle of the plane, A x (t) represents the position of the milling cutter at x v Vibration displacement in the direction, A y (t) represents the position of the milling cutter at y v Vibration displacement in the direction, A z (t) represents the milling cutter at z v The vibration displacement in the direction, where l is the overhang of the milling cutter;

[0178] S2.2. Based on the dynamic cutting process of the milling cutter under vibration, construct the milling cutter coordinate system transformation matrix A0, the tooth coordinate system transformation matrix B0, the transformation matrix A1 between the milling cutter coordinate system and the milling cutter cutting coordinate system under vibration, the transformation matrix B1 between the milling cutter cutting coordinate system under vibration and the milling cutter cutting coordinate system without vibration, and the milling cutter attitude angle in x... v o v z v The planar projection transformation matrix A2 and the milling cutter posture angle in y v o v z v Planar projection transformation matrix A3;

[0179]

[0180] in, For a cutting time t, the x0 axis of the milling cutter coordinate system and the x-axis of the tooth coordinate system are... i Angle between axes;

[0181]

[0182] Where, ψ i (t) represents the coordinate system x0 of the milling cutter structure and the coordinate system x of the milling cutter cutting under vibration. vThe included angle of the axis;

[0183]

[0184]

[0185] Among them, A x (t) represents the position of the milling cutter at x v Vibration displacement in the direction, A y (t) represents the position of the milling cutter at y v Vibration displacement in the direction, A z (t) represents the milling cutter at z v The vibration displacement in the x direction, δ1(t) is the milling cutter attitude angle δ(t) in the x direction. v o v z v The projection angle of the plane, δ2(t), is the milling cutter attitude angle δ(t) in y v o v z v The projection angle of the plane;

[0186] S2.3. Calculate the cutter attitude angle δ(t) and cutter direction angle δ'(t) to represent the cutter deflection angle caused by vibration. The calculation expression is:

[0187]

[0188]

[0189]

[0190]

[0191] S2.4. Construct the transformation matrix B2 between the milling cutter cutting coordinate system and the workpiece coordinate system under vibration-free conditions. The expression is:

[0192]

[0193] The expression for the trajectory of the origin of the cutting coordinate system in the workpiece coordinate system is as follows:

[0194]

[0195] Then, using the matrix transformation relationship between the graphical coordinate systems, the trajectory equation of any point on the cutter tooth is solved, and the expression is:

[0196] [xyz 1] T =B2B1A3A2A1A0B0[x i y i z i 1] T (16)

[0197] Obtain the origin o of the knife tooth coordinate system i The trajectory in the workpiece coordinate system is:

[0198] o i (x(t),y(t),z(t))=Φ i ·[0 0 0 1] T (17)

[0199] Where, Φ i Let Φ be the transformation matrix. i =B2B1A3A2A1A0B0;

[0200] S2.5. Calculate the effective cutting time of the cutter teeth, the contact angle of the cutter teeth when they cut out of the workpiece, and complete the construction of the instantaneous cutting posture calculation model of the milling cutter and cutter teeth under vibration; using the trajectory equation of the cutting edge of the (i+1)th cutter tooth, the workpiece side elevation equation, and the machining transition surface equation formed by the cutting edge of the (i+1)th cutter tooth and the machining transition surface equation formed by the ith cutter tooth, solve for the entry and exit cutting times of the (i+1)th cutter tooth, expressed as:

[0201]

[0202]

[0203] The cutting time t is any position of the (i+1)th cutting edge during the cutting time period. i+1 for:

[0204]

[0205] Among them, H i+1 (x(t s i+1 ), y(t) s i+1 ), z(t s i+1 H is the cutting edge equation when the (i+1)th cutting edge of the cutting tooth enters the workpiece. i+1 (x(t e i+1 )), y(t e i+1 ), z(t e i+1 )) is the cutting edge equation when the (i+1)th cutting edge cuts the workpiece, G i (x(t e i ), y(t) e i ), z(t e iLet t be the equation of the transition surface formed when the i-th cutting edge of the cutting tooth cuts out in the workpiece coordinate system. s i +1 For the (i+1)th cutting tooth engagement time, t e i+1 This refers to the moment when the (i+1)th cutting tooth makes its cut.

[0206] The expression for the brief time interval Δt corresponding to the i+1th cutter not yet cutting into the workpiece when the i-th cutter tooth has completely cut out of the workpiece is:

[0207] Δt=t e i+1 -t s i (twenty one)

[0208] The expression for the contact angle when the i-th cutting tooth cuts out of the workpiece is:

[0209]

[0210] A high-feed end mill with a diameter of 32mm was selected, with a spindle speed of 1104 r / min and a v. f 500 mm / min, a p 0.5mm, a e A milling experiment was conducted on titanium alloy using 16mm cutting parameters and climb milling. The error distribution of the milling cutter teeth is shown in the table below.

