SYNTHESIS ON THE ASSESSMENT OF CHIPS CONTRACTION COEFFICIENT C d

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1 SYNTHESIS ON THE ASSESSMENT OF HIPS ONTRATION OEFFIIENT Marius MILEA Technical University Gheorghe Asachi of Iași, Machine Manufacturing an Inustrial Management Faculty, B-ul D Mangeron, nr 59, A, , Iași, Romania, Department of Machinery an Tools milea_marius@yahoocom Abstract: The assessment of plastic eformation of chips can be one base on theoretical an experimental consierations This paper presents the two ways of assessing the chips contraction coefficient, namely the theoretical an experimental methos The results obtaine from both methos will be use to evelop a mathematical moel for chips contraction coefficient The theoretical an experimental methos have the avantage of fast assessment of eformations an the isavantage of using intermeiary elements such as correction coefficients Keywors: chips contraction coefficient, theoretical methos, experimental methos Introuction The chips contraction coefficient represents the capacity of plastic eformation of ifferent metals uring the cutting process The assessment of plastic eformation is base on both theoretical an experimental consierations, which are use to evelop a mathematical moel for In this mathematical moel, is epenent on the parameters of the cutting process 2 Theoretical onsierations An analysis of metal-cutting stuies reveals that there are a few known moels of this process regaring plastic eformation, chip formation or other relate concepts, like stress or strain In his moel, Timme consiers the interaction between the cutting tool, the work piece an the chip The Ernst an Merchant approach introuces the concept of the single shear plane an the angle it makes with the surface generate referre to as the shear angle It has become a classic approach in metal cutting an has been applie in analyzing the cutting of ifferent materials even when shearing cannot occur at all Authors like Shaw, ook an Finnie insist on the relationship between the shear an friction process in metal cutting Okushima an Hitomi assume that shearing takes place within a particular flow region rather than along a single shear plane Kececioglu stuies the metal cutting mechanics assuming a uniform stress-state in the zone of plastic eformation with parallel bounaries [Xiao, Astakhov, 2008] Zorev suggests a moel for the cutting of uctile materials in agreement with the theory of plasticity [Astakhov, 2003] Summarizing the ieas above, it can be sai that each cutting approach or moel reflects a particular aspect of metal cutting practice No moel can cover all various cutting conitions that can be foun uring the real process Historically, the chip contraction coefficient was introuce in stuies on metal cutting as a measure of plastic eformation It was shown that although is not a perfect measure of plastic eformation, it irectly reflects the final plastic eformation that takes place in cutting [Astakhov, 200] The most frequently use theoretical moel takes into consieration the 43

2 epenence of the chips contraction coefficient on the shear angle an the rake angle as in Fig 2 an Eq 2 t a t cos( ) (2) sin Figure 2: utting with a single shear plane Most publishe papers take into consieration the iniviual influence of some cutting parameters; only few stuies consier the influence of some pairs of parameters on the chips contraction coefficient (cutting spee, the nature of the cut material, fee, the angles of the cutting tool) The results of the stuies unertaken by researchers in USA an Russia show that the iniviual influence of the cutting spee (v), the fee (s), the inclination angle (λ) an the rake angle (γ) epens on the values of other parameters A case in point is the influence of the cutting spee v on, which is minimum for higher values of the rake angle an for harer an more resistant steels Knowing the values of the chips contraction coefficient obtaine in correlation with the main influential parameters an the exact assessing requirements of the cutting forces can help in characterizing metals from the point of view of machinability [Poenaru, 200] As mentione before, both analytical an experimental methos can be use in assessing an measuring the plastic eformation in cutting 2 Analytical an Experimental Methos Analytical methos consist in the mathematical calculus of the elements that characterize the plastic eformation of the cut metal in various conitions In orer for this metho to be applie it is necessary to know the yiel curves, the structural characteristics of the materials an the istribution of the efforts in the eformation zone Experimental methos irectly measure the elements of plastic eformation V Astakhov [200] suggests three experimental methos for the etermination of the chip contraction coefficient The simplest metho is to measure the chip thickness an calculate as in Eq (22): t2 / t (22) where t 2 is the chip thickness an t is the uncut chip thickness This metho cannot be always use because of the chip s sawtoothe free surface or its smallness The secon metho is the weighing of the chips After etermining the length L, the with w an the weight G ch, the chip thickness is calculate as in Eq (23): t 2 G L g (23) ch w w where ρ w is the ensity of the work material an g=9,8m/s 2 is the gravity constant The thir metho propose by Astakhov to etermine chips contraction coefficient is the irect metho, which can be applie in milling, turning, rilling an other processes is calculate as in Eq (24): L g L (24) g 2 which can be seen in Fig 22 44

3 2 Fee s ut material σ r (HB) s increases ecreases σ r increases ecreases 4 Rake angle γ γ increases ecreases 5 Inclination angle λ λ increases ecreases Table 2 Average Influential Parameters Figure 22 Experimental methos to etermine : a turning; b rilling; c milling These methos, either theoretical or experimental, can lea to errors in assessing the chips contraction coefficient To eliminate these errors, a theoretical-experimental moel of assessing is suggeste, base on both theoretical consierations, but mostly on experimental results 3 The Assessment of Base on the publishe results an experimental research, fifteen parameters which influence the plastic eformation of chips are pointe out They have been classifie into three categories accoring to their influence on as follows: highly influential parameters (table ), average influential parameters (table 2) an low influential parameters The first two categories have been synthesize in tables for an easier reaing No Parameter Symbol an Table Highly Influential Parameters Fiel Variation utting spee v Meaning variation v increases ecreases No Parameter Symbol an Tool cutting ege angle Ege raius Raius curvature of Ege sharpening raius Fiel Variation Meaning variation K increases K ecreases r r increases 03-4 ecreases R t R t ecreases 4 increases ρ ρ increases 00,3 ecreases Low influential parameters are worth mentioning: cutting epth t which increases while ecreases; rake surface raius increases while ecreases; rake surfacechip contact length increases at the same time with ; the influence of the cutting environment an the cutting material can be seen in the ecrease of the ; last, but not least, rake surface roughness increases while ecreases These parameters ten to be neglecte in assessing the chips contraction coefficient [Segal,993] The importance an role of the highly influential parameters have been establishe by comparison with the results publishe in the specialize stuies [Panait, 993] The parameters in table 2 may appear in some assessing moel for as correction coefficients for on the one han the tool cutting ege angle whose values are lower 45

4 than an on the other han, the three types of raius whose values are higher than Due to this classification, the assessing moel for the chips contraction coefficient can take into account either all types of parameters, or only one of the mentione categories 3 The First Moel of Assessing To etermine in the moel of assessment, the following Eq is use: = v x s y HB z γ n λ w K k K y K ρ K Rt (3) in which, x, y, z, n, w, k are obtaine experimentally an K represents correction coefficients, γ is the rake angle an λ is the inclination angle The values of the constant epen on the nature of the cut material an the cutting process an will be obtaine for each type of material experimentally After etermining the exponents an coefficients, the constant is obtaine as follows: v s HB K 0 x y z u w (32) in which 0 represents the value of the chips contraction coefficient for v 0, s 0, HB 0, λ 0, γ 0 The x, y, z, u, w exponents show their level of influence an the significant interepenencies Accoring to experimental research, by increasing the v, s, HB, λ, γ parameters the chips contraction coefficient ecreases an, implicitly, the exponents will become negative In orer to take into consieration the possible interepenencies, it is suggeste that the x, y, z, u, w exponents shoul have the following propose values: x f ( v, s, M,,, r, k,) y f ( v, s, M,,, r, k,) 2 z f3( v, s, M,,, r, k,) (33) n f ( v, s, M,,, r, k,) 4 w f ( v, s, M,,, r, k,) 5 in which M represents the epenence of the influence level on the nature of the cut material Since the plastic eformation capacity of ifferent materials is ifferent for the same cutting conitions, the level of influence of some of these factors is ifferent from one material to another The correction coefficients k take into consieration the influence of the parameters with low influence on Uner specific working conitions (cut material, rake angle, inclination angle, cutting spee or cutting fee), these coefficients will not appear in the assessing moel for the chips contraction coefficient If for specific working conitions, the factors o not influence, then the correction coefficients are k= If the factors influence, then increases an the values of k are higher than, k> If ecreases ue to these factors, then k< To obtain the values of the exponents, Eq 34 is suggeste, in which x 0, y 0, z 0, n 0, w 0 show the level of influence of these factors uner stanar constant working conitions accoring to the iniviual influential moels (Eq 35) x x a v b s c 0 y y a v b s c 0 z z a v b s c u u a v b s c w w a v b s c (34) The a, b, c, coefficients represent the interaction between the iniviual influence of the respective factor an the influence of the other factors of the cutting process 46

5 v x0 s y0 2 HB n0 w0 z0 (35) The basic moel in expresse in 3 raises problems because the γ an λ angles have the following values in reality γ=0 an λ=0 In this case, when assessing the chips contraction coefficient using the moel in 3, similar values will be use but they will be higher than, as for example, γ=,5 0 an λ=,5 0 Because the γ an λ angles get negative values, it is expecte that negative values will be obtaine for the constant experimentally This is the case when one of the γ an λ angles get negative values In the 3 moel, the real cutting angle( r ) is not use because it gets the same values for ±λ accoring to Eq 36 an Fig 3 parameters- has the avantage of being use for preicting the plastic eformations an the cutting forces without any further experimental eterminations The experimental etermination of the chips contraction coefficient is precise an is easier to o than the etermination of the correction coefficients [Shaw, 2005] 32 The Secon Moel of Assessing A group of researchers an professors from Iasi have propose a new moel for the coefficient assessment [ozminca, 200] Base on the fact that the known theoretical equations (Eq 37) for the chips contraction coefficient o not inclue all the highly influential parameters, it is suggeste a new moel (38) which takes into consieration the sense an the level of influence of each consiere parameter cos( ) / sin (37) o n5 n6 k HB n v n2 s n3 K n4 (38) In orer to avoi the negative an null values for the angles γ an λ in the 322 moel, complementary angles are use, δ=90- γ an ω=90-λ respectively Figure 3 The epenence r =f(γ, λ) 2 2 cosr cos cos sin 90 (36) The values of the constants, exponents an correction coefficients will be etermine with the help of the conventional methoology for processing the experimental results This moel for assessing the chips contraction coefficient after establishing the constants, exponents an correction coefficients in accorance with the cutting Figure 32 Experimental iagram in oublelogarithmic coorinates The influence levels of n n 6 are base on the experimental iagrams in oublelogarithmic coorinates of the functions 47

6 y=f(x), where y=log an x is in turn log HB, log v, log s, log K, log δ an log ω Base on the experimental values for iagrams as in Fig 32 are obtaine In orer to etermine the influence levels n n 6, Eq 39 is obtaine from these iagrams y ni tgi x y 2i i x 2i i (39) in which i=, 2, 3, 4, 5, 6 After obtaining the values n n 6, the correction coefficient k will be etermine with Eq 30 where v 0, s 0, K 0, δ 0, ω 0 an HB 0 are the values for the inepenent variables that provie the same value for 0 For this purpose, it can be use either the tables with experimental ata or the iagrams in oublelogarithmic coorinates HB v K k n n2 n3 n n5 n6 0 0 (30) The new moel propose in Eq (38) must be ajuste epening on the specific elements of each cutting process an cut material The values of the chips contraction coefficient for each metal are useful for establishing the eformation capacity through cutting The specific elements of the cutting process an of the nature of the cut material are pointe out through the values of the correction coefficient This secon moel for the assessment of takes into consieration six parameters which are highly influential, namely, the cutting spee, the fee an the constructive angles of the tool γ, λ, K 4 oncluing Remarks Theoretical an experimental results have shown that all the parameters of the cutting process influence the plastic eformations in cutting metals The assessment of the influence level of the working parameters on with the help of either normal coorinates or oublelogarithmic coorinates iagrams has lea to the evelopment of precise mathematical moels The values of the chips contraction coefficient are use to assess the measure of the cutting forces much closer to the existing reality The chips contraction coefficient enables us to take into account the interepenencies among the influences of the cutting parameters on the cutting forces Irrespective of the assessing metho, using for the assessment of some intermeiary elements or even components of the cutting forces can significantly reuce the number of experimental trials an increases the accuracy of the results The theoretical an experimental methos have the avantage of fast assessment of eformations an the isavantage of using intermeiary elements like the correction coefficients In the future, base on the existent moels, I will try to evelop a new an more complex mathematical moel which inclues the existent ata an the most significant parameters in assessing 5 Acknowlegements This paper was realize with the help of the professors from the epartment of machinery an tools an with the support of EURODO, a project finance by the European Social Fun an the Romanian Government 6 References [] Astakhov, Viktor, The Tribology of Metal utting, 200 available at wwwbooksgooglero, Accesse: [2] Astakhov, Viktor, Shvets, SV, The assessment of Plastic Deformation in Metal utting, in Journal of Materials Processing Technology, Vol 46(2), 2004 available at wwwscienceirectcom 48

7 Accesse: [3] Astakhov, Viktor, Osman, MO M, orrelations amongst Process Parameters in Metal utting an their Use for Establishing the Optimum utting Spee, in Journal of Materials Processing Technology 62, 996, available at wwwastvikcom Accesse: [4] Astakhov, Viktor, Shvets, SV, Osman, MO M, hip Structure lassification Base on Mechanics of its Formation, in Journal of Materials Processing Technology, 997, Vol 7(2), available at wwwastvikcom Accesse: [5] ozmîncă, I, ozmîncă, M, Ibănescu R, About a new metho for cutting forces evaluation, in Buletinul Institutului Politehnic Iaşi, Tom LVI (LX) Fascicol 2a, ISSN , 200, Iasi [6] Davim, JPaulo (e), Machining Funamentals an Recent Avances, Springer-Verlag Lonon Limite, 2008, available at wwwastvikcom Accesse: [7] Panait, S, Bazele aşchierii şi generării suprafeţelor, Univ Tehnice Gh Asachi, 993, Iaşi [8] Poenaru, Silviu, ontribuţii la moelarea matematică a forţelor e aşchiere funcţie e coeficientul e eformare plastică a aşchiilor la strunjire, Ph Thesis, Universitatea Tehnică Gheorghe Asachi, 200, Iaşi [9] Segal, R, ontribuţii la stuiul interepenenţelor intre influenţele parametrilor e lucru asupra eformaţiilor plastice la aşchierea oţelurilor, Ph Thesis, Universitatea Tehnică Gheorghe Asachi, 999, Iaşi [0] Shaw, M, Vyas A, The Mechanism of hip Formation with Har Turning Steel, in Annals of the IRP, vol 47/, p 77-83, 998 [] Shaw, M, Metal cutting principles, 2n eition, University of Oxfor, New York, 2005 available at wwwbooksgooglero Accesse: [2] Xiao, Xinran, Astakhov, V, A Methoology for Practical utting Force Evaluation base on the Energy Spent in the utting System, in Machining Science an Technology, 2008, available at wwwastvikcom Accesse:

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