梯形蓋塑料注塑模具設計【一模一腔】【側抽芯】【說明書+CAD+三維】,一模一腔,側抽芯,說明書+CAD+三維,梯形蓋塑料注塑模具設計【一模一腔】【側抽芯】【說明書+CAD+三維】,梯形,塑料,注塑,模具設計,說明書,CAD,三維 arXiv:1003.5062v1 physics.gen-ph 26 Mar 2010Automatic polishing process of plastic injection molds on a 5-axismilling centerJournal of Materials Processing TechnologyXavier Pessoles, Christophe Tournier*LURPA, ENS Cachan, 61 av du pdt Wilson, 94230 Cachan, Francechristophe.tournierlurpa.ens-cachan.fr, Tel : 33 147 402 996, Fax : 33 147 402 211AbstractThe plastic injection mold manufacturing process includes polishing operations whensurface roughness is critical or mirror effect is required to produce transparent parts. Thispolishing operation is mainly carried out manually by skilled workers of subcontractorcompanies. In this paper, we propose an automatic polishing technique on a 5-axis millingcenter in order to use the same means of production from machining to polishing andreduce the costs. We develop special algorithms to compute 5-axis cutter locations onfree-form cavities in order to imitate the skills of the workers. These are based on bothfilling curves and trochoidal curves. The polishing force is ensured by the compliance ofthe passive tool itself and set-up by calibration between displacement and force based ona force sensor. The compliance of the tool helps to avoid kinematical error effects on thepart during 5-axis tool movements. The effectiveness of the method in terms of the surfaceroughness quality and the simplicity of implementation is shown through experiments ona 5-axis machining center with a rotary and tilt table.KeywordsAutomatic Polishing, 5-axis milling center, mirror effect, surface roughness, Hilbertscurves, trochoidal curves1Geometric parametersCE(XE,YE,ZE)tool extremity point(u,v)coordinates in the parametric spaceTrochoidal curve parametersscurvilinear abscissaC(s)parametric equation of the guiding curveP(s)parametric equation of the trochoide curven(s)normal vector of the guiding curvepstep of the trochoidDtrdiameter of the usefull circle to construct the trochoidAamplitude of the trochoidStepstep between two loops of trochoideTechnological parametersDtool diameterDeffeffective diameter of the tool during polishingEamplitude of the envelope of the polishing stripedisplacement induced by the compression of the tooltilt angle of the tool axisu(i,j,k)tool axisftangent vector of the guide curveCcpoint onto the trochoidal curveMachining parametersNspindle speedVccutting speedVffeed speedfzfeed per cutting edgeapcutting depthatworking engagementTmachining time2Surface roughness parametersRaarithmetic average deviation of the surface (2D)Saarithmetical mean height of the surface (3D)Sqroot-mean-square deviation of the surfaceSskskewness of topography height distributionSkukurtosis of topography height distribution31IntroductionThe development of High Speed Machining (HSM) has dramatically modified the or-ganization of plastic injection molds and tooling manufacturers. HSM in particular hasmade it possible to reduce mold manufacturing cycle times by replacing spark machiningin many cases. In spite of these evolutions, HSM is not enable to remove the polishingoperations from the process. In this paper, we deal with the realization of surfaces withhigh quality of surface finishing and mirror effect behavior. This means that the partmust be perfectly smooth and reflective, without stripes. Such a quality is for examplenecessary on injection plastic mold cavities in order to obtain perfectly smooth or com-pletely transparent plastic parts. From an economic point of view, polishing is a long andtiresome process requiring much experience. As this process is expensive in terms of priceand downtime of the mold, automatic polishing has been developed. Our objective is touse the same means of production from machining to polishing, leading to cost reduction.The aim of the paper is thus to propose a method of automatic polishing on a 5-axismachine tool.Literature provides various automated polishing experiments. Usually, the polishing iscarried out by an anthropomorphic robot, 1. Anthropomorphic robots are used for twomain reasons. First, their number of axes enables them to have an easy access to any areaof complex form. Second, it is possible to attach a great variety of tools and particularlyspindles equipped with polishing force control mechanisms. Automatic polishing studieshave been also carried out on 3 or 5-axis NC milling machine with specially designed toolto manage polishing force 2 as well as on parallel robots 3.Indeed, the polishing force is a key parameter of the process. The abrasion rate in-creases when the polishing pressure increases 4. But as mentioned in 3 the contactpressure depends on the polishing force and also on the geometrical variations of the part.An adequate polishing force facilitates the removal of cusps and stripes left on the partduring milling or previous polishing operations. Nevertheless, the contact stress has tobe as constant as possible to avoid over-polishing and respect form deviation tolerances.Many authors have thus chosen to develop abrasive systems allowing a dynamic manage-ment of the polishing force. In 5, Nagata et al. use an impedance model following forcecontrol to adjust the contact force between the part and the sanding tool. In 6, Ryuh etal. have developed a passive tool, using a pneumatic cylinder to provide compliance and4constant contact pressure between the surface and the part. A passive mechanism is alsoused in 7. The contact force is given by the compressive force of a spring coil.In order to carry out an automatic polishing, it is important to use adapted tooltrajectories. According to 8, polishing paths should be multidirectional rather than mo-notonic, in order to cover uniformly the mold surface and to produce fewer undulationerrors. Moreover, the multidirectional polishing path is close to what is made manually.If we observe manual polishers, we can notice that they go back on surface areas accor-ding to various patterns such as trochoidal polishing paths (or cycloidal weaving paths8 (fig 1). Therefore, it could be profitable to follow such a process in order to obtainthe required part quality. For instance, some papers use fractal trajectories like the PeanoCurve fractal 9, which is an example of a space-filling curve, rather than sweepings alongparallel planes 10.ElementarypatternElementarypatternMultidirectionalpolishingMultidirectionalpolishingFigure 1 Manual polishing patternsThis brief review of the literature shows that there is no major difficulty in using a 5-axis machine for automatic polishing with a passive tool. This paper aims at showing thefeasibility of automatic polishing using 5-axis machine tools and proposing some polishingstrategies. In the first section, we expose how automatic polishing is possible using a 5-axisHSM center. In particular, we present the characteristics of the passive and flexible toolsused. A specific attention is paid to the correlation between the imposed displacement ofthe tool and the resulting polishing force. Once the feasibility of 5-axis automatic poli-shing is proved, the various dedicated polishing strategies we have developed are detailedin section 2. These strategies are for the most part issued from previous experiences asfor fractal tool trajectories coming from robotized polishing or cycloidal weaving paths5representative of manual polishing. In section 3, the efficiency of our approach is testedusing various test part surfaces. All the parts are milled then polished on the same pro-duction means : a 5-axis Mikron UCP710 milling centre. In the literature, the effectivenessof polishing is evaluated using the arithmetic roughness Ra 2. However, as it is a 2Dparameter, this criterion is not really suited to reflect correctly the 3D polished surfacequality. We thus suggest qualifying the finish quality of the polished surface through 3Dparameters. This point is discussed in the last section as well as the comparison of thesurface roughness obtained using automatic polishing with that obtained using manualpolishing, a point hardly addressed in the literature. 3D surface roughness measurementsare performed using non-contact measuring systems.2Experimental Procedure2.1Characteristics of the toolsAs said previously, our purpose is to develop a very simple and profitable system.Therefore, the tools used are the same than those used in manual polishing. The poli-shing plan is divided into two steps, pre-polishing and finishing polishing. Pre-polishing isperformed with abrasive discs mounted on a suitable support. The abrasive particle sizeis determined by the Federation of European Producers of Abrasives standard (FEPA).This support is a deformable part made in an elastomer material fixed on a steel shaftthat allows mounting in the spindle. We thus deal with a passive tool. Hence, we donot have a force feedback control but a position one. We have studied the relationshipbetween the deflection of the disc support and the polishing force applied to the part.To establish this relationship, we use a Quartz force sensor Kistler 9011A mounted on aspecially designed part-holder. The sensor is connected to a charger meter Kistler 5015itself connected to the computer through a data-collection device Vernier LabPro to savethe data. The experimental system is depicted in figure 2. In addition, the used sensor isa dynamic sensor. The effort must therefore change over time otherwise there would be adrift of the measure. To do so, the movement imposed on the tool over time is a triangularsignal.6Figure 2 Experimental set-upIn order to ensure the evacuation of micro chips during the polishing and guarantee anonzero abrasion speed at the contact between the part and the tool, the tool axis u istilted relatively to the normal vector to the polished surface n and to the feed directionf. The tilt angle (figure 3) is defined as follows :nuqfvCeCcWorkpieceCLFigure 3 Tool axis tilting7u = cos n + sin f(1)Polishing tests have been conducted considering three different tilt angles (5,10,15)between the tool axis and the normal vector to the surface in the feed direction. Thecorrelation between the tool deflection and the polishing force is shown in figure 4.Polishing?force0246810121416180,000,150,300,450,600,750,901,051,20Displacement?(mm)Force?(N)5?inclination?angle10?inclination?angle15?inclination?angleFigure 4 Polishing forces vs displacementThe green curve (5 deg) is interrupted because the abrasive disks unstick when thetool deflection is too large. In this configuration, the tilt angle is too low and the bodyof the disk support, which is more rigid, comes in contact with the workpiece, whichdeteriorates and unsticks the disk. With a 10 or 15 degrees tilt angle, this phenomenonappears for a higher value of tool deflection, outside the graph. However, low tilt angleconfigurations allow faster tool movements since the rotation axes of the 5-axis machinetool are less prompted 11. Furthermore, it has been showed that trochoidal tool pathsrequire a dynamic machine tool to respect the programmed feedrate 12. Then in si-multaneous 5-axis configurations, polishing time will be greater with low tilt angles. Inaddition, the flexibility of the tool will help to reduce or avoid 5-axis kinematic errors 13.Indeed, interfences between the tool and the part could happen because of great tool axis8orientation evolutions between two succesive tool positions. Therefore, the disc supportdeflection would avoid the alteration of the mold surface.If one considers the law of Preston 14, the material removal rate h in polishing isproportional to the average pressure of contact, P, and to the tool velocity relative to theworkpiece, V :h = KPPV(2)where KPis a constant (m2sN) including all other parameters (part material, abrasive,lubrification, etc.). Hence, in order to reach an adequate contact pressure, we must increasethe tool deflection and consequently we raise the shear stress and the disk unsticks. Froma kinematical behavior point of view, low rotational axes movements lead to decrease thepolishing time. So we must use a rather low tilt angle (5-10 degrees) and a quite high tooldeflection to ensure a satisfactory rate of material removal.2.25-axis polishing tool path planningTo generate the polishing tool path, the classical description of the tool path in 5-axis milling with a flat end cutter is used. This leads to define the trajectory of the toolextremity point CEas well as the orientation of the tool axis u (i,j,k) along the tool path.With regards to polishing strategy, we use trochoidal tool paths in order to imitate themovements imparted by the workers to the spindle. To avoid marks or specific patterns onthe part, we choose to generate trochoidal tool path on fractal curves in order to cover thesurface in a multidirectionnal manner. We use more particularly Hilberts curves whichare a special case of the Peanos curve. These curves are used in machining as they havethe advantage of covering the entire surface on which they have been generated 15. Wewill develop below the description of the Hilberts curve which is used as a guide curvefor the trochoidal curve then we will examine the trochoidal curve itself.2.2.1Hilberts curve definitionThe use of fractal trajectories presents two major interests. The first one is that toolpaths do not follow specific directions which guarantees an uniform polishing. The secondone is linked to the tool path programming. Indeed, tool paths are computed in the9parametric space u,v of the surface, that is restricted to the 0,12interval. Hilbertscurves are known as filling curves, covering the full unit square in the parametric space16, and consequently, the Hilberts curves fill the 3D surface to be polished. Hilbertscurves can be defined with a recursive algorithm, the n-order curve is defined as follows : If n = 0 :x0= 0y0= 0(3) Else :xn=0.50.5 + yn10.5 + xn10.5 + xn10.5 yn1yn=0.50.5 + xn10.5 + yn10.5 + yn10.5 xn1(4)It is then easy to compute first, second or third-order and so Hilberts curves (fig 5).-0.4-0.200.20.4-0.4-0.200.20.4-0.5-0.3-0.10.10.30.5-0.4-0.200.20.4-0.5-0.3-0.10.10.30.5-0.5-0.3-0.10.10.30.5Figure 5 Hilberts curves (first, second and third order curve)In order to maintain a tangency continuity along the Hilberts curve which is the guidecurve of the trochoidal tool path, we have decided to introduce fillets on the corners of thepolishing fractals. Otherwise, at each direction change on the fractal curve, the polishingtool path would be discontinuous. Resulting Hilberts curve is depicted in figure 6. Basedon this representation, the curve is easy to manipulate. For example, one could projectthis parametric representation directly in the 3D space or use it as the guide curve forbuilding trochoidal curves (fig 7) as can be seen in the next section.2.2.2Mathematical definition of trochoidal curvesBased on the description of trochoidal curves proposed in 17, we define a trochoidalcurve as follows. Let C(s) be a 2D parametric curve, where s is the curvilinear length (fig8).10Figure 6 Fourth order cornered Hilberts curvef(s)CciCinirCDTROiCjnjCcjOjqiqjFigure 7 Polishing trajectories on a convex free formC(s) = (s,f(s) is the guide curve of the trochoidal curve and n(s) the normal vectorto the curve C(s) at the considered point. p is the step of the trochoidal curve and wedenote Dtrits diameter. The parametric equation of the trochoidal curve is the following :P(s) = C(s) +p2n(s) + Dtrcos(2sp)sin(2sp)sin(2sp)cos(2sp)n(s)(5)The issue is now to link the trochoidal curve parameters to the polishing parameters.The amplitude A of the trochoidal curve is equal to twice its diameter A = 2Dtr. However,11Figure 8 Trochoidal curve parametersfrom a tool path generation point of view, we are more interested in the tool envelopeamplitude than in the trochoidal curve amplitude. One of the difficulties of modellingthe envelope surface of the tool movement is the tool itself, as abrasive polishing toolsare mounted on flexible supports. The tool polishing amplitude depends on the contactsurface between the tool and the part. This contact is influenced by the tilt angle , thetool diameter D and the imposed tool displacement e to be able to polish the surface.Indeed, when the tool is laid flat, the contact area is a disk, as can be seen in figure 9.However, when the tool is tilted and a given displacement e is imposed to the tool, thecontact area is a disc portion.ZDDeffleZequFigure 9 Contact area between the tool and the partThe effective tool diameter can be computed with the following expressions :12Deff= 2s?D2?2 (l)2(6)with :l =D2sin etan(7)and :E = A + 2Deff2= 2Dtr+ Deff(8)This yields to the definition of the parameter Dtradjusted to build the trochoidalcurve.Dtr=E Deff2=Deff6=13vuut?D2?2 D2tan etan!2(9)2.2.3Tool path generationWhatever the nature of the considered surface, the polishing tool paths generationconsists of three steps : computation of the tool path in the parametric space, computationof the resulting tool path in the 3D space and computation of the tool axis orientation.Tool path generation relies on the trochoidal curve as described above. The trajectory isdefined discretly. The only difficulty is to calculate the normal vector. This is done byusing the points Ci1and Ci+1and by calculating the next cross product :ni= Z Ci1Ci+1(10)We now describe the method for calculating the direction of the tool axis u (figure3). In a first approach we only use the tilt angle defined in the plane (f;n) where f isthe tangent vector to the guide curve, i.e., the Hilberts curve and n the normal vector tothe machined surface. The tool axis u is tilted in relation to the Hilberts curve tangentf rather than to the trochoidal curve in order to minimize the movements amplitude ofthe rotational axes of the machine tool.In order to compute the tangent vector fiat the contact point CCibetween the tooland the part, the following expression is used :fi= n CCiCC(i+1) n| CCiCC(i+1)|!|z(11)13The location of the tool extremity CE, which is the driven point during machining,depends on the polishing mode, i.e., by pulling or pushing the tool. The polishing modeis defined by the parameter : OCE= OCC+ r n + (R r) v r u e z(12)with :v =u n|u n| u(13)by noting = 1 when 0 and = 1 when 0 : profile has more peaks than valleys, Ssk 3 : the distribution is wide (the surface is rather plane), Sku 3 : the distribution is tighted (the surface has a tendency to present peaksor valleys).Once the parts are polished, we perform 3D surface roughness measurements using anon-contact measuring system (Talysurf CCI 6000). We perform measurements on poli-shed parts with our approach (the plane and the convex surface) and on a plane that hasbeen polished manually by a professional (figure 11). Measurement results are reportedin table 2.It can be observed that the convex surface automatically polished presents larger geo-metric deviations as well as a higher Sa and Sq than those observed for the planar surface.In other words, the rate of material removal is not as good as on the planar surface while16Figure 11 3D surface roughness : convex surface (top), planar automatic (middle),planar manual (bottom)OperationsNVcV ffzapatTToolrpmm/minmm/minmm/toothmmmmminparallel planes94388980000,0570,20,0335End mill ( 3)Operations ToolsAStepV fNeTmmmmmm/minrpmdegmmminP grade 120 ( 18)1211000200030,415P grade 240 ( 18)1211000200030,415P grade 600 ( 18)1211000200030,415P grade 1200 ( 18)1211000200030,415Diamond abrasive emulsion (9m) ( 6)1211000200030,315Diamond abrasive emulsion (3m) ( 6)1211000200030,315Diamond abrasive emulsion (1m) ( 6)1211000200030,315Table 1 Milling and polishing operationsSurfaceSaSqSskSkuConvex Autom.7.619 nm9.543 nm-0.23142.92Plane Autom.1.085 nm1.346 nm0.1032.713Plane Manual1.014 nm1.307 nm-0.59413.748Table 2 3D Roughness parameters17trajectories are the same in the (u,v) parametric space. There are several explanationsfor this behavior. First, the used polishing pattern, generated in the parametric space, isthe same than the plan