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THEORY OF METAL MACHINING
1. Overview of Machining Technology
2. Theory of Chip Formation in Metal Machining
3. Force Relationships and the MerchantEquation
4. Power and Energy Relationships in Machining
5. Cutting Temperature
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Material Removal Processes
A family of shaping operations, the commonfeature of which is removal of material from astarting workpart so the remaining part has thedesired geometry
Machining –
material removal by a sharpcutting tool, e.g., turning, milling, drilling
Abrasive processes – material removal byhard, abrasive particles, e.g., grinding
Nontraditional processes - various energyforms other than sharp cutting tool to removematerial
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Cutting action involves shear deformation of workmaterial to form a chip
As chip is removed, new surface is exposed
Figure 21.2 (a) A cross-sectional view of the machining process, (b)tool with negative rake angle; compare with positive rake angle in (a).
Machining
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Disadvantages with Machining
Wasteful of material
Chips generated in machining are wastedmaterial, at least in the unit operation
Time consuming
A machining operation generally takes moretime to shape a given part than alternativeshaping processes, such as casting, powdermetallurgy, or forming
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Machining in Manufacturing Sequence
Generally performed after other manufacturingprocesses, such as casting, forging, and bardrawing
Other processes create the general shape
of the starting workpart Machining provides the final shape,
dimensions, finish, and special geometricdetails that other processes cannot create
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Machining Operations
Most important machining operations:
Turning
Drilling
Milling
Other machining operations:
Shaping and planing
Broaching
Sawing
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Single point cutting tool removes material from arotating workpiece to form a cylindrical shape
Figure 21.3 Three most common machining processes: (a) turning,
Turning
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Used to create a round hole, usually by means ofa rotating tool (drill bit) with two cutting edges
Figure 21.3 (b) drilling,
Drilling
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Rotating multiple-cutting-edge tool is movedacross work to cut a plane or straight surface
Two forms: peripheral milling and face milling
Figure 21.3 (c) peripheral milling, and (d) face milling.
Milling
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Cutting Tool Classification
1. Single-Point Tools
One dominant cutting edge
Point is usually rounded to form a noseradius
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
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Figure 21.4 (a) A single-point tool showing rake face, flank, and toolpoint; and (b) a helical milling cutter, representative of tools withmultiple cutting edges.
Cutting Tools
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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
For certain operations, material removalrate can be computed as
R MR = v f d
where v = cutting speed; f = feed; d =depth of cut
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Cutting Conditions for Turning
Figure 21.5 Speed, feed, and depth of cut in turning.
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Roughing vs. Finishing
In production, several roughing cuts are usuallytaken on the part, followed by one or twofinishing cuts
Roughing - removes large amounts of materialfrom starting workpart
Creates shape close to desired geometry,but leaves some material for finish cutting
High feeds and depths, low speeds
Finishing - completes part geometry
Final dimensions, tolerances, and finish
Low feeds and depths, high cutting speeds
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Machine Tools A power-driven machine that performs a
machining operation, including grinding
Functions in machining:
Holds workpart
Positions tool relative to work
Provides power at speed, feed, and depththat have been set
The term is also applied to machines thatperform metal forming operations
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Simplified 2-D model of machining that describesthe mechanics of machining fairly accurately
Figure 21.6 Orthogonal cutting: (a) as a three-dimensional process.
Orthogonal Cutting Model
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Determining Shear Plane Angle
Based on the geometric parameters of theorthogonal model, the shear plane angle canbe determined as:
where r = chip ratio, and = rake angle
sin
cos
tan r
r
1
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Figure 21.7 Shear strain during chip formation: (a) chip formationdepicted as a series of parallel plates sliding relative to each other, (b)one of the plates isolated to show shear strain, and (c) shear straintriangle used to derive strain equation.
Shear Strain in Chip Formation
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Shear Strain
Shear strain in machining can be computedfrom the following equation, based on thepreceding parallel plate model:
= tan( - ) + cot
where = shear strain, = shear planeangle, and = rake angle of cutting tool
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Figure 21.8 More realistic view of chip formation, showing shearzone rather than shear plane. Also shown is the secondary shearzone resulting from tool-chip friction.
Chip Formation
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Brittle work materials
Low cutting speeds
Large feed and depthof cut
High tool-chip friction
Figure 21.9 Four types of
chip formation in metalcutting: (a) discontinuous
Discontinuous Chip
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Ductile work materials
High cutting speeds
Small feeds anddepths
Sharp cutting edge
Low tool-chip friction
Figure 21.9 (b) continuous
Continuous Chip
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Semicontinuous -saw-toothappearance
Cyclical chip forms
with alternating highshear strain then lowshear strain
Associated withdifficult-to-machinemetals at high cuttingspeeds
Serrated Chip
Figure 21.9 (d) serrated.
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Friction force F and Normal force to friction N
Shear force F s and Normal force to shear F n
Figure 21.10 Forces inmetal cutting: (a) forcesacting on the chip inorthogonal cutting
Forces Acting on Chip
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Resultant Forces
Vector addition of F and N = resultant R Vector addition of F s and F n = 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
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Coefficient of Friction
Coefficient of friction between tool and chip:
Friction angle related to coefficient of frictionas follows:
N
F
tan
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Shear Stress
Shear stress acting along the shear plane:
sin
w t A o s
where As = area of the shear plane
Shear stress = shear strength of work materialduring cutting
s
s
A
F S
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F , N , F s , and F n cannot be directly measured Forces acting on the tool that can be measured:
Cutting force F c and Thrust force F t
Figure 21.10 Forcesin metal cutting: (b)forces acting on the
tool that can bemeasured
Cutting Force and Thrust Force
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Forces in Metal Cutting
Equations can be derived to relate the forcesthat cannot be measured to the forces that canbe measured:
F = F c sin + F t cos
N = F c cos - F t sin F s = F c cos - F t sin
F n = F c sin + F t cos
Based on these calculated force, shear stress
and coefficient of friction can be determined
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The Merchant Equation
Of all the possible angles at which sheardeformation can occur, the work material willselect a shear plane angle that minimizesenergy, given by
Derived by Eugene Merchant
Based on orthogonal cutting, but validity
extends to 3-D machining
2245
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What the Merchant Equation Tells Us
To increase shear plane angle
Increase the rake angle
Reduce the friction angle (or coefficient offriction)
2245
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Higher shear plane angle means smaller shearplane which means lower shear force, cuttingforces, power, and temperature
Figure 21.12 Effect of shear plane angle : (a) higher with aresulting lower shear plane area; (b) smaller with a correspondinglarger shear plane area. Note that the rake angle is larger in (a), whichtends to increase shear angle according to the Merchant equation
Effect of Higher Shear Plane Angle
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Power and Energy Relationships A machining operation requires power The power to perform machining can be
computed from:
P c = F c v
where P c = cutting power; F c = cutting force;and v = cutting speed
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Power and Energy Relationships In U.S. customary units, power is traditional
expressed as horsepower (dividing ft-lb/min by33,000)
where HP c = cutting horsepower, hp 00033,
v F
HP c
c
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Power and Energy Relationships Gross power to operate the machine tool P g or
HP g is given by
or
where E = mechanical efficiency of machine tool
Typical E for machine tools 90%
E
P P c g
E
HP HP c
g
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Specific Energy in Machining
Unit power is also known as the specific energy U
Units for specific energy are typicallyN-m/mm3 or J/mm3 (in-lb/in3)
w vt
v F
R
P P U
o
c
MR
c
u ===
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Cutting Temperature
Approximately 98% of the energy in machiningis converted into heat
This can cause temperatures to be very high atthe tool-chip
The remaining energy (about 2%) is retainedas elastic energy in the chip
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Cutting Temperatures are Important
High cutting temperatures1. Reduce tool life
2. Produce hot chips that pose safety hazards tothe machine operator
3. Can cause inaccuracies in part dimensionsdue to thermal expansion of work material
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Cutting Temperature
Analytical method derived by Nathan Cookfrom dimensional analysis usingexperimental data for various work materials
where T = temperature rise at tool-chipinterface; U = specific energy; v = cutting
speed; t o = chip thickness before cut; C =volumetric specific heat of work material; K =thermal diffusivity of work material
333040
..
K
vt
C
U T o
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Cutting Temperature
Experimental methods can be used to measuretemperatures in machining
Most frequently used technique is thetool-chip thermocouple
Using this method, Ken Trigger determined thespeed-temperature relationship to be of theform:
T = K v m
where T = measured tool-chip interfacetemperature, and v = cutting speed
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