Lecture 07 Overview of the various cutting processes - · PDF filecontour turning workpiece...

100
© WZL/Fraunhofer IPT Cutting Processes Simulation Techniques in Manufacturing Technology Lecture 7 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

Transcript of Lecture 07 Overview of the various cutting processes - · PDF filecontour turning workpiece...

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Cutting Processes

Simulation Techniques in Manufacturing Technology

Lecture 7

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

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Aim of the lecture

This lecture is supposed to…

…give a general understanding of selected techniques of

machining with geometrically defined cutting edge.

…teach the characteristics and range of application of the

principles of manufacturing technologies.

…illustrate the characterizations of the different

manufacturing processes

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Modeling of Machining 5

Hard machining 4

Cutting processes with parallel translation 3

Cutting processes with rotary motion 2

Introduction 1

Outline

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Classification of manufacturing processes according to DIN 8580

Processes with translational primary movement

Processes with rotational primary movement

Manufacturing processes

Primary

Shaping Forming Separation Joining Coating

Change

material

characteristics

Cutting with

geometrically

defined cutting

edges

Cutting with

geometrically

undefined cutting

edges

Removal

operations Disassembling Cleaning Severing

Scraping,

chiseling

Brushlike

tools

Filing,

Rasping Turning

Drilling,

Reaming Milling

Planing,

Shaping Broaching Sawing

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Classification of processes with rotational primary movement

Turning

– Workpiece

rotation

– Tool translation

Milling

– Tool rotation

– Workpiece

translation

Drilling

– Tool rotation

– Workpiece

translation

Sawing

– Tool rotation

– Workpiece

translation

Primary movement

Subsidiary

movement

Primary movement Primary movement Primary movement

Sub. movement Sub. movement Sub. movement

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Classification of processes with translational primary movement

Workpiece Tool vA= vc

vr

f

Broaching

– multi teeth tool

– tool geometry implies

feed

– high cutting ability

– high surface quality

– high accuracy

– high tool costs

– inflexible

Planing

– cutting motion by work

piece

– tool feed

– stepwise, linear cutting

motion

– successive feed movement

– machining of large, planar

areas

Shaping

– cutting motion by tool

– workpiece feed

– stepwise, linear cutting

motion

– successive feed movement

– machining of large, planar

areas

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Modeling of Machining 5

Hard machining 4

Cutting processes with parallel translation 3

Drilling 2.3

Milling 2.2

Turning 2.1

Cutting processes with rotary motion 2

Introduction 1

Outline

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Modeling of Machining 5

Hard machining 4

Cutting processes with parallel translation 3

Drilling 2.3

Milling 2.2

Turning 2.1

Cutting processes with rotary motion 2

Introduction 1

Outline

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Turning of steel

vc = 200 m/min

f = 0.6 mm

ap = 5.0 mm

Ck 45

Source: ISCAR

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High speed filming of turning process

r = 102°

f = 0.35 mm

ap = 1.5 mm

Ck 45

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Turning processes (DIN 8589-1)

Turning DIN 8589-1

Face

Turning

Cylindrical

Turning

Helical

Turning

Form

Turning

Hob

Turning

Profile

Turning

tool

workpiece

tool tool tool tool tool

Getriebe

Source: Iscar, Seco, Sandvik Coromant, Lingenhöle

workpiece workpiece workpiece workpiece workpiece

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Face turning (Parting off)

Source: ISCAR

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Rough turning

Source: Widia

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Finish turning

Source: Widia

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Terms at the cutting edge

tool shank

cutting direction

major cutting edge S

major flank face Aa

minor flank face Aa‘

minor cutting edge S‘

rake face Ag

corner radius

feed direction

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Tool reference systems

cv

fv

ev

peP

reP

feP

nach DIN 6581

pP

rP

cv

fv

ev

fP

Pr = Tool reference plane

Pf = Assumed Working plane

PP = Tool back plane

Tool in hand system Tool in use system

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Definition of the tool cutting edge angle r

