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Design, evaluation and optimisation of cutter path strategieswhen high speed machining hardened mould and die materials

C.K. Toh *

School of Engineering (Mechanical), University of Birmingham, Edgbaston Park Road, Birmingham B15 2TT, UK

Received 24 February 2004; accepted 21 July 2004Available online 8 September 2004

Abstract

The use of high speed milling (HSM) for the production of moulds and dies is becoming more widespread. Critical aspects of thetechnology include cutting tools, machinability data, cutter path generation and technology. Much published information exists oncutting tools and related data (cutting speeds, feed rates, depths of cut, etc.). However, relatively little information has been pub-lished on the optimisation of cutter paths for this application. Most of the research work is mainly focused on cutter path generationwith the main aim on reducing production time. Work with regards to cutter path evaluation and optimisation on tool wear, toollife, surface integrity and relevant workpiece machinability characteristics are scant. Therefore, a detailed knowledge on the evalu-ation of cutter path when high speed rough and nish milling is essential in order to improve productivity and surface quality. Thepaper details techniques used to reduce machining times and improve workpiece surface roughness/accuracy when HSM hardenedmould and die materials. Optimisation routines are considered for the roughing and nishing of cavities. The effects of machiningparameters notably feed rate adaptation techniques and cutting tools are presented. 2004 Elsevier Ltd. All rights reserved.

Keywords: Cutter path strategies; Machining; Materials

1. Introduction

The term high speed milling (HSM) is generally usedto describe end milling with small diameter tools ( 6 10mm) at high rotational speeds ( P 10,000 rpm). Theprocess has been traditionally taken up by the mouldand die industry for the production of functional and

support components for forging, casting, injectionmoulding and stamping using hardened tool steels. Inaddition to the correct selection of cutting tools, mach-inability data and machine tool, an efficient HSM oper-ation requires the evaluation of cutter paths over the

part geometry. Modern computer aided design/compu-ter aided manufacture (CAD/CAM) systems allow freeform surfaces to be machined by utilising 3D CAD, pro-ducing cutter path programs via CAM modules anddownloading the programs to computer numerical con-trol (CNC) machining centres.

There are generally three main stages in the HSM of

dies/moulds machining:

Rough milling . Workpiece material is removed as fastas possible while leaving a semi-nishing allowance.There is little or no emphasis on workpiece dimen-sional accuracy or surface roughness. An end mill isgenerally employed for this process due to high effi-ciency of material removal and longer tool life, how-ever in the case of hardened steels, a corner radiusend mill or ball nose end mill is generally used.

0261-3069/$ - see front matter 2004 Elsevier Ltd. All rights reserved.doi:10.1016/j.matdes.2004.07.019

* Present address: Singapore Institute of Manufacturing Technol-ogy, Machining Technology Group, 71 Nanyang Drive, Singapore638075, Singapore. Tel.: +65 67938593.

E-mail address: [email protected].

www.elsevier.com/locate/matdes

Materials and Design 26 (2005) 517533

Materials& Design
mailto:[email protected]:[email protected].


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Semi-nish milling . The steps and shoulders remain-ing from the roughing stage are removed and a nish-ing allowance of uniform thickness is left. The processis generally performed using an end mill or a ball noseend mill. This operation is important in maintaining arelatively constant metal removal rate for subsequentnishing. This is particularly important at cornersand other difficult to access areas. The aim is to min-imise cutter deection and tool wear during nishing.Finish milling . The nal shape of the part is achievedusing a ball nose end mill. Dimensional accuracy,gouge prevention and workpiece surface roughnessare the most important criteria. As a result, nishinggenerally requires the largest amount of machiningtime due to low depths of cut and feed rate. In somecases, particularly with deep cavities or when smallinternal radii are required, sections of the cavity can-not be reached with a milling cutter. Therefore, Elec-trical Discharge Machining (EDM) may be necessaryto remove material from these sections. Finally, pol-ishing/grinding is often performed to achieve therequired workpiece surface roughness. This is gener-

ally performed manually. A nal EDM operationmay be utilised to provide a stochastic sparked sur-face to the mould/die. Alternatively, photochemicalmachining techniques are used for the production of deterministic textured surface e.g. the leather fronton automotive dashboards.

In order for the implementation of HSM to be suc-cessful, critical factors have to be taken into account.The following information relates primarily to cutterpath evaluation for HSM where one of the main chal-lenges is accommodation of the high feed rates (typically2,00010,000 mm/min), which are used. Choi et al. [1]identied critical factors for HSM cutter paths, whichincluded collision avoidance, the maintenance of con-stant chip loads/cutting loads, the use of smooth tool-paths and verication mechanisms. With HSM, a minorcollision will result in damage to the cutter, workpieceand the machine tool itself, hence the need to avoid col-lision. The maintenance of constant chip loads will en-sure long tool life since an abrupt change in chip loadwill have detrimental effects on the cutter. A smooth cut-ting action will be achieved with the optimisation of feedrates so as to avoid the existence of chatter. Last but notthe least, verication of NC programs is needed before

the actual HSM process is carried out. This will ensurea successful machining process since there is little timefor human intervention when a problem occurs, evenif the operator is monitoring the machining process.

Since the late eighties, numerous academic papershave been published on cutter path generation. Evalua-tion of cutter paths is an important area as correct selec-tion can signicantly reduce machining times and toolwear by reducing the total tool travel [2]. Cutter pathgeneration is a multi-disciplinary area requiring inputsfrom mechanical/electrical/manufacturing engineering,computer science and mathematics [3]. Dragomatz andMann [3] complied a database of classied bibliographyof published literature on cutter path generation asshown in Fig. 1 . The paper was subdivided into catego-ries related to cutter path generation. The majority of the papers were from the period of 19841994 and in-cluded a number of papers from 1996. The aim was toprovide a useful guide for those searching for literaturerelated to path generation. However, most articles men-tioned did not take cutter path evaluation into consider-ation with respect to the workpiece materials, cutting

tool geometries and machining responses such as cuttingforces, cutting temperature, workpiece surface integrityand tool life. The following section details the variousdesign and evaluation techniques for rough and nishmilling carried out by researchers over the past 15 years.

2. Design and evaluation for rough milling

Rough milling removes most of the material from apredened workpiece to be machined. It is thereforeimportant to apply a good machining strategy requiredto achieve minimum machining time and improve pro-ductivity. Elber and Cohen [4] suggested a contourmap machining method (also known as Z -level machin-ing or parallel-plane contouring) to remove excessiveworkpiece material by slicing the model to be machinedinto several levels and using three-axis milling, seeFig. 2 . A xed axial depth of cut and the intersectingcurves of a hypothetical slicing level to the sculpturedmodel determine the material volume to be machinedat each level. The material external to the part is re-moved at each level by applying 2D cutter path strate-gies. The contour map machining approach is verysuitable to mill core sculptured features since an end mill

Nomenclature

D cutter diameter (mm)h cusp height (mm)r eff effective cutter radius (mm)

R cutter radius (mm)R d radial depth of cut (mm)B angle of cutter inclination ( )

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can be positioned directly to machine from the outsideboundary of the workpiece.

Lee et al. [5] proposed a cutter selection procedurethat included the selection of appropriate cutters foreach plane with cutter size decisions based on surfaceinformation evaluation, geometric limitations and max-imum material removal rate embraced the contour mapmachining approach. In addition, merging based onminimum machining time criterion in order to reduceunnecessary cutter changes optimised cutters selected.The maximum depth of cut on each plane was thendetermined for each chosen cutter. Flat end mills wereused for roughing cavities in a series of cutting planes.An important conclusion by the authors was that thebest way to machine a cutting plane was in a continuousfashion with few interruptions or rapid traversals duringthe operation.

To reduce cutter retraction and traversal time, thesculptured area to be machined is partitioned into subregions and machined separately. When additional fea-tures such as concave shapes or internal islands areintroduced, evaluation is more complex. Bala andChang [6] developed an algorithm and procedure foroptimum cutter selection and cutter path generationfor parts, which contained all of the features found onprismatic parts, including slots, steps, projections, etc.These were implemented in a system called cutter selec-tion and pocketing system (CUSPS). A raster millingstrategy was used. Cutter path evaluation was basedon the number of rapid movements necessary whenmachining pockets with internal islands or bosses thatmust not be machined. In this case, the cutter was eitherretracted or moved over the bosses, or machining wascarried out in discrete segments, which were divided by

Region decompositionPoint-based roughing paths

Cleanup cut tool pathsSpace-filling curve based tool paths

Simulation & verificationPixel and point models

Mesh modelsFive-axis methods

Offset surface methodTool positioningRoughing paths

Sculptured surface pocketing paths

Planar pocketing pathsIsoparametric paths

Non-isoparametric paths

SystemsIssues

Surveys

0 20 40 60 80 100Note that certain literature appears in more than one classification.

Fig. 1. Classication of literature on cutter path generation [3].

Fig. 2. Parallel-level contouring to generate 2-axis cutter paths for rough milling.

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the bosses. Fig. 3 shows the deployment of cutter pathover a part that contains internal islands.

Machining without rapid cutter movements is some-times not possible because of the part features. In thisexample, the number of rapid traverses was minimised

by dividing segments into groups and then machiningthe part group by group. Here, the grouping was organ-ised in the following order: (1) {0,2,4,6,7}, (2) {1,5,3}and (3) {8}, such that the areas marked as 0, 2, 4,6 and 7 were machined rst and then the cutter retractedand positioned itself to start machining the areas 1,5 and 3. When this was completed, the cutter again re-tracted and positioned itself to machine the area marked8.

In order to reduce the non-milling time during whichthe cutter rapid traverses over protruding features, Mar-shall and Griffiths [7] engaged a methodology such thatsegments of the boundary path were machined followedby milling of the neighbouring region of the raster cutterpath (cutter moves back and forth across the surface,also known as zigzag path). The ordering of milling re-gions was critical in minimising non-machining time.This was achieved by reducing the model into surfaces.Cutter paths were deconstructed from full paths suchthat the adjacent surface was milled rather than travers-ing over the protruding surface. In some systems, islandsinside a cavity are approximated as a polygon for roughmachining in order to make the generation of cutterpaths more straightforward. Lee and Chang [8] devel-oped the constraint-based automatic system for sculp-

tured surface cavity machining (CASCAM) system,which simplied contours as polygons for roughmachining, see Fig. 4 . The raster cutter path was thengenerated within the polygonised boundary.

For machining free form surfaces using a contour

map machining, Vickers et al. [9] developed six cutterpath patterns: stock offset, component offset, stock/com-ponent offset, parallel offset, proportional blending off-set and maxmin offset which are shown in Fig. 5 . Themost appropriate cutter path pattern for each potentialcutting layer was selected through this study along withthe selection of other machining parameters, which in-cluded feed rate, depth of cut, number of cutting layersand distribution of cutting depth in order to generateminimum overall machining time. A CNC machinedhydrodynamic ship hull model was used as an exampleto illustrate the capabilities of this approach. Their re-sults showed that parallel offset cutter path patternwas the best for the rst one third of the cutting layers.Subsequently, maxmin cutter path pattern was the bestfor the remaining patterns. It was further concluded thatthe number of cutting levels had a primary inuence ontotal machining time.

Dong et al. [10] proposed an evaluation strategy forthe roughing of free form surfaces which took into ac-count stock and part geometry, selected cutter pathstrategies along with emphasis on related parametersincluding the number of cutting layers, distribution of cutting depth, feed rate and spindle speed. The cutterpath strategy was based on a contour map approach.

Fig. 3. Raster milling of a part with internal islands [6].

Fig. 4. Formation of a polygon from a free form shape for rough machining [8].



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When this was applied to die/mould cavity roughmachining, the 3D part was divided into 2D hypotheti-cal planes and machining was carried out layer by layer.In this work, minimum machining time was achievedwith respect to the machine tool specication, i.e. max-imum allowable cutting torque or cutting power wasmaintained to maximise volumetric removal rates andsubsequently reduce machining time.

An algorithm was developed by Vickers et al. [9] tocalculate the number of cutting levels and their thick-ness. A number of important conclusions were derivedfrom their study. First, the distribution of the cuttingdepths had little inuence on overall machining time.

Second, the determination of the optimum number of cutting layers reduced machining time and improvedproductivity. A comparison of production times wasmade between traditional rough machining, an adaptivemachining approach and this new method. The saving intime over the traditional approach was between 37%and 47% and over the adaptive machining approach a2628% reduction occurred.

Both of these studies are aimed at reducing roughmachining time and consideration of the volume of remaining material (shoulders, etc.), which determinesthe number of subsequent machining operations. Thisvolume is dependent on the part geometry and cuttinglayer thickness (axial depth of cut). If the thickness of cutting layers is arranged in order to minimise the vol-ume of remaining material, the amount of semi-nishmachining can be reduced or even eliminated. This obvi-ously results in savings in overall machining time.

Chon et al. [11] adopted a similar approach for roughmachining of sculptured surfaces using contour mapmachining approach. Here, different cutter path strate-gies and optimal cutter sizes were determined for eachcutting layer with the aim of achieving minimummachining time. Their experimental results highlightedthat selection of optimal cutter path strategies for each

particular cutting layer highly depended on the modelgeometry. Using optimal cutter sizes and cutter pathstrategies, machining time was improved tremendouslyby 82%.

Li et al. [12] carried out work on rough machining of free form surfaces to identify the optimum cutter pathpattern for each cutting layer in contour map machin-ing. The study focused on free form surfaces with a sin-gle island and no signicantly concave proles. Cutterpath planning/generation was automated and machiningtime was considerably reduced. The authors and Huet al. [13] claimed that because of the large differencesin volume between the stock and part shape, rough

machining of free form surfaces dominated overallmachining times. Therefore, productivity improvementand cost reduction were heavily dependent on reductionin rough machining time/cost. Conversely, otherresearchers such as Rodriguez et al. [14] and Rao et al.[15] claimed that nish milling required the largest pro-portion of the total machining time, due to high dimen-sional accuracy requirements.

Li et al. [12] used two different methods to identifythe optimum cutter path pattern for specic workpiecegeometry. In the rst one, the part was divided into 30cutting layers using hypothetical cutting planes. Thesix cutter path patterns shown in Fig. 9 were used togenerate six different groups of cutter path patterns foreach layer. It was realised that machining time differenceon different cutter path patterns were lower on thesmooth surface and low varying cross sectional shapeof the geometry. This difference became quite signicantwith rapidly changing cross sectional shape. Themachining time difference between the worst and bestpattern was 1347%. Their results showed that paralleloffset cutter path pattern gave the lowest machining timeon the rst four cutting layers. Towards the end of cut-ting layer 29 and 30, component offset cutter path strat-egy resulted in the lowest machining time. The authors

Fig. 5. Feasible cutter path strategies using a contour map strategy [9].



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suggested that an even greater difference would havebeen obtained with greater part complexity.

In order to reduce computation time, the secondmethod focused on the similarity between cutting layershapes. This entailed three steps: (1) cutting layer clus-tering, (2) cutter path pattern analysis for geometrylayer shapes, and (3) optimum cutter path pattern iden-tication. Essentially, layers generated from the work-piece were classied into a number of clustersaccording to their shapes and the cluster centres of thesegroups were taken as the geometry layer shape. Theoptimum cutter path pattern for each layer was thendetermined. The optimum number of cutting layer clus-ters for the workpiece was found to be four. This con-trasts markedly with the 30 cutting layers required forthe rst method. The computational time required wastherefore substantially reduced to 6 20% that of the rst

method. When layers have multiple islands, evaluationis more complex. Under such circumstances, the bestcutter path patterns were stock offset and parallel offset,as shown in Fig. 6 . This approach was generally applica-ble for a large variety of cutting layer shapes and led toefficient rough machining. The method grouped all is-lands and treated them as a single island in order to gen-erate an appropriate cutter path pattern.

Hu et al. [16] developed a reasoning system in orderto determine an optimal cutter path strategy based onFig. 6 for a given workpiece using a contour mapmachining approach. A set of knowledge-based para-metric procedures was developed to classify a givenworkpiece based on different shapes and surface featuresand cutter path strategies were then implemented. Theiraim was to improve machining efficiency, which trans-lates into high productivity at minimum cost.

