The international journal of advanced manufacturing technology, tập 58, số 5 8, 2012

Hence, analysis mentioned above gives explanation why the service life of the die processed by biomimetic laser-remelting process was improved compared to that without being processed in

ORIGINAL ARTICLE

Performance enhancements of high-pressure die-casting die

processed by biomimetic laser-remelting process

Zhi-xin Jia&Ji-qiang Li&Li-Jun Liu&Hong Zhou

Received: 16 December 2010 / Accepted: 30 May 2011 / Published online: 9 June 2011

# Springer-Verlag London Limited 2011

Abstract Die service life improvement is an important

problem in high-pressure die-casting industry Experiment

results on die steel shows that biomimetic laser-remelting

process provides a promising method to improve the

service life of die-casting die A casting with uneven wall

thickness was selected and problems existing in die-casting

production were analyzed The corresponding die-casting

die was processed by biomimetic laser-remelting process

The application result indicates that the service life of the

die processed by biomimetic laser-remelting process has

been increased from 12,000 to 28,000 shots, which is more

than twice that of no processed one under real high-pressure

die-casting conditions The application of laser-remelting

process provides desirable micro-structural changes in

biomimetic units, which induces the intensified particles

effect for improving the service life

Keywords Die-casting die Thermal fatigue

Laser-remelting process

1 Introduction

Die casting is a high-volume production process, which

produces geometrically complex parts of nonferrous metals

with excellent surface finishes and low scrap rate The diecastings are used extensively in automobile, motorcycle,computer, and consumer electronics These die castings aregenerally produced by using two steel die halves called thecover-die half and ejector-die half separately Each of thedie halves usually contains a portion of the die cavity Theprocess sequences are: (a) die closing, (b) cavity filling, (c)casting solidification, (d) parts ejection, and (e) lubrication.The most important modes of failure in die-casting dies arethermal cracking, soldering, and corrosion

Die wear and failure is a significant issue in casting industry, owing to the high cost of dies.Nevertheless, owing to the harshness of service condition

die-of the die-casting dies, the complexity die-of thermal fatigueprocesses, and the variety of factors affecting the process,die wear and failure has been a technical difficulty indie-casting industries for many years In order to prolongthe service life of die-casting dies, many researchers havebeen engaged in the theoretical and experimental studiesrelated

Research group from The Ohio State University, USA,did a lot of work aiming at elucidating the life-limitingfailure mechanisms in the die-casting die through experi-ments and CAE analysis [1–5] Venkatesan and Shivpuri [1,

2] carried out experiments under actual production ditions for a range of process and geometrical conditionswith the accelerated erosive wear of core pins being used as

con-a surrogcon-ate mecon-asure of die erosive wecon-ar Yu et con-al gcon-ave con-astudy of corrosion of die materials and die coatings inaluminum die casting [3] They also studied effects ofmolten aluminum on H13 dies and coatings [4] Theirexperiments have shown that single-layer hard PVD andCVD coatings do not protect the die steel surface fromcracking Kulkarni et al investigated the thermal crackingbehavior on nitrided die steels in liquid aluminum process-

The Key Lab of Automobile Materials,

The Ministry of Education, Jilin University,

5988# Renmin Road,

Changchun 130025, People ’s Republic of China

DOI 10.1007/s00170-011-3420-5

ing [5] Srivastava et al developed a model to predict the

thermal fatigue cracking using FEM software[6]

Persson et al studied the simulation and evaluation of

thermal fatigue cracking of hot work tool steels [7, 8]

Domkin et al studied the soldering and did some work to

tackle the problem of die life-time prediction based on a

quantitative analysis of soldering in the framework of the

full 3D simulations of the die casting process [9] Zheng et

al established an evaluation system for the surface defect of

casting and introduced artificial neural network to

general-ize the correlation between surface defects and die-casting

parameters, such as mold temperature, pouring temperature,

and injection velocity [10] Klobcar et al analyze the

influence of aluminum alloy die-casting parameters, die

material, and die geometry on in-service tool life by

immersion testing and FEM method [11]

With the development of laser technology, laser

processing method is used to change the property of

die material Grum et al reported results of CO2 laser

repair surfacing of maraging steel with a Ni–Co–Mo alloy

similar to the maraging steel [12] After laser surfacing of

the DIN 1.2799 maraging steel a very favorable

through-depth residual-stress profile of the surfaced layer and the

heat-affected zone is obtained Compressive residual

stresses in the surface layer reduce the risk of formation

and propagation of surface cracks Such a state of stress

will considerably extend the tool life Persson et al

studied the life-limiting failure mechanisms in dies aimed

for brass die casting [13] They examined and evaluated

cavity inserts and cores with respect to failure mechanisms

after use in actual brass die casting They found that the

dominating failure mechanism in the investigated tools

was thermal fatigue cracking

In order to improve the thermal conductivity of H13

die material, some studies that have been carried out to

develop molds with higher thermal conductivity have

concentrated on mixing copper and steel Beal et al

manufacture the 3D structures from a mixture of H13

and copper powders by using a laser beam to sinter or

melt the mixture of H13/Copper powder The method

employed is based on the layer manufacturing

technol-ogy [14] Khalid et al presents a novel approach to

replace a conventional steel die by a bimetallic die made

of Moldmax copper alloy coated with a protective layer of

steel using laser cladding technology, direct metal

deposi-tion on the cavity surface for high-pressure die casting of

aluminum alloys [15]

Nature provides a whole host of superior

multifunc-tional structures that can be used as inspiramultifunc-tional systems

for the design and synthesis of new, technologically

important materials and devices Since the 1980s, Ren et

al has been dedicating to the study of the cuticle

morphologies and principles of soil animals They found

that soil animals have “nonsmooth construction units,”which provide excellent anti-wear properties against soil[16] Recent works in the research group of JilinUniversity, China, also found that a considerable effectnot only on wear resistance [17], but also on the thermalfatigue resistance [18, 19] when applied biomimeticprinciple on the die and tool surfaces to form a series ofbiomimetic units by laser Experiments were focused onthe effects of laser input energy and biomimetic unitshape Zhang et al studied the size of units andinvestigated its effect on thermal fatigue behavior of3Cr2W8V steel [19] They also studied the tensileproperty of H13 die steel with convex-shaped biomimeticsurface [20] Shan et al did some experiments on injectionmolds by mimicking the injection conditions The resultsshowed that the adhesion biomimetic molds have abeneficial effect on decreasing the adhesion to ejectpolymer parts [21]

Studies [18–20] have shown that the biomimetic surfacewith units in varying shapes and distributions has anenhanced resistance not only to the thermal fatigue crackinitiation but also to the crack propagation But so far thesestudies are merely experiment result in laboratory onspecimen with simplified geometry by mimicking the realconditions Regarding the complex-shaped casting, espe-cially the performance of die-casting die processed bybiomimetic laser-remelting process under actual productionconditions is still scarce

In this paper, a set of die-casting die made of H13 ischosen to be processed by biomimetic laser-remeltingprocess and its performance under actual productionconditions is investigated The real die-casting conditionsare supplied by our partner, Donghao Die-casting Co.,Ltd The application result shows that service life of die-casting die processed by biomimetic laser-remeltingprocess is prolonged from 12,000 to 28,000 shots Thepurpose of this study is to further reveal the effectiveness

of thermal-fatigue-resistant mechanism of the units underactual production conditions, and finally to lay afoundation for the application of biomimetic laser-remelting process in the design and manufacturing ofdie-casting dies in the future

The rest of the paper is organized as follows Section2

gives the requirements and material of the selected casting,the die-casting parameters, the main problems, and theservice life of the die in die-casting production Section3

shows the experiment parameters, method of biomimeticlaser-remelting process, and the performance of the die-casting die under actual production conditions Section 4

illustrates the microstructure of the unit Section 5

describes the application of biomimetic laser-remeltingprocess on the succeeded die-casting die Section 6givesconclusions

2 The die casting and the die-casting die

Due to the high cost of die-casting die, one die casting and

the corresponding die were selected elaborately

2.1 The characteristics of the selected aluminum die casting

The selected aluminum casting was produced by

high-pressure die casting, as shown in Fig.1, called cover, which

is used in vehicles The material of the casting is ZL102

Though the geometry of the casting is not very complex, the

dimension accuracy and the surface roughness are required

strictly The inner surface of die casting is required to keep

the original die-casting surface There are two platforms

which have flatness checking requirements The outer

surface of the casting is cleaned by shot blast and then

sprayed with black paint, as depicted in Fig.1 The average

wall thickness of the die casting is about 7 mm, which is

thicker than general castings Moreover, the wall thickness is

not even In the two-platform region, the max thickness

reaches 18 mm, which create areas of high temperatures

during solidification, the so called hot spots Furthermore,

there are sharp angles or edges near the ribs on outer surface

and platforms on inner surface, which are known to promote

or increase the risk of soldering [9] and corner cracking [6]

The strict requirements, uneven wall thickness, and corners

in small radius lead to great difficulties in die-casting

production and short service life of the die-casting die

There are two reasons for this casting is selected One is the

short service life of the die-casting die, which embarrassed our

partner very much The other is our partner produces the

casting in large quantities, about 10,000 pieces per month for

the customer, which gives the great convenience to investigate

change of the service life of die before and after being

processed by biomimetic laser-remelting process

2.2 The die-casting process parameters

The processing parameters for the selected die casting are

listed below:

Preheat temperature of the die, 200∼220°C

Temperature of the aluminum molten liquid, 660°CDie cooling temperature, 250∼300°C

Clamping force, 2,800 MPaFilling time, 6 s

Inlet temperature of circulating water, 25°COutlet temperature of circulating water, 35°COne cycle time, 55 s

2.3 The defects regions on the casting

In real die-casting production, defects on outer surface ofthe casting appear firstly on edges with small radius of theribs, as shown in the red circle in Fig.2a While defects oninner surface of the die casting are concentrated on theboundary edges of the platforms, as shown in the red lines

in Fig.2b

2.4 The service life of the die-casting die made

by conventional processThe die-casting die consists of two separate halves: the ejectordie on the“bottom” side of the casting and the cover die on the

“top” side of the casting The die halves are manufactured ofhardened H13 die steel (0.36% C, 1.09% Si, 0.32% Mn,5.12% Cr, 1.32% Mo, 0.80% V, and <0.023% P and S), which

is the most commonly used die material

The manufacturing procedures of our partner for the dieare: (1) rough milling, (2) heat treatment and quenchingoperation, (3) EDM machining, and (4) polishing to obtainlow roughness of the die surfaces

When the die was used to die-casting production, theexisting problems on die castings occurred as follows Afterabout 2,500 shots, micro-cracks on the die surfaces withsmall radius were generated, which were invisible but could

be touched with unsmooth feeling While on the castingsurface regions corresponding to micro-cracks, small poxeswere pitted, which increased the roughness of the casting.Then the two die halves were disassembled Cleaning andpolishing maintenance works were done to the die surfaces,which called regular maintenance After about 5,000 shots,the cracks on the surface of the die could be observed So

Inner surface(b)

Outer surface(a)

Fig 1 Aluminum die casting

(material brand: ZL102)

the die halves were disassembled and sent to a heat

treatment company to do tempering Then the die surfaces

were polished and the die halves were reassembled After

about 7,500 shots, a regular maintenance was done again

After 10,000 shots, the die was tempered again The wear,

cracks and soldering on the die surface were even worse,

and more manual revised work needed to be done to the

surface of die castings As the cracks propagated, then

remedy works by argon-arc welding were needed to repair

the die in order to keep the die in production, which means

that a lot of time are spent on repairing and polishing and

leads to low production efficiency At last, the die was

abandoned after 12,000 shots and a new one is needed for

production

3 Experiment method for biomimetic laser-remelting

process

3.1 Experiment equipment

Biomimetic laser-remelting process is processed on a Laser

Welding Machine, as shown in Fig.3 The laser equipment

is current-feedback fiber-optic Welder WF300, Han’s Laser

It is composed of laser generator, worktable, a set of

software system and cooling water tank The worktable is

moveable along the x and y directions, and the laser is

moveable alongz-axis

The software system provides the tools for user to obtain

a series of points on the die surfaces, then form the routeand generate the NC code Consequently, the laserequipment is controlled by user’s NC program to finishthe required route

