A method for calculating the dynamic characteristics of the friction coefficient of the tooth flank of a square shoulder milling cutter

Abstract

A method for calculating the dynamic characteristics of the friction coefficient of the tooth pair flank of a square shoulder milling cutter belongs to the field of milling cutter processing technology. The present invention includes a method for calculating the area unit of the tooth pair flank of the milling cutter; calculating the friction velocity of the area unit of the tooth pair flank of the milling cutter; a method for extracting the characteristic parameters of the thermal-mechanical coupling field of the tooth pair flank of the milling cutter; constructing the instantaneous friction energy consumption distribution function of the tooth pair flank of the milling cutter; a method for verifying the cumulative friction energy consumption of the tooth pair flank of the milling cutter; and a method for calculating the instantaneous friction coefficient and instantaneous friction stress of the tooth pair flank of the milling cutter. The purpose is to solve the problem of proposing a method for calculating the dynamic characteristics of the friction coefficient of the tooth pair flank of a square shoulder milling cutter. By constructing the tooth pair flank area unit and giving a specific calculation method, a calculation method that can effectively characterize the instantaneous friction characteristic parameters is proposed based on the atomic interface theory, and a distribution function of the friction velocity and normal stress distribution function at the accurate friction characteristic point are constructed on the area unit.

Description

Technical Field

[0001] The invention relates to a method for calculating a unit of a flank area of ​​a milling cutter tooth pair, and belongs to the technical field of milling cutter processing. Background Art

[0002] During the intermittent milling process of a square shoulder milling cutter, the contact relationship between the tooth pair flank and the workpiece transition surface is unstable due to factors such as the milling cutter's own tooth errors and milling vibrations. This causes the friction coefficient at the characteristic points of the friction contact area between the tooth pair flank and the workpiece transition surface to change dynamically. Existing methods often consider the friction coefficient to be a constant, ignoring the interaction between factors such as the instantaneous contact microelement area of ​​the tooth pair flank, friction velocity, and normal stress. As a result, the calculated friction coefficient, friction stress, and friction energy consumption have large errors compared to the actual results. Therefore, it is very necessary to propose an accurate method for calculating the friction coefficient of the friction contact area of ​​the tooth pair flank to characterize the tribological characteristic parameters of the tooth pair flank, such as the distribution of friction stress and friction energy consumption on the tooth pair flank. Summary of the Invention

[0003] The purpose of this invention is to provide a method for calculating the dynamic characteristics of the friction coefficient of the flank face of a square shoulder milling cutter tooth pair. The following is a brief overview of the invention to provide a basic understanding of certain aspects of the invention. It should be understood that this overview is not an exhaustive overview of the invention. It is not intended to identify key or important aspects of the invention, nor is it intended to limit the scope of the invention.

[0004] The technical solution of the present invention:

[0005] A method for calculating the dynamic characteristics of the friction coefficient of the tooth pair flank of a square shoulder milling cutter comprises: step 1, a method for calculating the area unit of the tooth pair flank of the milling cutter; step 2, based on step 1, calculating the friction velocity of the area unit of the tooth pair flank of the milling cutter; step 3, a method for extracting characteristic parameters of the thermal-mechanical coupling field of the tooth pair flank of the milling cutter; step 4, constructing a distribution function of the instantaneous friction energy consumption of the tooth pair flank of the milling cutter; step 5, a method for verifying the accumulated friction energy consumption of the tooth pair flank of the milling cutter; and step 6, a method for calculating the instantaneous friction coefficient and the instantaneous friction stress of the tooth pair flank of the milling cutter.

[0006] Furthermore, the step 1 includes: a method for measuring the axial and radial errors of the milling cutter:

[0007] Δr i =r max -r i (i=1,2···m) (1)

[0008] Where Δr i is the radial error of the i-th tooth, r iis the turning radius of the i-th tooth tip of the milling cutter, where i=1,2,3, r max It is the maximum turning radius of the three cutting edge points of the milling cutter.

[0009] The axial error is calculated as follows:

[0010] Δz i =l1-l i (i=1,2···m) (2)

[0011] Where Δz i is the axial error of the i-th tooth, l1 is the distance from the lowest point of the milling cutter to the end face, l i is the distance from the lowest point to the end face of the i-th tooth.

[0012] Tooth i coordinate system o i -a i b i c i With the milling cutter structure coordinate system O s -The XYZ rotation matrix I1 and translation matrix M1 are:

[0013]

[0014] in is the instantaneous position angle of the i-th tooth;

[0015] Milling cutter structure coordinate system O s -XYZ and milling cutter cutting coordinate system under vibration O c -UVW instantaneous rotation matrix I2 is:

[0016]

[0017] in, is the instantaneous angle between the V axis and the Y axis in the UVW plane:

[0018]

[0019] Where, is the angle between the V axis and the Y axis in the UVW plane at the time when the milling cutter initially cuts in, that is, at time t=0:

[0020]

[0021] where a e is the cutting width.

[0022] Milling cutter cutting coordinate system O under vibration c -UVW and the instantaneous rotation matrix I3, I4, and the instantaneous translation matrix M2 of the milling cutter cutting coordinate system o0-uvw without vibration are:

[0023]

[0024]

[0025] Among them, θ1(t) is the instantaneous angle between the projection of the W axis on the vo0w plane and the w axis, θ2(t) is the instantaneous angle between the projection of the W axis on the uo0w plane and the w axis, A x (t), A y (t), A z (t) are the vibration displacements of the milling cutter along the x, y, and z axes, respectively.

[0026] The instantaneous translation matrix M3 of the milling cutter cutting coordinate system o0-uvw and the workpiece coordinate system o-xyz without vibration is:

[0027]

[0028] Where x o0 (t),y o0 (t),z o0 (t) is the instantaneous position coordinate of the origin oo of the milling cutter cutting coordinate system in the workpiece coordinate system o-xyz without vibration;

[0029]

[0030] Among them, v f is the feed speed of the milling cutter, L0 is the length of the workpiece, W0 is the width of the workpiece, H0 is the height of the workpiece, a p is the cutting depth of the workpiece;

[0031] The trajectory of the milling cutter center point O under vibration c The specific solution methods for variables such as (x, y, z), milling cutter posture angle θ(t), and milling cutter direction angle θ'(t) are as follows:

[0032] (1) Milling cutter cutting coordinate system O under vibration c -The movement trajectory of the UVW coordinate origin O c (x, y, z) is:

[0033] O c (x,y,z)=[x,y,z,1] T =M3·[A x (t),A y (t),A z (t),1] T (11)

[0034] (2) The instantaneous angle θ(t) between the W axis and the w axis is:

[0035]

[0036] Among them, θ(t) is the instantaneous attitude angle of the milling cutter; l is the overhang length of the milling cutter.

[0037] (3) The angles between the projections of the W axis on the vo0w and uo0w planes and the W axis are:

[0038]

[0039] (4) θ'(t) is the angle between the projection of the W axis on the uo0w plane and the v axis, which can be calculated as follows:

[0040]

[0041] (5) Tooth coordinate system o i -a i b i c i Conversion relationship matrix with workpiece coordinate system o-xyz as follows:

[0042]

[0043] (6) In the workpiece coordinate system, the secondary cutting edge l' f The equation is:

[0044]

[0045] in, It is the distance from any point on the secondary cutting edge of the tooth to the tip of the tool. k' is the total length of the tooth auxiliary cutting edge, r is the tooth flank angle, λ' s is the inclination angle of the secondary edge of the tooth flank;

[0046] (7) Order Then the tip point of tooth i is o i The motion trajectory o in the workpiece coordinate system i (x, y, z) is as shown in formula (17):

[0047]

[0048] (8) In the workpiece coordinate system, the back face A of the tooth pair i ' and workpiece processing transition surface B i Friction pairs m As shown in formula (18):

[0049]

[0050] Among them, the upper and lower boundaries of instantaneous friction wear formed on the flank surface of the tooth pair during the cutting process are shown in formula (19);

[0051]

[0052] Among them, l u is the upper friction boundary of the tooth pair flank friction pair, l d It is the lower friction boundary of the flank friction pair of the tooth pair.

