Albrecht Melhorado

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    P . A L B I R E C I H TResearch Associate/Physical Research Department,The Cincinnati M illing Machine Company,Cincinnati, Ohio

    N e w D e v e l o p m e n t s i n t i e T h e o r y o f t h eM e t a l - C u t t i n g P r o c e s sP a r t L T h e P l o u g h i n g P r o c e s s i nM e t a l C u t t i n g

    Revel a t i o n o f the s i gn i f i c ance o f " p l ough i ng " i n the m e ta l - cu t t i n g p r o ces s, wh i c hoccu r s because o f the f i n i t e sha r pn es s o f the cu t t i n g edge, l eads to a bet t e r un de r s tand i n go f the m echan i c s o f the m eta l - c u t t i n g p r o ces s. Th e concep t o f the p l ough i n g fo r c e on theex t r em e cu t t i n g edge a l l ows the devel opm en t o f a m o re com p le te fo r c e d i a g r am wh i c hsepa r a te s the p l ough i n g fo r c e f r om the ch i p - t oo l i n te r f a c e fo r c e. Com ponen ts o f th i sm o r e de ta i l e d fo r c e d i ag r am have been ve r i f i e d expe r im en ta l l y . In te rm s o f the newfo r c e d i ag r am the r ea l v a l ue o f the coef f i c i e n t o f f r i c t i o n on the ch i p - t oo l i n t er f a c e hasbeen found and the pa r adox o f va r i a t i o n o f the coe f f i ci e n t o f f r i c t i o n w i t h va r i a t i o n o fr a k e ang l e exp l a i ned .

    Th e pape r a l s o con t r i b u te s to a bet t e r und e r stan d i ng o f such even ts as the e f f ec t o fc u t t i n g vel o c i t y up on too l or c es , bu i l t - u p edge , ch i p cu r l i n g , an d r esi d ua l s t r e sses i n thewo r k su r f a c es .

    I n t r o d u c t i o ntheory of Metal-Cutting Process. The theory of the metal-cutting

    process has been considerably d eveloped since the end of the lastcentury. Th e principal mechanism in chip formation has beenrecognized to be a shearing process taking place along a shearplane in the work materia l. B y the shearing action the workmateria l is plastically deformed and separated from the work-piece. Usu ally the thickness of the chip is more than the "th ick-ness of bit e." In order to produce such plastic deformation of theme tal considerable forces are required. Thes e forces acting be-tween the cutting tool and work m ateria l are shown in the forcediagram, Fig. 1. Alth oug h the theory, as it is presently k nown ,

    Contributed by the Production Engineering Division and presentedat the Annual M eeting, Atlanti c City, N . J ., November 29-December4 , 1 9 59 , o f T H E A M E R I C A N S OC I E T Y O F M E C H A N I C A L E N G I N E E R S .NO TE : S tatements and opini ons advan ced in papers are to beunderstood as individual expressions of their authors and not thoseof the Society. M anuscri pt received at A SM E H eadquart ers, Au gust14, 1959. P aper N o. 59A- 243.

    clarifies to a great extent the mechanics of the metal-cuttingprocess, unexplained dark corners rem ain.

    To name a few such instances, we may note here that the co-efficient of friction on the chip-tool interface has usually beenfound to be rather high compared with values found by directexperiment on surfaces having contaminating films. Further, thiscoefficient of friction, as given b y the theory, has a peculiar prop-erty, i.e., to va ry w ith changing tool geometry. Th e chip-toolcoefficient of friction increases, namely, with increasing rakeangle of the cutter. These and other unexplained results haveexpressed the need for research and further development of thetheory of the metal-cutting process.

