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An investigation into tool-wear and phenomena influencing tool-life in milling Oyawoye, Orisunmbola A. 1993

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AN INVESTIGATION INTO TOOL-WEAR AND PHENOMENA INFLUENCINGTOOL-LIFE IN MILLINGbyORISUNMBOLA AYODEJI OYAWOYEB. Eng. (Mechanical Engineering)Ahmadu Bello University, Zaria, Nigeria; 1988A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTSFOR THE DEGREE OFMASTER OF APPLIED SCIENCEinTHE FACULTY OF GRADUATE STUDIESDEPARTMENT OF MECHANICAL ENGINEERINGWe accept this thesis as conformingto the required standardTHE UNIVERSITY OF BRITISH COLUMBIAMarch 1993© Orisunmbola A. Oyawoye, 1993In presenting this thesis in partial fulfillment of the requirements for an advanceddegree at the University of British Columbia, I agree that the Library shall make itfreely available for reference and study. I further agree that permission forextensive copying of this thesis for scholarly purposes may be granted by thehead of my department or by his or her representatives. It is understood thatcopying or publication of this thesis for financial gain shall not be allowed withoutmy written permissionMechanical Engineering DepartmentThe University of British Columbia2075 Wesbrook MallVancouver, B. C., V6T 1Z1CanadaDate: AbstractAbstractThe subjects of tool-life, tool-wear and machinability have attractedextensive research interest most of which have been directed toward turningoperations. The added complexity of milling operations, resulting from both thediscontinuous nature of the process and the varying chip thickness during cut,are the reason for reduced research interest in comparison to turning. Althoughseveral researchers have examined the milling process, considerablecontroversy still surrounds the basic factors influencing tool-life in milling. In thestudy of the basic factors involved in the milling of both high strength steel andtitanium alloy work materials, the basic form of the equations which result tend tosupport a thermal fatigue process as the most likely source of differencebetween continuous and discontinuous cutting. To validate this hypothesisfurther, special tests have been conducted within an inert atmosphere toascertain the influence of oxidation on wear rate. It is also found that theinfluence of exit conditions may be critical in some circumstances, andexperiments have again been carried out to examine this phenomenon. Finally,from a consideration of the tracking of tool-wear in milling operations, acomprehensive scheme which allows both identification of cutting conditions andtracking of wear on end mills and face mills is presented.iiTable of ContentsTable of ContentsAbstract^Table of Contents ^ iiiList of Figures viList of Tables^Acknowledgments xiDedication^ xiiINTRODUCTION 1Chapter 1 Literature Review^ 41.1 Milling 41.1.1 Classification of Milling Operations^ 61.1.2 Geometrical and Force Nomenclature in Milling^ 71.2 Tool-Wear^ 81.2.1 Types of Wear^ 81.2.2 Mechanisms of Wear 121.3 Tool-Life ^ 141.3.1 Determination of Tool-Life ^ 141.3.2 Tool-Life in Turning 161.3.3 Influence of Various Parameters on Tool-Life^ 18iiiTable of Contents1.4 Concept of Equivalent Feed^ 281.5 Concept of Thermal Fatigue 301.5.1 Tool-Life in Half and Full Immersion Tests^ 311.5.2 Explanation of Thermal Fatigue Phenomenon^ 331.5.3 Definition of Thermal Fatigue Parameter^ 341.5.4 Tool-Life Equation for Milling^ 35Chapter 2 Tool-Life Investigation: Experimentation and Analysis^ 372.1 Tool-Life Experimentation^ 372.1.1 Equipment Setup and Test Procedure^ 392.1.2 Tool-Life Data For Steel and Titanium Work Materials ^ 432.1.3 Data Analysis^ 442.1.4 Discussion of Results. ^ 592.1.5 Tool-Life Tests Within an Inert Atmosphere^ 612.2 Investigation of Exit Failure in Milling ^ 632.2.1 Sharp Corner Test^ 632.2.2 Investigation of Behavior at Tool Exit Leadingto Failure^ 65Chapter 3 Force Modeling and Tool-Wear Tracking in Milling^ 773.1 The Modeling of Instantaneous Forces in Milling 773.2 Tracking of Machining Condition and Tool-Wear in Milling ^ 933.2.1 Tracking Techniques for the Recognition of MachiningCondition ^ 973.2.2 Tracking Techniques for the Recognition of ToolCondition ^ 101ivTable of ContentsChapter 4 Conclusion and Recommendations^ 114Appendix 1 Derivation of Fourier Series Expressions for Force Modeling ^ 116Appendix 2 Program Listing for Fourier Series Based Cutting ForceSimulation^ 125References^ 131vList of FiguresList of Figures1.1 Simple Schematic of Milling Operation^ 51.2 Milling Operations: (a)Peripheral Milling; (b)Face Milling ^ 61.3 Milling Nomenclature^ 81.4 Flank Wear on an Insert 91.5 Crater Wear on an Insert^ 101.6 Notch Wear on an Insert 111.7 Typical Flank Wear Versus Cutting Time Relationship^ 151.8 Typical Relationship Between Tool-Life and Cutting Speed^ 171.9 Schematic of Turning Operation Showing Undeformed Area of Cut^ 181.10 Tool-Life as a Function of Number of Cutter Teeth^ 191.11 Proposed Shearing Action at Tooth Exit^ 241.12 Schematic of Initial Contact at Tooth Entry 251.13 Influence of Up- and Down-Milling on Rake Face Temperature^ 271.14 Variation of Feed in Milling Over One Cutter Revolution^ 281.15 Determination of Characteristic Tool-Wear Versus Time Relationshipfor Milling ^ 291.16 Tool-Wear Versus Active Cutting Time Relationship in Milling; ShowingDefinition of Equivalent Feed^ 301.17 The Comparison Between End Mill Slotting and Half Immersion Tests ^ 311.18 Slotted Workpiece Used to Investigate Influence of Entry and ExitConditions^ 33viList of Figures1.19 Temperature Distribution Within Tool During Heating and CoolingCycles^ 342.1 Equipment Set-Up for Tool-Life Tests on Steel Work Material^ 402.2 Two Axes Measuring Laboratory Microscope Used for Tests onTitanium Alloy^ 412.3 Tool-Wear - Time Relationship Under Constant Feed Conditions^ 452.4 Milling Tooth and Associated Wear Over One Cycle^ 46R2.5 Variation of S--es- With 7R in Milling^ 48St2.6 Plot of log Ta Vs. log St for Slotting Data to Determine 13 for Steel^ 532.7 log Ta Vs. log St Plots for All Test Conditions on Steel Using Known 0 ^ 542.8 Plot of log Ta Vs. log St for Half Immersion Data to Determine 13for Titanium^ 552.9 Plot of log Ta Vs. log St for All Test Conditions on Titanium^ 562.10 Plot of log Ta Vs. log Xto Determine n for Steel^ 572.11 Plot of log Ta Vs. log Xto Determine n for Titanium 582.12 Schematic of Arrangement Used for Argon Influenced Tests^ 622.13 Schematic Illustration of Sharp Corner Wear^ 642.14 Illustration of Sharp Corner Test Result 652.15 Schematic of Shear Plane Region of Cutting Operation and AssociatedVelocity Vector Polygon^ 662.16 Typical Exit Angles 682.17 Experimental Set-Up for Exit Failure Investigation^ 70viiList of Figures2.18a Traces for Exit Failure Investigation with Cutting Conditions 288 rpmand 24 mm/min^ 722.18b Traces for Exit Failure Investigation with Cutting Conditions 180 rpmand 14.4 mm/min^ 732.18c Traces for Exit Failure Investigation with Cutting Conditions 144 rpmand 14.4 mm/min^ 742.18d Traces for Exit Failure Investigation with Cutting Conditions 72 rpmand 14.4 mm/min^ 753.1^Forces Acting on a Single Tooth in Up- and Down-Milling^ 773.2^Experimental Force Data from Up-Milling Test on Titanium^ 833.3 Experimental Force Data from Down-Milling Test on Titanium^ 843.4^Experimental Force Data from Centerline-Milling Test on Titanium^ 853.5 Comparison of Actual and Simulated Force Data (Tangential andRadial Components)^ 873.6 Comparison of Actual and Simulated Force Data (X and YComponents)^ 883.7 Simulated and Actual Cutting Force Comparison For FourierSeries Based Model Investigation; 288 rpm, 14.4 mm/min^ 913.8 Simulated and Actual Cutting Force Comparison For FourierSeries Based Model Investigation; 288 rpm, 30 mm/min^ 923.9^Milling Force Locus^ 983.10 Relationship Between Immersion Parameter Q and Immersion forExperimental and Predicted Values^ 101viiiList of Figures3.11 Theoretical Values of the Wear Tracking Parameter as a Functionof Immersion^ 1043.12 The Performance of the Wear Tracking Parameters in Slotting^ 1053.13 The Performance of the Wear Tracking Parameters in HalfImmersion^ 1063.14 Influence of Wear on the Axial Component of Force in Slotting with aSingle Tooth Carbide Milling Cutter^ 1073.15 Predicted Values of the Magnitude of the Mean and FundamentalCoefficients of the Force in the Feeding Direction^ 1093.16 Predicted Values of the Magnitude of the Mean and FundamentalCoefficients of the Force Perpendicular to the Feeding Direction ^ 1103.17 Predicted Influence of Wear on the Force Ratio Fx( max)/Fy(max)^ 1113.18 Actual Values of the Force Ratio^ 112ixList of TablesList of Tables2.1 Tool-Life Data for AISI 4140 Low Alloy Steel Work Material^ 442.2 Tool-Life Data for Titanium Alloy Work Material^ 442.3 Thermal Fatigue Parameter Values for Steel 522.4 Thermal Fatigue Parameter Values for Titanium^ 522.5 Calculated Seq/St Values for Steel and Titanium 572.6 Tool-Life Data for Argon Influenced Milling of Steel and Titanium^ 623.1 Data Used to Determine Model Constants for Up-Milling Test (Ti.)^ 863.2 Data Used to Determine Model Constants for Down-Milling Test (Ti.)^ 863.3 Determined Force Model Constants for Titanium Alloy^ 86xAcknowledgmentsAcknowledgmentsForemost, I wish to express my profoundest sentiments of gratitude to mysupervisor and teacher, Professor Ian Yellowley, for his assistance, support andin particular his patience throughout the course of this study. I am deeplyindebted to him. I thank the faculty and staff of Mechanical Engineering in theirrespective capacities for various forms of assistance rendered to me over theyears and also thank my colleagues for their camaraderie.I acknowledge the assistance of several other members of the universitycommunity, in particular Kathleen Beaumont for her unyielding support andconstant encouragement, Adelia Livesey for proof-reading the text and for herinspiration, and Drs. Dawodu, Losso and McIntyre for all their encouragement.To my parents Professor and Mrs. Oyawoye and to my siblings (especiallySiyan in Seattle), I wish to say thank you for the constant love, support andencouragement; to good friends like Raji Atobiloye, Fran Munoz, JohnBrzustowski, Sola Esuruoso, Tunde Aiku and several others which space doesnot permit me to mention, I express gratitude for their friendship and support.Most importantly, I thank my wife Mariam, and my son Olaloye, for the tons oflove, support, encouragement and sacrifices which made this task possible.Finally, I gratefully acknowledge the financial support of Pratt and Whitneyof Canada and the National Science and Engineering Research Council ofCanada who provided the research funding.xiDedicationDedicationTo 'Loye and Mairo^^the sources of my pride and my joy.IntroductionINTRODUCTIONThe phenomenon of Tool-Wear in cutting tools is extremely complex,involving and affected by a variety of disparate parameters and cuttingconditions. Since the type and amount of wear to which a tool is subjectedultimately determine its total usefulness, Tool-Life is of extreme importance inany consideration of the economics of machining and the quality of finishedproducts.The economic benefits that can be achieved through a thorough knowledgeof the subject are extensive: An understanding of process economics can resultin the selection of machining conditions to optimize the life of the tool. Thismeans that fewer tools are expended on any given component and consequentlyfewer tool changes are required per batch. Significant savings in tooling, and inmachine and manpower costs thus result. These savings may well determinethe profitability of any machine shop, be it small or large.The Milling process is more complex than a process such as turning. Ofincreased complexity however is the subject of tool-wear in milling. Due to thecomplex nature of this machining process, the formulation of a realistic anduseful mathematical model which accurately describes the process and gives areliable, unique solution is difficult. The lack of previous research directedtoward tool-wear in milling, in contrast to tool-wear in turning, in whichsubstantial work has been carried out, may be attributed to the complex natureof the milling process itself (the variables affecting tool-life in turning are only half1Introduction^ 2the number in milling). Previous workers [11 have suggested that the maintechnical problem presented by milling as distinct from turning arises from thevariation in chip thickness during cut and the interruption which occurs in thecutting cycle.Of economic importance also is the subject of Tool-wear Monitoring orSensing. The impetus for research in this area is the need to prevent prematuretool failure which is devastating to surface finish, can lead to increased toolingcosts, and in the worst case can cause extensive damage to the machine tool.With wear monitoring, the large safety factors normally applied in practice to theuseful life of a cutting tool to prevent premature breakage (either by reducing thetime of use or by reducing the cutting speed) become unnecessary. Under suchcircumstances, the tool in general cuts longer so that savings in tooling costsresult.Needless to say, it would be economically beneficial if useful tool-lifeinformation could be achieved on-line with no machine stoppage or tool removal.If force is accepted as an indirect measure of wear, then information on thecondition of the tool should be obtainable from real-time force measurements,such measurements, of course, necessitating the use of dynamometers withreasonable bandwidth.This thesis presents work performed in the areas mentioned. Chapter 1discusses previous research in the general area of tool-wear and machinability.Chapter 2 describes the experimental work carried out in the investigation oftool-wear in milling and discusses the results in the light of previous work.Chapter 3 discusses force modeling, tool-wear monitoring and related concepts,Introduction^ 3describes the experimental work carried out in this area, and presents the resultsobtained. Chapter 4 presents conclusions and recommendations.Chapter 1 Literature ReviewChapter 1Literature ReviewMilling is a very important metal removal operation, yet a relatively smallamount of effort has been directed towards better understanding of the process.While recent work from many research groups [36] have attempted to examinethe increased efficiency in real milling operations, their work is generally basedupon a constraint-driven approach; in most cases, metal removal rates aremaximized consistent with constraints such as edge breakage, shank breakage,chatter, etc. Such investigations, however, have no basis in terms of thetraditional approach to process optimization which requires detailed tool-life andwear relationships. Without doubt, the complexity of the process and the costand time involved in the study of tool-life in milling has discouraged most groups,after an initial flurry of interest in the 1960's and 70's. This chapter reviews thebasic concepts of milling, tool-life and tool-wear, reviews earlier work in millingwhich is related to the present research, and attempts to indicate the areas inwhich considerable doubt remain.1.1^MillingMilling is the name given to a metal removal process or operation involvingthe use of a tool with one or more teeth rotating about a fixed axis, each tooth4Chapter 1 Literature Review^ 5removing material from a workpiece being fed past the tool. Fig. 1.1 shows aschematic representation of the process:Fig. 1.1. Simple Schematic of Milling OperationThere are basically two modes of milling: up- (or conventional) milling anddown- (or climb) milling. When the cutter is rotating so that its peripheral velocityis in the opposite direction to the direction in which the workpiece is being fed,the mode of milling is termed up-milling. It is characterized by a zero value ofundeformed chip thickness at entry into the workpiece and a finite value at exitfrom the workpiece. In down-milling, the reverse is the case. The cutter rotationis such that the peripheral velocity is in the same direction as that in which theworkpiece is being fed, and this operation is characterized by a finite value ofundeformed chip thickness at entry and a zero value at exit. Owing to theambiguity involved in determining the direction of the peripheral velocity fordifferent widths of cut, these definitions are valid only for widths of cut less thanthe radius of the cutter.Chapter 1 Literature Review^ 6The major distinct characteristics of milling, which lead to a significantincrease in complexity over turning, are its discontinuous or intermittent natureand the variable feed experienced by each tooth in cut (see Fig. 1.1).1.1.1 Classification pi Milling OperationsMilling operations can be classified into two types:• Peripheral (or slab) milling• Face (or end) millingFig. 1.2. Milling Operations: (a)Peripheral Milling; (b)Face Milling(after Armarego and Brown)In peripheral milling, (see Fig. 1.2a), cutting occurs on the teeth at theperiphery of the cutter, and the generated surface is a plane parallel to the cutteraxis. The teeth can either be straight cutting edges, helical or form teeth.In face milling however, cutting is performed by the edges on the peripheryand the face (or end) of the cutter, and the generated surface is a plane at rightangles to the cutter axis (see Fig. 1.2b).Chapter 1 Literature Review^ 71.1.2, Geometrical and Force Nomenclature  In MillinqWith reference to Fig. 1.3, the following are definitions of variablescommonly used in milling terminology:• a - Axial depth of cut• d - Radial width of cut• R - Cutter radius• d/R - Immersion; (2=full immersion, 1=1/2 immersion, 1/2=1/4 immersion)• V - Peripheral velocity• v - Feed-rate• St - Feed per tooth.0s - Swept angle of cut• 4) - Instantaneous angle of rotation• RPM - Spindle speed• FR - Radial component of cutting force• FT - Tangential component of cutting force• FX,FY,FZ f(FR,FT,O) - X, Y, and Z components of cutting forceChapter 1 Literature Review^ 8Fig. 1.3. Milling Nomenclature1.2 Tool-WearCutting tools, due to the nature of the cutting process, are subjected toextremely severe rubbing. They are in metal-to-metal contact with both theworkpiece and the chip under conditions of very high stress, and at hightemperature. The result is gradual breakdown of the tool material in the regionof cutting; this is termed "tool-wear". It is noteworthy that temperature plays asignificant role in the wearing process and that wear behavior may varysignificantly between one workpiece/tool combination and another.1.2.1 Types 21 WearTool-wear is of three major types: flank wear (or wear land), crater wearand notch wear. Depending on the circumstance, a tool can be affected by one,two, or all three types of wear.