Lecture 6 Principles of Cutting - wzl.rwth-aachen.de · Principles of Cutting Simulation Techniques...

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Principles of Cutting

Simulation 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

Seite 2 © WZL/Fraunhofer IPT

Intention of the lecture

This lecture is supposed to …

… describe the fundamental mechanisms of cutting.

… convey mechanical, thermal and chemical loads

affecting the cutting wedge.

… illustrate the resultant wear phenomena.


Chip Form 8

Surface Integrity 7

Tool Life 6

Force Components 5

Machinability 4

Shear Plane Model 3

Chip Formation 2

The Cutting Part 1

Outline


Cutting: Machining with geometrically defined cutting edge

source: DIN 8580

Manufacturing Processes

1

primary

shaping

2

secondary

shaping /

forming

3

cutting

4

joining

5

coating

6

changing

material

properties

3.2

cutting with

geometrically

defined

cutting

edges

(DIN 8598-0)

major groups

Definition (DIN 8589):

Machining is cutting, in which layers of materials

are mechanically separated from a workpiece in the

form of chips by means of a cutting tool.


Nomenclature at the wedge

tool shank

Direction of

primary motion

major cutting edge S

major flank Aa

minor flank Aa‘

minor cutting edge S‘

rake face Ag

corner radius


Tool-in-hand system (ISO 3002)

Plane of

the rake face Ag

Fix with the machine by turning,

if the cutting edge is positioned

in the centre of the spindle.

assumed working

plane Pf

tool orthogonal

plane Po

tool cutting edge

plane Ps

machine coordinate

system

rP

oPcv

fPr

ng

x

y

z

B

A

C

(DIN EN ISO 841)

sPVariable

with t

he p

rocess!

sfv

tool reference plane Pr

ev

r Tool cutting edge angle

s Tool cutting edge

inclination angle


Tool references systems (ISO 3002/1)