    Because it was felt by the author that the theory of the metal-cutting process based on the analytical description of the shear-ing process alone had reached its maximum development, it washoped that furth er progress could be achieved by in troducin g intothe theory some other mechanisms which may be present in themetal-cutting process and which, together w ith shearing, affect itsbehavior. Gene rally, the metal-cutting process, as well as an y

    - N o m e n c l a t u r e Variables of tool shape ( f o r t h e o r t h o g o n a lcutting process)r = sharpness radius, whi ch gives mag-

    nitude of sharpness rounding ofcutting edge

    r e = effective sharpness radius, whichaccounts for change of sharpnessrounding due to presence of thebuilt-up edge

    a = rak e angleS = included angle of cuttin g edge

    Dimensions of Cuth thickness of uncu t chipU = thickness of chip after its separation

    from the work3 4 8 / N O V E M B E R 1 9 6 0

    w = wid th of cut in orthogonal cuttingRatios of Cutting Processr t = U/h = chip thickness ratioX = r / h or r j k = ploughing ratio, for

    cutting process without or withbuilt-up edgeTool Forces

    R = resultant tool force (or briefly toolforce)

    Fc = cutting force (component of R indirection of tool motion)F, = thrust force (compon ent of R per-

    pendicular to direction of toolmot ion)

    P = mai n plough ing force or chipploughing force at extreme cut-ting edge

    Pi = component of force P in directionof tool motion

    Pa = component of force P perpendicu-lar to direction of tool motion

    Pn = norm al component of force PPf friction component of force PPs = component of ploughing forcepolygon which takes part in

    shearingQ tool face force

    (Con t i n ued on nex t page )

    T r a n s a c t i o n s o f t h e A S M E

    Copyright 1960 by ASME

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    H J X

    F ig, I Conventional force diagram of orthogonal cutting processesother physical event, can be expected to depend on a number offactors which will affect it to different degrees, as is symbolicallyshown in Fig. 2. Th e main factor in the metal-cutting processhas been recognized as the shearing process in chip formation.Now, as a second mechanism taking place in metal cutting, theploughing process is suggested here, the description of which andintroduction into the theory of metal cutting is the purpose ofthis paper.

    It will be shown in this paper that, by taking into accountploughing, metal-cutting theory is given more power to explainexperimental results which are virtually impossible to interpretwhe n the influence of this factor is omitted. Fo r this reasonploughing is believed to be the number two mechanism in m etalcutting and introduction of it into the theoiy makes the analytica lmodel of the me tal-cutting process more dependable in pred ictionand more powerful in explanation of experimental results.Sharpness of Metal-Cutting Tools. The sharpness of metal-cuttingtools should be discussed briefly at this point because it will be anessential ingredient of the theory developed in the main part ofthis paper. Often tool sharpness in metal cuttin g is associatedwi th tool wear. Thu s if the flank or crater wear of a cutting toolis in an ad vanced stage the tool is often described as blu nt or dull.In this paper, the term sharpness will be understood to definethe very small rounding of the extreme cutting edge, the tinyapproximately cylindrical surface connecting tool-flank and tool-face surfaces.Th is small cy lindrical surface is developed on the cutting edgeduring the grinding process of the cutting tool. Th e wa y in whichit happens is illustrated in Fig. 3(a). As the grinding wheel worksalong the tool face or tool flank, the tiny particles of tool materialwill break off at the extreme edge where the edge is so thin that

    N U M B E R O F E A C H F A C T O R A S C L A S S I F I E D A C C O R D I NGT O I T S S I G N I F I C A N C E I N A P H Y S I C A L E V E N T

    F ig. 2 Significance of various factors to a physical event

    ( a . )

    C R O S S S E C T I O N T H R O U G HT H E C U T T I N G E D G E

    tb)F ig. 3(a) In grinding of a cutter the wheel breaks off small parti cles atthe extreme edge. This results in a rounded surface between the flankand face of a tool , (b) The radius r of the circle approximating the crosssection of the rounded extreme edge is a measure of the sharpness of thecutting edge. The included angle 5 of the cutting edge is also shown.the material cannot stand the impact of grinding-wheel grains.Th is leads to a rounded surface as shown in Fig. 3. It should benoted here that the grinding wheel does not generate the roundedsurface and its surface finish can be expected to be much rougherthan those of the surfaces wh ich were produced by the grindingwheel directly.

    Th e cross section of this rounding would be a curve w hich canbe very well approximated by a segment of a circle as shown inFig. 3(6). Th e radius r of such a circle gives the magnitude ofthe rounding and thus can be adopted as a measure of the sharp-ness of the tool. Th e magnitud e of the radius characterizing t hetool sharpness depends on a number of factors such as tool ma-terial, m ethod of grinding, and some others.

    - N o m e n c l a t u r e -Qt = component of force Q in direction

    of tool motionQo = component of force Q perpendicu-

    lar to direction of tool motionQ n = norm al component of force QQ f = frictional component of force QQ s = component of Q in direction ofshear force S sP ' = w ork ploughing force. Th is force

    can be resolved into compo-nents in a w ay similar to force Pyielding the components Pi',P 2 ' , P n ' , an d P /L = land force; force on the wear landof the tool flank

    L i = component of force L in directionof tool motion, or frict ional com-ponent of force LLi = component of force L perpendicu-lar to direction of tool motion,or normal component of theforce LS total force on shear plane

    S, = component of S in direction ofshearing at shear planeShear Plane Position

    = shea r ang leWorkpiece Material PropertiesT S mean shear stress on shear plane

    Coefficients of Friction and Friction AnglesQ f / Q n ta n T Q = coefficient of

    Mr =

    T .

    M L =

    r L =

    friction on chip-tool interfacefriction angle corresponding to co-efficient of friction n QP f / P n = tan r r = coefficient offriction on sharpness rounding ofcutting edgefriction angle corresponding to co-efficient of frict ion jUiL J L 2 = t a n r L = coefficient offriction on wear land of toolflankfrictio n angle corresponding to co-efficient fj.L

    E X T R E M E E D G E O F T H E T O O L

    T O O LF L A N K

    T O O LF A C E

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    cause the}' react differently to changes in the metal-cuttingvariables.

    I n order to describe the term " plou ghin g" in the cutting processit is necessary to understand what happens to the small portionof workpiece material in front of the rounded portion of theextreme edge, shown in Fig. 7. As the tool progresses in the cut,this metal in front of the cutting edge should move out one wayor another. If this met al were to be pressed into the workpiecethe tool would be constantly moved up and progress along someinclined line by the virtue of the fact that more material would bebeneath the tool. Becau se experience shows tha t the tool doesnot move out of the cut, but keeps a constant depth, it may beconcluded that essentially all material above the horizontalclashed line in Fig. 7 must be removed in the form of a chip.Th is includes the small portion of the met al in front of the cut tingedge, which is pressed into and becomes par t of the chip. Th iswhole action w ill be termed here as ploughing.

    Brie fly, as the chip slides along the tool face, the metal in frontof the rounded portion of the extreme cutting edge will beploughed and pressed into the chip surface, as illustrated in Fig . 7.The plastic deformation of the metal in ploughing appears to beeven more severe than th at occurring on the shear plane. Also,ploughing usually occurs on a smaller scale. Gene rally, all themetal separated in the form of a chip has been sheared but onlypart of it along the chip surface has been ploughed.

    The amount of material sheared depends essentially on the un-cut chip thickness and the amou nt of ploughed me tal dependson the magnitu de of the sharpness radius of the cutting tool, oron the radius of the built-up edge ; t (effective radius). Thu s theratio of these two dimensions, X = ( r / U ) , will indicate in whichproportion the shearing and ploughing take place in the cuttingprocess.

    In Fig. 7 it is shown that a small portion of the ploughed metalwi ll be pressed into the work surface. Accom mo dating m orematerial in the surface layer will cause compressive stresses,kno wn as residual stresses in machined surfaces. Thes e residualstresses may cause the workpiece to bend a little if its rigidity isnot extremely high. As an analog to this event we can see tha tthe me tal pressed into the chip surface will cause similar compres-sive stresses in its surface and make the chip bend (so-called curl-ing of the chip). Because mu ch more of the ploughed metal w illbe pressed into the chip than into the workpiece, since the chipis usually mu ch less rigid than the work piece, we hav e much m orebending (curling ) of the chip than of the workpiece. Alte rnat ely,

    it may be said, in describing these events, that the chip beingflexible cau more easily yield to accommodate more additionalmaterial in its surface.

    New Force Diagram. B y taking the ploughing process into ac-count the tool force diagr am will be significantly changed. Ifonly the shearing process is accounted for, the tool-force diagramhas a familiar look, Fig. 1, Ref. [I], 1 where on ly one resultant forceT i on the tool face can be resolved in the direction of the tool faceand perpendicular to it, yielding the components F an d N , or theresultant R can be resolved in the direction of the shear plane andperpendicular to its yielding the components F s and F n . F ina l ly ,another pair of components is of interest, that is the cuttin g forceF c and the thrust force F which will be obtained by resolvingthe same resultant R in the direction of motion of the tool andperpendicular to it. Th is force diagram was derived by Me rch ant[1] and is used for the derivation of expressions for such quan-tities as coefficient of friction on the tool face, the shear angle re-lationship and others.

    Referring now to Fig. 8, where rounding of the cutting edge ofthe tool is introduced, the sum ming up of forces along the straightportion of tool face between the points 0 and A give the force Q ,inclined to the normal to the tool face by the friction angle r 0 .Th e force Q also can be seen in the force diagram in th e right pa rtof Fig . 8. Proceed ing further in summ ing up the infinitesimalforces from point A along the rounded portion of the edge tow ardpoint B it m ay be seen tha t each infinitesimal comp onent changesits direction on account of the curved nature of the surface.Th us th e resultan t in the force diagram wou ld be a polygon of in-finitesimal forces in the form of an arc which ends at point B .W e see tha t instead of the resultant R we have obtained the forceQ plus an arc-shaped polygon.

    It can lie seen read ily tha t in order to express the coefficient offriction on the tool face analytically one would not resolve intocomponents the resultant R but only the force Q which would beresolved into the component Q , along the tool face and com-ponent Qperpendicular to it.

    The following derivation of the analytical expressions for thefamiliar quantities of the metal-cutting process will be presentedon the basis of the more developed force diagram given in thissection. Th e mathe ma tical expressions thus obtained present apart of the improved analytical model of the metal-cutting proc-ess which will be tested against experiment, as described later inthe paper.

    A shear-angle relationship derived on the basis of the impr ovedinitial assumptions is presently under development and will bepresented later in a subsequent paper.

    1 N umber s in brackets designate References at end of paper .POINT o

    Fig. 7 Ploughing process. The shadowed area of metal in front of thesharpness rounding is displaced main ly into the chip; this flow of metalis indicated by arrows. The metal being pressed into the chip tends toexpand the layer adjacent to the tool face, contributing in this way, tochip curl ing. A minor portion of the metal will be pressed into the newl yproduced work surface causing residual compressive stresses usuallyfound after a machining operation.

    POINT A ~Y n ^X

    / / P 21 7 s'S i r ' p i

    ^ POINT 8 F 1, conditions may beobtained under which the tool face will be out of the range ofchip-tool contac t. Un der these conditions chip-tool contact wil lend in the rounded portion of the cutter so that this roundedportion will serve as a tool face under such conditions.This rounded "tool face" will blend smoothly into the toolflank without having any "small" sharpness rounding betweenthe tool face and flank. There would be no ploughing involvedunder such conditions. Exp erim ents conducted under theseconditions, X = r / l i > 1, showed that the chip obtained was per-fectly straight without an y cu rl at all. Of course, it should benoted th at in this case the rounded tool face has curvature in th eopposite direction from the usual curl of the chip and this may

