CN103823945A - Flutter stability domain modeling approach for face cutting process - Google Patents

Abstract

The invention belongs to the technical fields of simulating computational analysis and modal testing, and relates to a flutter stability domain modeling approach for a face cutting process. After all kinds of characteristic parameters of a material are known, a computer simulates a machining cutting process, calculates the cutting force in the machining process and analyzes the corresponding cutting coefficient. After the cutting coefficient is obtained, a modal experiment is utilized, modal testing is carried out on a machine tool spindle tool system, and the modal characteristic parameters of the machine tool spindle tool system are analyzed and comprise a multiple-order inherent frequency, a damping ratio, dynamic stiffness and the like. According to a flutter cutting theory, a stability lobe graph is drawn through combining the cutting coefficient and the system characteristic parameters and utilizing a computer assemble program, and is used for selecting the reasonable cutting parameter to avoid a flutter region, the processing precision and quality are improved, and a machine tool system is protected.

Description

A kind of flutter instability territory modeling method of surfacing process

Technical field

The invention belongs to Simulation Analysis and mode technical field of measurement and test, relate to a kind of flutter instability territory modeling method of surfacing process.

Background technology

Manufacturing industry is the mainstay industry that our national economy increases, as a more traditional field, it has set up the theoretical system of comparison system at present, accumulate abundant practical experience, but along with the raising of scientific and technological level, machinery manufacturing industry faces new challenges, and forces Machine Manufacturing Technology towards robotization, flexibility, precise treatment, informationization and intelligent direction development.Cut is most widely used processing mode, and along with the development of advanced manufacturing technology, stability, reliability to cut propose higher requirement.In actual cut processing, system of processing flutter and tool failure are the key factors that affects cut efficiency, precision, quality and stability and reliability.Processing and manufacturing high precision in recent years, high-quality part become a difficult problem.Therefore, in cutting process, choosing suitable cutting parameter is significant for improving machining precision and quality.

In machining, except cutting movement, sometimes also can and be cut between material surface at cutter and produce Relative Vibration, this cutting vibration meeting brings harmful effect to machining system, causes the reduction of machining precision, surface quality and system reliability.Wherein the most serious autovibration is in working angles, under the effect of the outside exciting force of aperiodicity, due to the caused a kind of cutting vibration of the feature of system of processing own, conventionally this cutting vibration is called to flutter.Cutting system is a very complicated dynamic system, in working angles, the thickness of smear metal changed with the cutting time, its cutting force is also directly proportional to the inherent characteristic of depth of cut, machine tool system, therefore between cutter and processing work except normal cutting movement, also can produce a kind of ferocious Relative Vibration, this cutting vibration will cause occurring in working angles unstable cutting.Cutting-vibration is to occur in a kind of strong autovibration in working angles.If can not effectively suppress unstable flutter in cutting, will affect so the crudy of parts, simultaneously by the wearing and tearing of aggravation cutter.So in order to improve precision and the efficiency of lathe, cutting system is carried out to cutting-vibration stability analysis, avoids occurring flutter, this is to enhancing productivity, improve parts machining quality, reduce tool wear and have very important significance, this is also the focus of domestic and international researcher's research.

Summary of the invention

The flutter instability territory modeling method that the invention provides a kind of surfacing process, technical matters to be solved is accurate simulation working angles and calculates cutting coefficient.

Technical scheme of the present invention is as follows:

A flutter instability territory modeling method for surfacing process, comprises the following steps:

Build binary cutting system, only consider x, the kinetic factor of y direction:

$\left\{\begin{array}{c}{m}_x\stackrel{\·\·}{x}+c_x\stackrel{\·}{x}+k_{x}x=\underset{j=1}{\overset{N}{\mathrm{\Σ}}}{F}_{\mathrm{xj}}=F_x\left(t\right)\\ m_y\stackrel{\·\·}{y}+c_y\stackrel{\·}{y}+k_{y}y=\underset{j=1}{\overset{N}{\mathrm{\Σ}}}{F}_{\mathrm{yj}}=F_y\left(t\right)\end{array}\right.$

In formula, m _x, m _y, c _x, c _y, k _x, k _ybe respectively x, the quality of lathe-tooling system, damping and rigidity in y direction; F _xjand F _yjbe respectively the cutting force acting on milling cutter tooth j at x, the component in y direction.

