A NEW S LIP L INE T HEORY F OR O RTHOGONAL C UTTING

7/8/ N OMENCLATURE ks = value of plasticity corresponding to yield strength kf = value of plasticity corresponding to fracture strength σy= yield strength of work material ε = shear strain σ0, n = parameters of hardening a = undeformed chip thickness a1 = chip thickness ξ = a1/a = chip thickness coefficient α = tool rake angle Φ = imaginary shear angle N = normal force on tool rake face F = friction force on tool rake face L = tool-chip contact length σ = average normal stress/hydrostatical pressure σn(x), τn(x) = normal and shear stress distribution on tool rake face θ(x) = angle between tangent to α-slip line at current point M on tool-chip interface and X-axis ϕ = angle between normal to the given contour and X-axis Sf = true fracture strength of work material

7/8/ B RIEF HISTORY  Timae proposed the model of chip formation with single shear plane  Zvorykin and Merchant applied minimum force and energy principles  Problems of model with single shear plane  Palmer and Oxley used cinema technique and found experimentally the behaviour of material particles in the primary deformation zone they used modified Henky and balance moment equations and concluded about acceptability of their model. The main problem in this approach is that the stress distribution on tool rake face is unknown and it is necessary to make an assumption about this distribution for solution of balance force equations  Lee and Shaffer were the first, who proposed the continuation of plastic deformation after primary shear.

7/8/ SLIP LINE MODEL

7/8/ S HEAR STRESS DISTRIBUTION

7/8/ S PLIT TOOL

7/8/ distinction in experimental results is most probably caused by different ways for stress measurement. Zorev and Bobrov used the split-tool method. (neglected the forces on the clearance face) caused by built-up-edge formation and “agglutination” between two parts of the tool. Gordon changed the design of the split-tool dynamometer, which can decrease the influence of forces on tool clearance face Bagchi and Wright applied photo-elastic sapphire tool and got the same behaviour of experimental shear stress distribution for steels 1020 and 12L14.( the application of photo-elastic sapphire tool makes possible the reduction of errors caused by general split-tool method)

7/8/2016 8

9 S LIP LINE MODEL & T OOL -C HIP C ONTACT L ENGTH Tresca Plastic flow criterion.(Assumed slip line field) FABDEF- Primary deformation zone AFG-Second central slip-line field assumed that in general, there is no* shear stress on the tool-chip interface at tool edge i.e. point A < FAG = < AGF = π /4 and so triangular AFG is isosceles from the suggested geometry of slip-line field …………..(1)

7/8/ STRESS DISTRIBUTION ON TOOL RAKE FACE ………….(2) (from Von Mises criterion) ………….(3) (due to hardening effect) ………….(4) (Saturation of hardening) Area AFG is also a zone of uniform compression.

7/8/ ……..(5) ( as there is a uniform stress state in AFGA.) ……...(6) ……………(7) (from theory of plasticity)

7/8/ …………(5) (from 5 & 7) FORCES ON TOOL-CHIP INTERFACE …………..(6) …………(7) Average coefficient of friction f on chip/tool interface ………(8)

7/8/ P ROOF ……………. Theoretical (a) [according to Eqs. (5)] and experimental (b) stress distributions on the tool rake face surface during the machining of 1020 steel at 10 m/min and an undeformed chip thickness of mm (rake angle –5°).

7/8/ It is assumed that value of plasticity kf probably corresponds to extreme stress state of material when its hardening is almost saturated and its behavior can be considered as ideal plastic From Eq. (1) for tool-chip contact length and Eq.(7) for total friction force, it can be obtained that average shear stress on tool-chip interface is defined as: ………..(9) ………..(10) ( Experimental results by Poletika) ……….(11)

7/8/ C OMPARATIVE ANALYSIS OF GIVEN SOLUTION FOR TOOL - CHIP CONTACT LENGTH WITH OTHER EXPERIMENTAL AND THEORETICAL FORMULAS From the scheme presented in Fig. 3, it can be geometrically obtained that : …………..(8) From (1) ……………….(9) Numerous experiments with different material (as armco-iron, carbon and stainless steels, different coppers and bronzes with different hardness) and cutting conditions conducted by Poletika M.F. show that tool/chip contact length is related with chip thickness coefficient ξ and unreformed chip thickness a. For the range of 1≤ξ≤10 this experimental dependence is expressed by formula as followed

7/8/ ……………(10) Theoretical line from formula (9) Experimental points from formula (10)

7/8/

7/8/ E XPERIMENTAL R ESULT

7/8/ T EMPERATURE D ISTRIBUTION …….

7/8/ ACHIEVEMENTS Friction and normal stress distribution on tool/chip interface is found analytically using classical theory of plasticity. Predicted the tool chip contact length, which is the most accurate among existing analytical ways to predict the parameter. The comparison of theoretical and experimental stress distribution is presented that show good correspondence of model to the real cutting conditions. Using given stress distribution the formulas for cutting forces prediction is found.

7/8/ Conclusion and future work 1. It was shown that imaginary shear line in cutting possibly corresponds to the trajectory of principle stress 2. Present experimental data, concerning form of primary deformation zone, tool-chipcontact length, and stress distribution on that area, give good evidence for suggested model 3. Further experimental research must be done to verify the accuracy of cutting force prediction according to Eqs.(6) and (7), and exact value of plasticity kf must be checked. 4. One of the open questions in the model is the analytical determination of imaginary shear angle Φ, 5. Suggested slip-line solution in primary deformation zone can be useful for finding of chip form, in particular for determination of chip radius. 6. Found stress distribution on tool rake face can be applied as a basis for analysis of tool crater wear, temperature phenomena in that area, and tool strength determination.

7/8/ REFERENCES Bagchi, A. and Wright, P.K., Stress analysis in machining with the use of sapphire Tools, Proc. Royal Society of London, A 409, pp , Lee, E. H. and B. W. Shaffer The theory of plasticity applied to a problem of machining, ASME J. Appl. Mech., 18, 405. THE CHIP-TOOL CONTACT LENGTH IN ORTHOGONAL METAL CUTTING-VALERY MARINOV.Department of Mechanical Engineering, Eastern Mediterranean University Gazimagusa, TRNC (via Mersin 10), Turkey Toropov, A. and Ko, S.-L., Prediction of tool chip contact length using new slip-line theory for orthogonal cutting Proc. Of the 3rd Intern. Asia Pacific Forum on Precision surface finishing and deburring technology, 26-28Mar., 2003, pp Determination of stress state in chip formation zone by central slip-line field Andrey Toropov and Sung-Lim Ko International Journal of the Korean Society of Precision Engineering, Vol. 4, No. 3, May 2003.

7/8/ Thank you

7/8/ INDEX AISI 12L14 is a Standard Resulfurized And Rephosphorized grade Carbon Steel. It is commonly called AISI 12L14 Lead steel. It is composed of (in weight percentage) 0.15%(max) Carbon (C), % Manganese (Mn), % Phosphorus (P), % Sulfur (S), % Lead (Pb), and the base metal Iron (Fe). Other designations of AISI 12L14 carbon steel include UNS G12144 and AISI 12L14

7/8/ AISI 1020 Composition %C Mn P 0.04 (max) S 0.05 (max) CMnPS Mechanical Properties Density (×1000 kg/m3) Poisson's Ratio Elastic Modulus (GPa) Tensile Strength (Mpa)394.7 annealed at 870°C Yield Strength (Mpa)294.8 Elongation (%)36.5 Reduction in Area (%)66.0 Hardness (HB)111 Impact Strength (J) (Izod) Thermal Properties Thermal Expansion (10-6/ºC)

7/8/ Experimental Verification Experiments verifying the suggested method to determine chip-tool contact length were executed in CNC turning machine. Radial slots were made on cylindrical specimens to produce discs with width of 2.0–2.5 mm. These discs were machined in radial feed by a wide tool to realize the scheme of orthogonal cutting. Four different materials were used for the experiments, namely, aluminum alloy A6061, copper, carbon steel SM45C, and stainless steel STS304. The length of contact track on tool rake face was measured using tool microscope after every cutting, which was experimental tool-chip contact length. Chip thickness was measured using a micrometer. Experimental values of relative tool-chip contact length L/a and chip thickness coefficient ξ were calculated as a result of these measurements and were then plotted The theoretical line according to formula (9) was presented in the figure for comparison with experimental data.

7/8/ Experimental setup

7/8/ All tests were performed using tools with brazed carbide inserts of P25. After brazing, tools were carefully ground on a tool grinder with tool orthogonal clearance αo = 6 o, tool cutting edge angle κr = 90 o, tool cutting edge inclination λs = 0 o, and tool orthogonal rake γo = 0 o and 10 o. In order to reduce the variation of cutting speed across the cutting edge, large workpieces of approximately 230-mm diameter were used. The workpieces were first bored to produce tubes of 1-mm wall thickness. The experimental set-up is shown in Fig.1. The experimental results of Young et al. [9] showed that the tube diameter does not significantly change the nature of cutting conditions, therefore, they can be to a great extent considered orthogonal. Experiments were carried out over a range of cutting conditions as follows: V = 91…291 m/min, a = 0.1…0.35 mm, b = 1 mm, no cutting fluids. The total contact length was obtained measuring chip traces on the rake face by an instrumental measuring loupe. The tool rake face was carefully polished and cleaned before each test. Each test was performed on a new section of the cutting edge to eliminate wear effects.