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Mechanics of metal cutting

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The document discusses the mechanics of metal cutting. It covers topics such as cutting models, turning forces, power and energies, tool terminology, cutting geometry, material removal rate, orthogonal and oblique cutting models, turning and facing forces, velocities, cutting forces, the merchant's circle diagram, stresses, power, specific cutting energy, and violations of orthogonal cutting models. It provides the theoretical framework for understanding metal cutting and machining processes.

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MECHANICS OF METAL CUTTING
Topics to be covered Inroduction to Machining Technology Cutting Models Turning Forces Merchants Circle Power & Energies
Elements of Metal Cutting
Heat Generation Zones (Dependent on sharpness of tool) (Dependent on ) (Dependent on 10% 30% 60%
Tool Terminology Side relief angle Side cutting edge angle (SCEA) Clearance or end relief angle Back Rake (BR),+ Side Rake (SR), + End Cutting edge angle (ECEA) Nose Radius Turning Cutting edge Facing Cutting edge
Cutting Geometry
油
Material Removal Rate
Cutting Models ORTHOGONAL GEOMETRY OBLIQUE GEOMETRY Tool workpiece Tool workpiece
Assumptions (Orthogonal Cutting Model) The cutting edge is a straight line extending perpendicular to the direction of motion, and it generates a plane surface as the work moves past it. The tool is perfectly sharp (no contact along the clearance face). The shearing surface is a plane extending upward from the cutting edge. The chip does not flow to either side The depth of cut/chip thickness is constant uniform relative velocity between work and tool Continuous chip, no built-up-edge (BUE)
Orthogonal Cutting
Turning Forces For Orthogonal Model End view section 'A'-'A' Note: For the 2D Orthogonal Mechanistic Model we will ignore the radial component F t 'A' 'A' c F
Facing Forces For Orthogonal Model End view Note: For the 2D Orthogonal Mechanistic Model we will ignore the Longitudinal component
'Turning' Terminology N is the speed in rpm D is the diameter of the workpiece is the feed (linear distance/rev) d is the depth of cut is the surface speed = DN Standard Terms Beware , for turning: In the generalized orthogonal model depth of cut (to) is f (the feed), and width of cut (w) is d (the depth of cut)
Orthogonal Cutting Model (Simple 2D mechanistic model) Mechanism: Chips produced by the shearing process along the shear plane t 0 + Rake Angle Chip Workpiece Clearance Angle Shear Angle depth of cut Chip thickness Tool Velocity V tool t c
tool Cutting Ratio (or chip thicknes ratio) t c t o ￥ A B Chip Workpiece
Experimental Determination of Cutting Ratio Shear angle may be obtained either from photo-micrographs or assume volume continuity (no chip density change): i.e. Measure length of chips (easier than thickness) w t L 0 0 0 w c L c c t
Shear Plane Length and Angle or make an assumption, such as adjusts to minimize cutting force: (Merchant) t c t o ￥ A B Chip tool Workpiece
Velocities (2D Orthogonal Model) Velocity Diagram (Chip relative to workpiece) V = Chip Velocity (Chip relative to tool) Tool Workpiece Chip V = Cutting Velocity (Tool relative to workpiece) Shear Velocity c 刻逸 V s V V s V c
Cutting Forces ( 2D Orthogonal Cutting) Free Body Diagram Generally we know: Tool geometry & type Workpiece material and we wish to know: F = Cutting Force F = Thrust Force F = Friction Force N = Normal Force F = Shear Force F = Force Normal to Shear c t s n Tool Workpiece Chip Dynamometer R R R R F c F t s F F n N F
Force Circle Diagram (Merchants Circle) R F t F c Tool F N F s F n
Results from Force Circle Diagram (Merchant's Circle)
Forces on the Cutting Tool and the workpiece Importance: Stiffness of tool holder, stiffness of machine, and stiffness of workpiece must be sufficient to avoid significant deflections (dimensional accuracy and surface finish) Primary cause: Friction force of chip up rake face + Shearing force along shear plane Cutting speed does not effect tool forces much (friction forces decrease slightly as velocity increases; static friction is the greatest) The greater the depth of cut the greater the forces on the tool Using a coolant reduces the forces slightly but greatly increases tool life
Stresses On the Shear plane: On the tool rake face:
Power Power (or energy consumed per unit time) is the product of force and velocity. Power at the cutting spindle: Power is dissipated mainly in the shear zone and on the rake face: Actual Motor Power requirements will depend on machine efficiency E (%):
Material Removal Rate (MRR)
Specific Cutting Energy (or Unit Power) Energy required to remove a unit volume of material (often quoted as a function of workpiece material, tool and process:
Specific Cutting Energy Decomposition 1. Shear Energy/unit volume (Us) (required for deformation in shear zone) 2. Friction Energy/unit volume (Uf) (expended as chip slides along rake face) 3. Chip curl energy/unit volume (Uc) (expended in curling the chip) 4. Kinetic Energy/unit volume (Um) (required to accelerate chip)
Specific Cutting Energy Relationship to Shear strength of Material SHEAR ENERGY / UNIT VOLUME FRICTION ENERGY / UNIT VOLUME APPROXIMATE TOTAL SPECIFIC CUTTING ENERGY
Relation between Pressure and Cutting velocity
Effect of Rake angle on Cutting Force
Average Unit Horsepower Values of Energy per unit volume
Typical Orthogonal Model Violations Geometry and form Violations (i.e. non zero angles of inclination, not sharp - radiused end) Shear takes place over a volume (not a line or plane) Cutting is never a purely continuous process (cracks develop in chip; material not homogeneous) 'Size Effect' - larger stresses are required to produce deformation when the chip thickness is small (statistical probability of imperfection in the shear zone) BUE - some workpiece material 'welds' to the tool face (cyclic in nature)

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Mechanics of metal cutting

  • 2. Topics to be covered Inroduction to Machining Technology Cutting Models Turning Forces Merchants Circle Power & Energies
  • 4. Heat Generation Zones (Dependent on sharpness of tool) (Dependent on ) (Dependent on 10% 30% 60%
  • 5. Tool Terminology Side relief angle Side cutting edge angle (SCEA) Clearance or end relief angle Back Rake (BR),+ Side Rake (SR), + End Cutting edge angle (ECEA) Nose Radius Turning Cutting edge Facing Cutting edge
  • 7. 油
  • 9. Cutting Models ORTHOGONAL GEOMETRY OBLIQUE GEOMETRY Tool workpiece Tool workpiece
  • 10. Assumptions (Orthogonal Cutting Model) The cutting edge is a straight line extending perpendicular to the direction of motion, and it generates a plane surface as the work moves past it. The tool is perfectly sharp (no contact along the clearance face). The shearing surface is a plane extending upward from the cutting edge. The chip does not flow to either side The depth of cut/chip thickness is constant uniform relative velocity between work and tool Continuous chip, no built-up-edge (BUE)
  • 12. Turning Forces For Orthogonal Model End view section 'A'-'A' Note: For the 2D Orthogonal Mechanistic Model we will ignore the radial component F t 'A' 'A' c F
  • 13. Facing Forces For Orthogonal Model End view Note: For the 2D Orthogonal Mechanistic Model we will ignore the Longitudinal component
  • 14. 'Turning' Terminology N is the speed in rpm D is the diameter of the workpiece is the feed (linear distance/rev) d is the depth of cut is the surface speed = DN Standard Terms Beware , for turning: In the generalized orthogonal model depth of cut (to) is f (the feed), and width of cut (w) is d (the depth of cut)
  • 15. Orthogonal Cutting Model (Simple 2D mechanistic model) Mechanism: Chips produced by the shearing process along the shear plane t 0 + Rake Angle Chip Workpiece Clearance Angle Shear Angle depth of cut Chip thickness Tool Velocity V tool t c
  • 16. tool Cutting Ratio (or chip thicknes ratio) t c t o ￥ A B Chip Workpiece
  • 17. Experimental Determination of Cutting Ratio Shear angle may be obtained either from photo-micrographs or assume volume continuity (no chip density change): i.e. Measure length of chips (easier than thickness) w t L 0 0 0 w c L c c t
  • 18. Shear Plane Length and Angle or make an assumption, such as adjusts to minimize cutting force: (Merchant) t c t o ￥ A B Chip tool Workpiece
  • 19. Velocities (2D Orthogonal Model) Velocity Diagram (Chip relative to workpiece) V = Chip Velocity (Chip relative to tool) Tool Workpiece Chip V = Cutting Velocity (Tool relative to workpiece) Shear Velocity c 刻逸 V s V V s V c
  • 20. Cutting Forces ( 2D Orthogonal Cutting) Free Body Diagram Generally we know: Tool geometry & type Workpiece material and we wish to know: F = Cutting Force F = Thrust Force F = Friction Force N = Normal Force F = Shear Force F = Force Normal to Shear c t s n Tool Workpiece Chip Dynamometer R R R R F c F t s F F n N F
  • 21. Force Circle Diagram (Merchants Circle) R F t F c Tool F N F s F n
  • 22. Results from Force Circle Diagram (Merchant's Circle)
  • 23. Forces on the Cutting Tool and the workpiece Importance: Stiffness of tool holder, stiffness of machine, and stiffness of workpiece must be sufficient to avoid significant deflections (dimensional accuracy and surface finish) Primary cause: Friction force of chip up rake face + Shearing force along shear plane Cutting speed does not effect tool forces much (friction forces decrease slightly as velocity increases; static friction is the greatest) The greater the depth of cut the greater the forces on the tool Using a coolant reduces the forces slightly but greatly increases tool life
  • 24. Stresses On the Shear plane: On the tool rake face:
  • 25. Power Power (or energy consumed per unit time) is the product of force and velocity. Power at the cutting spindle: Power is dissipated mainly in the shear zone and on the rake face: Actual Motor Power requirements will depend on machine efficiency E (%):
  • 27. Specific Cutting Energy (or Unit Power) Energy required to remove a unit volume of material (often quoted as a function of workpiece material, tool and process:
  • 28. Specific Cutting Energy Decomposition 1. Shear Energy/unit volume (Us) (required for deformation in shear zone) 2. Friction Energy/unit volume (Uf) (expended as chip slides along rake face) 3. Chip curl energy/unit volume (Uc) (expended in curling the chip) 4. Kinetic Energy/unit volume (Um) (required to accelerate chip)
  • 29. Specific Cutting Energy Relationship to Shear strength of Material SHEAR ENERGY / UNIT VOLUME FRICTION ENERGY / UNIT VOLUME APPROXIMATE TOTAL SPECIFIC CUTTING ENERGY
  • 30. Relation between Pressure and Cutting velocity
  • 31. Effect of Rake angle on Cutting Force
  • 32. Average Unit Horsepower Values of Energy per unit volume
  • 33. Typical Orthogonal Model Violations Geometry and form Violations (i.e. non zero angles of inclination, not sharp - radiused end) Shear takes place over a volume (not a line or plane) Cutting is never a purely continuous process (cracks develop in chip; material not homogeneous) 'Size Effect' - larger stresses are required to produce deformation when the chip thickness is small (statistical probability of imperfection in the shear zone) BUE - some workpiece material 'welds' to the tool face (cyclic in nature)