Prediction of tool-chip contact length using a new slip-line solution for orthogonal cutting

Size: px

Start display at page:

Download "Prediction of tool-chip contact length using a new slip-line solution for orthogonal cutting"

Lenard Garrison
5 years ago
Views:

1 Interntionl Journl of Mchine Tools & Mnufcture 43 (2003) Prediction of tool-chip contct length using new slip-line solution for orthogonl cutting Andrey Toropov, Sung-im Ko School of Mechnicl nd Aerospce Engineering, Konkuk University, 1 Hwyng-dong, Kwngjin-gu, Seoul , South Kore Received 31 Mrch 2003; received in revised form 1 My 2003; ccepted 20 My 2003 Abstrct Tool chip contct length is n importnt prmeter in mchining. Severl wys hd been proposed in different works to find its vlue, which gve discordnt results for the sme set of cutting conditions. In this pper, new slip-line solution for orthogonl cutting by tool with unrestricted rke fce is suggested. Bsed on the proposed solution, new formul for tool chip contct length hs been obtined. Comprtive nlysis of different methods to predict tool chip contct length hs been done nd experimentl verifiction conducted. The suggested formul hs shown to correspond well with experimentl dt nd predicts tool chip contct length better thn other known solutions Elsevier td. All rights reserved. Keywords: Orthogonl cutting; Slip-line solution; Tool chip contct length 1. Introduction Mchining of metls is lwys ccompnied by chip formtion. The chip contcts with tool rke fce during chip movement long the rke fce. One of the most importnt prmeters in this process is the tool chip contct length. Knowing this contct chrcteristic together with contct stress distribution mkes it possible to determine cutting forces nd temperture ptterns, ccurtely clculte tool strength, choose the optiml tool geometry, nd control the mchining process s whole. Mny reserches hd been devoted to the study of tool chip contct length [1 9]. The generl ssumption ws tht two regions of roughly equl length exist in whole tool chip contct length. The first is the sticking region close to the tool edge where contct sher stress is usully considered s hving uniform distribution nd mximum vlue [7]. This region is lso clled plstic tool chip contct length since it cuses plstic deformtion of chip nd curling [10]. The second is the sliding region where contct sher stress is ssumed to decrese Corresponding uthor. Tel.: ; fx: E-mil ddresses: ndrey@konkuk.c.kr (A. Toropov); slko@- konkuk.c.kr (S.-. Ko). down to zero s power function [7] t the end of the tool chip contct. In this prt of the contct, the chip probbly cts elsticlly on the rke fce; therefore this length is lso clled elstic tool chip contct length. The most importnt prmeter in considering the problem is totl tool chip contct length. This prmeter is interrelted with processes in the primry sher zone, the sher ngle in prticulr [1,2,5,6]. In the cse of cutting by tool with restricted rke fce, tool chip contct length directly influences sher ngle [11]. To predict tool chip contct length depending on conventionl sher ngle, mny wys hve been proposed bsed on different ssumptions. The solution of the given tsk my depend on suggested slip-line solution [1], ssumed stress distribution [2], or dditionl considertion [6]. In mny works, experimentl formule to determine tool chip contct length hve been presented [5,7 9,12]. Finite-element nlysis of metl cutting mechnics becme prevlent in recent yers. Applying this method, the problems of determining tool chip contct length nd other contct prmeters re solved utomticlly by computer. However, the solution of considering the problem using finite-element simultion depends on boundry conditions on the tool chip interfce, which must be given in dvnce s input dt, together with work mteril properties nd tool geometry. These /$ - see front mtter 2003 Elsevier td. All rights reserved. doi: /s (03)00155-x

