Principles of Cutting

7/25/2019 Principles of Cutting

1/81

WZL/Fraunhofer IPT

Principles of CuttingSimulation Techniques in Manufacturing Technology

Lecture 6

Laboratory for Machine Tools and Production Engineering

Chair of Manufacturing Technology

Prof. Dr.-Ing. Dr.-Ing. E.h. Dr. h.c. Dr. h.c. F. Klocke


2/81

Seite 1WZL/Fraunhofer IPT

Chip Form8

Surface Integrity7

Tool Life6

Force Components5

Machinability4

Shear Plane Model3

Chip Formation2

The Cutting Part1

Outline


3/81


Cutting: Machining with geometrically defined cutting edge

source: DIN 8580

Manufacturing Processes

1

primary

shaping

2secondaryshaping /

forming

3

cutting

4

joining

5

coating

6changingmaterial

properties

3.2cutting with

geometricallydefinedcuttingedges

(DIN 8598-0)

major groups

Definition (DIN 8589):Machining is cutting, in which layers of materialsare mechanically separated from a workpiece in theform of chips by means of a cutting tool.


4/81


Nomenclature at the wedge

shank

direction ofprimary motion

major cutting edge S

major flank A

minor flank A

minor cutting edge S

rake face A

corner radius


5/81


Tool-in-hand system

assumed workingplane Pf

cutting edgenormal plane Pn

tool cutting edgeplane Ps

tool orthogonal

plane Po

rP

nP

sP oP

tool reference plane Pr

r

cvr

fvr

fP

s

r Tool cutting edge angle

s Tool cutting edgeinclination


6/81


Tool-in-hand system (ISO 3002)

This is the plane ofthe rake face A.

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

in the centre of the spindle.

assumed workingplane Pf

tool orthogonalplane Po

tool cutting edgeplane Ps

machine coordinatesystem

rP

oPcv

r

fPr

n

x

y

z

B

A

C

(DIN EN ISO 841)

sPVariable

withtheprocess!

sfv

r


evr

r Tool cutting edge angle

s Tool cutting edgeinclination


7/81


Differences between reference systems

cvr

cvr

cvr

assumeddirection offeed motion

assumedworking

plane 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

rselected point onthe cutting edge

cvr

fvr

fvr


8/81


Definition of the tool cutting edge inclination during externalcylindrical turning

Working planePf

Tool referenceplane Pr

Tool cutting edge plane PS

Tool holder

Cutting insert

-

s

+

Direction of

primary motion

ap

n

Feed direction

Shoulder

Workpiece

= 90


9/81


Process kinematics at the wedge

Idealised wedge in theassumed working plane

The geometry of the idealised

cutting wedge is defined by

the rake angle O, the wedge

angle O and the clearance

angle Otool trace of the

plane of theflank A

trace of the planeof the rake face A

trace of thetool back

plane Pp

trace of the toolreference plane Pr

assumed working plane Pf

assumed direction

of primary motion

assumedfeed direction

tool orthogonal plane Po

O

O

O


10/81


Cutting edge angle and inclination angle

Tool cutting edge angle r Tool cutting edge inclination s

trace of theassumedworking planePftool

trace of the tool cuttingedge plane PS

trace of thetool backplane Pp


assumed feed

direction

r

re trace of thetool referenceplane Prtool

trace of theassumed

working plane Pf

tool cutting edge plane PS

major cutting edge S

assumed direction ofprimary motion

s


11/81


Orientation of the cutting edge: process kinematics

free orthogonal cut free oblique cut non-free oblique cut

workpiece

toolchvr

cvr

chip

chvr

cv

r

workpiece

tool

chip

chvr

cvr

Tool cutting edge inclination

s = 0and o = 90 Tool cutting edge inclination s

not equal to 0


12/81


Process kinematics at the idealised wedge

chip

trace of the plane of the flank

trace of the planeof the face A

trace of the plane of thetransient surface

workpiece

tool

h

cuttingdirection

The wedge geometry isdefined by the clearanceangle O, the wedge angle Oand the tool orthogonal rakeangle

