CN104392090B - The construction method of aluminum alloy materials end mill cutting force and machining distorted pattern - Google Patents

The construction method of aluminum alloy materials end mill cutting force and machining distorted pattern Download PDF

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CN104392090B
CN104392090B CN201410505390.8A CN201410505390A CN104392090B CN 104392090 B CN104392090 B CN 104392090B CN 201410505390 A CN201410505390 A CN 201410505390A CN 104392090 B CN104392090 B CN 104392090B
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焦黎
王西彬
钱钰博
孙厚芳
解丽静
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Beijing Institute of Technology BIT
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Abstract

The invention discloses a kind of aluminum alloy materials end mill cutting force and the construction method of machining distorted pattern, establish the Milling Force forecast model based on average cutting force, establish the Milling Force forecast model based on inclined cutting mechanism, based on the Milling Force forecast model based on average cutting force and the Milling Force forecast model based on inclined cutting mechanism established, carry out respectively single, multiple tooth transient state Milling Force is predicted and contrasted with test data, and establish aluminum alloy materials Deformation in Milling Process model, end mill processing surface planarity error is predicted based on the self-adapted genetic algorithm of real coding, there is important Research Significance to research machining deformation mechanism.

Description

The construction method of aluminum alloy materials end mill cutting force and machining distorted pattern
Technical field
The invention belongs to machine field, more particularly to a kind of aluminum alloy materials end mill cutting force and machining distorted pattern The construction method of type.
Background technology
Research at present both at home and abroad on cast aluminum alloy material casting technique is more ripe, but different cast aluminiums are closed The research of the mechanical characteristic of golden material is still only limitted to static mechanical characteristics research, for machining high temperature, Large strain, Gao Ying Cast aluminum alloy material dynamic characteristics research under the conditions of variability is not yet carried out, therefore studies cast aluminum alloy material and cutting at a high speed The dynamic mechanical come under the conditions of cutting at performance, there is important Research Significance to research machining deformation mechanism.
According to cast aluminum alloy material feature, the main machining method of cast aluminium alloy complexity box parts is cut for end mill, when When carrying out large scale plane machining, the influence of receiving end milling cutter diameter, although not selecting the higher speed of mainshaft during processing, select Larger diameter end milling cutter remains to reach higher cutting speed (＞ 1000m/min), therefore unsuitable biography in working angles The cutting theory of system carries out analysis, it is necessary to establish the research method of suitable high speed end milling cutting.
The content of the invention
It is an object of the invention to provide a kind of aluminum alloy materials end mill cutting force and the structure of machining distorted pattern Method, it is intended to high temperature, Large strain, the dynamic mechanical of high strain-rate shown to cast aluminum alloy material under the conditions of high-speed cutting Performance is studied.
The present invention is achieved in that a kind of specific steps of the construction method of aluminum alloy materials end mill cutting Force Model such as Under：
Step 1: establish the Milling Force forecast model based on average cutting force, according to instantaneous not deformed chip thickness degree with The parsing relation of transient state Milling Force, establish Milling Force solution key factor-Cutting Force Coefficient and cut on feed engagement, axially Deep, the quadratic polynomial model of four cutting parameters of cutting speed and unilateral cutting width, wherein unilateral cutting width illustrates Incision in end mill working angles caused by tool track difference cuts out angle change, by carrying out four factors, four horizontal end mill Cutting force measurement is tested, and coefficient in Cutting Force Coefficient model is returned with least square method, and study cutting parameter pair The influence of Cutting Force Coefficient, establish the Milling Force forecast model based on average cutting force；
Step 2: the Milling Force forecast model based on inclined cutting mechanism is established, for cutting force in inclined cutting with cutting The relation for cutting parameter carries out analytical Calculation, based on cast aluminium alloy Johnson-Cook material constitutive models, with finite element simulation Method is predicted solution to the cutting fundamental quantity such as angle of shear, and the Cutting Force Coefficient in Milling Force forecast model is calculated, builds The Milling Force forecast model for the inclined cutting mechanism that is based on；
Step 3: based on the Milling Force forecast model established based on average cutting force and based on inclined cutting mechanism Milling Force forecast model, carry out single, multiple tooth transient state Milling Force respectively and predict and contrasted with test data that binding model is established Process carries out the cutting force-induced error analysis of causes.
Further, the specific method of Milling Force forecast model of the described foundation based on average cutting force is：
First, it is discrete that multiple cutters tooth are simultaneously participated in the end mill working angles progress of cutting, if end mill(ing) cutter cutter tooth numbering is I, when i-th cutter tooth participates in cutting, by cutting edge it is equidistantly discrete be limited individual infinitesimal cutting edge dz, each infinitesimal is cut The process that sword participates in cutting can be equivalent to an Oblique Cutting Process；
The instantaneous cutting force dF acted on cutter tooth i cutting edge infinitesimals dziCan tangentially, radially, axially it be decomposed into respectively Three components：Tangential instantaneous cutting force dFti, radially instantaneous cutting force dFriAnd the instantaneous cutting force dF in axial directionai, establish instantaneous cutting Make every effort to solve relational expression such as following formula, K in formulatc、Krc、KacRespectively effect system of the shear action to tangential, radial and axial cutting force Number, Kte、Kre、KaeRespectively corresponding cutting edge force coefficient；
The single cutter tooth milling area schematic of end mill(ing) cutter, it is research object to take the dz infinitesimals on i-th of cutter tooth,With Respectively the entrance angle of cutter tooth, cut out angle.When pirouette to instant contact angleWhen, instantaneous not deformed chip thickness degreeCan be by formulaApproximate representation, wherein fzFor feed engagement；
WhenWhen cutter tooth infinitesimal within the scope of effective cutting,Calculation formula such as following formula, Wherein aeyPoint of penetration and cutter pivot are fixed a cutting tool perpendicular to the distance of direction of feed for workpiece, B is width of the machined surface, R is tool radius；
If ω is cutter angular velocity of rotation, t is process time, then cutter tooth cuts instantaneous instant contact angleWith cutter wink When cornerCutter angle between teethAnd transient deviation angle θ is (caused by cutter helixangleβWithDeviation) between Relation such as following formula；
When consideration cutter tool cutting edge angle is krWhen, instantaneous chip thickness degreeIt is expressed as：
, will be tangential, radially and the instantaneous cutting force of axial direction is converted to x directions (feed to), y directions by coordinate transform (direction of feed normal direction) and z directions (axial direction)：
Wherein, c=fzsinkr,, kβ=tan β/R, then integrate and obtain the instantaneous cutting force of three-dimensional, whereinRepresent that cutter tooth cutting edge participates in the axial upper and lower limit of cutting tip respectively；
It is unrelated with helical angle because the total amount of material of each cutter tooth excision in a cutter swing circle is a constant, because This takes dz=ap,kβ=0, the moment Milling Force in a cutter swing circle is integrated, is integrated knot Fruit divided by angle between teethDraw each cycle mean force：
X, y, z direction cutting mean force is calculated respectively：
Therefore averagely cutting force can be expressed as feed engagement fzIt is linear function and cutting edge power and, by testing and Cutting Force Coefficient can be calculated in regression analysis：
It is assumed that Cutting Force Coefficient is on axial cutting-in ap, feed engagement fz, cutting speed vcAnd unilateral cutting width aey Function, because the functional relation between Cutting Force Coefficient and parameter is complicated, it is impossible to represented, therefore used such as with simple linear function Quadratic expression form shown in following formula establishes Ktc、Krc、Kac、Kte、Kre、KaeMultinomial model on cutting data：
Carry out cutting force measurement experiment, the parameter in formula above formula can be solved according to test measurement result, so as to Cutting Force Coefficient multinomial is drawn, calculates Instantaneous Milling Force.
Further, the specific method for establishing the Milling Force forecast model based on inclined cutting mechanism is：
Shear strain in shear plane can be derived from according to geometrical relationship：
Wherein η is chip-flow angle, according to least-energy principle, is analyzed from geometrical point, shearing force FsF is represented by shear Projection in plane, expression formula such as following formula：
Fs=F [cos (θn+φn)cosθicosφi+sinθisinφi]
Or the average shearing stress τ on expression shear planesWith shear surface area AsProduct：
Wherein shear surface areal calculation is based on instantaneous not deformed chip thickness degreeAverage shearing stress τsIt can pass through The limit element artificial module based on Johnson-Cook constitutive models is established to solve；Act on milling cutter cutter tooth infinitesimal dz Cutting force is made a concerted effort dF, and three-dimensional cutting force component dF tangentially, radially, axiallyt、dFr、dFa：
Hypothesis below is done to the three-dimensional cutting force form acted on infinitesimal dz：
It then can obtain Cutting Force Coefficient Ktc、Krc、KacExpression formula：
In upper, due to dFt、dFr、dFaIt is on shear yield stress τs, resultant tool force direction θnAnd θi, cutting edge inclination λs With Shear Plane Angle in Oblique Metal Machining φnAnd φiFunction, numerous inclined cutting parameters make troubles to solution, therefore apply Armarego's Classical oblique cutting model is simplified the inclined cutting parameter for being difficult to solve based on following two hypothesis：Shear rate is with cutting Shear force is conllinear (one of maximum shear stress criterion)；Length of chip ratio is identical in orthogonal cutting and inclined cutting；
Based on above-mentioned it is assumed that can draw：
Draw Cutting Force Coefficient Ktc、Krc、Kac
Further, for how multiple tooth in the case of, if i-th cutter tooth relative to preferable cutter tooth position by axial positioning errors Δ zi, radial position error Δ ri, then：
A kind of method for building up of aluminum alloy materials Deformation in Milling Process model includes：
Single factor test mismachining tolerance model：
The collection S that sets up an office is the set all put on surface to be machined in end mill processing, pi∈ S are any one on surface to be machined Point, piPoint produces mismachining tolerance E in the presence of error influence factor FFi, EFiFor the vector representation of mismachining tolerance, error influences Factor F both can be part or power, the temperature field of lathe, can also be some random disturbances；
Analyze cutting process, EFiIt is not once to reach, but passes through the cumulative obtained result of multiple error；
If flush cut process time is T, in t1Moment (t1∈ [0, T]) piMismachining tolerance of the point in the presence of F is δ0 +δ1, wherein δ0For pi initial error state, then in t1+ time Δt, piThe processing that the mismachining tolerance of point then shows as accumulation misses Poor δ0+δ1+ Δ δ, if therefore taking t in the range of [0, T]1、t2、......、tmThe common m moment is analyzed, then EFiIt is represented by The form of pi point accumulated error vectors
Various factors coupling mismachining tolerance model：
If k error influence factor F is shared in process1、F2、...FkAct on workpiece to be machined, piPoint is each Mismachining tolerance E caused by the effect of error influence factor is lowerFiExpression formula it is as follows：
Wherein c is coefficient of rejection, λ1、λ2......λmFor each compositing factor error distribution curve shape it is relevant be λ=1/3 when number, λ=1/9 during normal distribution, equiprobability curve or unclear distribution, λ=1/6 during Triangle-Profile；
End mill processing surface error influence factor can draw point p on end mill processing surfaceiError Ei：
Self-adapted genetic algorithm based on real coding carries out end mill processing surface planarity error prediction.
The present invention establishes the Milling Force forecast model based on average cutting force, establishes the milling based on inclined cutting mechanism Power forecast model is cut, based on the Milling Force forecast model based on average cutting force and the milling based on inclined cutting mechanism established Power forecast model is cut, carries out single, multiple tooth transient state Milling Force respectively and predicts and contrasted with test data, and establish aluminium alloy Material Deformation in Milling Process model, end mill processing surface planarity error is carried out based on the self-adapted genetic algorithm of real coding Prediction, there is important Research Significance to research machining deformation mechanism.
Brief description of the drawings
Fig. 1 is aluminum alloy materials end mill cutting Force Model construction method flow chart provided in an embodiment of the present invention；
Fig. 2 is the discrete cutter tooth infinitesimal schematic diagram of end mill working angles provided in an embodiment of the present invention；
Fig. 3 is Tool in Milling area schematic provided in an embodiment of the present invention；
Fig. 4 is the relation schematic diagram of cutting force, speed and the angle of shear in inclined cutting provided in an embodiment of the present invention；
Fig. 5 is that the two class cutting Force Model monodentate prediction results provided in an embodiment of the present invention that are based on contrast with test data；
Fig. 6 is end mill(ing) cutter office cutter tooth site error schematic diagram provided in an embodiment of the present invention；
Fig. 7 is cutter tooth provided in an embodiment of the present invention radially, axially position deviation schematic diagram；
Fig. 8 is face milling with multiblade cutter prediction of Turning Force with Artificial provided in an embodiment of the present invention and test data comparison diagram；
Fig. 9 is that the flatness error provided in an embodiment of the present invention based on materialized view maintenance solves flow Figure；
Figure 10 is flatness error iteration convergence curve provided in an embodiment of the present invention；
Figure 11 is convergence curve contrast provided in an embodiment of the present invention.
Embodiment
In order to make the purpose , technical scheme and advantage of the present invention be clearer, it is right below in conjunction with drawings and Examples The present invention is further elaborated.It should be appreciated that the specific embodiments described herein are merely illustrative of the present invention, and It is not used in the restriction present invention.
