machining part i - cutting theory

8/12/2019 Machining Part I - Cutting Theory

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Computer Aided Manufacturing

Learning targets

Design chip removal

manufacturing processes.

Improve manufacturing

processes

Optimize costs in machining

2




Outline

Recall of material mechanical properties

Theory of metal cutting

Cutting forces

Cutting power

3




Machining processes

Goal: to remove material to transform the raw part

into the desired geometry.

In general they are the last processes performed

on the mechanical components.

If we compare them to casting or forming,

machining processes allow to obtain: Good tolerances

Good surface finish

4




Turning

Drilling

Milling

Grinding

Other

processes

Machining processes

5




Engineering stress-strain plot

6

o A

P R

P : applied force

Ao: origi

nal area of test specimen

l : length at any point during elongation

l o: original gage length

E : modulus of elasticityo

o

l

l l e

= E e


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True stress-strain plot

7

1100-O aluminum

plotted on a log-log

scale

A

P

A: actual (instantaneous)area resisting the load

o

l

l

l

l l

l l

l

dl

o

ln)ln(0

nk




Loading & unloading

8




Flow curve for various materials

9




Elastic and perfectly plastic

Stiffness defined by E

Once Y reached, deforms

plastically at same stress

level Flow curve: K = Y , n = 0

Metals behave like this

when heated to

sufficiently hightemperatures (above

recrystallization)

10




Ductility

Ability of a material to plastically strain without fracture

Ductility measure = elongation EL

where EL: elongation; l f : specimen length at fracture; and l o: originalspecimen length

l f is measured as the distance between gage marks after two piecesof specimen are put back together.

o

o f

l

l l EL

11




Elongation

12



Computer Aided Manufacturing13

Toughness

Amount of energy per unit volume that the material

dissipates prior to fracture



Computer Aided Manufacturing14

Y

Mechanical properties

Strength

DuctilityElastic Plastic

UTS

Toughness

Malleability

Stiffness




Mechanical properties

15




Recrystallization in Metals

● Most metals strain harden at room temperature

according to the flow curve (n > 0)

● But if heated to sufficiently high temperature

and deformed, strain hardening does not occur

o Instead, new grains are formed that are free of strain

o The metal behaves as a perfectly plastic material; that

is, n = 0

16

n = 0




Temperature effect

17

Most materials display

similar temperature

sensitivity for elastic

modulus, yield strength,

ultimate strength, and

ductility.

Increasing T




Strain rate effect

18

The effect of strain rate on the

ultimate tensile strength of

aluminum.

Note that as temperatureincreases, the slope increases.

Thus, tensile strength becomes

more and more sensitive to

strain rate as temperature

increases. Source: After J. H.

Hollomon.




Machining processes

We will study:

“Orthogonal” cutting

A “simplified” process

Industrial processes

Cinematically more complex:

Turning

Drilling Milling

etc

19




Orthogonal cutting

Not much used in the real world, we study it

because:

● It is simple to describe from the cinematic

(motions) and dynamic (forces) points of

views.

● It allows us to understand the elementary

mechanism of chip formation.

● Many of the variables met in orthogonal

cutting are present in the industrial processes

(turning, milling, etc).

20




Orthogonal cutting

We have orthogonal cutting when the cinematic anddynamic variables belong to a plane.

21

Relevant Variables:

• v c = cutting speed

• b = cutting width

• hD = cutting thickness(Uncut chip thickness)

Section

plane

HKLM

Section

tool

hD

b

hD

vc




Orthogonal cutting

Uncut chip area:

22

Chip thickness: hch

Chip transversal section: AD = hD b Cutting ratio:

Chip

transversal

section

ch

D

h

hr

tool

Section

plane

vc

b

hD




The tool

The tool is composed of:

● Rake face: surface

on which the chip

flows.● Flank face: surface

looking at the

machined surface.

● Cutting edge:intersection line

between rake face

and flank.

23

Rake

Flank

Cuttingedge




The tool

Cutting angles:

Rake angle g

Between the rake face and the

normal to the cutting direction:-15° < g < 30°

Clearance (or relief) angle

Between the flank and the

direction of the cutting direction:

2° < a < 15°

Solid angle

Between rake and flank faces:

a + b + g 90

24

vc

g

b

chip

thickness




Cutting process

Part

Uncut chip

R e l a t i v e t o o

l - p a r t m o t i o n

Heat

Chip

Forces

Machined

surface

The chip removal mechanism

Associated to chip removal:

● Forces: The tool and the part

exchange the forces needed to

deform the working stock, separate

it from the part and transform it into

chip.

● Heat: Plastic deformation of theuncut chip plus the friction

between the tool and the chip

involve the generations of a large

heat amount.

26

Tool




t e m p e r a t u r e

s t r e s s e s

Stress and temperature




Temperature

28





How does the machining allowancetransforms into chip ?

29

The tool stresses the material until

this deforms plastically. With goodapproximation it can be said that the

area where the material is deformed

is a plane, called shear plane.

The deformation proceeds until the

separation between chip and part. Itis therefore the working stock that is

transformed into chip, that flows on

the tool.

Shear

plane

Chip

Shear stress





Comparison with reality

30

Shear plane




Shear zone

31

h D

h ch

v c g

b

Cutting edge

a

Shear plane Shear zone





32

Source: After M.C. Shaw, P.K. Wright, and S.

Kalpakjian.




Discontinuos chip

33

Source: After M.C. Shaw, P.K.

Wright, and S. Kalpakjian.




Continuous chip

34






Serrated (segmented) chip

35






Built Up Edge

36






Chip orientation

37

(a) tightly curled chip

(b) chip hits workpiece and breaks

(c) continuous chip moving away from workpiece

(d) chip hits tool shank and breaks off

Source: G. Boothroyd, Fundamentals of Metal Machining and Machine Tools. Copyright ©1975; McGraw-Hill

Publishing Company.




Chip breakers

38

Grooves as

chip breakers




Card deck model of chip formation

Mechanics of chip formation

39

g ++ tancot

OC

OB

OC

AO

OC

ABShear strain

Shear Strain:

b

a

g

cos

sin

ch

D

h

hr Cutting ratio

g

g

a




Mechanics of chip formation

40

ch Dc hvhv g

Since hch > hD vg < v c

From the velocity diagram:

g g g

sincoscos

vvv shc

Where v sh is the velocity at which shearing takes place in the shear plane.

g

g

cos

sin

cc

ch

D

c vr vh

h

vv

Mass continuity

90+g

gg

90g

vc

vg

vsh




Shear strain rate

41

The shear strain rate is then the ratio of

v sh to the thickness a of the sheared

element (shear zone), or:

a

v

adt

dAB

OC

AB

dt

d

dt

d sh

1

Experimental evidence indicates that a is on the order of 10-2 to

10-3 mm. This means that, even at low cutting speed, the shear

strain rate is very high, on the order of 103 to 106 s-1.

g

g

a




Shear strain rate

42

vc




Force circle

43

b : friction angle b

Between the tool and the part a force F is developed that can be

subdivided in two components according to different directions:

● rake

● shear plane

● cutting direction




F g and F gN

44

F g : force tangential to the rake plane

● F g N : force normal to the rake plane

F g = F sen b F g N = F cos b

F g

F g N

b




F c and F

f

Cutting force (F c ), parallel

to the cutting speed .

● Feed force (F f ), normal to

the cutting speed.

These forces are not known,

but they can be measured orpredicted with mathematical

models.

45

F c = F cos ( b g )

F f = F sen ( b g )F f

F c




F sh

and F shN

46

F sh = F cos ( + b g )

F shN = F sen ( + b g )

F sh: force in the shear plane

● F shN : force normal to the shear plane




Estimation of forces (theory)

47

c

sh

D

cos sen

cos

F ( )

A ( )

b g

b g

+

γ f c f c

γN c f c f

cos sen tantan

cos sen tan

F F F F F

F F F F F

g g g b

g g g

+ +

Parameters:

• g is a property of the cutting tool

• b can be estimated:

g , b , , sh

g

g

g

g

g

g

)cos(

sen)(sensen)(sensen

D

c

DD

shNsh

g b

g b g b

+

+

A

F

A

F

A

F




Estimation of forces (theory)

48

F c = F cos ( b g )

F sh = F cos ( + b g ))cos(

sh

g b +

F

F

)cos(

)cos(shc

g b

g b

+

F

F

sen

D

shshshsh

A A F

)cos(

)cos(

sen

Dshc

g b

g b

+

A

F c

sh

D

cos sen

cos

F ( )

A ( )

b g

b g

+




Estimation of shear angle

49

Cutting ratio method

ch ch chD

c

ch D D D

b l l hr

h b l l

ch ch D ch DD

c

ch D D D

b l h b l hhr

h b l h M

c

c

costan

1 sen

r

r

g

g

Chip length

Chip mass

D D D ch ch chh b l h b l

Constant chip volume:

D chb b b

Orthogonal cutting:

c

ch

sin sin

cos cos

Dh A' B

r h A' B

g g




Pijspanen model

• No strain hardening

• No Built Up Edge

• No friction on the flank

• Plastic deformation begins

when max = sh (elastic strain isnot considered)

• No friction between tool’s rake

and chip


Angle assumes a value that minimizes the shear strain g

2 2

1 1cot tan( ) 0

sen cos ( )

g g

g

+ +

24

g +

50

(g)

( -g)

a

(g)

( -g)

a

A’





Ernst & Merchant model

• No strain hardening

• No Built Up Edge

• No friction on the flank

• Constant sh

• No friction between tool’s rake and chip

• Shear angle assumes the value that minimizes the energy

51

Angle assumes a value that minimizes the energy of cutting




Ernst & Merchant model


)cos(

)cos(

sen

Dshc

g b

g b

+

A

F

H A

H F U

+

)cos(

)cos(

sen

Dshcc

g b

g b

0c

U

224

b g +

52




The cutting pressure kc is defined from the relationship:

def

c c D F k A

Cutting pressure method

kc depends on:

• AD

• Mechanical characteristics of the workpiece material

• Tool material and geometry (g in particular)

• vc

• lubrication conditions




Kronenberg relationship:

y x bh

k k cs

c

where k cs is the specific cutting pressure to remove a chip

section of 1 mm2 with h = 1 mm and b = 1 mm

Typically, y 0, thus: cs

c

x

k k

h

• k cs related to the material to machine

• k c decreases as h increases

• x costant mainly related to the tool material

Cutting pressure



Cutting with an oblique tool

In practice most of the cutting processes use oblique tools

machining part i - cutting theory

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