3. Design and evaluation for nish milling

Selection of cutter path interval is dependent on thelocal curvature of the machined surface, cutter sizeand nal workpiece surface roughness values to beachieved. A path interval that is too large will result in

a rough surface. On the other hand, a value that is toosmall will increase machining time. Therefore, a cutterpath has to be generated such that the cutter path inter-val is maintained constant regardless of convex or con-cave surfaces. Lin and Koren [17] presented ananalytical study of a new algorithm for determinationof an efficient cutter path of a free form surface. Theirmethod was based on the maintenance of a constantscallop height. By selecting the rst cutter path 12 ona free form surface as shown in Fig. 7 , the next cutterpath 35 was found by calculating its path intervalsbased on the constant scallop height.

The resultant machined area based on this cutter pathand the previous one maintained a constant scallop.This cutter path was therefore chosen to be the next cut-ter path, which guarantees no redundant machining.This approach resulted in a lower machining time. Whena comparison was made between this approach and theone based on a constant stepover distance, the efficiency

was highly dependent on the surface curvature of thepart. The length of the cutter path generated with thenew method for a sample part was 39% shorter than thatusing a conventional isoparametric approach.

The drawbacks of a raster cutter path strategy whenused to machine sloping surfaces with a ball nose endmill are alleviated by Marshall and Griffiths [18] whodeveloped a cutter path routine, which combined twocutter path patterns for nish machining of free formworkpiece surfaces. The raster approach basically in-volves traversing the surface of the workpiece, with thecutting tool rising or falling in the Z direction as the toolmoves over the surface. The newly developed cutter pathis a combination of raster and 3D offset machining. 3Doffset cutter paths can be compared with the carto-graphic contours on a map. A characteristic of constantZ cutter paths is that the greater the surface slope, themore densely packed they are in the X and Y directions.This inuences cusp height, which is a function of theworkpiece surface inclination. The new combined cutterpath is shown in Fig. 8 . The straight lines above themodel show the rapid traverse movements.

Where the surface was sloped, the combination of araster cutter path strategy and 3D offset cutter path re-sulted in redundant machining. However, a big gap in

Fig. 6. Cutter path patterns for layers with multiple islands (a) stockoffset and (b) parallel offset [12].

Fig. 7. The isoparametric cutter paths that cause redundant machining[17].



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the machining of sloped surfaces was lled at that timeusing this combined strategy. Further development ena-bled a CAM system to divide a free form surface intosub surfaces based on the surface slope angle. This al-lowed the optimum cutter path to be selected for eachsub surface. Vosniakos and Papapanagiotou [19] alsoused this hybrid approach to machine convex core fea-tures without islands.

Griffiths [20] introduced a mathematical approach tothe generation of an optimal cutter path, which reducedthe amount of rapid traversal time and the number of occasions on which the cutter re-entered the surface.He developed a form of space lling method known asHilbert curves. An illustration of Hilbert s curve isshown in Fig. 9 . The cutter path shown might look con-voluted, however, Griffiths claimed that it had substan-tial advantages over less sophisticated cutter paths. Itslocal complexity adapted automatically to the localcomplexity of the free form surface such that more de-

tailed cutter path would concentrate on those parts of the surface that required it. Fig. 10 shows the nal cutterpath and the nished object. Here the cutter pathsadopted a raster strategy where the surface was fully ma-chined by previous convoluted cutter path strategies. Inthis stage, the convoluted cutter paths concentrated onsteep and complicated surfaces. Sharp corners in the cut-ter path were rounded off and the places where the sharpcorners present were for the cutter moving vertically,since the rounding was not apparent in the vertical

projection.In three-axis nish milling, two main types of nish-

ing cutter generation techniques are used. The rst tech-nique, known as parallel milling, generates parallelcutter paths over the surface. The surface is rst ana-lysed and a radial depth of cut is chosen so as to producethe maximum cusp height specied. It is quick and easyto program since the radial depth of cut only has to bedetermined. However, this technique may not be suita-ble for curved surfaces as uniform cusp heights willnot necessarily be generated [21]. The second technique,known as surface ow milling, generates cutter pathsthat result in a constant uniform cusp height over themachined surface. The radial depth of cut is chosenfor the area of largest curvature based on a speciedmaximum cusp height. The feed direction follows eitherthe constant u or v lines of the surfaces, which are indic-ative of the ow of the surface [21]. Patches of surfaceswith similar surface ows are selected and programmedtogether. Patches that are not connected smoothly or donot have similar ows will be programmed separately.Several disadvantages arise when using this technique.First, this surface ow milling creates varying workpiecesurface roughness values that results in a poor surfacequality. Second, risks of gouging increases that reduce

Fig. 8. Machining of a contoured surface using combination of rasterand constant Z cutter paths [18].

Fig. 9. Hilbert s curve cutter path [20].

Fig. 10. Final cutter path and nished machined surface [20].



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the efficiency of machining and subsequently increasemachining time. Thirdly, because of the increased com-plexity involved in calculating the cutter position, goug-ing and crashing of the cutter is common [21]. Theillustrations of both types of nish milling cutter pathgeneration methods are depicted in Fig. 11 .

4. Machining parameters evaluation

Work on feed rate selection has been carried outextensively over the past few years. Choudhury andRao [22] identied two cutting parameters namely cut-ting speed and feed rate to improve tool life. It is recog-nised that such an approach can reduce machining timeand costs of program verication or modication, en-sure process reliability, avoid chatter, minimise machin-ing times and costs and improve tool life [23]. To achieve

this, cutting forces must each be measured or estimatedto an acceptable accuracy, since variations of the cuttingconditions are characterised by rapid changes in the cut-ting forces [24]. As a result, if cutting is stable, adjustingfeed rate to maintain the constant average cutting forcenot only increases the metal removal rate but also main-tains the quality of machined surface due to the samestatic cutter deection [25].