The present invention is achieved in that a kind of specific steps of the construction method of aluminum alloy materials end mill cutting Force Model such as Under：
Step 1: establish the Milling Force forecast model based on average cutting force, according to instantaneous not deformed chip thickness degree with The parsing relation of transient state Milling Force, establish Milling Force solution key factor-Cutting Force Coefficient and cut on feed engagement, axially Deep, the quadratic polynomial model of four cutting parameters of cutting speed and unilateral cutting width, wherein unilateral cutting width illustrates Incision in end mill working angles caused by tool track difference cuts out angle change, by carrying out four factors, four horizontal end mill Cutting force measurement is tested, and coefficient in Cutting Force Coefficient model is returned with least square method, and study cutting parameter pair The influence of Cutting Force Coefficient, establish the Milling Force forecast model based on average cutting force；
Step 2: the Milling Force forecast model based on inclined cutting mechanism is established, for cutting force in inclined cutting with cutting The relation for cutting parameter carries out analytical Calculation, based on cast aluminium alloy Johnson-Cook material constitutive models, with finite element simulation Method is predicted solution to the cutting fundamental quantity such as angle of shear, and the Cutting Force Coefficient in Milling Force forecast model is calculated, builds The Milling Force forecast model for the inclined cutting mechanism that is based on；
Step 3: based on the Milling Force forecast model established based on average cutting force and based on inclined cutting mechanism Milling Force forecast model, carry out single, multiple tooth transient state Milling Force respectively and predict and contrasted with test data, wherein based on average The precision of prediction of the Milling Force forecast model of cutting force is better than the Milling Force forecast model based on inclined cutting mechanism, binding model Establish process and carry out the cutting force-induced error analysis of causes.
Further, the specific method of Milling Force forecast model of the described foundation based on average cutting force is：
First, it is discrete that multiple cutters tooth are simultaneously participated in the end mill working angles progress of cutting, if end mill(ing) cutter cutter tooth numbering is I, when i-th cutter tooth participates in cutting, by cutting edge it is equidistantly discrete be limited individual infinitesimal cutting edge dz, as shown in Fig. 2 each The process that individual infinitesimal cutting edge participates in cutting can be equivalent to an Oblique Cutting Process；
The instantaneous cutting force dF acted on cutter tooth i cutting edge infinitesimals dziCan tangentially, radially, axially it be decomposed into respectively Three components：Tangential instantaneous cutting force dFti, radially instantaneous cutting force dFriAnd the instantaneous cutting force dF in axial directionai, establish instantaneous cutting Make every effort to solve relational expression such as following formula, K in formulatc、Krc、KacRespectively effect system of the shear action to tangential, radial and axial cutting force Number, Kte、Kre、KaeRespectively corresponding cutting edge force coefficient；
The single cutter tooth milling area schematic of end mill(ing) cutter is as shown in figure 3, it is research pair to take the dz infinitesimals on i-th of cutter tooth As,WithRespectively the entrance angle of cutter tooth, cut out angle.When pirouette to instant contact angleWhen, instantaneous not deformed chip Thickness degreeCan be by formulaApproximate representation, wherein fzFor feed engagement；
WhenWhen cutter tooth infinitesimal within the scope of effective cutting,Calculation formula such as following formula, Wherein aeyPoint of penetration and cutter pivot are fixed a cutting tool perpendicular to the distance of direction of feed for workpiece, B is width of the machined surface, R is tool radius；
If ω is cutter angular velocity of rotation, t is process time, then cutter tooth cuts instantaneous instant contact angleWith cutter wink When cornerCutter angle between teethAnd transient deviation angle θ is (caused by cutter helixangleβWithDeviation) between Relation such as following formula；
When consideration cutter tool cutting edge angle is krWhen, instantaneous chip thickness degreeIt is expressed as：
, will be tangential, radially and the instantaneous cutting force of axial direction is converted to x directions (feed to), y directions by coordinate transform (direction of feed normal direction) and z directions (axial direction)：
Wherein, c=fzsinkr,kβ=tan β/R, then integrate and obtain the instantaneous cutting force of three-dimensional, whereinRepresent that cutter tooth cutting edge participates in the axial upper and lower limit of cutting tip respectively；
It is unrelated with helical angle because the total amount of material of each cutter tooth excision in a cutter swing circle is a constant, because This takes dz=ap,kβ=0, the moment Milling Force in a cutter swing circle is integrated, is integrated knot Fruit divided by angle between teethDraw each cycle mean force：
X, y, z direction cutting mean force is calculated respectively：
Therefore averagely cutting force can be expressed as feed engagement fzIt is linear function and cutting edge power and, by testing and Cutting Force Coefficient can be calculated in regression analysis：
It is assumed that Cutting Force Coefficient is on axial cutting-in ap, feed engagement fz, cutting speed vcAnd unilateral cutting width aey Function, because the functional relation between Cutting Force Coefficient and parameter is complicated, it is impossible to represented, therefore used such as with simple linear function Quadratic expression form shown in following formula establishes Ktc、Krc、Kac、Kte、Kre、KaeMultinomial model on cutting data：
Carry out cutting force measurement experiment, the parameter in formula above formula can be solved according to test measurement result, so as to Cutting Force Coefficient multinomial is drawn, calculates Instantaneous Milling Force.
Further, the specific method for establishing the Milling Force forecast model based on inclined cutting mechanism is：
The relation of cutting force, speed and the angle of shear when continuous band-shaped chip is formed in Oblique Cutting Process as shown in figure 4, Shear strain in shear plane can be derived from according to geometrical relationship：
Wherein η is chip-flow angle, according to least-energy principle, is analyzed from geometrical point, shearing force FsF is represented by shear Projection in plane, such as Fig. 4, expression formula such as following formula：
Fs=F [cos (θn+φn)cosθicosφi+sinθisinφi]
Or the average shearing stress τ on expression shear planesWith shear surface area AsProduct：
Wherein shear surface areal calculation is based on instantaneous not deformed chip thickness degreeAverage shearing stress τsIt can pass through The limit element artificial module based on Johnson-Cook constitutive models is established to solve；Act on milling cutter cutter tooth infinitesimal dz Cutting force is made a concerted effort dF, and three-dimensional cutting force component dF tangentially, radially, axiallyt、dFr、dFa：
Hypothesis below is done to the three-dimensional cutting force form acted on infinitesimal dz：
It then can obtain Cutting Force Coefficient Ktc、Krc、KacExpression formula：
In upper, due to dFt、dFr、dFaIt is on shear yield stress τs, resultant tool force direction θnAnd θi, cutting edge inclination λs With Shear Plane Angle in Oblique Metal Machining φnAnd φiFunction, numerous inclined cutting parameters make troubles to solution, therefore apply Armarego's Classical oblique cutting model is simplified the inclined cutting parameter for being difficult to solve based on following two hypothesis：Shear rate is with cutting Shear force is conllinear (one of maximum shear stress criterion)；Length of chip ratio is identical in orthogonal cutting and inclined cutting；
Based on above-mentioned it is assumed that can draw：
Draw Cutting Force Coefficient Ktc、Krc、Kac
Cutting force measurement experimental design
The embodiment of the present invention using ZL702A materials as milling test object, material chemical composition and physical property be shown in Table 1, Table 2.Lathe used in experiment is XS5040 vertical and high-speed knee-and-column milling machines, end mill(ing) cutter a diameter of 125mm, number of teeth 1-2, tool cutting edge angle 75 °, 15 ° of axial rake, -3 ° of radial rake, 15 ° of helical angle, cutter material is carbide alloy YG 8.
The cutting force test factor level table of table 1
The Cutting Force Coefficient coefficient regression of table 2
Cutting force measurement equipment uses the Kistler9257B three-dimensional dynamic force measurement instrument of Kistler companies of Switzerland production, if It is 2000Hz to determine sample frequency, during milling the change of workpiece institute stress cause the deformation of dynamometer internal resistance foil gauge, the shape The imbalance of electric bridge can be caused by becoming, and then cause the change of output voltage, using the detection of Kistler5017A charge amplifiers simultaneously Amplify this faint output signal, measured value is obtained after A/D is changed.According to dynamometer nominal data, draw and survey institute's dynamometry Relation between value and true force value.
To study the end mill cutting Force Model based on cutting scheme, the embodiment of the present invention considers workpiece material mechanical property Can, based on cast aluminium alloy gold ZL702A material constitutive equations, right angle milling two dimensional finite element simulation model is established, the angle of shear is entered Row prediction.
(1) the Milling Force forecast model based on average cutting force
Two groups of Milling Parameters are taken to be shown in Table 3 respectively, cutting-tool angle parameter calculates respectively with cutting force test parameter according to table 2 Ktc、Krc、Kac、Kte、Kre、KaeSix Cutting Force Coefficients, solve Instantaneous Milling Force Fx、Fy、Fz。
The simulation and prediction Milling Parameters table of table 3
(2) the Milling Force forecast model based on inclined cutting mechanism
Milling Force Prediction Parameters are solved based on inclined cutting mechanism with table 4, cutting-tool angle with cutting force test parameter Milling Force Model coefficient, so as to establish Milling Force forecast model.
The conventional magnetic shear angle expression formula of table 4
The Milling Force prediction result obtained based on two class Milling Force forecast models is compared with test data as shown in figure 5, right Understood than simulation and prediction cutting force data in Fig. 5 and test measurement cutting force data, change of the two class Milling Force Models to Milling Force Change trend has more preferable reflection, but numerically still has certain deviation, wherein the Milling Force mould based on average cutting force The precision of prediction of type is better than the Milling Force Model established based on inclined cutting mechanism.The former due to integrated use experiment with Analytic method, Cutting Force Coefficient is determined by milling test on the basis of theory solves, and non-fully obtained by empirical equation , because the empirical equation of the parameters such as the angle of shear has certain prediction error for corresponding the latter, according further to orthogonal cutting mistake Some assumed conditions are have also been introduced while journey simplifies to Oblique Cutting Process, therefore are formd in data prediction precision Difference.
Further, the cutter tooth site error of end mill cutter mainly includes radial position error and axial positioning errors, such as Fig. 6 Shown, when cutter tooth existence position is offset, cutter will be done around insert central axis and be revolved with or small radius bigger than preferable radius Turn cutting movement, axial cutting-in may also be more than or less than preferable cutting-in.
If i-th cutter tooth relative to preferable cutter tooth position by axial positioning errors Δ zi, radial position error Δ ri, such as Shown in Fig. 7, then formula 3.4 is rewritable such as formula：
It can thus be appreciated that in end mill cutting force calculating process, it is selected to refer to cutter tooth and determine remaining measure cutter tooth site error Afterwards, the instantaneous cutting force acted on different cutters tooth can be calculated respectively.The embodiment of the present invention is based on average cutting Force Model pair Face milling with multiblade cutter cutting force carries out simulation and prediction, number of teeth 2, and 180 ° of blade is symmetrically installed, -52 μm of cutter tooth axial positioning errors, - 13 μm of radial position error.Milling Parameters：fz=0.1mm/z, ap=1mm, n=800m/min, ae=30mm, prediction result and Result of the test is as shown in figure 8, have preferable uniformity in the cutting force variation tendency of the two.
A kind of method for building up of aluminum alloy materials Deformation in Milling Process model includes：
Single factor test mismachining tolerance model：
The collection S that sets up an office is the set all put on surface to be machined in end mill processing, pi∈ S are any one on surface to be machined Point, piPoint produces mismachining tolerance E in the presence of error influence factor FFi, EFiFor the vector representation of mismachining tolerance, error influences Factor F both can be part or power, the temperature field of lathe, can also be some random disturbances；
Analyze cutting process, EFiIt is not once to reach, but passes through the cumulative obtained result of multiple error；
If flush cut process time is T, in t1Moment (t1∈ [0, T]) piMismachining tolerance of the point in the presence of F is δ0 +δ1, wherein δ0For pi initial error state, then in t1+ time Δt, piThe processing that the mismachining tolerance of point then shows as accumulation misses Poor δ0+δ1+ Δ δ, if therefore taking t in the range of [0, T]1、t2、......、tmThe common m moment is analyzed, then EFiIt is represented by The form of pi point accumulated error vectors：
Various factors coupling mismachining tolerance model：
If k error influence factor F is shared in process1、F2、...FkAct on workpiece to be machined, piPoint is each Mismachining tolerance E caused by the effect of error influence factor is lowerFiExpression formula it is as follows：
Wherein c is coefficient of rejection, λ1、λ2......λmFor each compositing factor error distribution curve shape it is relevant be λ=1/3 when number, λ=1/9 during normal distribution, equiprobability curve or unclear distribution, λ=1/6 during Triangle-Profile；
End mill processing surface error influence factor can draw point p on end mill processing surfaceiError Ei：
Wherein each parameter declaration is as follows：
Table 5
The end mill processing surface planarity error prediction of self-adapted genetic algorithm based on real coding, flow chart such as Fig. 9 It is shown.
The textured surface point data is as shown in table 6,11 measuring points is respectively distributed with along x, y direction, surface amounts to 121 surveys Point.
The flatness error data (μm) of table 6
Initial population scale is 20, and maximum iteration 100, variable a, b excursion is asked according to least square method Obtain a0、b0It is determined that.By 100 iteration, it is 15.95 to draw flatness error, and parameter iteration convergence curve is as shown in Figure 10.
Compared with standard genetic algorithm, to be solved herein using standard genetic algorithm to the data in table 5, institute Obtained flatness error is 16.02, with using the convergence curve obtained based on materialized view maintenance to such as Shown in Figure 11.By contrast, calculated based on the flatness error ratio that real number self-adapted genetic algorithm is tried to achieve based on standard genetic The flatness error that method is calculated reduces about 0.07 μm, realizes the original of " survival of the fittest, the survival of the fittest " of genetic algorithm Reason.
