Cutting Processes. Simulation Techniques in Manufacturing Technology Lecture 7

Cutting Processes

Simulation Techniques in Manufacturing Technology

Lecture 7

Laboratory for Machine Tools and Production Engineering

Chair of Manufacturing Technology

Modeling of Machining

5

Hard machining

4

Cutting processes with parallel translation

3

Cutting processes with rotary motion

2

Introduction

1

Breakdown of the techniques involving a rotational main movement

Turning

– work piece rotation – tool translation

Milling

– tool- rotation – work piece-translation

Boring

– tool rotation – tool translation

Sawing

– tool rotation – tool translation

main movement

main movement

main movement

main movement

subsidiary

Breakdown of the techniques involving a translational main

movement

broaching

– multi teeth tool

– feed due to tool geometry – 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

tool

work piece track

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

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

Example: rough turning

Example: finishing

Terms at the cutting edge

tool shank

cutting direction

major cutting edge S

major flank face A

_α

minor flank face A

_α

‘

minor cutting edge S‘

rake face A

_γ

corner radius

Definition of the tool cutting edge angle

κκκκ

_r

tool reference Plane P_r tool orthogonal plane P_o

Definition tool cutting edge angle

κκκκ

_r

trace of the

working plane P

_f

tool

trace of the tool

cutting edge plane P

_S

tool reference plane P

_r

feed direction κr

rε

trace of the tool

orthogonal plane P

_o

Definition of the inclination angle

λλλλ

_s

working plane P

_f

tool cutting

edge plane P

_S

tool reference

plane P

_r

Definition of the inclination angle

λλλλ

_s

tool

trace of the

working plane P

_f

tool cutting edge plane P

_S

major cutting edge S

trace of the tool

reference plane P

_r

cutting direction

λ

_s +

Definition of the angles at the cutting edge

tool

trace of the

flank face

plane A

_α

trace of the rake

face plane A

_γ

trace of the tool

back plane P

_p

trace of the tool

reference plane P

_r

tool orthogonal plane P_o

expected

cutting direction

expected

feed direction

γo αo βo

Tool variants in longitudinal cylindrical turning

right hand

side cutting

left hand

side cutting

neutral

Facing (DIN 8589-1: ON 3.2.1.1)

cross face turning

tool

workpiece

longitudinal face turning

workpiece

tool

cross parting off

tool

workpiece

Cylindrical turning (DIN 8589-1: ON 3.2.1.2)

longitudinal-cylindrical turning

tool

workpiece

cross-cylindrical

turning

tool

workpiece

centreless rough turning

tool

workpiece

Threatening (DIN 8589-1: ON 3.2.1.3)

workpiece tool

thread turning

workpiece tool

chasing

workpiece tool

tapping

thread turning (external) thread turning (internal)

Profile turning (DIN 8589-1: ON 3.2.1.5)

trepanning

grooving

tool

workpiece

cross-profile turning

workpiece

tool

tool

workpiece

DIN 8589-1

Hob turning (DIN 8589-1: ON 3.2.1.4)

tool workpiece

Contour turning (DIN 8589-1: ON 3.2.1.6)

copy turning

tool

workpiece

reference formed part

kinematic-contour turning

workpiece

tool

gear

NC-contour turning

NC

tool

workpiece

Internal turning

skimming

tool

workpiece

undercut

tool

workpiece

cut in

workpiece

tool

DIN 8589-1 Source: Iscar

Internal turning tools

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

Milling processes DIN 8589-3

3.2.3

milling

DIN8589-3

3.2.3.1

slab / face

milling

3.2.3.2

circular

milling

3.2.3.6

form

milling

3.2.3.3

helical

milling

3.2.3.4

hobbing

3.2.3.5

profile

milling

Slab milling (ON 3.2.3.1): face- and peripheral milling

face milling

– Workpiece surface is generated by

face of the milling tool

peripheral milling

– Workpiece surface is generated by

peripheral surface of the milling tool

tool workpiece r

κ

s

P

p

a

n

z

f

f

v

tool workpiece f

v

z

f

e

a

c

v

n

ϕ

Up- and down milling

a_e f_z n F_c F_f

down milling

v_c v_t

up milling

f_z n F_c F_f v_t

Up- and down milling

up milling part

down milling part

Tool-in-hand system: peripheral milling

workpiece tool trace of trace of P_r p s

P

P

≡

o f

P

P

≡

E A c E

ω

ω

ω

ω

−

=

°

=

0

f

v

z

f

c

v

e

a

Tool-in-hand system: face milling

trace of the entrance plane workpiece tool trace of trace of trace of trace of

n

f

v

o

P

f

P

E

ω

c

ω

A

ω

e

a

r

P

z

f

p

a

r

κ

s

P

p

P

n

z

f

ν

f

Contact conditions and cutting edge geometry in face milling

ae a_e2 C a_e1 entry plane v_c vf ϕϕϕϕs ϕϕϕϕ n fz φ=0 tangential plane cutting C-C C ϕϕϕϕA -εεεεA +εεεε_E n view A

tool contact types

U T S_b γγγγp K S Sa V V_a

tool cutting edge A f_z ap b B plane B-B B n 2 D a arccos ei i = ϕϕϕϕ κ sin a b = p r sin sin z f h ϕϕϕϕ κκκκ ϕϕϕϕ = • •      (f_z << D)

Contact conditions depending on the radial and axial rake angle

S - contact T - contact ST - contact

U - contact V - contact SV - contact

workpiece milling cutter insert datum plane S T T S S V V U γγγγf> 0° γγγγp> 0° γγγγf> 0° γγγγp< 0° γγγγf> 0° γγγγp= 0° γγγγf< 0° γγγγp< 0° γγγγf< 0° γγγγp> 0° γγγγf= 0° γγγγp> 0°

Precision milling operations

a_p1 a_p2 f_z2 f_z1 a_p a_p f_z f_z finish-milling no. of teeth 10 to 60 a_p = 0.3 bis 1 mm f_z = 0.3 bis 0.5 mm

no. of teeth 1 bis 6

wide finish-milling

a_p = 0.05 to 0.2 mm f_z = 0.5 bis 6 mm

f_z2 = 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 a_p1 = 0.5 to 2 mm f_z1 = 0.1 to 0.3 mm a_p2 = 0.03 to 0.05 mm

Circular milling (DIN 8589-3: ON 3.2.3.2)

workpiece

v

_f

a

_p

n

w

n

_F Mill

additional axial cutting edges radial cutting edges

workpiece nF nW chipping space

n

_w

n

_F

v

_f tool tool workpiece Source: Walter

a

b

c

d

e

f

Hobbing (DIN 8589-3: ON 3.2.3.4)

-Fräserdrehung Radialvorschub Ta ng en tia lvo rs ch ub Werkraddrehung Fräserdrehung v_c cutting speed f_a axial feed f_w hob feed radial feed rotation of hobb rotation of workpiece

Different types of hobs

Monobloc gear hob

Indexable insert hob

Fotos: Fette, Saazor, Saacke

high revolutions of the mill

short milling times

short first cut length

high cutting ability

rough- and finish milling

easily to re-sharpen

large gearing

no sharpening

low accuracy

only for rough milling

large gearing

Profile milling (DIN 8589-3: ON 3.2.3.5)

profile milling cutter

DIN 8589-3

workpiece

workpiece

gang milling cutter

workpiece

Form milling (DIN 8589-3: ON 3.2.3.6)

form-profile milling workpiece tool

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

Drilling processes DIN 8589-2

3.2.2

drilling

countersinking

reaming

DIN 8589-2

3.2.2.1

spot facing

3.2.2.2

centre drilling

3.2.2.3

tapping

3.2.2.5

profile drilling

3.2.2.6

form drilling

Example of gun drilling

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

Reibung Werkstück Bohrwerkzeug Plastische Verformung Stofftrennung Reibung f n friction friction work-piece drill plastic deformation material seperation

Cutting conditions dependent on drill diameter

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

20 m/min 10 0

cutting speed v_c

Rake angle γ; clearance angle α

d ri ll ra d iu s r 1 0 m m 4 6 8 10 9 7 5 m a in c u tt in g e d g e c h is e l e d g e v_c γ_fe α_fe

Fundamental kinematics: centre drilling

β

γ

γf

αα

xe

η

f/2

f

cutting direction

effective direction

feed direction

cutting edge 1

cutting edge 2

cutting part

_{plunge (lettering point)}

tapered shaft

flat tang

point length

cutting length

flute length

total length

cone length

plunge length

d

ri

ll

d

ia

m

e

te

r

d

nach DIN 8589-2

HW 0.5

drill-point angle grain size

angle of twist

major clearance angle cutting material:

construction dimensions

Geometry at the cutting edge of a twist drill

DIN 6539, Typ N σ 118° α: 10° : 35° -D_K: -diameter d: 1 mm : 118° 10° δ: K20 K 0.7 µm Querschneide Freifläche Hauptschneide _α δ chisel edge flank face

major cutting edge _α

pointed transverse cutting edge

pointed cutting edge with corrected

major cutting edge

cross-wise polish

pointed trans-verse cutting edge with facetted cutting edge

corners

point angle 180° with centre tip cone shaped

drill (basic polish for form

A-D)

Form A Form B Form C Form D Form E

Drilling processes I

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 source: DIN 8589-2

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.

Gundrilling

Source: Sandvik

drill bushing

Schaft

HM-Kopf mit

eingeschliffenen

Führungsleisten

cutting edge

shaft

cemented carbide

head with indexable

inserts

lubrication

Drilling processes II

tool workpiece feed motion primary motion countersinking tool workpiece feed motion primary motion cylinder sinking source: DIN 8589-2

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

Fundamental kinematics: centre drilling

trace of trace of trace of f

v

o

P

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

σ

κ

_r

=

_a

_D

p

=

⋅

2

1

z

f

h

b

p

a

r

ε

σ

r

P

c

v

p

P

r

P

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

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

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

Planing processes

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 source: DIN 8589-4

Tool-in-hand system: planing

workpiece tool trace of trace of trace of trace of primary motion at the workpiece f

v

f

P

o

P

p

P

P

_r r

κ

s

P

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

Internal broaching tools (schematic)

end piece A

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

f_z t B bαααα01 αααα01 αααα02 detail A detail B αααα02 clearance angle αααα01 chamfer inclination γγγγ0 rake angle γγγγ₀₀₀₀ b_αααα01 width of chamber t division f_z inclination

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.

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

Tool-in-hand system: internal broaching

primary motion feed motion is realized with the stepping flutes trace of trace of f

v

tool workpiece

tool and workpieces p s

P

P

≡

r

P

o f

P

P

≡

z

f

⋅

4

p

a

z

t

c

v

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

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.

Terms and cutting part geometry of the sawing belt

tooth head width back of belt cutting part base of a gear tooth t H g₀ b₀ R a0 tooth gap (chip space) workpiece working plane ae f_z 90o ve v_c h belt saw v_c cutting speed v_e operating speed f_z tooth feed a_e width of cut t tooth division R base radius H tooth height tip of tooth

Tool-in-hand system: hack sawing

trace of trace of tool workpiece trace of trace of f

v

primary motion z

f

feed motion p s

P

P

≡

f o

P

P

≡

r

P

r

κ

r

P

P

_s

≡

P

_p o f

P

P

≡

Modeling of Machining

5

Hard machining

4

Cutting processes with parallel translation

3

Cutting processes with rotary motion

2

Introduction

1

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

Hardening steel leads to mechanically strong parts

Soft

Material volume: 100 %

Material volume: approx. 103 % non-uniform strain and

distortion Strain e S tr e ss s

Micro structure: ferrite Hardness: 20 - 35 HRC Strain e S tr e ss 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

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)

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.

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

Modeling of Machining

5

Hard machining

4

Cutting processes with parallel translation

3

Cutting processes with rotary motion

2

Introduction

1

Force calculation: time function

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

i m i i

k

b

h

F

=

_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 ωωωω?

( mi) r c f r p i i

v

z

v

D

a

k

F

−













⋅

⋅

⋅

⋅

⋅

⋅

⋅

≈

1 1 . 1

sin

sin

sin

ω

κ

π

κ

( mi) 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

κ

π

κ

t

v

b

=

c

⋅

)

D

b

)

⋅

=

2

ω

ω

κ

sin

sin

max

≈

f

z

⋅

r

⋅

h

r p

a

b

κ

sin

=

Force calculation: technical terms

discretisation of the equation:

discrete time function

Solving the equation for discrete times

discrete force components

)

(dt

dF

_i

transformation of the force components into the x- and y- direction addition of the force

components in x- and y- direction separately fo rc e i n x / N time / sec measured calculated

The same procedure for the other flutes!

( mi) 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

κ

π

κ

Penetration calculation: peripheral milling

vector field for representation the tool

vector field for representation the workpiece feed

velocity

matrix model for the penetration calculation

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

Modeling of Machining

5

Hard machining

4

Cutting processes with parallel translation

3

Cutting processes with rotary motion

2

Introduction

1

Modeling of Machining

5

Hard machining

4

Cutting processes with parallel translation

3

Cutting processes with rotary motion

2

Introduction

1

Process classification

source: DIN 8589-0

Manufacturing Processes

1 primary shaping 2 secondary shaping / forming 3 cutting 4 joining 5 coating 6 changing material properties 3.2 cutting 3.2.1 turning 3.2.2 drilling reaming 3.2.3 milling 3.2.4 planing shaping 3.2.5 broaching 3.2.6 sawing 3.2.7 filing rasping 3.2.8 brushing 3.2.9 scraping chiselling

Evaluation

Attend:

knowledge of the complete workpiece design (angel ω)

if the information is not available the modeling cannot success!

general model possibility to use

general software possibility to expand

with dynamic terms

mathematical formulation

advantages

no direct material information

disadvantage

This information is contained in the specific force parameter!