gear hobbing cutting process simulation and tool wear .... journals/12.5.pdf · gear hobbing...

10
K.-D. Bouzakis e-mail: [email protected] S. Kombogiannis A. Antoniadis N. Vidakis Laboratory for Machine Tools and Manufacturing Engineering, Mechanical Engineering Department, Aristoteles University, Thessaloniki 54006, Greece Gear Hobbing Cutting Process Simulation and Tool Wear Prediction Models Gear hobbing is an efficient method to manufacture high quality and performance toothed wheels, although it is associated with complicated process kinematics, chip formation and tool wear mechanisms. The variant cutting contribution of each hob tooth to the gear gaps formation might lead to an uneven wear distribution on the successive cutting teeth and to an overall poor tool utilization. To study quantitatively the tool wear progress in gear hobbing, experimental-analytical methods have been established. Gear hobbing ex- periments and sophisticated numerical models are used to simulate the cutting process and to correlate the undeformed chip geometry and other process parameters to the expected tool wear. Herewith the wear development on the individual hob teeth can be predicted and the cutting process optimized, among others, through appropriate tool tangential shifts, in order to obtain a uniform wear distribution on the hob teeth. To determine the constants of the equations used in the tool wear calculations, fly hobbing experiments were conducted. Hereby, it was necessary to modify the fly hobbing kinemat- ics, applying instead of a continuous tangential feed, a continuous axial one. The experi- mental data with uncoated and coated high speed steel (HSS) tools were evaluated, and correlated to analytical ones, elaborated with the aid of the numerical simulation of gear hobbing. By means of the procedures described in this paper, tool wear prediction as well as the optimization of various magnitudes, as the hob tangential shift parameters can be carried out. @DOI: 10.1115/1.1430236# 1 Introduction In gear hobbing, as in every cutting process, the predictability of such machining parameters as tool wear, cutting forces, etc., considering workpiece tool and production data is of immense research and industrial concern @1–12#. The generating-rolling principle governing the hobbing kinematics makes difficult the analytical approach of the tool wear. On the other hand, owing to their complex geometry, hobbing cutters are quite expensive and their extended exploitation becomes dominant. The variant chip formation on each cutting tooth during hobbing provokes different wear laws and usually leads to an unequal wear distribution on the hob teeth @6,12–15#. Hereby, through an appropriate tangential tool shifting a uniform wear on the hob teeth, before the sharpen- ing or the replacement of the tool can be reached. For this pur- pose, optimum values for the hob shift displacement and amount of gears per shift position have to be determined. The restricted cutting performance of HSS tools does not fulfill the high cutting speed requirements of modern CNC hobbing ma- chine tools. This led among others to the application of Physically Vapor Deposited ~PVD! coatings on such tools, which improved the performance of HSS tools at higher cutting speeds, and in- creased considerably the productivity of gear manufacturing @8,16–24#. In the present paper models to predict the wear development in gear hobbing are introduced, whereas the chip generation in full cut and in the transient workpiece cutting regions is considered. The wear laws in the individual generating positions investigated in @6,13–15# are exhibited with the aid of the developed algorithm FRSWEAR and procedures to determine the optimum tangential shift amount are proposed. In order to enable the monitoring of the wear progress in the individual generating positions and the determination of the included in the wear describing equations constants, the fly hobbing with continuous axial feed was applied. Application examples of these procedures as well as of the FR- SWEAR software will be demonstrated in manufacturing cases, with uncoated as well as coated HSS tools. 2 Chip Formation in Gear Hobbing The gear hobbing cutting procedure is schematically presented in the upper part of Fig. 1. Due to its complicated kinematics, modeling problems are caused, since each gear gap is produced through successive penetrations of the tool teeth into the work- piece in the individual Generating Positions ~GP!. Considering the tool rotation during each hob tooth penetration into a gear gap, a number of revolving positions has been introduced to describe the chip cross sections, as it is further explained. Significant param- eters affecting the tool wear are the chip formation and flow @6,13–15#. In the left part of Fig. 1, chip photos and the workpiece surfaces formed at the indicated generating positions, are illus- trated. The undeformed chip geometries are calculated in various revolving and generating positions during the formation of a gear gap, by means of the computer program introduced in @1#. The principle of this program is based on the mathematical description of the tool penetrations into the gear gaps. The undeformed chip cross sections on the development of the cutting edge are pre- sented in successive tool revolving positions at every generating position as illustrated in the right part of Fig. 1. If the tool cuts in a transient, entry or exit workpiece region the chip formation is modified in comparison the full cut region ~see Fig. 2!@12#. The undeformed chip geometry, considering the cut- ting direction, is a front or a back part of the full cut chip geom- etry. In the 11th and 12th cutting positions of the observed gener- ating position in the present hobbing case, chips of the same geometry per tool rotation and with maximum overall dimensions occur ~full cut chips!, whereas in the rest cutting positions only parts of the full cut chips are formed. The length of the chips in the successive tool entry cutting positions is increasing, whereas in the exit region cutting positions the corresponding chip length is continuously diminishing. The relation between the gear width b and the length q in the workpiece axial direction ~see Fig. 3! is Contributed by the Manufacturing Engineering Division for publication in the JOURNAL OF MANUFACTURING SCIENCE AND ENGINEERING. Manuscript received December 1998; Revised March 2001. Associate Editor: K. Ehmann. 42 Õ Vol. 124, FEBRUARY 2002 Copyright © 2002 by ASME Transactions of the ASME

Upload: others

Post on 21-Feb-2020

30 views

Category:

Documents


0 download

TRANSCRIPT

Page 1: Gear Hobbing Cutting Process Simulation and Tool Wear .... JOURNALS/12.5.pdf · Gear Hobbing Cutting Process Simulation and Tool Wear Prediction Models Gear hobbing is an efficient

thedn andgearteeth

s inng ex-ocesso thean be

toolTo

bbingemat-peri-

d, andearwell

an be

K.-D. Bouzakise-mail: [email protected]

S. Kombogiannis

A. Antoniadis

N. Vidakis

Laboratory for Machine Tools andManufacturing Engineering,

Mechanical Engineering Department,Aristoteles University,

Thessaloniki 54006,Greece

Gear Hobbing Cutting ProcessSimulation and Tool WearPrediction ModelsGear hobbing is an efficient method to manufacture high quality and performance toowheels, although it is associated with complicated process kinematics, chip formatiotool wear mechanisms. The variant cutting contribution of each hob tooth to thegaps formation might lead to an uneven wear distribution on the successive cuttingand to an overall poor tool utilization. To study quantitatively the tool wear progresgear hobbing, experimental-analytical methods have been established. Gear hobbiperiments and sophisticated numerical models are used to simulate the cutting prand to correlate the undeformed chip geometry and other process parameters texpected tool wear. Herewith the wear development on the individual hob teeth cpredicted and the cutting process optimized, among others, through appropriatetangential shifts, in order to obtain a uniform wear distribution on the hob teeth.determine the constants of the equations used in the tool wear calculations, fly hoexperiments were conducted. Hereby, it was necessary to modify the fly hobbing kinics, applying instead of a continuous tangential feed, a continuous axial one. The exmental data with uncoated and coated high speed steel (HSS) tools were evaluatecorrelated to analytical ones, elaborated with the aid of the numerical simulation of ghobbing. By means of the procedures described in this paper, tool wear prediction asas the optimization of various magnitudes, as the hob tangential shift parameters ccarried out. @DOI: 10.1115/1.1430236#

ien

h

e

i

p

lma

n

r

n

oi

FR-es,

ntedcs,ucedork-

p, athe

am-owcelus-iousear

tionchippre-ting

he

ut--

ner-menslyin

reasgthdth

h

1 IntroductionIn gear hobbing, as in every cutting process, the predictab

of such machining parameters as tool wear, cutting forces,considering workpiece tool and production data is of immeresearch and industrial concern@1–12#. The generating-rollingprinciple governing the hobbing kinematics makes difficult tanalytical approach of the tool wear. On the other hand, owingtheir complex geometry, hobbing cutters are quite expensivetheir extended exploitation becomes dominant. The variant cformation on each cutting tooth during hobbing provokes differwear laws and usually leads to an unequal wear distribution onhob teeth@6,12–15#. Hereby, through an appropriate tangenttool shifting a uniform wear on the hob teeth, before the sharping or the replacement of the tool can be reached. For thispose, optimum values for the hob shift displacement and amoof gears per shift position have to be determined.

The restricted cutting performance of HSS tools does not futhe high cutting speed requirements of modern CNC hobbingchine tools. This led among others to the application of PhysicVapor Deposited~PVD! coatings on such tools, which improvethe performance of HSS tools at higher cutting speeds, andcreased considerably the productivity of gear manufactur@8,16–24#.

In the present paper models to predict the wear developmegear hobbing are introduced, whereas the chip generation incut and in the transient workpiece cutting regions is consideThe wear laws in the individual generating positions investigain @6,13–15# are exhibited with the aid of the developed algorithFRSWEAR and procedures to determine the optimum tangeshift amount are proposed. In order to enable the monitoringthe wear progress in the individual generating positions anddetermination of the included in the wear describing equaticonstants, the fly hobbing with continuous axial feed was appl

Contributed by the Manufacturing Engineering Division for publication in tJOURNAL OF MANUFACTURING SCIENCE AND ENGINEERING. Manuscript receivedDecember 1998; Revised March 2001. Associate Editor: K. Ehmann.

42 Õ Vol. 124, FEBRUARY 2002 Copyright ©

litytc.,se

eto

andhipntthealen-ur-unt

filla-

llydin-

ing

t infulled.tedmtialof

thens

ed.

Application examples of these procedures as well as of theSWEAR software will be demonstrated in manufacturing caswith uncoated as well as coated HSS tools.

2 Chip Formation in Gear HobbingThe gear hobbing cutting procedure is schematically prese

in the upper part of Fig. 1. Due to its complicated kinematimodeling problems are caused, since each gear gap is prodthrough successive penetrations of the tool teeth into the wpiece in the individual Generating Positions~GP!. Considering thetool rotation during each hob tooth penetration into a gear ganumber of revolving positions has been introduced to describechip cross sections, as it is further explained. Significant pareters affecting the tool wear are the chip formation and fl@6,13–15#. In the left part of Fig. 1, chip photos and the workpiesurfaces formed at the indicated generating positions, are iltrated. The undeformed chip geometries are calculated in varrevolving and generating positions during the formation of a ggap, by means of the computer program introduced in@1#. Theprinciple of this program is based on the mathematical descripof the tool penetrations into the gear gaps. The undeformedcross sections on the development of the cutting edge aresented in successive tool revolving positions at every generaposition as illustrated in the right part of Fig. 1.

If the tool cuts in a transient, entry or exit workpiece region tchip formation is modified in comparison the full cut region~seeFig. 2! @12#. The undeformed chip geometry, considering the cting direction, is a front or a back part of the full cut chip geometry. In the 11th and 12th cutting positions of the observed geating position in the present hobbing case, chips of the sageometry per tool rotation and with maximum overall dimensiooccur ~full cut chips!, whereas in the rest cutting positions onparts of the full cut chips are formed. The length of the chipsthe successive tool entry cutting positions is increasing, whein the exit region cutting positions the corresponding chip lenis continuously diminishing. The relation between the gear wib and the lengthq in the workpiece axial direction~see Fig. 3! is

e

2002 by ASME Transactions of the ASME

Page 2: Gear Hobbing Cutting Process Simulation and Tool Wear .... JOURNALS/12.5.pdf · Gear Hobbing Cutting Process Simulation and Tool Wear Prediction Models Gear hobbing is an efficient

eea

bd

soi

tit-

ribero-ipipthe

acheallythechipvi-

a magnitude affecting the occurring chip geometry and thuscorresponding hob wear. In manufacturing cases withb.q or b5q, the entry, the full cut and the exit regions I, II and III respetively can be distinguished, according to the position of the cting tool concerning the gear width. On the other hand if the gwidth b is less than the lengthq, a transient region IV between thentry and the exit regions is detected, in which the chip is alwa part of the full cut one. These interactions are presented inlower part of Fig. 3, where the previous mentioned relationstweenb andq, in the same generating position, are considere

3 Tool Wear Development Description in the Indi-vidual Generating Positions in Gear Hobbing

The most wear endangered positions on a hob tooth are itcorner regions to the flanks. The flank wear VB near the tohead will be considered in the following analysis, as the criterof the tool wear status. Mathematical models predicting the wprogress in the individual generating positions are introduced

Fig. 1 Chip formation and typical chips at various tool gener-ating positions in gear hobbing, as well as the correspondinganalytically determined chip cross sections

Journal of Manufacturing Science and Engineering

the

c-ut-ar

ysthee-.

tipth

onear

in

former publications@6,13–15#. These models take into accounthe complicated chip formation, as well as the chip flow, exhibing a remarkable influence on the tool wear. In order to descsuch effects quantitatively, five different chip groups were intduced@6,13–15#. The criterion hereby was the intensity of chflow obstruction phenomena, due to reciprocal collision of chdistinct sections. The group classification is mainly based onshape of the undeformed chip considering its flow direction. Eof these groups~I, II, III, IV and 0! has a characteristic influencon the tool wear development. Figure 4 illustrates experimentderived typical wear laws for each chip group, as a function ofnumber of successive cuts AS. The figure includes equivalentdimensions that are further explained in the followings. It is e

Fig. 2 Undeformed chip cross sections in entry, full cut andexit or transient cutting positions in gear hobbing

Fig. 3 Undeformed chip length l in various regions duringhobbing versus the gear width, in a generating position

FEBRUARY 2002, Vol. 124 Õ 43

Page 3: Gear Hobbing Cutting Process Simulation and Tool Wear .... JOURNALS/12.5.pdf · Gear Hobbing Cutting Process Simulation and Tool Wear Prediction Models Gear hobbing is an efficient

c

a

t

tn

osi-the

Theua-eum-de-

cted

de-arede-

lawhips in-plertaintingde-ringon,cu-t inn-hip

hetheasy

dent, that the flank wear VB progress is at most intense in thegroup case I, whereas in the case of group 0~chip flow withoutobstruction!, the wear slope is significantly lower.

The simulation of gear hobbing, with the aid of the prograFRSWEAR@6,12–15#, yields the chip dimensions in the succesive revolving positions of every cutting position in individugenerating positions, taking into account all tool, workpiece acutting kinematics data. In a second stage, the chips are classin the previously described five different groups, regarding thformation and flow. The reasons for this task, as already mtioned, is that the tool wear strongly depends on the chip flobstruction described through the introduced chip groups andconstants of the applied mathematical equations to predict thewear in each chip group case are different. In a further calculastep, the representative magnitudes, equivalent chip lengththickness are analytically determined. Figure 5, illustrates thisfor the trailing flank of a hob tooth, in a generating position duri

Fig. 5 Determination of chip group and equivalent chip dimen-sions in a generating position, with the aid of the FRSWEARprogram

Fig. 4 The effect of chip geometry and shape „chip group … onthe wear development

44 Õ Vol. 124, FEBRUARY 2002

hip

ms-lndifiedeiren-owthetoolionandaskg

climb hobbing of a helix gear. For the presented generating ption, the corresponding magnitudes and parameters related toleading flank are calculated and demonstrated in the figure.equivalent chip dimensions are required in wear prediction eqtions, derived as described in@6,13–15#. These equations correlatsignificant gear hobbing parameter, such as the accumulated nber of successive cuts, the equivalent dimensions of the unformed chip, the chip group and the cutting speed to the expewear development.

The constants of such equations are usually determined asscribed in the following section. The mentioned equationsimplemented in the FRSWEAR program to predict the wearvelopment in gear hobbing.

The developed code selects automatically the proper wearaccording to the chip group and considering the equivalent cdimensions and the cutting speed starts counting the wear, adicated in the upper part of Fig. 6. A cutting tooth, as for examan unworn one, develops a specific wear status after a cenumber of successive cuts in the same cutting and generapositions during hobbing of a gear, predicted as previousscribed, considering the chip geometry and the manufactudata. If the same tooth has to cut in a further cutting positiwhich obeys to a different wear law, the wear starts to be acmulated on the already existing wear, occurred due to the cuthe previous cutting position. The further wear prediction is coducted according to the current wear law due to the actual cgeometry.