The wedge penetrates thematerial and causes elasticand plastic deformations

Due to the given geometry thedeformed material is forming achip which flows across therake face



13/81


Process kinematics and rounded cutting edge radius

chip

workpiece

tool

rounded cutting edger

cvr

cutting speed

fvr

feed velocity

effective cuttingspeed

evr In reality there are only

rounded cutting edges

The cutting edge radius isusually measured in the

tool orthogonal plane PO

Feed direction and cuttingdirection are enclosing thefeed motion angle

The directions of effectivecutting speed and cuttingspeed are enclosing theeffective cutting speedangle



14/81


Shearing zones in cutting processes

tool

flank

face

chip

workpiece

secondaryshearing zoneof the flank

primaryshearing zone

secondaryshearing zoneof the face

r

Shearing is very essentialin cutting.

So-called shearing zonesmight be formed.

The most importantshearing zone is calledprimary shearing zone.

The zones where shearing

is caused by friction arecalled secondary shearingzones.

Under a wearless con-

sideration the secondaryshearing zone of the flankdrops out.


15/81


nach: Warn74

turning tool

shearing zone

0,1 mm

1 primary shearing zone2 secondary shearing zone of the face3 seperative zone (stagnation point)4 secondary shearing zone of the flank5 preliminary deformation zone

workpiece material: C53Ecutting edge material: HW-P30cutting speed: vc = 100 m/mincross-section area of cut: ap x f = 2 x 0,315 mm

2

cut surface

workpiece structure

cut surface

turning tool

flankrake face

shearingplane

chipstructure

2

vc

15

3

4

Chip formation


16/81


Penetration of tool and work piece, cross-sectional area

workpiece

tool

rsinfh =

h

r

p

sin

ab

=

b

fv

r

kr

fvr

A ap

f

kr

direction of rotation The cross-sectional area

is determined by the toolcutting edge angle r , the

feed f and the depth of cutap

The undeformed chipthickness h and thewidthof cut bcan be calculatedfrom the feed f and thedepth of cut aprespectively, using thecutting edge angle r .


17/81


Chip Form8

Surface Integrity7

Tool Life6

Force Components5

Machinability4

Shear Plane Model3

Chip Formation2

The Cutting Part1

Outline


18/81


Chip formation depending on the material behaviour

continuous chip1 segmented chip2 shearing chip3 discontinuous chip4

0: degree of deformation inthe shear zone

E: limit of elasticity

B: breaking limitZ: tensile strength

flow area

E ZB

elongation

elastic area

plastic areaarea of segmented,

shearing anddiscontinuous chips

area of contin-uous chips

degree of deformation

0

she

arstrength

she

arstrength

1

2

34


19/81


Chip formation for brittle material behaviour

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


20/81


Chip Form8

Surface Integrity7

Tool Life6

Force Components5

Machinability4

Shear Plane Model3

Chip Formation2

The Cutting Part1

Outline


21/81


The shear plane model

shear plane

plastic deformation only in the shear plane plane strain deformation

ideal sharpness of the cutting edge

accounts:

realisation: the orthogonal cut

All the force compo-nents are in the toolorthogonal planePo.

tool cutting edgeangle kr= 90

tool cutting edge

inclination s= 0

trace of PS


22/81


Krystoff 1939: shear angle determination

+

4

=


23/81


Ernst and Merchant 1941: force equilibrium and shear angle

cF

o

fF

FzF

F

nF

nF

trace of theshear plane

o

workpiece tool

oa

shear plane location is determinedby the minimum for cutting energy

nec.: suff.:

nec.: suff.:


24/81


Shear plane model: force calculation

shear work friction work at the face

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

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

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

(advantage of analytical models)