• Flank wear (or wear land): this wear occurs on both the major and minorcutting edges under essentially all cutting conditions. It gives rise to what isChapter 1 Literature Review^ 9universally known as the "wear land" which is more or less a uniform wear zoneon the flank of the tool as shown in Fig. 1.4.Fig. 1.4. Flank Wear on an Insert (after Mills and Redford)According to Yellowley [2], flank wear can largely be attributed to amechanical process initiated when primary particles are released from the toolface by a temperature-dependent process. As these primary particles arereleased and travel down the flank, they scour its surface and in the processrelease secondary particles by abrasion. These secondary particles also actsimilarly to further abrade the rest of the flank. Progressively, this processresults in a wear land being formed on the flank. The effect of this wear landwhen it occurs on the major cutting edge (which is responsible for bulk metalremoval) is increased cutting forces and higher temperatures which, if leftunchecked, can lead to vibration of the tool and workpiece as well as to acondition yielding inefficient cutting. On the minor cutting edge, whichdetermines machining accuracy and surface finish, oversized products with poorsurface finish can result. However, under most practical conditions, a tool willChapter 1 Literature Review^ 10fail due to major flank wear before the minor flank wear is large enough to resultin the manufacture of an unacceptable component. Flank wear is quantified interms of the wear land width, VB.• Crater wear: this wear, found on the rake face of the tool, is caused byhigh contact stresses and high chip-tool interface temperatures which lead tolocalized pitting of the tool face some distance up the face. Diffusion is the majorwear mechanism at play, but other mechanisms also play a role. Thephenomenon, usually referred to as cratering, is commonly expressed in termsof the maximum depth of crater.Fig. 1.5. Crater Wear on an Insert (after Mills and Redford)Previous work [3] has shown that the maximum depth of crater occurs at asubstantial distance from the cutting edge and that the crater curvaturecorresponds to the chip's radius of curvature. Under most practical cuttingconditions, crater wear is less severe than flank wear, particularly at lowercutting speeds. However, since the rake face temperature is known to increasemore rapidly than that of the flank face with increased cutting speed, and highercutting speeds are known to generally lead to larger wear in a shorter time,Chapter 1 Literature Review^ 11naturally, with increased cutting speed, crater wear can become quite significant.As crater wear progresses, it will eventually intersect the wear land so that amajor fracture results. Nonetheless, crater wear is now of much less concernbecause rake face coatings (TiC, TIN, A102) have been developed to drasticallyretard its growth.• Notch wear: this occurs at the end of the major flank wear land where thetool is in contact with the uncut workpiece surface as shown in Fig. 1.6. Itappears as a pronounced wear or notch at this point, and is caused by localizedeffects such as a hardened layer on the uncut surface possibly resulting fromwork-hardening introduced by a previous cut or an oxide scale. Although thenotch will not significantly affect the cutting properties of the tool, it can becomesevere and relatively deep. As cutting continues, fracture of the tool will likelyresult.Fig. 1.6. Notch Wear on an Insert (after Mills and Redford)Chapter 1 Literature Review^ 121.2.2 Mechanisms sit WearWhile the scope of this work does not include examination of wearmechanisms in detail, a brief description is useful. There are five majormechanisms through which wear may occur:• Wear by abrasion: the most common type of wear, in which relativemotion, both between the underside of the chip and the face, as well as betweenthe newly cut surface and the flank, causes the tool to wear even though thenewly cut workpiece surface and the chip may be much softer than the toolmaterial. In many cases, the reason for this is that, even though the workpieceand the chip may be relatively soft, hard inclusions or precipitates arising fromthe manufacturing process or from heat treatment will be present in theworkpiece. Hard particles can also result from breakdown of work hardened,unstable built-up-edges. Abrasive wear is normally involved in the developmentof a wear land on the flank.• Wear by adhesion: this is a wear mechanism which is active on the faceof the tool at low cutting speeds. It has been shown that pressure welding existsbetween the face of the tool and the underside of the chip under essentially allcutting conditions and that this gives rise to welded junctions being formedbetween the chip and the tool. The relative motion between the faces causesthese welded junctions to be sheared broken and often the shearing occursbeyond the tool face. The shearing action results in tool material being removedwith the chip. Additionally, for those cases in which a built-up-edge (bue) ispresent, although adhesion will occur, the adhesion will not result in toolChapter 1 Literature Review^ 13material being removed if the bue is stable. For unstable bues, if strong bondingoccurs between the bue and the tool material, it is likely that, when the buedetaches itself from the face, it will carry with it small quantities of the toolmaterial.• Wear by diffusion: diffusion is a temperature-dependent process inwhich atoms are transferred (or diffuse) in the opposite direction to theconcentration gradient. The more recent concepts of wear consider diffusion tobe an integral part of other wear mechanisms, contrary to previous claims thatwear was caused purely by diffusion at contacting asperities. An example of acircumstance under which diffusion may be classified as a part of, for examplethe abrasion wear mechanism, is in the cutting of steel with a tungsten carbidetool. The chemical affinity between the steel and the cobalt binder in thetungsten carbide leads to diffusion of the cobalt out of the tool and into the steel.The result is the formation of a weakened surface layer on the tool face which ishighly susceptible to abrasive wear. The inclusion of alloying elements such astitanium and tantalum help to retard diffusion in tool carbides.• Wear by fatigue: this will only be significant when adhesive and abrasivewear rates are small. A tool surface will gradually fail owing to this mechanism ifit is repeatedly subjected to loading and unloading as in intermittent cutting.Previous research has also demonstrated that the motion of an asperity on asurface rubbing across a tool face causes alternating stresses which eventuallylead to fatigue failure. Fatigue cracking is unlikely to occur, however, if thestress is below a certain limit. Since the contact pressures are determined byChapter 1 Literature Review^ 14the yield properties of the workpiece material, fatigue wear can be reduced bythe use of cutting tools which are appreciably harder than the workpiece.1.3 Tool-LifeTool-life is a term used to describe the useful cutting life of a tool anddepends on the type and amount of wear to which the tool is subjected and thequality specification of the part being machined. The type and amount of wearare determined by the cutting conditions under which the tool is operating.Under all cutting conditions, tool-life information is of extreme significance in theprevention of economically undesirable catastrophic tool failure.1.3.1 Determination 9.1 Tool-LifeAs briefly mentioned, tool-life information is of extreme significance duringcutting operations if sudden tool failure is to be avoided. The economicrepercussions of sudden tool failure are large and undesirable. For this reason,the usual practice in most manufacturing environments assumes the tool hasreached the end of its life long before the onset of catastrophic failure. The toolis then replaced.Fig. 1.7 shows a typical relationship between tool-wear and cutting time forthe case of flank wear. There are three major regions of interest; namely theprimary wear, secondary wear and tertiary wear zones.Chapter 1 Literature Review^ 15Fig. 1.7. Typical Flank Wear Versus Cutting Time RelationshipInitially, with a new tool, the wear rate is high as is evident from the primarywear zone in Fig. 1.7. As the tool ages or "wears in", the wear rate slowsconsiderably in what is called the secondary wear zone. At the end of this regionby which time the flank wear is usually far greater than that recommended as thecriteria for failure, the wear rate rapidly increases again in the tertiary zone. Ifthis continues, it will rapidly lead to tool failure.To prevent catastrophic tool failure, the usual practice is to change the toolwell before the end of the secondary wear zone, i.e., well before the critical valueof wear land width, VB *, is attained. This end point, however, is actually afunction of the final tool-life. Since even for one tool-workpiece combination tool-wear and final tool-life are highly variable, it follows that judgment, expertise andexperience are necessary to determine the point at which the tool is changed. Atthis point of tool change, the tool is said to have reached the end of its useful lifeand the time elapsed termed the tool-life.Chapter 1 Literature Review^ 161.3.2 Tool-Life in TurningAs stated previously, owing to the relative simplicity of this cutting processover milling, considerably more research has investigated tool-life in the area.One of the pioneering workers was Taylor [8] who developed the well known"Taylor tool-life equation":V X Ta = constant^ 1.1where V is the cutting speed,T is the tool-life, anda is an empirical constant dependent on tool geometry.Several years later, workers in the area modified the Taylor tool-lifeequation to reflect the influence of the feed-rate and the depth of cut:V xr x S'13 x ce = constant^ 1.2where V and Tare as before,S is the feed-rate,a is the depth of cut, and0 and 7 are empirical constants.Because the empirical constants are typically less than one, Eqn. 1.2clearly shows that the influence of cutting speed is the most significant on tool-life. This is particularly true because of the practical cutting speeds at whichturning operations are performed. Fig. 1.8 shows a typical tool-life againstcutting speed relationship.Chapter 1 Literature Review^ 17Fig. 1.8. Typical Relationship Between Tool-Life and Cutting SpeedThe practical cutting speeds at which turning operations are performed fallin the region c to d, while milling operation are typically performed at lowerspeeds in the region a to b. Owing to the characteristics of the relationship, theinfluence of cutting speed on tool-life in turning is shown to be more marked thanin milling.Further work in the area of tool-life in turning has allowed a reduction in thenumber of variables in the modified tool-life equation (1.2). By introducing avariable called the "equivalent chip thickness", he, into the equation to replacethe feed-rate and the depth of cut, it is possible to account for the influences ofthe replaced variables and, in addition, two other important variables: theapproach angle of the turning tool and its nose radius (see Fig. 1.9). Thesimplified equation is:WorkpieceTool Feed DirectionChapter 1 Literature Review^ 18VxTa xh.6 = constant;^h, =^ 1.3where he is the equivalent chip thickness,A is the undeformed area of cut,La is the length of active cutting edge,w is the approach angle of the turning tool,r is the nose radius of the turning tool, and8 is an empirical constant.Fig. 1.9. Schematic of Turning Operation Showing Undeformed Area of Cut1.3.3 Influence DI Various Parameters ga Tool-Life In examining the complexity of the milling operation, Yellowley [1] listed anumber of variables which had been observed to influence tool-wear and hencelife. These were: work material, tool material, tool geometry, cutting speed, feedChapter 1 Literature Review^ 19per tooth, depth of cut, width of cut, time in cut, time out of cut, cutter diameter,entry conditions and exit conditions. The effect of any one of these factors ontool-life may be direct or through its effect on another variable. This sectiondiscusses the effect on tool-life, of some variables as investigated by previousworkers in the field.•Tool geometry: this affects tool-life through other variables such asnumber of teeth in cutter, cutter diameter and rake face angle. Kuljanic [4]investigated the influence of the number of cutter teeth on tool-life in face milling.The research was motivated by a desire to show that multi-tooth cutter life couldnot be predicted by single tooth tool-life tests as had previously been thepractice. His experiments showed that under constant milling conditions, thetool-life, T, is a nonlinear decreasing function of the number of cutter teeth,z. Heapproximated this function by a polynomial in z over the range 1-6 (see Fig.1 .1 0).Fig. 1.10. Tool-Life as a Function of Number of Cutter Teeth (after Kuljanic)Chapter 1 Literature Review^ 20By introducing a 'heat generated ratio', Kuljanic concluded that thermaleffects were the main reason for the results obtained in his tests. He had shownthat there was a significant increase in workpiece and cutter temperatures withan increased number of teeth in the cutter and that this had a dominant effect ontool-life over the effect of mechanical shock or impact resulting from two or moreteeth in the cutter. His recommendation was that, since the largest differences intool-life were obtained between one and two teeth in the cutter, tool-life tests topredict multi-tooth cutter life should be performed with at least a three toothcutter.The effect of rake face angle is observable from results of work performedby Tlusty et al. [5] although no reference was made to this aspect of the work intheir report. One-quarter, one-half and full immersion experiments were carriedout with tools having rake face angles of -5°, 0° and +5°. The results showedthat the tool with the +5° rake face angle generally gave the longest tool-lifevalues. The one of the other two geometries which gave a higher tool-lifedepended on the immersion and mode of milling.• Cutting speed: the influence of this variable was considered by Tlusty etal. [5] in their investigation of wear in the peripheral milling of low carbon steel. Aset of experiments had been performed at a typical practical cutting speed of120 m/min while influences of various variables on tool-wear and life wereinvestigated. One of the experiments was repeated at twice this cutting speed toobserve any significant differences arising. The results showed that, in general,tool-life was not significantly affected by the gross increase in cutting velocity.However, the previously observed differences between up- and down-millingChapter 1 Literature Review^ 21were vastly reduced, the down-milling results being worse at the higher velocitywhile the up-milling results were almost identical. The absence of chip adhesionat exit in up-milling with the higher cutting speed was also noticed. The authornotes that, following the explanation given in Sec. 1.3.2 with regard to thepractical cutting speeds in milling and the attendant influence on tool-life, theresult obtained by these workers is to be expected. If milling operations werecarried out at the same cutting speeds as turning operations, the influence of thecutting speed would be more pronounced than that experienced by the workers.For this same reason, typically, milling operations are performed at lower speedranges (see Fig. 1.8), i.e., to improve tool-life. No explanation was offered byTlusty et al. [5] for the reduced tool-life values obtained in down-milling at thehigher speed. However, based on the authors experience, it can probably beattributed to the effect on the tool of increased thermal shock resulting from thehigher temperatures at the higher cutting speed and/or mechanical shockresulting from the increased severity of impact during entry into the workpiece atthe higher cutting speed.• Feed per tooth: the influence of this parameter on tool-life was alsoinvestigated by Tlusty et al. [5]. An experiment was set up to examine tool-wearrates at various values of feed per tooth. The results showed that the feed pertooth had negligible influence on the wear rate and hence tool-life.• Width of cut: this variable affects tool-life predominantly through itsinfluence on times in and out of cut. These parameters directly determine theratio of active cuffing time to total cuffing time, i.e., as the width of cut decreases,since the time the tool spends in actual cut decreases, naturally this ratio wouldChapter 1 Literature Review^ 22decrease. Therefore, for a constant active cutting time, the number of cyclesundergone by the tool would increase and, at the same time, the range ofthermal strain in the cycle increases. Increases in the number of cyclesundergone and the range of thermal strain have actually been proven to bedetrimental to tool-life by Yellowley et al.[6]. The workers introduced the conceptof a thermal fatigue parameter which characterizes the influence of the width ofcut. This parameter is discussed in more detail later in this chapter.Nevertheless, results of experiments conducted by Tlusty et al. [5] seem to showthat, generally, for the same mode of cut, the smaller widths of cut yield shortertool-life values. Experiments discussed in Chapter 2, however, verify this.