    have ha d some straightening effect upon the chip. Ho we ver, con-tinuing this experiment for increasing uncut chip thickness t i , i.e.,for decreasing X, the curling started to appear again at a value ofuncut chip thickness such that the rounded part of the surfaceceased to function as a rounded tool face and started to act as asharpness rounding producing a ploughing effect, or, in otherwords, when the uncut chip thickness was sufficient to providechip-tool contact on the flat portion of the tool face.Furt her experiments on chip curling were carried out wi th con-tinuously varying l h i.e., the ratio X was decreased continuouslyfor one chip during a single cut. Because the amou nt of metalploughed remains essentially constant, due to comparatively littlechange of the effective sharpness radius rc, chip curling can be ex-pected to become less and less pronounced with increasing thick-ness of the chip because of its higher rigidity . In fact, thisphenomenon was observed in the experiment. A spiral shapedchip was obtained with curl of a greater curvature for the thinnerchip followed by a chip of continuously decreasing radius ofcurvature wit h increasing h. In additional experiments the rateof change of ti was altered and this was reflected in the rate ofchange of the spiral curvature in the way expected. Fo r the lowrate of change of ti a tighter spiral resulted, and for a high rate ofchange of h a loose spiral was obtained.All of these preliminary experiments have shown quantitativeagreement with the described relation between the ploughingprocess and chip curling. Fur the r, the experimentation points to

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    the fact that the ratio X = r j t i should have a pronounced roleamong the variables affecting chip curling in the analytical (quan-titative) description of this event.Complete Force Diagram of Orthogonal Cutting Process. It shouldbe noted that, apart from the ploughing force P wh ich occurs be-cause of the ploughing process, there is still another force in thecuttin g process, that whic h acts on the wear land of the tool flank.W e denote this force by the letter L (land force).Furthermore, a small part of the ploughed metal adjacent towear land is pressed into the workpiece, Fig. 6, contrary to themain part of the ploughed metal which is pressed into the chip.It might be appropriate to denote the small force performing thisaction differently, say by P ' , because of th e different direction ofits frictional component P / as compared with the direction of thefrictional component P t of the main ploughing force P .The complete force diagram, which includes forces L an d P ' , isshown in Fig. 15. Unlik e the ploughing force P which has aconsiderable magnitude e ven for a freshly groun d tool, the force Lis small when there is no appreciable wear land on the tool flank.

    Fig. 15 The complete force diagram of the orthogonal cutting processThe numbering of Fig. 15 relates the forces shown in the forcediagram to the portions of the engaged part of the tool wherethese forces occur. Th us between the points 0 and 1 of the tool

    face force Q is acting on the chip-tool contact area. Bet we en thepoints 1 and 2 is the main pa rt of the sharpness rounding (o rfront po rtion of the built-up edge if it is present). Th e pressuresalong this part of the engaged surface yields the arc-shaped por-tion of the force polygon between 1 and 2. Th is results in theploughing force P . A t point 2 the actual separation of the metalfrom th e workpiece occurs. Th e motion of the separated meta l oc-curs in the direction 2-1-0 along the engaged part of the cutter,and the m etal of the workp iece slides in the d irection of 2-3-4along the tool flank. Fo r this reason the friction forces P , andP / oppose each other on opposite sides of point 2. Th e differentdirection of the friction forces results in a discontinuity of theforce polygon at point 2. Th e angle formed by the two tangentsto the force polygon at this point is equal to double the frictionangle r r .A t points 1 and 3 discontinu ity can occur if the coefficient offriction on the tool face and on the wear land differs from that onthe sharpness rounding. If the coefficient of friction can be con-sidered as constant along the whole tool surface over which metalslides, the portions of the force polygon from 0 to 2 and from 2to 4 will be without discontinuities, as is shown in Fig. 15.This complete force diagram was abbreviated in Fig. 8 wherethe force L was considered small enough to be neglected for thefreshly ground tools wit h w hich the experiments were conducted.Th e force P ' was also considered to be small an d of mu ch the samedirection as the main ploughing force P . Th us in the force dia-

    gram of Fig . 8 the ploughing force P contains two small forces P 'an d L which, as we have seen, do not affect significantly the ex-perimental results.