2 1210 A. Toropov, S.-. Ko / Interntionl Journl of Mchine Tools & Mnufcture 43 (2003) boundry conditions especilly concern the fctor of friction or sher nd norml stress distribution on the tool chip interfce, which lso reflects conditions of friction. The generl lws of stress distribution nd chnge of coefficient of friction long the tool chip interfce hve not yet been found. The ssumptions bout constnt coefficient of friction long the tool chip contct re or uniform stress distribution, which cn be used for finiteelement nlysis, re not quite true [5,7,13 16] nd cn give incorrect results. From this point of view it is better to nlyze chip formtion by the generl methods of the theory of plsticity. In this pproch, once the solution is found for the generl cse in nlyticl form, it cn be redily pplied for ny prticulr cse. Thereupon, the generl nlyticl solution hs n dvntge in comprison with finite-element nlysis, which cn only solve prticulr problems. Moreover, the finite-element solution of every cse tkes more time then prticulr solution of the sme problem using the existing generl solution. One of the clssicl wys to solve problems of plstic flow is the slip-line method. Chip formtion is the prticulr cse of plstic flow, thus the slip-line method cn be pplied to this process. The essence of this pproch is tht zones of plstic deformtion must be given in dvnce ccording to the experience nd conception of the uthor. Therefore the slip-line method cn lso be clled the guessing method. Mny reserchers tried to find proper slip-line solution for orthogonl mchining [1,11,17 19] but there is still no generl model, which cn explin ll the mechnicl processes in metl cutting. The ccurcy of every slip-line model is defined by its correspondence with experimentl dt, nd chip tool contct length is one of the criteri for this estimtion. In this pper, unique nlyticl wy to predict tool chip contct length is proposed bsed on new slip-line solution for orthogonl cutting. Fig. 1. Principle sher stress distribution on tool rke fce ccording to experimentl dt of () Bobrov [13], (b) Zorev [7], nd (c) Gordon, Petruh, nd Bgchi nd Wright [14 16]. tken into ccount or not ws not reported. Thus, this study supposes tht these forces hd been neglected. This neglect, however, leds to serious distortion of the experimentl grph of stress distribution. As shown in Fig. 2, forces N c nd F c cting on the clernce fce crete dditionl prsiticl stress on contct 1 becuse prt 1 of the split tool mesures both forces N 1 nd F 1 on the rke fce nd N c nd F c on the clernce fce. These dditionl error stresses increse close to the tool edge, nd this is probbly the reson for the sher stress distribution experimentlly found by Bobrov [Fig. 1()]. The grph configurtion my be chnged depending on the cutting conditions nd split-tool geometry, including tool rke nd clernce ngles. For exmple, it is obvious tht decrese of the clernce ngle leds to n increse in the forces on the clernce fce nd the growth of error stresses on the rke fce for the split-tool method. For cutting conditions pplied by Zorev [7], these errors 2. Considertion of sher stress distribution on tool chip interfce The theory of plsticity implies tht the construction of slip-line field depends on ssumed boundry conditions, which, in the cse of cutting, re stress distribution on the tool rke fce. This especilly concerns the sher stress distribution, which defines the direction of slip-lines on the boundry. According to the vrious experimentl dt [7,13 16] the grphs of this distribution cn differ significntly from ech other especilly when close to the tool tip. Fig. 1 shows three different ides bout sher stress distribution. Such distinction in experimentl results is most probbly cused by different methods of stress mesurement. Zorev [7] nd Bobrov [13] used the split-tool method. However, in these works, whether forces on the tool clernce fce were Fig. 2. Scheme of force ction in cutting by the split tool.

