theory of metal 2

8/15/2019 Theory of Metal 2

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1. Overview of Machining Technology2. Theory of Chip Formation in Metal Machining

3. Force Relationships and the Merchant

Equation4. Power and Energy Relationships in Machining

5. Cutting Temperature

©2007 John Wiley & Sons, Inc. M P Groover,

Fundamentals of Modern Manufacturing 3/e


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A family of shaping operations, the commonfeature of which is removal of material from astarting workpart so the remaining part hasthe desired 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 ofwork material to form a chip

As chip is removed, new surface is exposed



(a) A cross-sectional view of the machining process, (b) tool withnegative rake angle; compare with positive rake angle in (a).

Machining


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Variety of work materials can be machined◦ Most frequently used to cut metals

Variety of part shapes and special geometricfeatures possible, such as:◦ Screw threads◦

Accurate round holes◦ Very straight edges and surfaces

Good dimensional accuracy and surface finish Generally performed after other manufacturing

processes, such as casting, forging, and bardrawing



Disadvantages

• Wasteful of material and time consuming


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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 froma rotating workpiece to form a cylindrical shape



Turning


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Used to create a round hole, usually by meansof a rotating tool (drill bit) with two cuttingedges



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



(c ) peripheral milling, and (d) face milling.

Milling


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(a) A single-point tool showing rake face, flank, and tool point; and(b) a helical milling cutter, representative of tools with multiple cutting

edges.

Cutting Tools


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Three dimensions of a machining process:◦ Cutting speed v – primary motion

◦ Feed f – secondary motion

◦ Depth of cut d – penetration of tool below originalwork surface

For certain operations, material removal rate can becomputed as

MRR = v f d

where v = cutting speed; f = feed; d = depth ofcut




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Roughing - removes large amounts ofmaterial from 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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A power-driven machine that performs amachining operation, including grinding

Functions in machining:◦ Holds workpart

◦ Positions tool relative to work

◦ Provides power at speed, feed, and depth thathave been set

The term is also applied to machines thatperform metal forming operations




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Simplified 2-D model of machining thatdescribes the mechanics of machining fairlyaccurately



Orthogonal cutting: (a) as a

three-dimensional process.

Orthogonal Cutting Model

c

o

t

tr =

chip ratio always less than 1.0

Based on the geometric parameters of the orthogonal model, theshear plane angleφ can be determined as:

α

α φ

sin

costan

r

r

−=1

where r = chip ratio, & α = rake angle


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Shear strain during chip formation: (a) chip formation depicted as a series ofparallel plates sliding relative to each other, (b) one of the plates isolated toshow shear strain, and (c) shear strain triangle used to derive strain equation.



Shear Strain in Chip Formation

γ = tan(φ -α ) + cotφ

where γ = shear strain, φ = shear plane angle, andα = rake angle of cutting tool


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1. Discontinuous chip2. Continuous chip

3. Continuous chip with Built-up Edge (BUE)

4. Serrated chip




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Ductile workmaterials

High cuttingspeeds

Small feeds anddepths

Sharp cutting edge

Low tool-chip

friction

(b) continuous



Continuous Chip


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Ductile materials Low-to-medium

cutting speeds

Tool-chip friction

causes portions ofchip to adhere torake face

BUE forms, thenbreaks off, cyclically



(c) continuous with built-upedge

Continuous with BUE


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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

©2007 John Wiley & Sons, Inc. M P Groover,Fundamentals of Modern Manufacturing 3/e


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Coefficient of friction between tool and chip:


Friction angle related to coefficient of frictionas follows:

N

F=µ

β µ tan=


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Shear stress acting along the shear plane:


φ sin

wt A os =

where As = area of the shear plane

Shear stress = shear strength of work materialduring cutting

s

s

A

FS =


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F , N , F s , and F

n cannot be directly measured

Forces acting on the tool that can bemeasured:◦ Cutting force F c and Thrust force F t


Forces in metal

cutting: (b) forces

acting on the tool that

can be measured

Cutting Force and Thrust Force


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Equations can be derived to relate the forcesthat cannot be measured to the forces thatcan be measured:

F = F c sin α + F t cos α

N = F c cos α - F t sin α

F s = F c cos φ - F t sin φ

F n = F c sin φ + F t cos φ

Based on these calculated force, shear stressand coefficient of friction can be determined



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Of all the possible angles at which sheardeformation can occur, the work material

will select a shear plane angle φ thatminimizes energy, given by

Derived by Eugene Merchant

Based on orthogonal cutting, but validity

extends to 3-D machining


2245 β α φ −+=


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To increase shear plane angle◦ Increase the rake angle

◦ Reduce the friction angle (or coefficientof friction)


2245

β α φ −+=


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Higher shear plane angle means smallershear plane which means lower shear force,cutting forces, power, and temperature


Effect of shear plane angle φ : (a) higher φ with a resulting lower shearplane area; (b) smaller φ with a corresponding larger shear planearea. Note that the rake angle is larger in (a), which tends to increaseshear angle according to the Merchant equation

Effect of Higher Shear Plane Angle


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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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Useful to convert power into powerper unit volume rate of metal cut

Called unit power , P u


MRR

P

P

c

U =

Unit power is also known as the specific energy U

wvt

vF

R

PPU

o

c

MR

c

u ===

Units for specific energy are typically

N-m/mm3 or J/mm3


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High cutting temperatures1. Reduce tool life

2. Produce hot chips that pose safety hazardsto the machine operator

3. Can cause inaccuracies in part dimensionsdue to thermal expansion of work material



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Analytical method derived by NathanCook from dimensional analysis usingexperimental data for various workmaterials


where T = temperature rise at tool-chip

interface; U = specific energy; v = cutting

speed; to = chip thickness before cut; ρ C =volumetric specific heat of work material; K =

thermal diffusivity of work material

333040

..

= K

vt

C

U

T o

ρ


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Experimental methods can be used tomeasure temperatures in machining◦ Most frequently used technique is the tool-chip

thermocouple

Using this method, Ken Trigger determinedthe speed-temperature relationship to be ofthe form:

T = K v m

where T = measured tool-chip interfacetemperature, and v = cutting speed

©2007John Wiley& Sons Inc MPGroover

theory of metal 2

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