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© WZL/Fraunhofer IPT
Cutting Processes
Simulation Techniques in Manufacturing Technology
Lecture 7
Laboratory for Machine Tools and Production Enginee ring
Chair of Manufacturing Technology
Prof. Dr.-Ing. Dr.-Ing. E.h. Dr. h.c. Dr. h.c. F. Klocke
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Seite 1© WZL/Fraunhofer IPT
Modeling of Machining5
Hard machining4
Cutting processes with parallel translation3
Cutting processes with rotary motion2
Introduction1
Outline
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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 movementmain movementmain movement
subsidiary movement sub. movement sub. movement sub. movement
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Breakdown of the techniques involving a translation al 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
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Seite 4© WZL/Fraunhofer IPT
Modeling of Machining5
Hard machining4
Cutting processes with parallel translation3
Drilling2.3
Milling2.2
Turning2.1
Cutting processes with rotary motion2
Introduction1
Outline
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Seite 5© WZL/Fraunhofer IPT
Modeling of Machining5
Hard machining4
Cutting processes with parallel translation3
Drilling2.3
Milling2.2
Turning2.1
Cutting processes with rotary motion2
Introduction1
Outline
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Example: rough turning
Source: Widia
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Example: finishing
Source: Widia
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Terms at the cutting edge
tool shank
cutting direction
major cutting edge S
major flank face Aα
minor flank face Aα‘
minor cutting edge S‘
rake face Aγ
corner radius
feed direction
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Definition of the tool cutting edge angle κκκκr
tool reference Plane Pr
tool orthogonal plane Po
tool cutting edge plane Ps
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Definition tool cutting edge angle κκκκr
trace of theworking plane Pf
tool
trace of the tool cutting edge plane PS
tool reference plane Pr
feed direction
κr
rε
trace of the tool orthogonal plane Po
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Definition of the inclination angle λλλλs
working plane Pf
tool cutting edge plane PS
tool reference plane Pr
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Definition of the inclination angle λλλλs
tool
trace of the working plane Pf
tool cutting edge plane PS
major cutting edge S
trace of the tool reference plane Pr
cutting direction
λs+-
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Definition of the rake angle γγγγ
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Definition of the angles at the cutting edge
tool trace of the flank face plane Aα
trace of the rake face plane Aγ
trace of the tool back plane Pp
trace of the tool reference plane Pr
tool orthogonal plane P o
expected cutting direction
expectedfeed direction
γo
αo
βo
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Tool variants in longitudinal cylindrical turning
right hand side cutting
left hand side cutting
neutral
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Facing (DIN 8589-1: ON 3.2.1.1)
cross face turning
tool
workpiece
longitudinal face turning
workpiece
tool
cross parting off
tool
workpiece
Source: Sandvik Coromant
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Facing (DIN 8589-1: ON 3.2.1.1): cross / longitudin al 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)
longitudinal-cylindrical turning
tool
workpiece
cross-cylindrical turning
tool
workpiece
centreless rough turning
tool
workpiece
Source: Iscar, Ceratizit
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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)
Source: Garant, Seco, Ceratizit
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Profile turning (DIN 8589-1: ON 3.2.1.5)
trepanning grooving
tool
workpiece
cross-profile turning
workpiece
tooltool
workpiece
DIN 8589-1
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Hob turning (DIN 8589-1: ON 3.2.1.4)
tool
workpiece
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Contour turning (DIN 8589-1: ON 3.2.1.6)
copy turning
tool
workpiece
reference formed part
kinematic-contour turning
workpiece
toolgear
NC-contour turning
NCtool
workpiece
Source: Sandvik Coromant
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Internal turning
skimming
tool
workpiece
undercut
tool
workpiece
cut in
workpiece
tool
DIN 8589-1
Source: Iscar
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Internal turning tools
Source: Sandvik
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Seite 26© WZL/Fraunhofer IPT
Modeling of Machining5
Hard machining4
Cutting processes with parallel translation3
Drilling2.3
Milling2.2
Turning2.1
Cutting processes with rotary motion2
Introduction1
Outline
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Milling processes DIN 8589-3
3.2.3
milling
DIN8589-3
3.2.3.1
slab / facemilling
3.2.3.2
circularmilling
3.2.3.6
formmilling
3.2.3.3
helicalmilling
3.2.3.4
hobbing
3.2.3.5
profilemilling
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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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Slab milling (ON 3.2.3.1): face- and peripheral mill ing
