CN112372372A

CN112372372A - Efficient milling cutter accumulated friction wear boundary identification and verification method

Info

Publication number: CN112372372A
Application number: CN202011439558.1A
Authority: CN
Inventors: 姜彬; 丁旺; 赵培轶; 季嗣珉
Original assignee: Harbin University of Science and Technology
Current assignee: Harbin University of Science and Technology
Priority date: 2020-12-07
Filing date: 2020-12-07
Publication date: 2021-02-19
Anticipated expiration: 2040-12-07
Also published as: CN112372372B

Abstract

The invention discloses a method for identifying and verifying an accumulated friction and wear boundary of a high-efficiency milling cutter, belongs to the technical field of milling cutters, and aims to research the defects that the maximum wear width of a rear cutter face of a cutter tooth changes along with a milling stroke and the formation process of the friction and wear boundary of the rear cutter face of the cutter tooth under the action of milling vibration and cutter tooth error cannot be disclosed by the conventional milling experiment method. The invention provides a method for measuring and characterizing the frictional wear boundary of the rear cutter face of a cutter tooth of an efficient milling cutter, a method for simulating and identifying the instantaneous frictional wear boundary of the rear cutter face of the cutter tooth, a method for calculating the cumulative frictional wear boundary of the rear cutter face of the cutter tooth and an effective model for revealing the forming process of the cumulative frictional wear boundary of the rear cutter face of the cutter tooth.

Description

Efficient milling cutter accumulated friction wear boundary identification and verification method

The technical field is as follows:

the invention belongs to the technical field of milling cutters, and particularly relates to a high-efficiency milling cutter accumulated friction wear boundary identification and verification method.

Background art:

the efficient milling cutter is widely applied to the machining of large titanium alloy structural members in the aerospace field due to the efficient cutting performance, is influenced by milling vibration and cutter tooth errors in the milling process, and uncertainty exists in the formation and evolution of accumulated friction and wear boundaries of the rear cutter face of the cutter tooth of the milling cutter, so that the overall service life of the efficient milling cutter is difficult to accurately evaluate and predict, the workpiece machining quality is unstable, and the production cost is increased.

The uncertainty of the forming process of the frictional wear boundary of the rear cutter face of the cutter tooth of the milling cutter under the influence of milling vibration and cutter tooth errors is the key for predicting the service life of the cutter. At present, although research on frictional wear of a rear cutter face of a milling cutter tooth is available, the research mainly focuses on revealing the change characteristic of the frictional wear width of the rear cutter face of the milling cutter tooth along with the milling stroke through a milling experiment, but the research on the frictional wear width of the rear cutter face of the milling cutter tooth cannot reveal the contact relation between the rear cutter face of the milling cutter tooth and a workpiece along with the change of the milling, and due to experiment limitations, an instantaneous frictional wear boundary of the rear cutter face of the milling cutter tooth cannot be obtained through the milling experiment, so that the relation between the instantaneous and accumulated frictional wear boundary curves of the rear cutter face of the milling cutter tooth and the forming process of the accumulated frictional wear boundary curves cannot be revealed through the milling experiment.

The invention content is as follows:

the invention provides a method for identifying and verifying the accumulated frictional wear boundary of a high-efficiency milling cutter, aiming at overcoming the defects that the forming and evolution process of the accumulated frictional wear boundary of the rear cutter face of the cutter tooth of the traditional milling cutter is difficult to accurately evaluate and predict the service life of the whole high-efficiency milling cutter, and the method utilizes a method for measuring and characterizing the frictional wear boundary of the rear cutter face of the cutter tooth of the milling cutter, a method for identifying the instantaneous frictional wear simulation boundary of the rear cutter face of the cutter tooth of the milling cutter, and a method for calculating the accumulated frictional wear simulation boundary of the rear cutter face of the cutter tooth of the milling cutter to verify the correctness of the method for calculating the accumulated frictional.

The technical scheme adopted by the invention is as follows: a high-efficiency milling cutter accumulated friction wear boundary identification and verification method specifically comprises the following steps:

step A: providing a method for measuring and characterizing the frictional wear boundary of the rear cutter face of the cutter tooth of the efficient milling cutter, constructing a measuring coordinate system of the frictional wear boundary of the rear cutter face of the cutter tooth of the milling cutter, and characterizing the curve shape and the position of the frictional wear boundary of the rear cutter face of the cutter tooth of the milling cutter in the measuring coordinate system;

and B: considering a milling mode, milling vibration, cutter tooth errors and differences of surfaces to be machined of different layers as simulation boundary conditions, and providing an axial layered milling simulation model of the efficient milling cutter and a boundary condition construction method;

and C: carrying out axial layered milling thermal coupling field simulation on the efficient milling cutter by using an axial layered milling simulation model of the efficient milling cutter, extracting an instantaneous temperature, an equivalent stress and an equivalent strain distribution field of a rear cutter face of a cutter tooth of the milling cutter, and providing a method for identifying an instantaneous frictional wear simulation boundary of the rear cutter face of the cutter tooth according to the process of forming the instantaneous frictional wear boundary of the rear cutter face of the cutter tooth of the milling cutter;

step D: and C, acquiring instantaneous frictional wear boundaries of the rear cutter face of the cutter tooth at different moments, analyzing the formation process of the accumulated frictional wear boundaries of the rear cutter face of the cutter tooth, providing a simulation boundary calculation method for the accumulated frictional wear boundaries of the rear cutter face of the cutter tooth of the milling cutter, calculating the gray correlation degree and average relative error of the curve of the accumulated frictional wear boundaries of the rear cutter face of the cutter tooth of the milling cutter obtained through simulation and experiments, and verifying the correctness of the calculation method for the accumulated frictional wear boundaries of the rear cutter face of the cutter tooth of the milling cutter.