3.2 Laser parametersThe laser parameters used for processing the die-casting dieare listed below

laser-3.3 The region determination for the biomimeticlaser-remelting process

As mentioned above in Section2.2, the die used formerly hasdemonstrated the regions where the defects are prone togeneration The cracked regions are the weakest in structure,

(a) Defect regions on outer surface (b) Defect regions on inner surface

Fig 2 The defect regions of the

Fig 3 The laser equipment

strength, and thermal resistance If such regions are to be

strengthened, the service life of the die-casting die will be

prolonged Hence, the biomimetic laser-remelting process is

carried out on the corresponding regions with the laser

parameters given in Section3.2 The two die halves processed

by the biomimetic laser-remelting process are shown in Fig.5

3.4 The application investigation of die-casting die

processed by biomimetic laser-remelting process

After the die-casting die was processed by laser-remelting

process, it was delivered to our partner We followed the die

for up to 3 months

Our partner assembled the die-casting die processed by

laser-remelting process on die-casting machine in operation

The first ten castings were checked and measured It was

found that the local thickness of the casting corresponding to

the regions on die surface processed by laser remelting

protruded out about 0.08∼0.09mm The ejector die and the

cover die were disassembled and manufactured by EDM

separately Then the processed die was in production

continuously for 18,000 shots Some unsmoothed spots

appeared on the die castings after 18,000 shots just like that

after 2,500 shots for the unprocessed die Then the die halves

were disassembled and sent to a heat treatment company to do

tempering After the die surface was cleaned and polished, it

was put into operation for further 5,000 shots (up to 2,300shots in total) Then cracks was found near the ejector pinopposite to the main runner because the ejector pin decreasedthe local wall thickness of the ejector half, as shown in Fig.6.Industrial experience reported in the past has indicated thatthe part exposed to the liquid metal attack in front of thegates exhibit the highest level washout [1] In order toremedy the cracks, the ejector pin hole was blocked andwelded by argon-arc welding Another 5,000 shots wereobtained and two big cracks were found in the weldingregion and some small cracks appeared around the smallradius regions processed by laser At last the die wasabandoned So the ultimate service life of the die processed

by biomimetic laser remelting process is 28,000 shots, which

is more than twice that of no processed one The die-castingdie after 28,000 shots is shown in Fig.7

4 Experimental details on specimen and discussion4.1 The microhardness value of the unit

As the die-casting die is expensive, prior to processing the die

by biomimetic laser-remelting process, a specimen with size of40×20×3 mm was machined by WEDM from the wastematerial in manufacturing the die halves The surface of the

The ejector half(b)

The cover half(a)

Fig 4 The die halves in

biomi-metic laser-remelting process

Ejector-die half(b)

Cover-die half(a)

Fig 5 The die-casting die after

biomimetic laser-remelting

process

specimen was polished using progressively finer grades of

silicon carbide impregnated emery paper, which is as same as

the die surface Subsequently, the specimens were processed

by the laser equipment with the parameters given in section3.2

After the laser processing, a transverse section was

obtained and the standard method of metallography was

followed to prepare the specimen for the microstructure

analysis and the microhardness measurement

The surface morphology of the specimen was put into

observation under optical microscope Figure8 shows the

cross-section appearance of the nonsmooth unit which

involves the bright field surrounded by the

parabola-shaped contour line The unit is comprised of the melting

zone and the transitional zone By the measurement, the

unit width is around 900um, while the depth is 800um

The microharness was tested on microharness tester

DHV-1000 The microharness values obtained alongx axis and y

axis were listed in Figs.9 and10, respectively We can see

the decrease from the unit hardness to the transition zone and

the substrate hardness The hardness of the unit varies from

562 to 608 HV, and the transition zone varies from 470 to

500 HV while the substrate microhardness is around 460 HV

4.2 Microstructure of the unit

The corroded cross-section microstructures of the unit by

biomimetic laser-remelting process were observed by

scanning electron microscope, as shown in Fig 11(modelHITACHI S-4800, Japan)

Compared with the substrate microstructure, the unitstructure is refined greatly, as shown in Fig.11 Under thecondition of the laser super fast heating, the larger degree ofoverheating was generated to cause the effective drivingforce of phase transformation, which contributed to thelarge number of the austenite nucleation, Because of thesuper fast heating, there was little time for austenite grain togrow up, finally the refinement of grains and alteration ofmicrostructure were induced During the subsequent mar-tensitic transformation, the tiny martensitic structure wasformed According to Zhou [12], everything happened inboth the super fast heating and cooling induced theformation of tiny martensitic structure, which contributedeffectively to high hardness and strength In the transitionarea, dentrite structure was formed

4.3 Discussion on the enhancement of resistance to crackfor the die surface with laser remelting unit

The cracking phenomenon can be divided into two stages[5]: (1) crack initiation: during the first few cycles, highthermal gradient can result in shock, causing crackinitiation (2) crack propagation: once the crack hasinitiated, the propagation depends entirely on the tough-ness of the substrate and the thermal stresses imposed

(a)The die half after 2,3000 shots (b) Die casting

Fig 6 The die half after 23,000

shots and the die casting

(a) Cover-die half (b) Ejector-die half

Fig 7 The die-casting die after

28,000 shots

After a number of thermal cycles, the die becomes so soft

that the applied thermal stresses are enough to cause

plastic deformation The plastic strains keep on

accumu-lating, resulting in low-cycle fatigue cracking

According to former works by Zhou [18] and Zhang

[19], when applied laser-remelting process on the die steel

surface, there had a considerable effect not only on

improving the wear resistance and decreasing the adhesion

against parts, but also on inhibiting the initiation and

propagation of thermal fatigue crack

The refinement of the grains and martensitic high

dislocation density were the primary factors enhancing the

hardness of the units processed by laser When the thermal

fatigue crack met the units, account for the high hardness in

the units, the cracks could not drill through and finally

stopped near the units This means that the crack

develop-ment has been subjected to large obstacles, which forced

the cracks to change the direction Moreover, the crack

propagation was prolonged, which decreases the rate of

crack propagation

Hence, analysis mentioned above gives explanation why

the service life of the die processed by biomimetic

laser-remelting process was improved compared to that without

being processed in real pressure die-casting condition

5 The succeeded die-casting die processed by biomimeticlaser-remelting process

As the first die-casting processed by biomimetic remelting process achieved good results The succeededdie-casting die made by H13 was processed again with thesame laser parameters as the former one However,considering the sinkage of the region processed bybiomimetic laser-remelting process, some adjustments weremade in the manufacturing of the die

laser-The manufacturing procedures of the second die are:(1) rough milling, (2) heat treatment and quenchingoperation, (3) roughing EDM machining with allowance

of 0.2mm, (4) biomimetic laser-remelting process tion, (5) finishing EDM machining with removal of0.2 mm, and (6) polishing to obtain low roughness of thedie surfaces So the biomimetic laser-remelting processcan be treated as one step in die making Figure 12

opera-shows the second die-casting die processed by biomimeticlaser-remelting process

The service life of the second die-casting die cessed by biomimetic laser-remelting process is 29,000shots, which also demonstrated the effectiveness of theprocess

pro-6 Conclusions

1 The service life of high-pressure die-casting dies can beimproved substantially by biomimetic laser-remeltingprocess

2 The units of H13 steel processed by laser-remeltingprocess have beneficial effects on inhibiting the thermalfatigue crack initiation and propagation The biomimetic

1.75 1.5 1.25 1 0.75 0.5 0.25

0

460.5 480.7

586.4 557.7 564.8 562.1

497.2 494.9

Fig 8 Profile of the unit on the cross section of the specimen

486 475.3

471.6 458.7

0 100 200 300 400 500 600 700

Distance along y axis (mm)

Fig 10 The microhardness value of the cell along y direction

die-casting die surface possesses superior resistance to

thermal fatigue compared to that without being processed

So the die-casting die obtains a longer service life

3 The biomimetic laser-remelting process provides apromising way to enhance the performance of die-casting die

)b()

a(

)d()

c(

)()

e(

Transition Area

Transition Area

Fig 11 SEM microstructure at

higher magnification near the

area of the unit a, b The

microstructure near the area of

the unit c The microstructure of

transition area d–f The

micro-structure of the unit

Fig 12 The second die-casting

die processed by biomimetic

laser-remelting process

4 Though the result of our experiment under real

die-casting condition shows a bright way to resist the crack,

a lot of research works are still needed to reveal the

efficiency of the biomimetic laser-remelting process

further For castings with the intricate shape, how to

determine and evaluate the layout of the regions for

laser remelting are our future works

Acknowledgments This research was supported by the Ningbo

Natural Science Foundation (no 2011A610149) and Zhejiang Natural

Science Foundation (no Y1100073) The authors wish to thank WH

Yang and YB Zhang from Ningbo Donghao Die-casting Co., Ltd for

their valuable suggestions and contribution to this research work.

References

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Exposition, USA

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4:175–181

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non-ORIGINAL ARTICLE

Implications of the reduction of cutting fluid in drilling AISI

P20 steel with carbide tools

Rodrigo P Zeilmann&Gerson L Nicola&Tiago Vacaro&

Cleiton R Teixeira&Roland Heiler

Received: 17 January 2011 / Accepted: 19 May 2011 / Published online: 3 June 2011

# Springer-Verlag London Limited 2011

Abstract The machining of hardened steel is becoming

increasingly important in manufacturing processes Machined

parts made with hardened steel are often subjected to high

service demands, which require great resistance and quality

The machining of this material submits the tools to high

mechanical and thermal loads, which increases the tool wear

and affects the surface integrity of the part In that context, this

work presents a study of drilling of AISI P20 steel with

carbide tools, analyzing the effects on the process caused by

the reduction of cutting fluid supply and its relation with the

tool wear and the surface integrity of the piece The major

problem observed in the tests was a difficulty for chips to flow

through the drill flute, compromising their expulsion from the

hole After a careful analysis, a different machining strategy

was adopted to solve the problem

Keywords Machining Drilling process Cutting tools

Wear Surface analysis

1 IntroductionThe machining of hardened steel is a topic of great interestfor industrial production and scientific research Somemachine components are made of hardened steel materialsand are required to function near their physical limits.Recent developments in machine tools as well as in processtechnology focus on cutting hardened steel and rapidly lead

to an increased awareness of the industrial relevance ofhard cutting [1] One major problem of machining hardenedsteels is the tool wear caused by the hardness of thematerial [2] Although hard machining avoids the shape andgeometrical errors that could occur on a workpiece whensubjected to heat treatment after machining and reduces therework, it increases the thermal loads on the tool

The heat generation and friction between tool and chipusually limit machining performance in metal-cuttingoperations [3] Cutting fluids are customarily used tocontrol the temperature in the cutting zone However, theuse of cutting fluids in machining processes has beenquestioned, due to some adverse effects which they cause.Prolonged contact of machine operators with cutting fluidsmay cause skin and respiratory diseases Improper disposal

of cutting fluids results in ground, water, and air pollution

In addition, the costs related to cutting fluids are higherthan those related to labor and overhead Thus, environ-mental and resource problems are forcing industry toimplement strategies to reduce the use of cutting fluids intheir production activities [4] With this purpose, somealternatives have been sought to minimize or even avoid theuse of cutting fluid in machining operations Two of thesealternatives are dry machining and machining with theminimum quantity of lubrication (MQL) [5,6] Among theprocesses in which these techniques are being applied isdrilling

R P Zeilmann ( *):G L Nicola:T Vacaro

Center of Exact Sciences and Technology,

University of Caxias do Sul (UCS),

1130, Francisco Getúlio Vargas,

95070–560, Caxias do Sul, Brazil

e-mail: rpzeilma@ucs.br

C R Teixeira

Federal University of Rio Grande (FURG),

Rio Grande, Brazil

R Heiler

Hochschule für Technik und Wirtschaft (HTW),

Berlin, Germany

DOI 10.1007/s00170-011-3401-8

Drilling is one of the most demanding machining

processes because a completely machined geometry and

surface are generated in one operation and usually

postmachining is impossible The demands in regard to

diameter precision, straightness, and surface quality are

enormously high Tools must meet the requirements for

diameter tolerances and shape–position tolerances [7] In

dry drilling, tool failure is a significant factor affecting

productivity and manufacturing efficiency Hence, one of

the main objectives of cutting research is the assessment of

tool wear and increasing tool life [8]

Beyond tool wear, the surface quality of the machined

components plays a key role The ability of a material to

withstand severe conditions of stress, temperature, and

corrosion depends on the quality of the surface generated

during machining, which consequently determines the

longevity and reliability of products made of these

materials The machined surface quality can be defined by

two measures: surface topography and subsurface integrity

The surface topography can be measured using standard

surface roughness measurement equipment, whereas the

measurement of subsurface integrity is a complex task [9]

In a technology transfer from conventional machining

with abundant lubricant to dry machining or with MQL, the

thermal behavior tends to be more pronounced Several

studies [10–14] present results which show the tendency

for a higher maintenance of the elevated temperatures in the

cutting zone when dry machining is applied These studies

also indicate the tendency of lower temperatures using

abundant fluid and intermediate temperatures applying

MQL

Previous works have shown good results for reducing or

removing the cutting fluids in drilling processes Rahim and

Sasahara [12] conducted drilling experiments under different

cooling and lubrication conditions such as air blow,

vegetable and synthetic MQL, and flood They used

coated (TiAlN) carbide drills in the drilling of titanium

alloy Ti-6Al-4 V The researchers found that MQL gave

comparable performance with the flood condition Bhowmick

et al [10] also reported similar performance between MQL

and flooded drilling in the machining of cast magnesium

alloy AM60 using HSS drills They used mineral oil in flood

condition, and two types of MQL fluids, distilled water and a

fatty acid-based Heinemann et al [15] demonstrated the

effect of MQL on the tool life of coated and uncoated HSS

twist drills They performed deep-hole drilling experiments

in plain carbon steel and found that a low viscous MQL oil

with a high cooling capability gave rise to a notably

prolonged tool life Bhowmick and Alpas [16] studied the

performance of diamond-like carbon (DLC)-coated HSS

drills under MQL condition in the machining of an Al–6%

Si (319 Al) alloy Results were compared with drilling using

conventional flooded coolant They applied two types of

DLCs (nonhydrogenated and hydrogenated) and distilledwater as the MQL agent The MQL cutting using either type

of DLC coating reduced the drilling torque compared to drydrilling to a level similar to the performance under theflooded condition Tasdelen et al [3] made drilling experi-ments with MQL at different oil amounts, dry compressedair, and emulsion The holes with 33-mm depth and 19-mmdiameter were drilled with 155 m min−1cutting speed and0.11 mm rev−1using indexable inserts The tests showed thatMQL and compressed air usage have resulted in lower wearboth on the center and periphery insert compared to drillingwith emulsion

It is well established that the main problems in drillingwhen the cutting fluid supply is reduced or removed are thehigher maintenance of elevated temperatures in the cuttingzone and the difficulty for removing the chips from the hole[6, 17–19] This second aspect is especially critical fordrilling, since the cutting process is involved by thematerial of the piece When the chip flow is compromised,

it leads to packing and clogging of the chip and can causethe collapse of the tool [20–23] It is also known that theseproblems are caused by the loss of the primary functions ofthe cutting fluids, which are lubrication, cooling, andtransport of chips [6,18,19] However, it is not clear whatare the changes in the interface tool/piece/chip due to theloss of these functions and how they affect the tool wearand the quality of the machined surface Therefore, in view

of the complexity and extent of difficulties and differentconditions in this type of change process, this work presents

a study of drilling of AISI P20 steel with carbide tools, withdifferent conditions for the application of cutting fluid Themain goal was to evaluate the effects on the process caused

by the reduction of the cutting fluid supply and its relationwith the tool wear and the surface integrity of the piece

2 Experiments2.1 WorkpieceThe workpieces were prepared with AISI P20 steel andwere hardened by heat treatment to obtain a final hardnessbetween 36 and 38 HRc This steel is frequently used in themanufacture of molds and die cavities The chemicalcomposition is given in Table 1

The workpiece dimensions were 250×80×60 mm Thedistance between holes was 1.5 times the diameter of theTable 1 Chemical composition of AISI P20 steel (% wt., ASTM)

0.35 –0.45 0.20–0.40 1.30–1.60 1.80–2.10 0.15–0.25 0.90–1.20

tool In the dry tests, a drilling sequence was used with a

distance between holes equal to three times the diameter of

the tool using, however, two such cycles to complete the

workpiece Thus, at the end of the second cycle, the same

distance between holes of 1.5 times the diameter of the tool

was obtained This strategy was applied in the dry tests to

avoid thermal influences that could compromise the results

of the experiment

2.2 Tools

The tools used in the experiments were coated carbide

drills, DIN 6537 K, provided by Walter AG Company The

diameter of the tools is 8.5 mm and they are coated with

TiAlN For the dry tests, some drill flutes were polished

with an abrasive cloth to obtain a smoother flute surface

and improve the chip flow Figure1shows the standard tool

used in the experiments

2.3 Equipment

The experiments were performed on an Okuma Ace Center

MB-46 VAE Vertical Machining Center, with maximum

rotation of 15,000 rpm and power of 18.5 kW A Universal

stereoscope was used in wear analysis and measurements

The same equipment was used for an optical analysis of the

texture of the machined surfaces The surface roughness,

Ra, parameter, was measured using a Taylor Hobbson 3+

surface roughness tester To analyze the microstructures and

to measure the depth of plastic deformations, a Nikon

Optical Microscope Epiphot 200 was used Microhardness

tests were carried out with a Shimadzu HMV-2

microhard-ness tester to determine if there was any metallurgical

alteration in the subsurface region of the machined material

2.4 Experimental procedures

The cutting parameters used in tests were a cutting speed of

50 m min and a feed of 0.1 mm The hole depth used was

three times the diameter of the tool (25.5 mm) The tests

were carried out for three different quantities of cutting

fluids: (1) the application of fluid in abundance, (2) the

MQL, and (3) a total absence of fluid For the emulsion, a

pressure of 3 bars was applied with a flow rate of 1,800 l

h−1 The oil used was Vasco 1000, in a concentration of

10% In the MQL condition, the same pressure of 3 barswas used with flow rate of 10 ml h−1 The MQL oil usedwas VASCOMILL MMS SE 1 Both oils were provided byBlaser Swisslube of Brazil

The flow rate applied in MQL tests is the default value ofthe machine used in the experiments Some of the first worksdealing with MQL [24,25] used to apply higher flow rates,

up to 300 ml h−1, but several studies showed that lowervalues tend to present similar performance Bhowmick et al.[10] analyzed the average torque responses when MQLfluids were supplied at the rates of 10, 20, and 30 ml h−1,and they did not find significant difference Braga et al [26]found similar results for tool wear using 10, 30, and 60 ml

h−1of oil Therefore, the flow rate of 10 ml h−1was fixed inthis work

Figure 2 shows the MQL system coupled to themachining center and also details of the nozzle positionregarding the tool

The quality surface analysis made in the holes wascarried out near the beginning of the hole and near thebottom of the hole The roughness measurements weremade at three equidistant points for each depth (initial andfinal regions) Figure 3 shows the analysis depths andillustrates the roughness measurement positions

Three repetitions were made for each condition of fluidapplication in order to get a satisfactory result The end oftool life criterion adopted was a maximum flank wear(VBmáx.) of 0.2 mm or the occurrence of chipping The testswere interrupted after 1,200 holes, even if the tool did notreach the end of life criterion

For the application of fluid in abundance, the strategy ofcontinuous drilling was adopted And for the MQL and dryconditions, a pecking cycle was used, with an advance of1.5 mm followed by retreat out of the hole This procedurewas used to facilitate the expulsion of the chip from thehole and to avoid crushing the chips and clogging the drill

3 Results and discussion3.1 Wear

The cutting parameters used in the tests were determinedthrough the analysis of cutting performance during prelim-inary experiments In these tests, no cutting fluid was

Type: carbide drill ALPHA 2

Standard: DIN 6537KDiameter: 8.5 mm Coating: TiAlN

applied, increasing the process severity, to facilitate the

occurrence and observation of problems

One of the main problems in dry drilling is the removal

of chips from the hole This problem was observed in

continuous drilling using the cutting parameters vc=40 m

min−1,f=0.10 mm, when the maximum number of drilled

holes obtained was 129 In this condition, chip flow was

difficult and obstruction of the drill flute occurred, as seen

in Fig 4a Also, microchippings were observed in the

margins and the consequent chip removal from the flute

through the margin and land, as seen in Fig 4b The

combination of these problems compromised the chip flow,

causing the obstruction of the flutes and led to tool

breakage

To improve chip flow, the drill flute of some tools was

polished with an abrasive cloth to obtain a smoother surface

and, in this way, to facilitate the expulsion of the chip

However, better results were not obtained and againmicrochipping occurred in the margins, as seen in Fig 5

An attempt to solve the microchipping at the marginswas made, maintaining the same values of cutting speedand feed, but adopting a pecking cycle, with an advance of1.5 mm without retreat out of the hole The intent with thisstrategy was to improve the chip breakage and thereforeenhance the chip flow But again, good results were notobtained The drill presented high adhesion of material inthe flute and in the margin, and a high packing factor(clogging of the drill by the chips) was observed Figure6

illustrates this condition

Therefore, a more detailed analysis of the chip formationwas necessary For this purpose, chip samples wereprepared for metallographic analysis Chips adhering tothe drill flutes were removed and mounted in order toanalyze their transverse section This process started fromthe chip region near the top of the drill, and the analyzeddepth increased successively by 1 mm after each analysis.Between 3 and 6 mm from the top, a higher packing factorwas observed This region is the same as that where themicrochipping of the margins occurred Figure 7a showsschematically the mechanics of cutting and shear zones, for

a better understanding of the results presented in Fig 7b,which shows the transverse section of the chip on the depth

of 3 mm below the top of the drill

Figure7b shows the disordered packing of the chip andmicrowelding points as well as the different regions(smoothed and sheared) resulting from chip formation.After severe machining, the material removed can presentseveral metallurgical alterations such as a high plasticdeformation, a hardness increase, or a white layer forma-tion The sheared region resulted from the primary shear

zone on cutting and, therefore, is submitted to severe strain

hardening The smooth region corresponds to the secondary

shear zone, and the material is submitted to high

compres-sion and attrition against the tool face Under severe

conditions of pressure and temperature, this region can

develop the so-called white layer, characterized by high

plastic deformation and high hardness Thus, smooth and

sheared regions present metallurgical alterations that tend to

increase the resultant hardness [28] And this increase in

hardness of the chip makes it more difficult to flow through

the flutes on its way to removal from the hole

The smooth and sheared regions, by having a high

mechanical strength and due to the forces generated by

compression and mechanical wear, tend to increase the heat

generation Thus, the three necessary conditions for the

formation of a white layer on the chip are present:

compression, friction, and high temperature [29] The

friction of the regions of high hardness with the hole wall

creates difficulty for disposing of the chip, resulting in a

volume increase, which compromises the chip flow out of

the hole The chip accumulation causes the obstruction of

the flutes and the consequent tool breakage

However, although this analysis has shown the

occur-rence of high compression and friction loads on the chip, it

did not explain the cause of these problems Then, a

complementary analysis was made with a broken drill

inside a hole An external cylinder of material involving the

hole with the tool and chip was removed from the

workpiece This cylinder was prepared for optical and

metallographic analyses with a special cold cure resin thatenabled transverse cuts of the cylinder in 2-mm-thicklayers, maintaining the position of the tool and the chipinside the hole (see below) The aim of this analysis was toevaluate the chip formation and the interface tool/chip/pieceand to investigate the cause of the elevated packing factor

of the chip Figure8illustrates the procedure and shows thetop surface of the layer cut from approximately 1.5 mmbelow the top of the tool

The layers were carefully analyzed and an unexpectedcutting behavior was observed Figure8shows that the chiphas been cut by the margin, but these tool elements are notdesigned for cutting The hypothesis raised for this casewas that the wear of the drill corners would lead to areduction of the tool diameter between the corners, and thusthe diameter between the margins would be larger and thecutting of the material would be made by the margins Thisdifference between the diameters makes the margins theprimary cutting surfaces of the drill and implies a change inthe shear planes regarding the feed axis, transferring theprimary shear plane, shown in Fig.7a, to the margin Thischange makes the chip flow toward the hole wall, instead offollowing the helical path along the flute This results inintense friction with the hole wall and elevated compressionloads on the chip, giving rise to the observed high packingfactor of the chip and the microchippings in the margins.These results explain the lower results for tool life in drycontinuous drilling experiments Based on these analyses, itwas decided to change the drilling strategy in order to

Fig 4 Flute obstruction (a) and

microchipping in the margin (b)

0.75 mm

Substrate Adhesion

Internal view margin/flute

b

1 mm

85 holes

Fig 5 Microchipping in the

margin, external (a) and internal

(b) view

facilitate the expulsion of the chips from the hole.

Therefore, it was adopted as the pecking cycle with an

advance of 1.5 mm followed by a retreat out of the hole

The retreat improved the chip expulsion from the hole, and

in this way, the microchippings at the margins no longer

occurred However, this strategy increased the drilling time

by about 150% To compensate part of this loss of

productivity, tests were made with the cutting speed of

50 m min−1, which showed similar results to those obtained

with 40 m min−1 Thus, for the main experiment, the

cutting speed of 50 m min−1was adopted, and the pecking

cycle for MQL and dry conditions was used For processing

with the emulsion, the tests were performed by continuous

drilling in order to attain lower cutting times With these

definitions, the main experiment was carried out, and the

results are presented below Figure 9 presents the wear

results from the experiments withvc=50 m min−1

Drilling with the emulsion gave the worst result and the

tools made 933 holes on average For MQL tests, all three

tools made 1,200 holes, but only one reached the end of

tool life For the other two, the test was interrupted by the

criterion of 1,200 holes drilled The dry drilling

experi-ments presented the best results, because all tests were

interrupted by the 1,200 holes criterion

The worst results for the emulsion tests can be explained

by the cooling of the machined material The presence ofthe cutting fluid removes the positive effect of the heat inthe cutting zone, which facilitates the material shear (lowerresistance to cutting) That way, the cooled materialpresents greater strength, increasing the mechanical loads

on the tool and, consequently, the tool wear In the emulsiontests, also a high adhesion of material on the flank of thetools was observed, which leads to microchipping and toolfailure Figure 10 shows the material adhesion and theconsequent microchipping

The tools machined under MQL conditions also sented material adhesion on the flanks, but in lesserquantities than observed for the emulsion condition Indry tests, it was observed that although material adhesionhad occurred on tool flanks, when this material detachedfrom the flank, it did not cause significant microchipping aswas observed in the emulsion and MQL experiments.3.2 Surface quality

pre-The quality of machined components is currently of highinterest, for the market demands mechanical components ofincreasingly high performance, not only from the stand-

b a

3 holes

Fig 6 High packing factor (a)

and material adhesion (b)

Secondary shear zone

Primary shear zone

Micro-welding

Smooth region

Sheared region

Fig 7 Shear planes [ 27 ] (a) and the transverse section of the chip distant approximately 3 mm from chip region near the top of the drill (b)

point of functionality but also from that of safety.

Components are produced through operations involving

the removal of material display surface irregularities

resulting not only from the action of the tool itself but

also from other factors that contribute to their superficial

texture such as cutting speed, tool wear, feed, tool

materials, tool geometry, etc This texture can exert a

decisive influence on the application and performance of

the machined component [30,31]

With the aim of facilitating the comparisons, in the

surface quality analysis made for this experiment, one

representative tool was selected and tested for each

condition of fluid application that made 1,200 holes without

attaining the end of tool life criterion Figure11shows the

values of roughness,Ra, measured near the beginning and

the bottom of the holes, for each drilling condition

Near the beginning of the holes, the dry tests gave the

highest roughness values, while the lowest values were

measured in holes machined with MQL The elimination of

cutting fluid tends to worsen the quality of the surface due

to the larger friction forces and the increased detachment of

material particle adhesions that are released from the tool

[32] For the emulsion condition, the fluid reaches the

initial region of the hole, providing good cooling and

lubrication, and for MQL condition, with the employment

of the pecking cycle, the edge receives a microlubrication

after each retreat, which reduces the attrition and produceslower roughness results However, after about 1,000 holes,the results of all lubricant conditions tend to convergetoward similar values The friction caused by dry drilling isreduced while producing the holes due to the adjustments

of the cutting edge, decreasing the roughness in themachined surface

The MQL conditions also resulted in the lowestroughness values in the analysis made near the bottom ofthe holes However, for this analysis condition, theemulsion tests presented a tendency toward larger rough-ness values, because the emulsion condition keeps theoriginal cutting edge geometry for a greater time, causingthe increased roughness But after approximately 1,000holes, the same tendency to similar values for all conditions

is observed, as it was in the previous analysis Texture andmicrohardness analyses made near the bottom of the holesshowed, especially for dry condition, the occurrence ofmicrowelding of the chip on the surface, which can becaused by elevated temperatures during machining resultantfrom the worn cutting edge A worn cutting edge has itsgeometry changed, which reduces its cutting ability,hindering the shear of the material With that, due tofriction and the high temperatures generated in the process,parts of the removed material are welded onto the surface,providing a smooth aspect, which reduces the values of

v c = 50 m/min f = 0.1 mm

Continuous drilling

Pecking cycle

Pecking cycle

Fig 9 Picture of the drilling

process (a) and wear results

expressed in terms of the

number of holes drilled (b)

roughness [33] Figure12shows the surface texture of the

first and last holes for the different fluid application

conditions

For drilling with the emulsion, the marks of the passage

of the cutting edge can be seen, and in the first hole, there

are deeper grooves which result in greater roughness values

than in the last hole The holes drilled with MQL presented

a more homogeneous texture along the holes, especially in

the last hole For the MQL condition, the microlubrication

associated with the facilitated material shear due to the

temperature increase in the cutting zone reduces the cutting

forces and allows the formation of a smooth surface The

holes obtained by dry drilling presented the worst visual

aspect, with evidence of material adhesion along the holes

and a smoothed surface in the final region of the holes,

probably due to the occurrence of microwelding

To complement this analysis, Fig 13 illustrates the

surface texture of the region near the bottom of the 1,200th

hole with a larger zoom and also shows the average value

of the microhardness measured on the surface of the hole

for each condition The measured values are approximately

twice as large as the bulk material hardness, 390 HV on

average These results corroborate the hypothesis of the

occurrence of microwelding, since the welded chip tends to

be submitted to high thermal and mechanical loads, which

can lead to the microhardening of the chip

As mentioned previously, none of the tools analyzed forsurface quality attained the end of life criterion, and thetests were interrupted after 1,200 holes drilled by each tool.However, wear analysis showed the maximum flank wear

to be 0.15 mm for the tool used in the emulsion condition,0.08 mm for the tool used under dry conditions, and0.06 mm for the tool used in the MQL condition.Considering that the tool has a cutting edge radius of0.05 mm, it can be stated that these wear values have asignificant influence on the surface changes

Beyond the surface region of the holes, the metallurgicalalterations in the surface integrity were also studied.Surface quality influences characteristics such as fatiguestrength, wear rate, corrosion resistance, etc The fatiguelife of a machined part depends strongly on its surfacecondition It has long been recognized that fatigue cracksgenerally initiate from free surfaces This is due to the factthat surface layers experience the highest load and areexposed to environmental effects Crack initiation andpropagation, in most cases, can be attributed to surfacedefects produced by machining The surface of a part hastwo important aspects that must be defined and controlled.The first aspect involves the geometric irregularities on thesurface, while the second aspect involves metallurgicalalterations of the surface and the subsurface layer The latterhas been termed surface integrity [34]

Emulsion Drill after 800 holes

Emulsion Drill after 1000 holes

Fig 10 Flank images with

material adhesion (a) and

0.0 0.5 1.0 1.5 2.0 2.5 3.0

Surface integrity analysis has great importance for

surface quality characterization, due to its direct relation

with the performance of the machined component This

characterization of the integrity can be performed by the

evaluation of the alterations of the structure under the

surface, as measurements of plastic deformations,

micro-hardness, among others Plastic deformations consist in the

deformation and change of orientation of the grains near the

surface of the material after the cutting The measured

values correspond to the vertical distance from the surface

to the point in the microstructure without visible alterations

Figure14presents the values of the plastic deformation

measured near the beginning and the bottom of the first and

last machined holes Each value plotted in the graphs is theaverage value of the five maximum plastic deformationsfound in the analyzed region The figure also showsmetallographic images of the last hole surface for thedifferent conditions tested

For both analyzed regions (near the beginning and nearthe bottom), the measured deformation values were largerwith the increase in the number of drilled holes due to thechanged cutting edge geometry; this tends to increase thetemperature in the cutting zone and, in turn, leads to theoccurrence of higher deformations It can also be observedthat the measurements made near the bottom tend to begreater than those made near the beginning of the holes

Emulsion

Hole 1 Hole 1200

Dry MQL

Hole 1 Hole 1200 Hole 1 Hole 1200

2 mm Dry

Region near the bottom of the 1200th hole

Fig 13 Surface texture in the

region near the bottom of the

last holes

This can be related to the greater difficulty of chip removal

from the hole in the final region, increasing the contact

between the chip and the piece, which causes the increase of

heat generation and consequently higher deformation values

Also, for the beginning and final regions, the dry tests

resulted in greater plastic deformation, due to the process

severity, because, as stated by the literature, this condition is

characterized by higher maintenance of elevated

temper-atures in the cutting zone [6,17–19] Near the beginning of

the holes, emulsion and MQL results were very similar,

while near the bottom of the holes, the emulsion

deforma-tion results were larger This difference is explained by the

cutting strategy adopted for each condition In the initial

region, the fluid can reach the cutting zone for both

conditions However, in the final region, the continuous

drilling employed in emulsion test impeded fluid access to

the cutting zone, while in the MQL test, with the

employment of the pecking cycle strategy, the edge receives

a microlubrication after each retreat, which reduces the

temperatures generated in cutting and results in lower

deformations values

To complement the subsurface analysis, microhardness

measurements were performed Because of equipment

limitations, the first possible distance for measurement is

0.02 mm from the machined surface As seen in Fig 15,

which presents the microhardness measurements made near

the beginning and the bottom of the last machined hole for

the different fluid application conditions, the measured

results presented a normal dispersion around the bulkmaterial hardness, and no significant trend was observed

4 ConclusionsThe preliminary tests for the dry condition with continuousdrilling presented great difficulty for chip flow through thedrill flutes, generating a high chip-packing factor Theseconditions led to obstruction of the flutes and theconsequent tool breakage After an analysis of the chipformation, it was concluded that the cutting was being done

by the margins, instead of the principal edges, whichchanged the shear planes regarding the feed axis, andcompromised the chip flow along the flutes To resolve thisproblem, the pecking cycle was adopted, with a periodicretreat out of the hole This strategy improved the chip flowand stopped the tool breakages Thus, the main experimentwas performed with continuous drilling for emulsion testsand with the pecking cycle for MQL and dry tests.The surface quality analysis showed that, near thebeginning and the bottom of the holes, the dry drillingcondition generated greater values of the roughness on themachined surface due to the higher friction on the interfacetool/chip/workpiece caused by the absence of the coolantand lubricant functions performed by the cutting fluid TheMQL application condition resulted in the lowest roughnessvalues in both analyzed regions of the holes Near the

Region near the beginning of the hole

1200th

hole

Region near the bottom of the hole

EmulsionMQLDry

Average plastic deformation [

0 20 40 60 80 100 120

Emulsion MQL Dry Bulk material hardness

340 380 420 460

0 20 40 60 80 100 120

Region near the bottom

of the 1200th hole

Distance from the surface [µm] Distance from the surface [µm]

Fig 15 Surface microhardness

versus the distance from

machined surface

beginning of the holes, differently from what occurred in the

region near the bottom, the emulsion tests presented a

tendency toward higher values of roughness, because

emul-sion keeps the original cutting edge geometry for longer times

and also cools the machined material, keeping its shear

strength high and causing well-defined grooves due to the

passage of the tool and the consequent greater roughness

The microhardness measurements on the surface of the last

holes, in the region near the bottom, resulted in values

approximately twice as large as the bulk material hardness,

which corroborates the hypothesis of the occurrence of

microwelding, because applying high thermal and mechanical

loads to the welded chip causes microhardening of the chip

Acknowledgments The authors would like to thank Walter A.G.