25/81


Chip Form8

Surface Integrity7

Tool Life6

Force Components5

Machinability4

Shear Plane Model3

Chip Formation2

The Cutting Part1

Outline


26/81


Overview: Influencing Variables on Machinability

machinability tool life

surface integrity

total force

chip form

material

workpiece

cutting material

tool

production conditions

tool type

geometry of the cuttingedge

clamping

type of the material

chemical configuration microstructure

strength property

surface treatment

geometry

surface integrity

clamping

type of the material

chemical configuration microstructure

strength property

heat treatment

production processes

engagement parameter

cooling

machine tool machine tool

machine condition


27/81


Chip Form8

Surface Integrity7

Tool Life6

Force Components5

Machinability4

Shear Plane Model3

Chip Formation2

The Cutting Part1

Outline


28/81


For the construction of

machine tools

For the definition of thecutting conditions

For the evaluation of the

cutting edge stresses and theexplanations of the wearprocess

For the evaluation of thematerials machinability

Resultant force and ist components in the cutting process

Fz: Resultant force

Fc: Cutting forceFf: Feed force

Fp: Passive force

Fa: Active force

FD: Thrust force

vc: Cutting speedvf: Feed velocityve: effective cutting speed

Fz

vc

Fc

Primary motion(Workpiece)

Direction of feed(Tool)

Fa

FD

Fp

Ffvf

ve The information about theabsolute values and thedirections of the forcecomponents provide a basis:


29/81


Dependencies of the force components

Cutting force Fc

Feed force Ff

Passive force Fp

Feed f

Fc

FfFp

Cutting speed vc

Tool cutting edge angle r

Fc

Ff

Fp

Depth of cut ap

Fc

Ff

Fp

Resultantforcecomp.Fi

Resultantforcecomp.

Fi



The peaks in the cutting speed chartare traced back to the fact of built-upedge growth

The decrease in force along withincreasing cutting speed is a result of

the material softening The force curves Fp and Ff have

opposing trends with increasing toolcutting edge angle r, which is theangle between the main cutting edge

and the direction of feed

The increase of the resultant forcecomponents dependent on the depthap can be traced back to the higherstock removal volume


30/81


Cutting force measuring during the turning process

3-component-cutting-force-measuring-platformMeasurement Fc, Ff, Fp

0 5 10 15 20 25

Zeit [s]

-50

0

50

100

150

200

Kraft[N]

Fx Vorschubkraft

Fy Passivkraft

Fz Schnittkraft

0 5 10 15 20 25

Zeit [s]

-50

0

50

100

150

200

Kraft[N]

Fx Vorschubkraft

Fy Passivkraft

Fz Schnittkraft

Force/

N

time tc / s

Fc

FPFf


31/81


Force approximation: empirical models

linear approximation: potential approximation:

result of a curve fit calculation of the cutting force

is statistically verified very precise

no theoretical basis calculation of the other force

components is not sufficiently

verified

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 fit first part is based on

the shear plane theory very easy function

not very precise calculations are not sufficiently verified

(method is not commonly used)

researchers


32/81


Correlation between the force and the undeformed chip thickness

Schnittkraftdiagramm

0

100

200

300

400

500

600

700

800

900

1000

1100

1200

1300

1400

1500

0 100 200 300 400 500 600 700 800

Spanungsdicke h / mm

SchnittkraftF

c/N

Schnittkraftdiagramm

100

10000

100


SchnittkraftF

c/N

Today you describe the problem by curve fitting on your computer!

linear system with a trend line double logarithmic system witha trend line

diagram of the cutting force diagram of the cutting force

cuttingforce

thickness of cut thickness of cut

cuttingfor

ce


33/81


Kienzle Equation to Calculate the Static Cutting Forces

bxayi +=

1'loglog'log ii FhaF +=

1'loglog)log( ii Fha

bF +=

1

1')( i

mi Fhb

Fi =

im

ii hbkF

= 1

1.1

)(log)(log

)('log)('log1tan

AhBh

AFBFm iii

==

i = c, f, p

Linear equation:

Kienzle equation:

Chip thickness h / mm

1

45

1

0,1 0,2 0,4 0,6 0,8 1,0 2,0

200

400

600

800

1000

2000

Fo

rceFi

Widthofcutb

=F

i/(N/mm)

