Method for calculating instantaneous contact stiffness and wear increment of milling cutter relief under vibration

Abstract

The vibration-acting milling cutter rear face instantaneous contact stiffness and abrasion increment solving method belongs to the milling cutter processing technical field.The present application solves the problem that the current milling cutter test method can only obtain the tool-work characteristic parameters under limited conditions, and the test data reliability and test condition adaptability are difficult to completely guarantee. The present application comprises the following steps: a: vibration-acting milling cutter instantaneous cutting state representation method; b: tool tooth rear face instantaneous deformation amount solving method; c: tool tooth rear face and workpiece machining transition surface contact equivalent model construction method; d: tool tooth rear face contact stiffness solving method under different deformation conditions; e: tool tooth rear face instantaneous friction variable and abrasion increment solving method; f: tool tooth rear face appearance verification method. The present application solves the problem that the existing method ignores the influence of different deformation stages on the tool tooth rear face contact stiffness.

Description

Technical Field

[0001] This invention belongs to the field of milling cutter processing technology, specifically a method for calculating the instantaneous contact stiffness and wear increment of the flank face of a milling cutter under vibration. Background Technology

[0002] During milling, factors such as the matching degree between the workpiece and the cutting tool, the hardness of the workpiece material, the cutting speed of the milling cutter, the feed rate, and the vibration of the milling cutter spindle can cause uneven stress distribution and dynamic changes in contact stiffness between the flank face of the cutting tool and the machined surface of the workpiece. As a result, it is difficult to accurately predict and effectively control the friction force of the milling cutter teeth and the wear degree of the flank face.

[0003] Due to the complexity of tool-work contact surface problems and the limitations of research methods, early studies primarily focused on experimental analysis of contact stiffness from a macroscopic perspective. For specific machining structures, the contact stiffness of a particular tool-work contact surface was indirectly identified by combining experimental modal or frequency response analysis with lumped parameters, distributed parameters, or finite element models of the structure. However, experimental methods often require extensive analysis, yielding tool-work characteristic parameters only under limited conditions, and the reliability of experimental data and adaptability to experimental conditions are difficult to fully guarantee.

[0004] Existing methods for calculating the contact stiffness of the milling cutter's flank face are insufficient to reveal the instantaneous distribution characteristics of the flank face and its influence on friction and wear. This paper utilizes an equivalent model of the contact between the flank face and the workpiece's machining transition surface to reveal the axial and cutting edge direction distribution characteristics of the instantaneous contact stiffness of the milling cutter's flank face. A method for calculating the frictional force, frictional velocity, and instantaneous wear increment of the flank face is proposed, revealing the response characteristics of cutting load and the contact stiffness of the flank face. Summary of the Invention

[0005] The purpose of this invention is to address the problem that current testing methods for milling cutters can only obtain tool-workpiece characteristic parameters under limited conditions, making it difficult to fully guarantee the reliability of test data and the adaptability to test conditions. A brief overview of this invention is provided below to offer a basic understanding of certain aspects of the invention. It should be understood that this overview is not an exhaustive summary of the invention. It is not intended to identify key or essential parts of the invention, nor is it intended to limit the scope of the invention.

[0006] The technical solution of this invention: a method for calculating the instantaneous contact stiffness and wear increment of the flank face of a milling cutter under vibration, comprising:

[0007] Step a: A method for characterizing the instantaneous cutting state of a milling cutter under vibration;

[0008] Step b: Method for solving the instantaneous deformation of the rake face;

[0009] Step c: Method for constructing an equivalent model of the contact between the flank face of the cutting tooth and the workpiece machining transition surface;

[0010] Step d: Solution method for the contact stiffness of the rake face under different deformation conditions;

[0011] Step e: Calculation method for instantaneous friction variable and wear increment on the flank face of the cutting tooth;

[0012] Step f: Verification method for the morphology of the back face of the cutting teeth.

[0013] Furthermore, step a specifically involves setting the structural parameters of the milling cutter in its instantaneous cutting state under vibration.

[0014] O-XYZ is the workpiece coordinate system, where X, Y, and Z represent the length, width, and height of the workpiece, respectively; o0-x0y0z0 is the milling cutter cutting motion coordinate system under vibration-free conditions, where axes x0, y0, and z0 are parallel to the length, width, and height of the workpiece, respectively.

[0015] o d -x d y d z d Let O be the coordinate system of the milling cutter structure. d x is the intersection of the plane containing the axis of the milling cutter and the lowest point of the cutter teeth. d The axis lies in the plane where the lowest point of the tool tip is located and is parallel to the y-axis. d The axis is perpendicular, y d The axis lies in the plane where the lowest point of the cutting tooth is located and points towards the cutting tip with the largest outer diameter;

[0016] o d '-x d 'y d 'z d 'This is the coordinate system of the milling cutter structure under the action of milling cutter vibration;' c -u c v c w c Let O be the coordinate system of the knife tooth structure. c Let u be a point on the intersection line of the plane containing the lowest point of the cutting tooth structure and the plane containing the end face of the cutting tooth, and let u be the projection plane of the perpendicular line from the inner limit point of the cutting edge of the cutting tooth along the Z-axis of the workpiece. c The line of intersection between the plane containing the lowest point of the cutter tooth structure and the plane containing the end face of the cutter tooth, v c The plane containing the lowest point of the cutter tooth structure;

[0017] a p The depth of cut for the workpiece; a e n is the cutting width of the workpiece; n is the milling cutter speed; v fδ(t) represents the feed rate of the milling cutter; δ(t) represents the instantaneous attitude angle of the milling cutter under vibration.

[0018] Furthermore, step b specifically involves setting structural parameters for the instantaneous wear and deformation at a point on the flank face of the milling cutter teeth:

[0019] N0 is a point on the rake face of the cutter teeth before the end mill enters the cutter; N m Point N0 represents the point where wear occurred during the milling cutter's entry; N m 'for N m The position after deformation; f p For friction, f pu f pv f pw Frictional force along the knife tooth structure u c v c w c Components in three directions; σ is stress, σ u σ v σ w For stress along the knife tooth structure u c v c w c Components in three directions;

[0020] ω is the point deformation on the back face of the cutting tooth:

[0021]

[0022] ω u ω v ω w These are the deformation components in the u, v, and w directions, respectively:

[0023]

[0024] ε u ε v ε w Let u, v, and w represent the strain components in the u, v, and w directions, respectively; u0, v0, and w0 are the coordinates of a point on the cutter tooth when no deformation has occurred.

[0025]

[0026] u1, v1, and w1 are the coordinates of points on the cutting teeth after deformation;

[0027] Therefore ω u ω v ω w It can be transformed into:

[0028]

[0029] Furthermore, step c specifically includes the following steps:

[0030] Step c1: Make the two elasto-plastic bodies of the cutter tooth flank face and the workpiece's machined surface into contact;

[0031] Step c2: There are multiple micro-protrusions on the micro-scale of the tool-worker contact surface. The change in the wear degree of the back face of the tool tooth is regarded as the change of the micro-protrusion structure on the back face of the tool tooth. The law of elastic, elastoplastic to plastic deformation of a single micro-protrusion is constructed, and the yield range characteristic curves of different deformations are obtained.

[0032] Step c, construct the force analysis of a single micro-protrusion on the back face of the cutter tooth-tooth matrix, and set the structural parameters of the single micro-protrusion-tooth matrix, k. a For the stiffness of the micro-convex body, k b d represents the stiffness of the blade base. e y is the distance between the two surfaces of the rigid plane and the average height of the micro-protrusion; s r is the distance between the average height plane of the surface and the average height plane of the micro-protrusions. t r is the equivalent radius of curvature of the micro-convexity. tj The contact radius between the micro-protrusion and the substrate; p is the workpiece interface pressure exerted on the flank face of the cutting tooth; h e h is the height of the micro-convex body before deformation. f The average height of the micro-protrusion after deformation;

[0033] Step c4, the equivalent radius of curvature r of the micro-convex surface t The method for calculating the height variance σ is as follows:

[0034]

[0035]

[0036] In the formula, G is the characteristic scale coefficient reflecting the size of the contour; γ is the spatial frequency of the random contour, and γ = 1.5 when the contour distribution conforms to a normal distribution; D is the fractal dimension of the contour; L is the sampling length; and a' is an intermediate variable.

[0037]

[0038] In the formula, E is the elastic modulus; H v λ is the hardness of the material; Y is the yield strength of the material; λ is the average contact surface compressive strength; μ a Poisson's ratio of the bonding surface material;

[0039] Step c5, the WM function is used to simulate the actual machined surface profile, and has the following expression:

[0040]

[0041] In the formula, Z(x) is the surface profile height; n is the lowest frequency index;

[0042] Step c6, perform fractal characterization using the power spectrum method:

[0043]

[0044] After performing Fourier transform on the fractal rough surface profile, a straight line fitting is performed on (lgω, lg[S(ω)]) in the double logarithmic coordinate lg[S(ω)] - lgω to obtain the slope k;

[0045]

[0046]

[0047] For the fractal profile, -3 < k < -1, and the profile fractal dimension D is:

[0048] D = (5 + k) / 2 (12)

[0049] The characteristic length scale parameter G can be obtained from the intercept of the fitting straight line as:

[0050]

[0051] Furthermore, in step c1, the contact between the two elastoplastic bodies of the flank face of the cutting tooth and the machined surface of the workpiece is changed to the contact between the flank face of the cutting tooth, which is an elastoplastic body, and the machined surface of the workpiece, which is a rigid body.

[0052] Furthermore, step d is specifically as follows

[0053] Step d1, elastic deformation stage, the average contact pressure p e , the contact area S e , the contact load F e and the contact stiffness k e are expressed as:

[0054]

[0055] S e = πr t ω e (15)

[0056]

[0057]

[0058] At this time, the size of r t is:

[0059]

[0060] Step d2, k v Mean contact pressure factor:

[0061]

[0062] K v Maximum contact pressure factor:

[0063] K v =0.454+0.41μ a (20)

[0064] μ a E* is Poisson's ratio; E* is the equivalent elastic modulus of the material in contact with the workpiece.

[0065]

[0066] E is the elastic modulus of the milling cutter tooth material; H v ω represents the material hardness. ec The yield critical point:

[0067]

[0068] ω ec Substituting into the above equation, we obtain the contact characteristics at the yield critical point:

[0069]

[0070] Step d3, the stage of complete plastic deformation, the deformation amount during complete plastic deformation is ω. p The critical deformation is ω pc :

[0071] ω pc =110ω ec (twenty four)

[0072] Its contact characteristics include average contact pressure p p Contact area S p Contact load F p and contact stiffness k ap for:

[0073] p p =H v (25)

[0074] S p =2πr t ω p (26)

[0075] F p =2πH v r tω p (27)

[0076] k p =2πH v r t (28) Step d4, elastic-plastic deformation stage, contact characteristics and contact load F during elastic-plastic deformation stage. ep and contact stiffness k ep for:

[0077]

[0078]

[0079]

[0080] Furthermore, step e specifically involves constructing the instantaneous frictional force and frictional velocity components on the back face of the cutting tooth, and setting the structural parameters;

[0081] P (τ) The common tangent surface between the milling cutter's flank and the workpiece; F N For normal load; V τ f is the sliding speed; P Friction:

[0082] f p =μF N =μ0|V τ | α F N (32)

[0083] μ=μ0|V τ | α (33)

[0084]

[0085] In the formula, μ is the friction coefficient, μ0 is the adhesive theoretical friction coefficient, α is a constant affected by temperature, and τ b For the shear strength limit, σ s This is the ultimate compressive strength.

[0086] Vc is the cutting speed:

[0087]

[0088] In the formula, V c(x) V c(y) V c(N) These are the velocity components of the cutting speed along the X, Y, and Z directions of the workpiece, respectively;

[0089] V fP Friction speed:

[0090] V fp =V τ -V c(xy) =V τ -V c ·cosθ m (36)

[0091]

[0092]

[0093] Δ represents the wear increment generated on the flank face of the cutting tooth.

[0094]

[0095] In the formula, V τ dt represents the sliding speed; T represents the interface temperature; and dt represents the time increment.

[0096] Furthermore, step f includes the following steps:

[0097] Step f1: The similarity FD of the cutting edge profile obtained from experiments and simulations is solved using the Framinger distance;

[0098]

[0099] In the formula, α and β are arbitrary continuous non-decreasing functions from [0,1] to [a,b]. When calculating the Franminger distance between arbitrary curves, a polygonal curve V is used. L To approximate these curves;

[0100] Step f2, the cutting edge curve obtained in the experiment is P L The cutting edge curve obtained from the simulation is Q. L Then we have σ(P) L )=(u1,…,u p ) and σ(Q L )=(v1,…,v q ) represents the corresponding sequence:

[0101] P L [0,n]→V L1 (41)

[0102] Q L [0,n]→V L2 (42)

[0103] In the formula, n is a positive integer for each i∈{0,1,...,n-1}, P represents the interval [i,i+1]; V L It is a polygonal curve; P L Q LThe coupling sequence between them is L;

[0104] Step f3, when σ(P) L ), σ(Q) L When the quantities of ) are not equal, a1 = 1, b1 = 1, a m =p,b m =q, then the coupling sequence is:

[0105] (u a1 ,v b1 ),(u a2 ,v b2 ),...,(u am ,v bm (43)

[0106]

[0107] ||L|| represents the maximum connection length in L;

[0108] Step f4, given the polygon curve P L Q L Its discrete Framinger distance is:

[0109] δ dF (P,Q)=min{||L||} (45).

[0110] The present invention has the following beneficial effects:

[0111] 1. The method for calculating the instantaneous contact stiffness and wear increment of the milling cutter flank face under vibration in this invention considers the influence of the instantaneous cutting state of the milling cutter on the deformation of the flank face, takes into account different stages of flank face deformation, and equivalences the contact relationship between the milling cutter flank face and the workpiece machining transition surface, providing a basis for studying the instantaneous contact stiffness of the flank face. This solves the problem of existing methods neglecting the influence of different deformation stages on the contact stiffness of the flank face, and the uncertainty of contact stiffness changes during dynamic cutting of the milling cutter.

[0112] 2. The method for calculating the instantaneous contact stiffness and wear increment of the milling cutter flank face under vibration of the present invention constructs a micro-convex body stiffness model of the milling cutter tooth flank face under the influence of cutting vibration, studies the variation law of contact stiffness, normal pressure of flank face and degree of tooth deformation, and solves the problem that existing methods ignore the instantaneous morphology of the flank face of the tooth during the cutting process, thus affecting the diversity of instantaneous contact stiffness of the flank face of the tooth.

[0113] 3. The method for calculating the instantaneous contact stiffness and wear increment of the milling cutter flank face under vibration in this invention considers the influence of stiffness on the wear of the cutter tooth flank face, analyzes the influence characteristics of contact stiffness on the instantaneous friction force and wear increment of the milling cutter tooth, and reveals the distribution characteristics of the instantaneous contact stiffness of the cutter tooth flank face along the axial direction of the tooth and the distribution characteristics along the cutting edge direction. A method for calculating the friction force, friction speed, and instantaneous wear increment of the cutter tooth flank face is proposed, revealing the response characteristics of the above parameters to cutting load and the contact stiffness of the cutter tooth flank face. Attached Figure Description

[0114] Figure 1 This is a flowchart illustrating the calculation method for the instantaneous contact stiffness and wear increment of the flank face of a milling cutter tooth under vibration.

[0115] Figure 2 It is a diagram of the instantaneous cutting state between the flank face of a high-feed milling cutter and the machined surface;

[0116] Figure 3 This is a schematic diagram showing the instantaneous wear and deformation at a point on the back face of the cutting tooth;

[0117] Figure 4 It is an equivalent model diagram of the contact between the flank face of the cutting tooth and the machined surface of the workpiece;

[0118] Figure 5 It is a curve showing the yield range characteristics of a single micro-protrusion under different deformations;

[0119] Figure 6 This is a schematic diagram of the force analysis of a single micro-protrusion on the back face of the cutting tooth and the cutting tooth matrix;

[0120] Figure 7 It is a model diagram of instantaneous frictional force and frictional velocity on the back face of the cutting tooth;

[0121] Figure 8 This is a schematic diagram of the cutting speed direction from the perspective of the instantaneous frictional force and frictional velocity on the back face of the cutting tooth;

[0122] Figure 9 This is a schematic diagram of a high-feed milling cutter cutting experiment;

[0123] Figure 10 This is a schematic diagram showing the selected feature points on the cutting teeth;

[0124] Figure 11 This is a wear simulation diagram of the thermo-coupling field of a Deform high-feed milling cutter;

[0125] Figure 12 The stiffness k of the first row of characteristic points on the back face of the cutting tooth varies with the rotation angle. Schematic diagram of the changes;

[0126] Figure 13This is a diagram showing the distribution of the stiffness of the rake face along the cutting edge direction;

[0127] Figure 14 This is a diagram showing the distribution of the stiffness of the rake face along the axial direction.

[0128] Figure 15 The frictional variable of the first row of feature points on the back face of the cutting tooth as a function of the rotation angle. Schematic diagram of the changes;

[0129] Figure 16 The wear depth d of the first row of feature points on the back face of the cutting tooth t With wear increment Δ Schematic diagram of the changes;

[0130] Figure 17 The wear depth d of the second row of feature points on the back face of the cutting tooth. t With wear increment Δ Schematic diagram of the changes;

[0131] Figure 18 The wear depth d of the third row of feature points on the back face of the cutting tooth. t With wear increment Δ Schematic diagram of the changes;

[0132] Figure 19 This is a schematic diagram showing the variation of frictional force and wear increment at the first row of characteristic points on the back face of the cutting tooth as a function of stiffness.

[0133] Figure 20 This is a schematic diagram showing the variation of frictional force and wear increment at the second row of feature points on the back face of the cutting tooth as a function of stiffness.

[0134] Figure 21 This is a schematic diagram showing the variation of frictional force and wear increment at the third row of characteristic points on the back face of the cutting tooth as a function of stiffness.

[0135] Figure 22 This is a schematic diagram of a white light interferometer measurement site;

[0136] Figure 23 This is a schematic diagram illustrating the method for comparing experimental and simulated morphology.

[0137] Figure 24 This is a schematic diagram showing the contour similarity of the regions where feature points are located under different cutting strokes;

[0138] Figure 25 This is a schematic diagram of the fractal dimension of the region where the feature points of the cutting edge are located under different cutting strokes. Detailed Implementation

[0139] To make the objectives, technical solutions, and advantages of this invention clearer, the invention is described below with reference to specific embodiments shown in the accompanying drawings. However, it should be understood that these descriptions are merely exemplary and not intended to limit the scope of the invention. Furthermore, descriptions of well-known structures and technologies are omitted in the following description to avoid unnecessarily obscuring the concept of the invention.

[0140] Example 1, combined with Figures 1-3 This embodiment describes a method for characterizing the instantaneous cutting state of the milling cutter under vibration in step a, and a method for solving the instantaneous wear and deformation of the cutter tooth rake face in step b.

[0141] Step a: A method for characterizing the instantaneous cutting state between the flank face of the milling cutter and the machined transition surface. Under vibration, the instantaneous contact relationship between the milling cutter and the workpiece changes, and the milling process is in an unstable state. This method characterizes the instantaneous cutting state between the flank face of the milling cutter and the machined transition surface, such as... Figure 2 As shown, the structural parameters of the milling cutter in the instantaneous cutting state under vibration are set;

[0142] O-XYZ is the workpiece coordinate system, where X, Y, and Z represent the length, width, and height of the workpiece, respectively; o0-x0y0z0 is the milling cutter cutting motion coordinate system under vibration-free conditions, where axes x0, y0, and z0 are parallel to the length, width, and height of the workpiece, respectively.

[0143] o d -x d y d z d Let O be the coordinate system of the milling cutter structure. d x is the intersection of the plane containing the axis of the milling cutter and the lowest point of the cutter teeth. d The axis lies in the plane where the lowest point of the tool tip is located and is parallel to the y-axis. d The axis is perpendicular, y d The axis lies in the plane where the lowest point of the cutting tooth is located and points towards the cutting tip with the largest outer diameter;

[0144] o d '-x d 'y d 'z d 'This is the coordinate system of the milling cutter structure under the action of milling cutter vibration;' c -u c v c w c Let O be the coordinate system of the knife tooth structure. c Let u be a point on the intersection line of the plane containing the lowest point of the cutting tooth structure and the plane containing the end face of the cutting tooth, and let u be the projection plane of the perpendicular line from the inner limit point of the cutting edge of the cutting tooth along the Z-axis of the workpiece. c The line of intersection between the plane containing the lowest point of the cutter tooth structure and the plane containing the end face of the cutter tooth, v cThe plane containing the lowest point of the cutter tooth structure;

[0145] a p The depth of cut for the workpiece; a e n is the cutting width of the workpiece; n is the milling cutter speed; v f δ(t) represents the feed rate of the milling cutter; δ(t) represents the instantaneous attitude angle of the milling cutter under vibration.

[0146] Step b describes the solution method for the instantaneous wear and deformation of the cutter tooth's flank face. During the cutting process, the milling cutter experiences sliding friction due to the pressure P from the relatively moving workpiece, leading to wear on the cutter surface. Simultaneously, the milling cutter deforms in the corresponding area to resist the external force P.

[0147] like Figure 3 As shown, N0 is any point on the rake face of the cutter tooth before the milling cutter enters the cutting area; N m Point N0 represents the point where wear occurred during the milling cutter's entry; N m 'for N m The position after deformation; f p For friction, f pu f pv f pw Frictional force along the knife tooth structure u c v c w c Components in three directions; σ is stress, σ u σ v σ w For stress along the knife tooth structure u c v c w c Components in three directions;

[0148] Where V τ dt is the sliding speed; T is the interface temperature (absolute degree); dt is the time increment.

[0149] ω represents the deformation at any point on the back face of the cutting tooth;

[0150]

[0151] ω u ω v ω w These are the deformation components in the u, v, and w directions, respectively;

[0152]

[0153] ε u ε v ε w, representing the strain components in the u, v, and w directions respectively; u0, v0, and w0 are the coordinates of any point on the cutter tooth when no deformation has occurred;

[0154]

[0155] u1, v1, and w1 are the coordinates of any point on the cutting tooth after deformation;

[0156] Therefore ω u ω v ω w It can be transformed into:

[0157]

[0158] Example 2, combined with Figure 1 , Figures 4-6 This embodiment describes a method for constructing an equivalent model of the contact between the flank face of the cutting tooth and the transition surface of the workpiece in step c.

[0159] The contact between the flank face of the cutting tool and the transition surface of the workpiece, which are two elasto-plastic bodies, is equivalent to the contact between the flank face of the cutting tool, which is an elasto-plastic body, and the transition surface of the workpiece, which is equivalent to a rigid body. Figure 4 As shown;

[0160] Numerous micro-protrusions exist on the tool-worker contact surface at the microscale. Changes in the wear degree of the cutting edge's flank can be viewed as changes in the structure of these micro-protrusions. The characteristics of individual micro-protrusions, from elastic and elastoplastic to plastic deformation, can be described using yield range curves for different deformations, as shown in the figure. Figure 5 As shown;

[0161] The stress condition of a single micro-protrusion on the back face of the cutting tooth and the cutting tooth matrix is ​​as follows: Figure 6 As shown, where k a For the stiffness of the micro-convex body, k b d represents the stiffness of the blade base. e y is the distance between the two surfaces of the rigid plane and the average height of the micro-protrusion; s r is the distance between the average height plane of the surface and the average height plane of the micro-protrusions. t r is the equivalent radius of curvature of the micro-convexity. tj The contact radius between the micro-protrusion and the substrate; p is the workpiece interface pressure exerted on the rake face of the cutting tooth; h e h is the height of the micro-convex body before deformation. f The average height of the micro-protrusion after deformation;

[0162] The equivalent radius of curvature r of the micro-convex surface t The method for calculating the height variance σ is as follows:

[0163]

[0164]

[0165] In the formula, G is the characteristic scale coefficient reflecting the contour size; γ is the spatial frequency of the random contour, and when the contour distribution conforms to the normal distribution, γ = 1.5; D is the fractal dimension of the contour; L is the sampling length; a' is an intermediate variable;

[0166]

[0167] In the formula, E is the elastic modulus; H v is the hardness of the material; Y is the yield strength value of the material; λ is the average contact surface pressure coefficient; μ a is the Poisson's ratio of the joint surface material;

[0168] The W-M function is widely used to simulate the actual mechanical machining surface contour and has the following expression:

[0169]

[0170] In the formula, Z(x) is the surface contour height; n is the lowest frequency index;

[0171] The fractal characterization is carried out by the power spectrum method:

[0172]

[0173] After performing Fourier transform on the fractal rough surface contour, a straight line fitting of (lgω, lg[S(ω)]) can obtain the slope k in the double logarithmic coordinate lg[S(ω)] - lgω;

[0174]

[0175]

[0176] For the fractal contour, -3 < k < -1, and the contour fractal dimension D is:

[0177] D = (5 + k) / 2 (12)

[0178] The characteristic length scale parameter G can be obtained from the intercept of the fitting straight line as:

[0179]

[0180] Example 3, combined with Figure 1 、 Figures 9-14 This example is described. This example is a method for solving the contact stiffness of the flank of the cutting tooth under different deformation conditions in step d,

[0181] Step d1, the elastic deformation stage, is represented by e, ep, and ep, which respectively represent the elastic deformation, elastic-plastic deformation, and plastic deformation stages.

[0182] Average contact pressure p e Contact area S e Contact load F e and contact stiffness k e Represented as:

[0183]

[0184] S e =πr t ω e (15)

[0185]

[0186]

[0187] At this time r t Size:

[0188]

[0189] Step d2, k v Mean contact pressure factor:

[0190]

[0191] K v Maximum contact pressure factor:

[0192] K v =0.454+0.41μ a (20)

[0193] In the formula, μ a E* is Poisson's ratio; E* is the equivalent elastic modulus of the material in contact with the workpiece.

[0194]

[0195] E is the elastic modulus of the milling cutter tooth material; H v ω represents the material hardness. ec The yield critical point:

[0196]

[0197] ω ec Substituting into the above equation, we can obtain the contact characteristics at the yield critical point:

[0198]

[0199] Step d3, the stage of complete plastic deformation, the deformation amount during complete plastic deformation is ω. p The critical deformation is ω pc :

[0200] ω pc =110ω ec (twenty four)

[0201] Its contact characteristics, average contact pressure p p Contact area S p Contact load F p and contact stiffness k ap for:

[0202] p p =H v (25)

[0203] S p =2πr t ω p (26)

[0204] F p =2πH v r t ω p (27)

[0205] k p =2πH v r t (28)

[0206] Step d4, elastoplastic deformation stage, contact characteristics during elastoplastic deformation stage, contact load F ep and contact stiffness k ep for:

[0207]

[0208]

[0209]

[0210] Experiments were conducted on cutting titanium alloy (Ti6Al4V) with high-feed carbide end mills. Images of the cutting experiment are shown below. Figure 9 As shown in Table 1, the experimental scheme was as follows: the milling method was climb milling, the tool used in the experiment was F2330.Z25 high feed milling cutter, and the insert was P26337R14 indexable insert.

[0211] Table 1 Experimental Scheme

[0212]

[0213] Feature points were selected in different regions on the rake face of the cutting teeth, and the selected points are shown in Table 2.

[0214] Table 2. Selection Criteria for Feature Points on the Rake Face of Cutting Teeth

[0215]

[0216] The wear state of the flank face of the cutting tool after the cutting test and the location of the selected feature points are as follows: Figure 10 As shown;

[0217] Finite element simulation was performed on the milling process of titanium alloy with a high-efficiency end mill according to the experimental scheme. The thermo-mechanical coupling field simulation of the high-efficiency end mill was conducted using the finite element simulation software Deform-3D, specifically its Machining [Cutting] module, to simulate the milling process. Figure 11 As shown in Table 3, the tool and workpiece models were constructed using UG and imported into the simulation module. The simulation boundary conditions are shown in Table 3.

[0218] Table 3 Simulation Boundary Conditions

[0219]

[0220] During the entire cutting process of the milling cutter, six time periods were selected, with each time period being three cycles of the milling cutter rotation. The instantaneous contact stiffness of the milling cutter tooth rake face and the machined transition surface under vibration was calculated as a function of time. Combined with... Figure 10 The mentioned feature point selection method, the stiffness change of the first period in the first time segment of the selected feature points N1 to N5 of the knife tooth is as follows: Figure 12 As shown;

[0221] The instantaneous contact stiffness of feature points on the centerline of the cutting edge is extracted, and the distribution characteristics of the instantaneous contact stiffness of the flank face of the cutting edge along the axial direction of the cutting edge at the same moment are studied. The results are as follows: Figure 13 As shown, the instantaneous contact stiffness of the feature points on the first row of the rake face, i.e., the feature points on the cutting edge of the cutter tooth, is extracted. Using the tooth rotation angle as a variable, the distribution characteristics of the instantaneous contact stiffness of the rake face along the cutting edge direction at different times are studied. The results are as follows: Figure 14 As shown.

[0222] Example 4, combined with Figure 1 , Figures 7-8 , Figures 15-21 This embodiment describes the method for calculating the instantaneous friction variable and wear increment on the back face of the cutter tooth in step e.

[0223] The instantaneous frictional force and frictional velocity components on the back face of the cutting tooth are as follows: Figure 7 As shown;

[0224] like Figure 8 As shown, P (τ) The common tangent surface between the milling cutter's flank and the workpiece; F N For normal load; V τ f is the sliding speed; P Friction:

[0225] f p =μF N =μ0|V τ | α F N (32)

[0226] μ=μ0|V τ | α (33)

[0227]

[0228] μ is the coefficient of friction, μ0 is the theoretical coefficient of adhesion friction, α is a constant affected by temperature, and τ b For the shear strength limit, σ s This is the ultimate compressive strength.

[0229] V c For cutting speed:

[0230]

[0231] V c(x) V c(y) V c(N) These are the velocity components of the cutting speed along the X, Y, and Z directions (normal direction of the common tangent plane) of the workpiece, respectively;

[0232] V fP Friction speed:

[0233] V fp =V τ -V c(xy) =V τ -V c .cOSθ m (36)

[0234]

[0235]

[0236] use Figure 9 The experimental scheme shown, combined with the solution methods of equations (33) to (39), calculates the friction coefficient and friction force of the back face of the cutter tooth at different time periods and cycles. The changes in friction coefficient and friction force of the first cycle of the first time period where the characteristic points N1 to N5 on the back face of the cutter tooth are located are as follows: Figure 15 As shown;

[0237] Δ represents the wear increment generated on the flank face of the cutting tooth.

[0238]

[0239] Where V τ dt is the sliding speed, T is the interface temperature (absolute degree), and dt is the time increment.

[0240] As can be seen from equation (1), the wear of the flank face of the cutting tooth is affected by the pressure p and the sliding speed V. τ The influence of temperature T, etc., is adopted Figure 9 The milling experiment scheme shown calculates the wear depth d of the cutter tooth flank face during different cutting cycles. t Wear increment Δ with rotation angle The changes, among which the result of cutting cycle one is as follows: Figures 16-18 As shown;

[0241] Based on the instantaneous contact stiffness k and frictional force f p The method for calculating the wear increment Δ integrates the instantaneous contact stiffness, friction force, and wear increment at different time periods and cycles of the same characteristic point. Instantaneous contact stiffness is used as the independent variable, and friction force and wear increment as dependent variables. Corresponding curves of friction force and wear increment as a function of instantaneous contact stiffness are plotted, such as... Figures 19-21 As shown.

[0242] Example 5, combined with Figure 1 , Figures 22-25 This embodiment describes a method for verifying the morphology of the cutting edge face after step f.

[0243] The similarity F between the cutting edge profiles obtained from experiments and simulations is solved using the Frechet distance. D The smaller the value, the higher the similarity between the two morphologies;

[0244]

[0245] α and β are arbitrary continuous non-decreasing functions from [0,1] to [a,b]. When calculating the Fréchet distance between arbitrary curves, a polygonal curve V is typically used. L To approximate these curves;

[0246] Let the cutting edge curve obtained from the experiment be P. L The cutting edge curve obtained from the simulation is Q. L Then we have σ(P) L )=(u1,…,u p ) and σ(Q L )=(v1,…,vq ) represents the corresponding sequence;

[0247] P L [0,n]→V L1 (41)

[0248] Q L [0,n]→V L2 (42)

[0249] n is a positive integer. For each i ∈ {0, 1, ..., n-1}, P is a positive integer, and V is a positive integer. L For a polygonal curve, P L Q L The coupling sequence between them is L;

[0250] When σ(P) L ), σ(Q) L When the quantities between ) are not equal, such as a1=1, b1=1, a m =p,b m =q, then the coupling sequence is:

[0251] (u a1 ,v b1 ),(u a2 ,v b2 ),...,(u am ,v bm (43)

[0252]

[0253] ||L|| represents the maximum connection length in L;

[0254] Given a polygon curve P L Q L Its discrete Fréchet distance is:

[0255] δ dF (P,Q)=min{||L||} (45)

[0256] Measurements were performed using Taylor Hobson's non-contact white light interferometer CCI·MP. Photos of the experimental setup are shown below. Figure 22 As shown. For different cutting strokes, the flank face morphology of each cutting tooth was verified. The specific verification method is as follows: Figure 23 As shown. The back face of the cutting edge uses a 512×512 pixel array, and the measured projected area is 400μm×400μm. Images of the measurement experiment are shown below. Figure 22 As shown. To further analyze the morphological data measured by the instrument, three-dimensional morphological plots were created by selecting regions containing different feature points on the rake face of the cutting tooth. The specific process is as follows: Figure 23 As shown in (a);

[0257] Based on the friction and wear data of the rake face obtained from the simulation, the surface profile at different times can be obtained. The simulation calculation of the surface roughness profile is performed multiple times, and the difference is fitted in the direction perpendicular to the roughness profile to establish a three-dimensional morphology model of the rake face. The results are as follows: Figure 23 As shown in (c);

[0258] The simulated cutting edge of the cutting tooth was used as the verification object, and its profile was compared with that obtained experimentally after different cutting strokes. The morphology of the 200μm region before and after the midpoints of five feature points N1-N5 was selected for verification. The comparison of the cutting tooth profile morphology obtained experimentally and from simulation at a 0.5mm stroke is as follows: Figure 23 As shown in (b);

[0259] Centered on five selected feature points, a 200μm wide area was extended forward and backward along the cutting edge direction as the surface morphology selection region. The contour similarity of the regions containing the feature points of the cutting edge under different cutting strokes was verified. The verification results are as follows: Figure 24 As shown;

[0260] The fractal dimension solution method proposed by equations (9) to (13) is used to calculate the fractal dimension D of the cutting edge profile obtained after the experiment and the cutting edge profile obtained by simulation. a With D b The solution is performed. A smaller difference in the dimensions of the two fractals indicates a higher similarity. The comparison results are as follows: Figure 25 As shown.

[0261] This embodiment is merely an exemplary illustration of this patent and does not limit its scope of protection. Those skilled in the art can make partial changes to it, as long as they do not exceed the spirit and essence of this patent, they are all within the scope of protection of this patent.

Claims

1. A method for calculating the instantaneous contact stiffness and wear increment of the flank face of a milling cutter under vibration, characterized in that, Comprising: Step a: A method for characterizing the instantaneous cutting state of a milling cutter under vibration; Set the structural parameter a of the milling cutter in the instantaneous cutting state under vibration. p a e、 n, v f , δ(t), a p The depth of cut for the workpiece; a e n is the cutting width of the workpiece; n is the milling cutter speed; v f δ(t) represents the feed rate of the milling cutter; δ(t) represents the instantaneous attitude angle of the milling cutter under vibration. Step b: A method for solving the instantaneous deformation amount of the flank of a cutter tooth; Structural parameters for setting the instantaneous wear amount and deformation amount of a point on the flank of a milling cutter tooth at a specific moment; specifically: N0 is a point on the rake face of the cutter teeth before the end mill enters the cutter; N m Point N0 represents the point where wear occurred during the milling cutter's entry; N m 'for N m The position after deformation; f p For friction, f pu f pv f pw Frictional force along the knife tooth structure u c v c w c Components in three directions; σ is stress, σ u σ v σ w For stress along the knife tooth structure u c v c w c Components in three directions; ω is the deformation amount of a point on the flank of a cutter tooth: （1） ω u ω v ω w These are the deformation components in the u, v, and w directions, respectively: （2） ε u ε v ε w Let u, v, and w represent the strain components in the u, v, and w directions, respectively; u0, v0, and w0 are the coordinates of a point on the cutter tooth when no deformation has occurred. （3） u1, v1, and w1 are the coordinates of a point on the cutter tooth after deformation; Therefore ω u ω v ω w It can be transformed into: （4）； Step c: A method for constructing an equivalent model of the contact between the flank of a cutter tooth and the workpiece machining transition surface; Step c1, contacting two elastoplastic bodies of the flank of a cutter tooth and the workpiece machining transition surface; Step c2, there are multiple micro-protrusions on the tool-workpiece contact surface at the microscale. The change in the wear degree of the flank of a cutter tooth is regarded as the change in the structure of the micro-protrusions on the flank of a cutter tooth, and the law of a single micro-protrusion from elastic, elastoplastic to plastic deformation and the characteristic curve of the yield interval of different deformations are constructed; Step c3: Construct a force analysis of the single micro-protrusion-tooth matrix on the back face of the cutter tooth, and set the structural parameters of the single micro-protrusion-tooth matrix, k. a For the stiffness of the micro-convex body, k b d represents the stiffness of the blade base. e y is the distance between the two surfaces of the rigid plane and the average height of the micro-protrusion; s r is the distance between the average height plane of the surface and the average height plane of the micro-protrusions. t r is the equivalent radius of curvature of the micro-convexity. tj The contact radius between the micro-protrusion and the substrate; p is the workpiece interface pressure exerted on the flank face of the cutting tooth; h e h is the height of the micro-convex body before deformation. f The average height of the micro-protrusion after deformation; Step c4: Calculate the equivalent radius of curvature r of the micro-convex surface. t and height variance σ; Step c5: Simulating the actual mechanical machining surface profile; Step c6: Using the power spectrum method for fractal characterization; Step d: A method for solving the contact stiffness of the flank of a cutter tooth under different deformation conditions; Step d1: Calculate the average contact pressure p e Contact area S e Contact load F e and contact stiffness k e ; Step d2: Solve for k v The average contact pressure factor, elastic modulus E*, and yield critical point ω are given by the following parameters: ec , to obtain the contact characteristics at the yield critical point; Step d3: Calculate the critical deformation ω p Contact characteristics, average contact pressure p p Contact area S p Contact load F p and contact stiffness k ap ; Step d4: Solve for contact characteristics and contact load F during the elastic-plastic deformation stage. ep and contact stiffness k ep ; Step e: A method for calculating the instantaneous friction variable and wear increment of the flank of a cutter tooth; Based on the normal load F N Sliding speed V τ Calculate the friction force f P Cutting speed Vc, friction speed V fP、 The wear increment Δ generated on the flank face of the cutting tooth; Step f: A method for verifying the flank morphology of a cutter tooth; Step f1: Obtaining the cutting edge profile similarity FD; Step f2: The cutting edge curve obtained from the experiment is P L The cutting edge curve obtained from the simulation is Q. L , thus obtaining σ(P) L ) and σ(Q L The corresponding sequence; Step f3: When σ(P) L ), σ(Q) L When the number of elements is unequal between the elements, a coupled sequence is obtained; Step f4: Given the polygon curve P L Q L The discrete Framinger distance is then obtained.

2. The method for calculating the instantaneous contact stiffness and wear increment of the milling cutter flank face under vibration according to claim 1, characterized in that, The specific content of step a is as follows: O-XYZ is the workpiece coordinate system, where X, Y, and Z are the workpiece length, width, and height directions respectively; o0-x0y0z0 is the milling cutter cutting motion coordinate system without vibration, and the axes x0, y0, and z0 are parallel to the workpiece length, width, and height directions respectively; o d -x d y d z d Let O be the coordinate system of the milling cutter structure. d x is the intersection of the plane containing the axis of the milling cutter and the lowest point of the cutter teeth. d The axis lies in the plane where the lowest point of the tool tip is located and is parallel to the y-axis. d The axis is perpendicular, y d The axis lies in the plane where the lowest point of the cutting tooth is located and points towards the cutting tip with the largest outer diameter; o d '-x d 'y d 'z d 'This is the coordinate system of the milling cutter structure under the action of milling cutter vibration;' c -u c v c w c Let O be the coordinate system of the knife tooth structure. c Let u be a point on the intersection line of the plane containing the lowest point of the cutting tooth structure and the plane containing the end face of the cutting tooth, and let u be the projection plane of the perpendicular line from the inner limit point of the cutting edge of the cutting tooth along the Z-axis of the workpiece. c The line of intersection between the plane containing the lowest point of the cutter tooth structure and the plane containing the end face of the cutter tooth, v c The plane containing the lowest point of the shaft through the cutter tooth structure.

3. The method for calculating the instantaneous contact stiffness and wear increment of the milling cutter flank face under vibration according to claim 2, characterized in that, The specific content of step c4 is as follows, Step c4, the equivalent radius of curvature r of the micro-convex surface t The method for calculating the height variance σ is as follows: （5） （6） In the formula, G is the characteristic scale coefficient reflecting the contour size; γ is the spatial frequency of the random contour. When the contour distribution conforms to the normal distribution, γ = 1.5; D is the fractal dimension of the contour; L is the sampling length; a' is an intermediate variable; （7） In the formula, E is the elastic modulus; H v λ is the hardness of the material; Y is the yield strength of the material; λ is the average contact surface compressive strength; μ a Poisson's ratio of the bonding surface material; The specific content of step c5 is as follows. The W-M function is used to simulate the actual mechanical machining surface profile and has the following expression: （8） In the formula, Z(x) is the surface profile height; n is the lowest frequency index; The specific content of step c6 is as follows. Using the power spectrum method for fractal characterization: （9） After performing Fourier transform on the fractal rough surface profile, a straight line fitting is performed on (lgω, lg[S(ω)]) in the double logarithmic coordinate lg[S(ω)]-lgω to obtain the slope k; （10） （11） For the fractal contour, -3 < k < -1, and the contour fractal dimension D is: （12） The characteristic length scale parameter G can be obtained from the intercept of the fitting straight line as: （13）。 4. The method for calculating the instantaneous contact stiffness and wear increment of the milling cutter flank face under vibration according to claim 3, characterized in that: In step c1, the contact of two elastoplastic bodies of the flank of a cutter tooth and the workpiece machining transition surface is the contact of an elastoplastic flank of a cutter tooth with a rigid workpiece machining transition surface.

5. The method for calculating the instantaneous contact stiffness and wear increment of the milling cutter flank face under vibration according to claim 3, characterized in that, The specific content of step d is as follows, Step d1, elastic deformation stage, average contact pressure p e Contact area S e Contact load F e and contact stiffness k e Represented as: （14） （15） （16） （17） At this time r t Size: （18） Step d2, k v Mean contact pressure factor: （19） K v Maximum contact pressure factor: （20） μ a E* is Poisson's ratio; E* is the equivalent elastic modulus of the material in contact with the workpiece. （21） E is the elastic modulus of the milling cutter tooth material; H v ω represents the material hardness. ec The yield critical point: （22） ω ec Substituting into the above equation, we obtain the contact characteristics at the yield critical point: （23） Step d3, the stage of complete plastic deformation, the deformation amount during complete plastic deformation is ω. p The critical deformation is ω pc : （24） Its contact characteristics include average contact pressure p p Contact area S p Contact load F p and contact stiffness k ap for: （25） （26） （27） （28） Step d4, the elastic-plastic deformation stage, contact characteristics and contact load F during the elastic-plastic deformation stage. ep and contact stiffness k ep for: （29） （30） （31）。 6. The method for calculating the instantaneous contact stiffness and wear increment of the milling cutter flank face under vibration according to claim 5, characterized in that, The specific content of step e is as follows. Constructing the instantaneous frictional force and frictional velocity components of the flank of a cutter tooth and setting the structural parameters; P （τ） The common tangent surface between the milling cutter's flank and the workpiece; F N For normal load; V τ f is the sliding speed; P Friction: (32) (33) (34) In the formula, μ is the friction coefficient, μ0 is the adhesive theoretical friction coefficient, α is a constant affected by temperature, and τ b For the shear strength limit, σ s This is the ultimate compressive strength. Vc is the cutting speed: (35) In the formula, V c（x） V c（y） V c（N） These are the velocity components of the cutting speed along the X, Y, and Z directions of the workpiece, respectively; V fP Friction speed: (36) (37) (38) Δ is the wear increment generated on the flank of a cutter tooth: (39) In the formula, V τ dt represents the sliding speed; T represents the interface temperature; and dt represents the time increment.

7. The method for calculating the instantaneous contact stiffness and wear increment of the milling cutter flank face under vibration according to claim 6, characterized in that, Step f Includes the following steps, Step f1, using the Fréchet distance to solve the cutting edge profile similarity FD obtained from experiments and simulations; （40） In the formula, α and β are arbitrary continuous non-decreasing functions from [0,1] to [a,b]. When calculating the Franminger distance between arbitrary curves, a polygonal curve V is used. L To approximate these curves; Step f2, the cutting edge curve obtained in the experiment is P L The cutting edge curve obtained from the simulation is Q. L Then we have σ(P) L )=(u1,…,u p ) and σ(Q L )=(v1,…,v q ) represents the corresponding sequence: （41） （42） In the formula, n is a positive integer in each... P is for the interval [i, i + 1]; V L It is a polygonal curve; P L Q L The coupling sequence between them is L; Step f3, when σ(P) L ), σ(Q) L When the quantities of ) are not equal, a1=1, b1=1, a m =p, b m If q = , then the coupling sequence is: （43） （44） ||L|| is the maximum connection length in L; Step f4, given the polygon curve P L Q L Its discrete Framinger distance is: （45）。

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