3 A. Toropov, S.-. Ko / Interntionl Journl of Mchine Tools & Mnufcture 43 (2003) probbly resulted in the sher stress distribution shown in Fig. 1(b). It should be noted tht the error of stress determintion by split-tool ppliction could lso be cused by built-up-edge formtion nd gglutintion between two prts of the tool. Gordon [14] chnged the design of the split-tool dynmometer, which cn decrese the influence of forces on the tool clernce fce, nd obtined the other vlues of sher stress [Fig. 1(c)]. Petruh [15] experimentlly found the sme view of sher stress distribution for cutting hrd-to-mchine mterils. A similr grph is presented for the cutting of led [5]. Bgchi nd Wright [16] pplied photo-elstic spphire tool nd obtined the sme behvior of experimentl sher stress distribution for steels 1020 nd In the ltter cse, the ppliction of photo-elstic spphire tool mkes possible the reduction of errors cused by the generl split-tool method. At first, the forces on the clernce fce decrese since the coefficient of friction is reduced for coupled steel nd spphire. For the sme reson, the built-up-edge formtion is lmost impossible in the spphire tool, excluding the errors cused by this phenomenon. The errors of stress determintion re distributed more uniformly long the tool chip contct length nd distort the rel grph of stress distribution, but not s significntly s the generl split-tool method. This implies tht experimentl sher stress distribution s described in [14 16] [Fig. 1(c)] is more ccurte compred with Zorev [7] nd Bobrov s [13] dt. According to the experimentl results given in [14 16], the view of sher stress distribution on the tool rke fce is independent of work mteril nd cutting conditions. In these works, the vlue of sher stress ws found by extrpoltion to be lwys zero t the tool edge. Thus, the sticking effect on the plstic contct re cn be cused by the ction of norml stress. Indeed, sher stress is very smll nd the norml stress is high close to the tool edge. According to experimentl dt [14 16], if the sher stress is zero t the tool edge, then there is no movement of mteril prticles in this re. Mteril stops nd sticks to the tool rke fce forming the initil built-up edge. However, in most cses, its life is very short. The built-up edge itself forms new tool geometry with very high positive rke ngle tht decreses the forces cting on the rke fce of the builtup edge. If the forces on the clernce fce of the builtup edge were sufficient, it would be removed from the rel tool rke fce together with tool mteril prticles, nd this cn be one of the resons for tool wer. If sticking forces were enough to mintin the built-up edge on tool rke fce, the growth of the built-up edge would continue until the forces on its clernce fce exceeded the strength of sticking. Thus, the division of the tool chip contct zone into two prts nd their reltionship with sher stress distribution, s suggested by Zorev [7], is not quite true. From this point of view, it is more correct to present totl tool chip contct length with ssumed stress distribution. 3. Review of some present methods to determine chip tool contct length According to ee nd Shffer s slip-line solution [1], the length of the sticking region on the tool chip interfce cn be obtined from the formul 2 s 2sin sin(45 ), (1) where is the undeformed chip thickness, is the sher ngle, nd is the tool rke ngle. Using nother construction of plstic field inside the chip, Abuldze [6] suggested nother formul to define plstic tool chip contct length: s (x [1 tn] sec), (2) where x = 1 is the chip thickness coefficient nd 1 is the chip thickness. The totl tool chip contct length is pproximtely two times lrger thn the sticking re. Thus this totl length cn be found by corresponding multipliction from Eqs. (1) nd (2). Mny reserchers suggested experimentl reltionships between tool chip contct length, chip thickness, nd chip thickness coefficient [5,7 9,12]. In some of these works, the influence of the coefficient of friction ws included. The length of the sticking re ws found to nerly equl chip thickness 1 [9], nd totl tool chip contct length is defined s: 2 1. (3) Numerous experiments with vrious mterils (such s rmco-iron, crbon nd stinless steels, different coppers, nd bronzes with different hrdness) nd cutting conditions conducted by Poletik [5] show tht tool chip contct length is uniquely relted with the chip thickness coefficient x nd undeformed chip thickness. For the rnge of 1 x 10, this dependence is pproximted by the formul [12]: (2.05 x 0.55). (4) One of the wys to determine tool chip contct length is bsed on the blnce moment eqution bout the tool cutting edge [2]. The min problem of this method is tht the solution depends on the correctness of ssumed norml stress distribution on the tool chip interfce nd sher plne. A vriety of wys to find the tool chip contct length gives different results for one set of cutting conditions

4 1212 A. Toropov, S.-. Ko / Interntionl Journl of Mchine Tools & Mnufcture 43 (2003) nd tool geometry. This proves tht there is still no cler nlyticl formul tht reflects the interreltionship between the sher process in the primry zone nd the tool chip contct length. 4. Suggestion of new slip-line model nd determintion of tool-chip contct length Fig. 3 presents the suggested slip-line field. Bsed on previous experimentl studies [5,17,18], the primry deformtion zone cn be simplified by the centrl slipline field ABD, which is composed of stright rys of b-slip lines nd rcs of -slip lines. ine AB is the initil boundry of this zone while AD is the finl boundry. The sid lines re inclined to the tool pth t ngles 1 nd 2, respectively. Angle is the conventionl sher ngle. Mteril prticles re known to be hrdened intensively when pssing through this zone. The stress stte of the work mteril on line AB cn probbly be represented by the yield stress for given temperture stress strin rte conditions of deformtion. On the finl boundry AD of the primry deformtion zone, mteril hrdening is sturted nd the chip cn be considered s n idel plstic body considering the hrdening fctor. The sturtion of hrdening in cutting hs been proved by microhrdness tests of quick-stop chip microsections [5]. Mteril hrdness is not chnged fter deformtion in the primry sher zone (re ABD, Fig. 3), resulting in ultimte hrdening of the chip mteril s result of deformtion. The presence of extreme hrdness itself hs been lso shown by Rozenberg nd Rozenberg [12]. According to the theory of plsticity [20], slip-lines must intersect the free trnsition mchined/inwrd chip surfce BD t 45 ngle. Therefore, in relity, - nd b-slip lines in the field ABD slightly differ from stright lines nd rcs of circle, respectively. However, the suggested simplifiction is cceptble since the deflection of Fig. 3. Slip-line field for cutting by tool with whole rke fce. corresponding slip lines from stright lines nd from rcs of circle is not sufficient [18]. A second centrl slip-line field ADE is found inside the chip body. ine DE is the finl boundry of the plstic zone in the chip. At point E, which is the end of the tool chip contct, it is obvious tht sher stress on the tool chip contct is zero. Thus, ccording to the boundry conditions for slip lines [20], line DE psses the tool rke fce t 45 ngle. At the sme time s the first pproximtion, it cn be ssumed tht the chip surfce close to point D is prllel to the rke fce. Since the chip surfce is free from stress, line DE psses this surfce t the sme 45 ngles ccording to the boundry conditions for stress. Therefore, the line DE is stright, pssing the tool rke fce nd inwrd chip surfce t the sme 45 ngle. Using the experimentl dt [14 16] discussed bove, it cn be ssumed tht in generl, there is no sher stress on the tool chip interfce t tool edge (point A, Fig. 3). According to the theory of plsticity [20], this mens tht ngle 2 in the suggested slip-line solution is constnt nd equl to 45 +, in other words DAE = DEA = 45, nd so ADE forms n isosceles tringle. Finlly, from the suggested geometry of the slip-line field, the tool chip contct length, which is equl to line AE, is expressed by sher ngle nd undeformed chip thickness s: 2 cos( ). (5) sin 5. Comprtive nlysis of given solution for tool chip contct length with other experimentl nd theoreticl formule One of the most widespred methods to experimentlly determine sher ngle is bsed on the mesurement of chip thickness 1. From the scheme presented in Fig. 3, it cn be geometriclly obtined tht: rctn x sin. cos (6) For convenience of comprtive nlysis, it is better to rewrite Eqs. (1) (5) for tool chip contct length, given bove, in reltive units /, which will be referred to s reltive tool chip contct length. Also, the reltive tool chip contct length is presented depending on vlue of chip thickness coefficient x. Substituting Eq. (6) into Eq. (5) nd doing some simple mthemticl trnsformtions, Eq. (5) cn be reduced to very short form: 2 x. (7) In the sme wy, ee nd Shffer s [1] solution for

5 A. Toropov, S.-. Ko / Interntionl Journl of Mchine Tools & Mnufcture 43 (2003) totl reltive tool chip contct length cn be presented in the form: (8) 2 sin rctn x sin sin 45 cos rctn x sin cos, nd Eq. (2) by Abuldze [6] for reltive tool chip contct length comes to: 2 (x [1 tn] sec). (9) Agin, concerning reltive tool chip contct length, experimentl Eq. (3) cn be expressed by chip thickness coefficient x s: 2 x, (10) nd experimentl dependence (4) is simply rewritten s: 2.05 x (11) Compring now the theoreticl Eq. (7) with the experimentl Eq. (10), their perfect correspondence cn be esily seen. Fig. 4 illustrtes grphicl comprison of theoreticl Eqs. (7) (9) nd experimentl Eqs. (10) nd (11). The figure shows tht the reltive tool chip contct length in formule of ee nd Shffer (8) nd Abuldze (9) depends not only on the chip thickness coefficient x but lso on the rke ngle. As result, Eqs. (8) nd (9) led to lrge errors, especilly for rther lrge rke ngles. For exmple, the solutions of ee nd Shffer nd Abuldze shown in Fig. 4() re for rke ngle 20. It cn be seen tht for n incresing vlue of chip thickness coefficient x, the error increses. If the rke ngle decreses, this error would lso decrese but it would still be significnt s shown in Fig. 4(b), in which the rke ngle is 0. The other reson for the inccurcy of the solutions of ee nd Shffer nd Abuldze is tht they do not correspond to the mechnicl sense of grphs presented in Fig. 4. It is obvious tht zero chip thickness coefficient x mens no cutting, nd reltive tool chip contct length must lso be zero. But s seen from Eqs. (8) nd (9), this sitution is impossible. The sme cn be sid bout experimentl Eq. (11). In this cse, incorrectness cn be explined by unsuccessful pproximtion of experimentl dt. However, s seen in Fig. 4, Eq. (7) offered by the new slip-line model shows very good correspondence with the experimentl results of Eqs. (10) nd (11). 6. Experimentl verifiction Experiments verifying the suggested method to determine the chip tool contct length were executed in CNC turning mchine. Rdil slots were mde on cylindricl specimens to produce discs with width of mm. These discs were mchined in rdil feed by wide tool to relize the scheme of orthogonl cutting. Four different mterils were used for the experiments, nmely, luminum lloy A6061, copper, crbon steel SM45C, nd stinless steel STS304. Tble 1 lists the tool geometry nd cutting conditions for ech mteril. Fig. 4. Grphicl comprison of different solutions for tool chip contct length. () Rke ngle = 20, (b) rke ngle = 0.

6 1214 A. Toropov, S.-. Ko / Interntionl Journl of Mchine Tools & Mnufcture 43 (2003) Tble 1 Conditions of the experiment Work mteril Cutting Undeformed chip thickness(mm) Tool rke ngle( ) Tool clernce ngle( ) velocity(m/min) A , 0.1, 0.15, 0.2, , 0, 5, 10, 20 5 Copper , 0.1, 0.15, 0.2, , 0, 5, 10, 20 5 SM45C , 0.1, 0.15, 0.2, , 0, 5, 10, 20 5 STS , 0.1, 0.15, 0.2 5, 0, 5, 10, 20 5 The length of contct trck on the tool rke fce ws mesured using tool microscope fter every cutting, which ws the experimentl tool chip contct length. Chip thickness ws lso mesured using micrometer. Experimentl vlues of reltive tool chip contct length / nd chip thickness coefficient x were clculted s result of these mesurements nd were then plotted (Fig. 5). The theoreticl line ccording to Eq. (7) is presented in the figure for comprison with experimentl dt. Considering the errors of mesurements nd other rndom experimentl fctors, the theoreticl solution for tool chip contct length presented in this study corresponds well for ll tested mterils in the given rnge of cutting conditions nd tool geometry. 7. Conclusion From the given comprtive nlysis nd experimentl verifiction, the suggested solution for tool chip contct length is most ccurte mong the existing n- lyticl wys to predict this prmeter. In prticulr, there is n exct correspondence between theoreticl Eq. (7) nd experimentl Eq. (10) for reltive contct length nd the sme good correspondence with given experimentl dt. This remrkble coincidence proved tht the contours of the suggested slip-line solution re relly true, t lest in the chip body, for ll mterils used, cutting conditions, nd rke ngles for tools with n unrestricted rke fce. The results of this study re the first step for subsequent nlyticl reserch of the processes occurring on the tool chip interfce, especilly for the prediction of stress distribution in tht region s well s cutting forces. This reserch could lso be helpful for the nlysis of tool strength, temperture phenomen, nd wer problems. Acknowledgements The Ministry of Science nd Technology supported this work through the 2001 Ntionl Reserch bortory (NR) progrm. References Fig. 5. Comprison of theoreticl Eq. (7) with experimentl dt for different mterils. [1] E.H. ee, B.W. Shffer, The theory of plsticity pplied to problem of mchining, Trns. ASME, Journl of Applied Mechnics 18 (1951) [2] W.F. Hstings, P. Mthew, P..B. Oxley, A mchining theory for predicting chip geometry, cutting forces, etc. from work mteril properties nd cutting conditions, Proc. Roy. Soc. ond. A 371 (1980) [3] M.Y. Friedmn, E. enz, Investigtion of the tool-chip contct length in metl cutting, Interntionl Journl of Mchine Tool Design nd Reserch 10 (1970) [4] S. Rmlingmn, P.V. Desi, Tool-chip contct length in orthogonl mchining, ASME Pper 80-WA/Prod-23, [5] M.F. Poletik, Contct ods on Tool Fces (in Russin), Mchinostroenie, Moscow, [6] N.G. Abuldze, Chrcter nd the length of tool-chip contct (in Russin), in: Proceedings Mchinbility of Het-resistnt nd Titnium Alloys, Kuibyshev, 1962, pp [7] N.N. Zorev, Interreltionship between sher process occurring long the tool fce nd on the sher plne in metl cutting, Interntionl Reserch in Production Engineering, ASME (1963),