Although above-mentioned the embodiment of the present invention is described with reference to accompanying drawing, model not is protected to the present invention The limitation enclosed, one of ordinary skill in the art should be understood that on the basis of technical scheme those skilled in the art are not Need to pay various modifications or deformation that performing creative labour can make still within protection scope of the present invention.

Claims (5)

  1. A kind of 1. construction method of aluminum alloy materials end mill cutting Force Model, it is characterised in that described aluminum alloy materials end mill The construction method of cutting Force Model includes：
    Step 1: the Milling Force forecast model based on average cutting force is established, according to instantaneous not deformed chip thickness degree and transient state The parsing relation of Milling Force, establish Milling Force solve key factor-Cutting Force Coefficient on feed engagement, axial cutting-in, cut The quadratic polynomial model of four cutting parameters of speed and unilateral cutting width is cut, is cut wherein unilateral cutting width illustrates end mill Incision during cutting caused by tool track difference cuts out angle change, by carrying out the horizontal ends milling cutting force of four factor four Measurement experiment, is returned with least square method to coefficient in Cutting Force Coefficient model, obtains cutting parameter to cutting force system Several influences, establish the Milling Force forecast model based on average cutting force；
    Step 2: establishing the Milling Force forecast model based on inclined cutting mechanism, join for cutting force in inclined cutting and cutting Several relations carries out analytical Calculation, based on cast aluminium alloy Johnson-Cook material constitutive models, with finite element simulation method Solution is predicted to angle of shear cutting fundamental quantity, the Cutting Force Coefficient in Milling Force forecast model is calculated, foundation is based on The Milling Force forecast model of inclined cutting mechanism；
    Step 3: based on the Milling Force forecast model based on average cutting force and the milling based on inclined cutting mechanism established Power forecast model, carry out single, multiple tooth transient state Milling Force respectively and predict and contrasted with test data that binding model establishes process Carry out the cutting force-induced error analysis of causes.
  2. 2. the construction method of aluminum alloy materials end mill cutting Force Model as claimed in claim 1, it is characterised in that described builds The specific method of Milling Force forecast model of average cutting force of being based on is：
    First, by multiple cutters tooth simultaneously participate in cutting end mill working angles carry out it is discrete, end mill(ing) cutter cutter tooth numbering be i, when i-th When individual cutter tooth participates in cutting, by cutting edge it is equidistantly discrete be limited individual infinitesimal cutting edge dz, the participation of each infinitesimal cutting edge The process of cutting can be equivalent to an Oblique Cutting Process；
    The instantaneous cutting force dF acted on cutter tooth i cutting edge infinitesimals dziCan respectively tangentially, be radially, axially decomposed into three points Amount：Tangential instantaneous cutting force dFti, radially instantaneous cutting force dFriAnd the instantaneous cutting force dF in axial directionai, establish instantaneous cutting force and solve Relational expression such as following formula, K in formulatc、Krc、KacRespectively shear action is to the function coefficient of tangential, radial and axial cutting force, Kte、 Kre、KaeRespectively corresponding cutting edge force coefficient；
    The single cutter tooth milling area schematic of end mill(ing) cutter, it is research object to take the dz infinitesimals on i-th of cutter tooth,WithRespectively For the entrance angle of cutter tooth, angle is cut out, when pirouette to instant contact angleWhen, instantaneous not deformed chip thickness degree Can be by formulaApproximate representation, wherein fzFor feed engagement；
    WhenWhen cutter tooth infinitesimal within the scope of effective cutting,Calculation formula such as following formula, wherein aeyFor unilateral cutting width, B is width of the machined surface, and R is tool radius；
    ω is cutter angular velocity of rotation, and t is process time, then cutter tooth cuts instantaneous instant contact angleWith the instantaneous corner of cutterCutter angle between teethAnd the relation such as following formula between the θ of transient deviation angle；
    When cutter tool cutting edge angle is krWhen, instantaneous not deformed chip thickness degreeIt is expressed as：
    By coordinate transform, the instantaneous cutting force of tangential, radial direction and axial direction is converted into x directions, y directions and z directions：
    Wherein, c=fzsin kr,kβ=tan β/R, then integrate and obtain the instantaneous cutting force of three-dimensional, whereinRepresent that cutter tooth cutting edge participates in the axial upper and lower limit of cutting tip respectively；
    It is unrelated with helical angle because the total amount of material of each cutter tooth excision in a cutter swing circle is a constant, therefore take Dz=ap,kβ=0, the moment Milling Force in a cutter swing circle is integrated, by integral result divided by Angle between teethDraw each cycle mean force：
    Wherein q=x, y, z
    X, y, z direction cutting mean force is calculated respectively：
    Therefore averagely cutting force is expressed as feed engagement fzIt is linear function and cutting edge power and, pass through and test and regression analysis Cutting Force Coefficient is calculated：
    Cutting Force Coefficient is on axial cutting-in ap, feed engagement fz, cutting speed vcAnd unilateral cutting width aeyFunction, Because the functional relation between Cutting Force Coefficient and parameter is complicated, it is impossible to represented, therefore used such as following formula institute with simple linear function The quadratic expression form shown establishes Ktc、Krc、Kac、Kte、Kre、KaeMultinomial model on cutting data：
    Carry out cutting force measurement experiment, the parameter in above formula can be solved according to test measurement result, cut so as to draw Force coefficient multinomial is cut, calculates Instantaneous Milling Force.