• Mode of milling: according to Tlusty et al. [5], this affects tool-lifeprincipally through its effect on the entry and exit conditions, which influence theseverity of both mechanical and thermal shock. Through their experiments theyhad generally observed that the down-milling mode led to higher active cuttinglives than up-milling, that the mechanical damage or chipping of the cutting edgewas more severe in up-milling than in down-milling, and that the active cuttinglife of the tool did not appear to be greatly influenced by the entry conditions indown-milling.These results illustrate the significance of chip adhesion in influencing tool-wear. In down-milling in which the tooth enters with a finite chip thickness andexits with zero chip thickness, the likelihood of chip adhesion, in comparison toup-milling in which the maximum chip thickness is encountered close to exit, isminimal. It is evident that the severity of damage which may be inflicted on thetooth on any one entry would be closely related to the intensity and extent ofChapter 1 Literature Review^ 23adhesion in the preceding exit [5]. As a result, it would be expected that up-milling would yield higher wear rates and thus shorter tool-life values than down-milling.Nevertheless, as had been shown in earlier work [1], the adhesion of chipsto the cutting edge is most significant only when machining work-hardening workmaterials. Formation of tensile cracks in the tool surface during the finalshearing process as the tool point approaches the free surface may beattributable to the ability of the work material to work-harden: according toYellowley [7] and on the basis of milling experiments performed on a titaniumalloy, with the tool experiencing a finite chip thickness as it exits from the workmaterial, the shear plane rotates to coincide with the cutting velocity vector (seeFig. 1.11) so that the final action is similar to a blanking and piercing operation[11]. This rotation of the shear plane causes the material to work-harden, andthe resulting tensile forces cause cracking of the tool. The chip or 'foot' formedin the process sticks to the tool and, as mentioned earlier, proves detrimental tothe tool on the succeeding entry.Chapter 1 Literature Review^ 24Fig. 1.11. Proposed Shearing Action at Tooth Exit (after Yellowley)Later work by Pekelharing et al. [12-14] into exit failure of cutting toolssuggested that the shear plane actually rotated past the cutting velocity vector toa negative position and that the forming foot, also rotating during this time, triedto take the chip with it in its rotation. The result is a dangerous change in thepressure distribution in the chip-tool contact zone; all remaining cutting forcesconcentrate near the cutting edge thus chipping the tool. According to theworkers, depending on the exit angle of the workpiece, the phenomenon couldeither be aggravated or suppressed. It is noteworthy that these suggestionswere made on the basis of interrupted cutting lathe experiments (performed onsteel work material) being used to simulate the milling operation. Irrespective, itis expected that these conflicting explanations will be verified by experiments tobe conducted in the course of this research.An exception to the supposedly harmless entry condition in down-millingwas observed by Yellowley [7] in the carbide milling of stainless steel. Hepointed out that chip adhesion could be critical in the initial stages of down-milling if the cutter was traversing into a sharp corner and therefore experienceda finite value of chip thickness at exit until it had traveled a distance into theworkpiece equal to its radius. In such a case, chip adhesion comparable inChapter 1 Literature Review^ 25intensity to that in up-milling occurs; as a result of the severe entry conditions ofdown-milling, the resulting mechanical damage is catastrophic. Thephenomenon would no doubt be even more pronounced with a work-hardeningwork material, resulting in almost immediate tool failure. In verifying, hedemonstrated that the phenomenon was non-existent when a cusp of the sameshape as the cutter was machined to replace the sharp corner before cuttingcommenced.One of the earliest workers to investigate the influence of the mechanicaleffect of impact, at tool entry, on tool-wear was Kronenberg [15]. He proposedthat the life of the tool was influenced by the location and magnitude of the initialimpact of the tool with the workpiece for a given tool geometry. Fig. 1.12 showsthe schematic of tool contact at entry into the workpiece proposed byKronenberg.Fig. 1.12. Schematic of Initial Contact at Tooth Entry (after Kronenberg)Chapter 1 Literature Review^ 26Fig. 1.12 shows that initial contact between workpiece and tool may occureither as a point, a line, or a full area contact, depending on the tool geometryand the positioning of the tool. For prevention of premature tool breakage atentry, impact should be kept away from the cutting point S. In an attempt toquantify the influence of impact at any point, Kronenberg defined the partial timeof penetration, Ts, to be the time which elapses between the initial contact andthe contact of the tool at point S. He concluded by suggesting that the mostdesirable condition to yield optimum tool-life could be obtained by carefulcoordination of axial and radial rake angles, corner angle, chamfer angle andangle of engagement. Later workers in the area (Opitz et al. [16]) consideredthe parameter Ts to be inadequate and went further to define the partial area ofengagement, Fs, as the area which is crossed by the index line before the pointS is reached (the index line being the line formed by the intersection of the planeSTUV and the plane in which the rake face of the tool lies). They further showedthat the higher the partial area of engagement, the higher the resulting tool-life.In reviewing the work of these early researchers in the light of results obtained inthe course of his own work, Yellowley [1] noted that their work had beenundertaken for the face milling operation, in which a change in cutter offsetaffected several variables simultaneously, and he demonstrated how therelationship between tool-life and cutter offset could vary in such a situation.Yellowley noted that in his own down-milling experiments on a titanium alloy, theresults did not show any discernible differences in tool-life, irrespective ofwhether the tool-work contact was a line or an area or, in the case of the line,whether the line was formed at the edge or across the face of the tool.Chapter 1 Literature Review^ 27With respect to thermal shock, however, Yellowley [7] suggested that theinfluence of thermal shock would be more severe in down-milling. The problemwas simulated by the application of a three-step increase in temperature to therake face with this increase similar to that which would be experienced by therake face in an up-milling operation. The rake face was then allowed to coolbefore the same three temperatures in reverse order were applied to simulatedown-milling conditions. The rake face was finally then allowed to cool (see Fig.1.13).Fig. 1.13. Influence of Up- and Down-Milling on Rake Face Temperature(after YeHowley and Barrow)As these results confirm, the level of compressive strain after a typicalcooling time was similar for both up- and down-milling cases. However, with themaximum value of compressive strain at the start of the next heating cyclehigher in the down-milling case, the range of thermal strains would naturally behigher in down-milling than in up-milling. In conclusion, the literature reviewedshowed that the mechanical influence of chip adhesion, where present, has apredominant effect on tool-life over the thermal shock effect.Chapter 1 Literature Review^ 281.4 Concept of Equivalent FeedAs already pointed out, one characteristic problem associated with millingis that of the varying feed experienced by each tooth in cut. Fig 1.14 shows aschematic of the variation in feed seen by a tooth over one cutter revolution forboth one-half and full immersion cutting.Fig. 1.14. Variation of Feed in Milling Over One Cutter RevolutionFig. 1.15a shows the approximately linear relationship between tool-wearand time when cutting is performed at either of constant feed-rates S1, S2, andS3, as would be the case in turning. The points corresponding to the varyingwear seen by the milling tooth at each of points a, b and c (with feed-rate valuesS1, S2 and S3 respectively) in Fig. 1.15b are shown on Fig 1.15a. The brokenline passing through these points describes the typical tool-wear - timerelationship for milling.Chapter 1 Literature Review^ 29Fig. 1.15. Determination of Characteristic Tool-Wear Versus Time Relationshipfor MillingTo cope with the problem of the varying feed in milling during tool-lifeanalyses, Yellowley et al. [1] introduced the concept of an equivalent feed, Seq.This was defined as that constant feed which, if applied, would give the samewear rate as in the actual case in which the feed is continuously varying. Fig.1.16 shows a schematic plot of tool-wear versus active cutting time for a millingoperation over three revolutions of the cutter. The equivalent feed is that feedwhich would give a constant wear rate equivalent to the dotted line shownpassing through the 'arc ends' of the plot. The equivalent feed is therefore afunction of the feed per tooth, the width of cut and the radius of the cutter,i.e., Secr---f(St, d, R)The concept of the equivalent feed allows the two variables (feed per tooth,St, and width of cut, d) to be combined and results in significant savings inmachinability testing time.Chapter 1 Literature Review^ 30Fig. 1.16. Tool-Wear Versus Active Cutting Time Relationship in Milling;Showing Definition of Equivalent Feed1.5 Concept of Thermal FatigueAs discussed, the influence of feed per tooth on tool-life was negligibleduring the tests performed by Tlusty et al. [5]. For some combinations of tooland workpiece materials, this has been found to be true. In such cases, theinfluence on tool-life of the highly emphasized varying undeformed chipthickness in milling may be ignored. According to Yellowley et al. [6], underthese conditions, any variation in tool-life may result from either mechanical orthermal effects or a combination of both. Until their work was performed, opinionon the relative influence of the two effects had been divided. To enhanceisolation of the two (mechanical and thermal) effects during experimentation,their work dealt with the end milling process only so that either of the entry or exitconditions could be kept constant while the influence of the thermal effect(s) wasinvestigated. The following discussion will show further that the work of11101^Nom.^ Nell^Noma,^ lia0^fivetmlismersoto imorrrarn aromenbew142 Manufecipre 1^1,12 Alsnuftetvre ll II NonsdocfurtMO Speed Stool EN NMI (Mc 500 rft Anin..00(.10,  1004RA1Slothay NMIStet•m^ law amigoka••••••••tht-SILANYerning  old NeN hivnersial *Ms Woe* Nell EN 76,1175 57 fen/!n:Corti* Enil( &twenty InsertsI i1 -Ii.,1400 /Am . fa I op I .100 OtethQ•Chapter 1 Literature Review^ 31Yellowley et al. [6] clarified much of the controversy surrounding tool-wear inmilling.1.51 Tool-Life j Half find Eig Immersion TestsThe geometry of the end milling process shows that a changed width of cut(1/2 immersion or full immersion cutting) will alter the relationships between thetime in and out of cut. This change would appear to be the major reason for thetool-life differences observed between 1/2 and full immersion cutting.Yellowley et al. [6] in performing a series of 1/2 and full immersion tests toinvestigate tool-life differences, employed a carbide end mill on EN28 (AISI 4140mild steel) work material. Fig. 1.17 shows the results of the tests conducted.Fig. 1.17. The Comparison Between End Mill Slotting and Half Immersion Tests(after Yellowley and Barrow)The results of the 1/2 immersion tests carried out for both up- and down-milling conditions showed that tool-life values obtained in both cases werecomparable during all tests. Workers noted that this was to be expected sinceChapter 1 Literature Review^ 32previous work had indicated that the influence of the mode of milling was onlysignificant when machining high strength or heavily work-hardening materials.However, a marked difference was observed between the 1/2 immersion testsand the slotting tests (see Fig. 1.17); a considerable increase in tool-life wasobtained with the slotting experiment. Considering that, for the same cuttingtime, the active cutting time in slotting is twice that in 1/2 immersion, i.e., inslotting, the tool is in cutting contact with the workpiece for twice as long as it isin 1/2 immersion, these results therefore suggested the influence of anotherfactor unaccounted for prior to this time.In further investigation of these results, Yellowley et al. [6] repeated theslotting tests with a 1/16 inch gap in the workpiece on the cutter center line (seeFig. 1.18) to verify whether the bad exit conditions of up-milling and the badentry conditions of down-milling influenced the results. The new results werecomparable to the previous results obtained without the gap in the workpiece. Itwas therefore concluded that the differences in heating and cooling timesexperienced by the cutter in slotting and 1/2 immersion were the reason for thedifferences observed in tool-life values for both cases. The workers realized theneed for a parameter which would characterize the influence of the repeatedheating and cooling, or thermal fatigue, of the workpiece during cutting. Oneobjective of this research will be to determine if another influence besidesthermal fatigue, presently unaccounted for, is responsible for the observedphenomenon.Chapter 1 Literature Review^ 33Fig. 1.18. Slotted Workpiece Used to Investigate Influence of Entry and ExitConditions (after Yellowley and Barrow)1.5.2 Explanation of Thermal Fatigue Phenomenon Milling cutter teeth are subjected to a low cycle, high plastic strain process,owing to the characteristic intermittent cutting which results in repeated heatingand cooling of the rake face. An explanation of the phenomenon would considerthe face of the milling tool to consist of several parallel layers of tool material.On entering the workpiece, the surface layer of the tool is rapidly heated to itsmaximum temperature; the time required for this has been shown by workers inthe area [9], [10] to be small when compared with the cutting cycle timesnormally encountered in milling. As a result, the layer begins to expandimmediately but, owing to restraint from subsequent layers below which have notattained the same temperature (see Fig. 1.19a), it is put into compression. Themagnitude of this compressive stress will decrease as the duration of heatingincreases and the temperature gradient between successive layers decreases.Upon exiting the workpiece, the surface of the tool is rapidly cooled. Accordingto Yellowley et al. [6], the temperature distribution within the tool is now asshown in Fig. 1.19b. This distribution indicates that, with increasing cooling time,Increasing cooling time(heating time constant)Chapter 1 Literature Review^ 34the temperature gradient within the tool will fall and result in reducedcompressive stresses in the surface layers of the tool.Fig. 1.19. Temperature Distribution Within Tool During Heating and CoolingCycles (after Yellowley and Barrow)During the heating cycle, the tool material is believed to yield incompression thereby giving rise to residual tensile stresses within the surfacelayers when the tool is cooled. The result of these residual tensile stresses isweakening and eventual cracking of the tool surface. As the number of cyclescompleted by the tool increases, the tool surface is further weakened by thefatigue process and is thus more susceptible to mechanical wear.1.5.3 Definition gt Thermal Fatigue ParameterFollowing extensive research and experimentation involving heating andcooling times of tools, Yellowley et al. [6] developed an expression for a thermalfatigue parameter, X. The preceding discussion indicates that such a parametershould account for the temperature range traversed as a result of the heatingand cooling of the tool, the proportion of cycle time over which the tool is beingintermittently heated and cooled, and the influence of cycling:Chapter 1 Literature Review^ 35X = f(Er, RPM, x); Er = f(tc, th)where^Eris the range of thermal strain parameter,RPM is the rotational speed of the cutter,xis the ratio of total cutting time to active cutting time, andtc, th are the cooling and heating times respectively.With the development of this parameter, the workers could use it to obtaina more realistic tool-life equation for milling. Experiments showed that the tool-life varying inversely with the thermal fatigue parameter would explain why, ingeneral, smaller widths of cut (which give larger values of thermal fatigueparameter) yield smaller tool-life values.1.5.4 . Tool-life Equation fat MillingAccording to Yellowley et al. [1], the simplest tool-life equation for milling isof the Taylor type. This equation can be written to include the influence of thevelocity and the depth of cut as:T=constant a VP xaq1.4where Ta is the active tool-life,Vis the cutting velocity,a is the depth of cut, andp and q are empirical constants.Chapter 1 Literature Review^ 36With the development of the equivalent feed, Seq, and the thermal fatigue,X, their influences could be included in the tool-life equation. The tool-lifeequation for milling was finally presented by Yellowley et al. [1] in the form:T^constant 1.5= Xn xS"A x VP x aqeqwhere n and 13 are empirical constants.Experiments verifying the validity of this tool-life equation for millingsuggest that the equation is limited to one mode of milling and should not beused when chip-sticking conditions prevail. Furthermore, the equation is notstrictly valid when the angle of lag between leading and trailing edges of thecutter become appreciable compared to the swept angle of cut.The work to be conducted by the author during the present research are:• Tool-life experiments on steel and titanium materials to obtain tool-life data.• Tool-life analyses to obtain tool-life equations for both materials and topermit an evaluation of the influence of various parameters on tool-wear.• Argon influenced tool-life test to verify the role of oxidation in tool-wear.• Experiments to verify the occurrence of exit failure resulting from sharpcorner conditions in down-milling.• Development of an experimental set-up to investigate the processesoccurring at tool-exit from the workpiece which result in exit failure in materialsaffected by the phenomenon.• Experiments to investigate the validity of a force model proposed for milling.• Experiments to enable the development of a wear tracking parameter devoidof the problems associated with previously developed wear tracking parameters.Chapter 2 Tool-Life Investigation: Experimentation and AnalysisChapter 2Tool-Life Investigation: Experimentation and AnalysisThis chapter describes a detailed investigation of tool-life. The initial seriesof experiments examine the validity of previously derived equations during thedetermination of tool-life equations for milling of high strength steel and titaniumworkpieces. The later sections of the chapter are concerned with theexamination of the influences of oxidation and exit conditions on tool-life.2.1^Tool-Life ExperimentationThe first series of tests examined tool-life when milling steel and titaniumwork materials under different cutting conditions, these data were used to obtaintool-life equations for the respective materials and to verify the influences ofchosen cutting parameters on tool-life. As mentioned earlier, because thevariables affecting tool-life in milling are numerous, isolation of the individualinfluences of these variables is difficult. On the basis of work reviewed, it wouldseem the most significant influences are likely to be exerted by the width of cut(through times in and out of cut), the cutter diameter (through thermal cycling),the feed-rate, and the mode of milling. The tool-life tests therefore which weredesigned to investigate the separate influences of these variables on tool-life,isolated each variable in turn, while keeping the other variables constant. Thedepth of cut and the peripheral velocity remained constant during each series of37Chapter 2 Tool-Life Investigation: Experimentation and Analysis^38tests. The influence of the width of cut on tool-life was isolated by tests thatemployed different widths of cut at the same feed-rate (or more correctly,equivalent feed). The influence of feed-rate was isolated by tool-life testsconducted with the same width of cut at different feed-rates. Identical tests usingtwo cutters of different diameters permitted isolation of the influence of cyclingfrequency. In this case, the change in peripheral velocity that would haveresulted from the change in cutter diameter was prevented by changing thespindle speed accordingly. To investigate mode of milling, up- and down-millingexperiments were performed under the same cutting conditions to determinetheir influence on tool-life.Spindle speeds selected for the experiments described used averagevalues within suggested ranges' for the respective work materials. The feed-rates were chosen so that the resulting feed-per-tooth values lay between theaverages 0.03 and 0.1 mm/tooth.For each experiment, the wear on the cutting tool used was monitored andrecorded at frequent intervals during cutting. When the wear on a cutting toolhad exceeded a preset limit, the tool was considered to have reached the end ofits life and removed from cut. A graph of wear against cutting time could then beplotted for the tool, and from it the time elapsed before the wear reached thepreset limit read off and recorded as the tool-life of the tool. With the tool-lifedata collected in this way, an analysis for both work materials was possible.1 Machinist's HandbookChapter 2 Tool-Life Investigation: Experimentation and Analysis^39The analysis presented is based on the validity of thermal fatigue as theproven major influence on tool-wear. However, this validity has been questionedby other workers [37] who suggested that perhaps the influence of thisphenomenon on wear was not quite as significant. On this basis, the possibilityof another major influence being at play, namely oxidation, was investigatedduring this research. The aim was to determine whether any major improvementin tool-life could be achieved by excluding oxygen from the immediate regionsurrounding the tool during cutting. Any major improvement would confirm thatoxidation was responsible for the influence of cut time ratio on tool-wear andthus dispel the validity of thermal fatigue being the major influence; otherwise,the validity of thermal fatigue would be corroborated. Further confirmation wouldbe obtainable from an experimental design that permits cutting in anenvironment that would alter the temperature range within which the tool isalternately heated and cooled during cutting. Similar work has however beencarried out by previous workers [38].2.1.1 Equipment Setup and Teat ProcedureThe milling machine used for all the tests in this research was a verticalspindle, 5.5 kW, Bridgeport 2S machine capable of 18 spindle speed changesand 18 longitudinal and cross feed changes. Other equipment for the tool-lifetests consisted of: an end mill chuck with a set of collets; a five pocket face millcutter; a hand-held microscope with a graduated reticle, retrofitted with a holderand a magnetic stand; a two axis, moving table, measuring laboratorymicroscope fitted with micrometers on each axis and a stop watch. The cuttingChapter 2 Tool-Life Investigation: Experimentation and Analysis^40tools used comprised 1/2 and 1/4 inch three flute High Speed Steel (HSS) endmills and tungsten carbide (H13A grade) inserts. As stated, the work materialswere AISI 4140 low alloy steel and a titanium alloy. The end mills wereemployed on the steel work material and the face mill inserts on the titaniumalloy work material. Fig. 2.1 shows the milling machine set up for tests on thesteel work material. Visible are the end mill cutter, the steel workpiece and thehand-held microscope for measuring the tool-wear.Fig. 2.1. Equipment Set-Up for Tool-Life Tests on Steel Work MaterialChapter 2 Tool-Life Investigation: Experimentation and Analysis^41The chief differences between this set-up and that used for the tests on thetitanium alloy were the replacement of the end mill with a face mill, and the useof the laboratory microscope rather than the hand-held microscope to measurethe wear on the inserts. Fig. 2.2 shows the laboratory microscope with an insertin place.Fig. 2.2. Two Axes Measuring Laboratory Microscope Used for Tests onTitanium Alloy, and Stopwatch Used for All TestsChapter 2 Tool-Life Investigation: Experimentation and Analysis^42The experimental procedure to obtain the tool-life data was:• for the experiments on the steel work material, for any chosen end millsize, mode of milling, width of cut, feed-rate and spindle speed, the toolwas allowed to cut over one pass (approximately 16 inches long). Prior tocommencing the test, a cusp, cutter-radius distant into the workpiece, wasmachined so as to prevent premature tool-wear caused by exit failure (seeSec. 2.2).• the hand held microscope was then positioned to measure the wear on allthree flutes.• with the wear recorded and the wear pattern on each flute sketched, thetool was put into cut over another pass and checked again.• the process was continued until the wear was observed to have exceededthe preset limit; in the case of the steel experiments, 0.01 inch.• in the manner described earlier, the time taken for the wear to reachexactly 0.01 inch was then read off as the tool-life of the tool for that onetest.In the case of the tests carried out on the titanium alloy, only one insert wasused in the face mill cutter, in order to conserve work material, and the insertwas removed and its wear checked often (thirty seconds to two minute intervals),depending on the cutting speed and feed-rate in operation. It was important tocheck the tool more often during these tests because of the high wear ratesassociated with titanium. The occurrence of sudden tool deterioration washigher with titanium than with steel. In the case of titanium, the wear limit wasset at 0.015 inch.Chapter 2 Tool-Life Investigation: Experimentation and Analysis^43The procedure to quantify the tool-wear differed slightly for both test cases.Irregularity in the wear patterns on the end mill flutes were observed in the steelexperiments; for this reason mean values were estimated and compared againstthe preset limit at each point at which the tool was checked. For titanium forwhich the wear pattern on the insert was rather uniform, the maximum wearvalue was used instead. Provided consistency was maintained, this difference inmeasuring procedure was not expected to influence the tool-life analysis.2.1.2 Tool-life Data For Steel and Titanium Work MaterialsTables 2.1 and 2.2 present the tool-life data obtained during the series oftests conducted. It is noteworthy to state that the tool-life values shown in bothtables represent averages of data obtained over three series of tests, in the caseof the steel, and as many as five series of tests in the case of the titanium.Test •:.:FeedSpindle1 576 62.4 .1083 1/2 imm. 5.182 1.2962 576 30.0 .0521 1/2 imm. 12.644 3.1613 576 24.0 .0417 1/2 imm. 34.91 8.7284 576 62.4 .1083 Slotting 6.105 3.0535 576 62.4 .1083 3/4 imm. 7.17 2.396 576 62.4 .1083 1/4 imm. 11.0 1.833Chapter 2 Tool-Life Investigation: Experimentation and Analysis^44Table 2.1. Tool-Life Data for ANSI 4140 Low Alloy Steel Work Material1 912 102 0.037 0.5 1/2 imm. Up 25.76 6.442 912 102 0.037 0.5 Slotting 34.91 17.4553 912 168 0.061 0.5 Slotting 25.77 12.8854 1800 168 0.031 0.25 Slotting_ 19.28 9.645 912 264 0.0965 0.5 Slotting 15.63 7.8156 912 264 0.0965 0.5 1/2 imm. Up 11.33 2.8337 912 264 0.0965 0.5 1/2 imm. Down 14.5 3.625• Cutter type: 3 flute HSS end mill• Depth of cut: 1.0 mm• T. = T, x 360 ; where Os is the swept angle of cutoTable 2.2. Tool-Life Data for Titanium Alloy Work Material• Mode of milling: Down• Cutter type: 5 pocket face mill, Dia. 3.15" with tungsten carbide insert• Depth of cut: 1.0 mm2.1.3 Data Analysis This section demonstrates the logic underlying the derivation of anexpression for the equivalent feed in milling and links this concept with the ideaChapter 2 Tool-Life Investigation: Experimentation and Analysis^45developed by previous workers of the thermal fatigue parameter to allow thedevelopment of tool-life equations for various workttool pairs. The validity ofprevious work is also reviewed in the light of new data obtained during thisresearch.The equivalent feed was defined earlier as that constant feed which, ifapplied, would give the same wear rate as the continuously varying feed inmilling. Fig. 2.3 illustrates the constant wear rates resulting from constant feed-rates S1, S2, and S3, as would be the case in, for example, turning. Thecorresponding times T1, T2, and T3 represent the active tool-life values obtainedbefore attaining the wear limit, VB0, under these respective conditions.Fig. 2.3. Tool-Wear - Time Relationship Under Constant Feed ConditionsAs a result of the linearity, the wear rate can be expressed as:dVB = VB0 2.1dt^Tawhere VB is the instantaneous wear, andTa is the active cutting life.Chapter 2 Tool-Life Investigation: Experimentation and Analysis^46If a Taylor type relationship is assumed between feed, S and active tool-life, Ta :S x TaP = constant = C^ 2.2where 11 is an empirical constant for millingthereforeT . (9x5= sSubstituting Eqn. 2.3 into 2.1:dVB = VBdt^0 . ('1)M'CA milling tooth subjected to wear during one pass through the work isshown in Fig. 2.4a. Fig. 2.4b shows how the wear would vary during the periodin cut.Fig. 2.4. Milling Tooth and Associated Wear Over One Cycle2.32.4Chapter 2 Tool-Life Investigation: Experimentation and Analysis^47The total wear, VB1, over this pass can be expressed as:dVBVB, = j---0 drwhere fa,/ is the time spent in cut.Substituting Eqn. 2.4 into 2.5:VB01VB1=-- (S)C/13 oFrom Fig. 2.4, the average wear rate over the pass can be expressed as:VBI ^V/30 0, (S, • sin ep)Xtart^C' ^4), 02.7where St is the feed per tooth, andOs is the swept angle of cut.If a constant equivalent feed, Seq, is defined so that it results in a wear rateequal to the average in the milling operation:r  ^.dVB =^Se^VB^sm= , °^(S,^4)) 110dr C^cA3^ 2 Tool-Life Investigation: Experimentation and Analysis^48S., = [1.1(sin 0) )/P" •c101Or S 0, 02.10For any given width of cut, the right hand side of Eqn. 2.10 results in aSconstant. Fig. 2.5 illustrates how the ratio - 25- typically varies with the ratio ofS,width of cut to cutter radius (or immersion), —d :RS^dFig. 2.5. Variation of --fs- With —R in MillingS,As a result of the symmetry between full and half immersion cutting, theSratio --fL is the same for both cases, i.e., for the same feed-per-tooth, St, theS,equivalent feed, Seq, is the same for both full and half immersion cutting. Thisinformation is useful in the ensuing analysis.Chapter 2 Tool-Life Investigation: Experimentation and Analysis^49The tool-life equation for milling developed by Yellowley et al. [1], aspresented in equation 1.5, is expressed as:T.= X" xSuil xVP xaqwhere Ta is the active tool-life,V is the cutting velocity,a is the depth of cut, andn, ii, p and q are empirical constants.If the influence of the cutting velocity and the depth of cut are consideredless significant as mentioned earlier, these variables are thus kept constant andthe equation can be rewritten as:constantT. =^X' X S il°eq2.12As a result of direct proportionality (Eqn. 2.10), the equivalent feed, Seq,can be replaced by the feed-per-tooth, St in Eqn. 2.12.constantTa = X" x SPTaking the logarithm of both sides of the expression:log T. = log constant — log X" — log STPFor experiments performed at the same immersion but different feed-rates,the thermal fatigue parameter, X, is constant.constant 2 Tool-Life Investigation: Experimentation and Analysis^501log To = --13 • log S, + constant 2.15If a graph of log71, is plotted against logS, the exponent 143 is defined bythe slope of the graph.For full and half immersion experiments performed at the same feed-rate,as pointed out earlier, the equivalent feed is the same.log T„ = — n • log X + constant^ 2.16If log T. is plotted against logX , the exponent n may be determined fromthe slope of the graph. The validity of the theory as well as the data obtained willbe verified by the accuracy of these graphs.Working back from the value of the constant given in Eqn. 2.15 enablesdetermination of the constant in the tool-life equation (Eqn. 2.12). This constantis given by the value of the intercept on the same log re against log S, plot usedto determine P.An expression for the thermal fatigue parameter, X, developed by Yellowleyet al. [6], can be written as:X = E, • (RPM • x)Y2^2.17where Er is the range of thermal strain parameter,RPM is the spindle speed, andx is the ratio of cutting time, t, to active cutting time, t a .Chapter 2 Tool-Life Investigation: Experimentation and Analysis^51An expression for the range of thermal strain parameter was alsodeveloped [6] and can be written as:E,= 39 . log t, — 23 • log th + 37.5^ 2.18where tc is the cooling time in milliseconds, andth is the heating time in milliseconds.This expression assumes that the rake face temperature is constant duringthe heating cycle. However, since the parameter is simply intended tocharacterize the relative influences of heating and cooling times at constantperipheral velocity, equivalent feed and depth of cut (and for one mode ofmilling), the assumption was considered justified. A series of tests conducted bythe workers also verified the validity of the expression.In Eqn. 2.18, the heating and cooling times th and tc can be obtained if thetime taken for one revolution of the cutter (cycle time) is split in the ratio of timein cut to time out of cut. The heating time will be given by the time in cut and thecooling time by the time out of cut. The cycle time of the cutter is given by theinverse of the spindle speed, and the ratio itself depends on the immersion of thecutter. With this knowledge and employing the expressions presented earlier,the thermal fatigue parameter may be computed for the different immersionsemployed in cutting the steel and titanium work materials. The following tablespresent the results of these computations.912 4 4564.0475.5749.3416.45SPINDLESPEEDfrpmlCYCLETIMEfmsec.1IMMERSIONHalf65.7965.79^Full 32.89 32.89 61.77 2638.26912 2IMMERSIONSPINDLE CYCLESPEED^TIME[rnsec.]576 104.17 One Quarter 17.36 86.81 84.55 6 4973.04576 104.17 Half 26.04 78.13 78.76 4 3780.40576 104.17 Three Quarter 34.72 69.44 73.85 3 3071.55576 104.17 Full 52.08 52.08 64.97 2 2205.06Chapter 2 Tool-Life Investigation: Experimentation and Analysis^52Table 2.3. Thermal Fatigue Parameter Values for SteelTable 2.4. Thermal Fatigue Parameter Values for TitaniumDetermination of constants in tool-life eayation The procedure for the determination of these constants is the same forboth work materials. It begins by determining the exponent 1/f3 of the equivalentfeed in the manner previously described. With 0 determined, the ratio -f-t canS,be evaluated, and therefore the equivalent feed computed. The other exponentn of the thermal fatigue parameter and the constant in the tool-life equation canthen both be determined as described previously.Chapter 2 Tool-Life Investigation: Experimentation and Analysis^53Fig. 2.6 shows the plot of the slotting data used in the determination of j3 forsteel. The predicted data points (linear fit points) and the original data points areboth shown, and the agreement is seen to be good.Fig. 2.6. Plot of log Ta Vs. log St for Slotting Data to Determiner?, forSteelThe line fit is achieved with a linear regression, and the inverse of the slopeobtained from the regression data gives 3 = 1.198. X^Actual Data Pts, Slotting"—D— Linear Fit Plot- 1/21mm, Up, Min RedSlotting, 1/4" Cutler- 1/21mm, Up, Max Feed— - 1/21mm, Dam, Max Feedlog StChapter 2 Tool-Life investigation: Experimentation and Analysis^54With the same slope, similar plots for the other cutting conditions given inTable 2.1 may be constructed (see Fig. 2.7). The same slope is applicable to allthe test conditions on this table since 0 is constant for the work/tool pair.Fig. 2.7. log Ta Vs. log St Plots for All Test Conditions on Steel UsingKnown 13Chapter 2 Tool-Life Investigation: Experimentation and Analysis^55In the same manner as that employed for the steel (in this case using halfimmersion data taken from Table 2.2), 13 can be determined for the titanium workmaterial (see Fig. 2.8):Fig. 2.8. Plot of log Ta Vs. log St for Half Immersion Data to Determine 13for TitaniumFrom the regression data, p = 0.554 for the titanium work material.Chapter 2 Tool-Life Investigation: Experimentation and Analysis^56With the same slope as the previous plot, plots for the other cuttingconditions employed on the titanium may be located (see Fig. 2.9):Fig. 2.9. Plot of log Ta Vs. log St for All Test Conditions on TitaniumWith the exponent ii determined, evaluation of the expression for the ratioS^ieq given n Eqn. 2.10 is possible for both work materials. However, to precludeS,the need for a numerical integration procedure, the exponent 13 is assumed suchthat the value of 1/13 is integer. Because of the magnitude of the error inintroduced in making this assumption (less than 2.5%), the simplification is notexpected to significantly influence the result of the integration. Table 2.5summarizes the integration results for the different immersions employed:SeqSrTitaniumWorkMaterialSteel0.5541.1980.51.0Assumed14321 0.6370.707U.Sir4Assurned p 0.777 0.7070.6370.542Chapter 2 Tool-Life Investigation: Experimentation and Analysis^57Table 2.5. Calculated Sect^ St Values for Steel and TitaniumAs expected, the ratio--t7- is equal in full and half immersion cutting.S,The determination of the exponent n for both the steel and the titaniummaterials can now be achieved with the aid of Figs. 2.10 and 2.11 respectively:Fig. 2.10. Plot of log Ta Vs. log X to Determine n for SteelThe exponent n is given by the slope of the plot. Each of the three sets oftest conditions plotted above, however, yield slightly different slopes:Chapter 2 Tool-Life Investigation: Experimentation and Analysis^58Slope of plot 1 = -1.82Slope of plot 2 = -1.85Slope of plot 3 = -1.40The value of n for steel is therefore taken to be the average of the slopes ofplots 1 and 2, i.e., n = 1.835.Fig. 2.11. Plot of log Ta Vs. log X to Determine n for TitaniumEvaluation of the slope of this plot gives n = 1.59 for the titanium workmaterial. Data points shown for both plots represent averages of valuesobtained over a series of tests.Finally, with the exponents obtained, the tool-life constant for both materialsmay be computed. Results of such computations give the values of the constantChapter 2 Tool-Life Investigation: Experimentation and Analysis^59for steel and titanium to be respectively 1503210 and 5652 and lead to final tool-life equations for both materials in the form:1503210 T =aX 1 .835 X *985652 Ta = X 1.59 X ei )354These equations are valid for feed-rates within the ranges employed forboth sets of tool-life tests performed.2.1.4 Discussion 91 Results. The results obtained from the tool-life tests and the attendant analysisshow that the original data are reproducible. The trends exhibited by both setsof data generally conform with results obtained during earlier research anddiscussed in Chapter 1. First, regarding the influence of feed per tooth (orequivalent feed) based on the values of the exponent 1/0 obtained for bothmaterials: the results of the analysis suggest that the influence of this variable ontool-life would be significantly stronger for the titanium (143.1.805) than for thesteel material (1/(3.0.835). These results agree with the findings of Yellowley etal. [1] and Tlusty et al. [5] during the cutting of titanium and steel respectively.The former's experimental data show significant changes in the tool-life withchange in feed-rate while milling titanium. Tlusty reports insignificant changes intool-life with change in the feed during the milling of steel. Second, regarding theinfluence of thermal fatigue (or immersion): the value of the exponent n obtained2.192.20Chapter 2 Tool-Life Investigation: Experimentation and Analysis^60for the steel (n.1.835) suggests a stronger influence of this variable than that ofthe feed-rate on tool-life. In contrast, however, the titanium result (n=1.59)suggests that the influence of thermal fatigue on tool-life for this material is lesssignificant than that of feed-rate. These results show that the influence ofthermal fatigue is somewhat stronger for the steel than for the titanium material.Considering the tool-life data obtained, for both materials, slotting leads tohigher tool-life values than half immersion cutting as a result of thermal fatigue.Regarding the other immersions employed on titanium, at the same feed-per-tooth, the 3/4 and 1/4 immersion tests both yield higher tool-life values than the1/2 immersion test yields. On the basis of the thermal fatigue theory, it is to beexpected that 3/4 immersion would result in a higher tool-life over 1/2 immersion;however, this theory is contradicted by the increased tool-life value of 1/4immersion over 1/2 immersion. This contradiction is likely attributable to thedomination of the influence of equivalent feed over that of thermal fatigue underthese circumstances (there is a 24% decrease in equivalent feed from 1/2 to 1/4immersion). The influence of cutter diameter is reflected in the steel data, whichshow that a smaller diameter yields a shorter tool-life than does an equivalenttest employing a tool of twice the former's diameter and cutting conditions whichyield a larger value of equivalent feed. As explained earlier, the logicalexplanation for this is thermal cycling. The influence of mode of milling isreflected in the steel data in which down-milling generally leads to higher tool-lifevalues under otherwise identical cutting conditions. This is consistent with theconclusion reached in Chapter 1. The likely chip adhesion occurring at exit fromthe workpiece in up-milling, even during the milling of mild steel which cannot beChapter 2 Tool-Life Investigation: Experimentation and Analysis^61considered to be a severely work-hardening material, proves more detrimental tothe life of the tool than any thermal or mechanical shock the tool may experienceat entry into the workpiece in down-milling.2.1.5 Tool-Life Tests Within nn Inert AtmospherePrevious sections have emphasized the significance of the thermal fatiguetheory in explanation of tool-life phenomena. This section describes testsdesigned and conducted to verify the theory further.Under some circumstances, oxidation plays a major role in the wear ofcutting tools. Therefore, if the effect of oxidation could be excluded from theregion surrounding the tool, it is expected that improved tool-life would beattainable. Since the level of significance apportioned to the oxidation factorwould therefore depend on the extent of the improvement observed, it should bepossible to determine whether oxidation is responsible in any way for theinfluence of cut time ratio on tool-life, or if in fact thermal fatigue is the primaryfactor.In the experiments conducted, oxygen was displaced from the tool regionby pumping argon into an enclosure surrounding the tool, thus creating an inertatmosphere. Argon was chosen to facilitate the creation and preservation of theinert atmosphere within the cutting zone.The apparatus comprised the milling machine in the form used for previoustool-life tests but with the addition of a sheet metal enclosure designed to fitaround the collar of the machine and surround the cutting environment (see Fig.SteelSteelTitaniumSpindleSpeedIrPm]912912576MachineFeedElm/min.]26426462.4Slotting1/2 imm1/2 immMode ofMillingDownDownTool-Life,[minutes]19.616.376.437ImprovementOver Non-Argon'Testf%125.412.924.2WorkMaterialChapter 2 Tool-Life Investigation: Experimentation and Analysis^622.12). Other equipment included a pressurized argon bottle with an attachedflow meter.Fig. 2.12. Schematic of Arrangement Used for Argon Influenced TestsThe flow rate of the argon was set at the maximum possible (50 ft 3/hour)and the gas was kept flowing for the duration of cutting. The procedure fordetermining tool-life data was the same as for previous tests and the dataobtained are shown in Table 2.6.Table 2.6. Tool-Life Data for Argon Influenced Milling of Steel and TitaniumChapter 2 Tool-Life Investigation: Experimentation and Analysis^63These results do not show a particularly significant improvement in the tool-life values. The improvements observed are much smaller than thoseassociated with a large change in immersion. Oxidation is evidently thereforenot the major factor influencing the wearing of cutting tools in milling and it mustbe concluded that thermal fatigue is indeed the dominant factor influencing tool-life in milling.2.2 Investigation of Exit Failure in MillingExit failure is the phenomenon by which a milling tool is mechanicallydamaged as it exits from the workpiece. The phenomenon is more likely tooccur during the milling of heavily work-hardening materials and can occurduring either up-cut or down-cut milling, depending on the cutting conditions.Conflicting theories have been advanced to explain the occurrence of thisphenomenon (see Chapter 1). In this section, the problem is furtherinvestigated, and an experiment designed and conducted to verify the validity ofthe theories is presented.2,2„1 Sharp Corner TestOne factor influencing damage of the tool as it exits from the workpiece isthe thickness of the chip at exit. A finite chip thickness at exit is more likely tocause chip-sticking and consequent damage upon exit and subsequent re-entrythan does a zero chip thickness. For this reason the phenomenon has beenobserved to occur more commonly in up-milling than in down-milling. The rareChapter 2 Tool-Life Investigation: Experimentation and Analysis^64occasion in which it occurs in down-milling was observed by Yellowley [7] whiletraversing into a corner of a stainless steel workpiece as illustrated in Fig. 2.13.Fig. 2.13. Schematic Illustration of Sharp Corner WearUnder these circumstances, before the tool has traveled a distance equalto its radius into the workpiece (or before a cusp, given by the dashed arc 2, isfully formed in the workpiece), the tool sees a finite chip thickness at exit fromthe workpiece, i.e., arc 1, and the result is catastrophic damage to the tool uponthe subsequent re-entry.An experiment on titanium alloy verified this phenomenon duringinvestigation of the present research into exit failure. Test 1 in Table 2.2 wasrepeated without first machining the cusp into the workpiece as had been thepractice for previous tests. Fig. 2.14 shows graphically a comparison of bothtests:Chapter 2 Tool-Life Investigation: Experimentation and Analysis^65Fig. 2.14. Illustration of Sharp Corner Test ResultThis illustrative comparison shows that if the cusp is pre-machined, it takes6 minutes for the tool to attain a wear of 0.025 inches whereas without the cusp,the tool-wears to 0.025 inches in 1 minute. Therefore the presence or absenceof the cusp has an extremely significant influence on the life of the tool.2.2.2 Investigation Di Behavior 1/ Tool Exit  Leading /Q Failure The influence of exit conditions on tool chipping and life has beendiscussed. The two main explanations are in fact similar: the early work byYellowley [7] considered that the shear plane would rotate until the shear anglewas approximately zero and that on work-hardening materials the final failurewould occur through crack propagation at an angle of 45 degrees to the directionof maximum shear stress (the mechanism has been described in detail by NobleChapter 2 Tool-Life Investigation: Experimentation and Analysis^66and Oxley [11] in relation to blanking and piercing operations). In later work,Pekelharing identified negative shear angles; the evidence shows that thesenegative angles are created by a combination of a reducing shear angle aspostulated by Yellowley, and a bending rotation of the workpiece free surfacewhich unlike a sheared part does not have a support at the free surface.The former explanation is supported by the result of an upper boundanalysis of the problem. A simple schematic of the shear plane region of acutting operation performed with a tool having zero degree rake is shown in Fig.2.15a. The attendant velocity vector polygon is shown in Fig. 2.15b:Fig. 2.15. (a)Schematic of Shear Plane Region of Cutting Operation;(b)Associated Velocity Vector PolygonPlastic Work = V,- A, + V., • A.,^ 2.21where Vs is the shear plane velocity,Vw is the resultant chip velocity, andAs and Aw are the shear plane and chip cross-sectional areasChapter 2 Tool-Life Investigation: Experimentation and Analysis^67respectively.Assuming unit width into the plane of the paper,A^x =^, and A,„ = h.cos0also,,^170v, =^ and v =vo • tan 0wcos 0 'where Vo is the workpiece approach velocity.Substituting into the expression for plastic work yields:Plastic Work =V0^+ (h • tan 0 ))(( x^1cos 0 cos e )^. 2.22Eqn. 2.22 shows that the minimum work will occur when 9=0. Sinceshearing will always take place along the direction of least work, the shear planewill obviously rotate into this position as the tool approaches exit as suggestedby Yellowley.The major differences between the two theories, however, results from theproposed influences of exit conditions on tool chipping. While Yellowley hadassociated this phenomenon with the removal of the formed foot in thesucceeding impact, Pekelharing associated the damage with the increasedforces arising in the final stages of tool exit. However, no matter whichexplanation is used, no damage would be expected at the extremes of exit angle(see Fig. 2.16).Chapter 2 Tool-Life Investigation: Experimentation and Analysis^68Fig. 2.16. Typical Exit AnglesAt the position shown in (a), the chip will likely continue to be formed untilexit, while with that shown in (c) a burr will be formed due to the bending away ofthe free surface. The position shown in (b) however will lead inevitably to one ofthe two possible mechanisms described.One more recent rigorous experimental investigation of the influence ofchipping at exit on tool failure was by van Luttervelt et al. [14]. This investigationconfirmed that the influence is restricted to a narrow zone of exit angles. Whilethe data from van Luttervelt's work showed the danger of such exits, it alsoshowed that several other factors associated with the geometry of cut and thetime in cut significantly influenced the tool damage. The most notable findingwas that smaller diameter cutters performed significantly better than largerdiameters; no explanation was suggested since the authors could not identifyany changes to similar parameters in the original work of Pekelharing. Laterexperiments attempted to examine the influence of reducing time in cut for thelarger cutters. Differences in tool-life were observed; however, the change intime in cut was associated with a change in entry conditions, thus makingdefinitive statements difficult.Chapter 2 Tool-Life Investigation: Experimentation and Analysis^69The data from the later paper is believed to be in agreement with theoriginal work of Yellowley in which both thermal and exit influences wereconsidered. The major influence of cutter diameter as far as the exit failure isconcerned is considered due to the decreased time out of cut (at the sameperipheral speed) which leads to reduced welding of the adhered chip foot. Theworst damage situation would be expected to occur if the adhered chip is madeto traverse a wide chip thickness upon re-entry rather than being removedinstantaneously upon impact as would likely be the case with reduced welding,i. e., the entry conditions will also be important.Great difficulty is clearly involved in the experimental verification of any oneof the theories presented, considering that the exit phenomenon at normalpractical conditions lasts for only a few milliseconds. The use of high speedphotography or even the capture of dynamic forces under these conditions isimpractical. The author has attempted to examine qualitatively the processesoccurring during the last few milliseconds of cut using a new test set-up shown inFig. 2.17. The idea is to examine the output of the accelerometer which isattached to the aluminum wedge.AluminumWedgeAccelerometerTitanium Workpiece0 0Oscilloscope\ I =000 oo I OMilling Machine0000 cD,no;Spindld Head ofMilling MachineCutting Zone (Magnified)^ ;Cutting/ZoneViceDigital FlterChargeAmplifiers Acceierometf‘flChapter 2 Tool-Life Investigation: Experimentation and Analysis^70Fig. 2.17. Experimental Set-Up for Exit Failure InvestigationThe wedge is positioned so that impact into the aluminum will occur at adistance of 0.25 mm (0.01 inch) after the cutting edge passes the undeformedoutside boundary of the titanium workpiece. In this manner the exit of the toolfrom the workpiece can be easily timed. Since the whole apparatus is mountedon top of the dynamometer, the output of the accelerometer can not be directlyassociated with dynamic force signal; nevertheless, a sharp increase ordecrease in force at exit should lead to useful qualitative information regardingthe processes occurring at exit.Chapter 2 Tool-Life Investigation: Experimentation and Analysis^71The majority of the tests were carried out at practical cutting speeds, andthe results obtained are reproducible. The Y component of the cutting force andthe output of the accelerometer (acceleration in the Y direction) were bothcaptured on an oscilloscope, the sampling time being either 100 or 200microseconds (depending on the spindle rotational frequency). Both signalswere also filtered before entering the oscilloscope.Fig. 2.18a shows the overall pattern. The accelerometer signal shows littleactivity during the initial impact; however, both at exit from the titaniumworkpiece and at entry into the aluminum wedge, activity is pronounced.100- 314--2.412^A^-100^0.45Spindle Speed: 288ipmFeed-Rate: 24mm/thinDepth of Cut: 2.0mmForce Signal Filter: 425Hz L.P.Accelerometer Signal Filter: 4kHz L.P.0.455^0:46^0.265^0.'47^0.475^0.148^0.485^049^0495TIME (SECONDS)FORCE FY^— ACCELEROMETER I05-2.80::1Chapter 2 Tool-Life Investigation: Experimentation and Analysis^72Fig. 2.18a. Traces for Exit Failure Investigation with Cutting Conditions288 rpm and 24 mm/minThe behavior of the signals during exit were examined over a range ofcutting conditions and are shown in Figs. 2.18b to d. As in the previous figure, atexit there is a sudden drop in force which is appreciable considering theaccelerometer is not attached directly to the titanium workpiece. Theaccelerometer then records the impact into the aluminum wedge almostinstantaneously (time period ranging approximately between 0.2 and 0.8milliseconds for the respective spindle speeds) after exit from the titanium.0.06^0.065^0.070.05^0.055TIME (SECONDS)-1.40.045Spindle Speed: 18OrpmFeed-Rale: 144mmtminDepth of Cut :2.0mmForce Signal Filler: 425Hz L.P.Accelerometer Signal Fitter: 2kHz L.P.200-100--100^0.03--1.7--1.8--1.9--2--22--2.3-2.40.075----• FORCE FY^— ACCELEROMETER I0.040.035--1.5Chapter 2 Tool-Life Investigation: Experimentation and Analysis^73Fig. 2.18b. Traces for Exit Failure Investigation with Cutting Conditions 180 rpmand 14.4 mm/minChapter 2 Tool-Life Investigation: Experimentation and Analysis^74Fig. 2.18c. Traces for Exit Failure Investigation with Cutting Conditions 144 rpmand 14.4 mm/min02Spindle Speed: 72IpmFeed-Rale: 14.4mmiminDepth of Cut:2.0mmForce Signal Filter: 425Hz L.P.Accelerometer Signal Fitter: 2kHz L.P.0:22^0225TIME (SECONDS)I FORCE FY^— ACCELEROMETER IChapter 2 Tool-Life Investigation: Experimentation and Analysis^75Fig. 2.18d. Traces for Exit Failure Investigation with Cutting Conditions 72 rpmand 14.4 mm/minThe time between the force changes is approximately equal to thatrequired for the tool to traverse the 0.25 mm between the undeformed boundaryof the workpiece and the aluminum wedge. The dynamic response of the wedgethen dominates the accelerometer signal. In general, the behavior is consistentfor all the test cases; however, at the very low speed of 72 rpm, the influence ofbuilt-up-edge is apparent with considerable perturbation in force levels both atChapter 2 Tool-Life Investigation: Experimentation and Analysis^76entry and exit. In all cases, as a result of the low pass filter employed, the outputof the dynamometer shows no large dynamic effects.Despite the qualitative nature of the tests, it is the authors belief that thetiming and sign of the accelerometer output lend some credibility to thepossibility of brittle fracture at exit as opposed to the continual shearing withrotation assumed by Pekelharing. It is noteworthy that in this experiment as wellas in the tool-life tests, the adhesion of chip roots and associated ribbon chipscomprising several individual elements welded on impact were observed. Thiswas reported by Yellowley in those cases in which exit conditions wereproblematic and more recently by Ghani and Barrow [16]. Pekelharing, in hisexperiments, reported seeing no such adherence. It is possible that, dependingupon the work-hardening capacity of the work material, the behavior at exitvaries and both mechanisms may play a role. In the case of the work materialexamined here, however, the major problem appears to be adhesion andsubsequent damage upon re-entry.Chapter 3 Force Modeling and Tool-Wear Tracking in MillingChapter 3Force Modeling and Tool-Wear Tracking in MillingThis chapter discusses: a) the development of a force model for the millingof titanium work material and experiments performed to verify the validity of themodel and b) tool-wear tracking (or monitoring), employing force data obtainedfrom sharp and worn tool tests, with the aim of developing techniques for the realtime identification of wear in complex milling operations.3.1^The Modeling of Instantaneous Forces in MillingIn the general case of peripheral milling, the forces acting on a single toothmilling cutter in up- and down-milling are shown in Fig. 3.1. Normal practiceresolves both the radial (FR) and tangential (F7) components of force into thefeed direction (X) and perpendicular to the feed direction (Y).Fig. 3.1. Forces Acting on a Single Tooth in Up- and Down-Milling77Chapter 3 Force Modeling and Tool-Wear Tracking in Milling^78The normal approach to force estimation assumes that FT may be obtainedfrom the product of the instantaneous area of out (A) and the specific cuttingpressure (Ks); it is also usually assumed that the ratio of radial to tangential forcecomponent (re) is known and constant. While in the simplest case Ks and re areassumed constant, later work has assumed these parameters to be knownfunctions of the mean chip thickness [18].In an early consideration of the problem, Yellowley [17] suggested that,since the chip thickness in peripheral milling was generally low, as a firstimprovement on a linear model of cutting forces, the edge forces (nose andflank), which are known to constitute a significant proportion of total forces atsuch conditions, should be considered. A model which considers FTto be madeup of two components was developed: one directly proportional to theundeformed area of cut and a second directly proportional to the length of cuttingedge engaged.A general form for the tangential force component may be expressed as:FT =^• a S, • Sill -I- K2 • Le^3.1where K1 is the cutting component of the specific cutting pressure,K2 is the edge force per unit length,a is the depth of cut,St is the feed-per-tooth,(1) is the instantaneous angle of rotation, andLa is the length of cutting edge engaged.Chapter 3 Force Modeling and Tool-Wear Tracking in Milling^79The corresponding expression for the radial component is given by:FR = ri •FTwhere ri is the ratio of radial to tangential force component.The instantaneous area of cut is expressed as:A = a • S, • sin 44)and the equivalent chip thickness, he is given by: Eqn. 3.1 can be re-expressed in the form:F---T- = ICI + K2A^he3.5Since the ratio of radial to tangential force components on the rake faceand flank/nose of the tool is expected to be different, the ratio must be brokeninto two components: r1 for the cutting forces and r2 for the edge forces. Typicalvalues for the ratios range between 0.2<r1<0.5 and 1<r2<4. The radial force cantherefore be expressed in terms of these and the R.H.S of Eqn. 3.5 as:FR^K2—=r, • IC, +r, -A ^- kEqns. 3.5 and 3.6 are final forms of the model equations to be used in thecurrent analysis.3.6Chapter 3 Force Modeling and Tool-Wear Tracking in Milling^80From a geometrical evaluation of Fig. 3.1, expressions can be written forthe instantaneous forces as follows.For up-milling:Fx = FT • COS 4) + FR • Sin 4:1)^ 3.7Fy = Fr • Sin 0 — FR • COS 0 3.8and for down-milling:Fx =FR • sin 4) — FT • COS 4)^ 3.9FY =FR • cos 4) + FT • Sin (1) 3.10In terms of the tangential and radial force components, these equationsmay be re-expressed as:For up-milling:FT = Fx • cos0+ FY • sin 0^ 3.11FR = Fx • sin 4) —Fr • cos4) 3.12and for down-milling:FT = FY • sin cp — Fx • cos (1)^ 3.13FR =FT • COS 0 + Fx • sin 4) 3.14A validation of the model has been attempted in this work in two inter-related ways. A series of cutting force tests conducted on a titanium alloy underup-, down- and centerline-milling (slotting with workpiece width less than cutterdiameter) conditions employed the same set-up used for the exit failureChapter 3 Force Modeling and Tool-Wear Tracking in Milling^81investigation tests. Using the force data (Fr, Fy from the up- and down-millingtests, the tangential and radial force components were obtained from theequations presented.For a tool with a nose radius such as that used in these tests, he is givenby the following expression:1 _ ^1^1^0.57. (r • cosy)wh, – S•cos + 2•a +^a•S 3.15where S is the instantaneous feed (in milling),w is the approach angle (zero for tooling used in these tests),r is the nose radius of the insert, anda is the depth of cut.(for the geometry of the milling insert used, r= 1.194 mm.)Eqns. 3.5 and 3.6 indicate that linear relationships exists between AT andAF'—1 , and also -A. and —1 . With these equations, sets of data values may beh^A^hecomputed for these parameters at regular intervals (of 0) through the workpiece,for both modes of milling. Plots can then be made of AT^hversus —1 , and —FRA ^Aversus-1 , from which Ki, K2 and then ri ,r2 may be determined for each modeheof milling.The simulation of a centerline-milling operation can be achieved bycombining the dynamics of an up-milling operation with that of a down-millingChapter 3 Force Modeling and Tool-Wear Tracking in Milling^82operation (in that order). By substituting the four constants K1, K2, r1 and r2 forthe respective milling modes in Eqns. 3.5 and 3.6, the tangential and radial forcecomponents for both the up-milling side and the down-milling side of anequivalent centerline-milling operation may be simulated. Comparison of thesimulated data with the actual experimental data gives a measure of theaccuracy of the simulation and therefore of the validity of the model employed.Figs. 3.2, 3.3 and 3.4 respectively show plots of the experimental dataobtained from up-, down- and centerline-milling tests conducted at 288 rpm and14.4 mm/min. In summary the first two plots are used to determine theconstants which are used to simulate the third plot. The simulation compared tothe actual plot verifies the validity of the model used.Chapter 3 Force Modeling and Tool-Wear Tracking in Milling^83Fig. 3.2. Experimental Force Data from Up-Milling Test on TitaniumChapter 3 Force Modeling and Tool-Wear Tracking in Milling^84Fig. 3.3. Experimental Force Data from Down-Milling Test on TitaniumChapter 3 Force Modeling and Tool-Wear Tracking in Milling^85Fig. 3.4. Experimental Force Data from Centerline-Milling Test on TitaniumThe data derived from the experiments illustrated by Figs. 3.2 and 3.3 areshown below in Tables 3.1 and 3.2 respectively:Chapter 3 Force Modeling and Tool-Wear Tracking in Milling^86Table 3.1. Data for Determining Model Constants for Up-Milling Test (Ti.)-68.5 124 0.1508 0.98865 0.15023 112.302 86.351 0.01502 7475.386 5747.955 178.675-72.5 160.5 0.3016 0.95486 0.29705 131.719 116.904 0.0297 4434.275 3935.514 90.4867-65 189.5 0.4524 0.8994 0.43713 142.023 141296 0.04371 3249.028 3232.398 61.5703-44.5 218 0.6032 0.82352 0.56728 154.284 160.314 0.05673 2719.718 2826.009 47.5011-20 251 0.754 0.72896 0.68456 169277 186.404 0.06846 2472.783 2722.971 39.40610 273 0.9048 0.61784 0.7863 176.534 208.482 0.07863 2245.12 2651.424 34.339550 295 1.0556 0.49271 0.8702 188.858 232.073 0.08702 2170.292 2666.9 31.053103 300.5 12064 0.35639 0.93434 203.331 244.061 0.09343 2176.198 2612.127 28.9384Table 3.2. Data for Determining Model Constants for Down-Milling Test (Ti.)re phi... .. ,, . . . ,,, . , ... :::::::i.:::: A....... .,,f„::: ,.„^. ..... .. ,. ... , . .,... ..^, „^^ ....  lAi-102.5 127 0.1508 0.98865 0.15023 120.416 110.16 0.01502 8015.481 7332.815 178.6752-98 190 0.3016 0.95486 0.29705 150.016 152.313 0.0297 5050212 5127.553 90.48669-69 242 0.4524 0.8994 0.43713 167.843 187.493 0.04371 3839.699 4289234 61.57031-28 292.5 0.6032 0.82352 0.56728 188.988 224.997 0.05673 3331.478 3966.239 47.5011425 325.5 0.754 0.72896 0.68456 204.6 254.389 0.06846 2988.787 3716.1 39.4060485 343.5 0.9048 0.61784 0.7863 217.578 279.065 0.07863 2767.106 3549.079 34.33954146 338 1.0556 0.49271 0.8702 222.191 293.583 0.08702 2553.347 3373.759 31.05301204 324 12064 0.35639 0.93434 230.023 306.074 0.09343 2461.882 3275.834 28.93836Determination of the model constants for each milling mode was achievedusing a regression analysis performed between the relevant variables of therespective tables as explained earlier. The results of these analyses are shownin Table 3.3.Table 3.3. Determined Force Model Constants for Titanium AlloyModel Constant^up-MiMng^Down-MillingKj [N/mm2] 2511 2302K9 [N/mm] 29.18 10.87ri^ 0.52 0.53r2 1.42^2.9Chapter 3 Force Modeling and Tool-Wear Tracking in Milling^87The substitution of these constants gives the simulated force data, so that acomparison between the actual data and the simulated data is possible. Thegraphical illustrations that follow (Figs. 3.5 and 3.6) show these comparisons.Fig. 3.5. Comparison of Actual and Simulated Force Data (Tangential andRadial Components)Chapter 3 Force Modeling and Tool-Wear Tracking in Milling^88Fig. 3.6. Comparison of Actual and Simulated Force Data (X and YComponents)These last two figures show that, in general, the simulated data are in goodagreement with the experimental data (within normal limits of error). In general,the down-milling data compare more favorably than do the up-milling data. Thisoccurrence can probably be attributed to the previously discussed phenomenaassociated with up-milling, and in particular with work-hardening work materials(chip-sticking, built-up-edge, exit failure etc.), that likely introduce error into thedata.Chapter 3 Force Modeling and Tool-Wear Tracking in Milling^89On the basis of this one data set, the model appears valid and provides agood representation of cutting forces.Further validation of the force model can be achieved if the model isemployed to simulate, on the basis of Fourier Series (F.S.) modeling, cuttingforces obtained during machining of the titanium alloy work material. The cuttingforces are filtered before display on the oscilloscope; this is the reason for theF.S. approach to the problem, i.e., to account for the effect of filtering on theforces. The theoretical basis for F.S. modeling was first presented by Yellowley[19]. Later work by Hosepyan [20] detailed the derivation of F.S. equations for aparticular work/tool set-up. The derivations of modified general equations usedfor the current simulation (based upon Yellowley's equations) are given inAppendix 1. Despite this reference to Appendix 1, the following commentsshould be noted with respect to the derivations: a) the constants K1, K2, r1 andr2 are assumed constant when actually they are not; previous workers haveshown that this is a reasonable assumption; b) only up-milling has beenconsidered although a similar analysis could be carried out for down-milling.The final forms of the derived expressions follow. From Eqns. A1.20 andA1.21 in Appendix 1:Fxi = K1 . a • S, •[azo +E[az,t • cos Icep + kk • sin kt4)]]k=1Fy1 = —K1 • a • S, •[ayo + y [ay, • cos ko + byk • sin k0]]k=1From Eqns. A1.54 and A1.55:OaIMO3.163.17Chapter 3 Force Modeling and Tool-Wear Tracking in Milling^90Fx2 = K1 • Le • it° •[a1.0 + E[a.k • cos 0 + bmk • sin kiti]]k=1F12 = -4(1 • 4 • lz ° .[a.,,,0 + Efawyk - cos k. + b,,,,k • sin kcd]k=1from which the total X and Y axes forces can be expressed as:Fx = Fx, + Fx2^3.20Fy = Fn + Fy2^3.21A simple program (see Appendix 2) was written on the basis of this theory,to simulate the cutting forces obtained during up-milling experiments on titaniumalloy. The simulation and the actual experimental results were then compared toconfirm again the validity of the underlying model employed. The constants K1,r1 and r2, supplied to the program, are obtained from the up-milling data in Table3.3. The comments in the program listing explain the determination of theremaining constants supplied to the program.The comparisons between the simulated cutting forces and the actualcutting forces are shown in Figs. 3.7 and 3.8:GOIII03.183.19- — -1— FX FY0.29^0.3^0.31^0.32^0.33TINE(SECOINDS)400 300-200-100--200^-0.2-100--150^0.27 028-100-k-89 TERMS. St.0.05 nwn'both0-0.5220, '2.1.4211mm. K1-2510.56 N'mm20 0.2^0.4^0.6^0.8PHI (RADIANS)1.2^14Chapter 3 Force Modeling and Tool-Wear Tracking in Milling^91Fig. 3.7. Simulated (Top) and Actual (Bottom) Cutting Force ComparisonFor Fourier Series Based Model Investigation,- 288 rpm, 14.4 mm/minChapter 3 Force Modeling and Tool-Wear Tracking in Milling^92Fig. 3.8. Simulated (Top) and Actual (Bottom) Cutting Force ComparisonFor Fourier Series Based Model Investigation; 288 rpm, 30 mm/minChapter 3 Force Modeling and Tool-Wear Tracking in Milling^93The simulated force data in both cases provide a good representation ofthe actual cutting forces within normal limits of experimental error. This goodrepresentation emphasizes the validity of the F.S. approach and, in particular,the underlying model used.On the basis of the results obtained from these analyses it is concluded themodel is valid for force representation in metal cutting in general and milling inparticular.3.2 Tracking of Machining Condition and Tool-Wear in MillingThis section will commence by discussing previous related researchconducted by other workers. It will then discuss work (past and current) carriedout within the Manufacturing Engineering Laboratory at the University of BritishColumbia [21] toward the development of tracking techniques for machiningcondition and tool-wear. The experimental and analytical contributions of theauthor to the research are also detailed.Several authors have attempted to derive relationships between cuttingforces and both wear and breakage [22], [23]; the majority of effort has, notsurprisingly, been directed toward the monitoring of turning operations. Previousapproaches which have demonstrated considerable promise have been basedupon either the tracking of a single force component [26], or the tracking of aratio of force components (ratio of thrust to tangential component) [27], [28].However, before any of such approaches may be adopted, any bias which mayhave been introduced due to changes in cutting conditions must be removedfrom the forces.Chapter 3 Force Modeling and Tool-Wear Tracking in Milling^94In contrast to turning, only recently have serious attempts been directedtoward the use of forces or other physical manifestations of the cutting processto track tool-wear in milling. Among interesting approaches related to real timemonitoring were those of Szabo [29] who examined the influence of wear on thedamping ratio of a major machine-tool/workpiece mode and Dornfeld [30] whoexamined the influence of wear on acoustic emissions from the cutting process.Recent publications concerned with the influence of wear on the mean anddynamic force components resulting from the cutting process include two papersfrom one research group which used force parameters based upon the lowfrequency force components. The first of these papers [31] examined theinfluence of wear on the total harmonic power in the low frequency range of themilling spectrum, while the second paper [25] attempted to identify critical ratiosof components which were most influenced by wear and suggested the use of anidentification technique to determine width of cut. The authors also suggestedthe construction of an intelligent system to assess likely force component ratiosand to identify the current wear land through simulation of the force equations inthe frequency domain.The main aim of the research at the Manufacturing Engineering Laboratoryin this area has been the development of methods or techniques that permit in-process (or real time) identification of wear in milling operations employing easilyobtainable force information from the cutting process. The methods consideredare based upon earlier research conducted by Yellowley [17], [19] and morerecent work in the area of tool-wear monitoring by Hosepyan [20]. Althoughforce is an indirect measure of wear, the monitoring of wear through force willChapter 3 Force Modeling and Tool-Wear Tracking in Milling^95continue to be one of the most practical and direct of approaches until directwear measurement in real time is available and proven.The model used in the current work is based upon a Fourier Seriesformulation (see Sec. 3.1). The applicable equations are therefore as presentedpreviously. Since in this application, the interest is in a limited frequency range,the use of the F.S. approach appears reasonable. As low a bandwidth aspossible is required for the transducers since the use of existing measurementtechniques and monitoring devices at conventional milling frequencies can thenbe permitted.The quasi-mean resultant force, Fqm, has proven useful in previous workconcerned with tool breakage detection in milling operations. The quasi meanresultant force (qrf) is the square root of the sum of the squares of the meanvalues of forces in two perpendicular directions in the plane perpendicular to theaxis of the cutter, i.e.,x2= $Fx(„,‘„,0 + kFro.„,) )23.22The qrf will be equal to the mean of the actual resultant force only if theforces are constant. Its most notable property is its independence of the cuttingdirection. Yellowley [19] has shown that, in those cases in which the metalcutting component of the total force largely exceeds the parasitic component, theqrf is directly related to the magnitude of the fundamental coefficients of thetangential force component for a single tooth cutter (determined from torquemeasurements). i.e.,Chapter 3 Force Modeling and Tool-Wear Tracking in Milling^96Fr.= 1 .(1+r2 )Y2 • (a, 2 + 12, 2 )Y2 •cos(W.23.23where al and b1 are the fundamental coefficients for the tangential force,r is the mean value for the force ratio, andWe is the effective approach angle.All tests were conducted on a Bridgeport universal milling machine, thesame one used for previous tests. Cutting forces were measured with thepiezoelectric based three component dynamometer also used for previous tests(the bandwidth of the dynamometer with workpiece attached is greater than 500Hz). In the first set of tests conducted by Hosepyan [20], a four tooth, insertedcarbide, square shoulder face mill (0° axial rake, 7° radial rake) was used tomachine a hardened low alloy steel (AISI 4140, 380 BHN) with only one insert inthe cutter (to facilitate signal observation). The force data were low pass filteredat a frequency above the fundamental frequency of a cutter with four teeth. Thedigitized data for the single tooth were then spaced in time and summed tosimulate a hypothetical four tooth cutter (all teeth identical) the simulation ofwhich could be analyzed. The second set of tests conducted by the author usedthree tooth standard length HSS end mills (1/2 inch diameter) again to machineAISI 4140 work material but with a lower hardness than before (300 BHN). As inthe previous set of tests, the force data were low pass filtered above thefundamental tooth frequency.Chapter 3 Force Modeling and Tool-Wear Tracking in Milling^973.2.1 Tracking Techniques for thg Recognition 9.1 Machining Condition The problem of tracking width of cut in milling has been treated byYellowley [17], [19], [32]. These research efforts showed that the most efficientmanner of tracking machining conditions in milling is to use a mean value of oneparameter and the corresponding magnitude of the fundamental component toestablish width of cut. The mean value alone may then be used to establishaxial depth of cut, providing prior cutting data are available. Alternatively in thecase of tools with a finite nose radius, depth of cut may be identified with the useof the ratio of the two orthogonal components of the thrust force. The lattertechnique is dangerous if large amounts of concentrated wear are present.The following are the most promising parameters for use in machinecondition identification procedures; they are all essentially independent of toolcondition and are direction insensitive:1. The mean and fundamental magnitude of torque. The theoreticalvalues of the ratio of these two have been shown to be a reasonable indicator ofswept angle of cut although with a single tooth the ratio is relatively insensitive[19].2. The mean and fundamental magnitude of the axial force. The ratio ofthese two parameters will produce essentially the same result as the methodusing torque values in cases in which the nose radius is large. It is, however, notapplicable to carbide inserted cutters with large facets.3. The deviatoric component of force and the quasi-mean resultant force.The ratio of these two parameters was shown by Altintas and Yellowley [32] toChapter 3 Force Modeling and Tool-Wear Tracking in Milling^98have potential. Unfortunately, significant computation is required. In cases inwhich only the mean and fundamental components are present in the signal, theratio becomes , more amenable to analysis.Since this final parameter is independent of cutting direction, depth of cut,cutting constants (rand K), and is only slightly influenced by tool condition, it hasbeen selected for further study in this work. The physical significance of thisimmersion tracking parameter may be appreciated by consideration of the forcelocus created in milling; a typical one is shown in Fig. 3.9.Fig. 3.9. Milling Force LocusThis illustration shows the quasi-mean resultant force vector, Fqm, and thedeviatoric vector, Fdev, which rotates through one revolution for each toothperiod. The mean value of the deviatoric component would be expected todecrease as immersion increases; at the same time, the qrf would be expectedChapter 3 Force Modeling and Tool-Wear Tracking in Milling^99to increase. The ratio of the two would be expected to provide an effectiveimmersion tracking parameter.The X and Y components of force for a cutter with N teeth in terms of themean and fundamental F.S. coefficients can be expressed as:Fx = N • axo +N •{a1,34 • cos(Ncot)+ bxN • sin (Mot)}^ 3.24FY =N • ayo + N •fayN • cos(Mot)+ kw • sin (Not)}^ 3.25where co is the spindle rotational frequency,t is the time, andaXN, bXN, axN and byN are coefficients of the F.S. representationof the forces in the X and Y direction.Since a parameter related to the area swept out by the deviatoric forcecomponent, Fdev is desired, expressions for the X and Y components of Fdevmay also be given as:Fae,x2 = [(axi 2 2+ bx1 2  )+ (axi2 — 1)11 2  )2^)+ axi • bx , • sin (2Mot)])and[114'1^Y1  ±  Y1 222 + b 2  ) ra 2 — 4'1 2 FanT2 = )+a,, • bn • sin (2No)t)]) ^)The magnitude of the mean squared deviatoric force can be given by:Fdev 2 = (  ary2 + bxN2 + ayN 2 + byN 3 Force Modeling and Tool-Wear Tracking in Milling^100At this point, the immersion tracking parameter, Q, can be defined. Q isproportional to the ratio of the area swept out by the mean deviatoric force andthe square of the qrf. It is both non-dimensional and direction insensitive. It isindependent of the average force ratio, r, and therefore should be insensitive toflank wear, i.e.,Q=kax,v + b xiv + ayN 2 + b 1yN 1^( Fdev 2i^2(2 2)axo +ayo =2. —Fq.2 3.29The real time computation involved in tracking the parameter 0 would berelatively minimal. Since only the fundamental and mean values are required,simple signal processing techniques and equipment are all that are necessary toextract data.The effectiveness of the immersion tracking parameter, Q, is illustrated inFig. 3.10 in which experimental data for both three and four tooth cutters aregiven together with expected values:-8- 4 ieeltir..0 -113- 4 leeth,n4.5 -MI- 4 leeth,W=1• 3 leeth,h*.0 411 • 3 Welh,n.0.3 -INI • 3 teetti,hn.1Chapter 3 Force Modeling and Tool-Wear Tracking in Milling^101Fig. 3.10. Relationship Between Immersion Parameter Q and Immersion forExperimental and Predicted ValuesIt is noteworthy that both sharp and worn tool data (O<VB<0.35 mm) areshown and that a variety of feed-rates were used for the three tooth cutter. Thehelix angle of the three tooth end mill would only significantly influence 0 incases in which the axial depth of cut is high. In these tests, the axial depth of cutwas 2 mm, therefore the influence was negligible and could be neglected.3.2.2 , Tracking Techniques fa./Le Recognition 91 Tool ConditionMinimizing the influence of changing cutting conditions on the parameterchosen to track tool condition is desirable. As stated earlier, the use of the ratioof thrust force to main cutting force has proven reliable as an indicator of toolChapter 3 Force Modeling and Tool-Wear Tracking in Milling^102condition in turning; for this reason extended use of the same parameter to themonitoring of milling operations is attempted. Unfortunately, two complicationsmake this approach difficult in milling:1. The thrust force required, when an inserted tooth carbide cutter isused, is the vector sum of the axial and radial force components. While the axialcomponent is easily measured, the instantaneous value of the radial componentis not. It follows that a situation arises in which both torque and axial force areadditive but cancellation of radial force components makes the straightforwardapplication of the force ratio impossible.2. In milling with carbide or ceramic cutting tools, there is a significantlygreater likelihood of sustaining edge chipping. Under such circumstances, thesimple use of the axial force and torque to infer a global state of wear around thetool is likely to cause problems, especially in those cases in which the approachangle of the tool is small or when chipping occurs on the primary cutting edge asopposed to the nose radius.Generally, in the case of inserted carbide milling cutters or indeed anycutter having a radius or chamfered geometry, use of the axial component offorce and the cutting torque to evaluate the condition around the radius is onlypossible if the following conditions are met:1. The axial depth of cut should be significantly greater than the axialprojection of the radius or chamfer, otherwise, a tracking parameter which is ableto identify actual depth of cut should be used.Chapter 3 Force Modeling and Tool-Wear Tracking in Milling^1032. No damage which is significant enough to mask the influence of wearon the tool radius (through a compensating increase in torque) should occur tothe primary (straight or fluted) portion of the cutting edge.For an assessment of tool condition along the primary edge, an indirectapproach based upon Eqn. 3.23 is employed, i.e.,Fqm2^ = 1 cost (we ) (1+ r2 ) (a12 +42) FTonean)2 ^a02where FT(mean) is the mean value of the tangential component of force,and all other variables are as defined earlier.A wear tracking parameter, P, may be defined as:2a P =(1+ r2). ^4^Fq„,^a02cost (V e) (FT(..)) (a12 +b1 2 )3.31While the qrf and torque values are easily measured, the mean andfundamental components of tangential force for a single tooth cutter will not beavailable within the torque signal for a multiple tooth cutter. The use of thistracking parameter is therefore dependent on the capacity to monitor width of cut(allowing the ratio of the torque, or tangential, F.S. coefficients to be calculated),and axial depth (allowing the effective approach angle to be estimated). Theproblem which inevitably arises is that the F.S. coefficients are also influencedby wear. While the influence is small, changes in the parameter being trackedare also small; the result is problems particularly at high values of immersion.Fig. 3.11 shows this difficulty with simulated values of (14-r2), calculated in two3.30Chapter 3 Force Modeling and Tool-Wear Tracking in Milling^104ways: first, with a knowledge of the influence of wear on the coefficients of thetorque series, and second, with the assumption of no influence and that sharptool values may be applied:Fig. 3.11. Theoretical Values of the Wear Tracking Parameter as aFunction of Immersion. (Values Denoted as (Fq,r/FT)2 are CalculatedWithout Knowledge of Changes in F. S. Coefficients Due to Wear)Fig. 3.11 shows that P is only likely to be effective for those immersionswhich are less than the cutter radius. An alternate strategy must be devised tocope with higher values of immersion.The initial series of tests performed by Hosepyan [20], employing a fourtooth carbide cutter upon a tempered low alloy steel material, provided a good0.250.15^ 0.2Wow bend (V8) I0.14 I0.120.10.06^ 0.14 Teeth CutterCrw.46 Do -75St_0.066 mmawl .5 rrwri-113- (1.e2)^-61s- (FZ(rnsanYFT(rnsan)) I0.05Chapter 3 Force Modeling and Tool-Wear Tracking in Milling^105indication of the problems involved in wear tracking. Two sets of data wereacquired: one in half immersion and the other in slotting. In both cases thedepth of cut was 1.5 mm and the nose radius of the tool was 0.75 mm. Thepotential difficulties were apparent in both sets of data. In the case of slotting,the tool nose sustained considerably greater wear than did the primary straightedge (approximately two times greater, based on maximum values). In the halfimmersion tests, localized chipping of the edge, occurring along the straightportion, caused considerable force changes and a distortion of the tool trackingparameter for the nose portion. The use of the axial force based trackingparameter in the full immersion test is shown on one Y axis in Fig. 3.12. Thepronounced wear around the nose radius enhances the ability of the parameterto indicate clearly the progression of wear. In contrast however, the trackingparameter based upon the qrf (shown on the other Y axis) only starts to show aninfluence at relatively high values of wear land.Fig. 3.12. The Performance of the Wear Tracking Parameters in SlottingChapter 3 Force Modeling and Tool-Wear Tracking in Milling^106The same wear tracking parameters are again shown in Fig. 3.13 for halfimmersion:Fig. 3.13. The Performance of the Wear Tracking Parameters in Half ImmersionIn this case, the insert developed relatively minor edge chipping on theprimary (straight) cutting edge. This damage is reflected clearly in theprogression of the parameter based upon the qrf; however, the change in torqueinduced by the chipping masked the increasing axial force (due to flank wear onthe nose) in the other parameter based on this force. In order to assess theeffectiveness of the parameters at higher wear values, a second tool, pre-wornin full immersion, was tested in half immersion. Fig. 3.13 shows the pronouncedwear evident in both tracking parameters.Chapter 3 Force Modeling and Tool-Wear Tracking in Milling^107To better understand the paradox at play, Fig. 3.14 shows a considerationof the characteristics of the axial force. This illustration suggests that the actualbehavior of the axial force is considerably more complex than that of the simplemodel used to derive the tracking parameters:Fig. 3.14. Influence of Wear on the Axial Component of Force in Slotting with aSingle Tooth Carbide Milling CutterIn the case of the sharp tool, a considerable discrepancy exists betweenforces in the up and down portions of the cut (similar behavior is exhibited byboth the radial and tangential components of force). In the case of the worn tool,the rubbing/cutting transition is clearly visible; it is likely that the force ratio on theflank changes markedly between the two regimes and that the higher frequencyChapter 3 Force Modeling and Tool-Wear Tracking in Milling^108terms influenced by this transition may distort methods which rely on higherfrequency components.The previous discussion indicates that the search for a simple force basedparameter to allow the tracking of tool condition at high values of immersion hasproved difficult. Initial attention was focused upon the shape of the force locusshown in Fig. 3.9 and parameters such as the amplitude of the deviatoric forcecomponent about its mean value were also examined. Even the phase anglebetween X and Y components of force was considered. While the use of theformer parameter would be ideal (owing to its direction insensitivity), simulationshowed that it is insensitive to wear with three and four tooth cutters in fullimmersion. Alternatively, very recently in the author's own research, the searchexamined the ratio of X and Y forces and experiments were carried out to obtaindata upon which investigation could be conducted. For analysis of thisconsideration, the predicted mean, amplitude and maximum values of the X andY forces are shown in Figs. 3.15 and 3.16:Chapter 3 Force Modeling and Tool-Wear Tracking in Milling^109Fig. 3.15. Predicted Values of the Magnitude of the Mean and FundamentalCoefficients of the Force in the Feeding DirectionChapter 3 Force Modeling and Tool-Wear Tracking in Milling^110Fig. 3.16. Predicted Values of the Magnitude of the Mean and FundamentalCoefficients of the Force Perpendicular to the Feeding DirectionThese figures show that the use of a ratio of peak forces should lead to aparameter which varies little over the region of interest (from half to fullimmersion). This ratio is shown in Fig. 3.17 and actual experimental dataobtained from the experiments (employing a three tooth cutter) are shown in Fig.3.18.Chapter 3 Force Modeling and Tool-Wear Tracking in Milling^111Fig. 3.17. Predicted Influence of Wear on the Force Ratio Fx(maxyFy(max)Chapter 3 Force Modeling and Tool-Wear Tracking in Milling^112Fig. 3.18. Actual Values of the Force RatioAs illustrated, the sensitivity of the parameter to wear is not desirablymarked; however, the parameter indicates the presence of wear and can bemeasured relatively simply.The result of the investigation is that two parameters are required for