THEORY OF METAL MACHINING 1. 2. 3. 4. Overview of Machining Technology Theory of Chip Formation in Metal Machining Force Relationships and the Merchant Equation Cutting Temperature (Video) CNC Lathe https://www.youtube.com/watch?v=MwgobIVj4fU Material Removal Processes A family of shaping operations, the common feature of which is removal of material from a starting work part so the remaining part has the desired geometry Machining – material removal by a sharp cutting tool, e.g., turning, drilling, milling Abrasive processes – material removal by hard, abrasive particles, e.g., grinding Nontraditional processes - various energy forms other than sharp cutting tool to remove material, e.g., mechanical, electromechanical, thermal, & chemical energy forms The family tree of material removal processes Machining Cutting action involves shear deformation of work material to form a chip As chip is removed, new surface is exposed: (a) positive and (b) negative rake tools Advantages of Machining Variety of work materials can be machined Most frequently used to cut metals Variety of part shapes and special geometric features possible: Screw threads Accurate round holes Very straight edges and surfaces Good dimensional accuracy and surface finish Achieve tolerances of +/- .001 in Achieve roughness values less than 16 microinches Disadvantages of Machining Wasteful of material Chips generated in machining are wasted material At least in the unit operation Chips are usually recycled Time consuming A machining operation generally takes longer to shape a given part than alternative shaping processes such as casting and forming Machining in the Manufacturing Sequence Generally performed after other basic manufacturing processes, such as casting, forging, and bar drawing Other processes create the general shape of the starting work part Machining provides the final shape, dimensions, finish, and special geometric details that other processes cannot create Machining Operations Most important machining operations: Turning (Video) Shaping Machine Drilling https://www.youtube.com/watch?v=Omsyy-RiaqU&t=1s Milling (Video) Planing Machine https://www.youtube.com/watch?v=W8-_9ziKiao&t=1s Other machining operations: Shaping and Planing (Video) Broaching https://www.youtube.com/watch?v=rAJx-6SLdP0 Broaching (Video) Band Sawing Machine https://www.youtube.com/watch?v=AwPmhsjYuck&t=2s Sawing (Video) Circular Sawing Machine https://www.youtube.com/watch?v=mlrxKJW5i8Y&t=1s Turning Single point cutting tool removes material from a rotating workpiece to form a cylindrical shape Drilling Used to create a round hole, usually by means of a rotating tool (drill bit) with two cutting edges Milling Rotating multiple-cutting-edge tool is moved across work to cut a plane or straight surface Peripheral milling: cutter axis parallel to surface being milled Face milling: cutter axis is perpendicular to surface being milled Cutting Tool Classification 1. Single-Point Tools One dominant cutting edge Point is usually rounded to form a nose radius Turning uses single point tools 2. Multiple Cutting Edge Tools More than one cutting edge Motion relative to work achieved by rotating Drilling and milling use rotating multiple cutting edge tools Cutting Tools (a) Single-point tool showing rake face, flank, and tool point (b) Helical milling cutter, representative of tools with multiple cutting edges Machine Tool A power-driven machine that performs a machining operation, including grinding Functions in machining: Holds work part Positions tool relative to work Provides power at speed, feed, and depth that have been set The term also applies to machines that perform metal forming operations Cutting Conditions in Machining Three dimensions of a machining process Cutting speed v : primary motion Feed f : secondary motion Depth of cut d : penetration of tool below original work surface Cutting Conditions in Machining For certain operations (e.g., turning), material removal rate RMR can be computed as RMR = v f d where v = cutting speed (in/s) f = feed (in) d = depth of cut (in) RMR = removal rate (in3/s) Roughing vs. Finishing Cuts In production, several roughing cuts are usually taken on a part, followed by one or two finishing cuts Roughing - removes large amounts of material from starting work part Some material remains for finish cutting High feeds and depths, low speeds Feeds of .015 - .050 in/rev, & depths of .100 - .750 in Finishing - completes part geometry Final dimensions, tolerances, and finish Low feeds and depths, high cutting speeds Feeds of .005 - .015 in/rev, & depths of .030 - .075 in Orthogonal Cutting Model Orthogonal cutting uses a wedge-shaped tool in which the cutting edge is perpendicular to the direction of speed motion as the tool is forced into the work material Simplified 2-D model of machining that describes the mechanics of machining fairly accurately Chip Thickness Ratio Chip thickness ratio to r tc where r = chip thickness ratio to = thickness of the chip prior to chip formation tc = chip thickness after separation Chip thickness after cut is always greater than before, so chip ratio is always less than 1.0 Shear Plane Angle Based on the geometric parameters of the orthogonal model, the shear plane angle can be determined as: r cos tan 1 r sin where r = chip thickness ratio = rake angle Shear Strain Shear strain in machining can be computed from the following equation, based on the preceding parallel plate model = tan( - ) + cot where = shear strain = shear plane angle = rake angle of cutting tool Example: Orthogonal Cutting In a machining operation that approximately orthogonal cutting, the cutting tool has a rake angle α = 10°. The chip thickness before the cut to = 0.50 mm and the chip thickness after the cut tc = 1.125 mm. Calculate the shear plane angle and the shear strain in the operation. The chip thickness ratio: r = to / tc = 0.50 / 1.125 = 0.444 The shear plane angle: tan = (r cosα) / (1-r sinα) = (0.444 cos10) / (1-0.444 sin10) = 0.4738 = 25.4° The shear strain: = tan( - ) + cot = tan(25.4-10) + cot25.4 = 2.386 Actual Chip Formation More realistic view of chip formation, showing shear zone rather than shear plane Also shown is the secondary shear zone resulting from tool-chip friction Four Basic Types of Chip in Machining 1. 2. 3. 4. Discontinuous chip Continuous chip Continuous chip with Built-up Edge (BUE) Serrated chip Discontinuous Chip Brittle work materials Low cutting speeds Large feed and depth of cut High tool-chip friction Continuous Chip Ductile work materials High cutting speeds Small feeds and depths Sharp cutting edge Low tool-chip friction Continuous with Built-Up Edge Ductile materials Low-to-medium cutting speeds Tool-chip friction causes portions of chip to adhere to rake face BUE forms, then breaks off, cyclically Serrated Chip Semicontinuous - sawtooth appearance Cyclical chip forms with alternating high shear strain then low shear strain Associated with difficult-to-machine metals at high cutting speeds Forces Acting on Chip Friction force F and Normal force to friction N Shear force Fs and Normal force to shear Fn Resultant Forces Vector addition of F and N = resultant R Vector addition of Fs and Fn = resultant R' Forces acting on the chip must be in balance: R' must be equal in magnitude to R R’ must be opposite in direction to R R’ must be collinear with R Cutting Force and Thrust Force F, N, Fs, and Fn cannot be directly measured Forces acting on the tool that can be measured Cutting force Fc and Thrust force Ft Forces in Metal Cutting Equations to relate the forces: F = Fc sin + Ft cos N = Fc cos - Ft sin Fs = Fc cos - Ft sin Fn = Fc sin + Ft cos Based on these calculated force, shear stress and coefficient of friction can be determined F s As F N Shear Stress Shear stress acting along the shear plane Fs As where As = area of the shear plane As t ow sin Shear stress equals shear strength S of work material during cutting Coefficient of Friction Coefficient of friction between tool and chip F N Friction angle related to coefficient of friction as tan The Merchant Equation Of all the possible angles at which shear deformation can occur, the work material will select a shear plane angle that minimizes energy 45 2 2 Derived by Eugene Merchant Based on orthogonal cutting, but validity extends to 3-D machining To increase shear plane angle ( ) Increase the rake angle (α) Reduce the friction angle (β) or the coefficient of friction (μ) Example: Shear Stress in Machining In a machining operation that approximately orthogonal cutting, the cutting tool has a rake angle α = 10° and shear plane angle = 25.4°. The chip thickness before the cut to = 0.50 mm and the chip thickness after the cut tc = 1.125 mm. Also Fc = 1559 N and Ft = 1271 N. The width of the orthogonal cutting operation w = 3.0 mm. Determine the shear strength of the work material. The shear force: Fs = Fc cos - Ft sin = 1559(cos25.4)-1271(sin25.4) = 863 N The shear plane area: The shear stress: As = tow / sin = (0.5)(3.0) / sin25.4 = 3.497 mm2 = S = Fs / As = 863 / 3.497 = 247 N/mm2 = 247 MPa Example: Estimating Friction Angle In a machining operation that approximately orthogonal cutting, the cutting tool has a rake angle α = 10° and shear plane angle = 25.4°. Determine the friction angle and the coefficient of friction. Using the Merchant equation: The friction angle: 45 2 2 β = 2(45) + α - 2 = 2(45) + 10 – 2(25.4) = 49.2° The coefficient of friction: μ = tan β = tan(49.2) = 1.16 Effect of Higher Shear Plane Angle Higher shear plane angle with a resulting lower shear plane area Smaller shear plane angle with a corresponding larger shear plane area Cutting Temperature Approximately 98% of the energy in machining is converted into heat This can cause temperatures to be very high at the tool-chip The remaining energy (about 2%) is retained as elastic energy in the chip High cutting temperatures result in the following: Reduce tool life Produce hot chips that pose safety hazards to the machine operator Can cause inaccuracies in part dimensions due to thermal expansion of work material