[0053] (9) In the workpiece coordinate system, the equation of the back face of the tooth pair is shown in formula (20).

[0054]

[0055] It is the back face of the tooth. Each edge of the back cutting edge of the tooth.

[0056] Workpiece machining transition surface B in the workpiece coordinate system i The solution method is shown in formula (21).

[0057]

[0058] in, The moment when the tool cuts into the workpiece. To complete the moment when the cutting tool cuts out the workpiece instantaneously.

[0059] Through material mechanics analysis, during the instantaneous cutting process of the cutter tooth, when the equivalent stress σ on the secondary cutting edge of the cutter tooth is greater than the yield strength σ of the material, s When , the material in the cutting edge area will fall off, so the upper boundary of the wear of the cutter teeth can be judged by using the equivalent stress as shown in formula (22);

[0060] σ≥σ s (twenty two)

[0061] Where σ is the equivalent stress, σ s is the yield strength.

[0062] Identify the equivalent stress at each section as the yield strength σ s The coordinate values ​​corresponding to the characteristic point positions are used to connect the characteristic points on all cross sections in the tool tooth coordinate system to construct the instantaneous friction upper boundary curve of the milling cutter tooth flank.

[0063] During the entire milling process, there is equivalent strain in both the contact area and the non-contact area of ​​the flank face of the milling cutter tooth from the cutting edge to the cutting edge, while the equivalent strain value in the friction contact area is large and gradually decreases along the normal vector direction of the cutting edge and undergoes a sudden change at the lower boundary of instantaneous wear. Therefore, the node of the lower boundary of the flank face wear can be identified by the equivalent strain change rate ε', as shown in formula (23);

[0064]

[0065] Where ε is the equivalent strain, ε' is the equivalent strain rate, and Y i is the ordinate of the tooth measurement coordinate system.

[0066] The position where the equivalent strain change rate has the maximum mutation at each section is identified, the maximum mutation position points of each section are connected, and the instantaneous friction lower boundary curve of the tooth flank is constructed in the tooth coordinate system.

[0067] By characterizing the instantaneous contact relationship of the friction pair, characteristic points are selected in the instantaneous contact friction area of ​​the tooth pair flank face, and the instantaneous contact area unit is solved. The solution method is as follows;

[0068]

[0069] ds is the instantaneous contact area unit of the back face of the tooth pair; da i is the area unit length in plane a i o i b i Projection on the plane; db i Area unit width in plane a i o i b i Projection on the plane; γ is the direction of the normal vector of the area element and c i The angle between the axes.

[0070] In formula (24), γ(a i , b i , c i )The function is constructed as shown in formula (25);

[0071]

[0072] Furthermore, the step 2 includes: solving formula (17) to obtain the following parameter equation of the trajectory of any point of the cutter tooth:

[0073]

[0074] Taking the partial derivative of the trajectory of any point on the tooth with respect to time in equation (26), we can obtain the arbitrary component velocity along the x, y, and z axes of the workpiece coordinate system as follows:

[0075]

[0076] In formula (27), v nx is the component velocity along the x-axis; v ny is the component velocity along the y-axis; v nz is the component velocity along the z-axis.

[0077] Relative velocity v of any point n The solution is as follows:

[0078]

[0079] Relative speed v n Unit vector in the workpiece coordinate system as follows:

[0080]

[0081] The intersection point o between the back face of the cutter tooth and the transition surface of the workpiece r as follows:

[0082]

[0083] Over r Point and the common tangent plane P with the back face of the tooth pair and the workpiece processing transition surface i as follows:

[0084]

[0085] Make v n On the common section P i The projection on and passes through point o r Unit vector in the projection direction as follows:

[0086]

[0087] Among them, l px is a unit vector The component vector in the x-axis direction; l py is a unit vector Component vector in the y-axis direction; l pz is a unit vector The component vector in the z-axis direction.

[0088] In the workpiece coordinate system, the friction velocity v at any point on the back tool surface is m for:

[0089] v m =v n cosθ m (33)

[0090] Among them, θ m is the relative velocity v n With unit vector The angle between them is calculated as follows:

[0091] θ m =π-θ c (34)

[0092]

[0093] In formula (35), θ c is the relative motion speed v n With friction speed v m The angle between them.

[0094] In the workpiece coordinate system, the friction velocity direction vector of any point on the secondary back tool surface is The solution is as shown in formula (36).

[0095]

[0096] Among them, v mx 、v my 、v mz is the friction velocity of the point on the back face of the cutter tooth in the workpiece coordinate system, which is converted to the cutter tooth coordinate system through coordinate transformation as shown in formula (37):

[0097]

[0098] Among them, v mai The point on the back face of the tooth is along a in the tooth coordinate system. i Friction velocity in the axial direction; v mbi The point on the back face of the tooth pair is located along b in the tooth coordinate system. i Friction velocity in the axial direction; v mci The point on the back face of the cutter tooth is located along c in the cutter tooth coordinate system. i Friction speed in the axial direction.

[0099] Therefore, the friction velocity v at any point in the tooth coordinate system is m for:

[0100]

[0101] In order to characterize the dynamic changes of the friction characteristic parameters of the area unit of the friction contact area of ​​the tooth flank from cutting in to cutting out, a solution model for the instantaneous cutting in to cutting out of the single-rotation tooth of the milling cutter is proposed.

[0102]

[0103] In formula (39), T i T is the time period from the i-th tooth cutting in to the cutting out, i s is the cutting time of the i-th tooth, T i e is the cutting time of the i-th tooth, κ is the k-th cutting time of the i-th tooth, φ i is the angle between the cutting entry and the cutting exit of the i-th tooth, ω is the angular velocity of the milling cutter, t i is the time when the i-th tooth instantly cuts into the workpiece.

[0104]

[0105] Similarly, in formula (40), T i-1 T is the time period from the i-1th tooth cutting in to the cutting out, i-1 s is the cutting time of the i-th tooth, T i-1 e is the cutting time of the i-1th tooth, η ii-1 is the angle between the i-th tooth and the i-1-th tooth, where φ i The solution method is shown in formula (41)

[0106]

[0107] Furthermore, the step 3 includes: in order to extract the temperature and equivalent stress based on the thermal-mechanical coupling field, a thermal-mechanical coupling field simulation of the shoulder milling cutter is performed, and the vibration signal measured in the experiment and the milling cutter trajectory and the cutter tooth trajectory are used as finite element simulation boundary conditions to perform finite element simulation, and a finite element tool and workpiece simulation model;

[0108] The point selection method of the friction area on the back face of the cutter tooth is parallel to the cutter tooth measurement coordinate system Y i The cross section in the axial direction has a spacing of Δl and the cross sections are m1,…m i …, m n , take points at equal intervals from the upper and lower edges of the tooth wear on each section, and the interval between the two is Δk,l mi is the distance between the i-th section and the origin of the tooth coordinates. Any point k on the section i The coordinate solution method is shown in formula (42);

[0109] Select any point k on the flank i Coordinate k in the tooth coordinate system i (a ki , b ki , c ki ) as shown in (42):

[0110]

[0111] in, Select the distance between two adjacent points in the same section.

[0112] Select point k i Converting to the workpiece coordinate system, the motion trajectory in the workpiece coordinate system is obtained as formula (43):

[0113]

[0114] F p is the normal stress on the tooth flank microelement, passing through the tooth flank node and perpendicular to the tooth flank and c i The axis angle is θ ci ; τ is the equivalent stress of the tooth flank at the network node under the thermal-mechanical coupling field; F1, F2, and F3 are the equivalent stresses in the direction of the tetrahedron microelement; θ k1 ,θ k2 ,θ k3 are the angles between the equivalent stress and the normal stress on the three edges; the equivalent stress is expressed in the component tooth coordinate system on the tetrahedron by vector It is expressed as shown in formula (44):

[0115]

[0116]

[0117] In formula (45), It is the unit vector of the normal stress in the normal direction on the infinitesimal area of ​​the back face of the tooth pair.

[0118] Therefore, from equations (44) and (45), we can get θ k1 ,θ k2 ,θ k3 As shown in formula (46);

[0119]

[0120] The normal stress is solved as shown in Equation (47);

[0121] F p (a i ,b i ,c i )=F1(a i ,b i ,c i )·cosθ k1 +F2(a i ,b i ,c i )·cosθk2 +F3(a i ,b i ,c i )·cosθ k3 (47)

[0122] Furthermore, the step 4 includes: obtaining the absorption energy change rate E by the interface atomic theory v for:

[0123]

[0124] In formula (48), E is the instantaneous absorbed energy at time t, and υ is the forced vibration frequency of the atom as shown in formula (49):

[0125]

[0126] The instantaneous energy distribution function of absorption is as follows:

[0127]

[0128] Where: ψ is the lattice constant (2.9506×10 -10 m); h is Planck's constant (h=6.62607015×10 -34 J·s); δ is the Boltzmann constant (δ=1.380649×10 -23 J / K);v m is the relative friction speed; t es1 With t es2 are the initial and final time of energy absorption, respectively; Ω is the temperature rise of the atomic interface. The calculation method is as follows:

[0129]

[0130] Where: m is the relative atomic mass of the atom, which is 4.34×10 -26 kg, ω n The atomic natural frequency is 4.39×10 11 rad / s, χ is the excitation force of the interface potential field, and is 1×10 -9 N.

[0131] Furthermore, the cumulative friction energy consumption in step 5 is accumulated by the instantaneous energy consumption boundary. In order to verify the correctness of the cumulative energy consumption distribution function solution model, a verification method for the cumulative friction energy consumption of the secondary flank is proposed as follows; the cumulative wear boundary G identification method at the section of the secondary flank of the tooth is as follows:

[0132] G(X i ,Y imax )=0 (52)

[0133] Yimax =max(Y i (t)) (53)

[0134] Using the instantaneous boundary of the cutter teeth, the whole cutting process from the cutter teeth entering to the cutter teeth cutting out of the workpiece is obtained. i The instantaneous boundary Y at position i Maximum Y imax , and finally get imax The cumulative friction energy consumption boundary G is formed;

[0135] The energy consumption distribution surface of the tooth flank surface is reconstructed by selecting characteristic points when the three teeth cut out the workpiece. The energy consumption boundary curve and the wear boundary of the experimental tooth flank surface are extracted by using the characteristic point selection method proposed in step 3. The correlation coefficient is analyzed as follows:

[0136]

[0137] Where Coυ is the covariance calculation formula, X i , Y i is the value of each characteristic point of the boundary curve measured in the tool tooth measurement coordinate system, and is the average value of the boundary curve at each point; the correlation coefficient ρ is calculated as follows:

[0138]

[0139] in and is the standard deviation, as shown below:

[0140]

[0141]

[0142] The closer ρ is to 1, the stronger the correlation between the two related variables is, and the closer it is to 0, the weaker the correlation between the two related variables is.

[0143] Furthermore, the step 6 includes: the normal pressure of the friction contact area unit is F n , the friction coefficient is μ, then the work dS done by the unit friction force in time dt is:

[0144] dS=μ(a i ,b i ,c i ,t)·F n (a i ,b i ,c i ,t)·v m (ai ,b i ,c i ,t)·dt (58)

[0145] Assume that during the friction motion of the tool interface, all the friction work is converted into the heat energy of the system.

[0146] dS=dE (59)

[0147] The friction coefficient distribution function can be obtained by solving equation (59) as equation (60):

[0148]

[0149] The friction stress distribution function obtained by solving equations (58) to (60) is shown in equation (61):

[0150] f p (a i ,b i ,c i ,t)=μ(a i ,b i ,c i ,t)·F p (a i ,b i ,c i ,t) (61)

[0151] The present invention has the following beneficial effects:

[0152] 1. This paper constructs a tooth pair flank surface area unit and provides a specific solution method. Based on the atomic interface theory, a solution method that can effectively characterize the instantaneous friction characteristic parameters is proposed. The distribution function of the friction velocity and normal stress distribution function at the friction characteristic point are accurately constructed on the area unit.

[0153] 2. This invention establishes a mapping relationship between parameters such as the friction velocity distribution function and the normal stress distribution function, solving the problem of treating the friction coefficient as a constant, which leads to large deviations between the calculated friction stress and friction energy consumption and the actual values.

[0154] 3. Existing studies on the friction coefficient often assume that the friction coefficient is a constant, which fails to reveal the dynamic variation characteristics of the friction coefficient throughout the cutting process. This results in inaccurate and large errors in the calculated characteristic parameters such as friction force and friction energy. Based on the interface atomic theory, the present invention can accurately calculate the unit friction coefficient of the tooth pair flank surface area by analyzing the thermal vibration under the excitation of the interface potential energy field, thereby accurately solving parameters such as friction force and friction energy consumption. BRIEF DESCRIPTION OF THE DRAWINGS

[0155] Figure 1It is a schematic flow chart of the present invention;

[0156] Figure 2 This is a model diagram of the blade tooth flank-workpiece friction pair of the present invention. Figure 2 (1) is the structure of the square shoulder milling cutter, and (2) is the instantaneous contact state between the flank face of the cutter tooth and the workpiece;

[0157] Figure 3 This is the equivalent stress distribution diagram of the flank of the tooth 1 of the present invention;

[0158] Figure 4 This is the equivalent stress curve at different positions of each cross section of the back face of the tooth 1 of the present invention. Figure 4 (a) is X i = 0.8mm equivalent stress at each node, (b) is X i = 2.5mm equivalent stress at each node, (c) is X i =Equivalent stress at each node of section C of 4.2mm;

[0159] Figure 5 This is the upper boundary diagram of the instantaneous wear of the flank of the cutter tooth 1 of the present invention;

[0160] Figure 6 This is the equivalent strain curve at different positions of each cross section of the back face of the tooth 1 of the present invention. Figure 6 (a) is X i = 0.8mm, and (b) is the equivalent stress strain of each node at X i = 2.5mm each node equivalent strain, (c) is X i =4.2mm equivalent strain at each node;

[0161] Figure 7 This is the lower boundary diagram of the instantaneous wear of the flank surface of the cutter tooth 1 of the present invention;

[0162] Figure 8 This is a unit representation diagram of the flank area of ​​the milling cutter tooth pair of the present invention;

[0163] Figure 9 This is a physical picture of the square shoulder milling cutter of the present invention;

[0164] Figure 10 This is a diagram of the milling experimental processing and vibration testing system of the present invention;

[0165] Figure 11 This is a time domain signal diagram of the workpiece cutting vibration of the present invention;

[0166] Figure 12 This is a model diagram for calculating the friction speed of the rear cutter area unit of the milling cutter tooth pair of the present invention;

[0167] Figure 13 This is a model diagram for solving the cutting-in and cutting-out periods of the milling cutter of the present invention;

[0168] Figure 14 This is a diagram showing the selection of characteristic points on the back face of the tooth pair of the present invention;

[0169] Figure 15 This is the friction velocity diagram from the cutting-in to the cutting-out stage of the three characteristic points of the blade teeth of the present invention. Figure 15 (1) is the friction speed of the three tooth feature points in the cutting-in stage, (2) is the friction speed of the three tooth feature points in the cutting-in second stage, (3) is the friction speed of the three tooth feature points in the cutting-in middle stage, (4) is the friction speed of the three tooth feature points in the cutting-out second stage, and (5) is the friction speed of the three tooth feature points in the cutting-out stage;

[0170] Figure 16 This is a finite element simulation model diagram of the present invention. Figure 16 Among them, (1) is the workpiece model, (2) is the shoulder milling cutter model;

[0171] Figure 17 This is a temperature simulation diagram under the thermomechanical coupling field of the present invention;

[0172] Figure 18 This is a simulation diagram of equivalent stress under the thermal-mechanical coupling field of the present invention;

[0173] Figure 19 This is a diagram of a method for selecting points in the friction contact area of ​​the flank face of a tooth pair according to the present invention;

[0174] Figure 20 It is a diagram of the equivalent stress decomposition method of the present invention;

[0175] Figure 21 This is the normal stress diagram from the cutting-in to the cutting-out stage of the three tooth characteristic points of the present invention. Figure 21 (1) is the normal stress of the three tooth feature points in the cutting stage, (2) is the normal stress of the three tooth feature points in the second cutting stage, (3) is the normal stress of the three tooth feature points in the middle cutting stage, (4) is the normal stress of the three tooth feature points in the second cutting stage, and (5) is the normal stress of the three tooth feature points in the cutting stage.