7 A. Toropov, S.-. Ko / Interntionl Journl of Mchine Tools & Mnufcture 43 (2003) [8] A. Bhttchryy, On the friction forces in metl cutting, in: Proceedings of the 6th Interntionl Mchine Tool Design nd Reserch Conference, 1963, pp [9] S. Kto, K. Ymguchi, M. Ymd, Stress distribution t the interfce between tool nd chip in mchining, Trns. ASME, Journl of Engineering for Industry 94 (1972) [10] M.I. Klushin, Metl Cutting (in Russin), Mshgiz, Moscow, [11] V.S. Kushner, Thermo-mechnicl Theory of Continuous Cutting of Plstic Metls (in Russin), Irkutsk University Press, Irkutsk, [12] A.M. Rozenberg, O.A. Rozenberg, Mechnics of Plstic Deformtion in Cutting nd Reching (in Russin), Nukov Dumk, Kiev, [13] V.F. Bobrov, Fundmentls of Metl Cutting Theory (in Russin), Mchinostroenie, Moscow, [14] M.B. Gordon, A Study of Friction nd ubriction in Metl Cutting (in Russin), Cheboksry Stte University Press, Cheboksry, [15] G.G. Petruh, Cutting of Difficult-to-cut Mterils (in Russin), Mchinostroenie, Moscow, [16] A. Bgchi, P.K. Wright, Stress nlysis in mchining with the use of spphire tools, Proc. Royl Soc. ond. A 409 (1987) [17] W.B. Plmer, P..B. Oxley, Mechnics of orthogonl mchining, Proc. Inst. Mech. Eng 173 (1959) [18] N.N. Zorev, Metl Cutting Mechnics, Pergmon Press, Oxford, [19] H. Kudo, Some new slip-line solutions for two-dimensionl stedy-stte mchining, Interntionl Journl of Mechnicl Sciences 17 (1965) [20].M. Kchnov, Fundmentls of the Theory of Plsticity (in Russin), Science, Moscow, 1969.

ADVANCEMENT OF THE CLOSELY COUPLED PROBES POTENTIAL DROP TECHNIQUE FOR NDE OF SURFACE CRACKS

ADVANCEMENT OF THE CLOSELY COUPLED PROBES POTENTIAL DROP TECHNIQUE FOR NDE OF SURFACE CRACKS F. Tkeo 1 nd M. Sk 1 Hchinohe Ntionl College of Technology, Hchinohe, Jpn; Tohoku University, Sendi, Jpn Abstrct: