CN104392090A - Construction method of aluminium alloy material end milling-cutting force and cutting processing deformation model - Google Patents

Abstract

The invention discloses a construction method of an aluminium alloy material end milling-cutting force and cutting processing deformation model. According to the construction method, a milling-cutting force prediction model on the basis of an average cutting force is established; a milling-cutting force prediction model on the basis of an inclined cutting mechanism is established; on the basis of the established milling-cutting force prediction model on the basis of the average cutting force and the established milling-cutting force prediction model on the basis of the inclined cutting mechanism, single-tooth and multi-tooth transient milling-cutting force predictions are respectively carried out and obtained data is compared with testing data; an aluminum alloy material milling-cutting processing deformation model is established; on the basis of a real number encoded adaptive genetic algorithm, a flatness error of an end milled surface is predicted; the construction method has the important research significance for researching the processing deformation mechanism.

Description

The construction method of aluminum alloy materials end mill cutting force and cut distorted pattern

Technical field

The invention belongs to machine work field, particularly relate to the construction method of a kind of aluminum alloy materials end mill cutting force and cut distorted pattern.

Background technology

The domestic and international research about cast aluminum alloy material casting technique is at present comparatively ripe, but static mechanical characteristics research is still only limitted to the research of the mechanical characteristic of different cast aluminum alloy material, not yet carry out for the cast aluminum alloy material dynamic characteristics research under high temperature, Large strain, high strain-rate condition in cut, therefore study the cast aluminum alloy material dynamic mechanical that performance place comes under high-speed cutting condition, to research machining deformation mechanism, there is important Research Significance.

According to cast aluminum alloy material feature, the main machining method of the complicated box parts of cast aluminium alloy is that end mill cuts, when carrying out large scale plane machining, the impact of receiving end milling cutter diameter, the higher speed of mainshaft is not selected man-hour although add, select the cutting speed (>1000m/min) that larger diameter end milling cutter still can reach higher in working angles, therefore be not suitable for carrying out analysis with traditional cutting theory, need to set up the research method being applicable to high speed end milling and cutting.

Summary of the invention

The object of the present invention is to provide the construction method of a kind of aluminum alloy materials end mill cutting force and cut distorted pattern, the high temperature being intended to show under high-speed cutting condition cast aluminum alloy material, Large strain, high-strain-rate dynamic mechanical are studied.

The present invention is achieved in that a kind of concrete steps of construction method of aluminum alloy materials end mill cutting Force Model are as follows:

Step one, set up the Milling Force forecast model based on average cutting force, according to instantaneous analytic relationship of not being out of shape chip layer thickness and transient state Milling Force, set up Milling Force and solve key factor-Cutting Force Coefficient about feed engagement, axial cutting-in, the quadratic polynomial model of cutting speed and monolateral cutting width four cutting parameters, incision wherein in monolateral milling width means end mill working angles caused by the tool track difference cuts out angle change, by carrying out four factor four horizontal ends milling cutting force measurement tests, least square method is used to return coefficient in Cutting Force Coefficient model, and study the impact of cutting parameter on Cutting Force Coefficient, set up the Milling Force forecast model based on average cutting force,

Step 2, set up Milling Force forecast model based on inclined cutting mechanism, relation for cutting force in inclined cutting and cutting parameter carries out analytical Calculation, based on cast aluminium alloy Johnson-Cook material constitutive model, use finite element simulation method to carry out prediction to cutting fundamental quantities such as the angles of shear to solve, calculate the Cutting Force Coefficient in Milling Force forecast model, set up the Milling Force forecast model based on inclined cutting mechanism;

Step 3, based on the set up Milling Force forecast model based on average cutting force and the Milling Force forecast model based on inclined cutting mechanism, carry out single, multiple tooth transient state Milling Force prediction respectively and contrast with test figure, combination model process of establishing carries out the cutting force-induced error analysis of causes.

Further, described foundation based on the concrete grammar of the Milling Force forecast model of average cutting force is:

First, the end mill working angles simultaneously being participated in by multiple cutter tooth cutting carries out discrete, if end mill cutter tooth is numbered i, when i-th cutter tooth participates in cutting, by equidistantly discrete for cutting edge be limited infinitesimal cutting edge dz, each infinitesimal cutting edge participate in cut process can be equivalent to an Oblique Cutting Process;

Act on the instantaneous cutting force dF on cutter tooth i cutting edge infinitesimal dz _ican respectively tangentially, radial, be axially decomposed into three components: tangential instantaneous cutting force dF _ti, radial instantaneous cutting force dF _riand axial instantaneous cutting force dF _ai, set up instantaneous cutting force and solve relational expression as shown in the formula, K in formula _tc, K _rc, K _acbe respectively the function coefficient of shear action to tangential, radial and axial cutting force, K _te, K _re, K _aebe respectively corresponding cutting edge force coefficient;

End mill single cutter tooth milling area schematic, the dz infinitesimal got on i-th cutter tooth is research object, with be respectively the digging angle of cutter tooth, cut out angle.When pirouette is to instant contact angle time, be not instantaneously out of shape chip layer thickness can by formula approximate representation, wherein f _zfor feed engagement;

When time cutter tooth infinitesimal be positioned within effective cutting scope, computing formula is as shown in the formula, wherein a _eyfor workpiece is fixed a cutting tool point of penetration and the cutter rotation center distance perpendicular to direction of feed, B is width of the machined surface, and R is tool radius;

If ω is cutter angular velocity of rotation, t is process time, then cutter tooth cuts instantaneous instant contact angle corner instantaneous with cutter cutter angle between teeth and transient deviation angle θ is (because cutter helixangleβ causes with deviation) between relation as shown in the formula;

As consideration cutter tool cutting edge angle k _rtime, instantaneous chip layer thickness be expressed as:

By coordinate transform, tangential, radial and axial instantaneous cutting force are converted to x direction (feeding to), y direction (direction of feed normal direction) and z direction (axis):

Wherein, c=f _zsink _r, k _β=tan/R, then integration obtains the instantaneous cutting force of three-dimensional, wherein represent that cutter tooth cutting edge participates in the axial upper and lower limit of cutting tip respectively;

Because the total amount of material of cutter tooth excision each in a cutter swing circle is a constant, has nothing to do with helix angle, therefore get dz=a _p, k _β=0, integration is carried out, by its integral result divided by angle between teeth to the moment Milling Force in a cutter swing circle draw each cycle mean force:

wherein q=x, y, z

Calculate x, y, z direction respectively and cut mean force:

Therefore average cutting force can be expressed as per tooth feeding f _zlinear function and cutting edge power and, by test and regretional analysis can calculate Cutting Force Coefficient:

Assuming that Cutting Force Coefficient is the function about axial cutting-in ap, feed engagement fz, cutting speed v and monolateral cutting width aey, because the funtcional relationship between Cutting Force Coefficient and parameter is complicated, can not represent with simple linear function, therefore adopt the quadratic expression form be shown below to set up K _tc, K _rc, K _ac, K _te, K _re, K _aemultinomial model about cutting data:

$\left.\begin{array}{c}{K}_{\mathrm{tc}}=a_0+a_1{f}_z+a_2{a}_p+a_3{v}_c+a_4{a}_{\mathrm{ey}}+a_5{f}_z{a}_p+a_6{f}_z{v}_c+a_7{f}_z{a}_{\mathrm{ey}}+a_8{a}_p{v}_c\\ +a_9{a}_p{a}_{\mathrm{ey}}+a_{10}{v}_c{a}_{\mathrm{ey}}+a_{11}{f_z}^2+a_{12}{a_p}^2+a_{13}{v_c}^2+a_{14}{a_{\mathrm{ey}}}^2\\ K_{\mathrm{rc}}=b_0+a_1{f}_z+b_2{a}_p+b_3{v}_c+b_4{a}_{\mathrm{ey}}+b_5{f}_z{a}_p+b_6{f}_z{v}_c+b_7{f}_z{a}_{\mathrm{ey}}+b_8{a}_p{v}_c\\ +b_9{a}_p{a}_{\mathrm{ey}}+b_{10}{v}_c{a}_{\mathrm{ey}}+b_{11}{f_z}^2+b_{12}{a_p}^2+b_{13}{v_c}^2+b_{14}{a_{\mathrm{ey}}}^2\\ K_{\mathrm{te}}=c_0+c_1{f}_z+c_2{a}_p+c_3{v}_c+c_4{a}_{\mathrm{ey}}+c_5{f}_z{a}_p+c_6{f}_z{v}_c+c_7{f}_z{a}_{\mathrm{ey}}+c_8{a}_p{v}_c\\ +c_9{a}_p{a}_{\mathrm{ey}}+c_{10}{v}_c{a}_{\mathrm{ey}}+c_{11}{f_z}^2+c_{12}{a_p}^2+c_{13}{v_c}^2+c_{14}{a_{\mathrm{ey}}}^2\\ K_{\mathrm{re}}=d_0+d_1{f}_z+d_2{a}_p+d_3{v}_c+d_4{a}_{\mathrm{ey}}+d_5{f}_z{a}_p+d_6{f}_z{v}_c+d_7{f}_z{a}_{\mathrm{ey}}+d_8{a}_p{v}_c\\ +d_9{a}_p{a}_{\mathrm{ey}}+d_{10}{v}_c{a}_{\mathrm{ey}}+d_{11}{f_z}^2+d_{12}{a_p}^2+d_{13}{v_c}^2+d_{14}{a_{\mathrm{ey}}}^2\\ K_{\mathrm{ac}}=e_0+e_1{f}_z+e_2{a}_p+e_3{v}_c+e_4{a}_{\mathrm{ey}}+e_5{f}_z{a}_p+e_6{f}_z{v}_c+e_7{f}_z{a}_{\mathrm{ey}}+e_8{a}_p{v}_c\\ +e_9{a}_p{a}_{\mathrm{ey}}+e_{10}{v}_c{a}_{\mathrm{ey}}+e_{11}{f_z}^2+e_{12}{a_p}^2+e_{13}{v_c}^2+e_{14}{a_{\mathrm{ey}}}^2\\ K_{\mathrm{ae}}=g_0+g_1{f}_z+g_2{a}_p+g_3{v}_c+g_4{a}_{\mathrm{ey}}+g_5{f}_z{a}_p+g_6{f}_z{v}_c+g_7{f}_z{a}_{\mathrm{ey}}+g_8{a}_p{v}_c\\ +g_9{a}_p{a}_{\mathrm{ey}}+g_{10}{v}_c{a}_{\mathrm{ey}}+g_{11}{f_z}^2+g_{12}{a_p}^2+g_{13}{v_c}^2+g_{14}{a_{\mathrm{ey}}}^2\end{array}\right\}$

Carry out cutting force measurement test, just the parameter in formula above formula can be solved according to test measurement result, thus draw Cutting Force Coefficient polynomial expression, calculate Instantaneous Milling Force.

Further, the concrete grammar set up based on the Milling Force forecast model of inclined cutting mechanism is:

Shear strain in shear plane can be derived according to geometric relationship and be drawn:

${\mathrm{\γ}}_s=\frac{\cos {\mathrm{\φ}}_c+\tan ({\mathrm{\φ}}_c-{\mathrm{\γ}}_r)}{\cos \mathrm{\η}}$

Wherein η is chip-flow angle, according to least-energy principle, from geometrical point analysis, and shearing force F _sthe projection of F on shear plane can be expressed as, expression formula as shown in the formula:

F _s＝F[cos(θ _n+φ _n)cosθ _icosφ _i+sinθ _isinφ _i]

Or the average shearing stress τ on expression shear plane _swith shear surface area A _sproduct:

Wherein shear surface areal calculation is not out of shape chip layer thickness based on instantaneous average shearing stress τ τ _ssolve by the limit element artificial module set up based on Johnson-Cook constitutive model; The cutting force acted on milling cutter cutter tooth infinitesimal dz is made a concerted effort dF, and tangentially, radial, axial three-dimensional cutting force component dF _t, dF _r, dF _a:

Following hypothesis is done to the three-dimensional cutting force form acted on infinitesimal dz:

Then can obtain Cutting Force Coefficient K _tc, K _rc, K _acexpression formula:

$\left.\begin{array}{c}{K}_{\mathrm{tc}}=\frac{{\mathrm{\τ}}_s(\cos {\mathrm{\θ}}_n+\tan {\mathrm{\θ}}_i\tan {\mathrm{\λ}}_s)}{[\cos ({\mathrm{\θ}}_n+{\mathrm{\φ}}_n)\cos {\mathrm{\φ}}_i+\tan {\mathrm{\θ}}_i\sin {\mathrm{\φ}}_i]\sin {\mathrm{\φ}}_n}\\ K_{\mathrm{rc}}=\frac{{\mathrm{\τ}}_s\sin {\mathrm{\θ}}_n}{[\cos ({\mathrm{\θ}}_n+{\mathrm{\φ}}_n)\cos {\mathrm{\φ}}_i+\tan {\mathrm{\θ}}_i\sin {\mathrm{\φ}}_i]\cos {\mathrm{\λ}}_s\sin {\mathrm{\φ}}_n}\\ K_{\mathrm{ac}}=\frac{{\mathrm{\τ}}_s(\tan {\mathrm{\θ}}_i-\cos {\mathrm{\θ}}_n\tan {\mathrm{\λ}}_s)}{[\cos ({\mathrm{\θ}}_n+{\mathrm{\φ}}_n)\cos {\mathrm{\φ}}_i+\tan {\mathrm{\θ}}_i\sin {\mathrm{\φ}}_i]\sin {\mathrm{\φ}}_n}\end{array}\right\}$

In above formula, due to dF _t, dF _r, dF _aformula is about shear yield stress τ _s, resultant tool force direction θ _nand θ _i, cutting edge inclination λ _sand Shear Plane Angle in Oblique Metal Machining with function, numerous inclined cutting parameter is made troubles to solving, therefore the inclined cutting parameter being difficult to solve simplifies based on following two hypothesis by the classical oblique cutting model of application Armarego: shear rate and shearing force conllinear (one of maximum shear stress criterion); Length of chip is than identical in orthogonal cutting with inclined cutting;

Based on above-mentioned hypothesis, can draw:

$\left.\begin{array}{c}\tan {\mathrm{\β}}_n=\tan {\mathrm{\β}}_r\cos \mathrm{\η},{\mathrm{\β}}_n={\mathrm{\θ}}_n+{\mathrm{\γ}}_n\\ \tan {\mathrm{\φ}}_n=\frac{r_c(\cos \mathrm{\η}/\cos {\mathrm{\λ}}_s)\cos {\mathrm{\γ}}_n}{1-r_c(\cos \mathrm{\η}/\cos {\mathrm{\λ}}_s)\sin {\mathrm{\γ}}_n}\\ \tan ({\mathrm{\φ}}_n+{\mathrm{\β}}_n)=\frac{\cos {\mathrm{\γ}}_n\tan {\mathrm{\λ}}_s}{\tan \mathrm{\η}-\sin {\mathrm{\α}}_n\tan {\mathrm{\λ}}_s}\end{array}\right\}$

Draw Cutting Force Coefficient K _tc, K _rc, K _ac

$\left.\begin{array}{c}{K}_{\mathrm{tc}}=\frac{{\mathrm{\τ}}_s}{\sin {\mathrm{\φ}}_n}\×\frac{\cos ({\mathrm{\β}}_n-{\mathrm{\γ}}_n)+\tan {\mathrm{\λ}}_s\tan \mathrm{\η}\tan {\mathrm{\β}}_n}{\sqrt{{\cos }^2({\mathrm{\φ}}_n+{\mathrm{\β}}_n-{\mathrm{\γ}}_n)+{\tan }^2\mathrm{\η}{\sin }^2{\mathrm{\β}}_n}}\\ K_{\mathrm{rc}}=\frac{{\mathrm{\τ}}_s}{\sin {\mathrm{\φ}}_n\cos {\mathrm{\λ}}_s}\×\frac{\sin ({\mathrm{\β}}_n-{\mathrm{\γ}}_n)}{\sqrt{{\cos }^2({\mathrm{\φ}}_n+{\mathrm{\β}}_n-{\mathrm{\γ}}_n)+{\tan }^2\mathrm{\η}{\sin }^2{\mathrm{\β}}_n}}\\ K_{\mathrm{ac}}=\frac{{\mathrm{\τ}}_s}{\sin {\mathrm{\φ}}_n}\×\frac{\cos ({\mathrm{\β}}_n-{\mathrm{\γ}}_n)\tan {\mathrm{\λ}}_s-\tan \mathrm{\η}\tan {\mathrm{\β}}_n}{\sqrt{{\cos }^2({\mathrm{\φ}}_n+{\mathrm{\β}}_n-{\mathrm{\γ}}_n)+{\tan }^2\mathrm{\η}{\sin }^2{\mathrm{\β}}_n}}\end{array}\right\}.$

Further, for the situation of the more tooth, if i-th cutter tooth relative to desirable 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 comprises:

Single factor test mismachining tolerance model:

The collection S that sets up an office is the set of in end mill processing, surface to be machined all being put, p _i∈ S is any point on surface to be machined, p _ipoint produces mismachining tolerance E under the effect of error effect factor F _fi, E _fifor the vector representation of mismachining tolerance, error effect factor F both can be the parts of lathe, also can be power, temperature field, can also be some random disturbance;

Analyze cutting process, E _fibe not once reach, and be through multiple error and add up the result obtained;

If surfacing process time be T, at t ₁moment (t ₁∈ [0, T]) p _ithe mismachining tolerance of point under the effect of F is δ ₀+ δ ₁, wherein δ ₀for the initial error state of pi, then at t ₁+ Δ t, p _ithe mismachining tolerance of point then shows as the mismachining tolerance δ of accumulation ₀+ δ ₁therefore+Δ δ, if get t in [0, T] scope ₁, t ₂..., t _mm moment is analyzed altogether, then E _fithe form of pi point cumulative errors vector can be expressed as

$E_{F_i}={\mathrm{\δ}}_0+{\mathrm{\δ}}_1+{\mathrm{\δ}}_2+...+{\mathrm{\δ}}_m$

Various factors coupling mismachining tolerance model:

If total k error effect factor F in process ₁, F ₂... F _kact on workpiece to be machined, p _ithe mismachining tolerance E that point produces under the effect of each error effect factor _fiexpression formula as follows:

$E_{F_i}=c\sqrt{{\mathrm{\λ}}_1{E}_{F_{i1}}^2+{\mathrm{\λ}}_2{E}_{F_{i2}}^2+...+{\mathrm{\λ}}_m{E}_{F_{\mathrm{ik}}}^2}$

Wherein c is rejection rate coefficient, λ ₁, λ ₂for the coefficient that the error distribution curve shape of each compositing factor is relevant, λ=1/9 during normal distribution, equiprobability curve or λ=1/3 when distributing unclear, during Triangle-Profile 1/6;

End mill finished surface error effect factor can draw, and end mill finished surface puts p _ierror E _i:

$\begin{array}{c}{E}_i=c({\mathrm{\λ}}_1{E}_{F_i}^2+{\mathrm{\λ}}_2{E}_{H_i}^2+{\mathrm{\λ}}_3{E}_{S_i}^2+{\mathrm{\λ}}_4{E}_{C_i}^2+{\mathrm{\λ}}_5{E}_{{\mathrm{CL}}_i}^2+{\mathrm{\λ}}_6{E}_{T_i}^2+{\mathrm{\λ}}_7{E}_{{\mathrm{TG}}_i}^2\\ +{\mathrm{\λ}}_8{E}_{M_i}^2+{\mathrm{\λ}}_9{E}_{{\mathrm{MG}}_i}^2+{\mathrm{\λ}}_{10}{E}_{R_i}^2{)}^{\frac{1}{2}}\end{array}$

Self-adapted genetic algorithm based on real coding carries out the prediction of end mill finished surface flatness error.

The present invention establishes the Milling Force forecast model based on average cutting force, establish the Milling Force forecast model based on inclined cutting mechanism, based on the set up Milling Force forecast model based on average cutting force and the Milling Force forecast model based on inclined cutting mechanism, carry out list respectively, multiple tooth transient state Milling Force prediction also contrasts with test figure, and establish aluminum alloy materials Deformation in Milling Process model, self-adapted genetic algorithm opposite end Milling Machining surface planarity error based on real coding is predicted, to research machining deformation mechanism, there is important Research Significance.

Accompanying drawing explanation

Fig. 1 is the aluminum alloy materials end mill cutting Force Model construction method process flow diagram that the embodiment of the present invention provides;

Fig. 2 is the end mill working angles discrete cutter tooth infinitesimal schematic diagram that the embodiment of the present invention provides;

Fig. 3 is the Tool in Milling area schematic that the embodiment of the present invention provides;

Fig. 4 is the relation schematic diagram of cutting force, speed and the angle of shear in the inclined cutting that provides of the embodiment of the present invention;

Fig. 5 is that predicting the outcome based on two class cutting Force Model monodentates of providing of the embodiment of the present invention contrasts with test figure;

In figure: (a) first group of parameter prediction of Turning Force with Artificial result; (b) first group of parameter cutting force actual measured results; (c) second group of parameter prediction of Turning Force with Artificial result; (d) second group of parameter cutting force actual measured results;

Fig. 6 is the end mill office cutter tooth site error schematic diagram that the embodiment of the present invention provides;

In figure: (a) radial position error; (b) axial positioning errors;

Fig. 7 is that the cutter tooth that the embodiment of the present invention provides is radial, axial location deviation schematic diagram;

Fig. 8 is the face milling with multiblade cutter prediction of Turning Force with Artificial that provides of the embodiment of the present invention and test figure comparison diagram;

In figure: (a) prediction of Turning Force with Artificial result; (b) test findings;

Fig. 9 is that the flatness error based on materialized view maintenance that the embodiment of the present invention provides solves process flow diagram;

Figure 10 is the flatness error iteration convergence curve that the embodiment of the present invention provides;

Figure 11 is the convergence curve contrast that the embodiment of the present invention provides.

Embodiment

In order to make object of the present invention, technical scheme and advantage clearly understand, below in conjunction with drawings and Examples, the present invention is further elaborated.Should be appreciated that specific embodiment described herein only in order to explain the present invention, be not intended to limit the present invention.

The present invention is achieved in that a kind of concrete steps of construction method of aluminum alloy materials end mill cutting Force Model are as follows:

Step one, set up the Milling Force forecast model based on average cutting force, according to instantaneous analytic relationship of not being out of shape chip layer thickness and transient state Milling Force, set up Milling Force and solve key factor-Cutting Force Coefficient about feed engagement, axial cutting-in, the quadratic polynomial model of cutting speed and monolateral cutting width four cutting parameters, incision wherein in monolateral milling width means end mill working angles caused by the tool track difference cuts out angle change, by carrying out four factor four horizontal ends milling cutting force measurement tests, least square method is used to return coefficient in Cutting Force Coefficient model, and study the impact of cutting parameter on Cutting Force Coefficient, set up the Milling Force forecast model based on average cutting force,

Step 2, set up Milling Force forecast model based on inclined cutting mechanism, relation for cutting force in inclined cutting and cutting parameter carries out analytical Calculation, based on cast aluminium alloy Johnson-Cook material constitutive model, use finite element simulation method to carry out prediction to cutting fundamental quantities such as the angles of shear to solve, calculate the Cutting Force Coefficient in Milling Force forecast model, set up the Milling Force forecast model based on inclined cutting mechanism;

Step 3, based on the set up Milling Force forecast model based on average cutting force and the Milling Force forecast model based on inclined cutting mechanism, carry out single, multiple tooth transient state Milling Force prediction respectively and contrast with test figure, wherein be better than the Milling Force forecast model based on inclined cutting mechanism based on the precision of prediction of the Milling Force forecast model of average cutting force, combination model process of establishing carries out the cutting force-induced error analysis of causes.

Further, described foundation based on the concrete grammar of the Milling Force forecast model of average cutting force is:

First, the end mill working angles simultaneously being participated in by multiple cutter tooth cutting carries out discrete, if end mill cutter tooth is numbered i, when i-th cutter tooth participates in cutting, by equidistantly discrete for cutting edge be limited infinitesimal cutting edge dz, as shown in Figure 2, the process that each infinitesimal cutting edge participates in cutting can be equivalent to an Oblique Cutting Process;

Act on the instantaneous cutting force dF on cutter tooth i cutting edge infinitesimal dz _ican respectively tangentially, radial, be axially decomposed into three components: tangential instantaneous cutting force dF _ti, radial instantaneous cutting force dF _riand axial instantaneous cutting force dF _ai, set up instantaneous cutting force and solve relational expression as shown in the formula, K in formula _tc, K _rc, K _acbe respectively the function coefficient of shear action to tangential, radial and axial cutting force, K _te, K _re, K _aebe respectively corresponding cutting edge force coefficient;

As shown in Figure 3, the dz infinitesimal got on i-th cutter tooth is research object to end mill single cutter tooth milling area schematic, with be respectively the digging angle of cutter tooth, cut out angle.When pirouette is to instant contact angle time, be not instantaneously out of shape chip layer thickness can by formula approximate representation, wherein f _zfor feed engagement;

When time cutter tooth infinitesimal be positioned within effective cutting scope, computing formula is as shown in the formula, wherein a _eyfor workpiece is fixed a cutting tool point of penetration and the cutter rotation center distance perpendicular to direction of feed, B is width of the machined surface, and R is tool radius;

If ω is cutter angular velocity of rotation, t is process time, then cutter tooth cuts instantaneous instant contact angle corner instantaneous with cutter cutter angle between teeth and transient deviation angle θ is (because cutter helixangleβ causes with deviation) between relation as shown in the formula;

As consideration cutter tool cutting edge angle k _rtime, instantaneous chip layer thickness be expressed as:

By coordinate transform, tangential, radial and axial instantaneous cutting force are converted to x direction (feeding to), y direction (direction of feed normal direction) and z direction (axis):

Wherein, c=f _zsink _r, k _β=tan/R, then integration obtains the instantaneous cutting force of three-dimensional, wherein represent that cutter tooth cutting edge participates in the axial upper and lower limit of cutting tip respectively;

Because the total amount of material of cutter tooth excision each in a cutter swing circle is a constant, has nothing to do with helix angle, therefore get dz=a _p, k _β=0, integration is carried out, by its integral result divided by angle between teeth to the moment Milling Force in a cutter swing circle draw each cycle mean force:

wherein q=x, y, z

Calculate x, y, z direction respectively and cut mean force:

Therefore average cutting force can be expressed as per tooth feeding f _zlinear function and cutting edge power and, by test and regretional analysis can calculate Cutting Force Coefficient:

Assuming that Cutting Force Coefficient is the function about axial cutting-in ap, feed engagement fz, cutting speed v and monolateral cutting width aey, because the funtcional relationship between Cutting Force Coefficient and parameter is complicated, can not represent with simple linear function, therefore adopt the quadratic expression form be shown below to set up K _tc, K _rc, K _ac, K _te, K _re, K _aemultinomial model about cutting data:

$\left.\begin{array}{c}{K}_{\mathrm{tc}}=a_0+a_1{f}_z+a_2{a}_p+a_3{v}_c+a_4{a}_{\mathrm{ey}}+a_5{f}_z{a}_p+a_6{f}_z{v}_c+a_7{f}_z{a}_{\mathrm{ey}}+a_8{a}_p{v}_c\\ +a_9{a}_p{a}_{\mathrm{ey}}+a_{10}{v}_c{a}_{\mathrm{ey}}+a_{11}{f_z}^2+a_{12}{a_p}^2+a_{13}{v_c}^2+a_{14}{a_{\mathrm{ey}}}^2\\ K_{\mathrm{rc}}=b_0+a_1{f}_z+b_2{a}_p+b_3{v}_c+b_4{a}_{\mathrm{ey}}+b_5{f}_z{a}_p+b_6{f}_z{v}_c+b_7{f}_z{a}_{\mathrm{ey}}+b_8{a}_p{v}_c\\ +b_9{a}_p{a}_{\mathrm{ey}}+b_{10}{v}_c{a}_{\mathrm{ey}}+b_{11}{f_z}^2+b_{12}{a_p}^2+b_{13}{v_c}^2+b_{14}{a_{\mathrm{ey}}}^2\\ K_{\mathrm{te}}=c_0+c_1{f}_z+c_2{a}_p+c_3{v}_c+c_4{a}_{\mathrm{ey}}+c_5{f}_z{a}_p+c_6{f}_z{v}_c+c_7{f}_z{a}_{\mathrm{ey}}+c_8{a}_p{v}_c\\ +c_9{a}_p{a}_{\mathrm{ey}}+c_{10}{v}_c{a}_{\mathrm{ey}}+c_{11}{f_z}^2+c_{12}{a_p}^2+c_{13}{v_c}^2+c_{14}{a_{\mathrm{ey}}}^2\\ K_{\mathrm{re}}=d_0+d_1{f}_z+d_2{a}_p+d_3{v}_c+d_4{a}_{\mathrm{ey}}+d_5{f}_z{a}_p+d_6{f}_z{v}_c+d_7{f}_z{a}_{\mathrm{ey}}+d_8{a}_p{v}_c\\ +d_9{a}_p{a}_{\mathrm{ey}}+d_{10}{v}_c{a}_{\mathrm{ey}}+d_{11}{f_z}^2+d_{12}{a_p}^2+d_{13}{v_c}^2+d_{14}{a_{\mathrm{ey}}}^2\\ K_{\mathrm{ac}}=e_0+e_1{f}_z+e_2{a}_p+e_3{v}_c+e_4{a}_{\mathrm{ey}}+e_5{f}_z{a}_p+e_6{f}_z{v}_c+e_7{f}_z{a}_{\mathrm{ey}}+e_8{a}_p{v}_c\\ +e_9{a}_p{a}_{\mathrm{ey}}+e_{10}{v}_c{a}_{\mathrm{ey}}+e_{11}{f_z}^2+e_{12}{a_p}^2+e_{13}{v_c}^2+e_{14}{a_{\mathrm{ey}}}^2\\ K_{\mathrm{ae}}=g_0+g_1{f}_z+g_2{a}_p+g_3{v}_c+g_4{a}_{\mathrm{ey}}+g_5{f}_z{a}_p+g_6{f}_z{v}_c+g_7{f}_z{a}_{\mathrm{ey}}+g_8{a}_p{v}_c\\ +g_9{a}_p{a}_{\mathrm{ey}}+g_{10}{v}_c{a}_{\mathrm{ey}}+g_{11}{f_z}^2+g_{12}{a_p}^2+g_{13}{v_c}^2+g_{14}{a_{\mathrm{ey}}}^2\end{array}\right\}$

Carry out cutting force measurement test, just the parameter in formula above formula can be solved according to test measurement result, thus draw Cutting Force Coefficient polynomial expression, calculate Instantaneous Milling Force.

Further, the concrete grammar set up based on the Milling Force forecast model of 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, can derive according to geometric relationship and draw by the shear strain in shear plane:

${\mathrm{\γ}}_s=\frac{\cos {\mathrm{\φ}}_c+\tan ({\mathrm{\φ}}_c-{\mathrm{\γ}}_r)}{\cos \mathrm{\η}}$

Wherein η is chip-flow angle, according to least-energy principle, from geometrical point analysis, and shearing force F _sthe projection of F on shear plane can be expressed as, as Fig. 4, expression formula as shown in the formula:

F _s＝F[cos(θ _n+φ _n)cosθ _icosφ _i+sinθ _isinφ _i]

Or the average shearing stress τ on expression shear plane _swith shear surface area A _sproduct:

Wherein shear surface areal calculation is not out of shape chip layer thickness based on instantaneous average shearing stress τ, τ _ssolve by the limit element artificial module set up based on Johnson-Cook constitutive model; The cutting force acted on milling cutter cutter tooth infinitesimal dz is made a concerted effort dF, and tangentially, radial, axial three-dimensional cutting force component dF _t, dF _r, dF _a:

Following hypothesis is done to the three-dimensional cutting force form acted on infinitesimal dz:

Then can obtain Cutting Force Coefficient K _tc, K _rc, K _acexpression formula:

$\left.\begin{array}{c}{K}_{\mathrm{tc}}=\frac{{\mathrm{\τ}}_s(\cos {\mathrm{\θ}}_n+\tan {\mathrm{\θ}}_i\tan {\mathrm{\λ}}_s)}{[\cos ({\mathrm{\θ}}_n+{\mathrm{\φ}}_n)\cos {\mathrm{\φ}}_i+\tan {\mathrm{\θ}}_i\sin {\mathrm{\φ}}_i]\sin {\mathrm{\φ}}_n}\\ K_{\mathrm{rc}}=\frac{{\mathrm{\τ}}_s\sin {\mathrm{\θ}}_n}{[\cos ({\mathrm{\θ}}_n+{\mathrm{\φ}}_n)\cos {\mathrm{\φ}}_i+\tan {\mathrm{\θ}}_i\sin {\mathrm{\φ}}_i]\cos {\mathrm{\λ}}_s\sin {\mathrm{\φ}}_n}\\ K_{\mathrm{ac}}=\frac{{\mathrm{\τ}}_s(\tan {\mathrm{\θ}}_i-\cos {\mathrm{\θ}}_n\tan {\mathrm{\λ}}_s)}{[\cos ({\mathrm{\θ}}_n+{\mathrm{\φ}}_n)\cos {\mathrm{\φ}}_i+\tan {\mathrm{\θ}}_i\sin {\mathrm{\φ}}_i]\sin {\mathrm{\φ}}_n}\end{array}\right\}$

In above formula, due to dF _t, dF _r, dF _aformula is about shear yield stress τ _s, resultant tool force direction θ _nand θ _i, cutting edge inclination λ _sand Shear Plane Angle in Oblique Metal Machining with function, numerous inclined cutting parameter is made troubles to solving, therefore the inclined cutting parameter being difficult to solve simplifies based on following two hypothesis by the classical oblique cutting model of application Armarego: shear rate and shearing force conllinear (one of maximum shear stress criterion); Length of chip is than identical in orthogonal cutting with inclined cutting;

Based on above-mentioned hypothesis, can draw:

$\left.\begin{array}{c}\tan {\mathrm{\β}}_n=\tan {\mathrm{\β}}_r\cos \mathrm{\η},{\mathrm{\β}}_n={\mathrm{\θ}}_n+{\mathrm{\γ}}_n\\ \tan {\mathrm{\φ}}_n=\frac{r_c(\cos \mathrm{\η}/\cos {\mathrm{\λ}}_s)\cos {\mathrm{\γ}}_n}{1-r_c(\cos \mathrm{\η}/\cos {\mathrm{\λ}}_s)\sin {\mathrm{\γ}}_n}\\ \tan ({\mathrm{\φ}}_n+{\mathrm{\β}}_n)=\frac{\cos {\mathrm{\γ}}_n\tan {\mathrm{\λ}}_s}{\tan \mathrm{\η}-\sin {\mathrm{\α}}_n\tan {\mathrm{\λ}}_s}\end{array}\right\}$

Draw Cutting Force Coefficient K _tc, K _rc, K _ac

$\left.\begin{array}{c}{K}_{\mathrm{tc}}=\frac{{\mathrm{\τ}}_s}{\sin {\mathrm{\φ}}_n}\×\frac{\cos ({\mathrm{\β}}_n-{\mathrm{\γ}}_n)+\tan {\mathrm{\λ}}_s\tan \mathrm{\η}\tan {\mathrm{\β}}_n}{\sqrt{{\cos }^2({\mathrm{\φ}}_n+{\mathrm{\β}}_n-{\mathrm{\γ}}_n)+{\tan }^2\mathrm{\η}{\sin }^2{\mathrm{\β}}_n}}\\ K_{\mathrm{rc}}=\frac{{\mathrm{\τ}}_s}{\sin {\mathrm{\φ}}_n\cos {\mathrm{\λ}}_s}\×\frac{\sin ({\mathrm{\β}}_n-{\mathrm{\γ}}_n)}{\sqrt{{\cos }^2({\mathrm{\φ}}_n+{\mathrm{\β}}_n-{\mathrm{\γ}}_n)+{\tan }^2\mathrm{\η}{\sin }^2{\mathrm{\β}}_n}}\\ K_{\mathrm{ac}}=\frac{{\mathrm{\τ}}_s}{\sin {\mathrm{\φ}}_n}\×\frac{\cos ({\mathrm{\β}}_n-{\mathrm{\γ}}_n)\tan {\mathrm{\λ}}_s-\tan \mathrm{\η}\tan {\mathrm{\β}}_n}{\sqrt{{\cos }^2({\mathrm{\φ}}_n+{\mathrm{\β}}_n-{\mathrm{\γ}}_n)+{\tan }^2\mathrm{\η}{\sin }^2{\mathrm{\β}}_n}}\end{array}\right\}.$

Cutting force measurement test design

The embodiment of the present invention is using ZL702A material as milling test object, and material chemical composition and physical property are in table 1, table 2.Testing lathe used is XS5040 vertical and high-speed knee-and-column milling machine, and end mill diameter is 125mm, number of teeth 1-2, tool cutting edge angle 75 °, axial rake 15 °, radial rake-3 °, helix angle 15 °, and cutter material is carbide alloy YG 8.

Table 1 cutting force test factor level table

Table 2 Cutting Force Coefficient coefficient regression

The Kistler9257B three-dimensional dynamic force measurement instrument that cutting force measurement equipment adopts Kistler company of Switzerland to produce, setting sample frequency is 2000Hz, the change that during milling, workpiece is stressed causes the deformation of dynamometer internal resistance foil gauge, this deformation can cause the imbalance of electric bridge, and then cause the change of output voltage, use Kistler5017A charge amplifier detect and amplify this faint output signal, after A/D conversion, obtain measured value.According to dynamometer nominal data, draw the relation surveyed between institute's dynamometry value and true force value.

For research is based on the end mill cutting Force Model of cutting scheme, the embodiment of the present invention considers workpiece material mechanical property, based on Birmasil ZL702A material constitutive equation, sets up right angle milling two dimensional finite element realistic model, predicts the angle of shear.

(1) based on the Milling Force forecast model of average cutting force

Get two groups of Milling Parameters respectively in table 3, cutting-tool angle parameter, with cutting force test parameter, distinguishes calculating K according to table 2 _tc, K _rc, K _ac, K _te, K _re, K _aesix Cutting Force Coefficients, solve Instantaneous Milling Force F _x, F _y, F _z.

Table 3 simulation and prediction Milling Parameters table

(2) based on the Milling Force forecast model of inclined cutting mechanism

Milling Force Prediction Parameters is with table 4, and cutting-tool angle, with cutting force test parameter, solves the Milling Force Model coefficient based on inclined cutting mechanism, thus sets up Milling Force forecast model.

Table 4 conventional magnetic shear angle expression formula

The Milling Force obtained based on two class Milling Force forecast models predict the outcome with test figure more as shown in Figure 5, in comparison diagram 5, to measure cutting force data known for simulation and prediction cutting force data and test, two class Milling Force Model all have the variation tendency of Milling Force and reflect comparatively preferably, but numerically still have certain deviation, the precision of prediction wherein based on the Milling Force Model of average cutting force is better than the Milling Force Model set up based on inclined cutting mechanism.The former is test and analytic method due to integrated use, by milling test determination Cutting Force Coefficient on the basis that theory solves, and non-fully is obtained by experimental formula, there is certain predicated error due to the isoparametric experimental formula of the angle of shear in corresponding the latter, some assumed condition is have also been introduced, because which form the difference in data prediction precision while Oblique Cutting Process being simplified according to orthogonal cutting process in addition.

Further, the cutter tooth site error of end mill cutter mainly comprises radial position error and axial positioning errors, as shown in Figure 6, when cutter tooth location offsets, cutter does rotary cutting motion by with the radius large or less than desirable radius around insert central axis, and axial cutting-in also may be greater than or less than desirable cutting-in.

If i-th cutter tooth relative to desirable cutter tooth position by axial positioning errors Δ zi, radial position error Δ ri, as shown in Figure 7, then formula 3.4 can rewrite such as formula:

It can thus be appreciated that in end mill cutting force computation process, selected reference cutter tooth also, after measuring all the other mensuration cutter tooth site errors, can calculate the instantaneous cutting force acted on different cutter tooth respectively.The embodiment of the present invention carries out simulation and prediction based on average cutting Force Model to face milling with multiblade cutter cutting force, and number of teeth is 2, and 180 °, blade symmetry is installed, cutter tooth axial positioning errors-52 μm, radial position error-13 μm.Milling Parameters: f _z=0.1mm/z, a _p=1mm, n=800m/min, a _e=30mm, predict the outcome and test findings as shown in Figure 8, the cutting force variation tendency of the two has good consistance.

A kind of method for building up of aluminum alloy materials Deformation in Milling Process model comprises:

Single factor test mismachining tolerance model:

The collection S that sets up an office is the set of in end mill processing, surface to be machined all being put, p _i∈ S is any point on surface to be machined, p _ipoint produces mismachining tolerance E under the effect of error effect factor F _fi, E _fifor the vector representation of mismachining tolerance, error effect factor F both can be the parts of lathe, also can be power, temperature field, can also be some random disturbance;

Analyze cutting process, E _fibe not once reach, and be through multiple error and add up the result obtained;

If surfacing process time be T, at t ₁moment (t ₁∈ [0, T]) p _ithe mismachining tolerance of point under the effect of F is δ ₀+ δ ₁, wherein δ ₀for the initial error state of pi, then at t ₁+ Δ t, p _ithe mismachining tolerance of point then shows as the mismachining tolerance δ of accumulation ₀+ δ ₁therefore+Δ δ, if get t in [0, T] scope ₁, t ₂..., t _mm moment is analyzed altogether, then E _fithe form of pi point cumulative errors vector can be expressed as:

$E_{F_i}={\mathrm{\δ}}_0+{\mathrm{\δ}}_1+{\mathrm{\δ}}_2+...+{\mathrm{\δ}}_m$

Various factors coupling mismachining tolerance model:

If total k error effect factor F in process ₁, F ₂... F _kact on workpiece to be machined, p _ithe mismachining tolerance E that point produces under the effect of each error effect factor _fiexpression formula as follows:

$E_{F_i}=c\sqrt{{\mathrm{\λ}}_1{E}_{F_{i1}}^2+{\mathrm{\λ}}_2{E}_{F_{i2}}^2+...+{\mathrm{\λ}}_m{E}_{F_{\mathrm{ik}}}^2}$

Wherein c is rejection rate coefficient, λ ₁, λ ₂for the coefficient that the error distribution curve shape of each compositing factor is relevant, λ=1/9 during normal distribution, equiprobability curve or λ=1/3 when distributing unclear, during Triangle-Profile 1/6;

End mill finished surface error effect factor can draw, and end mill finished surface puts p _ierror E _i:

$\begin{array}{c}{E}_i=c({\mathrm{\λ}}_1{E}_{F_i}^2+{\mathrm{\λ}}_2{E}_{H_i}^2+{\mathrm{\λ}}_3{E}_{S_i}^2+{\mathrm{\λ}}_4{E}_{C_i}^2+{\mathrm{\λ}}_5{E}_{{\mathrm{CL}}_i}^2+{\mathrm{\λ}}_6{E}_{T_i}^2+{\mathrm{\λ}}_7{E}_{{\mathrm{TG}}_i}^2\\ +{\mathrm{\λ}}_8{E}_{M_i}^2+{\mathrm{\λ}}_9{E}_{{\mathrm{MG}}_i}^2+{\mathrm{\λ}}_{10}{E}_{R_i}^2{)}^{\frac{1}{2}}\end{array}$

Wherein each parameter declaration is as follows:

Table 5

End mill finished surface flatness error based on the self-adapted genetic algorithm of real coding is predicted, process flow diagram as shown in Figure 9.

This textured surface point data is as shown in table 6, is respectively distributed with 11 measuring points along x, y direction, and surface amounts to 121 measuring points.

Table 6 flatness error data (μm)

Initial population scale is 20, and maximum iteration time is 100, and the variation range of variable a, b tries to achieve a according to least square method ₀, b ₀determine.Through 100 iteration, show that flatness error is 15.95, parameter iteration convergence curve as shown in Figure 10.

For comparing with standard genetic algorithm, the present invention adopts the data in standard genetic algorithm his-and-hers watches 5 to solve, and the flatness error obtained is 16.02, contrasts as shown in figure 11 with adopting the convergence curve obtained based on materialized view maintenance.Known by contrasting, the flatness error of trying to achieve based on real number self-adapted genetic algorithm reduces about 0.07 μm than the flatness error calculated based on standard genetic algorithm, achieves the principle of " survival of the fittest, the survival of the fittest " of genetic algorithm.

By reference to the accompanying drawings the specific embodiment of the present invention is described although above-mentioned; but not limiting the scope of the invention; one of ordinary skill in the art should be understood that; on the basis of technical scheme of the present invention, those skilled in the art do not need to pay various amendment or distortion that performing creative labour can make still within protection scope of the present invention.

Claims (5)

1. a construction method for aluminum alloy materials end mill cutting force and cut distorted pattern, is characterized in that, described aluminum alloy materials end mill cutting force and the construction method of cut distorted pattern comprise:

Step one, set up the Milling Force forecast model based on average cutting force, according to instantaneous analytic relationship of not being out of shape chip layer thickness and transient state Milling Force, set up Milling Force and solve key factor-Cutting Force Coefficient about feed engagement, axial cutting-in, the quadratic polynomial model of cutting speed and monolateral cutting width four cutting parameters, incision wherein in monolateral milling width means end mill working angles caused by the tool track difference cuts out angle change, by carrying out four factor four horizontal ends milling cutting force measurement tests, least square method is used to return coefficient in Cutting Force Coefficient model, obtain cutting parameter to the impact of Cutting Force Coefficient, set up the Milling Force forecast model based on average cutting force,

Step 2, set up Milling Force forecast model based on inclined cutting mechanism, relation for cutting force in inclined cutting and cutting parameter carries out analytical Calculation, based on cast aluminium alloy Johnson-Cook material constitutive model, use finite element simulation method to carry out prediction to angle of shear cutting fundamental quantity to solve, calculate the Cutting Force Coefficient in Milling Force forecast model, set up the Milling Force forecast model based on inclined cutting mechanism;

Step 3, based on the set up Milling Force forecast model based on average cutting force and the Milling Force forecast model based on inclined cutting mechanism, carry out single, multiple tooth transient state Milling Force prediction respectively and contrast with test figure, combination model process of establishing carries out the cutting force-induced error analysis of causes.

2. the construction method of aluminum alloy materials end mill cutting force as claimed in claim 1 and cut distorted pattern, it is characterized in that, described foundation based on the concrete grammar of the Milling Force forecast model of average cutting force is:

First, the end mill working angles simultaneously being participated in by multiple cutter tooth cutting carries out discrete, end mill cutter tooth is numbered i, when i-th cutter tooth participates in cutting, by equidistantly discrete for cutting edge be limited infinitesimal cutting edge dz, each infinitesimal cutting edge participate in cut process be equivalent to an Oblique Cutting Process;

Act on the instantaneous cutting force dF on cutter tooth i cutting edge infinitesimal dz _irespectively tangentially, radial, axis is decomposed into three components: tangential instantaneous cutting force dF _ti, radial instantaneous cutting force dF _riand axial instantaneous cutting force dF _ai, set up instantaneous cutting force and solve relational expression as shown in the formula, K in formula _tc, K _rc, K _acbe respectively the function coefficient of shear action to tangential, radial and axial cutting force, K _te, K _re, K _aebe respectively corresponding cutting edge force coefficient;

End mill single cutter tooth milling area schematic, the dz infinitesimal got on i-th cutter tooth is object, with be respectively the digging angle of cutter tooth, cut out angle, when pirouette is to instant contact angle time, be not instantaneously out of shape chip layer thickness by formula represent, wherein f _zfor feed engagement;

When time cutter tooth infinitesimal be positioned within effective cutting scope, computing formula is as shown in the formula, wherein a _eyfor workpiece is fixed a cutting tool point of penetration and the cutter rotation center distance perpendicular to direction of feed, 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 angle corner instantaneous with cutter cutter angle between teeth and relation between the θ of transient deviation angle as shown in the formula;

As cutter tool cutting edge angle k _rtime, instantaneous chip layer thickness be expressed as:

By coordinate transform, tangential, radial and axial instantaneous cutting force are converted to x direction, y direction and z direction:

Wherein, c=f _zsink _r, k _β=tan/R, then integration obtains the instantaneous cutting force of three-dimensional, wherein represent that cutter tooth cutting edge participates in the axial upper and lower limit of cutting tip respectively;

Because the total amount of material of cutter tooth excision each in a cutter swing circle is a constant, has nothing to do with helix angle, therefore get dz=a _p, k _β=0, integration is carried out, by integral result divided by angle between teeth to the moment Milling Force in a cutter swing circle draw each cycle mean force:

wherein q=x, y, z

Calculate x, y, z direction respectively and cut mean force:

Therefore average cutting force is expressed as per tooth feeding f _zlinear function and cutting edge power and, by test and regretional analysis calculate Cutting Force Coefficient:

Cutting Force Coefficient is the function about axial cutting-in ap, feed engagement fz, cutting speed v and monolateral cutting width aey, adopts the quadratic expression form be shown below to set up K _tc, K _rc, K _ac, K _te, K _re, K _aemultinomial model about cutting data:

$\left.\begin{array}{c}{K}_{\mathrm{tc}}=a_0+a_1{f}_z+a_2{a}_p+a_3{v}_c+a_4{a}_{\mathrm{ey}}+a_5{f}_z{a}_p+a_6{f}_z{v}_c+a_7{f}_z{a}_{\mathrm{ey}}+a_8{a}_p{v}_c\\ +a_9{a}_p{a}_{\mathrm{ey}}+a_{10}{v}_c{a}_{\mathrm{ey}}+a_{11}{f_z}^2+a_{12}{a_p}^2+a_{13}{v_c}^2+a_{14}{a_{\mathrm{ey}}}^2\\ K_{\mathrm{rc}}=b_0+a_1{f}_z+b_2{a}_p+b_3{v}_c+b_4{a}_{\mathrm{ey}}+b_5{f}_z{a}_p+b_6{f}_z{v}_c+b_7{f}_z{a}_{\mathrm{ey}}+b_8{a}_p{v}_c\\ +b_9{a}_p{a}_{\mathrm{ey}}+b_{10}{v}_c{a}_{\mathrm{ey}}+b_{11}{f_z}^2+b_{12}{a_p}^2+b_{13}{v_c}^2+b_{14}{a_{\mathrm{ey}}}^2\\ K_{\mathrm{te}}=c_0+c_1{f}_z+c_2{a}_p+c_3{v}_c+c_4{a}_{\mathrm{ey}}+c_5{f}_z{a}_p+c_6{f}_z{v}_c+c_7{f}_z{a}_{\mathrm{ey}}+c_8{a}_p{v}_c\\ +c_9{a}_p{a}_{\mathrm{ey}}+c_{10}{v}_c{a}_{\mathrm{ey}}+c_{11}{f_z}^2+c_{12}{a_p}^2+c_{13}{v_c}^2+c_{14}{a_{\mathrm{ey}}}^2\\ K_{\mathrm{re}}=d_0+d_1{f}_z+d_2{a}_p+d_3{v}_c+d_4{a}_{\mathrm{ey}}+d_5{f}_z{a}_p+d_6{f}_z{v}_c+d_7{f}_z{a}_{\mathrm{ey}}+d_8{a}_p{v}_c\\ +d_9{a}_p{a}_{\mathrm{ey}}+d_{10}{v}_c{a}_{\mathrm{ey}}+d_{11}{f_z}^2+d_{12}{a_p}^2+d_{13}{v_c}^2+d_{14}{a_{\mathrm{ey}}}^2\\ K_{\mathrm{ac}}=e_0+e_1{f}_z+e_2{a}_p+e_3{v}_c+e_4{a}_{\mathrm{ey}}+e_5{f}_z{a}_p+e_6{f}_z{v}_c+e_7{f}_z{a}_{\mathrm{ey}}+e_8{a}_p{v}_c\\ +e_9{a}_p{a}_{\mathrm{ey}}+e_{10}{v}_c{a}_{\mathrm{ey}}+e_{11}{f_z}^2+e_{12}{a_p}^2+e_{13}{v_c}^2+e_{14}{a_{\mathrm{ey}}}^2\\ K_{\mathrm{ae}}=g_0+g_1{f}_z+g_2{a}_p+g_3{v}_c+g_4{a}_{\mathrm{ey}}+g_5{f}_z{a}_p+g_6{f}_z{v}_c+g_7{f}_z{a}_{\mathrm{ey}}+g_8{a}_p{v}_c\\ +g_9{a}_p{a}_{\mathrm{ey}}+g_{10}{v}_c{a}_{\mathrm{ey}}+g_{11}{f_z}^2+g_{12}{a_p}^2+g_{13}{v_c}^2+g_{14}{a_{\mathrm{ey}}}^2\end{array}\right\}$

Carry out cutting force measurement test, just the parameter in above formula can be solved according to test measurement result, thus draw Cutting Force Coefficient polynomial expression, calculate Instantaneous Milling Force.

3. the construction method of aluminum alloy materials end mill cutting force as claimed in claim 1 and cut distorted pattern, it is characterized in that, the concrete grammar set up based on the Milling Force forecast model of inclined cutting mechanism is:

Shear strain in shear plane is derived according to geometric relationship and is drawn:

${\mathrm{\γ}}_s=\frac{\cos {\mathrm{\φ}}_c+\tan ({\mathrm{\φ}}_c-{\mathrm{\γ}}_r)}{\cos \mathrm{\η}}$

Wherein η is chip-flow angle, according to least-energy principle, from geometrical point analysis, and shearing force F _sbe expressed as the projection of F on shear plane, expression formula as shown in the formula:

F _s＝F[cos(θ _n+φ _n)cosθ _icosφ _i+sinθ _isinφ _i]

Or the average shearing stress τ on expression shear plane _swith shear surface area A _sproduct:

Wherein shear surface areal calculation is not out of shape chip layer thickness based on instantaneous average shearing stress τ, τ _ssolved by the limit element artificial module set up based on Johnson-Cook constitutive model; The cutting force acted on milling cutter cutter tooth infinitesimal dz is made a concerted effort dF, and tangentially, radial, axial three-dimensional cutting force component dF _t, dF _r, dF _a:

Three-dimensional cutting force form to acting on infinitesimal dz:

Then obtain Cutting Force Coefficient K _tc, K _rc, K _acexpression formula:

$\left.\begin{array}{c}{K}_{\mathrm{tc}}=\frac{{\mathrm{\τ}}_s(\cos {\mathrm{\θ}}_n+\tan {\mathrm{\θ}}_i\tan {\mathrm{\λ}}_s)}{[\cos ({\mathrm{\θ}}_n+{\mathrm{\φ}}_n)\cos {\mathrm{\φ}}_i+\tan {\mathrm{\θ}}_i\sin {\mathrm{\φ}}_i]\sin {\mathrm{\φ}}_n}\\ K_{\mathrm{rc}}=\frac{{\mathrm{\τ}}_s\sin {\mathrm{\θ}}_n}{[\cos ({\mathrm{\θ}}_n+{\mathrm{\φ}}_n)\cos {\mathrm{\φ}}_i+\tan {\mathrm{\θ}}_i\sin {\mathrm{\φ}}_i]\cos {\mathrm{\λ}}_s\sin {\mathrm{\φ}}_n}\\ K_{\mathrm{ac}}=\frac{{\mathrm{\τ}}_s(\tan {\mathrm{\θ}}_i-\cos {\mathrm{\θ}}_n\tan {\mathrm{\λ}}_s)}{[\cos ({\mathrm{\θ}}_n+{\mathrm{\φ}}_n)\cos {\mathrm{\φ}}_i+\tan {\mathrm{\θ}}_i\sin {\mathrm{\φ}}_i]\sin {\mathrm{\φ}}_n}\end{array}\right\}$

Upper, due to dF _t, dF _r, dF _aformula is about shear yield stress τ _s, resultant tool force direction θ _nand θ _i, cutting edge inclination λ _sand Shear Plane Angle in Oblique Metal Machining with function, numerous inclined cutting parameter is made troubles to solving, thus application Armarego classical oblique cutting model based on following, the inclined cutting parameter being difficult to solve is simplified: shear rate and shearing force conllinear; Length of chip is than identical in orthogonal cutting with inclined cutting;

Draw:

$\left.\begin{array}{c}\tan {\mathrm{\β}}_n=\tan {\mathrm{\β}}_r\cos \mathrm{\η},{\mathrm{\β}}_n={\mathrm{\θ}}_n+{\mathrm{\γ}}_n\\ \tan {\mathrm{\φ}}_n=\frac{r_c(\cos \mathrm{\η}/\cos {\mathrm{\λ}}_s)\cos {\mathrm{\γ}}_n}{1-r_c(\cos \mathrm{\η}/\cos {\mathrm{\λ}}_s)\sin {\mathrm{\γ}}_n}\\ \tan ({\mathrm{\φ}}_n+{\mathrm{\β}}_n)=\frac{\cos {\mathrm{\γ}}_n\tan {\mathrm{\λ}}_s}{\tan \mathrm{\η}-\sin {\mathrm{\α}}_n\tan {\mathrm{\λ}}_s}\end{array}\right\}$

Draw Cutting Force Coefficient K _tc, K _rc, K _ac

$\left.\begin{array}{c}{K}_{\mathrm{tc}}=\frac{{\mathrm{\τ}}_s}{\sin {\mathrm{\φ}}_n}\×\frac{\cos ({\mathrm{\β}}_n-{\mathrm{\γ}}_n)+\tan {\mathrm{\λ}}_s\tan \mathrm{\η}\tan {\mathrm{\β}}_n}{\sqrt{{\cos }^2({\mathrm{\φ}}_n+{\mathrm{\β}}_n-{\mathrm{\γ}}_n)+{\tan }^2\mathrm{\η}{\sin }^2{\mathrm{\β}}_n}}\\ K_{\mathrm{rc}}=\frac{{\mathrm{\τ}}_s}{\sin {\mathrm{\φ}}_n\cos {\mathrm{\λ}}_s}\×\frac{\sin ({\mathrm{\β}}_n-{\mathrm{\γ}}_n)}{\sqrt{{\cos }^2({\mathrm{\φ}}_n+{\mathrm{\β}}_n-{\mathrm{\γ}}_n)+{\tan }^2\mathrm{\η}{\sin }^2{\mathrm{\β}}_n}}\\ K_{\mathrm{ac}}=\frac{{\mathrm{\τ}}_s}{\sin {\mathrm{\φ}}_n}\×\frac{\cos ({\mathrm{\β}}_n-{\mathrm{\γ}}_n)\tan {\mathrm{\λ}}_s-\tan \mathrm{\η}\tan {\mathrm{\β}}_n}{\sqrt{{\cos }^2({\mathrm{\φ}}_n+{\mathrm{\β}}_n-{\mathrm{\γ}}_n)+{\tan }^2\mathrm{\η}{\sin }^2{\mathrm{\β}}_n}}\end{array}\right\}.$

4. the construction method of aluminum alloy materials end mill cutting force as claimed in claim 1 and cut distorted pattern, it is characterized in that, for multiple tooth situation, i-th cutter tooth relative to desirable cutter tooth position by axial positioning errors Δ zi, radial position error Δ ri, then:

5. the construction method of aluminum alloy materials end mill cutting force as claimed in claim 1 and cut distorted pattern, it is characterized in that, described aluminum alloy materials end mill cutting force and the construction method of cut distorted pattern comprise:

Single factor test mismachining tolerance model:

Point set S is the set of in end mill processing, surface to be machined all being put, p _i∈ S is any point on surface to be machined, p _ipoint produces mismachining tolerance E under the effect of error effect factor F _fi, E _fifor the vector representation of mismachining tolerance, error effect factor F is the parts of lathe, power, temperature field or some random disturbance;

Analyze cutting process, E _fibe not once reach, and be through multiple error and add up the result obtained;

Surfacing process time is T, at t ₁moment (t ₁∈ [0, T]) p _ithe mismachining tolerance of point under the effect of F is δ ₀+ δ ₁, wherein δ ₀for the initial error state of pi, then at t ₁+ Δ t, p _ithe mismachining tolerance of point then shows as the mismachining tolerance δ of accumulation ₀+ δ ₁therefore+Δ δ, if get t in [0, T] scope ₁, t ₂..., t _mm moment is analyzed altogether, then E _fibe expressed as the form of pi point cumulative errors vector:

$E_{F_i}={\mathrm{\δ}}_0+{\mathrm{\δ}}_1+{\mathrm{\δ}}_2+...+{\mathrm{\δ}}_m$

Various factors coupling mismachining tolerance model:

Total k error effect factor F in process ₁, F ₂... F _kact on workpiece to be machined, p _ithe mismachining tolerance E that point produces under the effect of each error effect factor _fiexpression formula as follows:

$E_{F_i}=c\sqrt{{\mathrm{\λ}}_1{E}_{F_{i1}}^2+{\mathrm{\λ}}_2{E}_{F_{i2}}^2+...+{\mathrm{\λ}}_m{E}_{F_{\mathrm{ik}}}^2}$

Wherein c is rejection rate coefficient, λ ₁, λ ₂for the coefficient that the error distribution curve shape of each compositing factor is relevant, λ=1/9 during normal distribution, equiprobability curve or λ=1/3 when distributing unclear, during Triangle-Profile 1/6;

End mill finished surface error effect factor draws, and end mill finished surface puts p _ierror E _i:

$\begin{array}{c}{E}_i=c({\mathrm{\λ}}_1{E}_{F_i}^2+{\mathrm{\λ}}_2{E}_{H_i}^2+{\mathrm{\λ}}_3{E}_{S_i}^2+{\mathrm{\λ}}_4{E}_{C_i}^2+{\mathrm{\λ}}_5{E}_{{\mathrm{CL}}_i}^2+{\mathrm{\λ}}_6{E}_{T_i}^2+{\mathrm{\λ}}_7{E}_{{\mathrm{TG}}_i}^2\\ +{\mathrm{\λ}}_8{E}_{M_i}^2+{\mathrm{\λ}}_9{E}_{{\mathrm{MG}}_i}^2+{\mathrm{\λ}}_{10}{E}_{R_i}^2{)}^{\frac{1}{2}}\end{array}$

Self-adapted genetic algorithm based on real coding carries out the prediction of end mill finished surface flatness error.