Preferably, the step a further comprises the following steps:

step A1: the milling mode of the efficient milling cutter under the vibration action is as follows: in a workpiece coordinate system, reflecting the influence of milling vibration on the cutting process of the efficient milling cutter by using the cutting state of the milling cutter under the biasing and vibration effects of the milling cutter coordinate system;

step A2: determining a milling cutter tooth error and a method for measuring the frictional wear of the rear cutter face of the milling cutter according to the structural characteristics of the efficient milling cutter;

step A3: measuring a relation matrix between a coordinate system by utilizing a workpiece coordinate system, a milling cutter coordinate system, a cutter tooth coordinate system and a rear cutter face friction and wear boundary under the influence of milling vibration and cutter tooth error, and reflecting the influence of the milling vibration and the cutter tooth error on the instantaneous contact relation between the rear cutter face of the cutter tooth and the workpiece;

step A4: and sequentially measuring the frictional wear boundary end points and inflection points of the rear cutter face of the cutter tooth in a cutter tooth rear cutter face wear boundary measurement coordinate system, constructing an upper boundary curve and a lower boundary curve of the frictional wear of the rear cutter face of the cutter tooth of the milling cutter, and determining the frictional wear boundary of the rear cutter face of the cutter tooth.

Preferably, the step B further comprises the following steps:

step B1: considering a milling mode, a cutter tooth error, milling vibration and differences of surfaces to be machined of different layers as simulation boundary conditions, designing an integral structure of an axial layered milling simulation model of the efficient milling cutter, and determining and resolving design variables of the simulation model;

step B2: constructing a simulation model milling unit, solving a milling cutter motion track and an instantaneous cutting attitude angle under the action of vibration, determining a milling unit cross section model, and constructing the milling unit by considering milling vibration and cutter tooth errors;

step B3: in the simulation process, according to the milling cutter motion trail under the vibration action in the axial layered milling experiment, determining the discrete time interval of the milling cutter motion trail points, and resolving the milling cutter motion trail points under the vibration action in the simulation process.

Preferably, the step C further comprises the following steps:

step C1: carrying out thermal coupling field simulation through an efficient milling cutter axial layered milling simulation model, and extracting the distribution conditions of an equivalent stress field, an equivalent strain field and a temperature field of the free instantaneous cutting of the rear cutter face of the cutter tooth of the milling cutter;

step C2: extracting node equivalent stress, equivalent strain and temperature values at different positions of a rear cutter face of the cutter tooth of the milling cutter, constructing a cutter face equivalent stress, equivalent strain and temperature distribution curved surface of the cutter tooth, sequentially making section planes which are perpendicular to the distribution curved surface through nodes on cutting edges in the direction of a midpoint normal vector of the cutting edges on a projection plane of the rear cutter face of the cutter tooth in parallel, and constructing section plane equivalent stress, equivalent strain and temperature distribution curves of the nodes on the section planes at different positions of the rear cutter face of the cutter tooth;

step C3: sequentially fitting equivalent stress, equivalent strain and temperature distribution curves at each section plane of the rear cutter face of the cutter tooth by using a unitary high-order polynomial, and obtaining a node change rate distribution curve by derivation;

step C4: identifying critical characteristic nodes with equivalent stress larger than and closest to yield on all section planes by taking the yield strength of the cutter tooth material as a criterion, wherein characteristic points on the section planes at different positions jointly form an instantaneous frictional wear simulation upper boundary of the cutter tooth rear cutter face in a cutter tooth rear cutter face frictional wear measurement coordinate system;

step C5: and sequentially identifying nodes with obvious abrupt changes of temperature, equivalent stress and equivalent strain change rate at each section plane of the rear cutter face of the cutter tooth, constructing a characteristic curve of the temperature, the equivalent stress and the equivalent strain abrupt changes of the nodes on the rear cutter face of the cutter tooth by taking the abrupt changes as characteristic points in a measurement coordinate system of the frictional wear boundary of the rear cutter face of the cutter tooth, and forming an outermost profile jointly formed by the characteristic curves of the temperature, the equivalent strain and the equivalent strain abrupt changes of the nodes to form an instantaneous frictional wear simulation lower boundary of the rear cutter face of the cutter tooth.

Preferably, the step D further comprises the steps of:

step D1: by means of the instant frictional wear boundary curve of the rear cutter face of the cutter tooth at different milling moments, taking the accumulated frictional wear lower boundary curve as an example, a method for calculating the accumulated frictional wear boundary of the rear cutter face of the cutter tooth of the milling cutter is provided;

step D2: designing a simulation and experiment comparison scheme of upper and lower boundaries of accumulated friction wear of the rear cutter face of the cutter tooth, constructing a simulation upper and lower boundary curve of the accumulated friction wear of the rear cutter face of the cutter tooth of the milling cutter by adopting a calculation method of the curve of the accumulated friction wear boundary of the rear cutter face of the cutter tooth of the milling cutter, and comparing the experiment upper and lower boundary curve of the accumulated friction wear with the simulation upper and lower boundary curve;

step D3: and calculating a grey correlation value and a mean relative error between simulation and experiment accumulated friction and wear boundary curves, analyzing shape similarity and position contact ratio between the simulation and experiment accumulated friction and wear boundary curves, and verifying the correctness of the accumulated friction and wear boundary calculation method.

The invention has the beneficial effects that:

1. the invention fully considers the characteristic information of the whole abrasion boundary of the rear cutter face of the milling cutter tooth, establishes the characteristic point curve of the upper and lower boundaries of the frictional abrasion of the rear cutter face of the milling cutter tooth by establishing the frictional abrasion boundary measuring coordinate system of the rear cutter face of the milling cutter tooth and taking the end points and inflection points on the left and right sides of the frictional abrasion boundary as characteristic points, can represent the shape and position information of the frictional abrasion boundary curve of the rear cutter face of the milling cutter tooth more completely, and is beneficial to disclosing the contact relation of a cutter worker and the forming process of the frictional abrasion boundary in the milling process by measuring the relation matrix among the workpiece coordinate system, the milling cutter coordinate system, the cutter tooth coordinate system and the frictional abrasion boundary of the rear cutter face under the influence of milling vibration and cutter tooth error.

2. The invention fully considers the influence of the milling mode, the milling vibration, the cutter tooth error and the difference of different layers of surfaces to be processed on the structure of the simulation model, considers the milling mode, the milling vibration, the cutter tooth error and the different layers of surfaces to be processed as simulation boundary conditions, and provides a novel design method of the axial layered milling simulation model of the efficient milling cutter.