Company, Blaser Swisslube do Brasil, and Okuma Latino Americana

Comércio They also wish to thank Prof Frank P Missell for useful

discussions This work was supported by the Brazilian agency CNPq.

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ORIGINAL ARTICLE

Virtual workpiece: workpiece representation for material

removal process

Seok Won Lee&Andreas Nestler

Received: 8 September 2010 / Accepted: 20 February 2011 / Published online: 5 October 2011

# Springer-Verlag London Limited 2011

Abstract In this paper, an efficient methodology to

generate a virtual workpiece (VWP) is presented VWP is

a workpiece in a virtual environment in which the

geometric, kinematic, and thermo-mechanical effects of

the process and resources can be reflected VWP

encom-passes not only the macro-information corresponding to the

shape of the“virtually” machined intermediate workpiece,

but also the micro-information, such as the surface

roughness, scallop heights, chatter mark, etc To represent

VWP, swept volume (SV) of geometrically defined cutters

is generated first by envelope profiles which are calculated

by the intersection of the Tool map with the Contact map of

the tool moving direction Then SV is tessellated to conduct

elementary 1D Boolean subtraction of SVs from the IPW

The Boolean subtraction is realized by means of an efficient

ray-triangle intersection test using Barycentric coordinates

Finally, VWP is reconstructed as a triangular mesh (STL,

stereolithography data format) from the orthogonal

triple-dexel model (TDM) which predicts machined surface

quality, such as surface roughness, gouging and sharp

edges and is reused for further operations, e.g., tool path

generation, simulation and geometric metrology, etc To

demonstrate the validity of VWP modeling, several material

removal processes, e.g., milling and micro-EDM

opera-tions, have been tested and the proposed approach has been

proven to be applicable to enhance the quality of NC

simulation and verification

Keywords Virtual workpiece Material removal Machining simulation Volume updating Five-axismachining

1 Introduction

A numerical control (NC) milling removes metal or othermaterial out of a stock by moving a cutting toolintermediate space Because the NC programs, whichcontain the control commands of the machine, are usuallynot always error-free and time to market is getting shorter

in modern production cycles, verification of millingoperations plays a crucial role in manufacturing processes[1] Since the cutting simulation is the material removalprocess with a geometrically defined cutting tool, which isequivalent to the Boolean subtraction of cutter volumesfrom raw stock It is essential to continually subtract theexact swept volume(SV) of tool from the raw stock in thevirtual environment in order to predict final shape asrealistically as possible Performance of the Booleansubtraction depends on execution time, accuracy, and thestorage (memory) needs There have been many attempts toverify material removal processes such as milling prior toreal machining and, as a result, many representationschemes of the workpiece model exist For instance, thereare workpiece models based on CSG, Z-map, dexel, voxel,NURBS and vector representation, etc Hereafter, theworkpiece representation methods applied for the purpose

of the milling simulation are presented

Z-map representation [2, 3] is the most prevailingmethod because of its simplicity and robustness, but it isimpossible to simulate the machining of the undercutgeometry, such as overhang shape To overcome the

S W Lee (*):A Nestler

Institute of Forming and Cutting Manufacturing Technology,

Dresden University of Technology,

01062 Dresden, Germany

e-mail: swlee@mciron.mw.tu-dresden.de

DOI 10.1007/s00170-011-3431-2

shortage of Z-map representation, Jerard et al [4] uses the

discrete vector model (DVM; or lawnmower method) that

is represented by the surface normal vectors at discrete

surface points In this model, if the cutting tool moves near

to the part surface, the vector is shortened, which

corresponds to the material cutting DVM is efficient for

the finishing operation where the finishing allowance is

removed from the design surface so that error assessment is

possible However, it is inadequate for roughing operations

where an intermediate workpiece is to be calculated Van

Hook [5] extends the Z-map representation to accomplish a

five-axis milling simulation Each dexel or depth element is

defined as a rectangular solid extending along the Z-axis

and consists of a near and far Z depth, a color, and a pointer

to the next dexel A dexel has the Z value of the farthest

surface as well as that of the nearest one and is linked with

the neighboring one This difference makes it possible to

visualize the undercutting during five-axis machining in

image space The dexel algorithm can be implemented in

read, write, comparison, and conditional branches without

geometrical complex computations Hence, it is fast and

robust so that it has been widely adopted in a lot of

simulation software [6,7] Huang and Oliver [8] develop an

NC milling verification system by extending the

aforemen-tioned dexel approach, which enables the interactive

visualization of milling simulation and modification of

five-axis milling tool paths by means of an assessment of

dimension errors

Voxel representation [9, 10] has advantages over other

representations in that the Boolean set operations are

conducted at the level of primitive volumetric element or

voxel, and so it reduces the computational complexity of

regular Boolean set operations Karunakaran and Shringi

[11] implement a solid model-based volumetric NC

simulation system using octree representation, which is an

adaptive version of the voxel representation and subdivides

the space into eight parts recursively to simulate cutting

process and optimize the cutting parameters

Benouamer and Michelucci [12] advocate a

multi-dexel model (MDM), which consists of three conventional

dexel models orthogonal to each other, and the marching

cubes (MC) algorithm to implement an NC milling

simulation module [13] Each dexel contains the entering

and exit hit (real value), material IN/OUT information

(binary value) and, if any, the material property The

cutting tool is sampled along each axis for each

interpo-lated time and the hit points are updated in MDM The

method is simple and easy to implement, but has many

considerable limitations First, several numerical and

topological inconsistencies caused by the multiple usage

of the single-dexel model (SDM) are to be clearly solved

under a certain presumption Additionally, there are

aliasing and under-sampling problems: if an initial

sampling size is too large it may lead to overlooking asmall object or featured areas such as sharp edges andsharp corners Therefore, determining an optimal samplingsize of an object as well as the huge storage managementrequired as compared to a SDM would be challengingproblems for MDM [14]

Gläser and Gröller [15] propose a robust algorithm toupdate workpiece volume in the framework of polygonalboundary representation at three-axis machining in order todesign optimal tool shapes and paths Granados et al [16]implement a complete, exact and correct Boolean operationvia Nef polyhedra which is the closure of half-spaces, e.g.,

axþ by þ cz < d Thereby the exact arithmetic is applied

to overcome an incorrect rounding problem of the point arithmetic [17] The algorithm is implemented inCGAL [18] and the resultant geometry after the Booleanoperation is precise and robust However, the calculationtime is not amenable for milling application even thoughthe algorithm is optimized later in Ref [19]

floating-By applying a graphics processing unit (GPU) Bohez et

al [20] developed sweep plane algorithm using the stencilbuffer to simulate the five-axis milling operation Inaddition to the color and depth buffers, the stencil buffer

is an extra buffer, which is usually used to restrict thedrawing area to certain portions of the screen [21] Using itthey reduce 3D Boolean subtraction into a laminated 2Dplane Boolean operation Inui and Kakio [22] exploit thehidden surface removal technique, which corresponds to theZ-map method, of GPU to perform the Boolean subtraction

of the workpiece The algorithm eliminates surfaces whichare positioned at a farther distance and thus is invisiblefrom the viewpoint and saves color and depth value (or Zvalue) of the nearest surface pixelwise Saito and Takahashi[23] introduce a simple and effective geometric buffer (G-buffer) method, which is integrated in one methodology, tosimulate three-axis NC machining [24]

From the investigation of workpiece representation els, it could be concluded that the simulation of five-axismachining is still a challenging problem despite muchachievement by many researchers This is in last decadesbecause (1) the exact SV generation is a critical hurdle toupdate the workpiece during five-axis machining due to thegeometrical and computational complexity The cuttingoperation of SVs from a workpiece model is still a bottleneck

mod-in the NC simulation [25]; (2) representation methods of SVand workpiece model are diverse so that the optimalcombination of them cannot be determined with ease; (3)the process of updating the workpiece is composed of threecalculating steps, i.e., SV generation, Boolean operation, andvisualization The identification and optimization of compu-tational bound for each step is still a challenging theme sothat the optimal distribution of the computation burdenamong them is not clearly reported [26]

2 Virtual workpiece

A practical NC simulation should guarantee the prediction

of potential errors prior to real cutting via a workpiece

model However, the robustness of the Boolean operation

and its execution time has a reciprocal relationship Thus

the efficient implementation of the Boolean operation and

the workpiece representation is a crux in NC verification In

this section, the virtual workpiece, which is the main focus

through the work, is introduced based on the related work

addressed in Section1

2.1 Definition of virtual workpiece

The virtual workpiece (VWP) is the workpiece in a

simulation environment in which the geometric, kinematic

and thermo-mechanical effects of the process and resources

are reflected VWP is influenced by the

machine-cutter-workpiece system, CAM/CNC systems, machining

oper-ations, etc (see Fig 1) It contains not only the

macro-information corresponding to the shape of the “virtually”

machined intermediate workpiece but also the

micro-information such as the surface roughness, scallop heights,

chatter mark, etc VWP stores such surface information at

any step of simulation so that the analysis at every stage of

simulation is possible The accuracy of VWP depends on

the geometric accuracy of SV of tools, mechanistic force

model of the cutting process and dynamics of the machine

tool in turn Therefore, VWP is the core in which

comprehensive characteristics of the physical workpiece

are collected

The goal “First part correct and fast” of virtual

machining could be reached by determining the extent of

how well the VWP could integrate the real machining

processes in the virtual manufacturing environment where

relevant databases, e.g., product, process, and resource are

tightly interlocked VWP comprises the interrelationship

among the process parameters, material characteristics of

the workpiece and cutter, the type of interpolation, the

kinematic and kinetic parameters of machine tools, etc [27]

and is worth considering together with the development ofdata models [28]

2.2 Application fields of virtual workpiece

NC machine tools enable accomplishing machiningoperations, in addition to achieving high accuracy andproductivity of machining parts However, conventional

NC machine tools need an NC program, with which it isdifficult to change cutting parameters (e.g., depth of cut,etc.) at machine level, to move axes Moreover, thecutting tools are to be pre-determined to generate partprograms properly before machining Therefore, the NCprogram is specified for the target machine tool andcutting tools The cause of this is a loss of flexibility ofmachining operations

The next generation NC controller is capable of adaptingand re-planning the machining schedules autonomouslydepending on machining conditions and available resources

in the machine tool in comparison to the legacy controllers.Adaptation and flexibility of machining and abnormalcondition avoidance can be achieved through a real-timemachining simulation The VWP can play a significant role

in the next generation CAM/CNC systems, which enableVWP to leverage synergic effects (flexible and intelligentapplication fields (AF) of VWP) as follows:

1 Authentic five-axis simulation: the cutting simulationbecomes an indispensible tool in modern CAM systems

to cope with the mass customization which is terized as adaptation and reconfiguration While the SV

charac-of three axis-machining is calculated in a simplemanner the SV of the five-axis machining is generatedvery limitedly because the capabability of prevailinggeometric modeling kernels such as Parasolild [29],ACIS [30], OpenCascade [31], etc Even machiningsimulation companies, such as MachineWorks (UK)[32], Vericut (USA) [33], and ModuleWorks (Germany)[34] are using the approximation of SV for five-axismachining to increase the simulation speed at theexpense of the accuracy of simulation results Threemain aspects, however—the accuracy, the calculationspeed, and the memory demand—need to be thorough-

ly considered in order to implement a realistic andpredictable machining simulation Therefore accurate SVcalculation and the machining simulation based on SV arethe key features used to meet these requirements

2 Intra-operability in machine tools: the interruptedmachining due to abnormal conditions (e.g., toolbreakage or tool wear) could be resumed if the VWP

is calculated and the tool path is regenerated based onthe VWP with available resources e.g., cutting tools inthe tool magazine

Virtual Workpiece

Machining Operation Model

Modeling of machining operations with geometrically defined cutter for:

- conventional and

- HSC machining

Cutting Simulation

Interaction of cutter,

workpiece, clamping devices and

updating of in-process workpiece

geometry

Virtual Machine Tool

Thermo-dynamical model

of machine tool for identifying influence factors

3 Inter-operability between machine tools: this is a

similar case as with AF2, but the level of usage of

VWP is different Owing to modification of a schedule,

or priority of orders, the current milling operation of

machine tool A should be halted and another order

should to be set up on the machine tool A The halted

operation could be resumed on another machine tool B

which is available at that moment The VWP on the

machine A is updated up to the halted time and used as

an input geometry, i.e., a raw stock for a machine B

4 Geometry-based process monitoring: the commercial

milling process monitoring systems [48] show a

strength during mass production but a lack of valid

monitoring system of lot size 1 This results from the

fact that the old G & M codes [35] contain no

geometric information so that the contour is not known

a priori On the other hand, the smart machine [49]

enables the geometry-based monitoring, which keeps

track of the VWP and distinguishes the areas where the

cutter begins to engage or exit the material

5 Feed rate/tool speed optimization: VWP contributes to

the optimization of the cutting tool’s feed rate The

actual volume of material removal eliminated from the

workpiece can be accurately calculated based on VWP

This volume is the crux for the prediction of the cutting

forces and optimization of the feed rate by means of

mechanistic process models [36,50]

6 Advanced tool path generation: today, the tool path

generation of modern CAM systems is based on the

solid/surface models which are constructed by CAD

systems As usual, the security plane of the tool is

defined with constant distance from the stock material

surface so that the tool movement is not actually

economized There is considerable room for

rationaliz-ing the air paths by usrationaliz-ing VWP That is, the cuttrationaliz-ing tool

could cross over the area that has already been cut in

order to save cutting time Moreover, tool path could be

calculated so that the engagement angle of the tool

could be kept constant by considering the updated

VWP

7 Collision prevention: a data model for the machine tool

and the VWP enables the prevention of collisions

between the machine components and the spindle, tool

holder and tool itself in the controller Additionally, the

collision check between VWP and other peripheries,

e.g., jig and fixture, etc., is especially useful for tool

path generation because the machine crash leading

to heavy personal and technical costs is preventable

In the following sections, a methodology to generate

VWP during five-axis machining is explored We

explain a cutting simulation kernel for five-axis

machin-ing which takes SV generated by the proposed approach

as input and then provide the practical implementation

of VWP which is necessary to accomplish each AF(AF1-7)

This paper presents an efficient methodology toperform a Boolean operation of triangulated SV in theframework of triple-dexel model (TDM), to keep track ofVWP and to save VWP as polygon model for analysis ofthe geometry and further usage Main contributions inthis work are:

& SV generation of conical tools undergoing five-axismotion via Gauss map

& Efficient methodology and algorithms to update thein-process workpiece during simultaneous five-axismachining using five-axis SV

& The sampling technique of triangulated SV in anefficient manner

& Surface reconstruction from sampled data by ing feature sensitive geometries, e.g., sharp edges andcorners

recogniz-& Practical implementation of cutting simulation

& Comprehensive performance analysis including detectingbottleneck among modules through various examplesThis paper is organized as follows: Section 3 providesthe SV representation method of prevailing cutters under-going simultaneous five-axis movement via contact map(C-Map) and tool map (T-Map) Section 4 presents VWPmodel Then the algorithms of the cutting operation inthe framework of the VWP model are elucidated inSection 5 Section 6 discusses the surface reconstructionfrom the sampled data In Section 7, implementationissues and performance analysis of the proposed approachare addressed with various examples, and finally, inSection 8this paper is concluded

3 Tool swept volume modelLee and Nestler [37] have presented the method formodeling SV of cylindrical tools that undergoes axis-varying motion via the Gauss map This section explainsthe basic idea and extends it to SV modeling of conicaltools undergoing simultaneous five-axis motion

3.1 Contact map

Given an arbitrary vectorτ tðk k 6¼ 0Þ in the space, a greatcircle is achieved by intersecting the unit sphere with theplane orthogonal toτ passing the center of the sphere Thisgreat circle is called the C-Map of the generating vector τ(Fig 2) The C-Map CM ofτ is defined as follows:

CM¼ n nf j  t ¼ 0; nk k ¼ 1; tk k 6¼ 0g ð1Þ

As shown in Fig.2, C-Map ofC partitions the unit sphere

into three different regions according to the scalar product

C·n where n is a position vector on the sphere: (1) positive

region (C·n>0), (2) zero region (C·n=0), and (3) negative

region (C·n<0)

Points on the hemisphere in the positive region of the

sphere are represented as a front-facing region of the tool

which contacts the material in Euclidean space

@ Φþ¼ fnjt  n > 0; nk k ¼ 1g

on the hemisphere in the negative region of the sphere are

represented as a back-facing region of the tool which leans

against the material ð@ Φ¼ fnjt  n < 0; nk k ¼ 1gÞ The

points on the great circle that is located between the positive

and negative regions are represented as points on the

brink of cutting and leaving the material which

corre-sponds to the envelope profiles in Euclidean space

@ Φ0¼ fnjt  n ¼ 0; nk k ¼ 1g

.3.2 Tool map

Given a milling tool Φ which is a body of rotation and

has a convex hull property, tool map TM is defined by

overΦ, however Φ can have irregular surfaces, such as sharp

edges and a corner in the case of flat-end mills and conical

mills, the sharp edge or corner is considered to have an edge

radiusε where ε represents a sufficiently smaller value than

that of the edge of a physical cutting tool Then tool map for

the point P on a sharp edge is mapped onto nPon the unit

sphere by interpolating the extreme normal vectors n1

PÞ= sinΦjΦ¼ cos1 n1P n2

P

; u 2 0; 1½ g (seeFig.3)

3.3 Description of a cutting toolFor simplicity of explanation, it is assumed that a cuttingtool is composed of quadratic components, such as a cone,torus and a sphere, and that it is located on its own localcoordinate system Thus, each tool component is investi-gated independently (see in Fig.4)

In the following subsections, the surface point and thesurface normal for each tool component are described indetail, and envelope profiles parameterized by (η, ξ) areresolved in that the surface normal vector n is congruentwith the C-Map CM=(CMx, CMy, CMz) of τ as described

in Section3.1.3.3.1 Conical and cylindrical part

Given a cone with height Hconand side angleα between theZ-axis and the surface of the cone, whose apex is located onthe origin and whose bottom is located on the positive Zcoordinate (see Fig 4a), the surface point scon and thesurface normal nconof the cone are represented in Eq.3:

24

35

for p

ð3ÞFrom both Eqs 1 and 3 the parameter pair (ηcon, ξ) isobtained under the condition of, sin x ¼ cos aCMx, cos x ¼ CMycos a

and CMz=−sin α forp

2< a < p; x 2 0; 2p½ 

Given a cylinder with radius r and height Hcyl, thesurface point Scyl, and the surface normal ncyl of thecylindrical surface are represented as follows (see Fig 4b):

scyl
hcyl; x¼ r cos xr sin x

hcyl

24

35; ncylð Þ ¼x cos xsin x

0

24

35

for hcyl2 0; Hcyl

From both Eqs.1and4the solution pair (ηcon,ξ) is obtained

where cos x ¼ CMx , sin x ¼ CMy Since ncyl is dependent

only on the parameterξ, and the Z component of the surface

normal is zero, values of CMz have no influence in root

finding

3.3.2 Spherical part

Figure 4c denotes the parameters by which a part of the

spherical surface is described Given a sphere with radius r

located at origin, the surface ssphand the normalnsphof the

sphere are represented as in Eq.5:

35

ð5Þwhere ηsphis the parameter with respect to the longitude,

andξ is the parameter with respect to the latitude

From both Eqs 1 and 5 the pair (ηsph,ξ) is solved for

hsph ¼ cos1½CMz, hsph 2 að 1; a2Þ and cos x ¼ CM x

sin x ¼ CMy

3.3.3 Sharp edges

Figure 4d denotes the sharp edge where neighboring

components meet discontinuously (α1≠α2) Figure 4

shows an example of the sharp edge on a tool Given a

sharp edge containing segment S3 between two adjacentconic components in this example, the surface sedg, which isdegenerate to the sharp edge itself, and the normalnedgofthe sharp edge are to be represented as follows:

24

3

24

35

I f  sin a2< CMz<  sin a1then hedg¼ cos1½CMzand ξ can be solved from cos x ¼ CMffiffiffiffiffiffiffiffiffiffiffix

solu-3.4 Principle of SV generation for three-axis motionThe idea behind the principle for SV generation for three-axis motion is that the envelope profile of a toolΦ is the set

of the point P where the tangency condition f ¼

vðPÞ  nðPÞ ¼ 0; P 2 @ ΦðtÞ is satisfied [7,38]

At first, given a tool geometry Φ undergoing three-axismovement and the moving direction C, the T-Map of Φ iscalculated by Eq.2(see Section3.3and Fig.5a, b) and theC-Map of C is obtained by Eq 1 (Fig 5c) Then the

x y

sph

z

x r

P

1 2

P

n

(a) Conical part (b) Cylindrical part (c) Spherical part

(d) Sharp edge (e) Parameterization w.r.t ξ

Fig 4 Parameterization of each

tool component Surface point P

and normal n with respect to η

and ξ are depicted

intersection of the C-Map with the T-Map is obtained,

which means that the tangency condition is satisfied

(Fig.5d) From the intersection on the sphere, the envelope

profile parameterized by (η, ξ) is found (Fig.5e) and the SV

is generated by stitching the back-facing and front-facing

surfaces with the swept surface (Fig.5f)

By using an inverse function of Eq.2, the closed envelope

profile is obtained in Euclidean space The side of a cylinder

and a cone is achieved as a line segment (Fig.5e) Finally, the

SV boundary is generated when the back-facing regionð@ ΦÞ

of the tool at its starting position, the front-facing region

@ Φþ

ð Þ at its ending position and the sweep region—where

the envelope profiles
@ Φ0

are linearly interpolated betweentwo subsequent NC blocks—are stitched up (Fig.5f)

Any shape of milling tool which has the convex hull

property on the cutting part is applicable to this proposed

method, for example, automatically programmed tool-type

milling cutters [39]

3.5 Extension to five-axis movement

In general, the resultant velocity vectorv of a cutting tool

during spatial movement can be described in a moving

frame as follows (see Fig.6):

where P 2 Φ h; x; t ð Þ

ð7Þwherer(t) is a trajectory of the origin O at time t, ω is the

angular velocity,C and σ are the translational and rotational

velocity, respectively, in a moving frame, andΦ is the tool

body parameterized by η and ξ at a prescribed time t As

usual, v is variable along the tool axisa due to ω≠0 during

five-axis movement, while v is constant during three-axismovement Thus, the C-Map of the velocity vA i at theposition Ai along a is to be acquired and then to beoverlapped with the corresponding T-Map

In general, if n (P) is a unit surface normal vector at

P2 Φ then the T-Map of Φ and the C-Map for P isdescribed as in Eqs 8and9

Σ

O

4

6 8

7 1

f)

Front facing region Back -

-facing region

Fig 5 Principles for finding SV

using Gauss map for

transla-tional motion

surface point P, the surface normal vector np at P is

determined by Eq 8
TMp¼ XjX  a ¼ 0; jjXjj ¼ 1f g

.Then, the intersection ofa with the line parallel to npgoing

through P is B Finally, the EC-Map for P is computed by

Eq.9ð¼ XjX  vf B¼ 0; jjXjj ¼ 1gÞ

For a sharp edge segment, for instance Ω4, the surface

normal vector nQ at the point Q is described as n Q ¼ Slerp

ðA !=jjA 2 Q !jj;A 2 Q !=jjA 3 Q !jj;uÞ 3 Q for u∈ [0,1] As far as a concrete

intersection C (located between A2and A3) is concerned, the

corresponding normal vector is n Q ¼ CQ !=jjCQ !jj TM
p ¼

Figure7shows some SV examples of a conical tool which are

generated by the proposed method (refer to Section 3.3.1)

Figure7a–c show SVs, which are closed from bottom to top,

of a flat-end, a ball-end, and a fillet-end mill undergoing

three-axis motion Figure7d–f shows the further examples of

this cutter undergoing five-axis motion The swept surface of

the tool is rendered with different colors: red for swept surface

by the tool bottom, blue and magenta for swept surface by the

tool shaft, green for swept surface by the tool top, and brownand yellow for the tool itself at starting and ending position.Note that the complete SV, which describes the side andbottom shape of a tool undergoing multi-axis movement, isgenerated by stitching up closed envelope profiles

The proposed method promises an efficient and robustsolution of SV generation, because a series of the partialdifferential equations can be omitted The SV is tessellatedfor polygon-oriented rendering An advantage of thetessellation is that Open GL-based graphics hardware can

be used for rendering, and the cutting operation iscommitted efficiently by the ray-triangle intersection testwhich will be explained in Section5

4 Workpiece representation4.1 Orthogonal triple-dexel model

To keep track of the intermediate workpiece, SV isgenerated and subtracted from the current workpiece atevery G-code block In this work, the orthogonal triple-dexel model (TDM) (see Fig 8b) [12] is adopted as a

Fig 7 Complete SV of flat-end,

ball-end, fillet-end mill

under-going three-axis (a –c) and

si-multaneous five-axis movement

(d–f)

workpiece model because the simulated geometry can be

saved as a geometric model for a subsequent usage With

this model the numerical instability such as parallelism and

coplanarity can be significantly reduced

Figure8a shows the dexel data structure which contains

near and far value, surface normal vectors and colors at both

ends, and the pointer to the next linked dexel TDM has triple

arrays of dexels, i.e., dexel×dz[wpN][wpN] on (x, y) array

4.2 Comparison of SDM and TDM

TDM demonstrates strengths over the SDM Figure9illustrates

a visual inspection and conveys that TDM with 3 (n×n) rays

provides superior sampling results in comparison to SDM

identical between both models, the maximum error of the

sampled object in TDM is usually smaller than that of SDM

in three dimensions, even though the grid resolution is a little

bit bigger than that of SDM (see Table1 and Fig.10)

Figure10shows the comparison of TDM with SDM It

demonstrates the maximal errors for both models

recon-structing the surface from the original sphere of radius R=

10 mm with respect to the amount of sampling in the givensampling interval 2R It implies that TDM requires muchfewer rays in comparison to SDM to adhere strictly to thesame geometric error For example, the TDM necessitates

147 (=3×7×7) rays while the SDM needs 2,916 (=54×54)rays, which is 20 times more than with the TDM, in order

to guarantee a maximal error of 0.2 mm

5 Tracking in-process workpiece5.1 Material removal processMilling is the metal cutting process which continuallyremoves the material cut by the tool from the workpiece.The formulation of such a process is well written with aBoolean expression as follows:

number of rays=20) a

Single-dexel model b Triple-Single-dexel

model

TVðtÞ ¼ rðtÞ þ AðtÞ  Φ; t 2 R; t 2 0; N½  ð13Þ

where r(·) is the trajectory of the origin of Φ, A(·) is the

orthogonal matrix andΦ is the cutting tool fixed in the tool

coordinate system The swept volume SVk of the tool

between kth and (k+1)th NC lines is expressed as the union

of the instantaneous tool volumes TV within the normalized

time interval [0, 1] (Eq.12) Then the machined workpiece

Wois to be calculated either by the subtraction of the inital

stock Wi from the summation [SVk of SVs or by the

continual subtraction of the current SVkfrom the in-process

workpiece Our concern is to update the boundary surface

@Wo of the actual workpiece Wo It implies that the

boundary@SVkof a swept volume is to be subtracted from

the previous workpiece boundary@Wo

The boundary surface∂SVkis the Boolean sum of surfaces

contributing to the SV (Eq.14).∂Φ

is responsible for finding the envelope profiles which are

shared concurrently on∂Φ and ∂SV at a prescribed time

process

5.2 Sampling the swept volume

The five-axis SV of the cutter is complex to calculate

Moreover, SV can be regarded as a deformable object with

time So computing intersection points of the deformable

object, such as SV of the tool undergoing axis-varying with

rays, is expensive [40] This is why most commercial NC

milling verification software approximates SV with the sum

of prismatic solids, such as cylinders, cubes and spheres,

where the intersection test of rays and quadratic equations

is performed in a canonical form [2,41]

In this subsection, an efficient sampling method is

introduced in order to relieve computational burdens and

to speed up the calculation of intersection points In order tocompute the intersection of the ray and triangles, theinformation for frequently used operations of similar calcula-tion routine is calculated once and used repeatedly later on

At first, the SV is assumed to be tessellated withtriangles as described in Section 3 Valid triangles of the

SVΨ, which are located inside the common volume of theraw stock and the bounding box of the SV, are gathered.For each valid triangle Δ∈∂Ψ, the intersection points arecalculated in the framework of the TDM model Figure12

illustrates the sampling technique of Δ in space for thegiven (x, y) array

Δ is composed of three vertices P1, P2, and P3(Fig.12a).Its surface normal n is calculated from three vertices by n¼a; b; c

ð Þ ¼ð P 2 P 1 Þ P ð 3 P 1 Þ

ð Þ P ð 3 P 1 Þso that the embedding planeΣ of

Δ can be described as ax þ by þ cz ¼ d, where d is thedistance of the plane from the origin Figure12d shows how

to calculate the Z value of the intersection point with vectorchains The vector chains are useful because:

& The starting point S of a scan line on a triangle isalready known, since S2 P1P3

& The vector !SP lies in the ZX plane and thus can be

described as a linear function z=f(x)

& The calculated slope of a triangle could be used for allother intersection tests of the triangle

& Both legsP !XY1 PXY2

3 , might be casted atarrays, a starting point S of a scan line is selected on the

0 1 2 2,5

3 p n1ffiffi3 p

n 2sin1 1ffiffi

3 p n

n number of dexels along an axis

1

Operator Λ is comparable with the calculation procedure described

in Sections 3.4 and 3.5

edge P1P2 for the lower triangle and on the edge P2P3 for

the upper triangle Therefore, the Z value of P on P onΔ is

Sxand Syare already known from S, and Szis determined

through the known parameter along P !XY1 PXY3

Then Px iscalculated from the multiplication of the index and the

resolution along the X-axis (i·dx) As a result, Eq 15 is

rewritten as follows:

Pz¼ Szþ m  i  dx  Sð xÞ for Sy¼ j  dy ð16Þ

When Eq 16 is observed in detail, it is obvious thatonly the index i varies for each calculation of a Z value ofthe point P along the X scanning line The point S changeswith an increment of j, so that Syis the multiplication ofthe index j and the resolution along the Y-axis (Sy= j·dy).The slope m is valid on the whole triangle Δ, and theresolution dx and dy are constant over the completesimulation

The strength of the sampling technique is that theintersection point P is exact at the sampling grid whilethe position between the sampling grids is linearlyinterpolated Moreover, the color c and surface normalvectors n at sampled point P can be determined directlywith the help of the Barycentric coordinate system on the

2 Y

2 Z

Fig 12 Sampling a triangle in

space in the framework of TDM.

a A triangle in space and its

embedding plane Σ b

Projec-tion of the triangle onto XY, YZ,

and ZX plane c Circumscribing

valid arrays by both legs of the

projected triangle d Chain of

vectors that leads to Z value of

the point P

Fig 11 Principle of material

removal process

where A1 (A2, A3) is the area of the triangle PP2P3

(PP3P1, PP1P2) and P is the intersection point of a dexel

with
2 @

As a result, sampling of the SV could be realized

efficiently with a smaller amount of effort by exploiting the

frequently repeating operations

5.3 TDM updating

The TDM is used as the workpiece representation model which

realizes the material removal process Using TDM, the Boolean

subtraction can be simplified from the complex 3D Boolean

operation to the numerical subtraction for each axis such that a

complex and numerically instable computation can be avoided

∂SV, which is computed in Eq.14, is triangulated within the

given tolerance and sampled for each axis (see Section5.2)

Then the dexelized SV is subsequently subtracted from the

TDM workpiece representation by Eq.11

Figure 13 illustrates the elementary 1D cutting

oper-ations (B–A) in the framework of TDM which cut the SV

(A) from the workpiece (B) at a grid point

It shows all cutting configurations which are dependent onthe spatial relationships between the SV and the workpiece, e.g., a partial or total inclusion of the SV in the workpiece and atotal exclusion of the SV, etc Algorithm 1 summarizes theaforementioned cutting operation in pseudo-codes Thefunction dexel_diff(&dz[x][y],svz[x][y]) executes the ele-mentary cutting operations which are described in Fig.13.After the cutting operation, the boundary of theworkpiece Wois reconstructed Section 6 deals with someissues during the surface reconstruction of∂Wo

6 Surface reconstructionThe MC algorithm has been originally used in the medicalfield to extract and visualize isosurface, which has anidentical scalar value, e.g., density (computer tomography)

or temperature (meteorology), etc as a 3D scalar field [13].The MC treats each cell independently to construct a closedsurface out of the discrete data so that the MC needs noconnectivity information between cells Because the TDMmodel can be also considered as a cell-based representationlike MC (Fig.8), the MC algorithm is applied to reconstructthe virtually machined surface The MC has, however,several drawbacks which result from the discretization

& It cannot represent features such as sharp edges orcorners (the sharp edge problem, refer to Fig.14)

& The surface accuracy depends on the resolution of grids(the sampling resolution)

Theoretically, sharp features can be recovered truly if thesampling interval l converges to zero In practice, however,the interval l is determined as large as possible as long asthe sampling deviation does not exceed the prescribedgeometric tolerance

Figure15shows a polygon on the 2D plane in order tohighlight the addressed problems In order to solve thesharp edge problem, the intersecting position P as well asthe outward surface normal vector n of a line segment is to

be saved when a ray meets the segment of the polygon(Fig 15a, b) The normal vectors are assigned in datastructure of dexel (Fig 8a) At first, the angle between thetwo successive normal vectors n1and n2is measured If theangle is greater than a threshold angleα (n1·n2<cosα) then

an additional point I is inserted between P1and P2and twosupplementary line segments P1I and P2I2 are inserted inplace of the line segment P1P2 so that the sharp feature ispreserved (see Fig.15c left) [43,44]

As for the optimal sampling resolution problem, thesampling interval l should be so determined that the linesegment of the polygon can be intercepted by at least one

of rays on the plane The Nyquist criterion in the samplingtheory states that the sampling frequency f must be at least

twice as large as the maximum frequency of a signal to

recover the original signal in frequency domain [45] This

criterion is adapted to our problem only in restricted

circumstances since it is to be solved not in the frequency

domain but in the object domain Thus, the samplinginterval l in the object domain, which corresponds to thesampling frequency f in the frequency domain, is deter-mined under the condition l < mini max lX

Fig 14 Surface representation

using orthogonal triple-dexel

model (a) entering and exit hits

(green points) (b) topological

skeleton: line segments (c)

ren-dered skin: triangulation

swept volume (A)

Fig 13 Elementary 1D cutting operations along an axis a, b Dexel is trimmed at top and bottom (A\ B 6¼ ;?); c dexel is split (A B?); d dexel

is deleted (A B?); e no interaction between SV and workpiece (A\ B ¼ ;?)

where lXi
lYi

is the projected line of a line segment li of

the polygon onto the X(Y)-axis By the proposed methods,

the 2D polygon could be recovered truly from the original

object Analogous to the polygon in 2D, the sampling

interval l could be determined under the condition l <

=2 for the triangle in 3D (Fig.12b)

Furthermore triangles of the lower aspect ratio are

desirable at triangulation of SV to avoid skinny triangles

which make the surface reconstruction complicated For

example, Delaunay triangulation is preferable, which

maximizes the minimum angle of all angles of the

triangles in the triangulation [46] In this paper, however,

the swept surface of the tool is triangulated depending on

the extent of the angle between a1and a2 and the angle

between vt and vb in order to accelerate NC simulation

speed (see Fig 7a, d) That is, If the maximal angle

allowance isδmax, then the numbers of the fractionization

are calculated by Eq.18

if a 1 a 2 or a 1  a 2 > cos d max ; n ¼ 2; otherwise; n ¼ cos1ð a 1 a 2 Þ

whereaiis the tool axis at position Pi,vt(vb) is the velocity

vector at the top (bottom) of the tool (Fig.7a, d), x is the

ceiling function which takes the minimal integer greater

than x

Figure 16 shows the VWP whose sharp features are

recognized and recovered by the proposed sampling

technique Figure 16a shows the in-process workpiece

introduced in Section 7.2 The number of dexel for each

axis amount to 64 (that is, the sampling interval is0.94 mm) Figure 16b shows the surface reconstruction inthe framework of the original MC algorithm As shown, thesharp edges could not be reconstructed truly On the otherhand, Fig.16c shows the VWP where the sharp edges arerecognized and recovered via the TDM model (refer to themagnified figures in detail)

7 Implementation7.1 Virtual workpiece as carrier of machined surfaceinformation

Based on the TDM model presented in Section4, a cuttingsimulation kernel for five-axis machining has been devel-oped The kernel is implemented with C++, OpenGLversion 2.0 [21] and Standard Template Library (STL).The simulation module runs on AMD® Athlon II X4 630CPU 2,81 GHz and 8 GB RAM which is equipped with anVidia® Quadro FX 580 PCI-E graphics accelerator with

512 MB RAM Validity tests of VWP generation are carriedout by many examples Figures 17, 18, 19, and 20 showseveral VWPs among them

Figure 17 shows VWPs rendered with the coloringscheme described in Section 3.6 If a material is removedfrom the VWP by the tool, the corresponding color of thetool is copied into the VWP Figure17a shows the principle

of the cutting operation, i.e., the volumetric engagement ofthe SV of a ball-end mill (ϕ 10 mm) into a cubic workpiece(503 mm3) The SV is subtracted continually from thecurrent workpiece as proposed in Section 4 Grids arealigned with 128 for each axis so that the sampling

a) Sampling with X rays b) Sampling with Y rays

c) Problems during surface reconstruction(Sharp feature, Resolution)

p1

p2

n1

n2I

Denser samplingRestoring sharp feature

Fig 15 Optimal sampling

reso-lution and preservation of the

sharp feature

resolution is 0.39 mm/grid It shows dozens of Boolean

subtractions of the tool, the path type of which is a 3D

spiral curve Figure17b shows the final shape of a model

automobile by means of the TDM model Figure17c shows

the virtual workpiece of a turbine blade which is“virtually”

machined during simultaneous five-axis machining

Figure18shows the possibility of simulation of a micro

part (5.8×1.6×5.8 mm3) which is processed by the EDM

machine SARIX® The diameter of the electrode is 200μm

and its tool paths, which are generated by Esprit®, are

composed of linear (G01 code) and circular interpolations

(G02, G03 code) Figure 18a shows the “virtually”

dis-charged part Figure 18b shows the virtual part incomparison with a real part in Fig 18d The simulatedworkpiece can be saved in the boundary representation (B-rep), e.g., in STL data format Figure 18c shows the partcontour in sectional view which is reconstructed from theTDM model

Figure 19 shows the real and virtual workpiece of atested sample The NC program is composed of 10,600lines and the part size is 70×118×44 mm3 The zero point

of the workpiece is located in the middle of the workpiece

on the top The cutting tool undergoes the three-axismovement The detail of the virtual workpiece (Fig 19b)

Fig 17 Virtual machining

using SV by means of TDM

model

(a) Simulated workpiece (b) Original MC algorithm (c) Sharp edge recognition

Fig 16 Sharp-edge recovery

is comparable to the real workpice: the scallop heights and

the dwell mark of the cutter are to be observed with high

resolution

Figure20 show the simulation process of an industrial

impeller The impeller is modeled and its tool paths are

generated in CATIA® manufacturing V5R19 (Fig 20l)

[47] The diameters of the applied cutting tools range from

ϕ 1 to ϕ 10 and the tool types are flat-end, ball-end and

fillet-end mills The process planning for machining of the

impeller is determined as following: first, raw stock is cut

by theϕ 4 flat-end mill as much as possible Figure20b–d

shows the intermediate machining status during a roughing

operation which is removed from the initial cubic raw stock

(60 × 51 × 25 mm3, see Fig 20a) Then the finishing

allowance 0.2 mm remains over the design surface through

the semi-finishing operation (Fig 20e) At the finishing

process the three blades, the bottom of blade, and the

boundary of the workpiece are machined with differentcutting tools subsequently (Fig 20f–h) Figure 20i showsthe finished workpiece where simultaneous five-axis ma-chining is applied, while fixed axis machining is appliedduring roughing and semi-finishing operations The five-axis SV, which is generated by the proposed method inSection 3, is subtracted for each G-code successively fromthe in-process workpiece Figure20j, k show the boundaryrepresentation of the in-process workpiece after roughingand finishing in STL data format, which could be used forfurther operations and analysis

VWP can reflect the micro surface structure of the machined workpiece as an information carrier of machin-ing For example, Fig 21a visualizes the micro surfacestructures, such as the scallop heights and ridges Further-more, VWP contains the macro geometric information,such as the in-process workpiece, and predicts machined

to-be-1600 µm(a) Finished EDM part

(b) Virtual part (c) Sectional view (d) Real part

H = 200 µm

Fig 18 Virtual workpiece of

EDM micro-machining (part

size, 5.8×1.6×0.2 mm3)

Fig 19 Comparison of real and

virtual workpieces

surface quality Figure21b shows the impeller blade surface

gouged by the cutter shank when the corner contour of the

impeller at the bottom is being machined during a pencil

operation

7.2 Performance analysis and discussion

In order to investigate the influence of the factors on simulation

speed, a machining scenario with different configurations is

prepared and evaluated The performance of the proposed

method is measured by the example of the impeller in

Section7.1(refer to Fig 20) The NC programs, with which

the impeller is machined as in Fig.20, are tested with different

resolutions to investigate the practical applicability of the

proposed simulation kernel The main interest of NC

simula-tion & verificasimula-tion tools lies in the quality of the simulated

workpiece as well as in the required time for simulation The

cutting operation is simulated with and without graphic output

of the simulation process in order to investigate the influence

of the graphic output The time measurement starts afterreading in the NC program and ends when the last line of the

NC program was worked on

Table 2 lists the simulation duration with respect todifferent configurations at impeller machining withoutgraphic display The applied resolutions are 0.94 mm (64dexels for each axis), 0.47 (128), 0.23 (256), 0.12 (512),and 0.06 (1,024), respectively The visualization of themachining process is omitted because it depends on theperformance of graphics cards Our concern is the purecomputation time of the SV generation (SVG) and cuttingoperation (C)

The total number of NC codes of the part programamounts to 48,810 lines which are composed of 10,680lines for three-axis machining and 38,130 lines for five-axismachining The machining process is composed of rough-ing, semi-finishing and finishing operations which machinethree blades, the bottom of the blades and the brink of theworkpiece

(a) Raw stock (b) Roughing (c) Roughing (cont‘d)

(f) Finishing of blade (e) Semi-finishing of blade (d) Roughing of blade

(g) Finishing of bottom (h) Finishing of boundary (i) Finished part

(j) B-rep between (d) & (e) (k) B-rep of (i) (l) Impeller model

Fig 20 Cutting procedure of an industrial part: impeller

Figure22shows the execution time with respect to the

experiment configurations based on the data measured from

Table 2 The asymptotic upper bound function of the

cutting simulation is O (lmn) with respect to the resolution

where l, m, n are the number of dexels per x-, y-, z-axes

(refer to Algorithm 1)

Figures 23 and 24 show the number of executed NC

codes per second with respect to the resolution during

three-axis and five-axis machining, respectively For each

configuration, there are four different settings: SVG means

SV generation without graphical output In SVG, SV is

generated as proposed in Section3and triangulated for the

cutting operation C stands for the cutting operation

explained in Section 5.2 and 5.3, V stands for the

visualization of the machining process which includes the

surface reconstruction as explained in Section6

With the various combinations of SVG, C, and V,Figs 23and 24 show the versatile aspects of the proposedapproach Performance for SVG amounts to 5,000~8,600 NC/

s, namely, 0.15~0.2 (μs/code) commonly for both The timefor SVG is negligible since the time for C and V is neededmuch more with a magnitude of 12~200 times Figure 24

shows the longer time of C at five-axis machining than atthree-axis machining The reason for this is that the removalvolume is as large as possible in roughing operation so thatthe number of the calculated dexels is large while theremoval volume in the finishing operation is small The morematerial should be removed, the more calculation time isneeded because dexels need to be computed to the extent ofthe removal material volume (refer to Algorithm 1)

On the other hand, the display operation (V) remainsquite constant (≈75 fps (frame/s)) independently of the

Table 2 Comparison of cutting simulation performance

Unit (s) Number of dexel per axis

face information carrier

configurations We use OpenGL® for the graphic display

and set 75 Hz refresh rate which is enough for the

continuous perception of the dynamic scene in principle

So V is the slowest operation and a bottle neck among

simulation operations up to 256 dexels configuration

Therefore, C might be so conducted that the total time

for C amounts to the time of V, e.g., 75 Hz

From Figs.23and24it is known in general that V is a

critical factor while the time for SVG is negligible C is a

crucial operation which depends on the dexel resolution

8 Conclusions

In this paper, an efficient methodology and implementation

for generating a virtual workpiece (VWP) during material

removal processes was presented VWP is the workpiece in

a virtual environment in which the geometric, kinematic,and thermo-mechanical effects of the process and resourcesare reflected VWP results from the interrelationship amongthe process parameters, material characteristics of theworkpiece and cutter, the type of interpolation, thekinematic and kinetic parameters of machine tools, etc Itencompasses not only the macro-information corresponding

to the shape of the “virtually” machined intermediateworkpiece, but also the micro-information such as thesurface roughness, scallop heights, chatter mark, etc.The first step in calculating VWP is the generation of

SV of prevailing milling cutters by envelope profiles,which are calculated by the intersection of the Contactmap of the tool moving direction with the Tool map.VWP is the result of continual volumetric subtraction ofSVs from the IPW The Boolean subtraction is realized

by an efficient ray-triangle intersection test from whichthe intersection points and colors at the point can beinterpolated from the triangle vertices by using Barycen-tric coordinates The workpiece model is representedwith the orthogonal TDM which enables the extraction

of a feature’s sensitive surfaces, e.g., sharp edges andcorner by the marching cube algorithm and the proposedsampling technique VWP could be well reconstructed as

a triangular mesh (STL data format) from TDM andreflect the surface roughness, i.e., scallop height andgouging regions by means of the complete SV generationproposed by the authors [37]

The VWP generation has been proven to be amenablefor practical purposes through many tests so that it might beapplicable to enhance the quality and application domain of

NC simulation and verification By using TDM, thenumerical instability, such as coplanarity, could be heavily

0 100 200 300 400 4700 4800 4900 5000 5100 5200 5300

Executed NC lines per second

at five-axis machining

SVG SVG+C SVG+V SVG+C+V

Executed NC lines per second

at three-axis machining

0.94 0.47 0.23 0.12 0.06 Resolution [mm]

Fig 23 Executed NC lines per second during three-axis movement

Executing time of impeller machining simulation

without graphic display

0.94 0.47 0.23 0.12 0.06 Resolution [mm ]

Fig 22 Elapsed time (s) of cutting simulation of the impeller