1. MFGE 541 THEORY OF METAL CUTTING Chapter 2 MECHANICS OF METAL CUTTING Prof. Dr. S. Engin KILIÇ

2. MFGE 541 THEORY OF METAL CUTTING Introduction What is Machining ? Machining is a process designed to change the size, shape, and surface of a material through removal of materials that could be achieved by straining the material to fracture. MECHANISM: Metal ahead of the cutting tool is compressed. This results in the deformation or elongation of the crystal structure — resulting in shearing of the metal. Benefits Excellent dimensional tolerances External and internal geometrical features Surface finish Removal of heat treat distortion Economical for small quantities Limitations Material waste Time consuming Energy, capital and labor intensive Why Machining ?

3. MFGE 541 THEORY OF METAL CUTTING  Early research in metal cutting  Cocquilhat (1851) measured the work required to remove a given volume of material in drilling  Time (1870) and Tresca (1873) the first attempts to explain how chips are formed  Hartig (1873) tabulated the work required in cutting metals  Mallock (1881) suggested correctly that the cutting process was basically one of shearing the work material to form the chip and emphasized the importance of the effect of friction occurring on the cutting-tool face as the chip was removed. History of Metal Cutting

4. MFGE 541 THEORY OF METAL CUTTING  Taylor (1906) reported the results of 26 years of research investigations and experience in his paper “On the Art of Cutting Metals” (ASME) optimum cutting conditions (the effect of tool material and cutting conditions on tool life) tool-life equation v.t n = c HSS tools (Taylor-White tools for high speed steel cutting) tool-life / tool-wear cutting fluids History of Metal Cutting

5. MFGE 541 THEORY OF METAL CUTTING Orthogonal cutting

6. MFGE 541 THEORY OF METAL CUTTING Rake Angle Positive Rake Neutral Rake Negative Rake Workpiece Cutter Velocity Workpiece Cutter Velocity -γ ne Cutter Velocity Workpiece It is the angle that the tool makes with the plane normal to the transient surface. +γ ne

7. MFGE 541 THEORY OF METAL CUTTING ► Positive rake angles  Reduced cutting forces  Smaller deflection of work, tool holder, and machine  Considered by some to be the most efficient way to cut metal  Creates large shear angle, reduced friction and heat  Allows chip to move freely up the chip-tool zone  Generally used for continuous cuts on ductile materials which are not too hard or brittle ► Negative rake angles  Initial shock of work to tool is on the face of the tool and not on the point or edge. This prolongs the life of the tool.  Higher cutting speeds/feeds can be employed Rake Angle

8. MFGE 541 THEORY OF METAL CUTTING Terms and Definitions Cutting process: Removal of the material from the surface of the workpiece (by producing chips) ► Orthogonal cutting: (2D case) tool workpiece chip The cutting edge of the wedge-shaped tool is perpendicular to the work-tool relative motion.

9. MFGE 541 THEORY OF METAL CUTTING ► Oblique cutting: (general case) cutting edge inclination chip tool workpiece chip flow angle A single, straight cutting edge of the wedge shaped tool is inclined to the work-tool relative motion Terms and Definitions

10. MFGE 541 THEORY OF METAL CUTTING Terms and Definitions Turning operation: Turning operation: The workpiece is rotated and a cutting tool removes a layer of material as it moves parallel to the work axis TOOL acac α ne aoao WORKPIECE a c : undeformed chip thickness a o : (deformed) chip thickness γ ne : working normal rake angle α ne : working normal clearance chip (cutting) ratio r c = a c / a o γ ne Motion of workpiece Motion of chip

11. MFGE 541 THEORY OF METAL CUTTING Chip: Chip: Removed material that is separated from the parent material by fracture. Half turn or “Perfect” chip Terms and Definitions

12. MFGE 541 THEORY OF METAL CUTTING Cutting tool: Terms and Definitions

13. MFGE 541 THEORY OF METAL CUTTING There are 3 important parameters in turning operation:  Cutting speed  Depth of cut  Feed rate Cutting Speed: Cutting Speed: Cutting speed refers to the relative surface speed between tool and work, Depth of Cut: Depth of Cut: The depth of cut relates to the depth the tool cutting edge engages the work. Feed Rate: Feed Rate: The feed rate for turning is the axial advance of the tool along the work for each revolution of the work. Terms and Definitions

14. MFGE 541 THEORY OF METAL CUTTING The choice of these cutting conditions will affect the productivity of the machining operation; the life of the cutting tool; the surface finish of the workpiece; the heat generated in the cutting operation (which in turn affects the life of the tool and the surface integrity of the machined parts); the power consumption. Terms and Definitions