[0211]

[0212] Milling experiments were conducted using the above experimental scheme. The high-efficiency milling vibration was measured using the DH5922 transient signal testing and analysis system. Five locations corresponding to the simulated morphology positions were selected within this range, as shown in the figure below, corresponding to the 15th, 30th, 45th, 60th, and 75th cycles of the milling cutter. The instrument used for this morphology inspection was a TaylorHobson CCI·MP non-contact interferometer. White light imaging was performed for different cutting strokes, using a 256×256 pixel array for surface morphology imaging. The workpiece material for this milling was titanium alloy, and a workpiece with a total cutting length of 110mm was selected. To facilitate point sampling on the workpiece for measurement, a measurement coordinate system ox was established. c y c z c The surface morphology was photographed and inspected at sampling points 20mm apart from the leftmost end of the workpiece. The white light interferometer measurement frame was Δx. cl ×Δy cl .

[0213] S3. Collect surface morphology images of the milled workpiece and construct the distribution equation of residual feature points on the machining transition surface;

[0214] Furthermore, the specific implementation method of step S3 includes the following steps:

[0215] S3.1. Acquiring surface morphology images of the milled workpiece: Measurements were performed using a Taylor Hobson CCI·MP non-contact interferometer. White light photography was conducted for different cutting strokes, and a 256×256 pixel array was used for surface morphology imaging to obtain surface morphology images of the milled workpiece.

[0216] S3.2. Perform feature point recognition on the surface morphology image of the milled workpiece obtained in step S3.1:

[0217] First, select A1-A along the positive y-axis of the workpiece coordinate system on the machined surface morphology. p There are a total of p sections, where A1 and A p These are two end faces, representing the results of white light interferometer testing of the milled surface morphology. The distance between any two cross-sections is Δy. jm The expression for the coordinates of the m-th section along the y-axis starting from the origin of the workpiece coordinate system is:

[0218] y m =y0+(m-1)Δy jm (twenty three)

[0219] Δy jm The distance is less than the distance of the smallest detection unit of the white light interferometer, where m is any one of p;

[0220] Select A1-A along the positive x-axis starting from the origin. p Feature points on the cross section, q1-q are selected on each cross section. k There are k feature points in total, where q1, q2, q3, q4, q5, q k and q min The two highest points and the three lowest points on the cross-section are given, with x1, x2, x3, x4, x5, x6, x7, x8, x9, x1, x10, x11, x12, x13, x14, x15, x16, x17, x18, x19, x10, x10, x11, x12, x13 ... k x m The remaining feature points are evenly distributed among the three points, with a spacing of Δx between them. jm Δx jm The selection method is as follows:

[0221] q k and q min q min All points between q1 and q2 are divided into two intervals, with interval lengths x and x respectively. k -x m and x m–x1, the lengths of the two intervals x k -x m and x m The expression for the least common multiple Δx of –x1 is:

[0222] [Δx]=[x k -x m x m –x1] (24)

[0223] Then we get Δx jm The expression is:

[0224]

[0225] Where M is the largest positive integer not exceeding [Δx];

[0226] Then, starting from the origin of the workpiece coordinate system, the expression for the coordinates of the s-th feature point along the positive x-axis is:

[0227] x s =x1+(s-1)Δx (26)

[0228] s can be any one of k;

[0229] Next, based on the feature point selection method described above, the highest residual feature point, the lowest residual feature point, and the intermediate transition inflection point on the milled surface morphology are selected along the depth of cut. The selected feature points are arranged along the cutting tooth movement trajectory. Using Matlab to fit the surface equation, the expression for the distribution equation P'(x,y) of the residual feature points on the machining transition surface is obtained as follows:

[0230] P'(x,y)=P 00 +P 10 x+P 01 y+P 20 x 2 +P 11 xy+P 02 y 2 +P 30 x 3 +P 21 x 2 y (27).

[0231] +P 12 xy 2 +P 03 y 3 +P 40 x 4 +P 31 x 3 y+P 22 x 2 y 2

[0232] +P 13 xy 3 +P 04 y 4 +P 50 x 5 +P 41 x 4 y+P 32 x 3 y 2

[0233] +P 23 x 2 y 3 +P 14 xy 4 +P 05 y 5

[0234] Furthermore, the coefficients of the fitted equation function are shown in the table below:

[0235]

[0236] To verify the accuracy of the fitting equation for the milled surface, cross sections with the same position were selected from the fitted milled surface morphology and white light detection results, and grey relational analysis was performed to verify the fitting accuracy of the milled surface.

[0237] Three corresponding cross sections, A1, are taken from the white light imaging surface morphology and the fitted milled surface. a -A a ', A m -A m ', A b -A b ',like Figure 9 As shown.

[0238] S4. Based on the distribution equation of residual feature points on the machining transition surface constructed in step S3, the instantaneous cutting pose function of the milling cutter and teeth is solved by the mesh optimization method;

[0239] Furthermore, the specific implementation method of step S4 includes the following steps:

[0240] S4.1. Set the expression for the change in the position X of the cutting edge as follows:

[0241] X={c x c y c z ,ω,γ} (28)

[0242] Among them, c x c y c zω and γ represent the offsets of the origin of the cutter tooth coordinate system in the x, y, and z directions of the workpiece coordinate system, respectively; ω and γ represent the z-direction offsets of the cutter tooth coordinate system, respectively. i The workpiece coordinate system is offset from the z-axis, and the cutter tooth coordinate system is offset from the y-axis. i Offset from the y-axis of the workpiece coordinate system;

[0243] S4.2. Identify the instantaneous pose of the cutting teeth and the milling cutter in the milled surface morphology, divide the instantaneous offset mesh of the cutting teeth, set the size of the discrete mesh of the instantaneous pose of the cutting teeth to be smaller than the time interval when selecting the feature points of the cross section, take the maximum value of the vibration displacement as the upper boundary and the minimum value as the lower boundary, and calculate the number of meshes λ as shown in expressions (29)-(30):

[0244]

[0245] λ=max(λ1,λ2) (30)

[0246] Set the partition offset mesh size as shown in expression (31):

[0247]

[0248] The instantaneous offset of the instantaneous cutting posture of the cutting teeth is set as shown in expression (32):

[0249]

[0250] Different cutting edge pose sequences are formed by setting different displacement increments of the origin of the cutting tooth coordinate system, as well as the increments of the attitude angle and direction angle, as shown in expressions (33)-(37):

[0251] c x (t)={c x (t)(1),c x (t)(2),...,c x (t)(λ)} (33)

[0252] c y (t)={c y (t)(1),c y (t)(2),...,c y (t)(λ)} (34)

[0253] c z (t)={c z (t)(1),c z (t)(2),...,c z (t)(λ)} (35)

[0254] ω(t)={ω(t)(1),ω(t)(2),...,ω(t)(λ)} (36)

[0255] γ(t)={γ(t)(1),γ(t)(2),...,γ(t)(λ)} (37)

[0256] The arbitrary combination of variables in each sequence represents the cutting edge of the cutting tooth under different poses. The sequence of cutting edges composed of arbitrary pose parameters is shown in expression (38):

[0257] H(x,y,z)={H(1),H(2),...,H(λ 5 )} (38)

[0258] The cutting edge of the cutting tooth is set as a spatial curve, and its shape characteristics are characterized by curvature and deflection. During the effective cutting time of the cutting tooth, the cutting edge equation at any cutting position is shown in expression (39):

[0259] H=H(x(t),y(t),z(t)) (39)

[0260] The curvature deflection at a certain point on the cutting edge equation is calculated using expressions (40)-(42):

[0261]

[0262]

[0263]

[0264] Where ρ is the curvature at any point on the cutting edge; τ is the deflection at any point on the cutting edge; and g is the total curvature.

[0265]

[0266] S4.3. Identify the lowest point formed by the cutting edge in the fitted milled surface. Construct a quadratic surface using the neighboring points of the lowest point to calculate its curvature. Then, match this surface with points in the cutting edge equation that have the same curvature and whose Euclidean distance is less than a minimum threshold. For any lowest point p on the fitted machined transition surface... n A quadratic surface is constructed using its neighboring points, and the surface equation is shown in expression (43):

[0267] p n (U,V)=(U,V,S(U,V)) (43)

[0268] Among them, S(U,V)=a U 2 +bUV+c V 2The S-axis is the direction of the surface normal vector where the lowest point of the fitted surface is located; U and V are orthogonal to each other and lie on the tangent plane of the lowest point;

[0269] If p n The nearest point p n 1 The coordinates in the local coordinate system (S-UV) are (U n 1 V n 1 ,S n 1 The linear equation system obtained from m neighboring points is shown in expression (44):

[0270]

[0271] S4.4. Solve the linear equation system (44) using the least squares method to obtain the surface equations p of the characteristic points and neighboring points. n (U,V), and then the Gaussian curvature and mean curvature of each point on the surface are obtained;

[0272] Furthermore, comparing the corresponding points of the fitting equation between the cutting edge and the transition surface point by point would result in a large computational burden for curvature and Euclidean distance calculations, leading to excessive errors. Therefore, the correlation analysis between the cutting edge curve and the fitted transition surface can be transformed into the matching and solution of feature segments on the curve, thereby reducing the search space when matching the cutting edge equation with the fitting equation of the milling surface. The feature points matching the lowest point on the cutting edge and the fitted milling surface are calculated using the above formula. Several points are then taken from both sides of the feature point on the cutting edge to form feature segments on the cutting edge, changing the matching between feature points to the matching between the cutting edge and the feature segments of the fitted surface. For any point on the cutting edge curve equation, its curvature ρ and deflection τ are calculated, forming a two-dimensional feature vector [ρ, τ]. This series of two-dimensional feature vectors constitutes the shape description parameters describing any point on the cutting edge.

[0273] S4.5. Assume H1, H2, ... H n and P1, P2, ... P n Let n be the n feature segments around the lowest point of the fitting equation between the cutting edge of the cutting tooth and the surface, and each feature segment has m feature sets. The curvature and torsion feature sets of each feature segment on the cutting edge of the cutting tooth and the fitting surface are represented as follows: (i = 1, 2, ..., n; j = 1, 2, ..., m), the feature points on each feature segment are represented as: h1, h2, ..., h n Correspondingly, the feature set of the corresponding feature segment of the fitted surface is represented as: (i = 1, 2, ..., n; j = 1, 2, ..., m), the feature points on each feature set are represented as: p1, p2, ..., pn ;

[0274] The discrimination is based on the fact that the Euclidean distance between the corresponding feature points of each cutting edge and the fitted surface equation is less than the minimum tolerance range. The Euclidean distance between any two feature points and the minimum tolerance discrimination are shown in expression (45):

[0275]

[0276] Wherein, ρ(h) n ), ρ(p n ) and τ(h n ), τ(p n ) represent the curvature and torsion between any corresponding feature points on the cutting edge and the fitted surface, respectively, and η is the minimum tolerance of the Euclidean distance, which depends on the solution accuracy.

[0277] S4.6. Repeat steps S4.1-S4.5. When the curvature and deflection of the feature points on the corresponding feature segments on the cutting edge and the machining transition surface are matched and the Euclidean distance is within the minimum tolerance range, the tooth pose variables during the entire effective cutting cycle can be solved.

[0278] S5. Construct the instantaneous cutting pose compensation function of the milling cutter based on the instantaneous cutting pose function of the milling cutter and the cutting teeth obtained in step S4;

[0279] Furthermore, the specific implementation method of step S5 includes the following steps:

[0280] S5.1. Based on the structural relationship between the origin of the cutter tooth coordinate system and the origin of the milling cutter coordinate system, the instantaneous pose of the milling cutter and the instantaneous pose of the cutter tooth are as shown in expression (46):

[0281]

[0282] S5.2. By comparing the instantaneous pose parameters obtained through the solution with the pose parameters obtained using vibration displacement, the instantaneous pose deviation of the milling cutter in the current cutting cycle is obtained as shown in expression (47):

[0283]

[0284] Where Δx0(t) is the milling cutter feed direction deviation, Δy0(t) is the milling cutter width deviation, Δz0(t) is the milling cutter depth deviation, Δω0(t) is the milling cutter attitude angle deviation, and Δγ0(t) are the milling cutter direction angle deviations; A x(t)-δ'(t) are the pose parameters obtained through experiments, respectively; A'x0(t) is the instantaneous position of the milling cutter in the feed direction, A'y0(t) is the instantaneous position of the milling cutter in the width direction, A'y0(t) is the instantaneous position of the milling cutter in the depth direction, ω'0(t) is the milling cutter z-axis offset angle, and γ'0(t) is the milling cutter y-axis angular offset; t s i Let t be the time when the i-th cutting tooth enters the workpiece. e i+2 The time when the (i+2)th cutting tooth makes a cut;

[0285] The instantaneous pose compensation function over time is fitted using the instantaneous deviation curve of the origin of the milling cutter coordinate system, as shown in expression (48):

[0286]

[0287] in, The coefficients of the pose compensation function fitting formula are l = 0, 1, ..., 7, j = 0, 1, 2, 3, 4, and t is the effective time within the milling cutter cutting cycle;

[0288] S6. Using the milling cutter instantaneous cutting posture compensation function obtained in step S5, the instantaneous cutting posture solution model of the milling cutter and tooth under vibration constructed in step S2 is corrected to complete the instantaneous cutting posture recognition of the high feed milling cutter under vibration.

[0289] Furthermore, the specific implementation method of step S6 includes the following steps:

[0290] S6.1. Based on the machining transition surface formed by the adjacent cutting edges of the cutting teeth, the cutting edge trajectory equation of the i-th cutting tooth is set in the workpiece coordinate system o-xyz as shown in expression (49):

[0291]

[0292] S6.2. The equation for the machining transition surface formed by the sweeping of the i-th cutting edge is shown in expression (50):

[0293]

[0294] The (i+1)th cutting edge sweeps to form a machining transition surface and intersects with the machining transition surface formed by the previous cutting edge, as shown in expression (51):

[0295]

[0296] The (i+2)th cutting edge sweeps to form a machining transition surface, and together with the previous cutting edge, forms the final milled surface as shown in expression (52):

[0297]

[0298] S6.3. Substitute the instantaneous cutting pose compensation function of the milling cutter into the pose transformation matrix to form a simulation model of the milling shape after pose compensation;

[0299] The transformation matrix of the milling cutter cutting coordinate system with the introduction of the pose compensation function is shown in expression (53):

[0300]

[0301]

[0302] in, These are the projection angles of the attitude angle offset in the xoz and yoz planes, respectively;

[0303] The transformation matrix of the milling cutter coordinate system under the direction angle offset is set as shown in expression (54):

[0304]

[0305] The pose-compensated transformation matrix is ​​constructed using the matrix after pose compensation and the solved matrix, as shown in expression (55):

[0306] [xyz 1] T =B2B1'A4A'3A2'A1A0B0[x i y i z i 1] T (55)

[0307] S6.4. The pose-compensated transformation matrix Φ' obtained in step S6.3 is... i =B2B1'A4A'3A2'A1A0B0 is re-introduced into the model of the cutting tooth forming the machining transition surface and simulated to obtain new simulation results, thus completing the instantaneous cutting posture recognition of the high feed milling cutter under vibration.

Claims

1. A method for recognizing the instantaneous cutting pose of a high-feed milling cutter under the action of vibration, characterized in that, The method comprises the following steps: S1. Constructing a milling cutter coordinate system and a tool tooth coordinate system, setting a tool tooth origin coordinate equation in the milling cutter coordinate system, and constructing a milling cutter instantaneous cutting edge equation; S2. Constructing a milling cutter and tool tooth instantaneous cutting pose solution model under the action of vibration; S3. Collecting a surface topography picture of a workpiece machined by milling, and constructing a machining transition surface residual feature point distribution equation; S4. Based on the machining transition surface residual feature point distribution equation constructed in step S3, a grid optimization method is used to solve a milling cutter and tool tooth instantaneous cutting pose function; S5. Based on the milling cutter and tool tooth instantaneous cutting pose function obtained in step S4, a milling cutter instantaneous cutting pose compensation function is constructed; S6. The milling cutter instantaneous cutting pose compensation function obtained in step S5 is used to correct the milling cutter and tool tooth instantaneous cutting pose solution model constructed in step S2 under the action of vibration, and high-feed milling cutter instantaneous cutting pose recognition under the action of vibration is completed.

2. The method according to claim 1, characterized in that, The specific implementation method of step S2 comprises the following steps: S2.

1. Constructing the milling cutter cutting coordinate system o without vibration action v - x v y v z v , the milling cutter cutting coordinate system o with vibration action v ′- x v ′y v ′z v ′, the workpiece coordinate system o-xyz; S2.

2. According to the dynamic cutting process of the milling cutter under the vibration action, the milling cutter coordinate system conversion matrix A0, the cutter tooth coordinate system conversion matrix B0, the milling cutter coordinate system and the milling cutter cutting coordinate system conversion matrix A1 under the vibration action, the milling cutter cutting coordinate system and the milling cutter cutting coordinate system conversion matrix B1 without vibration action, the milling cutter attitude angle in x v o v z v plane projection conversion matrix A2, the milling cutter attitude angle in y v o v z v plane projection conversion matrix A3; wherein, is the angle between the x0 axis of the cutter coordinate system and the x i axis angle; wherein ψ i (t) is the angle between the x0 axis of the milling cutter coordinate system and the x v axis of the milling cutter cutting coordinate system under the action of vibration; wherein A x (t) is the vibration displacement of the milling tool in the x v direction, A y (t) is the vibration displacement of the milling tool in the y v direction, A z (t) is the vibration displacement of the milling tool in the z v direction, δ1(t) is the projection angle of the milling tool attitude angle δ(t) in the x v o v z v plane, and δ2(t) is the projection angle of the milling tool attitude angle δ(t) in the y v o v z v plane. S2.

3. Solving a milling cutter attitude angle δ(t) and a milling cutter direction angle δ'(t) for representing a milling cutter deflection angle caused by vibration, and calculating an expression as follows: S2.

4. Constructing a milling cutter cutting coordinate system and a workpiece coordinate system conversion matrix B2 under the action of no vibration, and calculating an expression as follows: Wherein, an expression of a trajectory of a cutting coordinate system origin in a workpiece coordinate system is as follows: Wherein, W is the width of the workpiece, H is the height of the workpiece, v f is the feed speed of the high-efficiency milling cutter, a p is the cutting depth, a e is the cutting width, t is the cutting time, r max is the maximum rotary radius of the cutter tip point of the milling cutter tooth Then, a trajectory equation of any point on a tool tooth is solved by using a matrix transformation relationship between coordinate systems, and an expression is as follows: [x y z 1] T = B2B1A3A2A1A0B0[x i y i z i 1] T (16) The tool tooth coordinate system origin O is obtained i The trajectory in the workpiece coordinate system is: o i (x(t),y(t),z(t)) = Φ i • [0 0 0 1] T (17) where Φ i is a transformation matrix, Φ i = B2B1A3A2A1A0B0; S2.

5. Solving an effective cutting time period of a tool tooth, a contact angle of the tool tooth when cutting a workpiece, and completing construction of a milling cutter and tool tooth instantaneous cutting pose solution model under the action of vibration; a cutting-in and cutting-out cutting time of an i+1th tool tooth is solved by using a trajectory equation of the i+1th tool tooth cutting edge, a workpiece side vertical surface equation and a machining transition surface equation formed by the trajectory equation of the i+1th tool tooth cutting edge and an i th tool tooth, and an expression is as follows: The i+1th blade cutting edge cuts at any position in the cutting time period t i+1 is: wherein H i+1 (x(t s i+1 ), y(t s i+1 ), z(t s i+1 )) is the equation of the cutting edge of the i+1th tooth when it enters the workpiece, H i+1 (x(t e i+1 ), y(t e i+1 ), z(t e i+1 )) is the equation of the cutting edge of the i+1th tooth when it exits the workpiece, G i (x(t e i ), y(t e i ), z(t e i )) is the equation of the transition surface formed by the i th tooth when it exits the workpiece coordinate system, t s i+1 is the instant when the i+1th tooth enters, and t e i+1 is the instant when the i+1th tooth exits. For a short time interval Δt corresponding to a time period when the i+1th tool tooth has not cut into the workpiece while the i th tool tooth has completely cut out the workpiece, an expression is as follows: At = t e i+1 -t s i (21) An expression of a contact angle of the i th tool tooth when cutting out the workpiece is as follows: wherein r i is the radius of rotation of the i-th tooth tip of the milling cutter.

3. The method according to claim 2, characterized in that, The specific implementation method of step S3 comprises the following steps: S3.

1. Collecting a surface topography picture of a workpiece machined by milling: a Taylor Hobson non-contact interferometer CCI·MP is used for measurement, white light shooting is performed for different cutting strokes, a 256×256 pixel array is used for surface topography shooting, and a surface topography picture of a workpiece machined by milling is obtained; S3.

