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机械类外文翻译【FY070】单点金刚石车削加工中刀具干涉对表面成形的影响的预测【PDF+WORD】【中文5900字】
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机械类外文翻译【FY070】单点金刚石车削加工中刀具干涉对表面成形的影响的预测【PDF+WORD】【中文5900字】,机械类,外文,翻译,fy070,单点,金刚石,车削,加工,刀具,干涉,对于,表面,成形,影响,预测,pdf,word,中文
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外 文 文 献 翻 译 学校：河南理工大学 院系：机械学院 班级：机制本 08-2 班 学号： 320804010223 姓名： 谢道通 ntsInt J Adv Manuf Technol (2002) 19:245252 2002 Springer-Verlag London LimitedPrediction of the Effect of Tool Interference on SurfaceGeneration in Single-Point Diamond TurningC. F. Cheung and W. B. LeeDepartment of Manufacturing Engineering, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong KongTool interference has its origin from the small amplitude andlow frequency vibration existing between the tool and theworkpiece in single-point diamond turning (SPDT). It inevitablyaffects the surface quality of a diamond turned surface. In thispaper, a surface topography simulation model is proposed forthe prediction of the effect of tool interference on surfacegeneration in SPDT. It makes use of the surface roughnessprofiles predicted at a finite number of equally spaced radialsections of a workpiece to construct the surface topography ofa diamond turned surface. The approach overcomes thelimitation of the existing theories that can check only for theexistence of tool interference. The model was evaluated throughpractical cutting experiments. Experimental results were foundto agree well with the predicted results.Keywords: Simulation; Single-point diamond turning; Surfacegeneration; Tool interference; Vibration1. IntroductionSingle-point diamond turning (SPDT) is an ultra-precisionmachining technique which is used to produce optical surfaces(e.g. spherical and aspherical) of submicrometres form accuracyand surface finish in the nanometre range. It is frequentlyemployed for the machining of ductile materials such asaluminium and copper. The mechanism of surface generationdiffers from that of conventional machining 1. The diamondcutting process is usually carried out at very high cuttingspeeds so that the problems associated with the built-up-edge(BUE) do not arise. On the other hand, as most ultra-precisionmachines possess extremely high loop stiffness, variation ofcutting force, and hence surface roughness, due to regenerativechatter is unlikely.However, SPDT presents special phenomena such as theinterference of the tool 2 and anisotropy of the surfaceCorrespondence and offprint requests to: Dr C. F. Cheung, Departmentof Manufacturing Engineering, The Hong Kong Polytechnic University,Hung Hom, Kowloon, Hong Kong. E-mail: mfbennyL50560.hkroughness 3. These phenomena are negligible in conventionalmachining, but are significant in diamond turning. Most of theexisting surface roughness models, such as the well-knownideal roughness equation and its derivatives 1, fail to incorpor-ate the effect of these phenomena, and thus result in poorprediction of surface roughness. Although some attempts 4have been made at the development of machining models tosimulate the 3D surface topography of a workpiece, most ofthem were based on the determination of the surface topogra-phies, derived from 2D fast Fourier transform (FFT) analysisof the data obtained from interferometry or scanning electronmicroscopy (SEM). Most of these models did not take intoaccount the basic cutting mechanics. Only a few theoreticalmodels 5,6 have been found on the simulation of surfacetopography based on the kinematics and the dynamic character-istics of the cutting process. However, most of these modelswere developed for use in other machining processes such asmilling 7. In this paper, a surface topography simulationmodel is proposed to predict the effect of tool interference onsurface generation in SPDT. The simulation results were com-pared with the measured results obtained from cutting experi-ments.2. Prediction of Tool Interference and itsEffect on Surface Generation2.1 Tool InterferenceSurface generation for SPDT is complex and is affected by anumber of factors such as feed rate, tool geometry, and spindlespeed. Under ideal cutting conditions, the tool is ideally pos-itioned relative to the workpiece. The process of generation ofthe surface roughness profile is similar to the repetition of thetool tip profile at intervals of feed per workpiece revolution,as shown in Fig. 1. However, the tool positions usually varyrelative to the workpiece owing to a number of factors suchas spindle error motions 8 and the vibration of the ultra-precision machine tool 9. In such a case, the surface is cutto varying depths at successive revolutions, as shown in Fig. 2.For large feed rates and low spindle speeds, the cutting toolcuts sequentially the active cutting edge formed by the preced-nts246 C. F. Cheung and W. B. LeeFig. 1. Graphical illustration of ideal tool movement along the feeddirection under the cutting conditions: feed rate of 15 mm min1;spindle speed of 1000 r.p.m.; depth of cut of 2 H9262m; tool nose radiusof 1.55 mm; no relative vibration exists between the tool and theworkpiece (i.e. ITI H11009).Fig. 2. Graphical illustration of non-interference of tool under thecutting conditions: feed rate of 15 mm min1; spindle speed of1000 r.p.m.; depth of cut of 2 H9262m; tool nose radius of 1.554 mm;amplitude and frequency of toolwork vibration of 0.015 H9262m and45 Hz, respectively. The index of tool interference is 2.72.ing cutting action at each tool feed (see Fig. 2). The formationof the surface roughness profile can be considered as thetrimming of the lines above the intersecting points of theminimum edge profile 10. Therefore, a clear tool trace isfound in the surface roughness profile. This is referred to asthe “non-interference of tool” in the present study.In SPDT, a high spindle speed together with a fine feedrate is usually adopted to improve the surface finish of theworkpiece 10. Under these cutting conditions, a phenomenonknown as tool interference occurs in which the cutting per-formed at the preceding feed movement has already removedthe chip which should be cut away by some succeedingtool movement.Figure 3 illustrates the tool loci in the feed direction ascutting is performed under the tool interference condition. Astool interference occurs, the cutting edges of the precedingcuts remove the material that should be cut by the succeedingcuts. This results in non-perfect surface generation. Taking Cut2 and Cut 3 in Fig. 3 as an example, the cutting edges in thetwo cuts have already removed the material that should be cutFig. 3. Graphical illustration of interference of tool under the cuttingconditions: feed rate of 15 mm min1; spindle speed of 2000 r.p.m.;depth of cut of 2 H9262m; tool nose radius of 1.554 mm; amplitude andfrequency of toolwork vibration 0.2 H9262m and 45 Hz, respectively. Theindex of tool interference is 0.20.by Cut 4. Therefore, only two tool marks were formed in thethree cuts. Takasu et al. 2 have established a criterion for theoccurrence of tool interference, i.e.8RmaxH92782AH11349 1 (1)where Rmaxis the theoretical roughness of a diamond turnedsurface that is given byRmax=s28R=f28RV2(2)From Eq. (2), Eq. (1) can be rewritten in terms of the machiningparameters as:ITI=f2H92782ARV2H11349 1 (3)where ITIrefers, in the present study, to the index of tool inter-ference.According to Eq. (3), the value of the index of tool inter-ference should be positive, and tool interference is likely tooccur when the index of tool interference is less than or equalto 1. It is also interesting to note that diamond turning at alow feed rate, a high spindle speed, and large tool radius andhigh amplitude of the relative tool-workpiece vibration, is moresusceptible to the effect of tool interference. Although theabove criterion is useful for verifying the presence of toolinterference, it does not allow the determination of the exactlocations at which this phenomenon actually takes place. There-fore, the effect of tool interference on surface roughness cannotbe predicted with this criterion alone. To allow for the effectof tool interference to be predicted quantitatively for the surfacetopography of diamond turned surfaces, a surface topographysimulation model is proposed in the present study.2.2 The Surface Topography Simulation ModelThe surface topography simulation model uses a new approachfor the deterministic modelling of the 3D surface topographyof a diamond turned surface. It is based on the cutting mech-anics and the fundamental concepts of tool motion and thentsPrediction of the Effect of Tool Interference 247formation of tool marks. The model makes use of the surfaceroughness profiles, predicted at a finite number of equallyspaced radial sections of a workpiece, to construct the surfacetopography of a diamond turned surface (see Fig. 4). Thesurface roughness profile at each radial section is predictedbased on a 2D surface roughness model 11. This is differentfrom the conventional surface topography approaches that arebased on 2D FFT analysis 12, time-series techniques 13,and exponential autocorrelation functions 14.In the present study, the cutting process is assumed to beorthogonal and the workpiece materials are homogeneous andisotropic. In a face turning operation, the two possible errormotions of the spindle which affect surface generation areaxial and face error motions 8. Face error motion is relatedto the distance from the centre-line of the workpiece. It willbe a second order effect if the diameter of the workpiece issmall (i.e. diameter H1102150 mm). Therefore, only the axial errormotion of the spindle is taken into account, and the effect offace error is assumed to be negligible for ease of analysis.Only the dominant mode of the relative vibration between thetool and the workpiece in the infeed cutting direction isconsidered, since its effect is significant in surface generation15. The assumptions have been justified in our previous work9,16 in studying the effect of relative toolworkpiecevibration on surface generation in SPDT.Since only the dominant mode of the relative vibrationbetween the tool and the workpiece in the main cutting direc-tion (Zc(t) is considered in the present study, Zc(t) is a steadysimple harmonic motion in the time domain that can beexpressed as:Zc(t) = Azsin(2H9266fzt H9278) (4)where Azand fzare the amplitude and the frequency of thedominant mode of vibration. The phase shift H9278 is related tothe ratio between the frequency of the relative toolworkpiecevibration in the feed direction to spindle rotational speed as:H9278 = 2H9266H9280 (5)where H9280 is a decimal fraction in the range 0.5 H11349H9280H113490.5which is given by:Fig. 4. Tool locus and linear mapping of surface data on a cross-lattice.60fz/V = H9254 + H9280 (6)where H9254 is 0 or a positive integer.The number of sections, Np, can be expressed as:Np=2H9266/H9004H9258 (7)where H9004H9258 defines the angular resolution being adopted.Since the spindle rotational speed and the feed rate areassumed to be constant, i.e. H9275 = H9004H9258/H9004t and N = R0/s are con-stants, the total number of tool locus points, Nt, can begiven by:Nt=2H9266NH9275H9004t(8)The discrete form of the relative vibration between the tooland the workpiece can be derived based on Eqs (4) and (8) as:Zc(j) = Azsin(Cpj H9278) (9)for j = 0, 1, 2, . . ., Ntand Cp= 2H9266fzH9004H9258/H9275.As shown in Fig. 4, the cutting tool moves in the X, Y-plane with a spiral locus towards the centre of the workpiece.The spiral locus can be expressed in polar coordinates as:Rj= R0 jH9004r (10)H9258j= jH9004H9258 (11)for j = 0, 1, 2, . . ., Nt.From Eqs (10) and (11), its corresponding coordinates onthe X, Y-plane are given by:Xc(j) = Rjsin(H9258j) (12)Yc(j) = Rjcos(H9258j) (13)for j = 0, 1, 2, . . ., Nt.The locus of the tool for the kth radial section can be treatedas a transformation of the tool points from the X, Y, Z-coordinate system to the Rk, Zkpolar plane, whereas the Rk-axis is the radial axis for the kth radial section withk = 0, 1, 2, . . .,Np.At the kth radial section, the coordinates of the tool locuson the Rk, Zkpolar plane can be derived based on Eqs (9)(11) as follows:H9258t(i,k) = kH9004H9258 +2H9266(i 1) (14)rt(i,k) = R0 k +(i 1)NpH9004R (15)Zt(i,k) = AsinCpk + (i 1)Np H9278 (16)with i = 1, 2, . . ., N.The cutting edges of the ith tool profile and the (i + 1)thprofiles, counted from the first tool profile at the kth radialsection, can be derived as:Zk,i(rk,i) = Zt(i,k)+rk,i (i 1)s22R(17)Zk,i+1(rk,i+1) = Zt(i +1,k)+rk,i+1 is22R(18)where i = 1, 2, . . ., N 1 and (rk,i,Zk,i) are the coordinates of theith tool profile at the kth radial section of the workpiece.nts248 C. F. Cheung and W. B. LeeFig. 5. Graphical illustration of the 3D surface generation.Fig. 6. An architecture of the simulation software SYNSURF3D.At the location of the intersection, Tk,i,i+1,(rk,i,i+1,Hk,i,i+1), ofthe ith tool profile and the (i + 1)th profile at the kth radialsection, Zk,i= Zk,i+1and rk,i= rk,i+1, i.e.rk,i,i+1=RsZt(i +1,k) Zt(i,k) +H20873i 12H20874s (19)for i = 1, 2, . . ., N 1.From Eqs (18) and (19), the height Hk,i,i+1of the intersectionbetween the ith and the (i + 1)th tool profiles at the kth radialsection is determined as:Table 1. Cutting conditions for the experiments.Condition number I IISpindle speed 1000 r.p.m. 2000 r.p.m.Feed rate 15 mm min115 mm min1Depth of cut 2 H9262m10H9262mRake angle of the tool 0 0Tool nose radius 1.554 mm 1.554 mmIndex of tool 2.72 0.50interference, ITITool interference Non-interference (i.e. Interference (i.e.status ITIH11022 1) ITIH11021 1)Materials Copper alloy Aluminium alloyHk,i,i+1= Zt(i +1,k)+2RZt(i +1,k) Zt(i,k) s228Rs2(20)with i = 1, 2, . . ., N 1.Since the minimum edge profile below the intersecting pointsof each tool profile constitutes the surface roughness. Thesurface roughness profile at the kth radial section of theworkpiece can be constructed by trimming the lines above thepoints of intersection.Applying Eqs (14) to (20) for all the radial sections, i.e.k = 0, 1, 2, . . ., Np, it is possible to determine the surface top-ography data on all Rk, Zkpolar planes represented in polarcoordinates rk,Zk,kH9004H9258 for k = 0, 1, 2,. . ., Np. As shown inntsPrediction of the Effect of Tool Interference 249Fig. 7. Three-dimensional plot of the tool loci under (a) Condition Iand (b) Condition II.Fig. 4, these data are mapped on the surface elements of across lattice as defined by:XI =Lx+2rksin(kH9004)2Lxmx (21)YI =Ly+ 2rkcos(kH9004)2Lymy (22)ZI = Zk(23)where k = 0, 1, 2, . . ., Np; mxand myare the number of surfaceelements in the X and Y directions, respectively; and LxandLyare the length and the width of the simulated region. Thesurface elements are used to build the mesh and the parametricsurfaces that best fit the surface topography data. The contourlevels of the parametric surfaces are proportional to the sur-face height.In the surface topography simulation model, the exactlocations for the occurrence of tool interference are determinedby continual checking for the existence of intersecting pointsat each tool feed movement for each predicted sectional surfaceroughness profile based on Eqs (19) and (20). Should a toolFig. 8. Graphical representation of surface waviness generated underunder (a) Condition I and (b) Condition II.profile not intersect with its previous and succeeding toolprofiles in a sectional surface roughness profile, it is skippedand the next closest intersection of tool profiles is used instead,in the estimation of the sectional surface roughness profile.The surface roughness of face turned surfaces is characterisedby the maximum peak-to-valley height Rtand the arithmeticroughness Ra, which are widely used parameters in assessingthe surface quality in diamond turning. The predicted maximumpeak-to-valley height Rtis the difference between the maximumand the minimum of surface roughness height predicted withinthe simulation region. The arithmetic roughness Rais givenas follows:Ra=1NsH20888Nsis=1H20841Zs,is ZsH20841 (24)Zs=H208731NsH20888Nsis=1Zs,jsH20874(25)where Nsis the number of predicted surface roughness heightsover the simulated region. Zs,iis the isth predicted surfacents250 C. F. Cheung and W. B. Leeroughness height on the cross lattice. Figure 5 shows a graphi-cal illustration of the process of generating 3D surface topo-graphy.2.3 Simulation SoftwareA simulation software named SYNSURF3D was purposelybuilt for the implementation of the surface topography simul-ation model. The software was developed using the MATLABprogramming language. The construction of the SYNSURF3Dis shown in Fig. 6. The inputs of the software are the cuttingprocess parameters, the dimensions of the workpiece and thedynamic conditions of the cutting system. The cutting processparameters include feed rate, spindle speed, depth of cut, andtool nose radius. The amplitude and frequency of the dominantmode of the relative vibration between the tool and the work-piece are used to represent the dynamic conditions of thecutting system. These parameters have to be determined exper-imentally using a capacitive gauging method which will bediscussed later. Based on the input data, SYNSURF3D iscapable of simulating the 3D tool locus, the virtual surfacewaviness, the sectional surface roughness profile as well asthe 3D surface topography of a diamond turned surface. It canalso be used to predict surface roughness parameters such asthe arithmetic roughness Raand the peak-to-valley height Rt.Experimental EvaluationTwo face cutting experiments were conducted on a two-axisCNC ultra-precision machine (Nanoform 300 from Taylor Hob-son Pneumo Co.). As shown in Table 1, the first cuttingexperiment was performed under non-interference conditionsof the tool (Condition I), whereas the second one was carriedout under tool interference conditions (Condition II). The work-piece materials were aluminium alloy (6061) and a copperalloy with a chemical composition by percentage weight ofCu: balance; Al: 0.24; Fe: 0.20; Zn: 0.4; and Pb: 0.12. Thediameter of the workpiece was 12.7 mm.The dominant mode of the relative vibration between thetool and the workpiece was measured prior to the cuttingexperime
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