A

B

Fi1= 1740 N/mm2 = ki1.1

mi

1 - mi = 0,7265


34/81


Chip Form8

Surface Integrity7

Tool Life6

Force Components5

Machinability4

Shear Plane Model3

Chip Formation2

The Cutting Part1

Outline


35/81


Tool wear

Tool wearis influenced by high contact stresses, high cutting

temperatures and relative sliding velocities

These process values depend on:

toolandworkpiecematerials

toolgeometry

machiningparameters

interfaceconditions


36/81


Thermic stress segmenting the effective work during machining

Deformationwork

Frictionwork

Effective

work

Shearing work

Separation work

Face flank friction

Tool flank friction

Latent

energy

andheat

Quelle: Vieregge

Scherarbeit

The work transformed during themachining relates with the chipwidth

Especially the shearing work partincreases with wider chips

Tool flank friciton and Separationwork are in independent of thechip width h

The energy dedicated during themachining process is nearlycompletely transformed into heat

The heat emerges in the primaryshearing zone and the frictionzone at the tool (secondary

shearing zone)

Cutdistanc

e

Effectivework

We/(m

daN/m

) 7000

5000

4000

3000

2000

1000

Nm

Face flank friction

Total work

Chip h / mm0 0,2 0,4 0,6 0,8 1,0

Tool flank friction and separation work

Shearing work


37/81


Distribution of heat and temperature in workpiece, chip and tool

600

700650

600

400

450

500

300310

380 C130

80500

30

Workpiece

Chip

Tool

Material: steelYield stress: kf = 850 N/mm

2

Cutting material: HW-P20

Primary speed: vc = 60 m/minChip width: h = 0,32 mmChip angle: o= 10

Allocation of heat in the machining zone

Source: Kronenberg, Vieregge

QWpQchip

Qtool

Qair

Heat flows emerging from the machining zone

Qair = Heat flow to environment

Qchip= Heat flow to chip

QWp = Heat flow to workpiece

Qtool = Heat flow to tool


38/81


Cutting forces and chip temperatures in turning

aluminium steel / titaniumfeed 0,25 mm 0,1 mmdepth of cut 2 mm 1 mm

0

100

200

300

N

500

cuttingforceFc

tem

perature

cutting speed


39/81


Area of high levelof stress and

temperature, i.e. ofthe order of 1200C.

Tool wear locations

Tool Wear

Tool Wear appears at three locationsat the cutting tool

Crater Wear

Built-Up Edge

Observable for

ductile materials.Not stable,breaks offfrequently

Flank Wear

Mainly responsiblefor the resultingsurface quality

=> used as failurecriteria.


40/81


Wear mechanisms

The total wear at thewedge is a superpositionof distinct wearmechanisms.

During cutting all distinct

wear mechanisms occursimultaneously.

Diffusion and oxidation aredependent on the tem-perature level and occurmainly at high cuttingspeeds.

source: Vieregge

adhesion

Adhesion

ToolWear

Cutting Temperature(cutting speed, feed.)

DiffusionProcesses

Oxidation

Abrasion


41/81


Wear mechanisms at the wedge: adhesion

Low cutting speedscauses low contacttemperatures betweenchip and tool. This goesalong with high contactpressure.

Low contact temperatures,high contact pressure andmaterial affinity lead toadhesion.

Adhesion at the wedgemay cause built-up edges.

Built-up edges areunstable. They peel awayoff the edge and slide over

the flank and the faceperiodically.

deformedchip

built-up edge

undeformedbulk of theworkpiece

tool

tool

built-up edge


42/81


Wear mechanisms at the wedge: abrasion

Abrasion at the wedge iscaused by hard particlesin the chip, whichpenetrate into the toolmaterial and slide andscratch over the face.

As a result on the face acrater is generated.