2. Feature point recognition is performed on the surface topography picture of the workpiece machined by milling obtained in step S3.1: Firstly, A1-Ap are selected on the machined surface topography along the positive direction of the workpiece coordinate system y-axis p p cross sections, wherein A1 and A p are two end faces of the milling surface topography white light interferometer detection results, and the interval between any two cross sections is Δy jm wherein the expression of the mth cross section coordinate from the origin of the workpiece coordinate system along the y-axis is: y m = y0+ (m - 1) Ay jm (23) Δy jm the distance is less than the distance of the minimum detection unit of the white light interferometer, and m is any one of p; A1-A p q1-q k q1-q k k min q1-q k k m Δx jm k jm ​ q k and q min , q min and q1are all points between x k – x m and x m – x1are respectively divided into two intervals, the interval length is x k – x m and x m – x1, the expression of the least common multiple of the length of the two intervals Δx is: [Δx] = [x k - x m , x m - x1] (24) Thus, Δx jm The expression for Δx is Wherein, M is a maximum positive integer not more than [Δx]; Then, from a workpiece coordinate system coordinate origin, an expression of a coordinate of an s th feature point in a positive direction of an x axis is as follows: x s = x1+ (s - 1) Δx (26) Wherein, s is any one in k; Again, according to the feature point selection method shown above, the highest residual feature points, low feature points and intermediate transition inflection points on the milling surface topography along the depth direction are selected, the selected feature points are arranged along the tool tooth motion trajectory, the surface equation fitting is carried out by using Matlab, and the expression of the residual feature point distribution equation P'(x,y) of the machining transition surface is obtained: P'(x,y) = P 00 +P 10 x+P 01 y+P 20 x 2 +P 11 xy+P 02 y 2 +P 30 x 3 +P 21 x 2 y+P 12 xy 2 +P 03 y 3 +P 40 x 4 +P 31 x 3 y+P 22 x 2 y 2 +P 13 xy 3 +P 04 y 4 +P 50 x 5 +P 41 x 4 y+P 32 x 3 y 2 +P 23 x 2 y 3 +P 14 xy 4 +P 05 y 5 (27) 4. The method according to claim 3, characterized in that, The specific implementation method of step S4 includes the following steps: S4.

1. Set the expression of the tool tooth pose change X as: X = {c x , c y , c z , ω, γ} (28) wherein c x , c y , c z respectively represent the offset of the tool tooth coordinate system origin in the x, y, z directions in the workpiece coordinate system; ω and γ respectively represent the offset of the z i axis of the tool tooth coordinate system and the y i axis of the workpiece coordinate system; S4.

2. Identify the tool tooth and milling cutter instantaneous pose in the milling surface topography, divide the tool tooth instantaneous offset grid, set the size of the tool tooth instantaneous pose discrete grid to be smaller than the selected cross-section feature point time interval, take the maximum value of the vibration displacement as the upper boundary and the minimum value as the lower boundary, and divide the grid number λ, which is calculated as shown in expressions (29)-(30): Set the division offset grid size as shown in expression (31): Set the tool tooth instantaneous cutting pose instantaneous offset as shown in expression (32): Set the different tool tooth coordinate system origin displacement increments and attitude angle and direction angle increments to form different cutting edge pose sequences as shown in expressions (33)-(37): c x (t) = {c x (t)(1),c x (t)(2),...,c x (t)(λ)} (33) c y (t) = {c y (t)(1),c y (t)(2),...,c y (t)(λ)} (34) c z (t) = {c z (t)(1),c z (t)(2),...,c z (t)(λ)} (35) ω(t)={ω(t)(1),ω(t)(2),...,ω(t)(λ)} (36) γ(t)={γ(t)(1),γ(t)(2),...,γ(t)(λ)} (37) Set the variable combination in each group of sequences as the tool cutting edge under different poses, and the tool cutting edge sequence formed by any pose parameters is as shown in expression (38): H(x, y, z) = {H(l), H(2),..., H(λ 5 )} (38) Set the tool cutting edge as a space curve, and use curvature and torsion to characterize the shape features of the cutting edge. The cutting edge equation at any cutting position within the effective cutting time period of the tool tooth is as shown in expression (39): H=H(x(t),y(t),z(t)) (39) Set the curvature and torsion of a point on the cutting edge equation to be solved by expressions (40)-(42): Wherein, ρ is the curvature of any point on the cutting edge; τ is the torsion of any point on the cutting edge; g is the total curvature; S4.

3. Identify the lowest point formed by the cutting edge in the fitted milling surface, solve the curvature of the lowest point by establishing a quadric surface with its neighborhood points at the lowest point, and match the same curvature and the points with the Euclidean distance less than the minimum threshold value in the cutting edge equation, at any lowest point p n Establish a quadric surface with its neighborhood points at the lowest point p of the fitted machining transition surface, and the surface equation is shown in expression (43): p n (U,V) = (U,V,S(U,V)) (43) S(U, V) = aU + bUV + cV 2 where S(U, V) = aU 2 S-axis is the direction of the normal vector of the lowest point on the fitting surface; U and V are mutually orthogonal and on the tangent plane of the lowest point. If p n is a point on the line segment, then the coordinates of the point p n 1 The coordinate values in the local coordinate system (S-UV) are (U n 1 ,V n 1 ,S n 1 ), and the linear equations obtained from m adjacent points are shown in expression (44): S4.

4. Solve the linear equations (44) by least square method to obtain the characteristic point and the surface equation p of the neighboring point n (U, V), and then obtain the Gaussian curvature and mean curvature of each point on the surface. S4.