It has been recognised that by selecting optimal feedrate, metal removal rate can be increased. Tarng andShyur [25] identied that in order to evaluate machiningperformance, evaluating the radial depth of cut was nec-essary. This was because the radial depth of cut variednot only by different travelling cutter paths but also bydifferent positions of a path. They developed a geomet-rical cutting simulation program to recognise the appro-priate radial depth of cut with the aim of adjusting feedrate to achieve a constant average cutting force whenpocket machining. Fig. 12 shows the resultant cuttingforce and the machining time for constant and adjusta-ble feed rates when end milling 6061 Al. It was foundthat 20% of machining time was saved using this identi-cation strategy by adaptively adjusting the feed rate.

Eversheim et al. [26] suggested that adaptive milling,which maintains the cutting speed and chip thickness

within specic ranges, reduced milling time and mightimprove tool life. Bergs and co-workers [23] carriedout research on cutter path evaluation for adaptive n-ish milling of die/mould cavities on three-axis machinetools. Prototype software called OPTIMILL was devel-oped which varies the spindle speed and feed rateaccording to cutter engagement conditions such thatcutting speed and chip thickness can be maintained ina narrow operating range. When applied to a samplepart for nish milling, a timesaving of 47% was achievedover conventional milling. Longer tool life was also ex-pected. Rodriguez et al. [27] who concluded that adap-tive nish milling led to a signicant improvement intool life as well as a reduction of machining time furtherendorsed this nding. This is in contrast to roughmachining when adaptive milling is not widespread asthe contour map strategy obviates its use.

A machining strategy proposed by Lim and Menq

[28], known as the cutting-path-adaptive-feed rate strat-egy, was used to improve the productivity and quality of sculptured surface machining. This took force and geo-metrical constraints into account while at the same timeadaptively adjusting feed rates to optimise the cuttingdirection. In other words, by manoeuvring the cutteralong low cutting force and low machining error cuttingdirections, feed rates could be maximised to achieve thelowest possible machining time. A maximum feed ratemap was proposed and consisted of three main modules.Fig. 13 illustrates the layout structure of the proposedstrategy.

In the control point selection module, the number of control points was selected with constant/variable densi-ties depending on the surface curvature of the controlsurface. Next, the maximum feed rate map was deter-mined in the maximum feed rate map module. Theallowable maximum feed rates were determined for eachcontrol point along various machining directions. Cuttergeometry, pick feed, axial depth of cut, spindle speed,force constraints and dimensional tolerances wereamong the conditions to be considered to determinethe feed rates. Lastly, the information was fed to the cut-ter path/feed rate selection module such that the cutterpaths were selected for machining sculptured surfaces.

Fig. 11. (a) Parallel milling and (b) surface ow milling cutter paths [21].



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Simulation studies were performed on a two-dimen-sional curved surface. It was found that the time formachining highly curved surfaces could be dramaticallyreduced by cutting along low-force-low-error machin-ing directions and by maximising feed rates since cuttingforces and dimensional accuracy were under controlusing the proposed strategy. The machining time re-corded was a 72% reduction as compared to that of the original cutter path generation. In a second paper[29], the authors demonstrated their proposed strategyon real three-dimensional complex surfaces and the re-sults showed a substantial reduction in machining timeby using a multiple feed rate strategy as compared to asingle feed rate strategy.

Rodriguez et al. [14] developed FEDOPT, a cutterpath evaluation software module for rough and semi-nish milling of die/mould cavities. The program modi-ed the feed rate in an existing NC program by utilisingcalculations based on chip thickness and cutting forces.For a given cutter path and feed rate, the software cal-culated the permissible axial depth of cut and cutterengagement. It then modied the feed rate to maintaincutting forces within a specic range. When utilising thisadaptive machining approach, a sample part was roughmachined with a substantial reduction of 1017%machining time over using a constant feed rate. Themain criterion for the program is minimum machiningtime. Fig. 14 illustrates the process ow for generating

Fig. 12. Effect of feed rate adaptation on machining time and cutting force [25].

Fig. 13. Layout structure of the cutting-path-adaptive-feedrate strategy [28].



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adapted cutter paths using the feed rate adaptation pro-gram FEDOPT.

When milling sculptured surfaces, problems arise due

to constant cutter vibrations caused by the variations of the cutting forces and high cutter overhang and as a re-sult, process reliability is appalling. Weinert et al. [30]developed an algorithm based on an efficient, discretemodel that permits volumetric calculations for analysingthe engagement conditions between the cutter and theworkpiece. Feed rate evaluation in relation to themachining condition at a given time was achieved withthe aim of avoiding vibratory cutter loads while semi-nish milling sculptured surfaces. Their method signi-cantly improved dimensional accuracy and thusachieved process stability.

When machining free form sculptured surfaces, mill-ing characteristics change considerably when ball endmilling local shape features. Chu et al. [31] investigatedthe effect of varying the inclination workpiece angles,convex and concave corners in order to determine theoptimal feed rates for machining automobile prototypeproduction dies. Using fast fourier transform (FFT)analysis, the optimal feed rates were shown to decreasewith decrease in the radius of curvature of the concavecorner. On the other hand, optimal feed rates wereshown to decrease with increasing inclination workpieceangles when employing an upward orientation and con-tour milling.

In order to achieve high precision and efficientmachining in a face milling operation, Baek et al. [32]analysed the effects of the insert runout errors and the

variation of the feed rate on the surface roughness andthe dimensional accuracy by formulating a surfaceroughness model. Their results showed that the surfaceroughness was highly non-linear with respect to the feedrate. This was attributed to the insert runout errors. Thevalidity of their model was proved through their exper-iments from the information of the insert runouts andthe machining parameters and consequently the modelwas used to predict the machined surface roughness.The optimal feed rate that achieved a maximum mate-rial removal rate under the surface roughness constraintwas then selected by solving the objective function usinga bisection method.

Feng and Su [33] investigated the effect of integratedcutter path and feed rate evaluation for the nish millingof 3D plane surfaces. Here, feed rate selection wasachieved by maximising the feed per tooth based on cut-ting force and machining error calculations using aniterative procedure. The cutter feed direction was usedas a selection variable. The cutter path was determinedfor each cutter feed direction based on scallop heightrequirement and feed rate was maximised within the tol-erance requirements using a mechanistic cutting forcemodel for 3D ball end milling. Fig. 15 illustrates the ef-fect of varying the cutter feed direction on the feed per

Fig. 14. A owchart that details the generation of adapted NC cutter paths using FEDOPT [24].



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tooth. The feed direction is characterised by a 2D angle,a which represents the angular displacement between thecutter and the part coordinate system. The results indi-cate that the maximum feed rate varies signicantly withthe feed direction. The maximum feed rate is con-strained by machining errors caused by the cuttingforces with the feed direction, which is resulted fromchanges both in the cutting geometry of the ball end cut-ter and in particular cutter path orientations to generatethe cutter contact points on the 3D surface. The resultscan be used to assist the linking of linear cutter paths forsmall plane surface patches into a practical cutter pathfor machining sculptured surfaces to achieve processefficiency and product quality.

Takatsuto and Kishi [34] investigated the effect of adapting feed rate when milling an inclined plane.Two main cutter path orientations such as vertical up-ward and downward directions were investigated basedon different feed rates. The summary of evaluated feedrate results in relation to varying inclined plane surfacesis depicted in Fig. 16 . The evaluation of feed rates wasderived based on tool wear. From their results, they con-

cluded that longer tool life could be achieved using feedrate adaptation method by increasing the feed rate in avertical upward orientation and conversely by decreas-ing it in a vertical downward orientation. They deducedthat when milling in a vertical upward orientation, theupper cutting edge of the ball end cutter was able toaccommodate higher feed speeds whereas in a verticaldownward orientation, the central part near the tip of the cutter was used. They validated their results by mill-ing a concave surface as shown in Fig. 16 (a) based on2D surface roughness, cylindricity and micrographsevaluation of the machined workpiece surface. As a re-sult, longer tool life was achieved using feed rateadaptation.

When offset milling a pocket, a typical end mill movesalong one side of the pocket and changes direction whenit encounters the end of the side. As the cutter enters acorner, the radial depth of cut increases due to the mate-rial left behind by a larger cutter as illustrated in Fig. 17(a). As such, cutting forces increase and uctuate drasti-cally at the onset of the corner eventually leading to se-vere tool wear deterioration. Therefore, the magnitude

Fig. 15. Illustration of (a) part and cutter coordinate system and (b) the graph depicting the effect of varying the feed direction characterised by theangle a on the feed per tooth [33].

Fig. 16. Adaptation of feed rates when milling a concave surface [34].



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of the cutting forces has to be maintained at a constantlevel. Kline et al. [35] developed a mechanistic modelbased on chip load, cut geometry and relationship be-tween cutting forces and chip load. Force characteristicsduring cornering cuts were predicted by using the devel-oped model and validated via a set of cornering cutexperiments. The graph of Fig. 17 (b) describes that inorder to maintain a constant cutting force magnituderegardless of different axial depths of cut used, feed ratehas to be adaptively adjusted to an optimal.

Kloypayan and Lee [36] developed a technique todetermine the material removal rate (MRR) based ondifferent cutter geometries when a cutter moved in a lin-ear, circular or parametric motion. By analysing the

geometry and the cutting cross sectional area of differentend mill geometries, the material engagement along thecutter path motion was found. The MRR was thendetermined based on different cutter motions. Theinstantaneous cutting force for the particular motion

was then calculated by using the MRR, cutting speedand specic energy of the workpiece material. Figs.18(b) and (c) show the material engagement and adap-tive feed rate simulation for the cutter path milling alongthe outer pocket as shown in Fig. 18 (a). The results illus-trate that when milling along curved cutter path at thecorner of the pocket feature, feed rate was adaptively re-duced to accommodate the maximum material volumeto be removed to reduce chip overload and consequentlyimprove the tool life [37]. Subsequently when millingalong linear cutter path, feed rate was increased for mill-ing along low chip load.

5. Evaluation in relation to cutting tools

Finish milling with a ball nose end mill leaves cuspsbetween cutter paths. Utilising a ball nose end mill witha larger diameter, using smaller stepover distances and/

Fig. 18. (a) The generated offset cutter path for the example pocket feature, (b) calculated material removal rate along the curved path and (c)calculated adaptive feed rate for a constant cutting load for machining the example pocket feature [36].

Fig. 17. Effect of reducing the feed rate trajectories in order to maintain a constant cutting force [35].