� 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
rκ
sP
pa
n
zf
fv
tool
workpiece
fv
zf
eacv
n
ϕ
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Up- and down milling
ae
fz
n
Fc
Ff
down milling
vc
vt
up milling
fz
n
FcFf
vtUp- and down milling
up milling part
down milling part
v t
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Tool-in-hand system: peripheral milling
workpiece
tool
trace of
trace of Pr
ps PP ≡
of PP ≡
EAc
E
ωωωω
−=°= 0
fv
zf
cv
ea
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Tool-in-hand system: face milling
trace of theentrance plane
workpiece
tool
trace of
trace of
trace of
trace of
n
fvoP
fP
Eω
cω
Aω
ea
rPzf
par
κ
sP
pP
n
zf
νf
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Contact conditions and cutting edge geometry in fac e milling
ae
ae2
C
ae1
entry plane
vc
vf
ϕϕϕϕs
ϕϕϕϕ
n
fz
φ=0
tangential plane
cutting C-C
CϕϕϕϕA
-εεεεA
+εεεεE
n
view Atool
contact types
UT
Sb
γγγγp
K
S Sa V Va
tool cutting edge
A
fz
ap bB
plane B-B
B
n
2Da
arccos eii =ϕϕϕϕ
κsin
ab p=
rsinsinzfh κκκκϕϕϕϕϕϕϕϕ••=
(fz << D)
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Contact conditions depending on the radial and axia l rake angle
S - contact T - contact ST - contact
U - contact V - contact SV - contact
workpiecemillingcutter
insertdatum plane
S
T T
S
SVV
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°
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Precision milling operations
ap1
ap2fz2
fz1
ap
ap
fz
fz
finish-milling
no. of teeth 10 to 60ap = 0.3 bis 1 mm
fz = 0.3 bis 0.5 mm
no. of teeth 1 bis 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 knivesand wide finishing cutting edgeno. of planing knives 20 to 30no. of wide finishing cutting edges 1 to 2finishing cutting edges
wide finishing cutting edges
ap1 = 0.5 to 2 mmfz1 = 0.1 to 0.3 mm
ap2 = 0.03 to 0.05 mm
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Circular milling (DIN 8589-3: ON 3.2.3.2)
workpiece
vf
apnw
nF
Mill
additional axial cutting edges radial cutting edges
workpiece
nF
nW
chipping space
nw
nF
vf
tool
tool
workpiece
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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Hobbing (DIN 8589-3: ON 3.2.3.4)
-
FräserdrehungRadialvorschub
Tan
gen
tial
vors
chu
b
Werkraddrehung
Fräserdrehung
vc cutting speedfa axial feedfw hob feedradial feed
rotation of hobb
rotation of workpiece
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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
Roughing-finishing multi hob
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Profile milling (DIN 8589-3: ON 3.2.3.5)
profile milling cutter
DIN 8589-3
workpieceworkpiece
gang milling cutter
workpiece
Source: Sandvik Coromant, Ingersoll, ALESA AG
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Form milling (DIN 8589-3: ON 3.2.3.6)
form-profile milling
workpiece
tool
Source: Milltech, Dalscheid
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Modeling of Machining5
Hard machining4
Cutting processes with parallel translation3
Drilling2.3
Milling2.2
Turning2.1
Cutting processes with rotary motion2
Introduction1
Outline
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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
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Example of gun drilling
Source: Widia
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Example of gun drilling
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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
Reibung
Werkstück
Bohrwerkzeug
PlastischeVerformung
Stofftrennung
Reibung
f
n
frictionfriction
work-piece
drill
plastic deformation
material seperation
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Cutting conditions dependent on drill diameter
40° 30° 20° 10° 0° -10° -20° -30° -40° -50° -60°
20 10 0m/min
cutting speed vc
Rake angle γ; clearance angle αdr
ill r
adiu
s r
1
0
mm
4
6
8
10
9
7
5
mai
n cu
tting
edg
e
chis
el e
dge
vc γfe αfe
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Fundamental kinematics: centre drilling
β
γ
γf
ααxe
η
f/2f
cutting direction
effective directionfeed direction
cutting edge 1
cutting edge 2
η
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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
met
er d
nach DIN 8589-2
Geometry of the cutting part of a twist drill
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HW0.5 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°
-DK: -
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
δ
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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
Specific geometries of twist drills
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Twist drill for various materials
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Drilling processes I
centre drilling
tool
workpiece
feedmotion
primarymotion
gun drilling
feedmotion
primarymotion
workpiece
tool
tool
profile drilling
feedmotion
primarymotion
workpiece
tool
tapping
primarymotion
toolworkpiece
feedmotion
source: DIN 8589-2
drilling: Cutting with circular primary motion. The axis of rotation of the tool and ofthe produced internal area are identical. The direction of the feed has thedirection of this axis of rotation.
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Gundrilling
Source: Sandvik
drill bushing
SchaftHM-Kopf miteingeschliffenenFührungsleisten
cutting edge
shaft cemented carbidehead with indexable inserts
lubricationoutlet crimp
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Drilling processes II
tool
workpiece
feedmotion
primarymotion
countersinking
tool
workpiece
feedmotion
primarymotion
cylinder sinking
source: DIN 8589-2
sinking: Drilling for producing planes which are orthogonal to the axis of rotation orrotationally symmetric cone and form planes.
reaming: Bore up with a low undeformed chip thickness for producing better qualitiesof the surface.
tool
workpiece
feedmotion
primarymotion
reaming
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Fundamental kinematics: centre drilling
trace of
trace of
trace of
fv
oP
n
trace of
tool
work-piece
n
webthickness
major cutting edge
minor cutting edge
chisel edge trace of
trace of
sP
pP
fPrP
2
σκ =r Dap
⋅=2
1
zfh
bpa
rε
σrP
cv
pP
rP
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Modeling of Machining5
Hard machining4
Sawing3.3
Broaching3.2
Shaping/ Planing3.1
Cutting processes with parallel translation3
Cutting processes with rotary motion2
Introduction1
Outline
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Modeling of Machining5
Hard machining4
Sawing3.3
Broaching3.2
Shaping/ Planing3.1
Cutting processes with parallel translation3
Cutting processes with rotary motion2
Introduction1
Outline
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Definitions and kinematics
planing/shaping:
Cutting with repeated parallel translation as primary motion and successivefeed 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 primarymotion comes from the tool the process is called shaping .
shaping
primary motionat the tool
primarymotion at the
workpiece
planing
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Planing processes
finish planing
tool
workpiecefeedmotion
primarymotion
contour planing
feed motion
primarymotion
workpiece
tool
circular planing
feedmotion
primarymotion
workpiece
tooltool
profile planing
primarymotion
workpiece
feedmotion
source: DIN 8589-4
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Tool-in-hand system: planing
workpiece
tool
trace of
trace of
trace of
trace of
primarymotionat the workpiece
fvfP
oP
pP rP
rκ
sP
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Modeling of Machining5
Hard machining4
Sawing3.3
Broaching3.2
Shaping/ Planing3.1
Cutting processes with parallel translation3
Cutting processes with rotary motion2
Introduction1
Outline
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Internal broaching tools (schematic)
end pieceA
shank way roughing- finishing- calibrating part(f z=0)
fzt B bαααα01 αααα01
αααα02
detail A detail Bαααα02 clearance angle
αααα01 chamfer inclination
γγγγ0 rake angle
γγγγ0000
bαααα01 width of chamber
t division
fz inclination
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Broaching processes I
source: DIN 8589-5
workpiece
tool
primarymotion
feedmotion
plane broaching
workpiece
tool
external broaching
primarymotion
feed motion
workpiece
primarymotion
tool
feedmotion
internal broaching
broaching: Cutting with a tool with more than one flute. The flutes are orientated one afteranother with the stepping of the undeformed chip thickness. The feed motion issubstituted by the stepping. The last flutes of the tool produces the desiredprofile of the workpiece. After one run, the workpiece is ready and the surfacefinished.
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Broaching processes II
source: DIN 8589-5
workpiece
toolprimarymotionfeed
motion
profile broaching
workpiece
tool
primarymotions
helical broaching
workpiece
tool
primarymotions
cylindrical broaching
feedmotion
workpiece
tool
initial shape ofthe workpiece
end shape ofthe workpiece
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Tool-in-hand system: internal broaching
primarymotion
feed motion isrealized with thestepping flutes
trace of
trace of
fv
tool
workpiece
tool and workpiecesps PP ≡
rP
of PP ≡
zf⋅4
pa
zt
cv
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Modeling of Machining5
Hard machining4
Sawing3.3
Broaching3.2
Shaping/ Planing3.1
Cutting processes with parallel translation3
Cutting processes with rotary motion2
Introduction1
Outline
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Sawing processes
source: DIN 8589-6
workpiece
tool
primarymotion
feedmotion
hack sawing
tool
workpiece
feedmotion
primarymotion
circular sawing workpiece
tool
feedmotion
primary motion
band sawing
sawing: Cutting with circular motion or parallel translation as primary motion. TheTools have more than one flute. The depth of cut is low and the primarymotion comes from the tool.
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Terms and cutting part geometry of the sawing belt
tooth head
width
back of belt
cutting part
base of agear tooth
t
H
g0b0R
a0
tooth gap
(chip space )
workpieceworking plane
ae
fz90ove
vch
belt saw
vc cutting speed
ve operating speed
fz tooth feed
ae width of cut
t tooth division
R base radius
H tooth height
tip of tooth
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Tool-in-hand system: hack sawing
trace of
trace of
tool
workpiece
trace of
trace of
fv
primary motion
zf
feedmotion
ps PP ≡of PP ≡
rP
rκ
rP ps PP ≡
of PP ≡
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Modeling of Machining5
Hard machining4
Cutting processes with parallel translation3
Cutting processes with rotary motion2
Introduction1
Outline
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Hard machining with geometrically defined cutting e dgesTechniques
� 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 anddistortion
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 f orm and size,small and medium parts need to be oversized by appr ox. 0.3 - 0.5 mm
HardHardening /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 bydefined 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: X210CrW12hardened (63 HRC)
Machining: Hard turning of theprofile
Part: Precision profile rollerO 150 mm
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Modeling of Machining5
Hard machining4
Cutting processes with parallel translation3
Cutting processes with rotary motion2
Introduction1
Outline
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Force calculation: time functionSubstitution of the empirical force equation propos ed by Kienzle with the technical terms:
imii hbkF −⋅⋅= 1
1.1
polar coordinatenumber of teeth
diameter of the tool
equation proposed bySalomon or Kienzle
source: Diss. Rehse
discretisation of the equation:
basement for modeling
Question: What is the angle ωωωω?
( )im
r
c
f
r
pii
vz
vDakF
−
⋅⋅
⋅⋅⋅
⋅⋅≈1
1.1 sinsinsin
κωπ
κ
( )im
rc
c
f
r
pii
D
dtv
vz
vDakdF
−
⋅
⋅⋅⋅⋅
⋅⋅⋅⋅≈
1
1.1 sin2
sinsin
κπ
κ
tvb c ⋅=)D
b)⋅= 2ω
ωκ sinsinmax ⋅⋅≈ rzfh
r
pab
κsin=
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Force calculation: technical terms
discretisation of the equation:
discrete time function
Solving the equation fordiscrete times
discrete force components
)(dtdFi
transformation of theforce components intothe x- and y- direction
addition of the forcecomponents in x- andy- direction separately
forc
e in
x /
N
time / sec
measuredcalculated
The same procedurefor the other flutes!
( )im
rc
c
f
r
pii
D
dtv
vz
vDakdF
−
⋅
⋅⋅⋅⋅
⋅⋅⋅⋅≈
1
1.1 sin2
sinsin
κπ
κ
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Penetration calculation: peripheral milling
vector field for representation the tool
vector field for representation the workpiece
feedvelocity
matrix model for the penetration calculation
data of the machine tool data of the workpiecedata of the tool
thickness of cut h width of cut b
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Thank you for your attention!!
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Modeling of Machining5
Hard machining4
Cutting processes with parallel translation3
Cutting processes with rotary motion2
Introduction1
Outline
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Modeling of Machining5
Hard machining4
Cutting processes with parallel translation3
Cutting processes with rotary motion2
Introduction1
Outline
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Process classification
source: DIN 8589-0
Manufacturing Processes
1
primary shaping
2secondaryshaping /forming
3
cutting
4
joining
5
coating
6changingmaterial
properties
3.2cutting
3.2.1
turning
3.2.2drilling
reaming
3.2.3
milling
3.2.4planingshaping
3.2.5
broaching
3.2.6
sawing
3.2.7filing
rasping
3.2.8
brushing
3.2.9scrapingchiselling
rotary motion parallel translation
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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 materialinformation
disadvantage
This information is contained in thespecific force parameter!