thetracking of wear on the primary edge and a single parameter is required fortracking the wear on the radius or facet. In those instances in which the millingcutter has a large approach angle, the single parameter which is more readilymeasured for the nose will give a balanced representation of tool condition.Since in practice, however, a very large number of face mills and almost allcarbide and high speed steel end mills use a zero approach angle (to permitChapter 3 Force Modeling and Tool-Wear Tracking in Milling^113square shoulder cutting), any approach to tool condition monitoring should useinformation based upon the ratio of both the axial and radial components withthe tangential force.Chapter 4 Conclusions and RecommendationsChapter 4Conclusions and RecommendationsThe tool-life experiments discussed in previous chapters yielded workabledata for analyses and permitted the determination of tool-life equations for therespective steel and titanium work materials considered. Compared to thoseobtained from similar previous work, the data were reproducible and consistentand permitted confirmation of theories involving the influences of cuttingparameters on tool-wear and life.The problem of ascertaining through which phenomenon the cut time ratiomost influenced tool-wear so that a level of significance could be allotted to thephenomenon was accomplished through experimentation with machining in aninert atmosphere. The results removed any doubts that thermal fatigue was themost significant phenomenon at play and therefore confirmed a lesser level ofsignificance for oxidation.The process occurring at tool exit from the workpiece which led, undercertain conditions, to the problem of exit failure (of the tool) was investigatedqualitatively with an experimental set-up designed to detect the point of exit fromthe workpiece while monitoring the cutting force. The enlightening resultspermitted definite conclusions to be reached about previous theories that hadbeen put forward in explanation of the phenomenon. The potential for furtherresearch in this subject area is most promising. Future work should attempt to114Chapter 4 Conclusions and Recommendations^ 115isolate the accelerometer from the redundant dynamics of the cutting process towhich it is subjected as a result of being in indirect contact with thedynamometer. This isolation will permit cleaner impact detection signals to beobtained (see Sec. 2.2.2). Improved testpiece and experimental designs toachieve greater sensitivity in determining force behavior in the exit region canalso be pursued.A model which had been proposed earlier for force representation in millingwas investigated for validity. Model constants determined from experimental(up- and down-milling) force data were combined and used to simulate theforces in a center-line milling operation. The comparison obtained between theactual and simulated forces was good and therefore confirmed the validity of themodel. A Fourier Series program based on the model was also written and usedto simulate forces in up-milling cutting experiments (see Appendix 2). Thevalidity of the model was confirmed again by the close comparison obtainedbetween the actual and simulated data.Previous detailed work on the tracking of wear and machining condition inmilling was reviewed. The problems associated with the parameters suggestedfor wear tracking were identified. Alternate wear tracking parameters whichemploy X and Y force components were considered and the results showed thatgiven the simplicity of measuring these forces and despite the lack ofpronounced sensitivity, a tracking parameter based upon these components hadpotential. The development of direct wear sensors on inserts, if pursued, wouldprovide the best and most realistic wear tracking technique.Appendix 1 Derivation of Fourier Series Expressions for Force ModelingAppendix 1Derivation of Fourier Series Expressions for Force ModelingConsider first, the cutting component of Eqn. 3.1, and let it be given byFT1, a component of Fr.Fri = Ki . a • S, - sin 0^ A1.1The periodic function (sin 0) in the expression can be expressed in the formof an F.S. as follows:sin 0 = [ao + X [ak • cos 10) + bk • sin 01]^ A1.2k=1Substituting this in Eqn. A1.1 gives:Fn = K 1 • a • S, -[ao + 1[a k • cos kO+ bk • sin k4]]k=1Determination of the Fourier coefficients is achieved by integrating thefollowing standard equations for F.S.?1^.a s:, = — sin 0 . c14)27C1^.a l = _3.24. dO2/rSOA1.3A1.4A1.5116Appendix 1 Derivation of Fourier Series Expressions for Force Modeling^117b1 = — sin 2 4) • 614)1 7Ir JA1.6.ak = 1— 3 sin 4) • cos 0. Citi)IC 4,A1.7bk = —1 7 sin 0 . sin kO. dOIt JofIntegration of these expressions results in the following general forms forthe F.S. coefficients:a0 = T17c [COS 4) 1 —cos 4) 2 ]^ A1.9A1.8al = —41it [COS 20 1 — COS 20 2 ]b1 = 2 [((1)2 — 4) i) — -} (sin 24)2 — sin 201)]1 [cos(1+ k) oi^2^Icos(1+ k) 0^cos(k — 1) „ + cos(k —1) 02 1ak =27t^l+k^l+k^k-1^k-1 its^1 [sin° +k) (01 sin° + k) 02 +  sin (k —1) 02 sin(k —1) 40u k = 2n 1+k^1+ k^k-1^k-1A1.10A1.11A1.12A1.13Substitution of Eqn. 3.2 into Eqns. 3.7 and 3.8 results in the followinggeneral expressions for Fx and Fyas functions of FT, 0 and rFn =—c•[ayo +E[ayk •cosko+byk • sin lad]k=100A1.21118Appendix 1^Derivation of Fourier Series Expressions for Force ModelingFx = FT (cos0 + r • sin 0) A1.14Fr = Fr (sin 4)—r-cosO) A1.15Expressing these in terms of FT1 and r1 gives:Fx1 = Fri (COSO+ rl • sin 0) A1.16Fn = Fri (sin 4)— ?I - cos 4)) A1.17Further substitution of FT1 in terms of its F.S. coefficients into the last twoequations gives:ellFx1 = C • (cos 0 + ri • sin 0)I ao + 1 [a z - cos k4) + bk • sin lai)]k=1Fn = C • (sin 0— ii - cos Of ao + I [ak • cos k0 + bk • sin k4)]]k=1where C=KI . a • SiExpansion of the two expressions above gives:ODA1.18A1.19[-Fx1 = C azo + 1[a zz • cos kci) + kk • sin kO]^ A1.20k=1The coefficients for these modified F.S. can be expressed in terms of thecoefficients of the previous F.S., derived earlier:a2 + -b2ax, = ao +2A1.23= r, • a ° +2b2 —r, • a2ayl = r1 • a0 + 2r1 • a2 — b2Appendix 1 Derivation of Fourier Series Expressions for Force Modeling^119+ r, • b,azo = 2^ A1.221a = 2 [a(k-1) — r1 • b(k,i) a(k+l) ri • b(k+01b = —[b +r •a +b —r • ask^2^(k-1)^I^4-1)^(k+1)^1 - (k+1)And similarly,= r1 • a l —ay0 2A1.25A1.26A1.27A1.24A1.28r1 • b2 — a2bs = —a0 +^2A1.291 rayk = 2 Lr1 .a(k-1) + k^ri • a(k+1) —1)(k+0 ]b 1—{r^•- a is + a(k+l) + r, • b(w) ]yk^2^(k-1)^(k— )A1.30A1.31Laor K2 = • a• S. A1.35Appendix 1 Derivation of Fourier Series Expressions for Force Modeling^120The parasitic force component of Eqn. 3.1 must now also be expressed asan F.S.. The instantaneous feed, S in milling is given by:S=Sc sincl)^ A1.32By substituting this, Eqn. 3.1 can be re-expressed as:FT= K, • a•S+ K2 •La^A1.33Assuming that a critical feed S* is defined as that which yields a totalcutting force comprising of equal components of cutting and parasitic force; thenfrom Eqn. A1.33:.a.S* = K2 • La^A1.34In reality, no cutting occurs to cause this situation; however, the concept isuseful for modeling the component of total cutting force resulting fromprogressive wear of the tool. Substituting the last expression back into Eqn.A1.33 gives:FT = K, • a•S+Ki •a-S .^A1.36or FT = -a•S+Ki .La •h°^A1.37where h * is the critical value of he when cutting and parasitic forces areequal.Appendix 1 Derivation of Fourier Series Expressions for Force Modeling^121From here it can be seen that the parasitic term yields a rectangular forcepulse. In the form shown in Eqn. A1.37, let this term be expressed as FT2, thesecond component of the total tangential force FT; i.e.FT2 = K 1 . La • h.^A1.38The F.S. coefficients for this term can be determined from the followingstandard integral expressions:= 1 1 A1.39awo —2 7td4awl = —1 7cos 4) • d4) A1.407t Cillby,1 = —It ..1a.2 = —1icsin 4) • d4)/ cos 20 • doA1.41A1.42b,,,2 = —1 7 sin 24) - c/4) A1.43J7t1 .2awk = — i cos 14 • c14)E cA1.44Fn = K1 . La • lis •[awo + E ^• cos k4I)+ bwk • sin k0]]k=1ODA1.53Appendix 1 Derivation of Fourier Series Expressions for Force Modeling^1221bwk = — 7 sin k0 . d07c JA1.45These integrals can be evaluated to give the following general expressions:a o . [02 — 01] '^2 7cA1.46A1.47A1.48A1.49A1.50A1.51A1.52awl 7c[sin 0 2 — sin 01] bwl = [ COS 0 1 — COS 0 2 ]Itawe= [sin 20 2 —sin 20 1 ]27cbw2 --[cos24), — cos 20 2 ]27c= [sin k$2 — sin k0 1 ]awk7cbw, = [cosk0 1 — cosk4)2]kitThe parasitic force component can now be expressed in terms of its F.S.coefficients as:Appendix 1 Derivation of Fourier Series Expressions for Force Modeling^123Subsequent substitutions in the respective equations, as performed for thecutting component earlier, result in the final forms of the X and Y axes forcecomponents as:Fx2 = K1 • L.•11. •[a„,x0 +I[a„.k • cos kO + by„,,„ • sin Ic4)]]^A1.54Fy2 = -Ki • L.- h * •[a,0 + y [a.5,k • cos k0 + bwyk • sin 01] A1.55k=1Again, the F.S. coefficients for these last two equations can be expressedin terms of the previously derived coefficients:a 0^2= a,v1 + r2 • bw1 A1.56a +2 • b,v2a, = (two + w2 ^A1.57b., — r, • awebwzi = r2 •- a„,, + wh 24 ^A1.58a 1 b= —[a^— r. • b (k_I) + aw(k+i) + r. • w ,,,,,A^2 w(k-i)^h^ A^(k+1)1^ A1.591 ttb,„„21 = —2 [uw(k_i) + r2 • aw(k_i) + bw(k+i) — r2 • aw(k+o l^ A1.60AndOPk=140A1.61Appendix 1 Derivation of Fourier Series Expressions for Force Modeling^124awyl = r2 • aw0 +r2 . aw2 .'" bw22A1.62bwy1 = —awo + r2 * bw2 — aw2 2a =—[r -a^—b^1wyk^2 w(k-1) +b w(k-1) +r2 •a w(k+1)^w(k+1)21 rbwyk =1,-2 •b k —a ^+ ^+ r2 • bw (k+i) ]2^,.i -1)^w(k-i) w(k+i)A1.63A1.64A1.65With the coefficients defined, the total forces can now be expressed simplyas sums of the components:Fx = Fxi + FX2^ A1.66Fy = Fn + Fy2^A1.67Appendix 2 Program Listing for Fourier Series Based Cutting Force SimulationAppendix 2Program Listing for Fourier Series Based Cutting Force SimulationREM SIMPLE PROGRAM THAT SIMULATES CUTTING FORCES USING AFOURIERREM SERIES BASED MODEL.REM AUTHOR-SUNMBOLA OYAWOYE, DATE-JULY 1992OPEN "C:\SUMBI\DATA.DAT" FOR OUTPUT AS #1DIM A(500)DIM AX(500)DIM AY(500)DIM B(500)DIM BX(500)DIM BY(500)DIM AW(500)DIM AWX(500)DIM AWY(500)DIM BW(500)DIM BWX(500)DIM BWY(500)PI = 3.141593125Appendix 2 Program Listing for Fourier Series Based Cutting Force Simulation 126PHI1 = 0PHI2 = 1.353REM PHI1 AND PHI2 ARE WORKPIECE ENTRY AND EXIT ANGLESRESPECTIVELYDC = 2REM DC IS THE DEPTH OF CUTINPUT PHI, INC, K, R1, R2, ST, H, K1, LAREM PHI IS THE START POINT FOR THE INSTANTANEOUS ROTATION ANGLEREM INC IS THE PERIODIC INCREMENT OF THE ROTATION ANGLEREM K1, R1, R2 ARE THE CONSTANTS OBTAINED FROM ACTUAL CUTTINGDATAREM K IS THE NUMBER OF FOURIER SERIES TERMS CONSIDEREDREM ST IS THE FEED-PER-TOOTHREM H IS THE CRITICAL VALUE OF EQUIV. CHIP THICKNESS ALSO OBTAINEDREM FROM ACTUAL CUTTING DATAREM LA IS THE LENGHT OF ACTIVE CUTTING EDGEREM DETERMINATION OF F.S. COEFFICIENTS FOR CUTTING COMPONENTOF FORCE10^A(0) = (COS(PHI1) - COS(PHI2)) / (2' P1)A(1) = (COS(2 ' PHI1) - COS(2 ' PHI2)) / (4' PI)B(1) = ((PHI2 - PHI1) - .5 * (SIN(2 ' PHI2) - SIN(2 ' PHI1))) / (2' PI)Appendix 2 Program Listing for Fourier Series Based Cutting Force Simulation 127AX(0) = (A(1) + (R1 ' B(1))) / 2AY(0) = ((R1 * A(1)) - B(1)) / 2SUMX = AX(0)SUMY = AY(0)REM SUMX AND SUMY ARE RUNNING SUMMATIONS OR TOTALS FOR F.S.TERMSFOR J = 2 TO (K + 1)A(J) = (((COS((1 + J) * PHI1)) / (1 + J)) - ((COS((1 + J) * PHI2)) / (1 + J)) -((COS((J - 1) * PHI1)) / (J - 1)) + ((COS((J - 1) * PHI2)) / (J - 1))) / (2 • PI)B(J) = (((SIN((1 + J) ' PHI1)) / (1 + J)) - ((SIN((1 + J) ' PHI2)) / (1 + J)) -((SIN((J - 1) * PHI1)) / (J - 1)) + ((SIN((J - 1)' PHI2)) / (J - 1))) / (2' PI)IF J = 2 THENAX(J - 1) = A(0) + (A(J) + (R1 ' B(J))) / 2BX(J - 1) = (R1 ' A(0)) + (B(J) - (R1 * A(J))) / 2AY(J - 1) = (R1 ' A(0)) + ((RI* A(J)) - B(J)) / 2BY(J - 1) = (-1 ' A(0)) + ((R1 ' B(J)) - A(J)) / 2ELSEAX(J - 1) = (A(J - 2) - (R1 " B(J - 2)) + A(J) + (R1 " B(J))) / 2BX(J - 1) = (B(J - 2) + (R1 • A(J - 2)) + B(J) - (R1* A(J))) / 2AY(J - 1) = ((R1*A(J - 2)) + B(J - 2) + (R1* A(J)) - B(J)) / 2BY(J - 1) = ((R1 * B(J - 2)) - A(J - 2) + (R1 • B(J)) + A(J)) / 2Appendix 2 Program Listing for Fourier Series Based Cutting Force Simulation 128END IFRSUMX = (AX(J - 1) • COS((J - 1) * PHI)) + (BX(J - 1) SIN((J - 1) • PHI))RSUMY = (AY(J - 1) * COS((J - 1) PHI)) + (BY(J - 1) • SIN((J - 1) • PHI))REM INCREMENT RUNNING TOTALSSUMX = SUMX + RSUMXSUMY = SUMY + RSUMYNEXT JREM COMPUTE CUTTING FORCE COMPONENTSFX1 =K1 • DC ST *SUMXFY1 = (-1 * K1)* DC *ST SUMYREM DETERMINATION OF PARASITIC FORCE COMPONENTSAW(0) = (PHI2 - PHI1) / (2 PI)AW(1) = (SIN(PHI2) - SIN(PHI1)) / PIBW(1) = (COS(PHI1) - COS(PHI2)) / PIAWX(0) = (AW(1) + (R2 BW(1))) / 2AWY(0) = ((R2*AW(1)) - BW(1)) / 2WSUMX = AWX(0)WSUMY = AWY(0)Appendix 2 Program Listing for Fourier Series Based Cutting Force Simulation 129REM WSUMX AND WSUMY ARE RUNNING TOTALS FOR THE PARASITIC F.S.TERMSPHI))PHI))FOR J = 2 TO (K + 1)AW(J) = (SIN(J PHI2) - SIN(J " PHI1)) / (J * PI)BW(J! = (COS(J " PHI1) - COS(J PHI2)) / (J PI)IF J = 2 THENAWX(J - 1) = AW(0) + (AW(J) + (R2 BW(J))) / 2BWX(J - 1) = (R2 AW(0)) + (BW(J) - (R2* AW(J))) / 2AWY(J - 1) = (R2 * AW(0)) + ((R2 AW(J)) - BW(J)) / 2BWY(J - 1) = (-1 * AW(0)) + ((R2 * BW(J)) + AW(J)) / 2ELSEAWX(J - 1) = (AW(J - 2) - (R2 * BW(J - 2)) + AW(J) + (R2 * BW(J))) / 2BWX(J - 1) = (BW(J - 2) + (R2 AW(J - 2)) + BW(J) - (R2' AW(J))) / 2AWY(J - 1) = ((R2 AW(J - 2)) + BW(J - 2) + (R2' AW(J)) - BW(J)) / 2BWY(J - 1) = ((R2 * BW(J - 2)) - AW(J - 2) + (R2 ' 1 BW(J)) + AW(J)) / 2END IFRWSUMX (AWX(J - 1) COS((J - 1) * PHI)) + (BWX(J - 1) SIN((J - 1)RWSUMY = (AWY(J - 1) COS((J - 1) " PHI)) + (BWY(J - 1) " SIN((J - 1)Appendix 2 Program Listing for Fourier Series Based Cutting Force Simulation 130REM INCREMENT SUMMATIONSWSUMX = WSUMX + RWSUMXWSUMY = WSUMY + RWSUMYNEXT JREM COMPUTE PARASITIC FORCE COMPONENTSFX2 = K1 " LA * H * WSUMXFY2 = (-1 * K1) * LA * H * WSUMYREM COMPUTE TOTAL FORCESFX = FX1 + FX2FY = FY1 + P(2REM PRINT TO FILE AND SCREENWRITE #1, "FX=", FX, "FY=", FY, "PHI=", PHIPRINT USING "FX= ####.### FY= ####.### PHI= ####.###"; FX; FY; PHIREM INCREMENT INSTANTANEOUS ROTATION ANGLEPHI = PHI + INCREM TERMINATION CONDITIONIF PHI <= 1.4 THEN GOTO 10CLOSE #1ENDReferencesReferences[1] I. Yellowley and G Barrow; "The Assessment of Tool Life in Peripheral Milling."Proc. 19th Int. Mach. Tool Dee. Res. Conf.. p. 443: 1978.[2] MECH 490 Lecture Notes (Fall 1990). Instructor: I. Yellowley.[3] N. H. Cook; "Tool Wear and Tool Life." Trans. ASME. J. Engng. Ind.. v. 95. p. 931: 1973.[4] E. Kuljanic; "An Investigation of Wear in Single-Tooth and Multi-Tooth Milling."Int. J. Mach. Tool Des. Res.. v. 14. p. 95: 1974.[5] J. Tlusty, I. Yellowley and G. Konrad; "Tool Wear in the Peripheral Milling of aLow Carbon Steel." ASME. 76-WA/Prod-35: 1976.[6] I. Yellowley and G Barrow; "The Influence of Thermal Cycling on Tool Life inPeripheral Milling." kit. J. Mach. Tool Des. Res.. v. 16. p. 1: 1970.[7] I. Yellowley; "The Development of Machinability Testing Methods e.t.c.." Ph.DThesis, University of Manchester; 1974.[8] F. W. Taylor; "On the Art of Cutting Metals." Trans. ASME. v. 28. p. 31: 1907.[9] M. C. Shaw; "Metal Cutting Principles." M. I. T Press, Cambridge, Mass.; 1957.[10] H. 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Yellowley; "Observations on the Mean Values of Forces, Torques and SpecificPower in the Peripheral Milling Process." Jnt. J. Mach. Tool Des. Res.. v. 25. No. 4. p. 337: 1985.[18] H. J. Fu, R. DeVor and S. G. Kapoor. Trans. ASME. J. Engng. Ind.. v. 106. p. 81: 1984.[19] I. Yellowley; "A Note on the Significance of the Quasi-Mean Resultant Force andthe Modelling of Instantaneous Torque and Forces in Peripheral MillingOperations." Trans. ASME. J. Engng. Ind.. v. 110. p. 300: 1988.[20] Y. Hosepyan; "Tool Wear Monitoring in Face Milling." M.A.Sc. Thesis, Universityof British Columbia; 1991.[21] I. Yellowley, Y. Hosepyan and 0. Oyawoye; "The Identification of MachiningCondition and Tracking of Tool Wear in Milling Using Machining Forces." To bePublished.References^ 133[22] A. De Filippi and R. Ippolito; "Adaptive Control in Turning: Cutting Tool Wear andForce Relationships for P10, P20 and P30 Carbides." Annals of the CIRP. v. 17. p. 377: 1969.[23] G. F. Micheletti, W. Koenig and H. R. Victor; "In-Process Tool Wear Sensors forCutting Operations." Annals of the CIRP. v. 26. No. 2. p. 349: 1975.[24] W. A. Kline and R. DeVor; "The Affect of Runout on Cutting Geometry andForces in End Milling." Int. J. Mach. Tool Des. Res.. v. 23. p. 123: 1983.[25] M. A. Elbestawi, T. A. Papazafirou and R. X. Du; "In-Process Monitoring of ToolWear in Milling Using Cutting Force Signature." Int. J. of Mach. Tool. Manufact.,v. 31. No. 1. p. 55: 1991.[26] Y. Koren, T. R. Ko, A. G. Ulsoy and K. Danai; "Flank Wear Estimation UnderVarying Cutting Conditions." Trans. ASME. J. Dyn. Sys.. v. 113. p. 300: 1991.[27] L. V. Colwell, J. C. Manzur and W. R. DeVries; "Analytical Strategies forAutomated Tracking of Tool Wear." Proc. NAMRC 6. SME: 1976.[28] L. V. Colwell and J. C. Manzur; "Real Time Computer Diagnostics, A ResearchTool for Metal Cutting." Annals of the CIRP. v. 28. p. 49: 1979.[29] B. Szabo and S. M. Wu; "Tool Wear Monitoring for Milling Processes Using DDSMethodology." Proc. NAMRC 17. SME. p. 160: 1989.[30] C. L. Jiaa and D. A. Dornfeld. Proc. ASME Winter Annual Meeting. PED.. v. 40. p. 45:1989.[31] T. A. Papazafirou and M. A. Elbestawi; "Development of a Wear Related Featurefor Tool Condition Monitoring." Proc. USA/Japan Conf. on Flexible Automation,ASME. p. 1009: 1989.References^ 134[32] Y. Altintas and I. Yellowley; "In-Process Detection of Tool Failure in Milling UsingCutting Force Models." Trans. ASME. J. Engng. Ind.. v. 111. p. 149: 1989.[33] E. J. A. Armarego and R. H. Brown; "The Machining of Metals."  Prentice-Hall,Inc., 1969.[34] B. Mills and A. H. Redford; "Machinability of Engineering Materials."  AppliedScience Publishers Ltd.; 1983.[35] N. N. Zorev; "Metal Cutting Mechanics." Pergamon Press; 1966.[36] S. Smith and J. Tlusty; "NC Programming for Quality in Milling." Proc. 16thNAMRC. p. 279: 1988.[37] E. Orady and J. Tlusty; Proc. 9th NAMRC. p. 250: 1981.[38] N. Shinozaki; "Thermal Cracks of Carbide Face Milling Cutters." Bull. JSME,v. 5. No. 20. p. 753: 1962.


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