CN105608288B - One kind being based on overdamp effect milling parameter stability prediction method - Google Patents
One kind being based on overdamp effect milling parameter stability prediction method Download PDFInfo
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Abstract
The present invention provides a kind of based on overdamp effect milling parameter stability prediction method,This method is in carrying out workpiece milling process,Obtain milling cutter geometrical structure parameter and milling process dynamic parameter,Determine the gross energy that plow power generates in workpiece milling process in a pirouette period,Utilize law of conservation of energy,Obtain equivalent linearity process damped coefficient,The damping of equivalent linearity process is changed into the equivalent processes damping of the directions x and the damping of the directions y equivalent processes,The directions x equivalent processes damped coefficient and the directions y equivalent processes damped coefficient input milling dynamics equation are obtained into the milling dynamics model of Kernel-based methods damping effect,The milling dynamics model of Kernel-based methods damping effect is solved using ZOA methods,Obtain the flutter stability model of Kernel-based methods damping effect,To obtain the relationship between marginal stability cutting-in and cutter rotating speed,And draw the flutter stability flap figure of Kernel-based methods damping effect.
Description
Technical field
The invention belongs to field of machining, and in particular to one kind being based on overdamp effect milling parameter stability prediction side
Method.
Background technology
Milling Process is widely used in the industries such as aerospace mold, and Regenerative Chatter is the main restriction for improving production efficiency
One of factor.The development of High-speed machining theory keeps the incision frequency of cutter tooth synchronous with flutter frequency next by selecting the speed of mainshaft
Avoid the generation of flutter.In the high-speed milling stage of higher material removing rate, classical flutter flap figure provides accurate steady
Qualitative forecasting.However, in the low speed process segment, due to there are a large amount of complete vibration waves in a swing circle of main shaft
It is long, cause flap figure so dense so that classical flutter theory tends not to accurately predict stability.On the other hand, it tests
Observation shows that the stabilization cutting zone of system can dramatically increase when cutting speed is far below the intrinsic frequency of system of processing.This
Stablize dramatically increasing for cutting region when kind slow cutting, rubbing action institute between cutter flank and uneven workpiece surface can be attributed to
Caused cutting speed variation, i.e. process damping action.
The research of process damping effect is concentrated mainly in external experts and scholars' document, the domestic research phase in the field
To fewer.Professor Altintas thinks that process damping effect will be as most challenging research to the research of flutter stability
Project；Mentioning tool wear will cause process damped coefficient to increase, to increase flutter instability critical zone.Budak is mentioned
Process damping effect in low speed processing becomes one of research emphasis and difficult point with its complexity.The effect and cutting data are cut
It is closely related to cut the factors such as temperature, cutter material characteristic, shear surface variation；Heat height will be generated by cutting difficult-to-machine material, easily be led
Cause tool wear, the finished work corrugated surface that the geometry for changing cutting edge is contacted with flank, to increase
Process damping effect.
Invention content
One kind being based on overdamp effect milling parameter stability prediction method, includes the following steps：
Step 1：In carrying out workpiece milling process, obtains milling cutter geometrical structure parameter and milling process dynamic is joined
Number；
The milling cutter geometrical structure parameter includes：Cutter number of teeth Nf, tool clearance λ and cutter diameter D；
The milling process dynamic parameter includes：Cutter flutter angular frequencyc, cutter amplitude A0With tool angular velocity Ω.
Step 2：A pirouette period is determined according to milling cutter geometrical structure parameter and milling process dynamic parameter
The gross energy that plow power generates in interior workpiece milling process, using law of conservation of energy, the gross energy etc. which is generated
The energy that valence is generated in equivalent linearity process damping force in a cycle, obtains equivalent linearity process damped coefficient；
Step 2.1：The tangential displacement of cutter is determined according to milling cutter geometrical structure parameter and milling process dynamic parameter
With the radial displacement of cutter；
Step 2.2：The axial cutting-in a of cutter is divided into NzA infinitesimal determines the tangential plow infinitesimal power of cutter cutter tooth
With the radial plow infinitesimal power of cutter tooth；
Step 2.3：Determine the energy e that plow power generates within a vibration periodi, i.e., cutter cutter tooth is in a vibration wave
Rimmer knife tooth footpath the sum of is done work to plow infinitesimal power and tangential plow infinitesimal power；
Step 2.4：According to cutter flutter angular frequencycDetermine that cutter pirouette stays in work in one week with tool angular velocity Ω
The oscillation mark number on part surface；
Step 2.5：Determine the gross energy of plow power, i.e., plow power is in the one week work(done of cutter pirouette；
Step 2.6：Using law of conservation of energy, the gross energy of plow power is equivalent to use linear viscous in a cycle
The energy that the process damping force of damping generates, obtains equivalent linearity process damped coefficient.
Step 3：The damping of equivalent linearity process is changed into the equivalent processes damping of the directions x and the damping of the directions y equivalent processes, is obtained
To the equivalent processes damped coefficient of the directions x equivalent processes damped coefficient and the directions y；
Step 4：The directions x equivalent processes damped coefficient and the directions y equivalent processes damped coefficient are inputted into milling dynamics side
Journey obtains the milling dynamics model of Kernel-based methods damping effect；
Step 5：The milling dynamics model that Kernel-based methods damping effect is solved using ZOA methods obtains Kernel-based methods damping
The flutter stability model of effect to obtain the relationship between marginal stability cutting-in and cutter rotating speed, and is drawn and was based on
The flutter stability flap figure of journey damping effect.
The flutter stability model of the Kernel-based methods damping effect is：
Wherein,For cutter and work piece interface product transfer function matrix,
The direct transmission function that the directions x are accumulated for cutter and work piece interface is that cutter accumulates the direct of the directions y with work piece interface
Transmission function, to intersect transmission function, a is the axial cutting-in of cutter, ktFor tangential cutting force constant,
NfFor cutter number of teeth, ωcFor cutter flutter angular frequency, T is cutter swing circle, and i is plural number.
Beneficial effects of the present invention：
The present invention proposes that one kind being based on overdamp effect milling parameter stability prediction method, in difficult-to-machine material, complexity
Curved surface relatively low speed processing in, process damping effect play the role of in flutter stability it is very important, especially milling navigate
Empty material, have low heat conductivity titanium alloy when, will generate heat compare it is larger, so as to cause tool wear；Process damping system
Number will increase, proposed by the present invention steady based on overdamp effect milling parameter to change flutter instability region limit
Qualitative Forecast Methods are solved when low speed is processed, since flutter stability flap densification leads to not choose using stable region
The problem of cutting parameter, improves the accuracy of flutter instability regional prediction.Therefore in actual production, to joining in process
Several optimization improves production efficiency and has great importance.
Description of the drawings
Fig. 1 is the flow based on overdamp effect milling parameter stability prediction method in the specific embodiment of the invention
Figure；
Fig. 2 is that Kernel-based methods damp milling dynamics model in the specific embodiment of the invention；
Wherein, (a) is that cutter cuts part model, is (b) the vibration wavelength schematic diagram that cutter invades workpiece；
KxFor cutter x directional stiffness coefficients, CxFor the directions cutter x damped coefficient, KyFor cutter y directional stiffness coefficients, CyFor
The directions cutter y damped coefficient, FptFor tangential plow power, FprFor radial plow power, rjFor cutter cutter tooth j radial distances, ujFor knife
Have cutter tooth j tangential distances, λ is tool clearance, cutterj-1For -1 cutter tooth of cutter jth, cutterjFor j-th of cutter tooth of cutter,
V is cutter linear velocity, A0For cutter amplitude, L is the wavelength for the vibration that cutter invades workpiece, φjFor cutter cutter tooth j and work
The contact angle of part, Ω are tool angular velocity；
Fig. 3 is that the gross energy that plow power generates is equivalent to equivalent linearity in a cycle in the specific embodiment of the invention
The energy that process damping force generates obtains the flow chart of equivalent linearity process damped coefficient；
Fig. 4 is not consider the flutter stability flap figure of process damping effect in the specific embodiment of the invention and be based on
The flutter stability flap figure comparison diagram of journey damping effect；
Fig. 5 is that the flutter of the Kernel-based methods damping effect in the case of different tool clearances in the specific embodiment of the invention is steady
Qualitative flap figure comparison diagram；
Fig. 6 is that the flutter of the Kernel-based methods damping effect in the case of different cutter amplitudes in the specific embodiment of the invention is steady
Qualitative flap figure comparison diagram；
Fig. 7 is that the flutter of the Kernel-based methods damping effect in the case of different tool stiffness in the specific embodiment of the invention is steady
Qualitative flap figure comparison diagram；
Fig. 8 quivers for the Kernel-based methods damping effect in the case of different cutter structures dampings in the specific embodiment of the invention
Shake the stability lobes diagram comparison diagram；
Fig. 9 is the flutter instability of the Kernel-based methods damping effect in the case of different number of teeth in the specific embodiment of the invention
Property three-dimensional flap figure comparison diagram；
Figure 10 is the Kernel-based methods in the case of different radial the ratio between cutting-ins and cutter diameter in the specific embodiment of the invention
The flutter stability three-dimensional flap figure comparison diagram of damping effect.
Specific implementation mode
The specific embodiment of the invention is described in detail below in conjunction with the accompanying drawings.
The present invention provides one kind being based on overdamp effect milling parameter stability prediction method, the vibration decomposition of cutter
It for radial linear motion of reciprocating vibration and tangential, calculates within one vibration period of cutter tooth, since cutter flank invades
Then the invasiveness work done of workpiece machined surface is multiplied by one swing circle of cutter complete oscillation mark number, profit
With the linear damping of equal value of energy equivalence principle nonlinear dampling, flutter stability flap figure is solved using frequency domain method, low
In fast milling process, the flutter stability cutting-in limit can be efficiently and accurately predicted.Therefore to Optimizing Cutting Conditions, finished surface
Quality and processing efficiency provide theoretical direction.
One kind being based on overdamp effect milling parameter stability prediction method, as shown in Figure 1, including the following steps：
Step 1：In carrying out workpiece milling process, obtains milling cutter geometrical structure parameter and milling process dynamic is joined
Number.
In present embodiment, Kernel-based methods damp milling dynamics model as shown in Fig. 2, carbide-tipped milling cutter geometry
Parameter includes：The cutter number of teeth N that helical angle is 0f=4, tool clearance λ=10 degree, cutter diameter D=10mm；
Milling process dynamic parameter includes：Cutter flutter angular frequencyc, cutter amplitude A0With tool angular velocity Ω.
Step 2：A pirouette period is determined according to milling cutter geometrical structure parameter and milling process dynamic parameter
The gross energy that plow power generates in interior workpiece milling process, using law of conservation of energy, the gross energy etc. which is generated
The energy that valence is generated in equivalent linearity process damping force in a cycle, obtains equivalent linearity process damped coefficient, such as Fig. 3 institutes
Show.
Step 2.1：The tangential displacement of cutter is determined according to milling cutter geometrical structure parameter and milling process dynamic parameter
With the radial displacement of cutter.
In present embodiment, according to cutter flutter angular frequencyc, cutter amplitude A0, tool angular velocity Ω and cutter diameter D
The tangential displacement u (t) of determining cutter and the radial displacement r (t) of cutter are as shown in formula (1) and formula (2)：
R (t)=A0sin(ωct) (2)
Wherein, v is cutter linear velocity, and t is the time.
Step 2.2：The axial cutting-in a of cutter is divided into NzA infinitesimal determines the tangential plow infinitesimal power of cutter cutter tooth
With the radial plow infinitesimal power of cutter tooth.
In present embodiment, the axial cutting-in a of cutter is divided into NzShown in a infinitesimal such as formula (3)：
Nz=a/ Δs z (3)
Wherein, Δ z is infinitesimal.
The tangential plow infinitesimal power dF of determining cutter cutter toothpr[φj(t), kz]With the radial plow infinitesimal of stage property cutter tooth
Power dFpt[φj(t), kz]As shown in formula (4) and formula (5)：
dFpr[φj(t), kz]=KspdV[φj(t), kz]g[φj(t), kz] (4)
dFpt[φj(t), kz]=μ dFpr[φj(t), kz] (5)
Wherein, φj(t)=Ω t+ (j-1) 2 π/Nf, φj(t) it is the contact angle of cutter cutter tooth j and workpiece, by documents and materials
Know intrusion force constant Ksp=3000N/mm3, V cutters intrusion workpiece volume, kz∈Nz, by documents and materials know average friction coefficient μ=
0.3, g[φj(t), kz]For unit jump function, for determining cutter tooth whether in cutting.
Unit-step function g[φj(t), kz]As shown in formula (6)：
Wherein, φstFor cutter entrance angle, φexAngle is cut out for cutter.
Step 2.3：Determine the energy e that plow power generates within a vibration periodi, i.e., cutter cutter tooth is in a vibration wave
Rimmer knife tooth footpath the sum of is done work to plow infinitesimal power and tangential plow infinitesimal power.
In present embodiment, energy e that plow power generates within a vibration periodiSuch as formula (7), formula (8) and formula (9) institute
Show：
ei=eiu+eir (7)
Wherein, eiuFor the tangential plow infinitesimal power work done of one vibration wavelength cutter tooth of cutter cutter tooth, eirFor cutter cutter tooth
One vibration wavelength cutter tooth radial direction plow infinitesimal power work done, L=(2 π v)/ωc,
Step 2.4：According to cutter flutter angular frequencycDetermine that cutter pirouette stays in work in one week with tool angular velocity Ω
The oscillation mark number on part surface.
In present embodiment, according to cutter flutter angular frequencycCutter pirouette is determined with tool angular velocity Ω one week
Shown in the oscillation mark number such as formula (10) for staying in workpiece surface：
(ωc/ Ω)=the π of η+ζ/2 (10)
Wherein, η is the integer number of one week oscillation mark for staying in workpiece surface of cutter pirouette, and the π of ζ/2 are to generate wave
The decimal of line number.
Step 2.5：Determine the gross energy of plow power, i.e., plow power is in the one week work(done of cutter pirouette.
In present embodiment, the gross energy E of plow poweriAs shown in formula (11)：
Ei=Eiu+Eir=η (eiu+eir) (11)
Wherein, EiuFor one week tangential plow power infinitesimal power work done of pirouette, EirFor one week radial plough of pirouette
Cut infinitesimal power work done.
Step 2.6：Using law of conservation of energy, the gross energy of plow power is equivalent to use linear viscous in a cycle
The energy that the process damping force of damping generates, obtains equivalent linearity process damped coefficient.
In present embodiment, the energy such as formula of the process damping force generation of linear viscous damping will be used in a cycle
(12) and shown in formula (13)：
Wherein, Ep irFor equivalent radial process damping force within a pirouette period work done, Ep iuIt is equivalent
Tangential process damping force within a pirouette period work done.
Using law of conservation of energy, the gross energy of plow power is equivalent to use the mistake of linear viscous damping in a cycle
The energy that journey damping force generates, makes Ep ir=Eir, Ep iu=Eiu, obtain radial equivalent linearity process damped coefficient cprSuch as formula (14)
It is shown：
It can similarly obtain, tangential equivalent linearity process damped coefficient cpuAs shown in formula (15)：
Step 3：The damping of equivalent linearity process is changed into the equivalent processes damping of the directions x and the damping of the directions y equivalent processes, is obtained
To the equivalent processes damped coefficient of the directions x equivalent processes damped coefficient and the directions y.
In present embodiment, the directions x equivalent processes damped coefficient C is obtainedpxWith the equivalent processes damped coefficient C in the directions ypy
As shown in formula (16)：
Equivalent processes damped coefficient expression formula in the directions x and y is：
Step 4：The directions x equivalent processes damped coefficient and the directions y equivalent processes damped coefficient are inputted into milling dynamics side
Journey obtains the milling dynamics model of Kernel-based methods damping effect.
In present embodiment, the directions x equivalent processes damped coefficient and the input milling of the directions y equivalent processes damped coefficient are moved
Mechanical equation obtains shown in the milling dynamics model such as formula (17) of Kernel-based methods damping effect：
Wherein,For milling system quality coefficient, mxxFor cutter x-axis quality, myyFor cutter y-axis matter
Amount,For tool stiffness, KxFor cutter x directional stiffness coefficients, KyFor cutter y directional stiffness coefficients,It is damped for milling system, CxFor the directions cutter x damped coefficient, CyIt is hindered for the directions cutter y
Buddhist nun's coefficient,For the dynamic displacement of cutter,Inside and outside cutter
The difference of cyclic shift, Δ x are the difference of the directions cutter x inner-outer circulation displacement, and Δ y is the difference of the directions cutter y inner-outer circulation displacement, x
(t) it is cutter x direction outer circulations in t moment displacement, y (t) is cutter y direction outer circulations in t moment displacement, and x (t-T) is cutter
T moment displacement is circulated in the directions x, y (t-T) is that t moment displacement is circulated in the directions cutter y, and T is cutter swing circle, kt
=1596.3Mpa is tangential cutting force constant,For the direction coefficient of time-varying.
Shown in the direction coefficient A such as formulas (18) of time-varying：
Wherein, kr=0.25 is radial cutting force constant, and φ is the instant contact angle of cutter and workpiece.
Step 5：The milling dynamics model that Kernel-based methods damping effect is solved using ZOA methods obtains Kernel-based methods damping
The flutter stability model of effect to obtain the relationship between marginal stability cutting-in and cutter rotating speed, and is drawn and was based on
The flutter stability flap figure of journey damping effect.
In present embodiment, the milling dynamics model of Kernel-based methods damping effect is solved using ZOA methods, was based on
Shown in the flutter stability model such as formula (19) of journey damping effect：
Wherein,For cutter and work piece interface product transfer function matrix,
The direct transmission function that the directions x are accumulated for cutter and work piece interface is that cutter accumulates the direct of the directions y with work piece interface
Transmission function, to intersect transmission function, i is plural number.
Obtain marginal stability cutting-inAs shown in formula (20)：
Wherein, Δ RpIt is the real part of consideration process damping milling dynamics formulation character value Δ, κ is the damping milling of consideration process
Cut the ratio of the imaginary part and real part of kinetics equation characteristic value Δ.
Wherein, consider shown in process damping milling dynamics formulation character value Δ such as formula (21)：
Wherein, a0=φp xx(iωc)φp vv(iωc)(axxayy-axyayx), a1=φp xx(iωc)φp yy(iωc)
(axxayy-axyayx),
ωnxFor the intrinsic frequency in the directions main shaft tooling system x, ωnyFor the intrinsic frequency in the directions main shaft tooling system y, ζxFor main shaft knife
The structural damping ratio in the directions tool system x, ζyFor the structural damping ratio in the directions main shaft tooling system y, ζpxFor the main shaft tooling system side x
To process damping ratio, ζpyFor the process damping ratio in the directions main shaft tooling system y.
It obtains shown in cutter range of speeds n such as formulas (22)：
Wherein, ψ=arctan κ are the phase shift that consideration process damps milling dynamics formulation character value Δ, lrIt is followed for vibration
Number of rings.
The modal parameter of main axle cutter system is as shown in table 1.
The modal parameter of 1 main axle cutter system of table
In present embodiment, go out not consider the flutter stability flap figure of process damping effect using Matlab Software on Drawing
Flutter stability flap figure comparison diagram with Kernel-based methods damping effect is as shown in figure 4, as shown in Figure 4, Kernel-based methods damping is imitated
The flutter stability flap figure answered can more accurately describe the relationship between marginal stability cutting-in and cutter rotating speed.
In present embodiment, the flutter stability flap figure pair of the Kernel-based methods damping effect in the case of different tool clearances
Than figure as shown in figure 5, when taking tool clearance λ=5 degree and λ=10 degree respectively, other parameters are constant, are programmed by MATLAB
Draw influence of the different relief angles to Kernel-based methods damping effect flutter stability.From figure 5 it can be seen that cutting-in stability limit with
The increase of tool clearance and reduce.
In present embodiment, the flutter stability flap figure pair of the Kernel-based methods damping effect in the case of different cutter amplitudes
Than scheming as shown in fig. 6, taking cutter amplitude A0=20 μm and A0At=40 μm, other parameters are constant, and picture is programmed by MATLAB
Go out influence of the cutter amplitude to the flutter stability of Kernel-based methods damping effect.From fig. 6 it can be seen that cutting-in stability limit with
It the increase of cutter amplitude and increases.
In present embodiment, the flutter stability flap figure pair of the Kernel-based methods damping effect in the case of different tool stiffness
Than scheming as shown in fig. 7, it is respectively 1 times of rigidity in table 1,1.5 times, 2 times to take tool stiffness, other parameters are constant, pass through
MATLAB is programmed the influence for drawing tool stiffness to the flutter stability of Kernel-based methods damping effect.It can from Fig. 7
Go out, cutting-in stability limit increases with the increase of tool stiffness.
In present embodiment, the flutter stability flap of the Kernel-based methods damping effect in the case of different cutter structure dampings
Figure comparison diagram is as shown in figure 8, it is respectively 1 times, 1.5 times, 2 times of structural damping in table 1 to take cutter structure damping, and other parameters are not
Become, the influence for drawing cutter structure damping to the flutter stability of Kernel-based methods damping effect is programmed by MATLAB.From
As can be seen that cutting-in stability limit increases with the increase that cutter structure damps in Fig. 8.
In present embodiment, the flutter stability three-dimensional flap figure of the Kernel-based methods damping effect in the case of different number of teeth
For comparison diagram as shown in figure 9, when number of teeth being taken to be respectively 2,3,4,5, other parameters are constant, are programmed by MATLAB and draw knife
Influence of the number of teeth to the flutter stability of Kernel-based methods damping effect.It can be seen in figure 9 that cutting-in stability limit is with cutter
The increase of structural damping and reduce.
In present embodiment, the flutter of the Kernel-based methods damping effect in the case of different radial direction the ratio between cutting-ins and cutter diameter
Stability three-dimensional flap figure comparison diagram is as shown in Figure 10, take the ratio between radial cutting-in and cutter diameter be 0.5,0.7,0.9 when, other
Parameter constant is programmed the flutter for comparing Kernel-based methods damping effect for drawing radial cutting-in and cutter diameter by MATLAB
The influence of stability.It can be seen from fig. 10 that cutting-in stability limit with the increase of the ratio between radial cutting-in and cutter diameter and
Reduce.
Claims (3)
1. one kind being based on overdamp effect milling parameter stability prediction method, which is characterized in that include the following steps：
Step 1：In carrying out workpiece milling process, milling cutter geometrical structure parameter and milling process dynamic parameter are obtained；
Step 2：Work in a pirouette period is determined according to milling cutter geometrical structure parameter and milling process dynamic parameter
The gross energy that the plow power generates is equivalent to by the gross energy that plow power generates in part milling process using law of conservation of energy
The energy that equivalent linearity process damping force generates in a cycle, obtains equivalent linearity process damped coefficient, is as follows：
Step 2.1：The tangential displacement and knife of cutter are determined according to milling cutter geometrical structure parameter and milling process dynamic parameter
The radial displacement of tool；
Step 2.2：The axial cutting-in a of cutter is divided into NzA infinitesimal determines the tangential plow infinitesimal power and cutter tooth of cutter cutter tooth
Radial plow infinitesimal power；
Step 2.3：Determine the energy e that plow power generates within a vibration periodi, i.e., cutter cutter tooth is in a vibration wave rimmer knife
Tooth footpath the sum of is done work to plow infinitesimal power and tangential plow infinitesimal power；
Step 2.4：According to cutter flutter angular frequencycDetermine that cutter pirouette stays in workpiece table in one week with tool angular velocity Ω
The oscillation mark number in face；
Step 2.5：Determine the gross energy of plow power, i.e., plow power is in the one week work(done of cutter pirouette；
Step 2.6：Using law of conservation of energy, the gross energy of plow power is equivalent to use linear viscous damping in a cycle
Process damping force generate energy, obtain equivalent linearity process damped coefficient；
Step 3：The damping of equivalent linearity process is changed into the equivalent processes damping of the directions x and the damping of the directions v equivalent processes, obtains x
The equivalent processes damped coefficient of direction equivalent processes damped coefficient and the directions y；
Step 4：The directions x equivalent processes damped coefficient and the directions y equivalent processes damped coefficient input milling dynamics equation are obtained
To the milling dynamics model of Kernel-based methods damping effect；
Step 5：The milling dynamics model that Kernel-based methods damping effect is solved using ZOA methods, obtains Kernel-based methods damping effect
Flutter stability model, to obtain the relationship between marginal stability cutting-in and cutter rotating speed, and draw Kernel-based methods resistance
The flutter stability flap figure of Buddhist nun's effect.
2. according to claim 1 be based on overdamp effect milling parameter stability prediction method, which is characterized in that described
Milling cutter geometrical structure parameter includes：Cutter number of teeth Nf, tool clearance λ and cutter diameter D；
The milling process dynamic parameter includes：Cutter flutter angular frequencyc, cutter amplitude A0With tool angular velocity Ω.
3. according to claim 1 be based on overdamp effect milling parameter stability prediction method, which is characterized in that described
The flutter stability model of Kernel-based methods damping effect is：
Wherein,For cutter and work piece interface product transfer function matrix,For knife
The direct transmission function of tool and the directions work piece interface product x,The direct transmission in the directions y is accumulated for cutter and work piece interface
Function,To intersect transmission function, a is the axial cutting-in of cutter, ktFor tangential cutting force constant, NfFor
Cutter number of teeth, ωcFor cutter flutter angular frequency, T is cutter swing circle, and i is plural number.
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