pP

rP

cv

fv

ev

fP assumed

working plane

tool reference plane

tool back

plane

cv

fv

ev

peP

reP

feP

working plane

working reference plane

working

back plane

Tool-in-hand system Tool-in-used system


Definition of the tool cutting edge inclination during external

cylindrical turning

Working plane

Pf

Tool reference

plane Pr

Tool cutting edge plane PS

Tool holder

Cutting insert

-

s

+

Direction of

primary motion

ap

n

Feed direction

Shoulder

Workpiece

g = 90


Process kinematics at the wedge

Idealised wedge in the

assumed working plane

The geometry of the idealised

cutting wedge is defined by

the rake angle gO, the wedge

angle bO and the clearance

angle aO

tool trace of the

plane of the

flank Aa

trace of the plane

of the rake face Ag

trace of the

tool back

plane Pp

trace of the tool

reference plane Pr

assumed working plane Pf

assumed direction

of primary motion

assumed

feed direction

tool orthogonal plane Po

gO

aO

bO


Cutting edge angle and inclination angle

Tool cutting edge angle r Tool cutting edge inclination s

trace of the

assumed

working plane

Pf tool

trace of the tool cutting

edge plane PS

trace of the

tool back

plane Pp

tool reference plane Pr

assumed feed

direction

r

re trace of the

tool reference

plane Pr tool

trace of the

assumed

working plane Pf

Tool cutting edge plane PS

major cutting edge S

assumed direction of

primary motion

s


Orientation of the cutting edge: process kinematics

free orthogonal cut Free oblique cut Non-free oblique cut

workpiece

tool

chv

cv

chip

chv

cv

workpiece

tool

chip

chv

cv

Tool cutting edge inclination

s = 0° and o = 90°

Tool cutting edge inclination s

not equal to 0°


Process kinematics at the idealised wedge

chip

trace of the plane of the flank Aa

trace of the plane

of the face Ag

trace of the plane of the

transient surface

workpiece

tool

aO

bO

gO

h

cutting

direction

The wedge geometry is

defined by the clearance

angle aO, the wedge angle bO

and the tool orthogonal rake

angle gO

The wedge penetrates the

material and causes elastic

and plastic deformations

Due to the given geometry the

deformed material is forming a

chip which flows across the

rake face



Process kinematics and rounded cutting edge radius

chip

workpiece bO

tool

rounded cutting edge rb

cv

cutting speed

fv

feed velocity

h

j

effective cutting

speed e v r In reality there are only

rounded cutting edges

The cutting edge radius is

usually measured in the

tool orthogonal plane PO

Feed direction and cutting

direction are enclosing the

feed motion angle j

The directions of effective

cutting speed and cutting

speed are enclosing the

effective cutting speed

angle h



Shearing zones in cutting processes

tool

flank Aa

face Ag

chip

workpiece

secondary

shearing zone

of the flank

primary

shearing zone secondary

shearing zone

of the face

bo

rb

Shearing is very essential

in cutting.

So-called shearing zones

might be formed.

The most important

shearing zone is called

primary shearing zone.

The zones where shearing

is caused by friction are

called secondary shearing

zones.

Under a wearless con-

sideration the secondary

shearing zone of the flank

drops out.


nach: Warn74

turning tool

shearing zone

0,1 mm

1 Primary shearing zone

2 Secondary shearing zone of the rake face

3 Seperative zone (stagnation point)

4 Secondary shearing zone of the flank

5 Preliminary deformation zone

Workpiece material: C53E

Cutting edge material: HW-P30

Cutting speed: vc = 100 m/min

Cross-section area of cut: ap x f = 2 x 0,315 mm2

cut surface

workpiece structure

cut surface

turning tool

flank face

rake face

shear

plane chip

structure

2

vc

1

5

3

4

Chip formation


Penetration of tool and work piece, cross-sectional area

workpiece

tool

rsinfh =

h

r

p

sin

ab

=

b

fv

kr

fv

A ap

f

kr

direction of rotation The cross-sectional area

is determined by the tool

cutting edge angle r , the

feed f and the depth of cut

ap

The undeformed chip

thickness h and the width

of cut b can be calculated

from the feed f and the

depth of cut ap

respectively, using the

cutting edge angle r .


Chip Form 8

Surface Integrity 7

Tool Life 6

Force Components 5

Machinability 4

Shear Plane Model 3

Chip Formation 2

The Cutting Part 1

Outline


Chip formation depending on the material behaviour

Continuous chip

1 Segmented chip

2 Shearing chip 3 Discontinuous chip 4

E0: Degree of deformation in

the shear plane

E: Elastic limit

B: Breaking limit

Z: Fraction point

Yield range

E Z B

Strain e

elastic region

plastic region Range of lamellar-

segmented and

discontinous chip

Range of

continous

chips

Degree of deformation e

e0

Sh

ear

str

en

gth

t

Sh

ear

str

en

gth

t

1

2

3 4


Chip formation for brittle material behaviour

source: Codron 1906

1. Bring up

gathering

2. Split up, crack

segment

formation

3. Shearing and

next bring up

4. Second segment

formation

and bring up

5. Shearing and

next crack

6. Third segment

formation

and bring up

7. Shearing and

next crack

…

t

F

Dynamic

cutting force


Chip Form 8

Surface Integrity 7

Tool Life 6

Force Components 5

Machinability 4

Shear Plane Model 3

Chip Formation 2

The Cutting Part 1

Outline


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 tool

orthogonal plane Po.

tool cutting edge

angle kr= 90°

tool cutting edge

inclination s= 0°

trace of PS

F


Krystoff 1939: Shear angle determination

g

= Ο F


Ernst and Merchant 1941: Force equilibrium and shear angle

cF

og

fF

F

FFzF

gF

nFg

nFF

F

trace of the

shear plane

og

workpiece tool

o a

shear plane location is determined

by the minimum for cutting energy

Φ = 𝜋

4 +

1

2 × (γ0

− ρ)

tan 𝜌 =𝐹𝛾

𝐹γ𝑛

=𝐹𝑓 cos 𝛾 + 𝐹𝑐 sin 𝛼

𝐹𝑐 cos 𝛾 − 𝐹𝑓 sin 𝛼

𝜕𝐸𝑐

𝜕ϕ= 0

𝜕2𝐸𝑐

𝜕ϕ≠ 0 nec.: suff.:

𝑙𝑐 ∙ 𝜕 𝐹𝑐

𝜕ϕ= 0

𝜕2 𝐹𝑐

𝜕ϕ≠ 0 nec.: suff.: dadf

dffsdsafd


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 components

cutting force and feed force. (in the orthogonal cut)

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

(advantage of analytical models)

𝐹𝑧 =𝜏ϕ ∙ 𝑏 ∙ ℎ

sin ϕ ∙ cos(ϕ + 𝜌 − 𝛾0)

𝐹𝑓 =sin(𝜌 − 𝛾0)

sin ϕ ∙ cos(ϕ + 𝜌 − 𝛾0)∙ 𝜏ϕ ∙ 𝑏 ∙ ℎ 𝐹𝑐 =

cos(𝜌 − 𝛾0)

sin ϕ ∙ cos(ϕ + 𝜌 − 𝛾0)∙ 𝜏ϕ ∙ 𝑏 ∙ ℎ


Chip Form 8

Surface Integrity 7

Tool Life 6

Force Components 5

Machinability 4

Shear Plane Model 3

Chip Formation 2

The Cutting Part 1

Outline


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 cutting edge

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


Chip Form 8

Surface Integrity 7

Tool Life 6

Force Components 5

Machinability 4

Shear Plane Model 3

Chip Formation 2

The Cutting Part 1

Outline


For the construction of

machine tools

For the definition of the

cutting conditions

For the evaluation of the

cutting edge stresses and the

explanations of the wear

process

For the evaluation of the

material‘s machinability

Resultant force and ist components in the cutting process

Fz: Resultant force

Fc: Cutting force

Ff: Feed force

Fp: Passive force

Fa: Active force

FD: Thrust force

vc: Cutting speed

vf: Feed velocity

ve: effective cutting speed

Fz

vc

Fc

Primary motion (Workpiece)

Direction of feed (Tool)

Fa

FD

Fp

Ff vf

ve The information about the

absolute values and the

directions of the force

components provide a basis:


Dependencies of the force components

Cutting force Fc

Feed force Ff

Passive force Fp

Feed f

Fc

Ff

Fp

Cutting speed vc

Tool cutting edge angle r

Fc

Ff

Fp

Depth of cut ap

Fc

Ff

Fp

Re

su

lta

nt

forc

e c

om

p. F

i

Re

su

lta

nt

forc

e c

om

p. F

i

Re

su

lta

nt

forc

e c

om

p. F

i

Re

su

lta

nt

forc

e c

om

p. F

i

The peaks in the cutting speed chart are traced back to the fact of built-up edge growth

The decrease in force along with increasing cutting speed is a result of the material softening

The force curves Fp and Ff have opposing trends with increasing tool cutting edge angle r, which is the angle between the main cutting edge and the direction of feed

The increase of the resultant force components dependent on the depth ap can be traced back to the higher stock removal volume


Cutting force measuring during the turning process

3-component-cutting-force-measuring-platform

Measurement Fc, Ff, Fp

0 5 10 15 20 25

Zeit [s]

-50

0

50

100

150

200

Kra

ft [N

]

Fx Vorschubkraft

Fy Passivkraft

Fz Schnittkraft

0 5 10 15 20 25

Zeit [s]

-50

0

50

100

150

200

Kra

ft [N

]

Fx Vorschubkraft

Fy Passivkraft

Fz Schnittkraft

Fo

rce

/

N

time tc / s

Fc

FP

Ff


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

𝐹𝑖 = 𝐴 ∙ 𝑏 ∙ ℎ + 𝐵 ∙ 𝑏 𝐹𝑖 = 𝑘𝑖1.1 ∙𝑏 ∙ ℎ(1−𝑚)


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

Sch

nit

tkra

ft F

c / N

Schnittkraftdiagramm

100

10000

100

Spanungsdicke h / mm

Sc

hn

ittk

raft

Fc

/ N

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

Linear system with a trend line Double logarithmic system with

a trend line

Diagram of the cutting force Diagram of the cutting force

Cu

ttin

g f

orc

e

Thickness of cut Thickness of cut

Cu

ttin

g f

orc

e


KIENZLE Equation to calculate the static cutting forces

e

bxayi =

1'loglog'log ii FhaF =

1'loglog)log( ii Fha

b

F=

1

1')( i

mi Fhb

Fi =

im

ii hbkF

=1

1.1

)(log)(log

)('log)('log1tan

AhBh

AFBFm ii

i

==e

i = c, f, p

Linear equation:

KIENZLE equation:

Chip thickness h / mm

1

45º

1

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

200

400

600

800

1000

2000

Fo

rce

Fi

W

idth

of

cu

t b

=

Fi’

/ (N

/mm

)

A

B

Fi’1= 1740 N/mm2 = ki1.1

e

mi

1 - mi = 0,7265 e


Chip Form 8

Surface Integrity 7

Tool Life 6

Force Components 5

Machinability 4

Shear Plane Model 3

Chip Formation 2

The Cutting Part 1

Outline


Tool wear

Tool wear is influenced by high contact stresses, high cutting

temperatures and relative sliding velocities

These process values depend on:

tool

and

workpiece

materials

tool

geometry

machining

parameters interface

conditions


Thermic stress – segmenting the effective work during machining

Deformation

energy

Friction

energy

Effective

Energy

WE = Fe * le

Shear energy

Cutting energy

Friction of flank face

Friction of rake face

Latent

energy

and

heat

Quelle: Vieregge

Scherarbeit

The work transformed during the machining relates with the chip width

Especially the shearing energy increases with wider chips

Friction of flank face and cutting energy are in independent of the chip width h

The energy dedicated during the machining process is nearly completely transformed into heat

The heat emerges in the primary shearing zone and the friction zone at the tool (secondary shearing zone)

Cu

t d

ista

nc

e

Eff

ec

tive

wo

rk W

e / (

m d

aN

/m) 7000

5000

4000

3000

2000

1000

Nm

Friction of rakeface

Total energy

Chip h / mm

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

Friction of flank face and cutting energy

Shearing energy


Distribution of heat and temperature in workpiece, chip and tool

600

700 650

600

400

450

500

300 310

380 ºC

130

80 500

30

Workpiece

Chip

Tool

Material: steel

Yield stress: kf = 850 N/mm2

Cutting material: HW-P20

Primary speed: vc = 60 m/min

Chip width: h = 0,32 mm

Chip angle: go= 10º

Allocation of heat in the machining zone

Source: Kronenberg, Vieregge

QWp Qchip

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


Cutting forces and chip temperatures in turning

0

100

200

300

N

500

Cu

ttin

g f

orc

e F

c

Te

mp

era

ture

Cutting speed

Aluminium Steel/ Titanium

Feed 0,25 mm 0,1 mm

Depth of cut 2 mm 1 mm


Tool wear locations

Area of high level

of stress and

temperature, i.e. of

the order of 1200°C.

Crater Wear

Built-Up Edge

Observable for

ductile materials.

Not stable,

breaks off

frequently

Flank Wear

Mainly responsible

for the resulting

surface quality

=> used as failure

criteria.

Tool

Workpiece

Chip

Tool Wear appears at three locations at the cutting tool


Wear mechanisms

The total wear at the wedge is a superposition of distinct wear mechanisms

During cutting all distinct wear mechanisms occur simultaneously

Diffusion and oxidation are dependent on the tem-perature level and occur mainly at high cutting speeds

source: Vieregge

adhesion

Adhesion

Tool W

ear

Cutting Temperature

(cutting speed, feed et al.)

High Temp

Oxidation

Abrasion

Diffusive

wear


Wear mechanisms at the wedge: adhesion

Low cutting speeds causes low contact temperatures between chip and tool. This goes along with high contact pressure.

Low contact temperatures, high contact pressure and material affinity lead to adhesion.

Adhesion at the wedge may cause built-up edges.

Built-up edges are unstable. They peel away off the edge and slide over the flank and the face periodically.

deformed

chip

built-up edge

undeformed

bulk of the

workpiece

tool

tool

built-up edge


Wear mechanisms at the wedge: abrasion

Abrasion at the wedge is

caused by hard particles in

the chip, which penetrate

into the tool material and

slide and scratch over the

face.

As a result on the face a

crater is generated.

As a result on the flank a

wear land is generated.

flank wear land

crater

face


Catastrophic failure of the wedge

If the mechanical load at

the wedge surpasses the

resistance of the cutting

material, the cutting edge

fails.

little disruptions

at the cutting edge

face

flank

crater

Chipping and break outs

at cutting edge


The cutting edge influenced by thermic overload

The cutting material may heat massively through thermic load which reduces its resistance towards mechanical stress; the cutting edge may deform plastically

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 cools down in the disruption

In order to avoid comb cracks in discontinuous cutting (e.g. during milling) the use of coolant can often be avoided

Plastic

deformation

Comb crack


Formation of comb cracks and parallel cracks during milling

Source: Lehwald, Vieregge

VB

42CrMo4+QT

Comb cracks

vc = 275 m/min

Comb and parallel cracks

GJS70 vc = 200 m/min

Heating

during the

cut

-y

Temperature

Cooling down

Tension

ten. + 0 – comp.


Wear mechanisms at the wedge: diffusion

If the temperature level of

the contact area reaches a

limit and affinity of material

is given diffusion can be

activated

The diffusion is shown by

an analogue experiment.

Here a cemented carbide

tool works on quenched

steel

During cutting only a very

short time is available for

diffusion to occur

-80 -60 -40 -20 0 20 40

Depth / µm

Ma

ss

co

nc

en

tra

tio

n / %

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

Flank Wear

Crater Wear

VB

VB: Flank wear width

KM: Crater center distance

KF: Distance from crater to edge

KB: Crater width

KT: Crater depth

KM

KF

A

A

A-A

KB

KT


A

Crater

A

Cut A-A

KT

KB

KM SVa

Evaluation of crater wear

Indicators

according to DIN

ISO 3685

Crater wear

2,50 mm

0,0

-50,0

50,0

[µm]

2,50 mm

0,0

-50,0

50,0

[µm]

Measured indicators for

the evaluation of crater

wear are the crater depth

KT, the crater centre

distance KM, the crater

width KB and the

displacement of the

cutting edge SV in face

flank direction

Weakening of the cutting

edge is a result of

massive crater wear

Danger of a cutting

edge fraction

(crater edge fracture)


Evaluation of flank wear

A distinction is drawn between the measured indicators flank wear width VB and the

displacement of the cutting edge in flank direction SVa

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

Wear chamfer at the main

cutting edge

b

Flank wear width VB

VB

B m

ax.

C B N

b/4 VB

C

VB

B

A

re

VB

N

SV

a

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


The typical course of wear

0

20

40

60

80

100

120

140

160

180

0 1 2 3 4 5 Time / min

Wid

th o

f fl

an

k w

ea

r la

nd

VB

/ µ

m

16MnCr5 (62 HRC)

CBN20

vc = 200 m/min

f = 0,08 mm

ap = 0,2 mm

I II III


Taylor Function

Frederick Winslow Taylor

(USA, 1856-1915)

Tool-life function in a double logarithmic system has

the shape of a straight line

bxmy =

T

Vvc

C

Ck

log

logtan ==

vc CvkT logloglog =

with

v

k

c CvT =Taylor-equation

(simple) T

k

c CTv = /1

Cv (ordinate intercept):

standardised tool life T for

vc = 1 m/min 1

10

100

10 10010 100

10

100

1

Tool life function (logarithmic scale)

Cutting speed

vc / (m/min)

To

ol li

fe T

/ m

in

tool-life straight

line

vc

CT Taylor-equation

(extended) apfzvc k

p

k

z

k

cvfa afvCT =

CT (abscissa intercept):

standardised cutting speed vc

for T = 1 min


Wear diagram: Flank wear

the choice of the

tool life criterion

determination of the tool life consideration of the

boundary conditions

under fixed cutting

edge geometries

and

cutting 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

Tool life diagram

Cutting speed / m/min

too

l li

fe

T /

min

min 170 3 , 0 15

m v VB

=


Tool wear modelling

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

Empirical

tool wear model

Physical

tool wear model

Tool wear modelling

Tool wear rate models Tool life equations

Model by Usui: Model by Takeyama: Model by Archard:

H

SFK

dt

dV

3

=

)T

C(

1chn

2

eCvσdt

dV

= R

E

eDvGdt

dVc

=

dV/dt = Wear volume per time

H = Hardness

F = Mechanical load

S = Cutting path

K, C1, C2, G, D = Constants

n = Normal pressure

vch = Sliding velocity

= Temperature

Abrasion + Diffusion Abhesion

Adhesion /

Abrasion


Chip Form 8

Surface Integrity 7

Tool Life 6

Force Components 5

Machinability 4

Shear Plane Model 3

Chip Formation 2

The Cutting Part 1

Outline


Source: F. Betz

Cutting

speed,

feed

Wear on

minor

flank,

overall

wear

Corner and

flank wear,

friction and

welds,

cooling

Tool geometry,

work material,

temperature,

tool material

Dynamic stiffness of

the 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

Tool

motion

Cutting

edge

Chip formation

mechanisms,

BUE

Alteration of

cut surface

Vibrations, chips,

deformation of feed

tracks

Influenced by

Factors influencing surface quality in metal cutting

Influenced by Influenced by Influenced by Influenced by


Kinematic (theoretical) depth of roughness

e

ee

=

=

r8

fR

:oder

4

frrR

2

t

22

t

The theoretical depth of roughness Rt can be

derived from the geometrical engagement

specifications and is a function of the feed and the

corner radius rε

Kr

f

Rt rε

f

2

__

rε rε-Rt

Feed f

Feed f

Dep

th o

f ro

ug

hn

ess R

t

rε = 0,4

rε = 0,8

rε = 1,2

or


Theoretical and measured depths of roughness

The illustration

demonstrates a

comparison of theoretical

and measured depths of

roughness

The divergency between

the results in the low feed

area can be traced back to

the low chip width which

grows with increasing

rounded cutting edge

radius

Source: Moll und Brammertz

4

8

12

16

20

µm

28

0,2 0,3 mm 0,6 0,4 0 0,1 0

re = 0,25

2

0,5

1

measured depth of

roughness

theoretical depth of

roughness

Dep

th o

f ro

eu

gh

ness R

t /

µm

feed f / µm


Chip tip theory

The geometrical ideal surface

profile is determined by the

kinematic depths of roughness

Rkin

Due to the material resilience

and the cutting edge wear,

material of the work piece is

being displaced which partially

springs back afterwards

Chip tips are created because of

this process

Due to the creation of chip tips

the real depth of roughness is

higher than the theoretical

kinematic depth of roughness

Rkin.

z

x

Cutting edge plane Ps

Pr

r

re

f

Rkin

apmin

Source: Brammertz, 1961

Working plane Pf


Chip Form 8

Surface Integrity 7

Tool Life 6

Force Components 5

Machinability 4

Shear Plane Model 3

Chip Formation 2

The Cutting Part 1

Outline


Evaluation criterion: Chip Formation

1 Ribbon chip

2 Snarled chip

3 Flat helical chip

4 Angular helical chip

5 Helical chip

6 Helical chip segment

7 Cylindrical helical chip

8 Spiral chips

9 Spiral chip segment

10 Discontinous chip

2 3 4 5 6 7 8 9 10 1

Unfavourable Acceptable Good Acceptable


Thanks for your attention!

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Lecture 6 Principles of Cutting - wzl.rwth-aachen.de · Principles of Cutting Simulation Techniques...

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