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or nal grinding/polishing can reduce these. It has beenreported that grinding/polishing can take as much as20% of overall die/mould production time, includingcutter path generation. Furthermore, the productiontime for a variety of commercial die and mould cavitiesranges from 1200 to 3800 h [38], therefore grinding/pol-

ishing accounts for between 240 and 760 h work.When components featuring contours/proles are re-quired, ball nose end mills and to a lesser extent, radiusend mills and cutters equipped with round indexable in-serts can be used. These are capable of drilling or ram-ping/spiralling into workpieces to enable theproduction of closed pockets and slots. The tip of a ballnose end mill has geometry suitable for helical milling,while the peripheral edges are capable of a range of machining operations from slotting, to the cutting of vertical walls of a component. When nish milling work-pieces with a regular geometry, simple relationships be-tween the milling strategy and the cutter engagementscan be established [39]. However, in nish milling of freeform surfaces, the tool engagements change frequentlyand are difficult to predict [23].

In nish machining, the engagement of the cuttingtool with the workpiece constantly changes due to thefree form nature of die/mould cavities. This has a knockon effect in terms of tool life and workpiece surfaceroughness. In conventional CAD/CAM assisted partprogramming, the spindle speed and feed rate valuesare usually set according to the worst possible toolengagement conditions. Unfortunately, these valuesare generally held constant and machining is therefore

inefficient. A way round this is to change the operatingparameters, as and when necessary, via the part pro-gram or to tilt the cutting tool to provide optimalengagement. The main drawbacks of the approach arethe requirement for extensive computation and a costlyfour- or ve-axis machine. It has been reported that ator corner radius end mills are favoured in ve-axismachining instead of ball end mills. This is because theworkpiece surface roughness achieved is generally supe-rior compared to the latter [21]. When nish machining,the cusps left on the machined surface directly affectworkpiece roughness and accuracy. Selection of theappropriate cutter path is therefore critical in order tominimise grinding/polishing.

When machining at surfaces using a ball nose endmill with a constant stepover distance, cusps heightsare equal all over the workpiece surface. This is notthe case, however, when the workpiece surface iscurved/free form, e.g. in a die/mould cavity. In this case,the cusp height is a function of workpiece surface curva-ture. As a result, a stepover distance chosen for one areaof a free form surface will give different cusp heights forother segments.

For low curvature free form surface machining,Ralph and Lotus [40] proposed a method to reduce

cusps and increase tool life. Machining was performedwith an end mill rather than a ball nose end mill on athree-axis machining centre, with the workpiece tiltedduring machining. In order to minimise the amount of excess material on the machined surface, optimumpitch and roll angles were chosen at the work set up

stage. Comparative machining trials were carried outto verify results. These showed that the roughness of the machined surfaces was superior to surfaces ma-chined using a ball nose end mill. The resulting cusp vol-ume was reduced by 64%. However, it was deduced thatthis method was only suitable for milling low curvaturefree form surfaces.

Cusp heights generally depend on the types of cut-ters used, its geometry and dimensions, its orientationwith respect to the machined surface and the radialdepth of cut used. As previously outlined, cusp heightsresulting from using a ball end mill principally deter-mine workpiece surface roughness and a trade-off is al-ways necessary between productivity and surfaceroughness. When the machining strategy is based ona constant stepover distance, the result is either ineffi-cient machining or variable workpiece surface rough-ness. Fig. 19 shows two situations where: (a) has aworkpiece surface normal to the tool axis and (b) hasa surface at an angle to the tool axis. Using the samestepover distance (in this case equal to the cutter diam-eter), the cusp height on the sloping surface is largerthan that on the planar surface. With free form sur-faces therefore, the cusp height will be larger on areasof the workpiece with a higher slope angle, assuming a

xed stepover.Flat end mills are superior to ball nose end mills in

terms of MRR and the production of a lower work-piece surface roughness on a plane surface. In addition,ball nose end mills are more expensive to manufactureand regrind [41]. When milling using a ball end mill ona at surface, the cutting region occurs at a portion of the sphere near the cutter rotational axis resulting in aminimal cutting speed. When using a at end mill, theworkpiece material is always cut at the periphery of thecutter at a full and predetermined cutting speed [42].However, because of the free-form nature of most dieand mould cavities and corner chipping problems whencutting fully hardened steels, ball nose end milling isthe only practical option. When a concave pocket fea-ture is machined, a ball nose end mill with a radius lessthan the minimum curvature radius is generally used. If this is not the case, material will be left which has to beremoved by a further operation. Some mould/die sur-faces not only consist of concave areas, they also haveconvex surfaces. In order to increase MRR, convexsections can be machined using standard end millsassuming that the workpiece material/hardness allowsthis. Using this approach, Elber [43] developed an algo-rithm to differentiate the cutter path of a free form



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surface into two types of regions that could be ma-chined using either a standard end mill or a ball noseend mill. The former was utilised to machine at andconvex surfaces and the ball nose end mill utilised onother regions. An example is illustrated in Fig. 20 .

The method resulted in a faster machining operationand an improved workpiece surface roughness. Thedisadvantage of this method was that a ve-axismachining centre was required.

Cutter or workpiece inclination is utilised with theaim of achieving low workpiece surface roughness whenusing a three-axis machine tool. The cusp height orworkpiece surface roughness is a function of cutter ra-dius, cutter inclination, radial depth of cut and surfacecurvature [43]. Fig. 21 (a) shows the graph of the ratioof effective cutter radius to actual cutter radius versus

cutter angle inclination and the illustrations of the cuspheight formed when milling using ball end mill and atend mill respectively. The graph shows that at a cutterinclination angle of 5 , the effective cutter radius isroughly twelve times greater than a ball mill of equiva-lent size.

The effective cutter radius is derived as shown Eq. (1)[43], where r eff is the effective cutter radius. When using aball end mill, the cusp height h can be expressed asshown in Eq. (2). On the other hand when employingan inclined at end mill on a plane surface, the cuspheight is derived as shown in Eq. (3). The graph of Fig. 21 (a) suggests that high metal removal rates andlow workpiece surface roughness can be achieved byusing a at end mill at low inclination angles, i.e. theend mill cutters are suitable for milling low curvaturesurfaces [43].

r eff

R

sin / ; 1

R d 2 ffiffiffiffiffiffiffiffiffiffi2hR h 2p ; 2h sin / R ffiffiffiffiffiffiffiffi R 2 R 2d=4q : 3

When rough milling, at end mills are the preferredoption since cutting at its periphery generates maximumcutting speed that maximise efficiency. However, theedges tend to chip easily when milling hardened steel.

Fig. 20. Cutter path for a nger shaped workpiece (: at end mill, : ball nose end mill) [43].

Fig. 21. (a) A graph of ratio of effective cutter radius to actual cutter radius against cutter inclination angle, cusp height or workpiece surfaceroughness resulting from (b) ball end mill on a plane surface and (c) at end mill on a plane surface [42].

Fig. 19. Cusps produced on (a) planar surface and (b) sloped surface [18].



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A better choice would be to use a lleted or corner ra-dius end mill since the cutting force generated is lowat the end face edges to reduce stresses and prevent pre-mature failure of the cutter [44,45]. Kim and Chu [46] re-ported that the use of corner radius end mill is superiorto other end mills for the inclined end milling process in

terms of workpiece surface roughness and tool life.Moreover, the lower surface roughness and mean chipthickness permit a higher feed per tooth, hence reducingmachining time [47]. Large end mills can also be used tomachine low curvature surfaces. This means that largeradial depths of cut can be utilised to reduce machiningtime at the same time achieving a low workpiece surfaceroughness. The low curvature also reduces the risk of gouging [21].

When machining moulds and dies, the basic task is todetermine the machining strategies and cutter sizeaccording to the information about the geometry andshape of the free form surfaces [13]. Various researchershave highlighted the selection of cutter sizes over thepast 10 years. The overall aim is to achieve desired sur-face quality and at the same time reduce machining timeor cost. The work on optimal selection of cutters takesinto account the geometrical constraints of the work-piece model to be machined, technological or heuristicsviewpoint [48]. Lee et al. s approach [5] on cutter selec-tion took into considerations the rough and nish mill-ing processes. Cutter size was determined automaticallyby considering the geometrical constraints on each par-allel plane formed by intersecting the geometry of theworkpiece to be machined via the basis of maximum

material removal criteria in the rough milling processand minimum cutter movement with the required accu-racy in the nish milling process. Chen et al. [49] carriedout further integration of automatic cutter selection andparallel plane determination using an integer program-ming method and a dynamic programming method.The presented evaluation techniques can be used toautomate and improve the traditional experience basedapproach in reducing the total machining time. Glaeseret al. [50]s work was primarily concerned with local andglobal conditions for a collision free three-axis milling of sculptured surfaces based on the selection of cutters fora given surface. Hinduja et al. [48] developed an inte-grated evaluation procedure that took into considera-tion the various factors that affected the selection of the cutter via the optimum cutting conditions, lengthcut, the actual variation of the ratio of the radial depthof cut to the cutter diameter ( R d /D). Their resultsshowed that the length cut depended on the cutter diam-eter and the nominal value of R d /D. They concludedthat the nal determination of optimum cutter diameterwas a compromise between the increased costs andshorter length cut when using a larger cutter and thelower costs and higher length cut when using a smallercutter.

6. Conclusions

The following conclusions have been derived fromthis work:

There are three main necessary stages for HSM oper-

ation, namely, rough milling stage where the work-piece material is removed as quickly as possiblewhile leaving a semi-nishing allowance, semi-nishmilling stage where milling is carried out to ensureconsistent material removal rate for the next nishingstage and nish milling stage where the emphasis ison workpiece dimensional accuracy, gouge preven-tion and quality surface nish.Contour map machining technique has been com-monly used in rough milling stage by variousresearchers with the main aims on improving metalremoval rates and reducing machining time. Thenumber of cutting levels and the cutter path strategiesadopted on each level has a signicant effect onmachining time.A number of factors have to be taken into consider-ation when nish milling: shape, size and local curva-ture of the mould and die features, cutter geometry,radial depth of cut and cutter pat strategies.Substantial time savings can be achieved by usingadaptive machining to change the spindle speed andfeed rate accordingly when rough and nish millingin order to achieve consistent cutting loads. The ben-ets include good surface quality, prolong tool life,low machining time and improved metal removal

rates.Although at end mills are superior to ball noseend mills in terms of metal removal rate and pro-duction of a low workpiece surface roughness ona plane surface, the sculptured nature of die/mouldcavities restricts the use of a at end mill fornishing.

Nonetheless, some of the aspects on cutter path eval-uation with regards to machinability on hardened toolsteel as a mould and die material have been carriedout and detailed [5156] as a consequence.

Acknowledgements

The work was funded and supported by UniversitiesUK and University of Birmingham via the awards of anOverseas Research Scholarship and School of Manufac-turing and Mechanical Engineering Scholarship, Uni-versity of Birmingham, respectively. The author extendhis gratitude for their industrial support rendered byMr. Steve Hobbs, Delcam International plc and Mr.Alan Pearce, Miracle Engineering Europe. Furtherappreciation is extended to Mr. David Aspinwall and



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Ms. Richard Dewes for their initial proof reading of themanuscript.

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