5. Assume H1, H2, … H n and P1, P2, … P n are n characteristic segments on the left and right of the lowest point of the tooth cutting edge and the surface fitting equation respectively, and each characteristic segment has m feature sets, the curvature and torsion feature sets of each characteristic segment on the tooth cutting edge and the fitting surface are represented as: The feature points on each characteristic segment are represented as: h1, h2, … h n Correspondingly, the feature sets of the corresponding characteristic segment of the fitting surface are represented as: j = 1, 2, …, m), the feature points on each feature set are represented as: p1, p2, … p n ; According to the Euclidean distance between each cutting edge and the corresponding feature points of the fitting surface equation being less than the minimum tolerance range, the Euclidean distance between any two feature points and the minimum tolerance discrimination is as shown in expression (45): where, p(h n ), p(p n ) and τ(h n ), τ(p n ) represent the curvature and torsion between any pair of corresponding feature points on the cutting edge and the fitting surface respectively, and η is the minimum tolerance of the Euclidean distance, which depends on the calculation accuracy; S4.

6. Repeat steps S4.1-S4.5, when the feature point curvature and torsion on each corresponding feature segment on the cutting edge and the machining transition surface match and the Euclidean distance is within the minimum tolerance range, the tool tooth pose variable within the entire effective cutting period is solved.

5. The method according to claim 4, characterized in that, The specific implementation method of step S5 includes the following steps: S5.

1. According to the structural feature relationship between the tool tooth coordinate system origin and the milling cutter coordinate system origin, the milling cutter instantaneous pose and the tool tooth instantaneous pose are as shown in expression (46): S5.

2. By solving the instantaneous pose parameters obtained, the pose parameters solved by using the vibration displacement are compared, and the instantaneous pose deviation of the milling cutter in the current cutting period is solved as shown in expression (47): Wherein, Δx0(t) is the milling cutter feed direction deviation value, Δy0(t) is the milling cutter width direction deviation value, Δz0(t) is the milling cutter depth direction deviation value, Δω0(t) is the milling cutter attitude angle deviation value, Δγ0(t) is the milling cutter direction angle deviation value respectively; A x (t)-δ'(t) are respectively the pose parameters obtained through experiments; A'x0(t) is the instantaneous position of the milling cutter feed direction, A'y0(t) is the instantaneous position of the milling cutter width direction, A'y0(t) is the instantaneous position of the milling cutter depth direction, ω'0(t) is the z-axis offset angle of the milling cutter, γ'0(t) is the y-axis direction angle offset of the milling cutter; t s i is the time when the i th tooth enters the workpiece, t e i+2 is the time when the i+2 th tooth exits. The instantaneous pose compensation function of the milling cutter coordinate system is fitted by using the instantaneous deviation curve of the milling cutter coordinate system origin, as shown in expression (48): wherein, are the fitting formula coefficients for the pose compensation function, i = 0, 1,..., 7, j = 0, 1, 2, 3, 4, and t is the effective time within the milling tool cutting period.

6. The method according to claim 5, wherein The specific implementation method of step S6 includes the following steps: S6.

1. Forming a machining transition surface based on adjacent tooth cutting edges, arranged in the workpiece coordinate system o-xyz, the cutting edge locus equation of the ith tooth is shown in expression (49): S6.

2. The machining transition surface equation formed by the ith tooth cutting edge sweeping is shown in expression (50): The machining transition surface formed by the ith+1 tooth cutting edge sweeping and intersecting with the machining transition surface formed by the previous tooth is shown in expression (51): The machining transition surface formed by the ith+2 tooth cutting edge sweeping and forming a final milling surface with the machining transition surface formed by the previous tooth is shown in expression (52): S6.

3. Bringing the instantaneous cutting pose compensation function of the milling cutter into the pose transformation matrix to form a pose-compensated milling appearance simulation model; The milling cutter cutting coordinate system conversion matrix with the pose compensation function is shown in expression (53): wherein, respectively the projection angle of the attitude angle bias in the xoz and yoz plane; The transformation matrix of the milling cutter coordinate system under the direction angle offset is shown in expression (54): The pose-compensated transformation matrix is constructed by using the pose-compensated matrix and the calculated matrix, as shown in expression (55): [x y z 1] T = B2B1'A4A'3A2'A1A0B0[x i y i z i 1] T (55) S6.

4. The pose-compensated transformation matrix Φ' obtained in step S6.3 is re-entered into the model of the tool-forming machining transition surface and simulated to obtain new simulation results, and the instantaneous cutting pose of the high-feed cutter under vibration is identified. i = B2B1'A4A'3A2'A1A0B0

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