    C o n c l u s i o n sIn this paper some of the results of recent research into thetheory of the metal-cutting process have been presented.Progress has been made mainly by recognizing the presence ofthe ploughing process in me tal cutting. Th e mechanism ofploughing has been conceived and introduced into metal-cuttingtheory. Th is has made possible the construction of a more de-tailed force diagram which should serve as a basis for develop-ing a more complete analytical model of the cutting process.A method has been established for the experimental separationof the ploughing force P from other major cutting forces. Itsmagnitude has been found considerable as compared to the forcedue to shearing. Th e assessment of the tool-face force Q hasallowed th e determ ination of a real valu e of the coefficient of fric-tion on the tool face n Q and has shown tha t the valu e of [1q doesnot vary w ith varyin g rake angle a. In this way the old paradoxof the varying of the coefficient of friction on the tool face withrake angle a has been solved.Relation of the ploughing process to the curling of the chip andto the residual stresses in the work surface has been established.Bo th events have been found to be essentially of the same nature,

    the difference being only a matter of degree, because of the dif-ference in rigidity of the chip and of the workpiece. Ben din g ofthe workpiece due to the add itional metal pressed into themachined surface due to ploughing is essentially the same eventas bending of the chip (chip curling) due to the additional metalpressed into th e chip surface by the ploughing process.A study of the sharpness of cutting tools has been presented.The sharpness radius of cutting tools has been specifically meas-ured and its influence on the metal-cutting process studied forthe first time in metal-cutting research. These measurem entshave been carried out by the method of sharpness measurementwhich w as devised by the author.The magnitude of the sharpness radius was found to depend onseveral variables and usually to fa ll into the range between 0.0001and 0.001 in. Th e higher values of this range were found to

    correspond to the negative range of rake angles and the smallestvalues, of a few tenths of a thousandth of an inch, were found tocorrespond to high positive rake angles.Further, a complete new force diagram has been presentedwhich contains, apart from newly found ploughing forces, theforces on the wear land of the tool flank, which have long beenthought to be present there, because of the development of flankwear, bu t have never been separated and measured.Th e forces on the flank wear land have been found to be smallcompared to either the shearing or ploughing forces for a freshlyground tool. Fur the r research in this direction is presen tly inpreparation.The new findings about the nature of the metal-cutting process,presented in this paper, have pointed to a number of avenues forfurther research into the theory of the metal-cutting process.The author is presently working in these areas with the hopethat further accomplishments will be forthcoming in the nearfuture.

    A c k n o w l e d g m e n t sThe author wishes to acknowledge that the knowledge ofmetal cutting which emanated from these Laboratories con-tributed considerably to the research presented here. Espe ciallythe theory by Dr. M . E . Merchant, Director of Physica l Re-search, presented in his paper "Mechanics of the Metal Cutting

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    Proce!;!;, " inspired the author to further study of t.he subject onthe basis of the progress lweviollsly achieved.

    Th e author is fllso very much indebted to Mr. E. J . Krnbucher,Senior ReBearch Superv isor, who contl'ibuted grefltly ill thepreparat.ion of this paper.

    Appreciat.ion should be expressed to t.he Laboratories' technicfllpersonnel whosc ski ll was essential in performing th e experimenta l work.References

    !'I I. E. l \ l c r e h a l l ~ "Mechanics of the r.'Ietnl Cutting Process, "Journul of A1Jpliccl Physics, vol. 16, 1945, pp . 267-2 75 .2 H an s Ernst, "Physics of Cu t t ing ," IVInchining of Me t-als,.\meriel\ll Sodety for j\[ e tals, 1138, pp . 1- 34.

    Journa l of Engineer ing for Industry N OV ' M BE R 1 96 0 / 357