As a result on the flank a

wear land is generated.

flank wear land

crater

face


43/81


Catastrophic failure of the wedge

If the mechanical load atthe wedge surpasses theresistance of the cuttingmaterial, the cutting edgefails.

little disruptionsat the cutting edge

face

flank

crater

Chipping and break outs

at cutting edge

Th i d i fl d b h i l d


44/81


The cutting edge influenced by thermic overload

The cutting material may heat massively throughthermic load which reduces its resistance towardsmechanical stress; the cutting edge may deformplastically

The plastic deformation appears basically with high

speed steel Thermic alternating load may cause comb cracks at

the wedge

They appear mainly during discontinuous cuts

whereas the cutting edge heats in circuit and coolsdown in the disruption

In order to avoid comb cracks in discontinuouscutting (e.g. during milling) the use of coolant canoften be avoided

Plasticdeformation

Comb crack

F ti f b k d ll l k d i illi


45/81


Formation of comb cracks and parallel cracks during milling

Quelle: Lehwald, Vieregge

VB

42CrMo4+QT

Comb cracks

vc

= 275 m/min

Comb and parallel cracks

GJS70 vc = 200 m/min

Heating

during thecut -y

Temperature

Cooling down

Tension

ten. + 0 comp.

W h i t th d diff i


46/81


Wear mechanisms at the wedge: diffusion

If the temperature level ofthe contact area reaches alimit and affinity of materialis given diffusion can beactivated.

The diffusion is shown byan analogue experiment.Here a cemented carbidetool works on quenched

steel.

During cutting only a veryshort time is available fordiffusion to occur.

-80 -60 -40 -20 0 20 40

way / m

concentrationofmass/%

0

2

4

6

8

10

12

14

16

18

20

100

material (42CrMo4)cutting material (HT-P20)

Cr

Co

Ni

Fe

Co

Ni

Fe

Types of wear and values for the tool wear characterization


47/81


Types of wear and values for the tool wear characterization

Flank Wear

Crater Wear

VB

VB: flank wear width

KM

KM: crater center distance

KF

KF: distance from crater to edge

A

A

A-A

KT: crater depth

KB

KB: crater width

KT

Evaluation of crater wear


48/81


A

Crater

A

Cut A-A

KT

KB

KMSV

Evaluation of crater wear

Indicatorsaccording to DINISO 3685

Crater wear

2,50 mm

0,0

-50,0

50,0

[m]

2,50 mm

0,0

-50,0

50,0

[m]

Measured indicators forthe evaluation of craterwear are the crater depthKT, the crater centredistance KM, the crater

width KB and thedisplacement of thecutting edge SV in faceflank direction

Weakening of the cuttingedge is a result ofmassive crater wear Danger of a cuttingedge fraction

(crater edge fracture)

Evaluation of flank are wear


49/81


Evaluation of flank are wear

A distinction is drawn between the measured indicators flank wear width VB and thedisplacement of the cutting edge in flank direction SV

The flank wear width is refered to the cutting edge without wear

Wear chamfer

at the maincutting edge

b

Flank wear width VB

VBBmax.

C B N

b/4VBC

VBB

A

rV

BN

SV

Indicators according to DIN ISO 3685Flank wear examined with a microscope

The typical course of wear


50/81


The typical course of wear

0

20

40

60

80100

120

140

160

180

0 1 2 3 4 5time / min

Widt

hofflankwea

rlandVB/m 16MnCr5 (62 HRC)

CBN20vc = 200 m/minf = 0,08 mmap = 0,2 mm

I II III

Taylor Function


51/81


Taylor Function

Frederick Winslow Taylor(USA, 1856-1915)

Tool-life function in a double logarithmic system hasthe shape of a straight line

bxmy +=

T

Vvc

CCk

loglogtan ==

vc CvkT logloglog +=

with

v

k

c CvT =Taylor-equation(simple)

T

k

c CTv = /1

Cv (ordinate intercept):standardised tool life T forvc = 1 m/min

1

10

100

10 10010 100

10

100

1

Tool life function(logarithmic scale)

Cutting speedvc / (m/min)

Too

llifeT/min

tool-life straightline

vc

CTTaylor-equation

(extended)apfzvc k

p

k

z

k

cvfa afvCT =

CT (abscissa intercept):standardised cutting speed vcfor T = 1 min

Wear diagram: flank wear


52/81


Wear diagram: flank wear

the choice of thetool life criterion

determination of the tool lifeconsideration of theboundary conditions

under fixed cuttingedge geometries

andcutting conditions

wear diagram

Tool life straight line


53/81


Tool life straight line

Standzeitdiagramm

1

10

100

100 1000

Schnittgeschwindigkeit / m/min

S

tandzeit/min

HW - P25

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

T=15 min

tool life diagram

Cutting speed / m/min

to

ollife

T/min

min1703,015

mv VB =

Tool wear modelling


54/81


Tool wear modelling

DasBild kann zurzeitnicht angezeigtwerden.

tool life by Taylor: tool life by Hasting:

B

AT =

v

k

c CvT =

T = tool life

= temperature

k, A, B = constants

Cv = T for vc = 1 m/min

empiricaltool wear model

physicaltool wear model

tool wear modelling

tool wear rate modelstool life equations

model by Usui: model by Takeyama:model by Archard:

H

SFK

dt

dV

3

=

)T

C(

1chn

2

eCvdt

dV = R

E

eDvGdt

dVc

+=

dV/dt = wear volume per timeH = hardnessF = mechanical loadS = cutting path

K, C1, C2, G, D = constantsn = normal pressurevch = sliding velocity = temperature

Outline


55/81


Chip Form8

Surface Integrity7

Tool Life6

Force Components5

Machinability4

Shear Plane Model3

Chip Formation2

The Cutting Part1

Factors influencing surface quality in metal cutting


56/81


Source: F. Betz

cuttingspeed,

feed

wear onminor

flank,overallwear

corner andflank wear,

friction andwelds,cooling

tool geometry,work material,

temperature,tool material

dynamic stiffness ofthe system tool-work-machine tool, cutting

forces, chip formation,tool micro geometry,work material,

cutting parameter

influences on surface quality in metal cutting

kinematic roughness cutting roughness additional factors

toolmotion cutting

edge

chip formationmechanisms,

BUE

alteration ofcut surface

vibrations, chips,deformation of feed

tracks

Influenced by

g q y g

Influenced by Influenced by Influenced by Influenced by

Kinematic (theoretical) depth of roughness


57/81


( ) p g

=

=

r8fR

:oder

4

frrR

2

t

22

t

The theoretical depth of roughness Rt can bederived from the geometrical engagement

specifications and is a function of the feed and thecorner radius r

Kr

f

Rtr

f

2__

r r

-Rt

Feed f

Feed f

Depthofroughne

ssRt

r

= 0,4

r

= 0,8

r

= 1,2

or

Theoretical and measured depths of roughness


58/81


The illustrationdemonstrates acomparison of theoreticaland measured depths ofroughness

The divergency betweenthe results in the low feedarea can be traced back tothe low chip width whichgrows with increasing

rounded cutting edgeradius

Source: Moll und Brammertz

4

8

12

16

20

m

28

0,2 0,3 mm 0,60,40 0,10

r = 0,25

2

0,5

1

measured depth ofroughness

theoretical depth ofroughness

Depthof

roeughnessR

t/m

feed f / m

Chip Tip Theory


59/81


The geometrical ideal surface

profile is determined by thekinematic depths of roughnessRkin

Due to the material resilience

and the cutting edge wear,material of the work piece isbeing displaced which partiallysprings back afterwards

Chip tips are created becauseof this process

Due to the creation of chip tipsthe real depth of roughness ishigher than the theoretical

kinematic depth of roughnessRkin.

z

x

Cutting edge plane Ps

Pr

r

r

f

Rkin

apmin

Source: Brammertz, 1961

Working planePf

Outline


60/81


Chip Form8

Surface Integrity7

Tool Life6

Force Components5

Machinability4

Shear Plane Model3

Chip Formation2

The Cutting Part1

Evaluation criterion: Chip Formation


61/81


1 ribbon chips2 tangled chips3 corkscrew chips4 helical chips5 long tubular chips

6 short tubular chips7 spiral tubular chips8 spiral chips9 long comma chips10 short comma chips

2 3 4 5 6 7 8 9 101

unfavourable acceptable good acceptable


62/81


Thanks for your attention!

Gliederung


63/81


The Cutting Part1

Chip Formation2

Shear Plane Model3

Machinability4

Force Components5

Tool Life6

Surface Integrity7

Chip Form8

Cutting edges on the cutting part of a turning tool


64/81


shank

primary motion

feed motion

major cutting edge

major flank A

minor flank A

minor cutting edge

major face Ay

cutting edge corner

Standbedingungen: Schneideneingriff und Kinematik


65/81


cvr

fv

r

e

vr

peP

reP

feP

Werkzeug-Bezugssystem Wirk-Bezugssystem

nach DIN 6581

pP

rP

cvr

fvr

e

vr

fP

Pr = Grundebene

Index e = effective

The feed motion angle and the tool in use system in turning


66/81


trace of thetool-reference

plane Pr

vector of thecutting speed

vector of the

feed direction

trace of the tool-back plane Pp

O

O

vector of thecutting speed

vector of the

feed direction

trace of thetool-back plane Pp

trace of thetool-reference

plane Pr

O O

O

feed motion angle

negativ

Tool cutting edge inclination


67/81


Tool cutting edge inclination s = 0 Tool cutting edge inclination s not equal to 0

s

workpiece

tool

chvr

cvr

workpiece

tool

chip

chvr

cvr

Chip formation: types of chips I


68/81


continuous chip chip with build-up edgesegmented chip

Chip formation: types of chips II


69/81


shearing chip

Strain rates in different processes

S l ti d f ti


70/81


Super plastic deformation

Deep drawing

Warm rolling

Cold rolling

Beam and tube pulling

High speed forging

Wire pulling

Explosive deformation

Split-Hopkinson-Bar-Test

Cutting

10-510-410-310-210-110101102103104105106107 strain speeds

/ 1&

Calculation of the strain rates

h


71/81


workpiece

tool

source: Leopold

=

yxy

xyx

ij

2

22

chvr

cvr

tool

workpiece

o +

h

chh

0x

h

xF

yF

yu

chh

xu

chx 0=

=+

ch

xo

huarctan

hch

y

chx

lnh

hln

x

xln

==

=

0

+

+=

+

+

=

ho

ol

cho

och

xyln

ln

h

hln

xxln

2

2

2

2

2 0

oxy +=

strain rate

x

vxx

=&

shearing strain rate

y

vyy

=&

z

vzz

=&

x

v

y

v yxxy

+

=&

y

v

z

vzy

yz

+

=&

z

v

x

v xzzx

+

=&

strainspeed

strain tensor

The time based differentiation

delivers the strain speed!

hy lnt

=2&

=

0

2x

xln

t

chx&

Consideration of energy


72/81


shear plane

vcvch

F

h

hch

model

shear energy:

specific shear energy:

h

FFF

xD

sDx

s

xA

sF

V

Ee

D

D=

D

D== F

F

F

F

FF t

sFE D= FF

F

=

F=F

sinsin

hbAA

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

trace of the shear plane


73/81


B

trace of the shear plane

trace of thetool referenceplane Pr

toolworkpiece

C

A

4

0=0=

fc,

Mohrs circle diagram

og

oa nfo PPP

rgp -+=F o4

r2

da,

b

e

A

BC

D

h

F

Calculation of the shear angle, Hucks (1951)

T f th t l Determination of the


74/81


yr

FEy

FEz

3

n

3

1

yz

r

yr Tool

rP

ps PP

nfo PPP

zyr

zyr

1

Trace of the toolreference plane

Trace of

Trace of theshear plane

P

1,3: maximum normal stress

yzr

yr

Determination of the

directions of the maximumnormal stresses(1, 3) with Mohrs Circle

Calculation of the material

specific angle :

Calculation of the shear angle:

)2

arcsin(2

145

D

FD

=

n += )2arctan(2

11

)arctan( = 221

Dependencies of the force components


75/81


At the area of the roundedcorner the trend line of theforce components are not

linear!

The maxima are producedby the build up cutting edgeduring the area of low

cutting speed.

area of the roundedcorner

paf

force

force

force

feed cutting speed depth of cut

F F F

Fc

FfFp

Fc

FfFp

Fc

Fp

Ff

cv r

force

tool cutting edge angle

F

Fc

Fp

Ff

distribution of force

primary influence of the force components


76/81


In the theoretical cutting mechanics, the cross-sectional area was identified as primary

factor and for the calculation the following parameters were defined:

thickness of cut h width of cut b

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

technical cutting mechanics theoretical cutting mechanicsgeometrical relation

kr, ls, ao, go,

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

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

),( hbfFz =

Nomogram of the specific components of the cutting force

bxmy +=equation of the straight line:


77/81


hb

F

A

Fk iii

==

mmmm

Fk ii

111.1

=

im

ii hkk

=1.1

xx

yy

iAB

BAm

loglog

loglog

=

Kraftnomogramm

1000

10000

0,1 1


spez.

Kraftki/N/mm

ki1.1

A

B

slope of the straight line in the doublelogarithmic system:

You can determine directly the scaled specificcomponents of the cutting force divided byan area of 1 mm !

bxmy +

1.1logloglog iii khmk +=

equation of the straight line:

i.g.:

(scaling)

nomogram of the force

specificforce

thickness of cut

( ) im.ii m/hhbkF = 11

xx

yy

iAB

Bm

loglog

loglog

=

Example: potential approximation


78/81


scaled force nomogram

100

1000

10000

0,1 1

thickness of cut h / mm

scaledforce

Fi'/

N/mm

log(hB)-log(hA)

log(FiB)-log(FiA)

1'iF

A

Bi

Tan i=1-mi

potential approximation:

logarithmic scale of the axes!

triangle of the slope!

Undeformed Chip thickness h / mm

( )imii h'F'F =

11

bxay i +=

'Floghloga'Flog ii 1+=

imi

ih

kk 1.1=

imii hbkF

-= 11.1

hbkF ii =

Types of wear


79/81


craterflank wear land

VBB

ABC N

SV

KF

A

A

SV

face

flank

A

A

faceflank AA

KT

KM

Notch wear in machining of nickel base alloys

formation of a sawtooth profile


80/81


chip removal

chip lamella

flank

feed

notch wearon the face

notch wearon the flank

transverse materialflow followingupsetting of thechip lamella

transverse materialflow following

upsetting of thechip lamella

turning direction

at the edge of the chip lamellaabrasionsurface damage

cutting edge sector with- high pressures

- high temperatures- high shear stresses- high thermal and mechanicalstress gradients

- high thermal and mechanicalalternating stresses

adhesion

surface damagetribooxydation

Spanzipfeltheorie

Das geometrisch ideale


81/81


Oberflchenprofil wird durch diekinematische Rauhtiefe Rkinbeschrieben.

Aufgrund von Werkstoff-

elastizitt und Schneiden-verschlei wird im Bereich derNebenschneide Werkstoffverdrngt, der anschlieendteilweise elastisch zurckfedert.

Durch diese Effekte entstehendie sogenannten Spanzipfel.

Die tatschliche Rauhtiefe istdurch die Bildung der

Spanzipfel grer als dietheoretisch berechnetekinematische Rautiefe Rkin.

z

x

Werkzeugschneidenebene Ps

Pr

r

r

f

Rkin

apmin

Quelle: Brammertz, 1961

Werkzeugar-beitsebene Pf

Principles of Cutting

Documents

Transcript of Principles of Cutting