The influence of the chip formation and flow in the entry, texit and in the full cut and the transient workpiece regions onwear development is considered in the FRSWEAR programshown in the bottom part of Fig. 6. A tooth, with an alreadexisting wear VBstart,k on it, cuts in the generating positionk, for

Fig. 6 Wear prediction in hobbing considering the chip forma-tion at various cutting and individual generating positions

Transactions of the ASME

Page 4: Gear Hobbing Cutting Process Simulation and Tool Wear .... JOURNALS/12.5.pdf · Gear Hobbing Cutting Process Simulation and Tool Wear Prediction Models Gear hobbing is an efficient

h

c

i

hrs

to

h

r

r

e

f

t

i

en-essd ofting

toolToolineal-

tedby

data-on-he

phi-utt byicalcted

veryutre-can

othhobthethe

earen-ith

example in the entry workpiece region. The flank wear of this htooth after cutting in allz2 gear teeth gaps in the same cuttinposition 1 of the generating positionk, continuous to increaseaccording to the wear law of the next cutting position 2 of tsame generating positionk. After working in all cutting positions,i.e. in every possible, entry, exit, full cut or transient workpieregion of the same generating positionk, the resulting flank wearVBfinish,k is the starting flank wear VBstart,k in the first cuttingposition of the same generating position in hobbing of the ngear.

4 Wear Development Description Considering theTool Tangential Shifting in Gear Hobbing

If the tool cuts only at a certain relative position to the worpiece, each hob tooth cuts always in the same generating posand thus the occurring wear distribution on the cutting teethhighly dissimilar. To achieve a uniform wear at the majority of tcutting teeth, a tool tangential shifting is required. The corsponding shift amount, i.e., the number of hobbed gears perposition, depends on the geometrical and the technologicaland workpiece data and can be determined by means of theSWEAR algorithm, as presented in Fig. 7.

To elucidate this computational procedure, it is assumedthe manufacturing of a tooth gap contour is conducted in fdistinct generating positions~I to IV !. The produced workpiecesurfaces and typical chips are illustrated in the left part of tfigure. During the formation of one gap, four of the seven teeththe specific assumed tool take part to the cutting process forfirst time. The corresponding wear regularities in those generapositions are determined as described in the previous paragDue to these regularities each hob tooth exhibits a different wdevelopment after cutting a certain number of gears in the invidual generating positions, which corresponds to a numbecuts AS. The course of the maximum width of flank wear VB,illustrated in the bottom part of the same figure for each gerating position. To achieve a uniform distribution of the weover the contest of the cutting teeth, the hob must be shitangentially.

Assuming a tangential shift equal to the tool axial pitch (SH5e) the cutting toothi takes the generating position of the tooi 11. Hereby, the tooth 1 quits cutting, whereas the tooth 5 cfor the first time in the generating position IV. The wear behav

Fig. 7 Determination of the wear distribution at individual hobteeth considering the shift data

Journal of Manufacturing Science and Engineering

obg

e

e

ext

k-tion,isee-hift

toolFR-

hatur

isofthe

tingaph.eardi-of

isn-

arted

Dhutsor

of each tooth is now obeying the wear law that governs the gerating position, where they cut after shifting. The wear progron a hob tooth starts from the status developed by the enthe former cut of the observed tooth in the previous generaposition.

In this way the wear on the hob teeth becomes uniform, theexploitation is enhanced and the manufacturing cost reduced.wear calculations to determine optimum shifting conditionsspecific cutting cases, will be presented in a later paragraph ding with uncoated and coated HSS tools.

The wear prediction in gear hobbing with uncoated or coatools and the optimization of the tool shifting can be conductedmeans of the FRSWEAR program~see Fig. 8!. This softwareenables the hobbing process simulation and incorporates abase of experimentally-analytically derived wear equation cstants, for a variety of tool coatings and workpiece materials. Tcode is built in an open and modular structure and offers a gracal interface with interactive communication for the data inpand results output. The tool wear prediction can be carried outaking into account the process kinematics and all technologparameters of an examined manufacturing case. This is conduafter determined the group and the equivalent dimensions of echip in all generating positions, either in transient or in full cworkpiece regions. Optimized shift conditions to achieve a pscribed and almost uniform wear distribution on the hob teethalso be provided by means of the FRSWEAR program.

5 Development of an Experimental Procedure to In-vestigate the Wear Development in the Individual Hob-bing Generating Positions

During gear hobbing, as already described, each cutting tocuts in a certain generating position in a gear gap and after arevolution, in the case of a hob with one helix, penetrates intosame generating position of the next gear gap. To investigatewear development in the individual generating positions, ghobbing wear experiments have to be conducted. Since thehanced wear on hob teeth, working in generating positions w

Fig. 8 The flow chart diagram to the developed FRSWEARprogram

FEBRUARY 2002, Vol. 124 Õ 45

Page 5: Gear Hobbing Cutting Process Simulation and Tool Wear .... JOURNALS/12.5.pdf · Gear Hobbing Cutting Process Simulation and Tool Wear Prediction Models Gear hobbing is an efficient

a

iD

s

e

ps,

th.s asstinu-nd iti-ingnt

er-nd

ache aheth

iateo-nu-thearrn-

othted

ll becor-onend,theted in

s oflmostap-oolearin-

n 6avesient

large chips, imposes the termination of the experiments, the wdevelopment on hob teeth cutting in less endangered generpositions cannot be investigated.

To cope with this problem an experimental procedure with ocutting tooth, the so-called fly hobbing, is applied. In this tecnique, the cutting tool is replaced with a cylindrical holder,which in the case of simulating a hob with one helix, one cutttooth has to be fixed. The tooth geometry corresponds to the3972 regulations. The tool workpiece system in this approachthe hobbing process is illustrated in the upper part of Fig. 9. Tholder is constructed in such a way as to enable easy mounand release of the cutting tooth, as well as increased stiffnesensure cutting stability at high speeds or feedrates.