Tool reference plane Pr

Tool orthogonal plane Po

Tool cutting edge plane Ps

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Definition of tool cutting edge angle r

r

f rε

Direction of feed

Tool orthogonal plane Po

Tool cutting edge plane PS

Working plane Pf

Tool

Workpiece

Tool reference plane Pr

ap

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Definition of the inclination angle ls

Working plane Pf

Tool cutting

edge plane Ps

Tool reference

plane Pr

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Definition of the inclination angle for longitudinal cylindrical turning

Working plane Pf

Tool reference

plane Pr

Tool cutting edge plane PS

Tool holder

Cutting insert

-

ls

+

Cutting direction

ap

n

Feed direction

Shaft

Workpiece

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Definition of the tool orthogonal rake angle g

Tool orthogonal plane Po

Tool reference plane Pr

Tool cutting edge Ps

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Process kinematics at the idealised wedge

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

Chip

Flank face Aa

Rake face Ag

Cutting surface

Workpiece

Tool

ao

bo

go

h Cutting

direction

ao + bo + go = 90

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Penetration of tool and workpiece: Cross-sectional area

Workpiece

Tool

r

p

sin

ab =

b

fv

kr

fv

A ap

f

kr

Direction of rotation

rsin= fh

h

Tool cutting edge angle r

Depth of cut ap

Feed f

Width of b

undeformed chip

Undeformed h

chip thickness

Cross section of

undeformed chip A

hbfaA == p

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Tool variants in longitudinal cylindrical turning

right hand

side cutting

left hand

side cutting

neutral

Feed direction Source: ISCAR

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Facing (DIN 8589-1: ON 3.2.1.1)

Source: Sandvik Coromant

tool

Cross face turning

tool

workpiece

Longitudinal face turning

tool

Cross parting off

workpiece workpiece

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Facing (DIN 8589-1: ON 3.2.1.1): cross / longitudinal face turning

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Facing (DIN 8589-1: ON 3.2.1.1): cross parting off

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Cylindrical turning (DIN 8589-1: ON 3.2.1.2)

n

n

f f

vc n

f

n

f

Source: Iscar, Ceratizit

Longitudinal-

cylindrical turning

Cross-cylindrical

turning

Centreless rough turning

Workpiece

Tool

Tool

Workpiece

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Helical turning (DIN 8589-1: ON 3.2.1.3)

Thread turning Thread chasing Gewindedrehen (außen)

Gewindedrehen (innen)

n

f

n

f

Source: ISCAR Sandvik

outer

Inner

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Profile turning (DIN 8589-1: ON 3.2.1.5)

Source:

Trepanning Grooving

tool

workpiece

Cross-profile turning

workpiece

tool tool

workpiece

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Contour turning (DIN 8589-1: ON 3.2.1.6)

Source: Sandvik Coromant

Copy turning

tool

workpiece

reference formed part

Kinematic

contour turning

workpiece

tool gear

NC contour turning

NC tool

workpiece

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Internal turning

Skimming

tool

workpiece

Undercut

tool

workpiece

Cut in

workpiece

tool

f

f

f

n n n

Source: Lach-Diamant, Iscar, Boehlerit

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Internal turning tools

Source: Sandvik

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Modeling of Machining 5

Hard machining 4

Cutting processes with parallel translation 3

Drilling 2.3

Milling 2.2

Turning 2.1

Cutting processes with rotary motion 2

Introduction 1

Outline

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Face milling (DIN 8589-3: ON 3.2.3.1)

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Face milling (DIN 8589-3: ON 3.2.3.1)

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Profile

milling

Milling processes (DIN 8589-3)

Milling

Face

milling

Circular

milling

Form

milling

Helical

milling

Hob

milling

workpiece

Source: Sandvik Coromant, Walter, Fette, Milltech, Seco, Gleason

tool tool tool tool tool tool

workpiece workpiece workpiece workpiece workpiece

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Slab milling: face and peripheral milling

Source: Sandvik Coromant

Face milling

– Workpiece surface is created with the

face plane

Peripheral milling

– Workpiece surface is created with the

peripheral plane

Workpiece

Tool

r

sP

pa

n

zf

fv

Tool

fv

zf

eacv

n

Workpiece

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vf vf

Up and down milling

ae

fz n

Fc

Down milling

vc

Up milling

fz n

Fc

Chip

vc

Down

milling

Up

milling

Ploughing ▼ ▲

Surface quality ▲ ▼

Chatter ▼ ▲

Clamping forces ▼ ▲

Up milling part

Down milling part

n n n n

Up- and down milling

vf

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Tool-in-hand system: Face milling

trace of the

entrance plane

workpiece

tool

trace of

trace of

trace of

trace of

n

fvo P

f P

E w

c w

A w

e a

r P z f

p a

r

s P

p P

n

z f

νf

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Tool-in-hand system: Peripheral milling

workpiece

tool

trace of

trace of Pr

p s P P

o f P P

E A c

E

w w w

w

- =

= 0

f v

z f

c v

e a

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Contact conditions and cutting edge geometry in face milling

ae

ae2

C

ae1

entry plane

vc

vf

s

n

fz

φ=0

tangential plane

cutting C-C

C A -eA

+eE

n

A tool

contact types

U T

Sb

gp

K

S Sa V Va

tool cutting edge

A

fz

ap b B

plane B-B

B

n

2D

a arccos ei

i =

sin

ab

p=

rsinsin

zfh

=

(fz << D)

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Precision milling operations

ap

ap

ap1

ap2

fz

fzfz2

fz1

ap

ap

ap1

ap2

fz

fzfz2

fz1

Finish milling

no. of teeth: 10 to 60

ap = 0.3 bis 1 mm

fz = 0.3 bis 0.5 mm

no. of teeth: 1 to 6

Wide finish milling

ap = 0.05 to 0.2 mm

fz = 0.5 bis 6 mm

fz2 = 2 to 5 mm

Finish milling with planing knives

and wide finishing cutting edge no. of planing knives: 20 to 30

no. of wide finishing cutting edges: 1 to 2

finishing

cutting edges

wide finishing

cutting edges

ap1 = 0.5 to 2 mm

fz1 = 0.1 to 0.3 mm

ap2 = 0.03 to 0.05 mm

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Indexable end mills

Source: Coromant Sandvik, Seco

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Inserted tooth milling cutter

Source: Coromant Sandvik, Seco-Tools

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Example of use: Blisk (Blade Integrated Disk)

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Circular milling (DIN 8589-3: ON 3.2.3.2)

vf

ap nw

nF

Mill

radial cutting edges

nF

nW

additional axial cutting edges

chipping space

workpiece

nw

nF

vf

tool

workpiece

workpiece

tool

Source: Walter

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A B C D E F

Helical milling (DIN 8589-3: ON 3.2.3.3)

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Hob milling

Source: WZL,Gleason

vc

fa

fw

rotation

of hub

radial feed axial feed rotation of

workpiece

vc: Cutting speed

fa: Axial feed

fw: Hob feed

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Different hob types

Source: Fette, Saazor, Saacke

Solid steel hob Indexable cutter Inserted blade hob

High rotational speeds

Short milling times

Short setting distance

High material removal rates

Roughing and Finishing

Easy regrinding

Large gear diameters

and modules

No regrinding

Relatively low accuracy

Roughing

Large gear diameters

and modules

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Profile milling (DIN 8589-3: ON 3.2.3.5)

Source: Sandvik Coromant, Ingersoll, Alesa, Seco

Profile milling cutter Gang milling cutter

tool

workpiece

workpiece

workpiece

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Form milling (DIN 8589-3: ON 3.2.3.6)

Source: Milltech, Dalscheid

tool

worpiece

Form profile milling

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Modeling of Machining 5

Hard machining 4

Cutting processes with parallel translation 3

Drilling 2.3

Milling 2.2

Turning 2.1

Cutting processes with rotary motion 2

Introduction 1

Outline

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Example of gun drilling

Source: Widia

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Example of gun drilling

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Drilling processes DIN 8589-2

Drilling, Countersinking, Reaming

Spot facing Centre drilling Tapping Profile drilling Form drilling

tool

workpiece

tool tool tool tool

workpiece workpiece workpiece workpiece

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Criteria for drilling

Material separation and reaming at the major

cutting edge

Plastic deformation at the chisel edge

Cutting speed drops down to zero in the centre

of the drill

Chips are difficult to remove

Unfavourable heat distribution at the interface

Increased wear at the sharp-edged corner

Reaming between leading lands and drilling wall

Source:

n

f friction

friction

workpiece plastic

deformation

material

separation

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cutting part plunge (lettering point)

tapered shaft

flat tang

point length

cutting length

flute length

total length

cone length

plunge length drill

dia

mete

r d

Geometry of the cutting part of a twist drill (DIN 8589-2)

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Major clearance angle: a = 10°

Twist angle: d = 35°

Cutting material: HW-K20

Grain size: DK = 0.5 – 0.7 µm

Construction dimensions DIN 6539

Type: N

Diameter: d = 1 mm

Drill-point angle: s = 118°

Geometry at the cutting edge of a twist drill

Querschneide

Freifl ä che

Hauptschneide a

d

chisel edge

flank face

major cutting edge a

d

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Cutting conditions dependent on drill diameter

40° 30° 20° 10° 0° -10° -20° -30° -40° -50° -60°

20 10 0 cutting speed vc in m/min

Rake angle g and candlearance angle a

drill

radiu

s r

1

0

in m

m

4

6

8

10

9

7

5

main

cuttin

g e

dge

chis

el edge

vc gfe afe

2

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Fundamental kinematics: Centre drilling

b

g

gf

a axe

h

f/2 f

cutting direction

effective direction feed direction

cutting edge 1

cutting edge 2

h

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Fundamental kinematics: Centre drilling

trace of

trace of

trace of

fv

oP

n

trace of

tool

work-

piece

n

web

thickness

major cutting edge

minor cutting edge

chisel edge trace of

trace of

s P

p P

f P r P

2

s =

r D a p =

2

1

z f h

b p a

r e

s r P

c v

p P

r P

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Twist drill for various materials

Source: DIN 1414

σ

σ

σ

Type Point angle

s / °

Twist angle

d / ° Material

N 118 18 to 30 e.g. steel

H 118 10 to 15 e.g. grey cast iron

W 130 35 to 45 e.g. Aluminum

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Kegelmantel-anschliff (Grundanschliff für Form A-D)

AusgespitzteQuerschneide

AusgespitzteQuerschneidemit korrigierterHauptschneide

Kreuzanschliff AusgespitzteQuerschneidemit facettiertenSchneidenecken

Spitzenwinkel180° mitZentrumsspitze

Form A Form B Form C Form D Form E

Form A

Kegelmantel-anschliff (Grundanschliff für Form A-D)

AusgespitzteQuerschneide

AusgespitzteQuerschneidemit korrigierterHauptschneide

Kreuzanschliff AusgespitzteQuerschneidemit facettiertenSchneidenecken

Spitzenwinkel180° mitZentrumsspitze

Form A Form B Form C Form D Form E

Form B

Kegelmantel-anschliff (Grundanschliff für Form A-D)

AusgespitzteQuerschneide

AusgespitzteQuerschneidemit korrigierterHauptschneide

Kreuzanschliff AusgespitzteQuerschneidemit facettiertenSchneidenecken

Spitzenwinkel180° mitZentrumsspitze

Form A Form B Form C Form D Form E

Form C

Kegelmantel-anschliff (Grundanschliff für Form A-D)

AusgespitzteQuerschneide

AusgespitzteQuerschneidemit korrigierterHauptschneide

Kreuzanschliff AusgespitzteQuerschneidemit facettiertenSchneidenecken

Spitzenwinkel180° mitZentrumsspitze

Form A Form B Form C Form D Form E

Form D

Kegelmantel-anschliff (Grundanschliff für Form A-D)

AusgespitzteQuerschneide

AusgespitzteQuerschneidemit korrigierterHauptschneide

Kreuzanschliff AusgespitzteQuerschneidemit facettiertenSchneidenecken

Spitzenwinkel180° mitZentrumsspitze

Form A Form B Form C Form D Form E

Form E

Kegelmantel-anschliff (Grundanschliff für Form A-D)

AusgespitzteQuerschneide

AusgespitzteQuerschneidemit korrigierterHauptschneide

Kreuzanschliff AusgespitzteQuerschneidemit facettiertenSchneidenecken

Spitzenwinkel180° mitZentrumsspitze

Form A Form B Form C Form D Form E

Specific geometries of twist drills

cone shaped

drill (basic polish

for form A-D)

Pointed

transverse

cutting edge

pointed cutting edge

with corrected major

cutting edge

cross-wise

polish

pointed transverse

cutting edge with

facetted cutting

edge corners

point angle 180°

with centre tip

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Drilling processes I (DIN 8589-2)

Centre drilling

tool

workpiece

feed

motion

primary

motion

Gun drilling

feed

motion

primary

motion

workpiece

tool

tool

Profile drilling

feed

motion

primary

motion

workpiece

tool

Tapping

primary

motion

tool workpiece

feed

motion

Drilling: Cutting with circular primary motion. The axis of rotation of the tool and of

the produced internal area are identical. The direction of the feed has the

direction of this axis of rotation.

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Gun drilling

Source: Sandvik

drill bushing

Schaft HM - Kopf mit

eingeschliffenen

F ü hrungsleisten

cutting edge

shaft cemented carbide

head with indexable

inserts

lubrication

outlet crimp

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Deep hole drilling

Single lip drilling BTA-Method Ejector-Method

Diameter range

0,8 to 40 mm

Diameter range

6 to 300 mm

Diameter range

18 to 250 mm

Source: Sandvik

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Example of use: Micro deep hole drilling

Source: TITEX

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Drilling processes II (DIN 8589-2)

tool

workpiece

feed

motion

primary

motion

Countersinking

tool

workpiece

feed

motion

primary

motion

Cylinder sinking

Sinking: Drilling for producing planes which are orthogonal to the axis of rotation or

rotationally symmetric cone and form planes.

Reaming: Bore up with a low undeformed chip thickness for producing better qualities

of the surface.

tool

workpiece

feed

motion

primary

motion

Reaming

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Round reaming

Tool

Workpiece

Reiben

Boring with small uncut chip thickness with a reamer in order to produce a

high precision cylindrical inner surface with excellent surface quality

Reiben Reaming

Form reaming

n n

vf

vf

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Solid-carbide reamer

Source: Iscar, Rübig, Gühring

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Construction principle of a reamer with guide rail

Source: MAPAL

Mounting screw Cutting insert

Adjusting screw

Mounting

plate

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Reamer with two PCD-cutting edges and PCD-guide rail

EN-GJL-250, vc = 120 m/min, vf = 675 mm/min Source: MAPAL

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Construction types of multibladed reamers

Source: SECO, DIHART, MAPAL

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Modeling of Machining 5

Hard machining 4

Sawing 3.3

Broaching 3.2

Shaping/ Planing 3.1

Cutting processes with parallel translation 3

Cutting processes with rotary motion 2

Introduction 1

Outline

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Modeling of Machining 5

Hard machining 4

Sawing 3.3

Broaching 3.2

Shaping/ Planing 3.1

Cutting processes with parallel translation 3

Cutting processes with rotary motion 2

Introduction 1

Outline

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Definitions and kinematics

Planing/

shaping:

Cutting with repeated parallel translation as primary motion and successive

feed motion which is orientated orthogonal to the primary motion.

The kinematics of planing and shaping are identical. When the primary motion

comes from the workpiece the process is called planing, when the primary

motion comes from the tool the process is called shaping.

Shaping

primary motion

at the tool

primary

motion at the

workpiece

Planing

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Planing processes (DIN 8589-4)

Finish planing

tool

workpiece feed

motion

primary

motion

Contour planing

feed motion

primary

motion

workpiece

tool

Circular planing

feed

motion

primary

motion

workpiece

tool tool

Profile planing

primary

motion

workpiece

feed

motion

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Modeling of Machining 5

Hard machining 4

Sawing 3.3

Broaching 3.2

Shaping/ Planing 3.1

Cutting processes with parallel translation 3

Cutting processes with rotary motion 2

Introduction 1

Outline

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Broaching processes I

source: DIN 8589-5

workpiece

tool

primary

motion

feed

motion

Plane broaching

workpiece

tool

External broaching

primary

motion

feed motion

workpiece

primary

motion

tool

feed

motion

Internal broaching

Broaching: Cutting with a tool with more than one flute. The flutes are orientated one after

another with the stepping of the undeformed chip thickness. The feed motion is

substituted by the stepping. The last flutes of the tool produces the desired

profile of the workpiece. After one run, the workpiece is ready and the surface

finished.

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Broaching processes II

source: DIN 8589-5

workpiece

tool

primary

motion feed

motion

Profile broaching

workpiece

tool

primary

motions

Helical broaching

workpiece

tool

primary

motions

Cylindrical broaching

feed

motion

workpiece

tool

initial shape of

the workpiece

end shape of

the workpiece

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Internal broaching tools (schematic)

end piece A

shank way roughing- finishing- calibrating part (fz=0)

fz t B ba01

a01

a02

detail A detail B

a02 clearance angle

a01 chamfer inclination

g0 rake angle

g0

ba01 width of chamber

t division

fz inclination

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Broaching tools

Source: Forst

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Example of use for internal broaching

Source: Forst

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Used proceedings for the production of turbine discs

End milling

Turning

Drilling

Broaching Source: MTU

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Modeling of Machining 5

Hard machining 4

Sawing 3.3

Broaching 3.2

Shaping/ Planing 3.1

Cutting processes with parallel translation 3

Cutting processes with rotary motion 2

Introduction 1

Outline

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Sawing processes

source: DIN 8589-6

workpiece

tool

primary

motion

feed

motion

Hack sawing

tool

workpiece

feed

motion

primary

motion

Circular sawing workpiece

tool

feed

motion

primary motion

Band sawing

sawing: Cutting with circular motion or parallel translation as primary motion. The

Tools have more than one flute. The depth of cut is low and the primary

motion comes from the tool.

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Nomenclature and tool geometry of the saw band

Tooth point

Width

Back

of blade

Cutting

part

Tooth root

t

H

go bo R

ao

Tooth space (chip space)

Workpiece Working plane

a e

fz 90° ve

vc

h

Band saw

v c cutting speed

v e Effective cutting speed

f z

Tooth feed

a e Intervention width

t Tooth pitch

R Base radius

H Tooth height

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Modeling of Machining 5

Hard machining 4

Cutting processes with parallel translation 3

Cutting processes with rotary motion 2

Introduction 1

Outline

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Hard machining with geometrically defined cutting edges

Techniques

turning

milling

broaching

Cutting materials

ultra fine grained carbides

ceramics

PCBN

Technological specialties

cutting process is conducted by a single or a few cutting edges

strong relation between the condition of single cutting edges and the surface rim zone of

the workpiece, because the materials are hard and thus the tools posses a high wear risk

risk of white layers

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Hardening steel leads to mechanically strong parts

Soft

Material volume: 100 % Material volume: Approx. 103 %

non-uniform strain and

distortion

Strain e

Str

ess s

Micro structure: Ferrite

Hardness: 20 - 35 HRC

Strain e

Str

ess s

Micro structure: Martensite

Hardness: 55 - 65 HRC

=> Final cut necessary to achieve high accuracy in form and size,

small and medium parts need to be oversized by approx. 0.3 - 0.5 mm

Hard Hardening /

Tempering

Mechanically strong steel parts need to be hardened / tempered

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Cams shaft

Bearing rings

Gears

Slipping load

(e.g. contact with bucket tappet)

Rolling load

(contact with rollers)

Rolling load

(Contact with partner gear)

Slipping load

(Contact with synchronising ring)

Micro slipping

(Contact with shaft)

Bending load

(at tooth ground)

Typical parts for hard machining

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Hard machining, turning and grinding

Hard machining can be realised by

defined and undefined machining principles.

Hardened steel can only be cut defined if the

material in front of the cutting tip is heated

and softened by the process itself.

This leads to special requirements for the

cutting material and the press design.

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Application for Precision Hard Turning

10

20

30

40

50

60

70

80

90

100

10

20

30

40

50

60

70

80

90

100

Machining time [%] Machining Cost [%]

Grinding Hard Turning Grinding Hard Turning

Material: X210CrW12

hardened (63 HRC)

Machining: Hard turning of the

profile

Part: Precision profile roller

O 150 mm

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Modeling of Machining 5

Hard machining 4

Cutting processes with parallel translation 3

Cutting processes with rotary motion 2

Introduction 1

Outline

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Force calculation: Time function

Substitution of the empirical force equation proposed by Kienzle with the technical terms:

im

ii hbkF-

=1

1.1

polar coordinate number of teeth

diameter of the tool

equation proposed by

Salomon or Kienzle

source: Diss. Rehse

Discretisation of the equation

basement for modeling

Question: What is the angle w?

( ) i m

r

c

f

r

p

i i v z

v D a k F

-

1

1 . 1 sin sin sin

w p

( ) i m

r c

c

f

r

p

i i D

dt v

v z

v D a k dF

-

1

1 . 1 sin 2

sin sin

p

t v b c =

)

D

b )

=

2 w

w sinsinmax rzfh

r

pab

sin=

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The same procedure

for the other flutes!

Force calculation: Technical terms

discretisation of the equation:

discrete time function

Solving the equation for

discrete times

discrete force components

)(dtdFi

transformation of the

force components into

the x- and y- direction

addition of the force

components in x- and

y- direction separately

forc

e i

n x

/

N

time / sec

measured calculated

( ) i m

r c

c

f

r

p

i i D

dt v

v z

v D a k dF

-

1

1 . 1 sin 2

sin sin

p

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Penetration calculation: Peripheral milling

vector field for representation of the tool

vector field for the representation of the workpiece

feed

velocity

Matrix model for the penetration calculation

data of the machine tool data of the workpiece data of the tool

thickness of cut h width of cut b

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Thank you for your attention!!

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Questions

How can one differ the manufacturing processes by their primary movement?

Which contact conditions exist in external circular cylindrical turning?

Why is there a necessity to have both a tool in hand and tool in use system?

Describe the most important angles at the cutting wedge.

Name the benefits and disadvantages of up- and down milling.

List different process variants for drilling.

Why is reaming used?

Which correlation exists between the helix angle and the hardness of the workpiece

material in drilling?

Please name the different sawing processes and their process characteristics.

Which characteristics distinguish the different methods of planing and shaping?

How is broaching characterized?

Which are the most important processes to manufacture involute gear profiles?