[0176] Figure 22 This is a graph showing the change in friction energy consumption from the cutting-in to the cutting-out stages of the three characteristic points of the blade teeth of the present invention. Figure 22 (1) is the change of friction energy consumption in the cutting stage of the three tooth feature points, (2) is the change of friction energy consumption in the second cutting stage of the three tooth feature points, (3) is the change of friction energy consumption in the middle cutting stage of the three tooth feature points, (4) is the change of friction energy consumption in the second cutting stage of the three tooth feature points, and (5) is the change of friction energy consumption in the cutting stage of the three tooth feature points;

[0177] Figure 23 This is a coordinate diagram of the cumulative boundary extraction method of the tooth flank surface of the present invention, Figure 23(1) is the instantaneous friction energy consumption of the flank face of the tooth pair (t = 24.55s), (2) is the instantaneous energy consumption of each cross-sectional node of the flank face of the tooth pair, and (3) is the cumulative friction energy consumption boundary of the flank face of the tooth pair;

[0178] Figure 24 The instantaneous cutting energy consumption diagram of the back face of the cutter tooth of the present invention is shown in FIG1 , wherein (1) is the energy consumption of the cutter tooth in the initial cutting state, and (2) is the cumulative friction energy consumption of the cutter tooth in the cutting-out state;

[0179] Figure 25 This is the energy consumption boundary point diagram of the blade flank of the present invention. Figure 25 (1) is the boundary of cumulative friction energy consumption on the flank of the simulated tooth, and (2) is the boundary of wear on the flank of the experimental tooth.

[0180] Figure 26 It is the boundary diagram of energy consumption and wear of the flank surface of the cutter teeth under the simulation and experimental conditions of the present invention;

[0181] Figure 27 This is the instantaneous friction coefficient diagram of the three blade feature points of the present invention, Figure 27 Where (1) is the instantaneous friction coefficient of the characteristic point of tooth 1, (2) is the instantaneous friction coefficient of the characteristic point of tooth 2, and (3) is the instantaneous friction coefficient of the characteristic point of tooth 3;

[0182] Figure 28 This is a graph showing the change in friction coefficient from the cutting-in to the cutting-out stage for the three characteristic points of the blade teeth of the present invention. Figure 28 (1) is the change of friction coefficient of the three tooth feature points in the cutting stage, (2) is the change of friction coefficient of the three tooth feature points in the cutting stage, (3) is the change of friction coefficient of the three tooth feature points in the cutting stage, (4) is the change of friction coefficient of the three tooth feature points in the cutting stage, (5) is the change of friction coefficient of the three tooth feature points in the cutting stage (Xi = 0.8 mm);

[0183] Figure 29 is the instantaneous friction stress diagram of the three characteristic points of the blade teeth of the present invention, Figure 29 Where (1) is the instantaneous friction stress at the characteristic point of tooth 1, (2) is the instantaneous friction stress at the characteristic point of tooth 2, and (3) is the instantaneous friction stress at the characteristic point of tooth 3;

[0184] Figure 30 This is a graph showing the change in friction stress from cutting in to cutting out at the three characteristic points of the blade teeth of the present invention (Xi=0.8mm). Figure 30 (1) is the friction stress change of the three tooth feature points during the cutting-in stage, (2) is the friction stress change of the three tooth feature points during the cutting-in stage, (3) is the friction stress change of the three tooth feature points during the cutting-in stage, (4) is the friction stress change of the three tooth feature points during the cutting-out stage, and (5) is the friction stress change of the three tooth feature points during the cutting-out stage. DETAILED DESCRIPTION

[0185] To make the objectives, technical solutions, and advantages of the present invention more clearly apparent, the present invention is described below using specific embodiments shown in the accompanying drawings. However, it should be understood that these descriptions are merely illustrative and are not intended to limit the scope of the present invention. In addition, in the following description, descriptions of well-known structures and technologies are omitted to avoid unnecessary confusion of the concepts of the present invention.

[0186] Specific implementation method: Figure 1-Figure 30 This embodiment describes a method for calculating the dynamic characteristics of the friction coefficient of the tooth pair flank face of a square shoulder milling cutter, including the following steps: Step 1: a method for calculating the area unit of the tooth pair flank face of the milling cutter; Step 2: based on Step 1, calculating the friction velocity of the area unit of the tooth pair flank face of the milling cutter; Step 3: a method for extracting the characteristic parameters of the thermal-mechanical coupling field of the tooth pair flank face of the milling cutter; Step 4: constructing a distribution function of the instantaneous friction energy consumption of the tooth pair flank face of the milling cutter; Step 5: a method for verifying the cumulative friction energy consumption of the tooth pair flank face of the milling cutter; Step 6: a method for calculating the instantaneous friction coefficient and instantaneous friction stress of the tooth pair flank face of the milling cutter. A contact model of the instantaneous friction pair of the tooth pair flank face is constructed to characterize the instantaneous contact friction area of ​​the cutter and the tool, and an area unit is selected in the friction contact area. A method for calculating the area unit is given and a friction velocity distribution function and a normal stress distribution function on the area unit are constructed. The friction velocity distribution function and the normal stress distribution function are then used to construct the instantaneous friction energy consumption, the instantaneous friction coefficient, and the instantaneous friction stress distribution function based on the atomic interface theory. The characteristic point selection method of the friction contact zone of the tooth pair flank face is used to select the boundary characteristic points of the energy consumption distribution surface and construct the energy consumption boundary curve. The correctness of the solution method is verified by correlation analysis with the experimental tooth wear boundary curve.

[0187] Step 1: Calculation method of the area unit of the milling cutter tooth pair flank face:

[0188] During the cutting process, the milling cutter's contact moment changes due to the influence of the milling cutter's own structure and vibration. Therefore, it is very important to study the contact relationship between the cutter tooth flank and the processing transition surface. The relationship between the milling cutter structure and the instantaneous contact of the cutter is as follows: Figure 2 shown.

[0189] Table 1 Variable explanation of square shoulder milling cutter structure and instantaneous cutting state of cutter teeth

[0190]

[0191] Figure 2 (1) The measurement method of the axial and radial errors of the milling cutter:

[0192] Δr i =r max -r i (i=1,2···m) (1)

[0193] Where Δr i is the radial error of the i-th tooth, r i is the turning radius of the i-th tooth tip of the milling cutter, where i=1,2,3, r max It is the maximum turning radius of the three cutting edge points of the milling cutter.

[0194] The axial error is calculated as follows:

[0195] Δz i =l1-l i (i=1,2···m) (2)

[0196] Where Δz i is the axial error of the i-th tooth, l1 is the distance from the lowest point of the milling cutter to the end face, l i is the distance from the lowest point to the end face of the i-th tooth.

[0197] Figure 2 (2) In the tooth i coordinate system o i -a i b i c i With the milling cutter structure coordinate system O s -The XYZ rotation matrix I1 and translation matrix M1 are:

[0198]

[0199] Milling cutter structure coordinate system O s -XYZ and milling cutter cutting coordinate system under vibration O c -UVW instantaneous rotation matrix I2 is:

[0200]

[0201] in, is the instantaneous angle between the V axis and the Y axis in the UVW plane:

[0202]

[0203] Where, is the angle between the V axis and the Y axis in the UVW plane at the time when the milling cutter initially cuts in, that is, at time t=0:

[0204]

[0205] where a e is the cutting width.

[0206] Milling cutter cutting coordinate system O under vibration c-UVW and the instantaneous rotation matrix I3, I4, and the instantaneous translation matrix M2 of the milling cutter cutting coordinate system o0-uvw without vibration are:

[0207]

[0208]

[0209] Among them, θ1(t) is the instantaneous angle between the projection of the W axis on the vo0w plane and the w axis, θ2(t) is the instantaneous angle between the projection of the W axis on the uo0w plane and the w axis, A x (t), A y (t), A z (t) are the vibration displacements of the milling cutter along the x, y, and z axes, respectively.