The fly hobbing kinematics with discontinuous axial feedra~DAF! are illustrated in the middle of Fig. 9. In this hobbinprocedure, the cutting tooth cuts with continuous tangential fand without axial feed one generating position in all gear gaduring one workpiece revolution and moreover all generatingsitions in further workpiece revolutions. After completing thetasks, the tool is moved axially for the amount of the axial feed

Fig. 9 Experimental procedure with modified fly hobbing kine-matics, to monitor the wear development on hob teeth in indi-vidual generating positions

46 Õ Vol. 124, FEBRUARY 2002

earting

neh-inng

INof

heting, to

tegedps,o-eto

manufacture in this way discontinuously the entire gear widThis experimental procedure is applied in many research workfor example in@1–8,11,13–15#. The main disadvantages of thiexperimental approach is that the cutting tooth penetrates conously in all successive generating positions of the gear gaps, ais not possible to mount efficiently into the tool holder an indvidual tooth per generating position, or for a batch of generatpositions in which chips with approximately similar equivalegeometries are formed.

In order to enable wear investigations in the individual genating positions, the kinematics of fly hobbing were modified athe continuous axial feed~CAF! fly hobbing was introduced, asillustrated in the bottom part of Fig. 9@23,24#. The aim of thisprocedure is to investigate the wear behavior separate in egenerating position. According to this experimental techniqucutting tooth works along the entire width of all gear gaps in tsame generating position. After the formation of the entire widof all gear gaps, in a generating position, through an approprrotation and shifting of the tool holder, the cutting tooth is relcated to work in the next generating position, and keeps on mafacturing in this new generating position for the whole gear widof all workpiece gaps. In this way the wear progress during ghobbing of a chip corresponding to a certain chip group conceing its geometry can be monitored, by replacing the hob tobefore moving it, to a next generating position. Hence, the relawear equations constants may be easily determined, as it wifurther described. The experiments and the evaluation of theresponding results will be demonstrated as a case study forcoated tool, workpiece material combination. On the other hareference experiments with uncoated HSS tools in hobbing ofsame gear material have been carried out and are also presenthis paper.

To reduce the experiments duration, the generating positionthe observed gear hobbing case are classified in batches of asimilar chips belonging to the same chip group and havingproximately the same dimensions and contribution to the twear. Figure 10 illustrates an example of how the observed ghobbing case, with nominally 35 generating positions, can bevestigated using only 4 different cutting teeth. Hereby at least igenerating positions small chips are formed, which do not hany contribution to the wear progress on the endangered tran

Fig. 10 Chip batches of various generating positions, withcorresponding dimensions

Transactions of the ASME

Page 6: Gear Hobbing Cutting Process Simulation and Tool Wear .... JOURNALS/12.5.pdf · Gear Hobbing Cutting Process Simulation and Tool Wear Prediction Models Gear hobbing is an efficient

c

i

re

in

s

ot

ah

A

,tingennceini-

ndhe

flentincetheir

rst

cutting edge regions from the tooth head to the flanks. The ocring chips in the present manufacturing case are classified togroup 1 or 0. Their equivalent chip dimensions, as well ascorresponding group for each of the four generating positbatches are inserted in Fig. 10. The equivalent chip dimensare mean values of the corresponding chip dimensions of ebatch. The analytically derived equivalent chip dimensions as was the experimentally derived flank wear versus the numbecuts were used, as described in the next paragraph, in orddetermine the wear prediction equation constants in the caschip groups 0 and 1, included in the database of the develoFRSWEAR code.

The flank wear progress was monitored by means of optmicroscopy. The coating wear was investigated through ScanElectron Microscopy~SEM! and Energy Dispersive X-Ray~EDX!microanalyses. The wear development for one generating ptions batch is presented in Fig. 11. According to these resultthe present hobbing case the most endangered cutting edgetion is on the trailing flank. The micrograph of the same figuillustrates an oblique view of the transient position from the tohead to the trailing flank. In this micrograph can be observedthe coating has been removed mainly on the flank. EDX analyalso proved this optical observation. The flank wear, was msured by means of optical microscopy, whereas in random cthe corresponding values were successfully crosschecked witaid of more accurate SEM measurements.

6 Evaluation of Experimental Results in Order to De-termine the Hob Wear Prediction Equation Constants

The basic equation used in the algorithms of the FRSWEprogram is the following@6,13–15#:

Fig. 11 Wear progress and SEM photos of the hob tooth trail-ing flank

Journal of Manufacturing Science and Engineering

ur-the

theiononsachellof

r toe ofped

caling

osi-in

posi-rethhatsesea-sesthe

R

~ log ASi !/CAS1~ log hsi!/Chs1~ log l i !/Cl

5~2~ log v i !/~Cv CAS~VB i /~CASCVB!112VB/ ~CVBCAS!!!

111~ log v !/~CvAAS~VB i /~CASCVB!

112VB/ ~CVBCAS!!!!~VB i /~CASCVB!

112VB/ ~CVBCAS!! (1)

whereas the parameters ASi , hsi , l i andv i are the number of cutsthe equivalent chip thickness, the cutting length and the cutspeed respectively. VBi describes the flank wear progress betwea predefined minimum and a maximum value VB as a refereone. The flank wear between the zero and the predefined mmum VB values is determined through a linear interpolation.

The constantsCAS , Chs , Cl , CVB and CV in the previousequation are different for every combination of cutting tool aworkpiece material and have to be experimentally derived. Tmeasured values of the flank wear VBi versus the number osuccessive cuts, in combination with the calculated equivachip dimensions, allow the calculation of these constants. Sthe constant values depend on the chip group, to enabledetermination, experimental data are necessary.

Figure 12 illustrates the hereby applied procedure. In a fistage, the coefficient of the wear zone widthCVB is determined.

Fig. 12 Determination of the wear equation constant CVB aswell as of the Chs , Cl and CAS ones

FEBRUARY 2002, Vol. 124 Õ 47

Page 7: Gear Hobbing Cutting Process Simulation and Tool Wear .... JOURNALS/12.5.pdf · Gear Hobbing Cutting Process Simulation and Tool Wear Prediction Models Gear hobbing is an efficient

themiccasemm

arnd

f atffer-12,rat-ach

inheirfer-earetion

This

nd-thebase

ofVBnd. 13ithll

f theum-erall

or

anhisictedus.ts are

e-ned,of

ppertheachidthk9th

ringthed 5ci-toolthe

Fig. 13 Comparison between the achieved number of cuts upto a flank wear of 0, 3 mm in gear hobbing with uncoated andcoated HSS tools in the cases of chips of the same group withdifferent dimensions

Fig. 14 Comparison between the experimentally and the com-putationally derived wear progress in CAF fly hobbing

48 Õ Vol. 124, FEBRUARY 2002

For this purpose, the diagrams of the flank wear VB versusachieved number of cuts are transformed into semi logarithones, regarding their abscissa. In the considered hobbingwith coated tools, the flank wear values between 0.1 and 0.3form an inclined line. The tangent of the inclinationw of this lineis the coefficientCVB . Considering these results flank wecalculations using Eq.~1! can be conducted, between 0.1 a0.3 mm.

In a further stage, the determination of the coefficientsCl , CHSand CAS necessitate hobbing experimental flank wear data oleast three chips, belonging to the same chip group, having dient equivalent dimensions. The intermediate diagram of Fig.illustrates measured flank wear values for three different geneing position batches, which belong to the same chip group. Echip corresponds to a point of the three dimensional diagramthe bottom figure part, the Cartesian coordinates of which are tequivalent width, length and number of achieved cuts, at a reence flank wear of VB50.3 mm. With the aid of at least threpoints the indicated plane is defined. If more than three pointsconsidered to determine the previous mentioned plane, its locais defined by means of the least square optimization method.plane intersects the axes log(hs), log(l) and log(AS) at points cor-responding to the coefficientsCl , Chs andCAS respectively~seethe bottom diagram of Fig. 12! @6,13–15#. If another reference VBvalue is set as tool life criterion a further plane is defined aconsequently differentCi ~i: l, hs, AS! coefficient values are determined. By means of this procedure, the coefficients ofmathematical model are defined and implemented in the dataof the FRSWEAR program.

With the aid of this program the determination of the numbersuccessive cuts, until a set VB criterion, as for example of50.3 mm is fulfilled, in gear hobbing of various chip groups adifferent dimensions can be conducted. The diagrams of Figillustrate such results, in hobbing with uncoated and wSUPERTIN® coated HSS tools. The workpiece material in athese cases is the steel 42 CrMo4 V. The superior behavior ocoated tools relatively to the uncoated ones is evident. The nber of successive cuts can easily be transformed to an ovwidth of gears to be manufactured, until the tool re-sharpeningreplacement is necessary.

The reliability of the determined wear prediction constants cbe judged considering the results illustrated in Fig. 14. In tfigure the convergence between the measured and the predVB wear values, in three different generating positions is obvioFurther comparisons between measured and calculated resulpresented in@6,12–15#.

7 Applications of the Tool Wear Prediction Modelsto Determine Optimum Shifting Conditions in GearHobbing

With the aid of the introduced analytical-experimental procdures, optimum tangential shifting parameters can be determiin order to achieve a uniform wear distribution on the majoritythe tool cutting teeth.

These calculations are carried out as demonstrated in the upart of Fig. 15, where the accumulated wear, occurring onindividual hob teeth after the manufacturing of ten gears in eshift position is illustrated. In this case the test gear has of a wof 25 mm. After the sixth tangential shifting, the maximum flanwear amounts approximately 0.3 mm on the most endangeredhob tooth.

The expected wear development on the used hob teeth duthe previous described tool shifting procedure is shown inlower figure part. As it can be observed the cutting teeth 4 anafter the 4th and the 5th tool shifting respectively, don’t partipate to the hobbing process, due to the fact that through theshift they exit from the contact area between the hob andworkpiece.

Transactions of the ASME

Page 8: Gear Hobbing Cutting Process Simulation and Tool Wear .... JOURNALS/12.5.pdf · Gear Hobbing Cutting Process Simulation and Tool Wear Prediction Models Gear hobbing is an efficient

oi

e

r

.r

oh

r

are

ari-liedifi-ults

olare

ela-ov-icalualear

ble.andarpro-

pro-cess-tototedntlys.

By means of the introduced hob wear calculations the approate shift amount i.e. the number of gears per shift positionvarious shift displacements, can be determined~see Fig. 16!.Hereby two manufacturing cases are considered. In the first cagear with a relatively small width of 25 mm is examined, wherein the second one a gear with ten times bigger width. In bcases, the number of gears are illustrated, after which, for vartangential displacements a tool shift is necessary, in order totain concrete flank wear values. The appropriate numbers of gper shift position to achieve a prescribed maximum flank wdepends as expected on the gear width.

The overall gear width per hob tooth, as well as the numbecuts per hob tooth, up to a flank wear of 0.3 mm in the previoconsidered manufacturing cases are demonstrated in Fig. 17required number of gears to be hobbed per shift position in oto get the previous mentioned maximum flank wear is also shoBy increasing the tangential displacement amount, a slight gring of the overall gear width per hob tooth as well as of tnumber of cuts per hob tooth can be observed. This increasinexplained through the better exploitation of the cutting teeth inhob external regions~hob teeth 148 and 15422). For exampleon the 6th hob tooth in the cases of 1«, 2«, and 3« displacementper shift, in hobbing of a gear width of 25 mm, the flank weamounts 0.18, 0.20 and 0.22 mm respectively~see Fig. 16!.

On the other hand, in the case of a larger gear width asexample the examined case withb5250 mm, the overall hobbedwidth is lower in comparison to the corresponding one when gewith a width of 25 mm are manufactured.

This can be explained through the diminishing in the case ogear width of 250 mm, of the number of cuts in transient wo

Fig. 15 Calculation of the wear development on certain hobteeth and the overall wear distribution over the hob teeth, cal-culated by means of the FRSWEAR program

Journal of Manufacturing Science and Engineering

pri-for

se aasth

ousob-earsar

ofusThe

derwn.w-e

g isthe

ar

for

ars

f ak-

piece cutting regions, where chips with small dimensionsformed, in relation to the overall number of cuts.

The better cutting performance of the coated tools in compson to uncoated ones, can be observed in Fig. 18. In all appshifting conditions the SUPERTIN® coated tool leads to a signcant higher cutting performance. Further corresponding reswith TINALOX® coatings @16–18,21# ascertain this tendency.

8 ConclusionsThe aim of this paper is to exhibit methods to predict the to

wear development in gear hobbing. The introduced proceduresbased on the analytical determined chip geometry and its corrtion to experimental results in order to establish wear laws, cering every possible hobbing case. In this way, mathematmodels to determine the wear progress on hob teeth in individcutting and generating positions as well as to describe the wdevelopment considering the hob tangential shifting are availaWith the aid of the described experimental results evaluationapplying fly hobbing with continuous axial feed, the tool weequations constants of the used algorithms in the FRSWEARgram can be efficiently determined.

The results of the presented investigations show that theposed numerical experimental approach can be applied sucfully to predict the tool wear behavior in gear hobbing andoptimize cutting and hob tangential shifting conditions in orderachieve a uniformly distributed wear on the tool teeth. The coahob teeth showed in the conducted investigations a significaincreased cutting performance in comparison to uncoated one

Fig. 16 Flank wear development on the hob teeth at variousshift conditions and gear widths

FEBRUARY 2002, Vol. 124 Õ 49

Page 9: Gear Hobbing Cutting Process Simulation and Tool Wear .... JOURNALS/12.5.pdf · Gear Hobbing Cutting Process Simulation and Tool Wear Prediction Models Gear hobbing is an efficient

l

rch

itss-Dis-

senTH

ft-N,’’

ft-eter

a-ilita-

im

S-

eared

rta-

lz-

r

desodenelnen

desVer-Pro-

o-P

n.is,

g,nalnol-

ue

ing

.,o-

es,’’

to-ar

AcknowledgmentsThis research was financially supported by the General Se

tariat for Research and Technology of the Greek Ministry for Dvelopment in the frame of the BE411 PAVE project~program forthe development of industrial research! entitled ‘‘Determination oftool life time in gear hobbing, to increase the productivity andreduce the manufacturing costs.’’ Besides the Laboratory for Mchine Tools and Manufacturing Engineering of the AristoteUniversity, an industrial partner to this project was NortheGreek Workshops ORFANIDES SA. The authors would likethank CemeCon GmbH~Aachen, Germany! for the coating ser-vice required by the experimental project needs.

Fig. 17 Achieved overall gear width and number of cuts perhob tooth at various shift conditions and gear widths

Fig. 18 Achieved overall gear width per hob tooth with coatedand uncoated tools

50 Õ Vol. 124, FEBRUARY 2002

cre-e-

toa-

esrnto

Nomenclature

AS 5 number of cutsb 5 gear width~mm!

CAF 5 continuous axial feedCP 5 cutting position

DAF 5 discontinuous axial feedf a 5 axial feed~mm/wrev!G 5 chip group

LF 5 leading flankni 5 number of hob columns

SHD 5 tangential displacementSHN 5 number of gears per tangential displacement

TF 5 trailing flankv 5 cutting speed~m/min!

VB 5 wear flankz1 5 number of hob helixesz2 5 number of gear teeth« 5 tool helix axial pitch~mm!

References@1# Sulzer, G., 1974, ‘‘Leistungssteigerung bei der Zylinderradherstellung du

genaue Erfassung der Zerspankinematik,’’ Dissertation, TH Aachen.@2# Joppa, K. 1977, ‘‘Leistungssteigerung beim Waelzfraesen mit Schnellarbe

tahl durch Analyze, Beurteilung und Beinflussung des Zerspanprozesses,’’sertation, TH Aachen.

@3# Tondorf, J., 1978, ‘‘Erhoehung der Fertigungsgenauigkeit beim Waelzfraedurch systematische Vermeidung von Aufbauschneiden,’’ Dissertation,Aachen.

@4# Bouzakis, K.-D., 1979, ‘‘Ermittlung des zeitlichen Verlaufs der Zerspankrakomponenten beim Waelzfraesen Teil 1: Digitalrechnerprogramm FRDYVDI-Z, 121, No. 19, Oct., pp. 943–950.

@5# Bouzakis, K.-D., 1979, ‘‘Ermittlung des zeitlichen Verlaufs der Zerspankrakomponenten beim Waelzfraesen Teil 2: Einfluesse technologischer Paramder Werkzeuggeometrie und der Werkradgeometrie,’’ VDI-Z,121, No. 20,Oct., pp. 1016–1026.

@6# Bouzakis, K.-D., 1980, ‘‘Konzept und technologishe Grundlagen zur automtiserten Erstellung optimaler Bearbeitungsdaten beim Waelzfraesen,’’ Habtion, TH Aachen VDI-Z,2, No. 42.

@7# Venohr, G., 1985, ‘‘Beitrag zum Einsatz von Hartmetall Werkzeugen beWaelzfraesen,’’ Dissertation, TH Aachen.

@8# Kauven, R. H., 1987, ‘‘Waelzfraesen mit Titannitridbeschichteten HSWerkzeugen,’’ Dissertation, TH Aachen.

@9# Antoniadis, A., 1988, ‘‘Determination of the Impact Tool Stresses During GHobbing and Determination of Cutting Forces During Hobbing of HardenGears,’’ Dissertation, Aristoteles University of Thessaloniki.

@10# Gutman, P., 1988, ‘‘Zerspankraftberechnung beim Waelzfraesen,’’ Dissetion, TH Aachen.

@11# Mundt, A., 1992, ‘‘Modell zur rechnerichen Standzeitbestimmung beim Waefraesen,’’ Dissertation, TH Aachen.

@12# Bouzakis, K.-D., and Antoniadis, A., 1995, ‘‘Optimizing Tool Shift in GeaHobbing,’’ CIRP Ann.,44, pp. 75–79.

@13# Bouzakis, K.-D., 1980, ‘‘Mathematische Beschreibung des VerlaufesWerkzeugverschleißes beim Waelzfraezen. Teil 1: Untersuchungsmethund Kenngroeßen zur Erfassung des Werzeugverschleißes in den einzWaelzstellungen,’’ VDI-Z, No. 20, Oct., pp. 857–868.

@14# Bouzakis, K.-D., 1980, ‘‘Mathematische Beschreibung des VerlaufesWerkzeugverschleißes beim Waelzfraezen. Teil 2: Berechnung derschleißentwicklung in den einzelnen Waelzstellungen und beim Shiften;grammkette Waelzfraeservershleiß,’’ VDI-Z,122, No. 21, Nov. 1, pp. 951–965.

@15# Bouzakis, K.-D., and Koenig, W., 1981, ‘‘Process on Models for the Incorpration of Gear Hobbing into an Information Center for Machining Data,’’ CIRAnn., 30, pp. 77–82.

@16# CemeCon GmbH, 1997, Informational Bulletins: Coating Services, Aache@17# Bouzakis, K.-D., Antoniadis, A., Kombogiannis, S., Orfanidis, N., Stamatiad

Ch., and Vidras, A., 1998, ‘‘Determination of Tool Life Time in Gear Hobbinto Increase the Productivity and to Reduce the Manufacturing Costs,’’ fireport of PAVE project BE411, General Secretariat for Research and Techogy, Ministry for Industry and Development of Greece.

@18# Bouzakis, K.-D., et al., 1998, ‘‘Experimental and FEM Analysis of the FatigBehavior of PVD Coatings on HSS Substrate in Milling,’’ CIRP Ann.,47, pp.69–73.

@19# Klocke, F., et al., 1998, ‘‘Improved Cutting Processes with Adapted CoatSystems,’’ CIRP Ann.,47, pp. 65–68.

@20# Bouzakis, K.-D., Vidakis, N., Kallinikidis, D., Leyendecker, T., Erkens, GFuss, H.-G., and Wenke, R., 1998, ‘‘Failure Mechanisms of Multi- and MonLayer Physically Vapor Deposited Coatings in Interrupted Cutting ProcessSurf. Coat. Technol.,108–109, pp. 526–534.

@21# Bouzakis, K.-D, Kombogiannis, S., Antoniadis, A., Vidakis, N., and Anaspoulos, J., 1999, ‘‘Lifetime Prediction of PVD Coated HSS Tools in Ge

Transactions of the ASME

Page 10: Gear Hobbing Cutting Process Simulation and Tool Wear .... JOURNALS/12.5.pdf · Gear Hobbing Cutting Process Simulation and Tool Wear Prediction Models Gear hobbing is an efficient

d

t

si-

9,-thend

Hobbing,’’ 1st International Conference THE Coatings, October, Ziti EThessaloniki pp. 139–158.

@22# Bouzakis, K.-D, Kombogiannis, S., Antoniadis, A., Vidakis, N., and Anaspoulos, J., 1999, ‘‘Lifetime Prediction of PVD Coated Tools in Gear Hobing,’’ 5th Conference on Machine Tools-Manufacturing Processes, DecemZiti Ed., Thessaloniki, pp. 224–245.

@23# Bouzakis, K.-D, Kombogiannis, S., Antoniadis, and A., Vidakis, N., 199‘‘Modeling of Gear Hobbing. Cutting Simulation and Tool Wear Predictio

Journal of Manufacturing Science and Engineering

.,

o-b-ber,

9,n

Models,’’ ASME International Mechanical Engineering Congress and Expotion, MED-Vol. 10, pp. 253–259.

@24# Bouzakis, K.-D, Kombogiannis, S., Antoniadis, A., and Vidakis, N., 199‘‘Modeling of Gear Hobbing. Cutting Simulation, Tool Wear Prediction Models and Computer Supported Experimental-Analytical Determination ofHob Life-time,’’ ASME International Mechanical Engineering Congress aExposition, MED-Vol. 10, pp. 261–269.

FEBRUARY 2002, Vol. 124 Õ 51