3. The invention provides a method for identifying upper and lower boundaries of the instantaneous frictional wear simulation of the rear cutter face of the cutter tooth of a milling cutter based on the forming process of the instantaneous frictional wear simulation boundary of the rear cutter face of the cutter tooth of the milling cutter and according to the distribution characteristics of the temperature field, the equivalent stress and the equivalent strain of the instantaneous cutting node of the rear cutter face of the cutter tooth, a method for calculating the cumulative frictional wear simulation boundary of the rear cutter face of the cutter tooth of the milling cutter, a forming process of the cumulative frictional wear boundary of the rear cutter face of the cutter tooth of the milling cutter and a method for verifying the method for calculating the cumulative.

Description of the drawings:

FIG. 1 is a flow chart of a method for calculating the accumulated frictional wear boundary of the rear cutter face of a high-efficiency milling cutter tooth;

FIG. 2 is a state diagram of efficient milling by the milling cutter under the action of vibration;

FIG. 3 is a diagram showing the instantaneous cutting of the milling cutter under vibration;

fig. 4 is a structure of a high-efficiency milling cutter and a tooth error measurement method thereof, wherein fig. 4(a) is a schematic diagram of an overall structure of the high-efficiency milling cutter, and fig. 4(b) is a schematic diagram of a tooth structure of the milling cutter;

FIG. 5 is a schematic diagram of a method for measuring a frictional wear boundary and characterizing a wear depth of a flank of a cutter tooth, wherein FIG. 5(a) is a method for measuring a frictional wear boundary of a flank of a cutter tooth, and FIG. 5(b) is a wear depth of a flank of a cutter tooth;

FIG. 6 is a graph of the upper and lower boundaries of the frictional wear of the flank surface of a milling cutter tooth;

FIG. 7 is a schematic diagram of a vibration acceleration time domain signal of an effective milling stroke of a layer 4 in a layered milling mode;

fig. 8 is a wear state diagram of a bottom edge flank of a high-efficiency milling cutter tooth with a milling stroke of 5m, wherein fig. 8(a) is a wear state diagram of a first flank of the tooth, fig. 8(b) is a wear state diagram of a second flank of the tooth, and fig. 8(c) is a wear state diagram of a third flank of the tooth;

fig. 9 is a distribution graph of upper and lower boundary characteristic points of the frictional wear of the rear face of the milling cutter tooth, in which fig. 9(a) is a distribution graph of upper boundary characteristic points of the frictional wear of the rear face of the milling cutter tooth, and fig. 9(b) is a distribution graph of lower boundary characteristic points of the frictional wear of the rear face of the milling cutter tooth;

FIG. 10 is a diagram of an overall structure and a unit cross-section model of an axial layered milling simulation workpiece of the high-efficiency milling cutter, wherein FIG. 10(a) is a diagram of an overall structure of an axial layered milling simulation workpiece model of the high-efficiency milling cutter, and FIG. 10(b) is a diagram of an i (i is not less than 2) th layer of cross-section model of a milling unit;

FIG. 11 is an identification view of the cut-in of the ith (i.gtoreq.2) layer of the milling cutter;

FIG. 12 is a schematic diagram of the path of the milling cutter movement under vibration;

fig. 13 is a signal diagram of an instantaneous cutting attitude angle of the milling cutter of the i-th layer, in which fig. 13(a) is a deflection angle of the milling cutter in a feeding direction and fig. 13(b) is a deflection angle of the milling cutter in a cutting width direction;

FIG. 14 is a solid view of the milling unit of the i-th layer, wherein FIG. 14(a) is a schematic surface view of the milling unit of the i-th layer, FIG. 14(B) is a cross-sectional view taken along line A-A in FIG. 14(a), and FIG. 14(c) is a cross-sectional view taken along line B-B in FIG. 14 (a);

fig. 15 is a simulation diagram of an axial layered milling process of the high-efficiency milling cutter, wherein fig. 15(a) is a simulation diagram of a cutting-in stage of the milling cutter, fig. 15(b) is a simulation diagram of a cutting-in middle section of the milling cutter, and fig. 15(c) is a simulation diagram of a cutting-out stage of the milling cutter;

FIG. 16 is a graph of instantaneous equivalent stress, equivalent strain field and temperature field distribution for the flank of a milling cutter tooth, wherein FIG. 16(a) is a graph of equivalent stress distribution, FIG. 16(b) is a graph of equivalent strain field distribution, and FIG. 16(c) is a graph of temperature field distribution;

FIG. 17 is a sectional plane parallel to the normal vector direction of the midpoint of the cutting edge of the cutter tooth and perpendicular to the curved surface of the equivalent stress, equivalent strain and temperature distribution of the rear face of the cutter tooth at equal intervals, wherein fig. 17(a1) is a profile of equivalent stress of the flank of the tooth, fig. 17(a2) is a profile of equivalent strain of the flank of the tooth perpendicular to fig. 17(a1) sequentially made across a node on the cutting edge in a direction parallel to a normal vector of a midpoint of the cutting edge on a projection plane of the flank of the tooth, fig. 17(b1) is a profile of equivalent strain of the flank of the tooth, fig. 17(b2) is a profile of equivalent strain of the flank of the tooth perpendicular to fig. 17(b1) sequentially made across a node on the cutting edge in a direction parallel to a normal vector of a midpoint of the cutting edge on a projection plane of the flank of the tooth, fig. 17(c1) is a profile of temperature of the flank of the tooth, and fig. 17(c2) is a profile of equivalent strain of equivalent stress of the flank of the tooth perpendicular to a curve of fig. 17(c1) sequentially made across a node on the cutting;

fig. 18 is a graph of equivalent stress distribution at nodes at different positions of the flank of the tooth, in which fig. 18(a) is a graph of stress distribution at a node at a section a, fig. 18(B) is a graph of stress distribution at a node at a section B, and fig. 18(C) is a graph of stress distribution at a node at a section C;

FIG. 19 is a graph showing equivalent strain and temperature distribution at a node B on a section B of the flank of a tooth, wherein FIG. 19(a) is a graph showing equivalent strain distribution at the section B, and FIG. 19(B) is a graph showing temperature distribution at the section B;

FIG. 20 is a graph showing the distribution of equivalent stress, equivalent strain and temperature change rate at section B of the flank of a tooth, in which FIG. 20(a) is a graph showing the distribution of equivalent stress change rate, FIG. 20(B) is a graph showing the distribution of equivalent strain change rate, and FIG. 20(c) is a graph showing the distribution of temperature change rate;

FIG. 21 is a graph of an upper boundary of an instantaneous frictional wear simulation of a flank face of a milling cutter tooth;

FIG. 22 is a graph of simulated lower boundary recognition of instantaneous frictional wear of the flank face of a milling cutter tooth;

FIG. 23 is a graph of the evolution process of the cumulative frictional wear boundary formation on the flank face of a milling cutter tooth;

FIG. 24 is a graph showing the upper and lower boundary of instantaneous frictional wear of a first flank of a milling cutter tooth, wherein FIG. 24(a) is a graph showing the upper boundary of instantaneous frictional wear of the first flank of the milling cutter tooth, and FIG. 24(b) is a graph showing the lower boundary of instantaneous frictional wear of the second flank of the milling cutter tooth;

FIG. 25 is a graph comparing upper and lower boundary curves of a simulated and experimental cumulative frictional wear of a milling cutter tooth I.

The specific implementation mode is as follows:

as shown in fig. 1, the method for identifying and verifying the accumulated friction and wear boundary of the milling cutter of the present invention is characterized in that a relation matrix among a workpiece coordinate system, a milling cutter coordinate system, a cutter tooth coordinate system and a rear cutter face friction and wear boundary measurement coordinate system under the influence of milling vibration and cutter tooth error is used for reflecting the influence of milling vibration and cutter tooth error on the instantaneous contact relation between the rear cutter face of the cutter tooth and the workpiece, a cutter tooth rear cutter face friction and wear boundary measurement coordinate system is established, a method for measuring and characterizing the cutter tooth rear cutter face friction and wear boundary is provided by using end points and inflection points on the left side and the right side of the friction and wear boundary as characteristic points, and the curve shape and the position of the cutter tooth rear cutter face friction and wear boundary are completely characterized in the measurement coordinate system; considering milling vibration, cutter tooth error, milling mode and difference of surfaces to be machined of different layers as simulation boundary conditions, and providing an axial layered milling simulation model of the efficient milling cutter and a boundary condition construction method; providing an upper boundary simulation criterion and a lower boundary simulation criterion of the instantaneous frictional wear of the rear cutter face of the milling cutter tooth based on the formation process of the instantaneous frictional wear boundary of the rear cutter face of the cutter tooth and the distribution characteristics of the instantaneous node temperature field, the equivalent stress and the equivalent strain of the rear cutter face of the cutter tooth; the method for calculating the accumulated friction and wear boundary of the rear cutter face of the milling cutter tooth is provided based on an instantaneous friction and wear simulation criterion, the similarity degree of the shape and the position between simulation and experiment accumulated friction and wear boundary curves is analyzed by calculating the gray correlation value and the average relative error between the simulation and experiment accumulated friction and wear boundary curves, and the correctness of the method for calculating the accumulated friction and wear boundary of the rear cutter face of the milling cutter tooth is verified.

The method for identifying and verifying the accumulated friction and wear boundary of the efficient milling cutter specifically comprises the following steps:

step A: method for measuring and characterizing frictional wear boundary of rear cutter face of cutter tooth of efficient milling cutter

Milling mode of efficient milling cutter under vibration action of step A1

In a workpiece coordinate system, the influence of milling vibration on the cutting process of the efficient milling cutter is reflected by the offset and the cutting state of the milling cutter under the action of the milling cutter coordinate system, as shown in figures 2 and 3, and variable parameter explanations in figures 2 and 3 are shown in a table 1-1.

TABLE 1-1 efficient milling cutter milling mode and instantaneous cutting state variable interpretation under vibration

Step A2 cutter tooth error and flank friction wear measurement

In order to research the characteristic of influence of the cutter tooth error of the milling cutter on the frictional wear boundary of the rear cutter face of the cutter tooth, the radial error of the cutter tooth is measured by taking the maximum excircle radius of the cutter tooth of the milling cutter as a reference in a milling cutter coordinate system, and the axial error of the cutter tooth is measured by taking the lowest point of the cutter tooth of the milling cutter as a reference. As shown in fig. 4, the explanation of the variable parameters in fig. 4 is shown in tables 1-2.

TABLE 1-2 advanced milling cutter structure and variable interpretation of tooth error measurement method thereof

Making the knife tooth installation reference surface vertical to the measurement horizontal plane, and on the projection of the knife tooth rear knife surface on the measurement horizontal plane, making the normal vector passing through the knife tooth outer side knife point and being parallel to the cutting edge midpoint and the reverse intersection point O of the tangent vector along the cutting edge midpoint_jEstablishing a measuring coordinate system O of the frictional wear boundary of the rear cutter face of the cutter tooth of the milling cutter as an origin_jUVS, axis U parallel to the vector tangential to the midpoint of the cutting edge of the tooth on the projection plane, axis V parallel to the vector normal to the midpoint of the cutting edge on the projection plane, and axis S perpendicular to the measurement plane. And the flank face frictional wear upper and lower boundaries are measured on a parallel plane of the measurement coordinate system parallel to the plane of the midpoint tangent of the tooth cutting edge, as shown in fig. 5 (a). The method for characterizing the frictional wear depth of the flank of the tooth is shown in fig. 5 (b).

The explanation of the variable parameters in fig. 5 is shown in tables 1-3.

TABLE 1-3 knife teeth flank friction wear boundary measurement method variable interpretation

Step A3 influence of milling vibration and cutter tooth error on instantaneous contact relation between cutter tooth flank and workpiece

And reflecting the influence of the milling vibration and the cutter tooth error on the instantaneous contact relation between the rear cutter face of the cutter tooth and the workpiece by utilizing a relation matrix among a workpiece coordinate system, a milling cutter coordinate system, the cutter tooth coordinate system and the rear cutter face frictional wear measurement coordinate system under the influence of the milling vibration and the cutter tooth error. The relation matrix between the milling cutter coordinate system and the workpiece coordinate system under the vibration-free action is shown as a formula (1-1), the relation matrix between the milling cutter coordinate system under the vibration-free action is shown as a formula (1-3), the relation matrix between the cutter tooth coordinate system and the milling cutter coordinate system is shown as a formula (1-5), and the relation matrix between the cutter tooth coordinate system and the rear cutter face friction wear measurement coordinate system is shown as a formula (1-7).

[x_g y_g z_g 1]^T＝M₁[a b c 1]^T (1-1)

[a b c 1]^T＝M₂T₁[a_v b_v c_v 1]^T (1-3)

[a b c 1]^T＝M₃T₂[a_q b_q c_q 1]^T (1-5)

[a_q b_q c_q 1]^T＝M₄T₄T₃[U V S 1]^T (1-7)

Wherein M is₁、M₂、M₃、M₄For translation matrices, T₁、T₂、T₃、T₄For a rotation matrix, M₁Wherein x (T), y (T), z (T) are the positions of the milling cutter center in the workpiece coordinates at time T, T₄In (1),

is an included angle between the cutter tooth positioning surface and the milling cutter groove mounting surface,

is pi/2.

Step A4 cutter tooth flank frictional wear boundary determination

In order to completely represent the shape and position information of the upper and lower boundaries of the frictional wear of the rear cutter face of the milling cutter tooth, a measuring coordinate system O of the wear boundary of the rear cutter face of the milling cutter tooth measured under a microscope with ultra-depth of field_jProjection plane on UV plane, left and right edges of frictional wear of rear face of tooth successively identified in cutting edge directionAnd measuring coordinate values of the end points and the inflection points along the V-axis direction in turn in a tool tooth rear tool face wear boundary measurement coordinate system, and constructing a milling cutter tooth rear tool face friction wear upper and lower boundary curve by taking the left and right side end points and the inflection points as characteristic points. As shown in fig. 6, wherein V ═ V₀(U) is the original cutting edge profile curve V of the rear cutter face of the milling cutter tooth_rq(U, L) (q is more than or equal to 1 and less than or equal to 3) is a characteristic point curve of the upper boundary of the frictional wear of the rear face of the milling cutter tooth q with the milling stroke of L, and V is V_hqAnd (U, L) is a lower boundary characteristic point curve of the frictional wear of the rear cutter face of the milling cutter tooth q with the milling stroke L.

The method comprises the following implementation steps of carrying out an experiment of milling titanium alloy by axial layering of the high-efficiency milling cutter to obtain the friction and wear result of the rear cutter face of the cutter tooth of the high-efficiency milling cutter, wherein the milling scheme is shown in tables 1-4.

TABLE 1-4 Experimental scheme for milling titanium alloy by using efficient milling cutter

In tables 1-4, L is the total effective milling stroke of 5m, Δ c_z ⁱIs the axial error, Δ c, of tooth i_j ⁱIs the radial error of the cutter tooth i. And calculating the axial and radial errors of each cutter tooth of the milling cutter by taking the reference of the lowest point of the cutter tooth of the milling cutter and the maximum radius of the cutter point of the cutter tooth of the milling cutter as the reference.

After the cutter tooth error measurement is finished, a titanium alloy milling experiment is carried out on a triaxial milling machining center, wherein the length and width of a workpiece are 250 multiplied by 100 multiplied by 10mm, the axial layered milling experiment is finished in 20 layers, in the milling experiment process, an acceleration sensor is adopted to detect a vibration signal generated by the excitation of cutting force on the surface of the workpiece close to a cutting area, and a DH5922 transient signal test analysis system is adopted to carry out data analysis on the collected vibration signal. As shown in fig. 7.

After the experiment is finished, the ultra-depth-of-field microscope is used for sequentially detecting the frictional wear boundaries of the rear tool faces of the cutter teeth of the milling cutter, as shown in fig. 8.

The characteristic points of the upper and lower boundary curves of the wear of the rear cutter face of the cutter tooth of the milling cutter in fig. 8 are sequentially extracted by adopting the method for identifying the characteristic points of the upper and lower boundary curves of the friction wear, as shown in fig. 9.

As can be seen from FIG. 9, the measurement method can completely characterize the shape and position of the upper and lower boundaries of the wear of the rear cutter face of the milling cutter tooth; under the influence of cutter tooth errors and milling vibration, the distribution of the upper and lower boundaries of the wear of the rear cutter faces of different cutter teeth of the milling cutter presents obvious difference.

And B: efficient milling cutter axial layered milling simulation model and boundary condition construction method

Step B1 high-efficiency milling cutter axial layered milling simulation model overall structure design

Considering the milling mode, the cutter tooth error, the milling vibration and the difference of the surfaces to be machined of different layers as simulation boundary conditions, designing the overall structure of the axial layered milling simulation model of the efficient milling cutter, and determining and calculating the design variables of the simulation model, as shown in fig. 10.

In fig. 10(a), the simulated workpiece is composed of a plurality of milling units, each layer of milling unit corresponds to a workpiece form in an axial layered milling process, rectangular groove structures are formed among the milling units, the profiles of the surfaces to be processed of different layers have differences but are positioned on the same horizontal height, and L is a height_i ⁽ⁱ⁺¹⁾And H' is the height of the rectangular groove, and is the distance between the (i-1) th layer milling unit and the ith layer milling unit.

In FIG. 10(b), O_iThe center of a circle where a bottom edge cutting edge of a milling cutter tooth is positioned, r₀Radius of the circle on which the cutting edge of the milling cutter tooth is located, d_mAs axis C of milling cutter₁C₂Distance from work piece in cutting width direction, J_dFor the lowest point of participation in cutting on the cutting edge of the milling cutter tooth, J_hIs the highest contact point, delta r, of the side edge of the cutter tooth and the surface to be machined_z ^maxAnd Δ r_j ^maxThe maximum axial error and the maximum radial error of the cutter teeth of the milling cutter are respectively; h_iThe height of the milling unit of the ith (i ≧ 2) layer is represented, wherein the cross section of the milling unit of the first layer is the same size as the initial cross section of the workpiece.

The control parameters of the simulation workpiece are as follows: l is_i ⁽ⁱ⁺¹⁾、H'、L_i-1 ⁱ、H_i、W、L₀、d_m、a_p、Δr_z ^max、Δr_j ^max、r₀、r、α、J_d、J_h。L_i ⁽ⁱ⁺¹⁾The solving method of (2) is as follows:

wherein, T_i ⁱ⁺¹For milling cutters in actual machining processes from P_3iTo P_2(i+1)Time of (d).

H_i＝H+(i-1)a_p(i≥2) (2-3)

Step B2 simulation model milling unit construction

(1) According to the steps A shown in the figures 2 and 3, the instantaneous deflection angles delta of the milling cutter along the feed speed direction and the cutting width direction at the time t in the milling process are solved₁(t)、δ₂(t) is represented by the following formulae (2-4) and (2-5).

Solving the track equation f of the milling cutter central point in the workpiece coordinate system under the vibration action^v＝(x_gv,y_gv,z_gvAnd t) is shown as formula (2-6).

In the formula (2-6), A_x(t)、A_y(t)、A_z(t) the vibration acceleration signal is obtained by performing secondary integration on the vibration acceleration signal measured in the experimental process and then using 8 times of Sun of sin Function fitting in Matlab. t is t_eFor milling cutters from P_4iTo P_1(i+1)The time used is as shown in formula (2-7), T_iFor milling cutters from P_1(i+1)Move to P_1(i+1)The time period of (2) is as shown in the formula (2-8).

T_i＝[T_si,T_ei]＝[(i-1)(T_c+t_e),iT_c+(i-1)t_e] (2-8)

Wherein, T_siIs the milling cutter edge x_gMoment of starting point of tool path for ith axial feed, T_eiIs the milling cutter edge x_gThe tool lifting time of the ith feeding in the axial direction; t is_cMilling cutter from P_1iMove to P_4iThe time used is as in formula (2-9).

(2) Identifying the cut-in and cut-out time in the ith (i is more than or equal to 2) layer milling vibration signal, and solving the ith layer cutting section T according to the formula (2-6) as shown in FIG. 11_mEquation f of motion track of milling cutter^v＝(x_gv,y_gv,z_gvT), as shown in fig. 12.

(3) The i-layer milling cutter instantaneous cutting attitude angle was solved using matlab according to equations (2-4) and (2-5), and the result is shown in fig. 13.

(4) As shown in fig. 14, according to the milling unit cross section model in fig. 10(b), the i-th layer milling unit cross section is constructed, and NJ is added_hThe section is swept along a milling cutter track curve to form a surface to be machined of the milling unit, an i-th layer of milling cutter instantaneous cutting attitude angle is introduced in the sweeping process, and finally other surfaces of the milling unit are constructed in sequence to form an entity, wherein parameter explanation of variables in the graph 14 is shown in a table 2-1.

TABLE 2-1 milling Unit variable resolution for ith layer

B3 axial layered milling simulation motion trail calculation of efficient milling cutter under vibration action

In the simulation process, in order to introduce the vibration displacement of the milling cutter in the milling process, according to the motion trail of the milling cutter under the vibration action in the axial layered milling experiment, on the premise of not changing the feeding speed, the discrete time interval of the motion trail points of the milling cutter is determined, the motion trail points of the milling cutter under the vibration action in the simulation process are solved, and the method comprises the following steps:

(1) determining discrete time interval of trace points, and determining minimum unit size L of minimum grid unit of workpiece in order to make simulation result more accurate_min1/3 is the simulation step size, t_dAs shown in formulas (2-10).

(2) And (4) re-calculating the coordinate value of the cutting-in to cutting-out of any ith (i is more than or equal to 2) layer of the milling cutter, as shown in a formula (2-11).

(3) And (3) the coordinates of the milling cutter track points between any ith layer of cutting points and the (i + 1) th layer of cutting points are supplemented, the time step number between the ith layer of cutting points and the (i + 1) th layer of cutting points is solved as shown in the formula (2-12), the step distance between adjacent track points between the ith layer of cutting points and the (i + 1) th layer of cutting points is as shown in the formula (2-13), and the coordinate solving method between the adjacent two layers of track points is as shown in the formula (2-14).

And C: method for identifying instantaneous frictional wear boundary of rear cutter face of cutter tooth

C1 simulation of axial layered milling thermal coupling field of efficient milling cutter

And C, in order to obtain the instantaneous frictional wear simulation boundary of the rear cutter face of the cutter tooth of the milling cutter, utilizing the milling experimental parameters in the step A, milling a simulation model in an axial layered mode according to the efficient milling cutter designed in the step B, and carrying out thermal coupling field simulation, wherein a Johnson-Cook constitutive model adopted by the simulation is shown as a formula (3-1), and the titanium alloy milling experimental processing parameters of the efficient milling cutter in the table 1-4 are adopted as the simulation milling parameters.

In the formula: σ — equivalent flow stress; a, B, n, c, m-yield stress strength, strain strengthening constant, strain strengthening index, strain rate strengthening parameter and temperature strain rate sensitivity; t, T_r，T_m-real time temperature, room temperature, 25 ℃ and material melting temperature/° c; the sum of the distances of epsilon,

material equivalent strain, equivalent strain rate/s^-1The reference strain rate takes 1s^-1(ii) a Wherein the high-efficiency milling cutter base material is hard alloy WC, the cutter coating material is TiN, the thickness is 5 mu m, and the yield strength sigma is_sThe intrinsic parameters of the TC4 titanium alloy material J-C are shown in the table 3-1 when the thickness is 5.9 GPa. The milling simulation process is shown in fig. 15.

TABLE 3-1 TC4 titanium alloy J-C constitutive parameter Table

After the simulation is finished, an equivalent stress field, an equivalent strain field and a temperature field of any instantaneous cutting of the rear cutter face of the cutter tooth of the milling cutter are extracted, as shown in fig. 16.

C2 curve of equivalent stress, equivalent strain and temperature change of instantaneous node at different positions of cutter tooth rear cutter face

Extracting node equivalent stress, equivalent strain and temperature values at different positions of the rear cutter face of the cutter tooth of the milling cutter, constructing a cutter tooth rear cutter face equivalent stress, equivalent strain and temperature distribution curved surface, sequentially drawing a plurality of section planes which are perpendicular to the distribution curved surface and are parallel to the nodes on the cutting edge in the middle point normal vector direction on the projection plane of the rear cutter face of the cutter tooth, constructing equivalent stress distribution curves of the nodes on the section planes at different positions of the rear cutter face and identifying that the equivalent stress on the section planes is greater than and most close to the yield strength sigma_sFig. 18 shows that a curve of equivalent strain and temperature distribution of the nodes on the section plane at different positions of the flank face is constructed, and fig. 19 shows an example of the section plane B.

Step C3 curve of stress, strain and temperature change rate at different positions of cutter tooth rear cutter face

In the cutting process of the high-efficiency milling cutter, shear and friction exist between the rear cutter face of the cutter tooth and the transition surface of a workpiece, so that stress concentration is formed inside the cutter tooth in a contact area and is diffused and distributed to a non-contact area, and the stress value is sharply reduced at a contact and non-contact boundary node; meanwhile, the temperature of the contact surface of the rear cutter face of the cutter tooth is sharply increased by heat generated in the shearing and rubbing process, the generated heat is transferred to a non-contact area at the rear cutter face of the cutter tooth, and the temperature value is sharply reduced at a contact and non-contact boundary node, so that a very large temperature gradient is generated on the rear cutter face of the cutter tooth; in the milling process, the interaction between the rear cutter face of the cutter tooth and the transition surface of the workpiece generates extrusion deformation, so that the contact boundary node of the rear cutter face of the cutter tooth and the transition surface of the workpiece generates strain concentration, and the non-contact boundary generates micro strain; based on the analysis, the stress, strain and temperature values at the nodes of the instantaneous frictional wear boundary of the rear cutter face of the cutter tooth are mutated, so that the node temperature, equivalent stress and equivalent strain distribution curves at all the sections are sequentially fitted through a unitary high-order polynomial, the node change rate distribution curve is obtained by derivation through the formulas (3-2), (3-3) and (3-4), and the node inflection points at which the temperature, stress and strain change rate are mutated at all the section positions of the rear cutter face are respectively identified by taking the section B as an example, as shown in fig. 20.

Step C4 cutter tooth flank instantaneous friction wear simulation upper boundary identification

Based on the mechanical property of the material, when the equivalent stress on the cutting edge of the cutter tooth is greater than the yield strength, the material on the cutting edge is peeled off and taken away by the cuttings, so that the shape of the edge is changed to form an instantaneous frictional wear upper boundary of the rear cutter face of the cutter tooth, and based on the analysis, the yield strength sigma of the cutter tooth material is used_sThe simulation upper boundary identification judgment for the instantaneous frictional wear of the rear cutter face of the milling cutter tooth is shown as a formula (3-5), a critical characteristic node with equivalent stress larger than and closest to yield strength on all the section planes is identified, and in a rear cutter face frictional wear measurement coordinate system, a boundary surrounded by the characteristic nodes on the section planes is the upper boundary of the instantaneous frictional wear of the rear cutter face of the milling cutter tooth, as shown in fig. 21.

σ≥σ_s (3-5)

Step C5 cutter tooth flank instantaneous frictional wear simulation lower boundary identification

In the instantaneous cutting process, the rear cutter face of the milling cutter tooth and the transition surface of the workpiece are sheared, extruded and rubbed to form an instantaneous frictional wear lower boundary of the rear cutter face of the milling cutter tooth, the temperature, equivalent stress and equivalent strain between contact and non-contact areas of the rear cutter face of the milling cutter tooth and the transition surface of the workpiece are obviously different, based on the analysis, a simulation lower boundary identification method for the instantaneous frictional wear of the rear cutter face of the milling cutter tooth is provided, the temperature, the equivalent stress and the nodes where the equivalent strain is obviously mutated at each section plane of the rear cutter face of the milling cutter tooth are sequentially identified by adopting the method, the temperature, the equivalent stress and the equivalent strain mutation curves of the nodes on the rear cutter face of the milling cutter tooth are shown in a graph 22, and the calculation method for the instantaneous frictional wear simulation lower boundary curves of the rear cutter face of the milling cutter tooth is shown in.

V_m(U_i,t)＝max{V_T(U_i,t),V_σ(U_i,t),V_ε(U_i,t)}(0≤i≤10.7) (3-6)

V_m(U,t)＝{V_m(U₁,t),V_m(U₂,t)...V_m(U_i,t)} (3-7)

As shown in fig. 22, V ═ V₀(U) is the boundary of the original profile of the milling cutter, V ═ V_T(U,t)、V＝V_σ(U,t)、V_ε(U, t) are respectively the curves of the temperature, stress and strain abrupt change node of the rear cutter face of the milling cutter tooth at the time t, and in the formula (3-6), V_T(U_i,t)、V_σ(U_i,t)、V_ε(U_iAnd t) are respectively the temperature, stress and strain abrupt change node curves U of the rear cutter face of the cutter tooth at the time t_iThe V-direction coordinate value at the position. V in the formula (3-7)_m(U_iT) is a lower boundary curve U of instantaneous frictional wear of the rear cutter face of the milling cutter tooth at the time t_iCoordinate value of V direction at position, V_mAnd (U, t) is a lower boundary curve of instantaneous frictional wear of the rear cutter face of the milling cutter tooth at the time t.

Step D: method for calculating and verifying accumulated friction and wear boundary of cutter tooth rear cutter face

Step D1 cutter tooth flank cumulative frictional wear boundary resolution

In the milling process, under the influence of milling vibration and cutter tooth errors, instantaneous contact boundaries between rear cutter faces of cutter teeth of the milling cutter and transition surfaces of a workpiece dynamically change along with time, accumulated friction and wear boundaries of the rear cutter faces of the cutter teeth of the milling cutter are formed by accumulating a plurality of instantaneous friction and wear boundaries, based on the analysis, by taking the lower boundary simulated by the accumulated friction and wear of the rear cutter faces of the cutter teeth of the milling cutter as an example, instantaneous friction and wear lower boundary curves of the rear cutter faces of the cutter teeth at different milling moments are extracted, and as shown in fig. 23, a calculation method for the accumulated friction and wear boundaries of the rear cutter faces of the cutter teeth of the milling cutter is provided, and is shown in a formula (4.

V_a(U_i,Δt)＝max{V_m(U_i,t₁),V_m(U_i,t₂)...V_m(U_i,t_n)}Δt＝t_n-t₁ (4-1)

V_a(U,Δt)＝{V_a(U₁,Δt),V_a(U₂,Δt)...V_a(U_i,Δt)} (4-2)

In the formula (4-1), V_a(U_iAnd delta t) is the accumulated friction wear boundary curve of the rear cutter face of the milling cutter tooth in the time period of delta t at U_iCoordinate value of V direction at position, in formula (4-2), V_a(U, delta t) is a boundary curve of accumulated friction wear of the rear face of the milling cutter tooth in a delta t time period.

D2 cutter tooth flank accumulated friction wear lower boundary simulation and experiment comparison scheme

In order to verify the correctness of the method for calculating the accumulated friction and wear boundary of the efficient milling cutter, firstly, the simulation recognition criteria of the upper and lower boundary of the instantaneous friction and wear of the rear cutter face of the cutter tooth of the milling cutter in the steps C4 and C5 are adopted, and the simulation upper and lower boundaries of the instantaneous friction and wear of the cutter face of each cutter tooth of the milling cutter at the time of 0.5m, 1m, 1.5m, 2m, 2.5m, 3m, 3.5m, 4m, 4.5m and 5m in the simulation of the thermal coupling field in the step C1 are extracted, taking the cutter tooth I as an example, as shown in FIG. 24.

And D1, constructing a simulation upper and lower boundary curve of the accumulated frictional wear of the rear cutter face of the milling cutter tooth by adopting the calculation method of the boundary curve of the accumulated frictional wear of the rear cutter face of the milling cutter tooth in the step D1, and comparing the simulation upper and lower boundary curve of the accumulated frictional wear of the rear cutter face of the milling cutter tooth with the experimental frictional wear upper and lower boundary curve of the rear cutter face of the milling cutter tooth with the milling stroke of 5m in the step A4, taking the cutter tooth I as.

Step D3 simulation and experiment cumulative friction wear boundary shape and position similarity analysis

Calculating a gray correlation value and a mean relative error between simulation and experimental accumulated friction and wear boundary curves, analyzing shape similarity and position contact degree between the simulation and experimental wear boundary curves, and verifying the correctness of the accumulated friction and wear boundary calculation method, wherein the gray correlation analysis method comprises the following steps:

firstly, respectively taking coordinate values of V axes of characteristic points of wear boundaries of rear cutter faces of experimental and simulated cutter teeth as a reference sequence and a comparison sequence, wherein the coordinate values are expressed as formulas (4-3) and (4-4).

V_q＝(V_q(1),V_q(2),...,V_q(m),...,V_q(n)) (4-3)

V_q*＝(V_q(1)*,V_q(2)*,...,V_q(m)*,...,V_q(n)*) (4-4)

V in the formulae (4-3) and (4-4)_q(m) and V_q(m) is the coordinate value V of the mth characteristic point V along the cutting edge direction on the boundary curve of the wear of the flank of the q (q is more than or equal to 0 and less than or equal to 3) th cutter tooth after the experiment and simulation respectively_m。

The method for calculating the average relative error of the wear curves of the rear cutter face of the simulated and experimental cutter teeth is shown as the formula (4-5).

In the formula (4-5), δ_qThe relative error of the wear boundary curve of the q-th cutter tooth rear cutter surface is simulated and tested.

By adopting the correlation and average relative error calculation method, the correlation and relative error of the upper and lower boundary curves of the wear of the rear cutter face of the simulated and experimental cutter tooth are shown in the table 4-1, wherein gamma (V)_q,V_q(1 is more than or equal to q is less than or equal to 3) represents the grey correlation degree between the simulation of the cutter tooth q and the experimental accumulated friction wear boundary curve, delta_qThe average relative error between the tooth q simulation and the experimental cumulative wear boundary curve is shown.

TABLE 4-1 simulation and experiment of tool tooth flank wear upper and lower boundary curve correlation and relative error

From table 4-1, the correlation values of the upper and lower boundary curves of the simulation and the experiment accumulated frictional wear of each cutter tooth rear cutter face of the milling cutter are all above 0.75, and the average relative errors are all less than 20%, and the results show that the curves and the positions of the simulation and the experiment accumulated frictional wear boundary curves of each cutter tooth rear cutter face of the milling cutter have high similarity, the effectiveness of the design method of the high-efficiency milling cutter axial layered milling simulation model is achieved, and meanwhile, the correctness of the calculation method of the accumulated frictional wear boundary of the cutter tooth rear cutter face of the milling cutter is verified.

The above description is only a preferred embodiment of the present invention, and these embodiments are based on different implementations of the present invention, and the scope of the present invention is not limited thereto, and any changes or substitutions that can be easily conceived by those skilled in the art within the technical scope of the present invention are included in the scope of the present invention. Therefore, the protection scope of the present invention shall be subject to the protection scope of the claims.

Claims

1. A high-efficiency milling cutter accumulated friction and wear boundary identification and verification method is characterized by comprising the following steps:

step A: providing a method for measuring and characterizing the frictional wear boundary of the rear cutter face of the cutter tooth of the efficient milling cutter, constructing a measuring coordinate system of the frictional wear boundary of the rear cutter face of the cutter tooth of the milling cutter, and characterizing the shape and the position of the frictional wear boundary of the rear cutter face of the cutter tooth on a plane parallel to a measuring coordinate system parallel to a mid-point tangent plane of the cutting edge of the cutter tooth;

2. A high efficiency milling cutter cumulative frictional wear boundary identification and verification method as claimed in claim 1, wherein: the step A further comprises the following steps:

step A2: determining a milling cutter tooth error and a method for measuring a frictional wear boundary of a rear cutter face of the milling cutter according to the structural characteristics of the efficient milling cutter;

3. A high efficiency milling cutter cumulative frictional wear boundary identification and verification method as claimed in claim 1 or 2, wherein: the step B further comprises the following steps:

4. A high efficiency milling cutter cumulative frictional wear boundary identification and verification method as claimed in claim 3, wherein: the step C further comprises the following steps:

5. A high efficiency milling cutter cumulative frictional wear boundary identification and verification method as claimed in claim 1, wherein: the step D further comprises the following steps: