Simulation in Manufacturing Technology - RWTH … and Merchant 1941: force equilibrium and shear...

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Simulation in Manufacturing Technology

Lecture 8: Principles of Cutting

Prof.Dr.-Ing. Fritz Klocke

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Structure of the lecture

Introduction: Metal Cutting

The Cutting PartTool-in-Hand System

Terms at the Wedge

Chip FormationSpecification

Shear Plane Model

Machinability

Force Components

Tool Life

Surface Integrity

Chip Form

Modeling of MachiningFE- Model of Chip Formation

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The Cutting PartTool-in-Hand-System

Terms at the Wedge


Shear Plane Model

Machinability

Force Components

Tool Life

Surface Integrity

Chip Form

Modeling of MachiningFE- Model of Chip Formation

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Cutting: Machining with geometrically defined cutting edge

source: DIN 8580

Manufacturing Processes

1

primary shaping

2secondar

yshaping /forming

3

cutting

4

joining

5

coating

6changingmaterial

properties

3.2cutting with

geometricallydefinedcuttingedges

(DIN 8598-0)

major groups

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The Cutting PartTool-in-hand system

Terms at the Wedge


Shear Plane Model

Machinability

Force Components

Tool Life

Surface Integrity

Chip Form

Modeling of MachiningFE-Model of Chip Formation

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Cutting edges on the cutting part of a turning tool

shank

primary motion

feed motion

major cutting edge

major second flank

minor flank

minor cutting edge

major second face

cutting edge corner

γA

αA

α'A

S'S

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Tool and workpiece motions

chip

tool

workpiece

trace of the plane

of the flank Aa

β

trace of the plane of the face Ag

cutting speed

feed speedresultant cuttingspeed

η ϕ

trace of the plane of

the transient surface

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Tool-in-hand system

assumed workingplane Pf

cutting edgenormal plane Pn

tool cutting edgeplane Ps

tool orthogonalplane Po

tool back plane Pp

rP

nP

sPoP

tool reference plane Pr

pPrκ

cvr

fvr

fP

sλ

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Differences between reference systems

assumeddirection offeed motion

assumedworkingplane Pf

assumed directionof primary motion

tool backplane Pp

working backplane Ppe

workingplane Pfe

direction offeed motion

direction of the resultantcutting speed

tool referenceplane Pr

working referenceplane Pre

cvr ev

r

selected point onthe cutting edge

tool

-in-h

and

tool

-in-u

se

syst

em

syst

em

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Tool-in-hand system (ISO 3002)

This is the plane ofthe face Aγ.

Fix with the machine by turning,if the cutting edge is positioned

in the centre of the spindle.

assumed workingplane Pf

cutting edgenormalplane Pn

tool cutting edgeplane Ps

machine coordinatesystem

rP

nPcvr

fPrκ

nγ

x

y

z

B

A

C

(DIN EN ISO 841)

Fix with

the to

ol!

Fix

with

the

tool

!

Fi x with the

tool !

sPVa

riabl

e w

ith th

e p

roce

ss!

sλ−fvr

tool reference plane Pr

evr


Theoretical terms at the process

trace of theworking cutting edge plane

tool

nefeoe PPP ≡≡

selected point on the cutting edge

workpiece

trace of the shear plane

Φ

y

z

hr

neγ

chhr

seP

ePΦ

trace of the working reference plane reP





Terms at the Wedge

Chip Formation Specification

Shear Plane Model

Machinability

Force Components

Tool Life

Surface Integrity

Chip Form



Chip formation: types of chips I

continuous chip chip with build-up edgesegmented chip


Chip formation: types of chips II

shearing chip discontinuous chip


Chip formation: The cutting operation

source: Codron 1906

1. bring upgathering

2. split up, cracksegmentformation

3. shearing andnext bring up

4. second segmentformationand bring up

5. shearing andnext crack

6. third segmentformationand bring up

7. shearing andnext crack

…

t

F

dynamiccutting force




The Cutting PartTool-in-Hand system

Terms at the Wedge


Shear Plane Model

Machinability

Force Components

Tool Life

Surface Integrity

Chip Form



The shear plane model

shear plane

Φplastic deformation only in the shear planebiaxial stress conditionideal sharpness of the cutting edge

accounts:

realisation: the orthogonal cut

This model is acceptable, because the biaxial andthe triaxial stress condition are in neighbourhood.

All the force compo-nents are in the toolorthogonal plane Po.

tool cutting edgeangle kr= 90°tool cutting edgeinclination ls= 0°

trace of Pp


Consideration of energy

Φ⋅

=Φ

=Φ sinsin

hbAA

shear plane

vc

vchF

h

hch

model

h

x∆

s∆

Φ

sFE ∆⋅= ΦΦshear energy:

x

s

xA

sF

V

Ee

∆∆⋅=

∆⋅∆⋅

== ΦΦ

Φ

Φ

ΦΦ τspecific shear energy:

ΦF


Krystoff 1939: shear angle determination

oγ

oα

Φ−°90

3

nfo PPP ≡≡

trace of theshear plane

trace ofthe toolreferenceplane Pr

workpiece

tool

ΦF

2

( ) °=Φ+− 45oγρ

zF

y

z

oγρ −

nFΦ

major axis system

machine coordinate system

ργπ−+=Φ o4

principle of maximum shear stress


Ernst and Merchant 1941: force equilibrium and shear angle

cF

oγ

oα

fF

ΦΦFzF

γF

nFγ

nFΦ

nfo PPP ≡≡

Φ

trace of theshear plane

trace of thetool referenceplane Pr

ρ

oγρ −

workpiece tool

shear stress in the shear plane:

( )hb

FF

A

F fc

⋅

Φ⋅Φ⋅−Φ⋅==

Φ

ΦΦ

sinsincosτ

0=ΦΦ

d

dτ( )ργπ

−⋅+=Φ o2

1

4

Eugene M. Merchant


Application: theory of the ideal plastic body Lee/Shaffer (1951)

oγ

oα

B

nfo PPP ≡≡

trace of the shear plane

trace of thetool referenceplane Pr

toolworkpiece

C

A

Φ

B

A

4

π

C0=σ0=τ

Φτ η

D

Φ

ργπ

−+=Φ o4

da,

b

fc,

e

ρ⋅2σ

τ

ρη

Mohr‘s circle diagram


Shear plane model: force calculation

shear workfriction work at the face

demonstration of the total force as a function of the shear stress with consideration of:

( )0cossin γρτ

−+Φ⋅Φ⋅⋅

= Φ hbFz

By using the circle of Thales, the total force can be substitute with the two force componentscutting force and feed force. (in the orthogonal cut)

( )( ) hbF

o

ocortho ⋅⋅⋅

−+Φ⋅Φ−

= Φτλργρ

cossin

cos ( )( ) hbF

o

ofortho ⋅⋅⋅

−+Φ⋅Φ−

= Φτγργρ

cossin

sin

Calculation of the force components with a physical and theoretical background!

(advantage of analytical models)





Terms at the Wedge


Shear Plane Model

Machinability

Force Components

Tool Life

Surface Integrity

Chip Form



Force components

feed motion(tool)

fFpF

cFaF

zF

fv

cvev

cutting force

back force

total force

active force

feed force

cutting speedfeed speed

resultant cutting speed the three force componentsFc, Ff and Fp are perpendicularthe total force Fz is theirgeometrical sumback force Fp does notinfluences the power

primary motion(workpiece)


Dependencies of the force components

At the area of the roundedcorner the trend line of theforce components are notlinear!

The maxima are producedby the build up cutting edgeduring the area of lowcutting speed.

area of the roundedcorner

paf

forc

e

forc

e

forc

e

feed cutting speed depth of cut

F F F

Fc

FfFp

Fc

FfFp

Fc

Fp

Ff

cv rκ

forc

e

tool cutting edge angle

F

Fc

Fp

Ff

distribution of force


primary influence of the force components

In the theoretical cutting mechanics, the cross-sectional area was identified as primaryfactor and for the calculation the following parameters were defined:

thickness of cut hwidth of cut b

technical terms: vc, vf, ap, … theoretical terms: b, h, hch, …

technical cutting mechanics theoretical cutting mechanicsgeometrical relation

kr, ls, ao, go, …

Plagens has found a good approximation of the cutting force with a linear function of thewidth of cut (b).

),( hbfFz =

The approximation of the force components with a function of the thickness of cut h wasoften discussed and lead to empirical models:


Force approximation: empirical models

bBhbAFi ⋅+⋅⋅= ( )imii hbkF −⋅⋅= 1

1.1

linear approximation: potential approximation:

result of a curve fitcalculation of the cutting forcestatistic protectedvery precise

a theoretical reason is missingcalculation of the other forcecomponents are not protected

Schlesinger (1931)Pohl (1934)Klein (1938)Richter (1954)Hucks (1956)Thomson (1962)Altintas (1998)

Taylor (1883/1902)Fischer (1897)Friedrich (1909)Hippler (1923) Salomon(1924)Kronenberg (1927)Klopstock (1932)Kienzle (1952)

result of a curve fitfirst part has a basis ofthe shear plane theoryvery easy function

not so preciseall calculations are not so protected(low number of user)

researcher


Example: linear approximation

0 20 40 60 80 100 120 140 160 180100

200

300

400

500

600

700

800

Ac=131,69 NBc=3,98 N/µm

Af=154,71 NBf=2,48 N/µm

Kra

ft [N

]

Spanungsdicke [µm]

Fc242 Ff242 Linear Fit of Data1_Fc242 Linear Fit of Data1_Ff242

thickness of cut / µm

forc

e /

N

…..

bBhbAF iii ⋅+⋅⋅=

linear approximation:

1 2 3 4 50

100

200

300

400

500

600

vc=242 m/min

h =100 µm

Kra

ft [N

]

Zeit [s]

Fc Ff

fF

cF

time/ s

forc

e /

N

µmh 100=min

242m

vc =


Example: potential approximation

scaled force nomogram

100

1000

10000

0,1 1

thickne ss of cut h / mm

sca

led

fo

rce

Fi'

/ N

/mm

log(hB)-log(hA)

log(F‘iB)-log(F‘iA)

1'iF

A

Bei

tanei=1-mi

Otto Kienzle(1893-1969)

hbkF ii ⋅⋅=im

ii h

kk 1.1=

imii hbkF −⋅⋅= 1

1.1potential approximation:

logarithmic scale of the axes!

triangle of the slope!




The Cutting PartTool-in-hand System

Terms at the Wedge


Shear Plane Model

Machinability

Force Components

Tool Life

Surface Integrity

Chip Form



Types of wear

craterflank wear land

VBB

ABC N

αSV

KF

A

AγSV

tool

face

clearance

γA

αA

faceflank γAαA

KT

KM


Taylor’s tool life theory

tool life straight line or Taylor’s straight line

bxmy +⋅=

vcvc CvT loglogtanlog +⋅= δ vcvc k=δtan∧

vcvc CvkT logloglog +⋅=

vk

c CvT vc ⋅=

Frederick Winslow Taylor(1856-1915)

Application of the generalequation of a straight line!

Consideration of the logarithmic scale of the axes!

Standzeitdiagramm

1

10

100

10 100

Schnittgeschwindigkeit vc / m/min

Sta

nd

zeit

T /

min

vcδ

too

l lif

e

T /

min

cutting speed vc / m/min

tool life diagram


Wear diagram: flank wear

Verschleißdiagramm

0

0,1

0,2

0,3

0,4

0 5 10 15 20 25 30

tc / min

VB

/ m

m

vc=160 m/min

vc=200 m/min

vc=300 m/min

the choice of thetool life criterion

determination of the tool lifeconsideration of theboundary conditions

under fixcutting edge geometries

andcutting conditions

wear diagram


Tool life straight line

Standzeitdiagramm

1

10

100

100 1000

Schnittgeschwindigkeit / m/min

Sta

nd

zeit

/ m

in

HW - P25

determination of the cutting speed for a tool life of 15 minutes

T=15 min

min 1703,0 15

mv VB =

tool life diagram

Cutting speed / m/min

too

l lif

e

T /

min




The Cutting PartTool-in-hand System

Terms at the Wedge


Shear Plane Model

Machinability

Force Components

Tool Life

Surface Integrity

Chip Form



Engagement conditions

z

x

Pr

f/2

P1Rt

εr tRr −ε

P2

rκ

4

2frrRt −−= εε

εrf

Rt ⋅≈

8

2

Tschebyschow (1874): MillingBauer (1934): Turning

tool referenceplane Pr





Terms at the Wedge


Shear Plane Model

Machinability

Force Components

Tool Life

Surface Integrity

Chip Form



Chip forms

source: Stahl-Eisen Prüfblatt





Terms at the Wedge


Shear Plane Model

Machinability

Force Components

Tool Life

Surface Integrity

Chip Form

Modeling of MachiningFE-Model of Chip formation


FE-Model: orthogonal cut

CAD-data of the tool

material data

flow

str

ess

/ M

Pa

temperature / °Cstrain rate

stressdistributionof the tooltemperaturedistributionof the tool

results:

FE-Software

nonlinear FEmultiphysicsmodeling

plastomechaniccalculationthermodynamiccalculation

Simulation in Manufacturing Technology - RWTH … and Merchant 1941: force equilibrium and shear...

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Transcript of Simulation in Manufacturing Technology - RWTH … and Merchant 1941: force equilibrium and shear...