MFGE 307 THEORY OF MANUFACTURING TECHNOLOGY II 1 Chapter 2 MECHANICS OF METAL CUTTING MECHANICS OF METAL CUTTING Prof. Dr. S. Engin KILI MFGE 307 THEORY OF MANUFACTURING TECHNOLOGY II 2 Content Terms and Definitions Chip Formation Cutting Forces and Force Diagram Shear Angle Orthogonal Cutting Geometry Mathematical Models Metal Removal Rate Power Requirement Examples Photos from internet sites. MFGE 307 THEORY OF MANUFACTURING TECHNOLOGY II 3 Terms and Definitions Machining : Removal of material in the form of chips from the workpiece by shearing with a sharp tool. Resultant Cutting Motion in Cylindrical Turning MFGE 307 THEORY OF MANUFACTURING TECHNOLOGY II 4 Terms and Definitions Kalpakjian-Schmid, 2008 MFGE 307 THEORY OF MANUFACTURING TECHNOLOGY II 5 Oblique Cutting Terms and Definitions Orthogonal Cutting MFGE 307 THEORY OF MANUFACTURING TECHNOLOGY II 6 Terms and Definitions ( a) Schematic illustration of cutting with an oblique tool. (b) Top view, showing the inclination angle, i. (c) Types of chips produced with different inclination angles. Oblique Cutting MFGE 307 THEORY OF MANUFACTURING TECHNOLOGY II 7 Orthogonal Cutting Analogy in Turning (for =0 0 ) Terms and Definitions MFGE 307 THEORY OF MANUFACTURING TECHNOLOGY II 8 Relative Motion between tool and workpiece Primary motion Cutting motion Cutting speedFeed rate Feed motion Depth of cut Secondary motion Depth of cut adjustment Terms and Definitions MFGE 307 THEORY OF MANUFACTURING TECHNOLOGY II 9 Chip Formation MFGE 307 THEORY OF MANUFACTURING TECHNOLOGY II 2/3/2016ME Section 05a10 Chip Formation Basic types of chips produced in metal cutting and their micrographs: (a) continuous chip with narrow, straight primary shear zone; (b) secondary shear zone at the tool-chip interface; (c) continuous chip with built-up edge; (d) serrated (segmented or nonhomogeneous) chip; and (e) discontinuous chip. Source: After M.C. Shaw, P.K. Wright, and S. Kalpakjian. Shiny (burnished) surface on the tool side of a continuous chip produced in turning. MFGE 307 THEORY OF MANUFACTURING TECHNOLOGY II 11 Continuous Chip Common in machining ductile materials MFGE 307 THEORY OF MANUFACTURING TECHNOLOGY II 12 Discontinuous Chip Machining brittle materials Small rake angle Large depth of cut Machining ductile materials at low cutting speed high feed MFGE 307 THEORY OF MANUFACTURING TECHNOLOGY II 13 Serrated Chip MFGE 307 THEORY OF MANUFACTURING TECHNOLOGY II 14 Continuous Chip with BUE Occurs in machining ductile materials with high friction at tool- chip interface C hip welds to tool face Destroys accuracy and surface finish Increases tool wear Can be reduced by decreasing depth of cut increasing cutting speed MFGE 307 THEORY OF MANUFACTURING TECHNOLOGY II 15 Cutting Forces F c : tangential (main) cutting force F t : thrust (feed) cutting force F f : frictional force on rake F n : normal force on rake F s : shear force on shear plane F n s : normal force on shear plane F r : resultant force shear angle n normal rake angle MFGE 307 THEORY OF MANUFACTURING TECHNOLOGY II 16 Cutting Forces MFGE 307 THEORY OF MANUFACTURING TECHNOLOGY II 17 Orthogonal Cutting Geometry MFGE 307 THEORY OF MANUFACTURING TECHNOLOGY II 18 Theoretical Models Only two of the simple thin shear-zone models will be covered: Ernst and Merchants model Lee and Shaffers model MFGE 307 THEORY OF MANUFACTURING TECHNOLOGY II 19 Common assumptions: Sharp tool tip no rubbing or ploughing between tool and w.p. Two dimensional deformation no side spread Uniform stress distribution on shear plane Resultant force on shear plane equal and opposite to res. force at chip-tool interface. Ernst and Merchant Model MFGE 307 THEORY OF MANUFACTURING TECHNOLOGY II 20 Shear angle would take up such a value as to reduce the work done in cutting to a minimum. For given cutting conditions, work done in cutting is proportional to F c, it is necessary to develop an expression for F c in terms of and then to obtain the value of for which F c is a minimum: Main Assumption (EM Model) MFGE 307 THEORY OF MANUFACTURING TECHNOLOGY II 21 Shear Angle (EM Model) MFGE 307 THEORY OF MANUFACTURING TECHNOLOGY II 22 Strain Stress Lee and Shaffers Model Work material is rigid plastic. Elastic strain is negligible. Behaviour of work material is independent of the rate of deformation. Temperature effects are neglected. Inertia effects are neglected. Uniform stress distribution at the chip-tool interface. MFGE 307 THEORY OF MANUFACTURING TECHNOLOGY II 23 Main Assumptions (LS Model) A slip-line field is formed in the triangular plastic zone extending from the shear plane to the interface between the tool and the chip where no deformation takes place except for the transmission of forces from tool-chip interface to shear plane and for the material being stressed to its yield point. All the deformation takes place in the plane (Shear Plane) extending from the tool cutting edge to the point of intersection of the free surfaces of the work and the chip. MFGE 307 THEORY OF MANUFACTURING TECHNOLOGY II 2/3/2016ME Section 05a24 Assumptions (Contd) Maximum shear stress throughout the zone is s, shear stress on the shear plane and two directions of this max. shear stress are indicated by two orthogonal sets of lines (slip lines). Top surface of the triangular plastic zone then becomes a free surface across which no stresses are transmitted. Therefore between this surface and the max. shear stress plane (shear plane) there is an angle of /4. Principal stresses act on the chip-tool interface (secondary def. Zone) at angles and + /2. Directions of max. shear stress lie at /4 to the dir. of principal stress MFGE 307 THEORY OF MANUFACTURING TECHNOLOGY II 25 Lee-Shaffer Theory (Contd) Hence, n MFGE 307 THEORY OF MANUFACTURING TECHNOLOGY II 26 Metal Removal Rate w = v.f.d where, w: metal removal rate v: cutting speed f: feed rate cutting conditions d: depth of cut A c : f.d = undeformed chip cross sectional area MFGE 307 THEORY OF MANUFACTURING TECHNOLOGY II 27 Power Requirement E: Energy required to remove unit volume of chips or Resistance to cutting force E Specific cutting energy Energy to remove unit volume of chips or E Specific cutting pressure Force to produce chips with unit cross sectional area MFGE 307 THEORY OF MANUFACTURING TECHNOLOGY II 28 Power Requirement MFGE 307 THEORY OF MANUFACTURING TECHNOLOGY II 29 Power Requirement Power required at the spindle: E is a function of material property and the undeformed chip thickness If E o is the specific cutting energy for an undeformed chip thickness of 1 mm, then the specific cutting energy for a chip thickness a c : MFGE 307 THEORY OF MANUFACTURING TECHNOLOGY II 30 Power Requirement MFGE 307 THEORY OF MANUFACTURING TECHNOLOGY II 2/3/2016ME Section 05a31 Power Requirement MFGE 307 THEORY OF MANUFACTURING TECHNOLOGY II 32 Power Requirement EXAMPLE: For an orthogonal cutting operation where v= 36 m/min f= 0.25 mm/rev it was found E = 3.8 (W-sec/mm 3 ) (m/min). If the power available at the spindle = 5 hp, find the maximum metal removal rate and corresponding depth of cut. Note that 1 hp = 746 W. MFGE 307 THEORY OF MANUFACTURING TECHNOLOGY II 33 Specific Cutting Energy MFGE 307 THEORY OF MANUFACTURING TECHNOLOGY II 34 Problem 1 In an orthogonal cutting test on mild steel, the following results were obtained: a c = 0.25 mmF c = 900N a 0 = 0.75 mmF t = 450N d = 2.5 mm n = 10 0 a) Calculate the mean angle of friction on the tool rake b) Calculate the cutting ratio c) Calculate the shear angle MFGE 307 THEORY OF MANUFACTURING TECHNOLOGY II 35 Problem 2 For an orthogonal turning operation it was found that power consumption of lathe when idle = 325 W power consumption of lathe when cutting = 2580 W For the following conditions: spindle speed, N = 124 rpm;cutting speed, v = 24.5 m/min depth of cut, d = 3.8 mm;feed rate, f = 0.2 mm/rev Find: a) specific cutting energy of the work material, b) torque at the spindle, c) cutting force, d) specific cutting energy for 1 mm undeformed chip thickness assuming = 0.4. MFGE 307 THEORY OF MANUFACTURING TECHNOLOGY II 36 Problem 3 25 mm holes will be drilled on a steel workpiece, having a hardness of R c =45 {specific cutting energy, E = 77 W/(cm 3 /min)} using an HSS twist drill at the following conditions: cutting speed, v = 24.5 m/min feed rate, f = 0.2mm/rev Find: a) the motor power if the efficiency of the transmission is 85%, b) torque required.