CN109746766B - Method and system for determining temperature field of wear zone of rear cutter face of integral end mill - Google Patents

Method and system for determining temperature field of wear zone of rear cutter face of integral end mill Download PDF

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CN109746766B
CN109746766B CN201910061762.5A CN201910061762A CN109746766B CN 109746766 B CN109746766 B CN 109746766B CN 201910061762 A CN201910061762 A CN 201910061762A CN 109746766 B CN109746766 B CN 109746766B
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heat source
end mill
head end
zone
temperature
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CN109746766A (en
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岳彩旭
都建标
刘献礼
梁越昇
王立翚
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Harbin University of Science and Technology
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Abstract

The invention discloses a method and a system for determining a temperature field of a wear zone of a rear cutter face of an integral end mill. Establishing a model of an instantaneous contact angle between the milling cutter and a workpiece; establishing an undeformed chip thickness model, and calculating the undeformed chip thickness according to the undeformed chip thickness model; establishing a temperature field model for generating temperature rise on the wear zone of the rear cutter face of the milling cutter by a heat source in a first deformation area; establishing a temperature field model for generating temperature rise on the wear zone of the rear cutter face of the milling cutter by a heat source in a second deformation area; and establishing a temperature field model for generating temperature rise on the wear zone of the rear cutter face of the milling cutter by the heat source in the third deformation area. And calculating the instantaneous temperature of the wear zone of the rear cutter face of the milling cutter according to the first temperature field model, the second temperature field model, the third temperature field model and the temperature field model of the wear zone of the rear cutter face of the milling cutter. Temperature fields of the heat source of the first deformation area, the heat source of the second deformation area and the heat source of the third deformation area are respectively established, and the accuracy of monitoring the temperature of the milling cutter in the cutting process is improved.

Description

Method and system for determining temperature field of wear zone of rear cutter face of integral end mill
Technical Field
The invention relates to the field of integral flat-head end mills, in particular to a method and a system for determining a temperature field of a rear cutter face wear zone of an integral end mill.
Background
Titanium alloys have been widely used in aerospace, energy and military applications because of their excellent specific strength, specific stiffness, heat resistance and corrosion resistance. In order to meet the application requirements of the fields on higher processing efficiency and better workpiece surface processing quality, the high-speed precise milling mode is particularly important. When the thin-walled part is milled at high speed, severe cutter abrasion is easy to occur, and the processing efficiency and the processing quality are reduced. For milling, the choice of milling cutter temperature and lubrication regime are two important factors affecting tool wear. In order to meet the requirement of green cutting, research aiming at peripheral milling of the integral hard alloy end mill for processing titanium alloy thin-wall parts focuses more on the aspect of cutter temperature.
The factors influencing the temperature field distribution in the cutting process mainly include heat source heat intensity, heat source geometric characteristics, machining parameters, a workpiece material constitutive model, a tool shank, the thickness of undeformed chips, the number of cutting edges participating in machining and the like, and scholars at home and abroad carry out relevant research on the factors. The time-varying load among the cutting chips can directly influence the heat source heat intensity of the second deformation region, so Coskun Islam and the like solve partial differential equations representing a milling cutter heat mass transfer model by adopting a two-order implicit time discrete format in a finite difference method, and further establish a milling cutter temperature field. The distribution of a cutting temperature field can be directly influenced by the complex geometric characteristics and asymmetry of a cutting heat source, and therefore F.Klocke and the like consider the influence of the geometric characteristics and the radius of the cutting edge on the cutting heat source, and a cutting temperature analytic model based on a surface element method in the field of hydrodynamics is established. Temperature change in the milling process presents a periodic characteristic, for more specifically developing the research of milling temperature, Wu Baohai and the like divide a temperature change period of end milling into a temperature rise period and a temperature fall period, and for the temperature rise period, the real friction state between cutting chips is considered, and the heat flux and the contact length of the cutting chips are obtained through finite element simulation; for the temperature decay period, modeling was based on one-dimensional dish-shaped thermal convection. The machining parameters are important factors influencing the cutting temperature, and therefore an end milling temperature rise model is established based on a response surface method, such as P.S. Sivasakthevil and the like, the influence of the milling parameters on the end milling temperature rise model is researched, the machining parameters are optimized by utilizing a genetic algorithm to obtain the minimum temperature rise, and the spiral angle is found to be the most important milling parameter influencing the temperature rise peak value. The structural model of the workpiece material can influence the flow deformation of the first deformation region, so that the Yang Y and the like establish a new structural model of the workpiece material under the milling conditions of large strain, high strain rate and high temperature, and the accuracy of the finite element simulation cutting temperature result is improved when the double-helix edge end mill is used for processing Ti6Al 4V. The conduction of cutting heat during cutting is affected by the tool shank, and for this reason, the temperature of the contact surface of the chips is calculated based on the reverse heat conduction method by simultaneously considering the factors of the tool and the tool shank. The time-varying property of the contact length of the cutting chip in the end milling process can directly influence the thickness of the undeformed cutting chip and further influence the temperature distribution of the cutting chip, and therefore Masahiko Sato and the like consider the time-varying property of the contact length of the cutting chip in the end milling process and establish a rake face temperature distribution model of the indexable milling cutter by using a Green function. The peripheral edge and the bottom edge of the integral end mill participate in the machining process when milling a plane, and further generate milling heat.
According to the current situation of cutter temperature modeling research in machining at present, research work mainly focuses on temperature modeling of an indexable milling cutter with the characteristic of interrupted machining, related research on modeling of a transient temperature field of a rear cutter face wear zone of a helical-edge end mill is not involved, and the temperature field of the rear cutter face wear zone of the milling cutter cannot be accurately determined.
Disclosure of Invention
The invention aims to provide a method and a system for determining the instantaneous temperature of a wear zone of the rear cutter face of an integral flat-head end mill, which can accurately determine the temperature field of the wear zone of the rear cutter face of the milling cutter.
In order to achieve the purpose, the invention provides the following scheme: a method of determining an instantaneous temperature of a back facet wear zone of a unitary flat-head end mill, the method comprising:
converting a coordinate system XYZ of a first deformation area heat source and a coordinate system X 'Y' Z 'of a second deformation area heat source into a coordinate system of a third deformation area heat source, namely a coordinate system X' Y 'Z' corresponding to a milling cutter flank wear zone;
Figure BDA0001950828580000021
wherein, VB1For flank wear band length, beta0Is the wedge angle of the tool, /)cIs the contact length of the cutting scraps;
establishing a model of an instantaneous contact angle theta between the milling cutter and the workpiece; establishing an undeformed chip thickness h model under the condition that the workpiece is not deformed and vibrated in the process of machining the workpiece by the milling cutter, and the cutting edge cuts into the workpiece from a position away from the machined surface every time of milling;
calculating the thickness h of the undeformed chip according to the model of the thickness h of the undeformed chip;
establishing a temperature field model of which the heat source of a first deformation area generates temperature rise influence on the wear zone of the rear cutter face of the milling cutter to obtain a first temperature field model, wherein the heat source of the first deformation area is heat generated in shearing sliding of the chips in a shearing plane;
establishing a temperature field model of which the heat source of a second deformation area generates temperature rise influence on the wear zone of the rear cutter face of the milling cutter to obtain a second temperature field model, wherein the heat source of the second deformation area is heat generated by extrusion friction between the chips and the front cutter face of the milling cutter;
establishing a temperature field model of which the heat source of a third deformation area generates temperature rise influence on the wear zone of the rear cutter face of the milling cutter to obtain a third temperature field model, wherein the heat source of the third deformation area is heat generated by extrusion friction between the machined surface of the workpiece and the wear zone of the rear cutter face of the milling cutter;
establishing a temperature field model under a coordinate system X ' Y ' Z ' corresponding to the wear zone of the rear cutter face of the milling cutter to obtain a temperature field model of the wear zone of the rear cutter face of the milling cutter;
and calculating the instantaneous temperature of the milling cutter flank wear zone according to the first temperature field model, the second temperature field model, the third temperature field model and the milling cutter flank wear zone temperature field model.
Optionally, the establishing a model of the instantaneous contact angle θ between the milling cutter and the workpiece specifically includes: discretizing the milling cutter along the axial cutting direction into m pieces with thickness w ═ dz ═ ApA wafer of/m, ApWhen the thickness of each wafer is small enough, the thread is a straight line BD, the straight line BD is used as a hypotenuse to establish a right-angle triangle ABD, the right-angle side in the horizontal direction is AB, and the right-angle side in the vertical direction is AD;
Figure BDA0001950828580000022
Figure BDA0001950828580000023
Figure BDA0001950828580000031
calculating an instantaneous contact angle theta between the milling cutter and the workpiece according to formulas (2), (3) and (4);
wherein A ispBeta is the helix angle of the milling cutter, and R is the radius of the milling cutter.
Optionally, the establishing the undeformed chip thickness h model specifically includes: each milling of the cutting edge cuts into the workpiece from the machined surface.
Figure BDA0001950828580000032
Wherein the content of the first and second substances,
Figure BDA0001950828580000033
wherein v isfFor feed rate, AeFor milling width, fzThe feed per tooth, z is the milling cutter edge number, n is the machine tool rotation speed, thetaenAt an angle of cut, θexTo cut out the corners.
Optionally, the establishing a temperature field model in which the first deformation zone heat source has a temperature rise influence on the wear zone of the rear cutter face of the milling cutter, and the obtaining the first temperature field model specifically includes:
establishing a pair of a first deformation region primary heat source point dl and a mirror image heat source point dl' of the first deformation region primary heat source point along an arbitrary point P in the X directionI(x,0, z) respectively calculating the temperature rise value delta T of the primary heat source point of the first deformation regionI(x,0, z) and a temperature rise value DeltaT of the mirror image heat source pointI'(x,0,z)；
Figure BDA0001950828580000034
Figure BDA0001950828580000035
Figure BDA0001950828580000036
Calculating an arbitrary point P along the first deformation region in the X directionITemperature rise value DeltaT of (x,0, z)rake-I(x,0,z)；
ΔTrake-I(x,0,z)＝ΔTI(x,0,z)+ΔTI'(x,0,z) (9)
Wherein λ istH (theta) is the undeformed chip thickness, phi, for the thermal conductivity of the milling cutternNormal shear angle, ηcFor chip discharge angle, αwIs the thermal diffusivity of the workpiece; k0For zero order of modified Bessel function of the second kind, RlHeat source point dl to point P of the primary heat source of the first deformation zoneIDistance of (x,0, z), Rl' Heat source point dl to point P of heat source mirrored to the first deformation regionI(x,0, z);
established first deformation zone heat intensity qIA model;
Figure BDA0001950828580000041
Figure BDA0001950828580000042
Vsh＝Vcosλs (12)
wherein A is the reference strain rate and the initial yield stress at the reference temperature, B is the strain hardening modulus of the workpiece, εABCD-PIs the effective plastic strain of the shear plane ABCD, n is the strain hardening index of the workpiece, C is the strain rate hardening parameter of the workpiece,
Figure BDA0001950828580000043
for an effective plastic strain rate of the shear plane ABCD,
Figure BDA0001950828580000044
reference strain rate, T is the current temperature, TrFor reference temperature, TmM is a heat softening index of the workpiece.
Optionally, the establishing a temperature field model in which the heat source in the second deformation region exerts a temperature rise influence on the wear zone of the rear cutter face of the milling cutter, and the obtaining the second temperature field model specifically includes:
establishing a primary heat source point pair of the second deformation region and a mirror image heat source point pair of the second deformation region at any point P along the X' directionII(x ',0, z') respectively calculating the temperature rise delta T of the primary heat source point of the second deformation regionII(x ',0, z') and the second deformation zone mirror heat source point Δ TII'(x',0,z')；
Figure BDA0001950828580000045
Figure BDA0001950828580000046
Figure BDA0001950828580000047
Calculating an arbitrary point P within the second deformation region heat source along the X' directionIITemperature rise Δ T of (x',0,0)rake-II(x',0,0)；
ΔTrake-II(x',0,0)＝ΔTII(x',0,0)+ΔTII'(x',0,0)(16)
Wherein R isi-2Point to point P for the heat source of the second deformation regionII(x ',0, z') distance, Ri-2'Point to point P of heat source on mirror image heat source of the second deformation zoneII(x ',0, z'), w is the bevel turning width, λsThe inclination angle of the blade;
establishing the second deformation zone thermal strength qII(θ, x') model;
Figure BDA0001950828580000048
Figure BDA0001950828580000051
Figure BDA0001950828580000052
Achip(θ)＝lc(θ)wc (20)
Figure BDA0001950828580000053
wherein σtipIs a positive stress at the tip of the milling cutter,
Figure BDA0001950828580000054
Figure BDA0001950828580000055
is the average friction angle of the contact surface between the milling cutter and the chip, Achip(θ) is the contact area of the milling cutter and the chip;
calculating the heat distribution ratio B of the heat source heat in the second deformation region to the front tool faceII-rake(θ)；
Figure BDA0001950828580000056
Optionally, the establishing a temperature field model in which a heat source in a third deformation region exerts a temperature rise influence on the wear zone of the rear cutter face of the milling cutter, and the obtaining the third temperature field model specifically includes:
establishing a primary heat source point pair of a third deformation region and a mirror image heat source point pair of the third deformation region at any point P along the X' directionIII(x',0,0) temperature rise model, respectively calculating the temperature rise Delta T of the primary heat source point of the third deformation zoneIII(x ", 0,0) and the third deformation zone mirror heat source point Δ TIII'(x”,0,0)；
Figure BDA0001950828580000057
Figure BDA0001950828580000058
Figure BDA0001950828580000059
Calculating an arbitrary point P within the heat source of the third deformation zone along the X' directionIIITemperature rise DeltaT of (x',0,0)flank-III(x”,0,0)；
ΔTflank-III(x”,0,0)＝ΔTIII(x”,0,0)+ΔTIII'(x”,0,0) (26)
Wherein R isi-3Point to point P of heat source of the third deformation regionII(x ',0, z') distance, Ri-3'Point-to-point P of heat source on mirror image heat source of the third deformation zoneIIIDistance of (x ", 0,0), w is bevel turning width, λsThe inclination angle of the blade;
establishing said third deformation zone thermal strength qIII(x ") a model;
Figure BDA0001950828580000061
Figure BDA0001950828580000062
Figure BDA0001950828580000063
Figure BDA0001950828580000064
Figure BDA0001950828580000065
wherein f isLibrary(x') is the friction between the tool contact surfaces, lambdasThe inclination angle of the cutting edge of the cutter,
Figure BDA0001950828580000066
is the average coefficient of friction, σ, on the tool-to-tool contact surfacen-f(x') is the positive stress on the flank wear strip, σtipNormal stress on the infinitesimal tip, VBCRIs the critical point of the plastic flow area and the elastic contact area, K is the ratio of the shear stress on the cutting edge to the shear flow stress on the workpiece, phi is the shear angle, gamma is0Is the front angle of the cutter,
Figure BDA0001950828580000067
is the rake face average friction angle.
Calculating the heat distribution ratio B of the heat source heat in the third deformation region to the front tool faceIII-flank(θ)；
Figure BDA0001950828580000068
Optionally, the establishing a temperature field model under a coordinate system X "Y" Z "corresponding to the milling cutter flank wear zone, and the obtaining the temperature field model of the milling cutter flank wear zone specifically includes:
calculating the temperature T of any point P (X ',0,0) along the X ' direction under the coordinate system X ' Y ' Z ' corresponding to the established wear zone of the rear cutter face of the milling cutterflank(x”,0,0)；
Figure BDA0001950828580000071
An instantaneous temperature determination system for a solid end mill relief wear strip, the determination system comprising:
a coordinate system establishing module for converting a coordinate system XYZ of the first deformation area heat source and a coordinate system X 'Y' Z 'of the second deformation area heat source into a coordinate system of the third deformation area heat source, namely a coordinate system X' Y 'Z' corresponding to the milling cutter flank wear zone;
the instantaneous contact angle model establishing module is used for establishing a model of an instantaneous contact angle theta between the milling cutter and a workpiece;
an undeformed chip thickness model building module, which builds an undeformed chip thickness h model under the condition that the milling cutter does not deform and vibrate and the cutting edge cuts from a position away from the machined surface every time in the process of machining the workpiece by the milling cutter;
the undeformed chip thickness calculation module is used for calculating the undeformed chip thickness h according to the undeformed chip thickness h model;
the first temperature field model establishing module is used for establishing a temperature field model of which the temperature rise influence is generated on the wear zone of the rear cutter face of the milling cutter by a first deformation zone heat source to obtain a first temperature field model, wherein the first deformation zone heat source is heat generated in the shearing slippage of the cutting chip in a shearing plane;
the second temperature field model establishing module is used for establishing a temperature field model of which the temperature rise influence is generated on the wear zone of the rear cutter face of the milling cutter by a second deformation zone heat source to obtain a second temperature field model, wherein the second deformation zone heat source is heat generated by extrusion and friction of the chips and the front cutter face of the milling cutter;
the third temperature field model establishing module is used for establishing a temperature field model of which the temperature rise influence is generated on the milling cutter rear cutter face wear zone by a third deformation zone heat source to obtain a third temperature field model, wherein the third deformation zone heat source is heat generated by extrusion and friction between the machined surface of the workpiece and the milling cutter rear cutter face wear zone;
the temperature field model building module is used for building a temperature field model under a coordinate system corresponding to the milling cutter rear cutter face wear zone to obtain a milling cutter rear cutter face wear zone temperature field model;
and the instantaneous temperature calculation module is used for calculating the instantaneous temperature of the milling cutter rear cutter face wear zone according to the first temperature field model, the second temperature field model, the third temperature field model and the milling cutter rear cutter face wear zone temperature field model.
According to the specific embodiment provided by the invention, the invention discloses the following technical effects: the invention discloses a method and a system for determining the instantaneous temperature of a rear cutter face wear zone of an integral flat-head end mill, which improve the accuracy of temperature monitoring of the mill in the cutting process, prolong the service life of the mill and simultaneously improve the surface quality and the machining precision of a machined workpiece by establishing temperature field models of a heat source of a first deformation zone, a heat source of a second deformation zone and a heat source of a third deformation zone respectively.
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In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required to be used in the embodiments will be briefly described below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and it is obvious for those skilled in the art to obtain other drawings based on these drawings without inventive labor.
FIG. 1 is a flow chart of a method of determining the instantaneous temperature of a wear zone of the back face of an integral flat-head end mill provided by the present invention;
FIG. 2 is a schematic diagram of the heat distribution of the heat source of the first deformation region, the heat source of the second deformation region and the heat source of the third deformation region provided by the present invention;
fig. 3 is a schematic view of a micro-element blade of the milling cutter provided by the invention;
FIG. 4 is a schematic illustration of the undeformed chip thickness provided by the present invention;
FIG. 5 is a schematic view of a heat source in a first deformation region according to the present invention;
FIG. 6 is a schematic view of a heat source in a second deformation region according to the present invention;
FIG. 7 is a schematic view of a heat source in a third deformation region according to the present invention;
FIG. 8 is a schematic view of the transient temperature field of the wear zone of the flank face of the milling cutter provided by the present invention;
FIG. 9 is a schematic diagram of the milling cutter provided by the invention, wherein the transient temperature field of the wear zone of the rear cutter face of the milling cutter changes along with milling time;
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
The invention aims to provide a method and a system for determining the instantaneous temperature of a wear zone of a rear cutter face of an integral flat-head end mill, which can accurately determine the temperature field of the wear zone of the rear cutter face of the milling cutter.
In order to make the aforementioned objects, features and advantages of the present invention comprehensible, embodiments accompanied with figures are described in further detail below.
As shown in fig. 1, a method of determining an instantaneous temperature of a flank wear zone of a one-piece flat-head end mill, the method comprising:
step 100: converting a coordinate system XYZ of a heat source of the first deformation area and a coordinate system X 'Y' Z 'of a heat source of the second deformation area into a coordinate system of a heat source of the third deformation area, namely a coordinate system X' Y 'Z' corresponding to a milling cutter flank wear zone;
Figure BDA0001950828580000081
wherein, VB1For flank wear band length, beta0Is the wedge angle of the tool, /)cIs the contact length of the cutting scraps;
step 200: establishing a model of an instantaneous contact angle theta between the milling cutter and a workpiece;
step 300: in the process that the milling cutter machines the workpiece, the milling cutter does not deform and vibrate, and an undeformed chip thickness h model is established under the condition that a cutting edge cuts from a position away from a machined surface every time of milling;
step 400: calculating the thickness h of the undeformed chip according to the model of the thickness h of the undeformed chip;
step 500: establishing a temperature field model of which the heat source of a first deformation area generates temperature rise influence on the wear zone of the rear cutter face of the milling cutter to obtain a first temperature field model, wherein the heat source of the first deformation area is heat generated in the shearing sliding of the cutting chip in a shearing plane;
step 600: establishing a temperature field model in which a second deformation area heat source generates temperature rise influence on the wear zone of the rear cutter face of the milling cutter to obtain a second temperature field model, wherein the second deformation area heat source is heat generated by contact of the chips and the front cutter face of the milling cutter;
step 700: establishing a temperature field model in which a third deformation zone heat source generates temperature rise influence on the milling cutter rear cutter face wear zone to obtain a third temperature field model, wherein the third deformation zone heat source is heat generated by extrusion friction between the machined surface of the workpiece and the milling cutter rear cutter face wear zone;
step 800: establishing a temperature field model under a coordinate system X ' Y ' Z ' corresponding to the wear zone of the rear cutter face of the milling cutter to obtain a temperature field model of the wear zone of the rear cutter face of the milling cutter;
step 900: and calculating the instantaneous temperature of the milling cutter rear cutter face wear zone according to the first temperature field model, the second temperature field model, the third temperature field model and the milling cutter rear cutter face wear zone temperature field model.
The model for establishing the instantaneous contact angle theta between the milling cutter and the workpiece specifically comprises the following steps:
as shown in fig. 3, the milling cutter is discretized in the axial cutting direction into m pieces having a thickness w ═ dz ═ apA wafer of/m, ApFor milling depth, when the thickness of each wafer is small enough, the thread is a straight line BD, the straight line BD is used as a hypotenuse, a right-angle triangle ABD is established, the right-angle side in the horizontal direction is AB, and the right-angle side in the vertical direction is AD;
Figure BDA0001950828580000091
Figure BDA0001950828580000092
Figure BDA0001950828580000093
calculating an instantaneous contact angle theta between the milling cutter and the workpiece according to formulas (2), (3) and (4);
wherein A ispBeta is the helix angle of the milling cutter, and R is the radius of the milling cutter.
As shown in fig. 4, the establishing of the undeformed chip thickness h model specifically includes:
each milling of the cutting edge cuts into the workpiece from a distance from the machined surface;
Figure BDA0001950828580000094
wherein the content of the first and second substances,
Figure BDA0001950828580000095
wherein v isfFor feed rate, AeFor milling width, fzThe feed per tooth, z is the milling edge number, n is the machine tool rotation speed, thetaenAt an angle of cut, θexTo cut out the corners.
As shown in fig. 2, 5, and 6, the establishing a temperature field model in which the first deformation region heat source generates a temperature rise influence on the milling cutter flank wear zone, and the obtaining the first temperature field model specifically includes:
establishing a pair of a first deformation region primary heat source point dl and a mirror image heat source point dl' of the first deformation region primary heat source point along an arbitrary point P in the X directionI(x,0, z) respectively calculating the temperature rise value delta T of the primary heat source point of the first deformation regionI(x,0, z) and a temperature rise value DeltaT of the mirror image heat source pointI'(x,0,z)；
Figure BDA0001950828580000101
Figure BDA0001950828580000102
Figure BDA0001950828580000103
Calculating an arbitrary point P along the first deformation region in the X directionITemperature rise value DeltaT of (x,0, z)rake-I(x,0,z)；
ΔTrake-I(x,0,z)＝ΔTI(x,0,z)+ΔTI'(x,0,z) (9)
Wherein λ istH (theta) is the undeformed chip thickness, phi, for the thermal conductivity of the milling cutternNormal shear angle, ηcFor chip discharge angle, αwIs the thermal diffusivity of the workpiece; k0For zero order of modified Bessel function of the second kind, RlHeat source point dl to point P of the primary heat source of the first deformation zoneIDistance of (x,0, z), Rl' Heat source point dl to point P of heat source mirrored to the first deformation regionI(x,0, z);
established first deformation zone heat intensity qIA model;
Figure BDA0001950828580000104
Figure BDA0001950828580000105
wherein A is the reference strain rate and the initial yield stress at the reference temperature, B is the strain hardening modulus of the workpiece, εABCD-PIs the effective plastic strain of the shear plane ABCD, n is the strain hardening index of the workpiece, C is the work pieceThe strain rate enhancement parameters of the article,
Figure BDA0001950828580000106
for an effective plastic strain rate of the shear plane ABCD,
Figure BDA0001950828580000107
for reference strain rate, T is the current temperature, TrFor reference temperature, TmM is a heat softening index of the workpiece.
The establishing of the temperature field model with the temperature rise influence of the heat source in the second deformation area on the wear zone of the rear cutter face of the milling cutter specifically comprises the following steps:
establishing a primary heat source point pair of the second deformation region and a mirror image heat source point pair of the second deformation region at any point P along the X' directionII(x ',0, z') respectively calculating the temperature rise delta T of the primary heat source point of the second deformation regionII(x ',0, z') and the second deformation zone mirror heat source point Δ TII'(x',0,z')；
Figure BDA0001950828580000108
Figure BDA0001950828580000111
Figure BDA0001950828580000112
Calculating an arbitrary point P within the second deformation region heat source along the X' directionIITemperature rise Δ T of (x',0,0)rake-II(x',0,0)；
ΔTrake-II(x',0,0)＝ΔTII(x',0,0)+ΔTII'(x',0,0) (16)
Wherein R isi-2Point to point P for the heat source of the second deformation regionII(x ',0, z') distance, Ri-2'Is the second deformation zone is heatedHeat source point-to-point P on mirror image heat source of sourceII(x ',0, z'), w is the bevel turning width, λsThe inclination angle of the blade;
establishing the second deformation zone thermal strength qII(θ, x') model;
Figure BDA0001950828580000113
Figure BDA0001950828580000114
Figure BDA0001950828580000115
Achip(θ)＝lc(θ)wc (20)
Figure BDA0001950828580000116
wherein σtipIs a positive stress at the tip of the milling cutter,
Figure BDA0001950828580000117
Figure BDA0001950828580000118
is the average friction angle of the contact surface between the milling cutter and the chip, Achip(θ) is the contact area of the milling cutter and the chip;
calculating the heat distribution ratio B of the heat source heat in the second deformation region to the front tool faceII-rake(θ)；
Figure BDA0001950828580000121
The establishing of the temperature field model in which the heat source in the third deformation area generates temperature rise influence on the wear zone of the rear cutter face of the milling cutter to obtain the third temperature field model specifically comprises the following steps:
establishing a primary heat source point pair of a third deformation region and a mirror image heat source point pair of the third deformation region at any point P along the X' directionIII(x',0,0) temperature rise model, respectively calculating the temperature rise Delta T of the primary heat source point of the third deformation zoneIII(x ", 0,0) and the third deformation zone mirror heat source point Δ TIII'(x”,0,0)；
Figure BDA0001950828580000122
Figure BDA0001950828580000123
Figure BDA0001950828580000124
Calculating an arbitrary point P within the heat source of the third deformation zone along the X' directionIIITemperature rise DeltaT of (x',0,0)flank-III(x”,0,0)；
ΔTflank-III(x”,0,0)＝ΔTIII(x”,0,0)+ΔTIII'(x”,0,0) (26)
Wherein R isi-3Point to point P of heat source of the third deformation regionII(x ',0, z') distance, Ri-3'Point-to-point P of heat source on mirror image heat source of the third deformation zoneIIIDistance of (x ", 0,0), w is bevel turning width, λsThe inclination angle of the blade;
establishing said third deformation zone thermal strength qIII(x ") a model;
Figure BDA0001950828580000125
Figure BDA0001950828580000126
Figure BDA0001950828580000127
Figure BDA0001950828580000131
Figure BDA0001950828580000132
wherein f isLibrary(x') is the friction between the tool contact surfaces, lambdasThe inclination angle of the cutting edge of the cutter,
Figure BDA0001950828580000133
is the average coefficient of friction, σ, on the tool-to-tool contact surfacen-f(x') is the positive stress on the flank wear strip, σtipIs a positive stress on the infinitesimal tip, VBCRIs the critical point of the plastic flow area and the elastic contact area, K is the ratio of the shear stress on the cutting edge to the shear flow stress on the workpiece, phi is the shear angle, gamma is0Is the front angle of the cutter,
Figure BDA0001950828580000134
is the rake face average friction angle.
Calculating the heat distribution ratio B of the heat source heat in the third deformation region to the front tool faceIII-flank(θ)；
Figure BDA0001950828580000135
The establishing of the temperature field model under the coordinate system X ' Y ' Z ' corresponding to the milling cutter rear cutter face wear zone and the obtaining of the temperature field model of the milling cutter rear cutter face wear zone specifically comprise:
calculating the temperature T of any point P (X ',0,0) along the X ' direction under the coordinate system X ' Y ' Z ' corresponding to the established wear zone of the rear cutter face of the milling cutterflank(x”,0,0)；
Figure BDA0001950828580000136
As shown in fig. 9, an instantaneous temperature determination system for a wear strip of a flank of an integral flat-head end mill, the determination system comprising:
the coordinate system establishing module 1 is used for converting a coordinate system XYZ of a first deformation area heat source and a coordinate system X 'Y' Z 'of a second deformation area heat source into a coordinate system of a third deformation area heat source, namely a coordinate system X' Y 'Z' corresponding to a milling cutter flank wear zone;
the instantaneous contact angle model building module 2 is used for building a model of an instantaneous contact angle theta between the milling cutter and a workpiece;
an undeformed chip thickness model building module 3, which builds an undeformed chip thickness h model under the condition that the milling cutter does not deform and vibrate and the cutting edge cuts into the workpiece from a position away from the machined surface every time the milling cutter mills the workpiece;
the undeformed chip thickness calculation module 4 is used for calculating the undeformed chip thickness h according to the undeformed chip thickness h model;
the first temperature field model establishing module 5 is used for establishing a temperature field model in which a first deformation zone heat source generates temperature rise influence on a milling cutter rear cutting surface wear zone to obtain a first temperature field model, wherein the first deformation zone heat source is heat generated by the contact surface of the cutting chip and the workpiece;
the second temperature field model establishing module 6 is used for establishing a temperature field model in which a second deformation zone heat source generates temperature rise influence on a milling cutter rear cutting surface wear zone to obtain a second temperature field model, and the first deformation zone heat source is heat generated in shearing sliding of the cutting chips in a shearing plane;
a third temperature field model establishing module 7, configured to establish a temperature field model in which a third deformation zone heat source generates a temperature rise influence on the milling cutter rear cutter surface wear zone, to obtain a third temperature field model, where the third deformation zone heat source is heat generated by extrusion and friction between the machined surface of the workpiece and the milling cutter rear cutter surface wear zone;
the temperature field model building module 8 is used for building a temperature field model under a coordinate system corresponding to the wear zone of the rear cutter face of the milling cutter to obtain a temperature field model of the wear zone of the rear cutter face of the milling cutter;
and the instantaneous temperature calculation module 9 is configured to calculate an instantaneous temperature of the milling cutter flank wear zone according to the first temperature field model, the second temperature field model, the third temperature field model and the milling cutter flank wear zone temperature field model.
The embodiments in the present description are described in a progressive manner, each embodiment focuses on differences from other embodiments, and the same and similar parts among the embodiments are referred to each other. For the system disclosed by the embodiment, the method disclosed by the embodiment corresponds to the method disclosed by the embodiment, so that the description is simple, and the relevant places can be referred to the method part for description.
The principle and the implementation of the present invention are explained herein by using specific examples, and the above description of the embodiments is only used to help understand the method and the core idea of the present invention; meanwhile, for a person skilled in the art, in light of the above description, the present invention should not be construed as limited to the embodiments and the application scope of the present invention.

Claims (8)

1. A method of determining an instantaneous temperature of a flank wear zone of a one-piece flat-head end mill, the method comprising:
converting a coordinate system XYZ of a heat source in a first deformation area and a coordinate system X 'Y' Z 'of a heat source in a second deformation area into a coordinate system of a heat source in a third deformation area, namely a coordinate system X' Y 'Z' corresponding to a rear cutter face wear zone of the integral flat-head end mill;
Figure FDA0003281408660000011
wherein, VB1For flank wear band length, beta0Is the wedge angle of the tool, /)cIs the contact length of the cutting scraps;
establishing a model of the instantaneous contact angle theta between the integral flat-head end mill and the workpiece, and assuming that the integral flat-head end mill and the workpiece are not deformed and vibrated in the process of machining the workpiece, and the cutting edge cuts into the workpiece from a position close to a machined surface each time the integral flat-head end mill is milled;
establishing an undeformed chip thickness h model, and calculating the undeformed chip thickness h according to the undeformed chip thickness h model;
establishing a temperature field model in which a first deformation zone heat source generates temperature rise influence on a rear cutter face wear zone of the integral flat-head end mill to obtain a first temperature field model, wherein the first deformation zone heat source is heat generated in shearing sliding of chips in a shearing plane;
establishing a temperature field model of which the temperature rise influence is generated by a second deformation zone heat source on the rear cutter face wear zone of the integral flat-head end mill to obtain a second temperature field model, wherein the second deformation zone heat source is heat generated by extrusion friction between the chips and the front cutter face of the integral flat-head end mill;
establishing a temperature field model in which a third deformation zone heat source generates temperature rise influence on the rear cutter face wear zone of the integral flat-head end mill to obtain a third temperature field model, wherein the third deformation zone heat source is heat generated by extrusion friction between the machined surface of the workpiece and the rear cutter face wear zone of the integral flat-head end mill;
establishing a temperature field model under a coordinate system X ' Y ' Z ' corresponding to the wear zone of the rear cutter face of the integral flat-head end mill to obtain a temperature field model of the wear zone of the rear cutter face of the integral flat-head end mill;
and calculating the instantaneous temperature of the wear zone of the rear tool face of the integral flat-head end mill according to the first temperature field model, the second temperature field model, the third temperature field model and the temperature field model of the wear zone of the rear tool face of the integral flat-head end mill.
2. The method of claim 1, wherein the modeling of the instantaneous contact angle θ between the solid end mill and the workpiece comprises:
discretizing the monolithic flat-head end mill along an axial cutting direction into k pieces with thickness y-dz-ApDisks of/k, ApFor milling depth, when the thickness of each wafer is small enough, the thread is a straight line BD, the straight line BD is taken as a hypotenuse, a right-angle triangle ABD is established, the right-angle side in the horizontal direction is AB, and the right-angle side in the vertical direction is AD;
Figure FDA0003281408660000021
Figure FDA0003281408660000022
Figure FDA0003281408660000023
calculating an instantaneous contact angle theta between the integral flat-head end mill and the workpiece according to the formulas (2), (3) and (4); wherein A ispBeta is the helix angle of the monolithic flat-head end mill and R is the radius of the monolithic flat-head end mill for milling depth.
3. The method of claim 1, wherein the establishing the undeformed chip thickness h model specifically comprises:
each time the cutting edge is cut into the workpiece close to the machined surface
Figure FDA0003281408660000024
Figure FDA0003281408660000025
Figure FDA0003281408660000026
Wherein, VfFor feed rate, AeFor milling width, fzThe feed per tooth, z is the number of edges of the integral flat-end milling cutter, n is the rotation speed of the machine tool, thetaenAt an angle of cut, θexTheta is the instantaneous contact angle between the monolithic flat-head end mill and the workpiece for the cut-out angle, and R is the radius of the monolithic flat-head end mill.
4. The method for determining the instantaneous temperature of the wear zone of the rear face of the integral flat-head end mill according to claim 1, wherein the establishing a temperature field model of the temperature rise influence of the heat source in the first deformation region on the wear zone of the rear face of the integral flat-head end mill specifically comprises:
establishing a pair of a primary heat source point dl of the first deformation zone and a mirror image heat source point dl' of the primary heat source point of the first deformation zone along an arbitrary point P in the X directionI(x,0, z) respectively calculating the temperature rise value delta T of the primary heat source point of the first deformation regionI(x,0, z) and a temperature rise value DeltaT of the mirror image heat source pointI'(x，0，z)；
Figure FDA0003281408660000031
Figure FDA0003281408660000032
Figure FDA0003281408660000033
ComputingAt any point P along the first deformation zone in the X directionITemperature rise value DeltaT of (x,0, z)rake-I(x,0,z)；
ΔTrake-I(x,0,z)＝ΔTI(x,0,z)+ΔTI'(x,0,z) (9)
Wherein l is the distance from the primary heat source point dl of the first deformation region to the origin (0,0,0), and VshThe movement speed of the heat source in the first deformation region, parameter gammanMeaning the normal rake angle, λtFor the thermal conductivity of the integral flat-head end mill, h (theta) is the undeformed chip thickness, phi, corresponding to different instantaneous contactsnIs the normal shear angle, ηcFor chip discharge angle, αwIs the thermal diffusivity of the workpiece; k0For modifying the zero order of Bessel functions of the second kind, RlHeat source point dl to point P of the primary heat source of the first deformation zoneIDistance of (x,0, z), RlFrom 'heat source point dl' to point P which is a mirror image of the heat source of the first deformation zoneI(x,0, z);
established first deformation zone heat intensity qIModel (model)
Figure FDA0003281408660000034
Figure FDA0003281408660000035
Vsh＝Vcosλs (12)
Wherein the parameter τABCD-maxMaximum shear stress for shear plane ABCD, parameter σABCDThe yield stress of the shear plane ABCD, parameter V means the cutting speed, λsIs the edge rake angle, A is the reference strain rate and the initial yield stress at the reference temperature, B is the strain hardening modulus of the workpiece, εABCD-PIs the effective plastic strain of the shear plane ABCD, n is the strain hardening index of the workpiece, C is the strain rate hardening parameter of the workpiece,
Figure FDA0003281408660000041
effective plastic strain rate for shear plane ABCD
Figure FDA0003281408660000042
For reference strain rate, T is the current temperature, TrFor reference temperature, TmM is the melting temperature of the workpiece and m is the heat softening index of the workpiece.
5. The method for determining the instantaneous temperature of the wear zone of the rear face of the integral flat-head end mill according to claim 1, wherein the establishing of the temperature field model of the temperature rise influence of the heat source in the second deformation region on the wear zone of the rear face of the integral flat-head end mill specifically comprises:
establishing a primary heat source point pair of the second deformation region and a mirror image heat source point pair of the second deformation region at any point P along the X' directionII(x ',0, z') respectively calculating the temperature rise delta T of the primary heat source point of the second deformation regionII(x ',0, z') and the second deformation zone mirror heat source point Δ TII'(x'，0，z')；
Figure FDA0003281408660000043
Figure FDA0003281408660000044
Figure FDA0003281408660000045
Wherein the parameter lc(theta) is the contact length of the tool scraps corresponding to different instantaneous contacts;
calculating an arbitrary point P within the second deformation region heat source along the X' directionIITemperature rise Δ T of (x',0,0)rake-II(x'，0，0)；
ΔTrake-II(x'，0，0)＝ΔTII(x'，0，0)+ΔTII'(x'，0，0) (16)
Wherein R isi-2Point to point P of heat source of second deformation zoneII(x ',0, z') distance, Ri-2' Heat source point to point P on mirror image heat source of the second deformation zone heat sourceII(x ',0, z'), w is the bevel turning width, λsThe inclination angle of the blade;
establishing a second deformation zone heat strength qII(θ, x') model;
Figure FDA0003281408660000051
Figure FDA0003281408660000052
Figure FDA0003281408660000053
Achip(θ)＝lc(θ)wc (20)
Figure FDA0003281408660000054
wherein the parameter σs-wIs the yield stress of the material of the workpiece, parameter wcFor chip width, parameter frake-chip(theta, x') is the friction between the chip contact surfaces, parameter sigman-r(theta, x ') represents the positive stress on the rake face at the instantaneous contact angle theta, coordinate x' between the monolithic flat-head end mill and the workpiece, parameter VcFor the chip movement speed, the parameter ζ is a coefficient determining the pressure distribution of the chip contact surface, and the parameter φnIs the normal shear angle, parameter ηcAngle of chip discharge, σtipIs that it isThe positive stress at the nose of the integral flat-end mill,
Figure FDA0003281408660000055
Figure FDA0003281408660000056
average angle of friction of said integral flat end mill and said chip contact surface, Achip(theta) is the contact area between the integral flat-head end mill and the chip, alphawIs the thermal diffusivity, parameter gamma, of the workpiecenBy normal rake angle;
calculating the heat distribution ratio B of the heat source heat in the second deformation region to the front tool faceII-rake(θ)
Figure FDA0003281408660000057
Wherein λ istIs the thermal conductivity of the integral flat-end milling cutter, parameter lambdawW' is the component of the bevel turning width in the direction of the cutting edge, which is the workpiece material thermal conductivity.
6. The method for determining the instantaneous temperature of the wear zone of the rear face of the integral flat-head end mill according to claim 1, wherein the establishing of the temperature field model of the temperature rise influence of the heat source in the third deformation region on the wear zone of the rear face of the integral flat-head end mill specifically comprises:
establishing a primary heat source point pair of a third deformation region and a mirror image heat source point pair of the third deformation region at any point P along the X' directionIII(x',0,0) temperature rise model, respectively calculating the temperature rise Delta T of the primary heat source point of the third deformation zoneIII(x ", 0,0) and the third deformation zone mirror heat source point Δ TIII'(x”，0，0)；
Figure FDA0003281408660000061
Figure FDA0003281408660000062
Figure FDA0003281408660000063
Calculating an arbitrary point P within the heat source of the third deformation zone along the X' directionIIITemperature rise DeltaT of (x',0,0)flank-III(x”，0，0)；
ΔTflank-III(x”,0,0)＝ΔTIII(x”,0,0)+ΔTIII'(x”,0,0) (26)
Wherein R isi-3From the heat source point to the point P in the third deformation regionII(x ',0, z') distance, Ri-3'Point-to-point P of heat source on mirror image heat source of the third deformation zoneIIIDistance of (x ", 0,0), w is bevel turning width, λsThe inclination angle of the blade;
establishing a third deformation zone heat intensity qIII(x ") a model;
Figure FDA0003281408660000064
Figure FDA0003281408660000065
Figure FDA0003281408660000066
Figure FDA0003281408660000071
Figure FDA0003281408660000072
wherein the parameter rho means the anteversion angle of a workpiece right in front of the cutter, and the parameter etawMeaning the angle of the slip field, f, rubbed on the flank wear surfaceLibrary(x') is the friction between the tool contact surfaces, lambdasThe inclination angle of the cutting edge of the cutter,
Figure FDA0003281408660000073
is the average coefficient of friction, σ, on the tool-to-tool contact surfacen-f(x') is the positive stress on the flank wear strip, σtipNormal stress on the tip of the knife, VBCRIs the critical point of the plastic flow area and the elastic contact area, K is the ratio of the shear stress on the cutting edge to the shear flow stress on the workpiece, phi is the shear angle, gamma is0Is the front angle of the cutter,
Figure FDA0003281408660000074
is the rake face average friction angle;
calculating the heat distribution ratio B of the heat source heat in the third deformation region to the front tool faceIII-flank(θ)
Figure FDA0003281408660000075
7. The method for determining the instantaneous temperature of the wear zone of the rear face of the integral flat-head end mill according to claim 1, wherein the establishing a temperature field model under a coordinate system X "Y" Z "corresponding to the wear zone of the rear face of the integral flat-head end mill, and the obtaining the temperature field model of the wear zone of the rear face of the integral flat-head end mill specifically comprises:
calculating the temperature T of any point P (X ',0,0) along the X ' direction under the coordinate system X ' Y ' Z ' corresponding to the built integral flat-head end mill rear cutter surface wear zoneflank(x”,0,0)，
Tflank(x”,0,0)＝ΔTflank-I(x"-VB1,0,0)+ΔTtoolflank-II(lc-Z",0,VB1-X")+ΔTflank-III(x”,0,0)+T0 (33)
Wherein, T0Is the initial temperature.
8. An instantaneous temperature determination system for a flank wear zone of a one-piece flat-head end mill, the determination system comprising:
a coordinate system establishing module for converting a coordinate system XYZ of the first deformation area heat source and a coordinate system X 'Y' Z 'of the second deformation area heat source into a coordinate system of the third deformation area heat source, namely a coordinate system X' Y 'Z' corresponding to the wear zone of the rear tool face of the integral flat-head end mill;
the instantaneous contact angle model establishing module is used for establishing a model of an instantaneous contact angle theta between the integral flat-head end mill and a workpiece;
the undeformed chip thickness model building module is used for building an undeformed chip thickness h model under the condition that the integral flat-head end mill does not deform and vibrate and a cutting edge cuts from a position close to a machined surface during machining of the workpiece;
the undeformed chip thickness calculation module is used for calculating the undeformed chip thickness h according to the undeformed chip thickness h model;
the temperature field model establishing module is used for establishing a temperature field model of which the temperature rise influence is generated on a rear cutter face wear zone of the integral flat-head end mill by a first deformation zone heat source to obtain a first temperature field model, wherein the first deformation zone heat source is heat generated in shearing sliding of chips in a shearing plane;
the second temperature field model establishing module is used for establishing a temperature field model of which the temperature rise influence is generated on the rear cutter face wear zone of the integral flat-head end mill by a second deformation zone heat source to obtain a second temperature field model, and the second deformation zone heat source is heat generated by extrusion and friction of the chips and the front cutter face of the integral flat-head end mill;
the third temperature field model establishing module is used for establishing a temperature field model of which the temperature rise influence is generated on the rear cutter face wear zone of the integral flat-head end mill by a third deformation zone heat source to obtain a third temperature field model, wherein the third deformation zone heat source is heat generated by extrusion and friction between the machined surface of the workpiece and the rear cutter face wear zone of the integral flat-head end mill;
the integral flat-head end mill rear cutter surface wear zone temperature field model building module is used for building a temperature field model under a coordinate system corresponding to the integral flat-head end mill rear cutter surface wear zone to obtain an integral flat-head end mill rear cutter surface wear zone temperature field model;
and the instantaneous temperature calculation module is used for calculating the instantaneous temperature of the wear zone of the rear cutter face of the integral flat-head end mill according to the first temperature field model, the second temperature field model, the third temperature field model and the temperature field model of the wear zone of the rear cutter face of the integral flat-head end mill.
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