[0210] The instantaneous translation matrix M3 of the milling cutter cutting coordinate system o0-uvw and the workpiece coordinate system o-xyz without vibration is:

[0211]

[0212] Where x o0 (t),y o0 (t),z o0 (t) is the origin o of the milling cutter cutting coordinate system without vibration o Instantaneous position coordinates in the workpiece coordinate system o-xyz;

[0213]

[0214] Among them, v f is the feed speed of the milling cutter, L0 is the length of the workpiece, W0 is the width of the workpiece, H0 is the height of the workpiece, a p is the cutting depth of the workpiece;

[0215] The trajectory of the milling cutter center point O under vibration c The specific solution methods for variables such as (x, y, z), milling cutter posture angle θ(t), and milling cutter direction angle θ'(t) are as follows:

[0216] (1) Milling cutter cutting coordinate system O under vibration c -The movement trajectory of the UVW coordinate origin O c (x, y, z) is:

[0217] O c (x,y,z)=[x,y,z,1] T =M3·[A x (t),A y (t),A z (t),1] T (11)

[0218] (2) The instantaneous angle θ(t) between the W axis and the w axis is:

[0219]

[0220] Among them, θ(t) is the instantaneous attitude angle of the milling cutter; l is the overhang length of the milling cutter.

[0221] (3) The angles between the projections of the W axis on the vo0w and uo0w planes and the W axis are:

[0222]

[0223] (4) θ'(t) is the angle between the projection of the W axis on the uo0w plane and the v axis, which can be calculated as follows:

[0224]

[0225] (5) Tooth coordinate system o i -a i b i c i Conversion relationship matrix with workpiece coordinate system o-xyz as follows:

[0226]

[0227] (6) In the workpiece coordinate system, the secondary cutting edge l' f The equation is:

[0228]

[0229] in, It is the distance from any point on the secondary cutting edge of the tooth to the tip of the tool. k' is the total length of the tooth auxiliary cutting edge, r is the tooth flank angle, λ' s is the inclination angle of the secondary edge of the tooth flank;

[0230] (7) Order Then the tip point of tooth i is o i The motion trajectory o in the workpiece coordinate system i (x, y, z) is as shown in formula (17):

[0231]

[0232] (8) In the workpiece coordinate system, the back face of the tooth pair A′ i Processing transition surface B with workpiece i Friction pairs m As shown in formula (18):

[0233]

[0234] Among them, the upper and lower boundaries of instantaneous friction wear formed on the flank surface of the tooth pair during the cutting process are shown in formula (19);

[0235]

[0236] Among them, l u is the upper friction boundary of the tooth pair flank friction pair, l d It is the lower friction boundary of the flank friction pair of the tooth pair.

[0237] In the workpiece coordinate system, the tooth pair back face equation is as follows:

[0238]

[0239] It is the back face of the tooth. Each edge of the back cutting edge of the tooth.

[0240] Workpiece machining transition surface B in the workpiece coordinate system i The solution method is shown in formula (21).

[0241]

[0242] in, The moment when the tool cuts into the workpiece. To complete the moment when the cutting tool cuts out the workpiece instantaneously.

[0243] Figure 2 (2) In the u The upper boundary of the instantaneous wear of the milling cutter teeth is analyzed by material mechanics. During the instantaneous cutting process of the cutter teeth, when the equivalent stress σ on the secondary cutting edge of the cutter teeth is greater than the yield strength σ of the material, s When the wear of the cutting edge is too great, the material in the cutting edge area will fall off. Therefore, the upper boundary of the wear of the cutting teeth can be determined by using the equivalent stress as the criterion, as shown in formula (22).

[0244] σ≥σ s (twenty two)

[0245] Figure 3 In the figure, take three parallel to Y i The cross sections of the shaft are C1, C2, and C3, and points are taken at equal intervals on the three cross sections to draw the equivalent stress curves of the points on each cross section. Figure 3 shown.

[0246] Figure 2 (2) In the dis the lower boundary of the instantaneous wear of the milling cutter teeth. During the entire milling process, from the entry to the exit of the cutter teeth, the equivalent strain exists in both the contact area and the non-contact area of ​​the milling cutter tooth flank. The equivalent strain value in the friction contact area is large and gradually decreases along the normal vector direction of the cutting edge and suddenly changes at the lower boundary of the instantaneous wear. Therefore, the node of the lower boundary of the cutter tooth flank wear can be identified by the equivalent strain change rate, as shown in Equation (23).

[0247]

[0248] Where ε is the equivalent strain, ε' is the equivalent strain rate, and Y i is the ordinate of the tooth measurement coordinate system.

[0249] By characterizing the instantaneous contact relationship of the friction pair, characteristic points are selected in the instantaneous contact friction area of ​​the flank face of the tooth pair, and the instantaneous contact area unit is solved. The solution method is as follows.

[0250] Figure 8 In the figure, ds is the instantaneous contact area unit of the back face of the tooth pair; da i is the area unit length in plane a i o i b i Projection on a plane; db i Area unit width in plane a i o i b i Projection on the plane; γ is the direction of the normal vector of the area element and c i The angle between the axes, ds, is calculated as follows.

[0251]

[0252] In formula (24), γ(a i ,b i ,c i ) function is constructed as shown in formula (25).

[0253]

[0254] In step 2, the method for calculating the friction velocity per unit area of ​​the flank surface of the milling cutter tooth pair is as follows:

[0255] The tooth error of a selected square shoulder milling cutter was experimentally measured, along with the vibration signal throughout the entire machining process. This cutting experiment was conducted on a Dalian Machine Tool (VDL-1000E) machining center. The cutter had a diameter of 25 mm and three teeth, and the workpiece dimensions were 200 mm × 100 mm × 20 mm. The milling method was climb milling, and the geometric characteristics of the milling process were straight sidewalls. The cutter's entry and exit points were determined during the milling process. The square shoulder milling cutter and milling parameters are shown below.

[0256] Table 2 Milling parameters

[0257]

[0258] Before the milling experiment, the above-mentioned square shoulder milling cutter tooth error measurement method was used to measure the axial and radial tooth errors of the upper shoulder milling cutter using a tool setter, as shown in Table 3.

[0259] Table 3 Radial error and axial error of the cutter teeth

[0260]

[0261] In the actual cutting process, the milling cutter vibrates due to the impact force during the cutting process. Therefore, it is necessary to use a transient signal test and analysis system to detect the vibration acceleration signal generated by the cutting force on the workpiece. Since the tool is in a continuous motion state with the spindle during the cutting process, the tool cutting edge is always in contact with the workpiece and accompanied by cutting outflow, and its vibration signal is difficult to detect. Therefore, in order to avoid the acceleration sensor from interfering with the workpiece when it is installed on the spindle, the sensor is placed on the upper surface of the workpiece and the vibration signal is collected. The experimental processing site and vibration test operation are as follows Figure 10 shown.

[0262] The contact state between the flank face of the tooth pair and the workpiece transition surface changes dynamically during the cutting process, causing the friction velocity at the center point of the area unit of the flank face of the tooth pair to change dynamically at all times. The solution method for the center point of the area unit is as follows.

[0263] Solving formula (17) to obtain the parameter equation of the trajectory of any point on the cutter tooth is as follows:

[0264]

[0265] Taking the partial derivative of the trajectory of any point on the tooth with respect to time in equation (26), we can obtain the arbitrary component velocity along the x, y, and z axes of the workpiece coordinate system as follows:

[0266]

[0267] In formula (27), v nx is the component velocity along the x-axis; vny is the component velocity along the y-axis; v nz is the component velocity along the z-axis.

[0268] Relative motion speed v of any point n The solution is as follows:

[0269]

[0270] Relative speed v n The unit vectors in the workpiece coordinate system are as follows:

[0271]

[0272] The intersection point o between the back face of the cutter tooth and the transition surface of the workpiece r as follows:

[0273]

[0274] Over r Point and the common tangent plane P with the back face of the tooth pair and the workpiece processing transition surface i as follows:

[0275]

[0276] Make v n On the common section P i The projection on and passes through point o r Unit vector in the projection direction as follows:

[0277]

[0278] Among them, l px is a unit vector Component vector in the x-axis direction; l py is a unit vector Component vector in the y-axis direction; l pz is a unit vector The component vector in the z-axis direction.

[0279] In the workpiece coordinate system, the friction velocity v at any point on the back tool surface is m for:

[0280] v m =v n cosθ m (33)

[0281] Among them, θ m is the relative velocity v n With unit vector The angle between them is calculated as follows:

[0282] θ m =π-θ c (34)

[0283]

[0284] In formula (35), θ c is the relative velocity v n With friction speed v m The angle between them.

[0285] In the workpiece coordinate system, the friction velocity direction vector of any point on the secondary back tool surface is The solution is as shown in formula (36).

[0286]

[0287] Among them, v mx 、v my 、v mz is the friction velocity of the point on the back face of the cutter tooth in the workpiece coordinate system, which is converted to the cutter tooth coordinate system through coordinate transformation as shown in formula (37):

[0288]

[0289] Among them, v mai The point on the back face of the tooth is along a in the tooth coordinate system. i Friction velocity in the axial direction; v mbi The point on the back face of the tooth pair is located along b in the tooth coordinate system. i Friction velocity in the axial direction; v mci The point on the back face of the cutter tooth is located along c in the cutter tooth coordinate system. i Friction speed in the axial direction.

[0290] Therefore, the friction velocity v at any point in the tooth coordinate system is m for:

[0291]

[0292] In order to characterize the dynamic changes of the friction characteristic parameters of the area unit of the friction contact area on the back face of the cutter tooth from cutting in to cutting out, the solution model for the instantaneous cutting in to cutting out of the single-rotation cutter tooth of the milling cutter is proposed as shown below.

[0293] Figure 13 In, η ii-1 is the angle between the i-th tooth and the i-1-th tooth, φ i is the angle between the entry and exit of the i-th tooth, and the solution is as shown in equations (39) to (41).

[0294]

[0295] In formula (39), T i T is the time period from the i-th tooth cutting in to the cutting out, i s is the cutting time of the i-th tooth, T i e is the cutting time of the i-th tooth, κ is the k-th cutting time of the i-th tooth, φ i is the milling contact angle of the milling cutter, and ω is the angular velocity of the milling cutter. i is the time when the i-th tooth instantly cuts into the workpiece.

[0296]

[0297] Similarly, in formula (40), T i-1 T is the time period from the i-1th tooth cutting in to the cutting out, i-1 s is the cutting time of the i-th tooth, T i-1 e is the cutting time of the i-1th tooth, η ii-1 is the angle between the i-th tooth and the i-1-th tooth, where φ i The solution method is shown in formula (41).

[0298]

[0299] By using the point selection method of the technical feature sheet, the three tooth flanks are parallel to the tooth coordinate system. i The axis is divided into 10 sections. The third section is taken and three points k0, k1, k2, and k3 are equally spaced on the upper and lower boundaries of the section. Point k2 is used as the example point for solution. The three teeth of the milling cutter are selected. The entire cutting process is from cutting in to cutting out. The effective cutting time period of the three teeth is solved. The five cutting time periods T of the three teeth k2 point from cutting in to cutting out are solved. 11 -T 15 .

[0300] Table 4 Selected cutting time of three teeth of milling cutter

[0301]

[0302] Through the two technical features, the friction speed of the three teeth and five cutting time periods is simulated, and the friction speed is calculated as follows: Figure 15 shown.

[0303] Step 3, a method for extracting characteristic parameters of the thermal-mechanical coupling field of the flank of the milling cutter tooth pair:

[0304] In order to extract the temperature and equivalent stress based on the thermal-mechanical coupling field, the thermal-mechanical coupling field simulation of the shoulder milling cutter was carried out. The Johnson-Cook constitutive model was used to take the vibration signal measured in the experiment and the milling cutter trajectory and tooth trajectory as the finite element simulation boundary conditions for finite element simulation. The finite element tool and workpiece simulation model is as follows: Figure 18 shown.

[0305] The method of selecting points in the friction area of ​​the blade flank is as follows: Figure 19 As shown, make a measurement parallel to the tooth coordinate system Y i The cross section in the axial direction has a spacing of Δl and the cross sections are m1,…m i …, m n On each section, take points at equal intervals from the upper and lower edges of the tooth wear, with the interval between the two points being Δk,l mi is the distance between the i-th section and the origin of the tooth coordinates. Any point k on the section i The coordinate solution method is shown in formula (42).

[0306] Figure 19 In the flank, select any point k i Coordinate k in the tooth coordinate system i (a ki , b ki , c ki ) as shown in (42):

[0307]

[0308] Where l is the distance between two adjacent points selected in the same section.

[0309] Select point k i Converting to the workpiece coordinate system, the motion trajectory in the workpiece coordinate system is obtained as formula (43):

[0310]

[0311] Figure 20 In, F p is the normal stress on the tooth flank microelement, passing through the tooth flank node and perpendicular to the tooth flank and c i The axis angle is θ ci ; τ is the equivalent stress of the tooth flank at the network node under the thermal-mechanical coupling field; F1, F2, and F3 are the equivalent stresses in the direction of the tetrahedron microelement; θ k1 ,θ k2 ,θ k3 are the angles between the equivalent stress and the normal stress on the three edges; the equivalent stress is expressed in the component tooth coordinate system on the tetrahedron by vector It is expressed as shown in formula (44):

[0312]

[0313]

[0314] Therefore, from equations (44) and (45), we can get θ k1 ,θ k2 ,θ k3 As shown in formula (46).

[0315]

[0316] Solve for the normal stress F p As shown in formula (47).

[0317] F p (a i ,b i ,c i )=F1(a i ,b i ,c i )·cosθ k1 +F2(a i ,b i ,c i )·cosθ k2 +F3(a i ,b i ,c i )·cosθ k3 (47)

[0318] Step 4, constructing a method for distributing the instantaneous friction energy consumption of the flank face of the milling cutter tooth pair;

[0319]

[0320] In formula (48), E is the instantaneous absorbed energy at time t, and υ is the forced vibration frequency of the atom as shown in formula (49):

[0321]

[0322] The instantaneous energy distribution function of absorption is as follows:

[0323]

[0324] Where: ψ is the lattice constant (2.9506×10 -10 m); h is Planck's constant (h=6.62607015×10 -34 J·s); δ is the Boltzmann constant (δ=1.380649×10 -23 J / K);v m is the relative friction speed; tes1 With t es2 are the instantaneous initial time and end time of energy absorption respectively; Ω The calculation method for the atomic interface temperature rise is as follows:

[0325]

[0326] Where: m is the relative atomic mass of the atom, which is 4.34×10 -26 kg, ω n The atomic natural frequency is 4.39×10 11 rad / s, χ is the excitation force of the interface potential field, and is 1×10 -9 N.

[0327] In step 3, the friction energy consumption is obtained by simulating three teeth in five time periods. Figure 22 shown.

[0328] Step 5, verifying the cumulative friction energy consumption on the flank of the milling cutter tooth pair;

[0329] The cumulative energy consumption is accumulated by the instantaneous energy consumption boundary. In order to verify the correctness of the cumulative energy consumption distribution function solution model, the following verification method for the cumulative friction energy consumption of the auxiliary flank is proposed. The mutation node identification method at the section of the auxiliary flank of the tooth is as follows:

[0330] G(X i ,Y imax )=0 (52)

[0331] Y imax =max(Y i (t)) (53)

[0332] Using the instantaneous boundary of the cutter teeth, the whole cutting process from the cutter teeth entering to the cutter teeth cutting out of the workpiece is obtained. i The instantaneous boundary Y at position i Maximum Y imax , and finally get imax The cumulative friction energy consumption boundary composed of.

[0333] The energy consumption distribution surface of the tooth flank is reconstructed by selecting characteristic points when the three teeth cut out the workpiece, and the energy consumption boundary curve is extracted by using the characteristic point selection method proposed in step 3. The correlation coefficient is used to perform correlation analysis with the wear boundary of the experimental tooth pair flank surface as shown below.

[0334]

[0335] Where Coυ is the covariance calculation formula, X i , Y iis the value of each characteristic point of the boundary curve measured in the tool tooth measurement coordinate system, and is the average value of the boundary curve at each point; the correlation coefficient ρ is calculated as follows:

[0336]

[0337] in and is the standard deviation, as shown below:

[0338]

[0339]

[0340] The closer ρ is to 1, the stronger the correlation between the two related variables is, and the closer it is to 0, the weaker the correlation between the two related variables is. It is generally believed that a correlation below 0.40 is low; 0.40-0.69 is moderate; 0.70-0.89 is high; 0.90-1.00 is very high.

[0341] In order to verify the correctness of the energy consumption calculation method of the cutting edge, the energy consumption surface curve obtained by simulation and the friction and wear boundary curve measured by experiment were used for correlation analysis.

[0342] The energy consumption when the cutter teeth initially cut into the workpiece and the cumulative energy consumption of the workpiece are shown in the curve Figures 24-26 shown.

[0343] The correlation coefficient between the two boundary curves obtained by the solution method of equations (59) to (61) is 0.9977, which shows that the two boundaries have a strong correlation, and further explains the correctness of using the energy consumption boundary to verify the flank wear of the cutter tooth.

[0344] Step 6: Constructing a method for the instantaneous friction coefficient and instantaneous friction force distribution function of the back face of the milling cutter tooth pair

[0345] The normal pressure of the friction contact area unit is F n , the friction coefficient is μ, then the work dS done by the unit friction force in time dt is:

[0346] dS=μ(a i ,b i ,c i ,t)·F n (a i ,b i ,c i ,t)·v m (a i ,b i ,c i ,t)·dt (58)

[0347] Assume that during the friction motion of the tool interface, all the friction work is converted into the heat energy of the system.

[0348] dS=dE (59)

[0349] The friction coefficient distribution function can be obtained by solving equation (59) as equation (60):

[0350]

[0351] The friction stress distribution function obtained by solving equations (58) to (60) is shown in equation (61):

[0352] f p (a i ,b i ,c i ,t)=μ(a i ,b i ,c i ,t)·F p (a i ,b i ,c i ,t) (61)

[0353] The friction coefficient is obtained by simulating the three teeth and five time periods in step 3 as follows: Figure 27 and 28 shown.

[0354] The friction stress is obtained by simulating the characteristic points selected in the five time periods of the three teeth in step 3. Figure 29 and 30 shown.

[0355] It should be noted that the terms used herein are only for describing specific embodiments and are not intended to limit the exemplary embodiments according to the present application. As used herein, unless the context clearly indicates otherwise, the singular form is also intended to include the plural form. In addition, it should be understood that when the terms "comprise" and / or "include" are used in this specification, they indicate the presence of features, steps, operations, devices, components and / or combinations thereof.

[0356] It should be noted that in the above embodiments, as long as the technical solutions are not contradictory, they can be permuted and combined. Those skilled in the art can exhaust all possibilities based on the mathematical knowledge of permutations and combinations. Therefore, the present invention will no longer describe the technical solutions after permutations and combinations one by one, but it should be understood that the technical solutions after permutations and combinations have been disclosed by the present invention.

[0357] The foregoing description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Those skilled in the art will readily appreciate that various modifications and variations of the present invention are possible. Any modifications, equivalent substitutions, or improvements made within the spirit and principles of the present invention are intended to be within the scope of protection of the present invention.

Claims

1. A method for calculating the dynamic characteristics of the friction coefficient of the tooth pair flank of a square shoulder milling cutter, characterized in that: include: Step 1, a unit solution method for the flank area of ​​the milling cutter tooth pair; Step 2: Based on step 1, calculate the friction velocity per unit area of ​​the flank face of the milling cutter tooth pair; Step 3, a method for extracting characteristic parameters of the thermal-mechanical coupling field of the flank face of the milling cutter tooth pair; Step 4, constructing the instantaneous friction energy consumption distribution function of the flank face of the milling cutter tooth pair; Step 5, verification method of cumulative friction energy consumption of the flank face of the milling cutter tooth pair; Step 6, a method for calculating the instantaneous friction coefficient and the instantaneous friction stress of the flank face of the milling cutter tooth pair; The cumulative friction energy consumption in step 5 is accumulated by the instantaneous energy consumption boundary. In order to verify the correctness of the cumulative energy consumption distribution function solution model, the verification method of the cumulative friction energy consumption of the secondary flank is proposed as follows; Cumulative wear boundary at the flank section of the tooth pair G The identification method is as follows: （52） （53） Using the instantaneous boundary of the cutter teeth, the whole cutting process from the cutter teeth entering to the cutter teeth cutting out of the workpiece is obtained. Instantaneous boundary at position Maximum , and finally get The cumulative friction energy consumption boundary G ; The energy consumption distribution surface was reconstructed by selecting characteristic points on the flank surface of the three teeth when the teeth cut out the workpiece. The energy consumption boundary curve was extracted by using the characteristic point selection method. The correlation coefficient was used to analyze the wear boundary of the flank surface of the experimental tooth pair. The results are shown below: （54） In the formula is the covariance calculation formula, , is the value of each characteristic point of the boundary curve measured in the tool tooth measurement coordinate system, and is the average value of the boundary curve at each point; Correlation coefficient The calculation is as follows: （55） in is the equivalent stress; in and is the standard deviation, as shown below: （56） （57） The closer it is to 1, the stronger the correlation between the two related variables is; the closer it is to 0, the weaker the correlation between the two related variables is. The step 6 comprises: The normal pressure of the friction contact area unit is , the friction coefficient is ， Tooth coordinate system , then in The work done by friction per unit time for: （58） Assume that during the friction motion of the tool interface, all the friction work is converted into the heat energy of the system. （59） The friction coefficient distribution function can be obtained by solving equation (59) as equation (60): （60） in: is the lattice constant; is Planck's constant; is the Boltzmann constant; is the atomic interface temperature rise; is the normal stress on the infinitesimal element of the tooth flank surface; The friction stress distribution function obtained by solving equations (58) to (60) is shown in equation (61): （61）。 2. The method for calculating the dynamic characteristics of the friction coefficient of the tooth pair flank of a square shoulder milling cutter according to claim 1, characterized in that: The step 1 comprises: Method for measuring axial and radial errors of milling cutters: （1） in, For the The radial error of each tooth, For milling cutter The turning radius of the cutting edge of the tooth is: The maximum turning radius of the three cutting edge points of the milling cutter; The axial error is calculated as follows: （2） in, For the The axial error of each tooth, is the distance from the lowest point of the milling cutter to the end face, For the The distance from the lowest point of each tooth to the end face; Teeth Coordinate system Coordinate system of milling cutter structure The rotation matrix , translation matrix They are: （3） in For the The instantaneous position angle of each tooth; Milling cutter structure coordinate system Milling cutter cutting coordinate system under vibration The instantaneous rotation matrix for: （4） in, for Axis and Axis Instantaneous angle in the plane: （5） Where, is the initial cutting moment of the milling cutter, that is t =0 time Axis and Axis The angle within the plane, that is: （6） in is the cutting width; Milling cutter cutting coordinate system under vibration Milling cutter cutting coordinate system without vibration The instantaneous rotation matrix , the instantaneous translation matrix They are: （7） （8） in, for The axis is Projection on the plane and The instantaneous angle of the axis, for Axis Projection of the surface and The instantaneous angle of the axis, Milling cutter edge Vibration displacement in the axial direction; Milling cutter cutting coordinate system without vibration With the workpiece coordinate system The instantaneous translation matrix for: （9） Where, The origin of the milling cutter cutting coordinate system without vibration In the workpiece coordinate system The instantaneous position coordinates in ; （10） in, is the milling cutter feed speed, is the width of the workpiece, is the height of the workpiece, is the cutting depth of the workpiece; The trajectory of the milling cutter center point under vibration Milling cutter attitude angle Milling cutter direction angle The specific solution method for variables is as follows: (1) Milling cutter cutting coordinate system under vibration The trajectory of the coordinate origin for: （11） (2) Axis and Instantaneous angle of the axis θ(t) for: （12） in, θ (t) is the instantaneous attitude angle of the milling cutter; l is the overhang length of the milling cutter; (3) Among them, The axes are noodle, Projection of the surface and The angle between the axes is: （13） (4) for Axis Projection on the plane and The angle between the axes is calculated as follows: （14） (5) Tooth coordinate system With the workpiece coordinate system The conversion relationship matrix is ​​as follows: （15） (6) In the workpiece coordinate system, the secondary cutting edge The equation is: （16） in, It is the distance from any point on the secondary cutting edge of the tooth to the tip of the tool. is the total length of the secondary cutting edge of the cutter tooth, is the secondary deflection angle of the tooth flank, is the inclination angle of the secondary edge of the tooth flank; (7) Order , then the blade teeth Tip point Motion trajectory in the workpiece coordinate system As shown in formula (17): （17） (8) The back face of the tooth pair in the workpiece coordinate system Machining transition surface with workpiece Friction pair As shown in formula (18): （18） Among them, the upper and lower boundaries of instantaneous friction wear formed on the back face of the tooth pair during the cutting process are shown in formula (19); （19） in, is the upper friction boundary of the tooth pair flank friction pair, The lower friction boundary of the flank friction pair of the tooth pair; (9) In the workpiece coordinate system, the equation of the back face of the tooth pair is: （20） It is the back face of the tooth. Each edge of the tooth back surface; Workpiece machining transition surface in workpiece coordinate system B i The solution method is shown in formula (21); （21） in, The moment when the tool cuts into the workpiece. To complete the moment when the cutting tool cuts out the workpiece instantaneously; Through material mechanics analysis, during the instantaneous cutting process of the cutter teeth, when the equivalent stress on the cutting edge of the cutter teeth Greater than the yield strength of the material When , the material in the cutting edge area will fall off, so the upper boundary of the wear of the cutter teeth can be judged by using the equivalent stress as shown in formula (22); （22） Where, is the yield strength; Identify the equivalent stress at each section as the yield strength σ s The coordinate values ​​corresponding to the characteristic point positions are connected on all cross sections in the cutter tooth coordinate system to construct the instantaneous friction upper boundary curve of the milling cutter tooth flank; During the entire milling process, there is equivalent strain in both the contact area and the non-contact area of ​​the flank face of the milling cutter tooth from the cutting edge to the cutting edge, while the equivalent strain value in the friction contact area is large and gradually decreases along the normal vector direction of the cutting edge and undergoes a sudden change at the lower boundary of instantaneous wear. Therefore, the node at the lower boundary of the flank face wear can be identified by the rate of change of equivalent strain, as shown in Equation (23); （23） Where, is the equivalent strain, is the equivalent strain rate, is the ordinate of the tooth measurement coordinate system; By characterizing the instantaneous contact relationship of the friction pair, characteristic points are selected in the instantaneous contact friction area of ​​the tooth pair flank face, and the instantaneous contact area unit is solved. The solution method is as follows; is the instantaneous contact area unit of the flank face of the tooth pair; is the area unit length in the plane projection onto a plane; Area unit width in plane projection onto a plane; is the direction of the area element normal vector and The angle between the axes, The solution is as follows: （24） In formula (24), The function is constructed as shown in formula (25); （25）。 3. The method for calculating the dynamic characteristics of the friction coefficient of the tooth pair flank of a square shoulder milling cutter according to claim 2, characterized in that: The step 2 includes: The parametric equation of the trajectory of any point on the tooth is obtained by solving formula (17) as follows: （26） Taking the partial derivative of the trajectory of any point on the tooth with respect to time, we can obtain The arbitrary component speed in the axial direction is as follows: （27） In formula (27), For the Component velocity in the axial direction; For the Component velocity in the axial direction; For the Component velocity in the axial direction; Relative motion speed at any point The solution is as follows: （28） Relative speed Unit vector in the workpiece coordinate system as follows: （29） The intersection of the tooth flank and the workpiece transition surface as follows: （30） Pass Point and common tangent plane with the back face of the cutter tooth and the transition surface of the workpiece as follows: （31） Do On the public cutting surface The projection on and through the point Unit vector in the projection direction as follows: （32） in, is a unit vector exist Component vector in the axis direction; is a unit vector exist Component vector in the axis direction; is a unit vector exist Component vector in the axis direction; In the workpiece coordinate system, the friction speed at any point on the back tool surface is for: （33） in, Relative motion speed With unit vector The angle between them is calculated as follows: （34） （35） In formula (35), Relative motion speed and friction speed The angle between In the workpiece coordinate system, the friction velocity direction vector of any point on the secondary back tool surface is Solve as formula (36); （36） in, is the friction velocity of the point on the back face of the cutter tooth in the workpiece coordinate system, which is converted to the cutter tooth coordinate system through coordinate transformation as shown in formula (37): （37） in, The point on the back face of the cutter tooth is along the tooth coordinate system Friction speed in the axial direction; The point on the back face of the tooth pair is along the tooth coordinate system b i Friction speed in the axial direction; The point on the back face of the cutter tooth is along the tooth coordinate system Friction speed in the axial direction; Therefore, the friction velocity at any point in the tooth coordinate system is for: （38） In order to characterize the dynamic changes of the friction characteristic parameters of the area unit of the friction contact area of ​​the tooth flank from cutting in to cutting out, a solution model for the instantaneous cutting in to cutting out of the single-rotation tooth of the milling cutter is proposed. （39） In formula (39), For the The time period from the cutting in to the cutting out of each tooth, For the The cutting time of the blade teeth, For the Each tooth cuts out time, For the Teeth Cutting is performed For the The angle between the cutting edge and the cutting edge, is the angular velocity of the milling cutter, For the The time it takes for a tooth to instantly cut into the workpiece; （40） Similarly, in formula (40), For the The time period from the cutting in to the cutting out of each tooth, For the The cutting time of the blade teeth, For the Each tooth cuts out time, For the The first tooth and the The included angle between the teeth is The solution method is shown in formula (41) （41）。 4. The method for calculating the dynamic characteristics of the friction coefficient of the tooth pair flank of a square shoulder milling cutter according to claim 3, characterized in that: The step 3 includes: in order to extract the temperature and equivalent stress based on the thermal-mechanical coupling field, a thermal-mechanical coupling field simulation of the shoulder milling cutter is performed, and the Johnson-Cook constitutive model is adopted. The vibration signal measured in the experiment and the milling cutter trajectory and the cutter tooth trajectory are used as finite element simulation boundary conditions to perform finite element simulation, and a finite element tool and workpiece simulation model is constructed; The point selection method of the friction area on the back face of the cutter tooth is parallel to the measuring coordinate system of the cutter tooth. The cross-sections in the axial direction are spaced by , the cross sections are On each section, take points at equal intervals from the upper and lower edges of the tooth wear, with the interval between the two being , For the The distance between the section and the origin of the tooth coordinates, any point on the section The coordinate solution method is shown in formula (42); （42） in, The distance between two adjacent points selected in the same section; Select the point Converted to the workpiece coordinate system, the motion trajectory in the workpiece coordinate system is as follows: （43） is the normal stress on the tooth flank microelement, passing through the tooth flank node and perpendicular to the tooth flank and The axis angle is are the equivalent stresses in the directions of the tetrahedron microelement; are the angles between the equivalent stress and the normal stress on the three edges; the equivalent stress is expressed in the component tooth coordinate system on the tetrahedron by vector It is expressed as shown in formula (44): （44） （45） In formula (45), is the unit vector of the normal stress in the normal direction on the infinitesimal area of ​​the tooth pair flank surface; Therefore, from equations (44) and (45), we can get As formula (46); （46） The normal stress is solved as shown in Equation (47); （47）。 5. The method for calculating the dynamic characteristics of the friction coefficient of the tooth pair flank of a square shoulder milling cutter according to claim 4, characterized in that: The step 4 comprises: The change rate of absorbed energy obtained from the interface atomic theory for: （48） In formula (48), For time Absorb energy instantly at all times. is the atomic forced vibration frequency as shown in formula (49): （49） The instantaneous energy distribution function of absorption is as follows (50): （50） in: is the relative friction speed; and are the instantaneous initial time and end time of energy absorption respectively; The calculation method is as shown in formula (51): （51） in: The relative atomic mass of the atom is 4.34×10 -26 kg, The atomic natural frequency is 4.39×10 11 rad / s, The excitation force of the interface potential field is 1×10 -9 N .

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