15. MFGE 541 THEORY OF METAL CUTTING In general, two subsequent cutting operations take place Roughing Cuts: GOAL: maximum stock removal in minimum time with minor consideration given to surface finish Finishing Cuts: GOAL: achievement of the desired shape with required surface finish Terms and Definitions

16. MFGE 541 THEORY OF METAL CUTTING Chip Formation FACTORS INFLUENCING THE CHIP FORMATION PROCESS CHIP FORMATION Work Material Properties Cutting Conditions Cutting FluidsTool Geometry Chip Control Devices Machine Tool Tool Material Properties

17. MFGE 541 THEORY OF METAL CUTTING 17 Chip Formation

18. MFGE 541 THEORY OF METAL CUTTING Chip Formation Chip formation affects  the surface finish,  cutting forces,  temperature,  tool life, and  dimensional tolerance. The chip forming process occurs by a mechanism called plastic deformation. This deformation can be visualized as shearing. The crystals of the metal elongate through an action of slipping or shearing, which takes place within the crystals and between adjacent crystals.

19. MFGE 541 THEORY OF METAL CUTTING 1) Continuous Chip 2) Continuous with Build-up Edge (BUE) 3) Discontinuous Chip 4) Segmented (serrated) Chip Types of chips: A chip consists of two sides : 1.the side in contact with the tool called shiny side (flat, uniform) due to frictional effects, 2.the other side is the free workpiece surface that has a jagged appearance due to shear. Chip Formation

20. MFGE 541 THEORY OF METAL CUTTING Continuous Chip: Continuous chips are usually formed at high rake angles and/or high cutting speeds in ductile materials e.g low carbon steel A good surface finish is generally produced. Continuous chips are not always desirable, particularly in automated machine tools, as they tend to get tangled around the tool and the operation has to be stopped to clear away the chips. Remedy: Use Chip-breakers Chip Formation

21. MFGE 541 THEORY OF METAL CUTTING BUE forms when there is a chemical affinity between workpiece and the tool. Favorable growth conditions such as high strain- hardening, low speed, large depth of cut, low rake angle, and high temperature BUE consists of layers of material from the workpiece that are gradually deposited on the tool. BUE then becomes unstable and eventually breaks up, but forms again. The process is repeated continuously. BUE material is carried away on the tool side of the chip the rest is deposited randomly on the workpiece surface. Thin and steady BUE may help improve the tool life but results in poor surface finish Continuous with Build-up Edge (BUE): Chip Formation

22. MFGE 541 THEORY OF METAL CUTTING Remedy: 1) Increase the cutting speed 2)Increase the rake angle, decrease the depth of cut 3)Use appropriate cutting fluids and coated tools Chip Formation

23. MFGE 541 THEORY OF METAL CUTTING Discontinuous Chip: During chip formation, material undergoes severe strain, and if the materişal is brittle, fracture will occur in the primary deformation zone when the chip is only partly formed. These chips occur when machining hard brittle materials such as cast iron at low rake angles (large depths of cut). Discontinuous chip formation is not necessarily detrimental to cutting performance, but is caharacteristic to the brittle material machining. It may also occur when machining ductile materials at very low speeds and high feeds. Chip Formation

24. MFGE 541 THEORY OF METAL CUTTING Remedy: 1)Increase the rake angle, decrease feed/depth of cut. 2)Use moderate cutting speed 3)Use cutting fluids and coated tools to reduce friction Chip Formation

25. MFGE 541 THEORY OF METAL CUTTING Segmented or serrated chip: Semicontinuous with zones of high and low shear strains –Occurs in metals where strength decreases sharply with temperature. e.g Titanium alloys. –Result of thermo-plastic instability and accompanied by fluctuations in cutting forces –Occurs at very high cutting speeds and in machining more difficult to machine materials –Characterisedby regions of intense shear separated by regions of material with relatively little deformation Chip Formation

26. MFGE 541 THEORY OF METAL CUTTING FORCES in TURNING Tangential (Cutting) Force Longitudinal (Thrust-Feed) Force Radial (Passive) Force Forces This acts in a direction tangential to the revolving workpiece and represents the resistance to the rotation of the workpiece. Longitudinal force acts in the direction parallel to the axis of the work and represents the resistance to the longitudinal feed of the tool. Radial force acts in a radial direction from the center line of the workpiece.

27. MFGE 541 THEORY OF METAL CUTTING Forces TOOL WORKPIECE FcFc FrFr FtFt FsFs FnFn FfFf F ns F r : resultant tool force F t : thrust force F c : cutting force F s : shear force on shear plane F ns : normal force on shear plane F f : frictional force on tool face F n : normal force on tool face β β: mean angle of friction

28. MFGE 541 THEORY OF METAL CUTTING Forces F r : resultant tool force F t : thrust force F c : cutting force F s : shear force on shear plane F ns : normal force on shear plane F f : frictional force on tool face F n : normal force on tool face TOOL WORKPIECE FcFc FrFr FtFt FsFs FnFn FfFf F ns β β: mean angle of friction

29. MFGE 541 THEORY OF METAL CUTTING Forces Influence of cutting parameters on the cutting forces

30. MFGE 541 THEORY OF METAL CUTTING The rate of energy consumption during machining P m is P m = F c. V Energy consumed per unit volume of metal removed, specific cutting energy p s is where P m = Power consumed F c = Cutting force V = Cutting speed Z w = Metal removal rate A c = Undeformed chip cross section area p s = Specific cutting energy Specific cutting energy

31. MFGE 541 THEORY OF METAL CUTTING Specific Cutting Energy Approximate energy requirements in cutting operations Specific energy MaterialW-s/mm 3 Aluminum alloys Cast irons Copper alloys High-temperature alloys Magnesium alloys Nickel alloys Refractory alloys Stainless steels Steels Titanium alloys 0.4–1.1 1.6–5.5 1.4–3.3 3.3–8.5 0.4–0.6 4.9–6.8 3.8–9.6 3.0–5.2 2.7–9.3 3.0–4.1 Specific Cutting Energy: Specific Cutting Energy: A parameter giving an indication of the efficiency of the process, independent of cutting speed, defined as the energy consumed per unit volume of removed metal

32. MFGE 541 THEORY OF METAL CUTTING Plowing force and the “size effect” Plowing force (F p ) is force acting on the tool edge and work-tool interface region due to the deformation of tool edge. F p is almost independent of a c. F r = F p + F’ r

33. MFGE 541 THEORY OF METAL CUTTING Effect of maximum undeformed chip thickness a cmax on specific cutting energy P s during slab milling where the material is steel, 57 ton/in 2. The existence of F p results important effect called “Size Effect” which refers to increase P s in at low values of a c. Size effect

34. MFGE 541 THEORY OF METAL CUTTING The apparent mean shear strength of the work materıal

35. MFGE 541 THEORY OF METAL CUTTING Shear plane TOOL φ workpiece structure chip structure 1 2 3 1 : Primary zone 2 : Secondary zone 3 : Tertiary zone φ : shear angle Shear plane

36. MFGE 541 THEORY OF METAL CUTTING The length of the shear plane is given by Shear plane Φ : Shear angle r c : Cutting Ratio(given by a c / a o ) a c : Undeformed Chip Thickness a o : Chip Thickness  ne : Working Normal Rake Angle Where:

37. MFGE 541 THEORY OF METAL CUTTING Apparent mean shear strength of work material The force F s required to shear the work material may be expressed in terms of cutting ( F c ) and thrust( F t ) force F s = (F c cos  ) – (F t sin  ) The area of shear A s is given by and thus the apparent shear strength of the material  s on the shear plane may be obtained:

38. MFGE 541 THEORY OF METAL CUTTING Apparent mean shear strength of work material Where  s is constant over a wide range of cutting condition for a given work material. However, at small feeds (f),  s increases with a decrease in feed (or a c ). This is due to the effect of plowing force. Therefore, the force required to remove the chip and acting on the tool face (F’ r ) is obtained; F’ r = F r – F p Thus, F’ c = Cutting component of F’ r F’ t = Thrust component of F’ r  ’ s = Constant property of the work material

39. MFGE 541 THEORY OF METAL CUTTING  s tends to be constant because metals deform under constant stress at high strain rates. In metal cutting strain rate is high (10 3 to 10 5 s -1 ).  s is constant if calculated by considering F r Apparent mean shear strength of work material

40. MFGE 541 THEORY OF METAL CUTTING Chıp thickness  a o  (mean friction high cutting inefficient) bad  a o  (mean friction low cutting efficient) good

41. MFGE 541 THEORY OF METAL CUTTING Theory of Ernst and Merchant

42. MFGE 541 THEORY OF METAL CUTTING Ernst and Merchant's theory suggests that  is formed up in such a way that the energy required to shear the material will be minimum. Theory of Ernst and Merchant

43. MFGE 541 THEORY OF METAL CUTTING Theory of Ernst and Merchant F s = F r cos (  +  -  ne ) where  s = shear strength of the material on the shear plane A s = Area of the shear plane A c = Area of the uncut chip  = Mean angle of the friction between chip and tool(given by arctan (F t / F n ))  ne = Working Normal Rake Angle

44. MFGE 541 THEORY OF METAL CUTTING F c = F r cos (  -  ne ) Equation may now be differentiated with respect to  and equated to zero to find the value of  for which F c is a minimum. The required value is given by Theory of Ernst and Merchant

45. MFGE 541 THEORY OF METAL CUTTING Theory of Ernst and Merchant

46. MFGE 541 THEORY OF METAL CUTTING  s =  so + k  s The results did not agree with experimental results. When differentiating F c it is assumed that  s independent of .Merchant reconsidered the assumption and he included his new assumption in his analysis: Modified Theory of Ernst and Merchant

47. MFGE 541 THEORY OF METAL CUTTING F ns = F r Sin (  +  -  ne ) Modified Theory of Ernst and Merchant

48. MFGE 541 THEORY OF METAL CUTTING Combination of these equations: Modified Theory of Ernst and Merchant

49. MFGE 541 THEORY OF METAL CUTTING This equation shows that  s =f( , ,  ne ). Finally, a new equation for F c in terms of . Modified Theory of Ernst and Merchant

50. MFGE 541 THEORY OF METAL CUTTING It is now assumed that k and  so are constant for the particular work material and that A c and  ne are constant for the cutting operation. Where C is given by arctan(k) and is a constant for the work material. Experimental work indicates that  s is constant for a given material over a wide range of cutting conditions and hence k  0 Modified Theory of Ernst and Merchant

51. MFGE 541 THEORY OF METAL CUTTING Theory of Lee and Shaffer The theory of Lee and Shaffer was the result of an attempt to apply the plasticity theory to the problem of orthogonal metal cutting.

52. MFGE 541 THEORY OF METAL CUTTING Assuptions: 1.The material is assumed to be rigid plastic 2.The behavior of the material is independent of the rate of deformation. 3.Temperature effects are neglected. 4.The inertia effects are neglected Theory of Lee and Shaffer

53. MFGE 541 THEORY OF METAL CUTTING Theory of Lee and Shaffer

54. MFGE 541 THEORY OF METAL CUTTING Fig.16 Comparison of theoretical and experimental shear-angle relationship for orthogonal metal cutting, where Φ=Shear angle,  ne =Working Normal Rake Angle,  =Mean friction angle on tool face Correlation between experimental results and theory on predicting shear angle

55. MFGE 541 THEORY OF METAL CUTTING Theories predicting shear angle AuthorsProposed Geometry Ernst&Merchant (USA 1941) Merchant (USA 1945) Stabler (Scotland 1951) Lee&Schaffer (USA 1951) Hucks (Germany 1951) Shaw&Cook&Finnie (USA 1953)

56. MFGE 541 THEORY OF METAL CUTTING Sliding friction Sticking friction Friction in metal cutting

57. MFGE 541 THEORY OF METAL CUTTING The real area of contract A r is only a small friction of the apparent contact area A a and is given by Friction in metal cutting

58. MFGE 541 THEORY OF METAL CUTTING Where F n is the normal force and σ y is the yield stress of the softer metal. The total friction F f is therefore given by Where τ f is the shear strength of the softer metal. Friction in metal cutting

59. MFGE 541 THEORY OF METAL CUTTING Friction in metal cutting

60. MFGE 541 THEORY OF METAL CUTTING Model of Chip-Tool Friction in Orthogonal Cutting Distribution of normal and shear stresses on the toolface (Zorev, 1963)

61. MFGE 541 THEORY OF METAL CUTTING It is assumed that the normal stress distribution on the tool face could be represented by the expression (Zorev, 1963) :(1963)zorv,1963 Model of Chip-Tool Friction in Orthogonal Cutting The maximum normal stress  fmax occurs when x equal l f, and therefore

62. MFGE 541 THEORY OF METAL CUTTING Model of Chip-Tool Friction in Orthogonal Cutting Combining the last two equations: In the sliding region, the distribution of shear stress  f from x = 0 to x = l f - l st is given by

63. MFGE 541 THEORY OF METAL CUTTING In the sticking region, the shear stress becomes a maximum,  st, and therefore from x = l f - l st to x = l f,  f =  st Model of Chip-Tool Friction in Orthogonal Cutting

64. MFGE 541 THEORY OF METAL CUTTING Integrating the previous expression to find the normal force F n acting on the tool face gives Model of Chip-Tool Friction in Orthogonal Cutting

65. MFGE 541 THEORY OF METAL CUTTING The friction force F f on the tool face is given by Model of Chip-Tool Friction in Orthogonal Cutting

66. MFGE 541 THEORY OF METAL CUTTING Model of Chip-Tool Friction in Orthogonal Cutting

67. MFGE 541 THEORY OF METAL CUTTING Model of Chip-Tool Friction in Orthogonal Cutting

68. MFGE 541 THEORY OF METAL CUTTING Model of Chip-Tool Friction in Orthogonal Cutting Experimentally it was found by Zorev that the term remains constant for a given material over a wide range of unlubricated cutting conditions, hence: