# The emulation of outline of surface of diamond turning workpiece and analysis

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Css" Type=text/css Rel=stylesheet> is in in exceeding accurate turning to machine, inevitably existence is oscillatory, make thereby the method that cutting tool deviate books. The opposite vibration between rotate speed of speed of the geometrical figure that affects the main factor that already machined exterior form appearance to include cutting blade, feed, main shaft and cutting tool and workpiece. The workpiece surface Zhen Wen that causes when the existence between cutting tool and workpiece is relatively oscillatory. For convenient for the purpose of, the acme that chooses blade of cutting tool cutting is cutting blade reference point. The relatively oscillatory frequency Ftw between cutting tool and workpiece and main shaft rotate of frequency Fsp than be Ftw=If+Dffsp(1) type in, if is blame negative integer, df is fraction and - 0.

5<Df ≤ 0.

5. Oscillatory the phasic deflection Ø that produces Zhen Wen between revolution of work look adjacent; The Sf=Sf of π of function λ S2 of the feed Sf(mm/rev) that the wavelengh λ S that can define the Zhen Wen that forms to be relative to vibration between cutting tool of Ø=2 π Df(2) and workpiece on direction of feed of cutting tool of workpiece surface edge can express to for Ø and cutting tool every turn | Ø | | Df | (3) is facilitating analysis, can set the opposite vibration between cutting tool and workpiece to be one simple harmonic motion in time domain, in expressing to be type of Z(t)=Atw[1-cos(2 π Ftwt+Ø)](4) , atw is the relatively oscillatory amplitude between cutting tool and workpiece (µm) , t is handling time (S) , Ø is starting phase, to be not broken run-of-mill, set Ø=0. Inside the plane of R- θ polar coordinates of workpiece surface, in having type of Fspt(5) of π of {r=Rw-Sffspt θ =2, rw is workpiece radius, right now θ ∈ [0, 2N π ) , among them, n gives priority to axial revolution and N=Rw/Sf. Its are {x=rcos θ Y=rsin(- θ in the corresponding coordinate on X-Y plane) (6) type (4) , type (5) and type (6) described the cutting tool in cutting process the contrail of three-dimensional motion. The length that sets emulation area and width are Lx respectively, ly, resolution is Mx, My respectively. The center of emulation area is workpiece the centre of a circle, criterion (I, the coordinate that J) nods is Xi, j=imx-Lx2Yi, j=imy-Ly2(7) correspondence is R= √ Xi to polar coordinates plane, j2+Yi, j2 θ =arctanYi, JXi, j(8) computation is in θ radial is sectional on the radius cost that reference point of all cutting blade experiences: Rk=Rw-Sffsp(2k π + θ ) (K=0, 1, 2, ... , n) ω (θ & ∈ is taken in 9) type [0, 2 π ] . Appearance of workpiece surface form is made by the side of the lowermost outline after by cutting blade outline happening is cut, reason needs computation to be in some is sectional on outline of all cutting blade produces cut result, must go to work thereby this sectional outline. Computational form is as follows: Hk=Atw{1-cos[If θ + Df(2k π + θ ) ] }+R[1- √ ] (K=0, 1, 2, ... , n)r-rkR(10) takes Zi of the least value, j=min(hk)(11) such, according to type (7) ～ (11) can be calculated the contour line height that gives point of every reseau on X-Y plane, make the appearance of three-dimensional outline form inside emulation area thereby. When Nextpage undertakes the FFT of exterior outline is analysed, its frequency and cycle and common time alignment signal are different, count the sampling in 1mm less than foothold to count a definition to be sampling frequency normally, periodic correspondence is wavelengh λ N(mm) , a number that the frequency correspondence of outline data is the wave that appears inside unit time length (Cycles/mm) namely the frequency Vn of weaveform of workpiece surface outline. λ N and Vn existence concern below: When λ N=1=Lvn N(12) expresses by Z(x) when surface roughness outline (among them X delegate position) , the amplitude chart of surface roughness curve can express to be | Z(vn) | The N in the type on Nx]dx0L(13) of π of = ∫ Ly(x)exp[-j2 is integer, the measurement that L is surface roughness curve length. Use disperse form to express to be: | Z(vn) | Jkvn]L(14) of π of =1NpNp-1 Σ K=0z(k) Exp[-2 expresses 1 emulation condition to emulate limits (speed of Mm) main shaft (Rpm) feed speed (Mm/min) cutting deepness (the horn before µm) cutting tool (° ) point radius (Mm) oscillatory frequency (Hz) oscillatory amplitude (µm)1Ø4100025201.

5002Ø4200050201.

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The Np in 02 type is check the number of emulated workpiece outline position. In the meantime, fold to prevent to mix, should abide by Shannon sampling theorem, make signal of sampling frequency prep above highest the 2 times above of frequency. Use above algorithm to part direction of helix of radial of edge workpiece surface, Zhou Xianghe undertakes to sectional outline FFT is analysed, whole emulate the flow that reachs analytic program. The theory of sectional outline analyses 3 workpiece 3.

The spectrum of good appearance outline that feed of analysis of outline of radial of 1 workpiece surface studies to by computer basis the geometrical appearance of cutting tool and feed speed are generated above all to the influence of workpiece surface spectrum. Use in the watch 1 in emulation set number 1 undertake emulation. The ideal and sectional outline that the amplitude between cutting tool and workpiece is zero hour (show a 0125mm limits) only, have these data FFT analyses gotten spectrum. Visible, feed appears for Nvf with frequency (among them N is one integer, feed frequency Vf=1/Sf) , can observe apparent feed heft. When feed speed is reduced, feed divides quantitative change to be taller frequency, the height of every peak value is reduced. In these feed heft, frequency is Vf head rank heft takes main place. The opposite vibration to workpiece surface spectrum influence between cutting tool and workpiece should exist between cutting tool and workpiece when opposite vibration, workpiece is sectional outline is the academic surface outline that forms by feed opposite vibration is in between the cutting tool on overlay and workpiece the radial of workpiece surface is moire and form, frequency of generated workpiece surface space is go up doubly by the M of feed heft frequency opposite vibration is in between cutting tool and workpiece the N of the frequency heft of workpiece radial times and form, the Vs in following Fsurface=mvf+nvs(15) type is its expression radial and oscillatory frequency, vs= | Df | M of Vf , n=0, ± 1, ± 2... . Use in the watch 1 in the 2nd group cutting condition undertakes emulation, by type (1) has Ftw=42=1+0.

26fsp2000/60(16) right now, if=1, Df=0.

26, and Vf=2000/50=40, criterion Vs= | Df | Vf=0.

26 × 40=10.

Outline of 4 workpiece surface reachs spectrum, among them, f1=vs=10.

4, f2=vf-vs=29.

6, f3=vf=40, f4=vf+ Vs=50.

4, f5=2vf-vs=69.

6, f6=2vf=80, f7=2vf+vs=90.

4, f8=3vf-vs=109.

6, f9=3vf=120... 3.

The work week that week of 2 workpiece surface analyses ideal cutting condition to fall to outline is to outline below the ideal cutting condition that does not have vibration, workpiece is circumferential and sectional the outline appearance that go up and this radius of circumferential place is concerned, go to the lavatory for the analysis, express outline amplitude with corresponding and circumferential angle, the frequency instead that does FFT analysis every turn the undee number that attend shows (Cycles/rev) , right now the changeover of FSL(cycles/mm) of dimensional sampling frequency on length is workpiece every turn the sampling frequency FSL(cycles/rev) that go up expresses, namely: The Rsm in FSr=fSLRsm(17) type -- , emulation radius uses a list 1 in the cutting condition of 3 is in emulation set number radius is 0.

When 15mm place undertakes emulation, gotten result, among them outline appearance, in this radius circumferential and sectional go up the kill that makes FFT analysis. Can see, the week of workpiece has frequency FSr=1cycles/rev to outline. Because edge workpiece is circumferential and sectional,this is when surveying a week, gotten sectional outline just right is cycle of Sf(mm/r) of a feed rough sketch of makes ideal surface roughness. Vibration uses a list to the influence of sectional outline to work week 1 in the 4th group cutting condition is in for 0115mm in radius when undertaking emulation, gotten result. By type (1) gets Ftw=48=5-0.

2fsp600/60(18) right now, if=5, Df=0.

2. Can see two apparent frequency heft, among them 1cycles/rev is heft of speed of cutting tool feed, 5cycles/rev rotates through main shaft for vibration the value of integral part If that frequency changes. 3.

When the outline with sectional contrail of cutting of helix of cutting tool of surface of 3 edges workpiece analyses contrail of cutting of helix of edge cutting tool to analyse workpiece surface outline, its outline appearance and spectrum and cutting tool are concerned in the initial drop inside a feed Sf. When the contrail of helix of positional edge cutting tool in cutting blade reference point is analysed, right now outline appearance basically is formed in the vibration inside time domain by cutting tool, clear oscillatory frequency spectral line can see in spectrum. Use a list 1 in the emulation result of condition of the 4th group of cutting, the initial drop that emulates data right now is in cutting blade reference point, have 48Hz of apparent oscillatory frequency spectral line among them. The Dong2Sik Kim of test and verify of 4 emulation results measurement that uses its to be developed by oneself the system undertook detecting to the surface of Al test specimen of treatment. Its basically machine parameter to be feed speed 01020mm/rev, 25rps of main shaft rotate speed, point radius 210mm, relative to oscillatory frequency 19215Hz, the article undertook emulation to its. Appearance of emulated three-dimensional surface form; The FFT of circumferential and sectional outline analyses workpiece surface, have apparent frequency weight among them 1 with If=8; The FFT of radial and sectional outline is analysed, have apparent frequency weight 15, can get Df=15/(1/0 thereby.

02)=0.

3; Along contrail of feed of cutting tool helix sectional FFT analyses a result, can see apparent frequency heft 192.

5Hz. From these emulation graphs and analysis the result can see, emulation result detects actually with its the form appearance with analyse a result to have better is similar gender and diagnostic consistency. Machine tool of 5 conclusion union is kinematic built with cutting theory exceed end panel of accurate turning workpiece the emulation model of appearance of three-dimensional surface form, use this model to be able to forecast all sorts of sectional outline and appearance of three-dimensional surface form, have direct effect to effective treatment thereby. The specific value of oscillatory frequency and workpiece rotate speed is greater to influence of workpiece surface outline. Different sectional outline contains different oscillatory frequency information. The method that uses disperse teach to establish a leaf to alternate differs 3 kinds to workpiece surface the feature of sectional outline undertook theoretical analysis. The result makes clear, the spectrum of sectional outline basically suffers workpiece radial feed, oscillatory frequency and main shaft rotate the influence of the compare decimal part of frequency, workpiece is circumferential direction is sectional the spectrum of outline basically is by vibration frequency and main shaft rotate the integral part of the comparing of frequency is formed, analyse workpiece when direction of contrail of helix of edge cutting tool when sectional outline, its spectrum contains the complete information that has oscillatory frequency. Can you adopt two kinds of methods to undertake differentiating to the opposite vibration between cutting tool and workpiece thereby: ? Does Yuan of Bei of tadpole of the mow that break Mou cast is treated show ê to spit Yuan of Dang Bei to cast is treated show ā ? CNC Milling