By above formula is arranged, and carry out after Laplace transformation, its transport function can be expressed as:

$\left\{\begin{array}{c}{G}_{\mathrm{xx}}\left(s\right)=\frac{x\left(s\right)}{F_x\left(s\right)}=\frac{{\mathrm{\ω}}_{\mathrm{nx}}^2}{K_x(s^2+2{\mathrm{\ζ}}_x{\mathrm{\ω}}_{\mathrm{nx}}s+{\mathrm{\ω}}_{\mathrm{nx}}^2)}\\ G_{\mathrm{yy}}\left(s\right)=\frac{y\left(s\right)}{F_y\left(s\right)}=\frac{{\mathrm{\ω}}_{\mathrm{ny}}^2}{K_y(s^2+2{\mathrm{\ζ}}_y{\mathrm{\ω}}_{\mathrm{ny}}s+{\mathrm{\ω}}_{\mathrm{ny}}^2)}\end{array}\right.$

Wherein, ζ _x, ζ _yfor damping ratio, ω _nx, ω _nyfor system frequency.

In cut, only consider that the dynamic thickness of cutting expression formula of Regenerative Chatter is:

h _j(φ)＝Δxsinφ _j+Δycosφ _j

Wherein: $\mathrm{\Δx}=(x_c-x_c^0)-(x_w-x_w^0),\mathrm{\Δy}=(y_c-y_c^0)-(y_w-y_w^0).$

The model that proposes orthogonal cutting theory based on the theory of Tlusty, when intermittent angle displacement is φ, acts on tangentially can be expressed as with dynamic cutting force radially on cutter tooth j:

$\left\{\begin{array}{c}{F}_{\mathrm{tj}}\left(\mathrm{\φ}\right)=K_t{a}_p{h}_j\left(\mathrm{\φ}\right)\\ F_{\mathrm{rj}}\left(\mathrm{\φ}\right)=K_r{F}_{\mathrm{tj}}\left(\mathrm{\φ}\right)\end{array}\right.$

Wherein, K _rfor coefficient ratio, K _r=K _rck _tc.Above formula is rewritten into the form of matrix:

$\left\{F\left(t\right)\right\}=\frac{1}{2}{a}_p{K}_t\left[A\left(t\right)\right]\left\{\mathrm{\Δ}\left(t\right)\right\}$

Wherein, A (t) is and intermittent angle displacement φ _jrelevant periodic function, its angular frequency=Nn60, cycle T=2 π ω.A (t) is carried out Fourier series expansion and retains Section 1, and above formula can be rewritten into:

$\left\{F\left(t\right)\right\}=\frac{1}{2}{a}_p{K}_t\frac{N}{2\mathrm{\π}}\left[\begin{array}{cc}{\mathrm{\α}}_{\mathrm{xx}}& {\mathrm{\α}}_{\mathrm{xy}}\\ {\mathrm{\α}}_{\mathrm{yx}}& {\mathrm{\α}}_{\mathrm{yy}}\end{array}\right]\left\{\mathrm{\Δ}\left(t\right)\right\}$

Wherein, α _xx, α _xy, α _yx, α _yxfor mean direction coefficient.

The necessary and sufficient condition of system stability is that the root of transport function G (s) secular equation all has negative real part.Therefore, in frequency domain, cutting force can be expressed as:

$\left\{F\right\}{e}^{i{\mathrm{\ω}}_{c}t}=\frac{1}{2}{a}_p{K}_t(1-e^{i{\mathrm{\ω}}_{c}t})\left[A_0\right]\left[G\left({\mathrm{i\ω}}_c\right)\right]\left\{F\right\}{e}^{i{\mathrm{\ω}}_{c}t}$

Wherein, ω _crepresent flutter frequency.The secular equation of the closed loop feedback system under cutting Regenerative Chatter frequency is:

$\det \left[\right[I]-\frac{1}{2}{a}_p{K}_t(1-e^{i{\mathrm{\ω}}_{c}t})[A_0\left]\right[G\left({\mathrm{i\ω}}_c\right)\left]\right]=0$

Λ is the eigenwert of equation, and its expression formula is

$\mathrm{\Λ}=-\frac{N}{4\mathrm{\π}}{a}_p{K}_t(1-e^{-i{\mathrm{\ω}}_{c}t})$

Its eigenwert Λ analytical method is expressed as:

$\mathrm{\Λ}=-\frac{1}{2a_0}(a_1\±\sqrt{{a_1}^2-4a_0})$

Wherein, a ₀=G _xx(i ω _c) G _yy(i ω _c) (α _xxα _yy-α _xyα _yx), a ₁=α _xxg _xx(i ω _c)+α _yyg _yy(i ω _c).

Make imaginary part equal zero, obtain threshold shaft by flutter instability theory ZOA analytical method wherein and to cutting-in be:

$a_{\mathrm{plim}}=-\frac{2\mathrm{\π}{\mathrm{\Λ}}_R(1+{({\mathrm{\Λ}}_I/{\mathrm{\Λ}}_R)}^2)}{{\mathrm{NK}}_{\mathrm{tc}}}$

The rotating speed expression formula of main shaft is:

$n=\frac{60{\mathrm{\ω}}_c}{N((2k+1)\mathrm{\π}-2\arctan ({\mathrm{\Λ}}_I/{\mathrm{\Λ}}_R))}$

Wherein, k is the leaf lobe number in leaf lobe figure, Λ _rand Λ _ibe respectively real part and the imaginary part of ssystem transfer function characteristic root, N is number of teeth, K _tccutting coefficient, ω _cfor characteristic frequency.

ω _cfor characteristic frequency, by modal test, analyze data result and obtaining.Repeatedly encourage then averaged in order to improve the employing of mode measuring accuracy, and from the different multi-modes of multi-direction tester, the corresponding various characteristic parameters of ultimate analysis, comprise multistage characteristic frequency.

K _tcfor cutting coefficient, understand cutter material, workpiece material, by emulation machining working angles, and cutting force in calculating processing process, analyze data, finally calculate cutting coefficient.In cutting finite element simulation, select chip separation criterion: physical criteria and geometric criterion.Geometric criterion is that defiber is set before solving in advance in finite element model.By judging whether point on defiber reaches separation condition with the distance between cutting edge and determine whether smear metal separates.Physical criteria is whether to reach preset critical by some physical quantity in solution procedure to judge whether smear metal separates.This failure stress criterion can be expressed as:

${\left(\frac{\left|{\mathrm{\σ}}_n\right|}{{\mathrm{\τ}}_n}\right)}^2+{\left(\frac{\left|{\mathrm{\σ}}_s\right|}{{\mathrm{\τ}}_s}\right)}^2\≥1$

Wherein, σ _n, σ _srepresent respectively smear metal-workpiece interphase normal stress and shear stress; τ _nrepresent the critical value of normal stress, τ _sfor the critical value of shear stress.Based on cutting separation criteria, the process of emulation cut.And calculate cutting force, by the Cutting Force Coefficient theory of computation and regretional analysis, can calculate Cutting Force Coefficient.Conventionally cutting coefficient is to utilize cutting force acquisition system Real-time Collection cutting signal, and utilize the relevant device system analysis computation to go out results needed, and computer simulation analysis cutting coefficient has been saved the time that actual experiment gathers cutting force data and analyzes cutting coefficient greatly.In the middle of cutting force modeling:

$\left\{\begin{array}{c}{\mathrm{dF}}_t=K_{\mathrm{tc}}\·h\·\mathrm{dz}+K_{\mathrm{te}}\·\mathrm{ds}\\ {\mathrm{dF}}_r=K_{\mathrm{rc}}\·h\·\mathrm{dz}+K_{\mathrm{re}}\·\mathrm{ds}\\ {\mathrm{dF}}_a=K_{\mathrm{ac}}\·h\·\mathrm{dz}+K_{\mathrm{ac}}\·\mathrm{ds}\end{array}\right.$

Wherein, dF _tfor tangential force infinitesimal, dF _rfor radial force infinitesimal, dF _afor axial force infinitesimal, ds is cutting edge length infinitesimal, and dz is axial cutting-in infinitesimal, and h is thickness of cutting, K _tcfor tangential force coefficient, K _rcfor radial force coefficient, K _acfor axial force coefficient, K _tefor tangential cutting edge force coefficient, K _refor cutting edge force coefficient radially, K _aefor axial cutting edge force coefficient.The cutting force effective value of simulation calculation all directions, and by repeatedly different cutting parameter emulation, simulate the cutting coefficient of all directions.

The invention has the beneficial effects as follows for given lathe-cutter-workpiece system, just can calculate axial critical cutting-in and the corresponding speed of mainshaft by near flutter frequency (system frequency), cutter tooth number, Tool in Cutting coefficient, cutting system frequency response function, and then can construct flutter stability leaf lobe figure, complete the modeling of flutter instability territory.

Accompanying drawing explanation

Fig. 1 is the schematic flow sheet that builds stability cutting parameter selection leaf lobe figure.

Fig. 2 is main axle cutter hammering model analysis process flow diagram.

Fig. 3 is cutting system two degrees of freedom reduced graph.

Fig. 4 is machine tool system mode schematic diagram.

In figure: 1 machine tool system; 2 signal transducers; 3 exciting force hammers; 4 data acquisition cards; 5PC.

Fig. 5 cutting parameter rotating speed 1000r/min, cutting-in 0.2mm, speed of feed 200mm/min are at Y-direction cutting forces simulation curve.

Fig. 6 cutting parameter rotating speed 1000r/min, cutting-in 0.2mm, speed of feed 200mm/min are at Y-direction cutting force measured curve.

Fig. 7 is the stability lobes diagram of certain material of having built.

Embodiment

Describe embodiments of the invention in detail below in conjunction with technical scheme and accompanying drawing.

As depicted in figs. 1 and 2, wherein, material characteristic parameter comprises the material of workpiece and cutter, calculates the total cutting force of its working angles, and utilizes regression fit to go out cutting coefficient.The characteristic parameter drawing in conjunction with mode experiment, draws the stability lobes diagram, is used for selecting cutting parameter, comprises revolution, cutting-in etc.

Utilize vibrator (power hammer or vibrator) to encourage machine tool chief axis tooling system, pumping signal and the response signal collecting are collected to signal collecting device after treatment, utilize FFT conversion and mode matching, by the characterisitic parameter of Computerized analysis system, comprise multistage natural frequency, corresponding damping ratio, dynamic stiffness etc.

Concrete steps are:

The first step: carry out mode test experiments for lathe-cutter, analyze data, draw corresponding each rank natural frequency, dynamic stiffness, damping ratio etc.

Second step: understand cutter for same material and workpiece material, inquiry data is known the characteristic parameter of cutter material and rapidoprint, as Young modulus, Poisson ratio etc.

The 3rd step: simulation calculation process, and calculate corresponding cutting force, go out cutting coefficient by cutting force Modeling Theory the Fitting Calculation.

The 4th step: in conjunction with the cutting coefficient of the inherent characteristic in the first step and the 3rd step, the stability lobes diagram is drawn in programming, is used for selecting optimum cutting parameter, improves crudy and efficiency.

The rapidoprint of embodiment is the material of common impeller.First carry out mode testing experiment in machine tool system, instrument is exciting force hammer, data acquisition card.

As shown in Figure 4, obtain the characteristic parameter of cutter material and part material, by Computer Simulation working angles, and calculate the cutting force effective value of its all directions.For contrast simulation degree of accuracy, adopt simulation result and actual result to compare.

As shown in Figure 5 and Figure 6, be 65.88N by simulation curves Y-direction cutting force effective value, measured data effective value is 66.2N, error is in allowed band.And carry out emulation at all directions, different cutting parameter, result, in conjunction with cutting force Modeling Theory, is returned to the cutting coefficient that simulates this material.The cutting coefficient of this material is as following table 1:

K tc	K rc	K ac	K re	K te	K ae
						4074	1918	4787	95.5	155	268

In conjunction with gained natural frequency and cutting coefficient, then draw the stability lobes diagram by computer programming, be used for selecting optimum cutting parameter, improve crudy and efficiency.

As shown in Figure 7, from leaf lobe figure, for the cut of this kind of material, select the machined parameters of the cutting-in about revolution, the 0.6mm about 800r/min to cut, both can improve working (machining) efficiency and energy utilization, can improve again crudy and precision.

Claims (3)

1. the flutter instability territory modeling method of a surfacing process, to given lathe-cutter-workpiece system, by flutter frequency, cutter tooth number, Tool in Cutting coefficient, cutting system frequency response function, calculate axial critical cutting-in and the corresponding speed of mainshaft, and then construct flutter stability leaf lobe figure, complete the modeling of flutter instability territory; It is characterized in that

Obtaining threshold shaft by ZOA analytical method to cutting-in is:

$a_{\mathrm{plim}}=-\frac{2\mathrm{\π}{\mathrm{\Λ}}_R(1+{({\mathrm{\Λ}}_I/{\mathrm{\Λ}}_R)}^2)}{{\mathrm{NK}}_{\mathrm{tc}}}$

The rotating speed expression formula of main shaft is:

$n=\frac{60{\mathrm{\ω}}_c}{N(\left(2k1\right)\mathrm{\π}-2\arctan ({\mathrm{\Λ}}_I/{\mathrm{\Λ}}_R))}$

Wherein, k is the leaf lobe number in leaf lobe figure, Λ _rand Λ _ibe respectively real part and the imaginary part of ssystem transfer function characteristic root, N is number of teeth, K _tccutting coefficient, ω _cfor characteristic frequency.

2. flutter instability according to claim 1 territory modeling method, is characterized in that, described cutting coefficient K _tccomputation process as follows:

By emulation machining working angles, the cutting force in calculating processing process, analyzes data, finally obtains cutting coefficient; In cutting finite element simulation, select chip separation criterion: physical criteria and geometric criterion; Failure stress standard is expressed as:

${\left(\frac{\left|{\mathrm{\σ}}_n\right|}{{\mathrm{\τ}}_n}\right)}^2+{\left(\frac{\left|{\mathrm{\σ}}_s\right|}{{\mathrm{\τ}}_s}\right)}^2\≥1$

Wherein, σ _n, σ _srepresent respectively smear metal-workpiece interphase normal stress and shear stress; τ _nrepresent the critical value of normal stress, τ _sfor the critical value of shear stress; In the middle of milling force modeling:

$\left\{\begin{array}{c}{\mathrm{dF}}_t=K_{\mathrm{tc}}\·h\·\mathrm{dz}+K_{\mathrm{te}}\·\mathrm{ds}\\ {\mathrm{dF}}_r=K_{\mathrm{rc}}\·h\·\mathrm{dz}+K_{\mathrm{re}}\·\mathrm{ds}\\ {\mathrm{dF}}_a=K_{\mathrm{ac}}\·h\·\mathrm{dz}+K_{\mathrm{ac}}\·\mathrm{ds}\end{array}\right.$

Wherein, dF _tfor tangential force infinitesimal, dF _rfor radial force infinitesimal, dF _afor axial force infinitesimal, ds is cutting edge length infinitesimal, and dz is axial cutting-in infinitesimal, and h is thickness of cutting, K _tcfor tangential force coefficient, K _rcfor radial force coefficient, K _acfor axial force coefficient, K _tefor tangential cutting edge force coefficient, K _refor cutting edge force coefficient radially, K _aefor axial cutting edge force coefficient.

3. flutter instability according to claim 1 and 2 territory modeling method, is characterized in that, described characteristic frequency ω _cacquisition process is: by modal test, adopts and repeatedly encourages then averaged, and from the different multi-modes of multi-direction tester, finally by FFT and mode matching, analyze corresponding various characteristic parameter, comprise multistage characteristic frequency, analyze data result and obtaining.

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