  3. 3. the construction method of aluminum alloy materials end mill cutting Force Model as claimed in claim 1, it is characterised in that foundation is based on The specific method of the Milling Force forecast model of inclined cutting mechanism is：
    Shear strain in shear plane is derived from according to geometrical relationship：
    Wherein η is chip-flow angle, according to least-energy principle, is analyzed from geometrical point, shearing force FsF is represented by shear plane On projection, expression formula such as following formula：
    Fs=F [cos (θn+φn)cosθicosφi+sinθisinφi]
    Or the average shearing stress τ on expression shear planesWith shear surface area AsProduct：
    Wherein shear surface areal calculation is based on instantaneous not deformed chip thickness degreeAverage shearing stress τsFoundation can be passed through Limit element artificial module based on Johnson-Cook constitutive models solves；The cutting acted on milling cutter cutter tooth infinitesimal dz Power is made a concerted effort dF, and three-dimensional cutting force component dF tangentially, radially, axiallyt、dFr、dFa：
    To acting on the three-dimensional cutting force form on infinitesimal dz：
    Then obtain Cutting Force Coefficient Ktc、Krc、KacExpression formula：
    In upper, due to dFt、dFr、dFaIt is on average shearing stress τs, resultant tool force direction θnAnd θi, cutting edge inclination λsCut with oblique angle Cut angle of shear φnAnd φiFunction, numerous inclined cutting parameters make troubles to solution, therefore apply Armarego classical oblique angle Cutting Model is based on below being simplified the inclined cutting parameter for being difficult to solve：Shear rate is conllinear with shearing force；Chip is grown Degree is more identical than in orthogonal cutting and inclined cutting；Draw：
    Draw Cutting Force Coefficient Ktc、Krc、Kac
  4. 4. the construction method of aluminum alloy materials end mill cutting Force Model as claimed in claim 1, it is characterised in that for multiple tooth Situation, i-th cutter tooth relative to preferable cutter tooth position by axial positioning errors Δ zi, radial position error Δ ri, then：
  5. A kind of 5. construction method of aluminum alloy materials Deformation in Milling Process model, it is characterised in that described aluminum alloy materials milling Cutting the construction method of machining deformation model includes：
    Single factor test mismachining tolerance model：
    Point set S is the set all put on surface to be machined in end mill processing, pi∈ S be surface to be machined on any point, piPoint Mismachining tolerance is produced in the presence of error influence factor F For the vector representation of mismachining tolerance, error influence factor F is both part, power, temperature field or some random disturbances of lathe；
    Analyze cutting process,It is not once to reach, but passes through the cumulative obtained result of multiple error；
    Flush cut process time is T, in t1Moment (t1∈[0,T])piMismachining tolerance of the point in the presence of F is δ0+δ1, its Middle δ0For pi initial error state, then in t1+ time Δt, piThe mismachining tolerance of point then shows as the mismachining tolerance δ of accumulation0+δ1 + Δ δ, if therefore taking t in the range of [0, T]1、t2、……、tmThe common m moment is analyzed, thenIt is expressed as the accumulation of pi points The form of error vector sum：
    Various factors coupling mismachining tolerance model：
    K error influence factor F is shared in process1、F2、…FkAct on workpiece to be machined, piPoint influences in each error Mismachining tolerance caused by factor effect is lowerExpression formula it is as follows：
    Wherein c is coefficient of rejection, λ1、λ2……λmFor the relevant coefficient of the error distribution curve shape of each compositing factor, normal state λ=1/3 when λ=1/9 during distribution, equiprobability curve or unclear distribution, λ=1/6 during Triangle-Profile；
    End mill processing surface error influence factor draws point p on end mill processing surfaceiError Ei：
    Self-adapted genetic algorithm based on real coding carries out end mill processing surface planarity error prediction.
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