v10 Grinding II
Transcript of v10 Grinding II
Modelling and Simulation
in Manufacturing Technology
„„ Modeling and Simulation of Grinding processes““
Prof. Dr.-Ing. F. Klocke
Structure
Introduction and motivation
The Grinding process - important aspects for process modeling
Classification of the process models
Kinematic penetration calculation
Simulation of the grinding process with FEM
Summarization
Introduction and Motivation
Continously increasing claims of the market lead toincreasing requirements for manufacturing processes.
Product
Innovativauthenticcost-saving
Components
High qualityHigh precisionLong product life
Manufacturing process
EconomicReproduceableFlexibel
For Controlling and Development of the grinding process a high degree of technological knowledge is required.
A high potential for amplification the process knowledge and to optimizationis based on modeling and simulation the grinding process.
Finishing manufacturing method to achieve a high product quality and precision
High dimension and contouring accuracy
High surface quality
High performance process with high stock removal rate
The grinding process
Introduction and Motivation
Modeling and Simulation: aims and requirements
4
12
16
8
24
12
Manufacturing tests
FEM-Calculating
76 w
eeks
Todaywithout process simulation Product specification-
Component
Concept design(Work piece choice)
Lay-out of design
Manufacturing aspects
Construction
Manufacturing planning
Manufacturing
Work piece-test
AIMS
Fore cast of the process stability
Increase of the process understanding
Amplification of the process knowledge
Cost reduction
Fore cast of the component characteristics
Reduction of planning- and development steps
54 w
eeks
Product specification-Component
Concept design(Work piece choice)
Lay-out of design
Construction
Manufacturing planning
Manufacturing
Work piece-test
4
12
14
12
12
Reduction of the cycle time of 30%
FEM-Berechnungen
Pro
zess
-
s imulation
Futurewith process simulationAIMS
Fore cast of the process stability
Increase of the process understanding
Amplification of the process knowledge
Cost reduction
Fore cast of the component characteristics
Reduction of planning- and development steps
Modeling and Simulation: aims and requirements
REQUIREMENTS
High result savety
High result quality
Realistic fore cats of process results
Accomodation of technological innovations
AIMS
Fore cast of the process stability
Increase of the process understanding
Amplification of the process knowledge
Cost reduction
Fore cast of the component characteristics
Reduction of planning- and development steps
Modeling and Simulation: aims and requirements
Structure
Introduction and motivation
The Grinding process - important aspects for process modeling
Classification of the process models
Kinematic penetration calculation
Simulation of the grinding process with FEM
Summarization
The grinding process - Basics
vW
vS
Cutting speeds:vc ≈ 15 till 200 m/s
Temperatures:above 1200°C
Temperature gradients:106 °C/s / 103 °C/mm
Forming speeds:ϕ ≈ till 107 1/s
The grinding process - Chip formation in grinding
workpiece
chipaccumulation
grain trajectory
vs
elasticdeformation
I
elastic and plasticdeformation and
chip removal
III
bond
grain (cutting edge)
hcu eff hcu
Ft,S
Fn,S
grinding wheel
II
Tµ
Werkstück
chipAufwurf
grinding wheel
bond
grain (cutting edge)
Qs+ QkQkss +Qw +Pc = Ft vc = Pm +
Ft,S
Qs
Qk
grain trajectory
vs
Work piece
Qw
True rake friction
shear energy
displacement energy
blank friction
environment(coolant, air) Qkss
The grinding process - Chip formation in grinding
Micro ploughingenergetic inconvenient
removal mechanisms
Vremoval
Vforming≈
1
150... 1
200
The grinding process - Metal removal mechanisms of grinding
Micro furrowingenergetic very inconvenient removal mechanisms
Micro flow cuttingenergetic convenient removal mechanismsbig depth of cut hcu
Micro curled chippingenergetic convenient removal mechanisms
Vremoval
Vforming
1big depth of cut hcu
Inc
rea
sin
g c
utt
ing
sp
ee
d v
c
Inc
rea
sin
g e
ng
ag
em
en
t d
ep
th h
cu
Conclusion in between: The grinding process - a complex method
Output parameters
Process behaviour
Grinding forceswear
amplitudes
Work result
Surface qualityform accuracy
work piece structure
Process
Removal mechanisms
Mechanical stress
Wear mechanisms
Mechanicalforming
Thermalforming
Thermalstress
Input parameters
Grinding wheel
Kinematic
Work piece
Environment
Process parameters
Structure
Introduction and motivation
The Grinding process - important aspects for process modeling
Classification of the process models
Kinematic penetration calculation
Simulation of the grinding process with FEM
Summarization
Definitions
Simulation
A simulation is a replication of a dynamic process in a model.
Model
A model is an abstract system that accords to a real system and thats used for expensive and impossible
investigations andcalculations and explanations- or demonstration purposes.
It delivers general information about
elements,structure and behaviour
Of a part of the reality.
Classification of the process models
Process models
empiric process models physical process models
Good description of special problems
little development input necessary for easy problems
Conditional transfer to othermanufacturing terms
Based on experimental investigations
Manufacturing independent
Exact formulation of the context often impossible
high development input necessary
Deduced from physical
constitutional laws
Describes inner contexts
Classification of the process models
Process models
empiric process models physical process models
Regressions-analysis
x
x xx x
xx
x x
x
xx
ANNNumericModeling
Analytic Modeling
mx+bx-cx = CU0sin(ωt)
u = U0sin(ω t)
x, x, x
Kinematicpenetration calculation
FEM-Simulation(Microscopic)
Physical cutting simulation
FEM-Simulation(Macroscopic)
Structure
Introduction and motivation
The Grinding process - important aspects for process modeling
Classification of the process models
Kinematic penetration calculation- Modelling of the grinding wheel topography- Modelling of the Kinematic- Output parameters
Simulation of the grinding process with FEM
Summarization
Process models
Grindingforces/-power
Single graingrinding wheel
thermal-flows
Model concept of kinematic simulation in grinding processes
Kinematicmetal cutting-
parameters
cutting thickness,-width, -length,
-profile
Process kinematicand
penetration calculation
Process parameters
Numeric Modelof a grinding wheel
Macro- Micro-geometry geometry
Numeric Modelof the work piece
Macro- Mikro-geometry geometrie
Micro-geomtry
Model concept of kinematic simulation in grinding processes
Process models
Grindingforces/-power
Single graingrinding wheel
thermal-flows
KinematicMetal cutting-parameters
cutting thickness-width, -length,
-profile
Process kinematicand
penetration calculation
Process parameters
Numeric Modelof a grinding wheel
Macro- Micro-geometry geometry
Numeric Modelof the work piece
Macro- Mikro-geometry geometrie
Micro-geomtry
Macro geometry
Numeric model of a grinding wheel
Profile
Waviness
Excentricity
Concentricity deviation
Concentricity deviationWavinessProfile
Macro geometry
Micro geometryTopography
Profile
Waviness
Excentricity
Concentricity deviation
Specification- grain material- bond- grain dispersal- pore volume
Grain size
Grain form
grain
Numeric model of a grinding wheel
Analysis and modeling of the grain geometry
Octahedron Tetrahedron
8/8 8/6 8/4 8/2 8/0
Oct
ahed
ron
Cub
e
8/8
6/8
4/8
2/8
0/8
8 6 4 2 0
8
7
6
5
4
Analysis of the realgrain geometry
Inquiry of the statisticdispersion of the grain model
parameter
Analysis of the realgrain geometry
Determination of the ideal
basic-form and grain parameters
Analysis of the realgrain geometry
Determination of the ideal
basic-form and grain parameters
Generation of the ideal grain form
Finalization of the number and orientation of further grain layer
Generation of the final grain geometry
Analysis and modeling of the grain geometry
Ellipsoid
Tetrahedron
Ball
Octahedron Cube
Analysis of the realgrain geometry
Inquiry of the statisticdispersion of the grain model
parameter
Analysis of the realgrain geometry
Determination of the ideal
basic-form and grain parameters
Analysis of the realgrain geometry
Determination of the ideal
basic-form and grain parameters
Generation of the ideal grain form
Finalization of the number and orientation of further grain layer
Generation of the final grain geometry
Analysis and modeling of the grain geometry
Octahedron
qm = Length dilation coefficientlAklAl
lAk Length of the short grain axis
lAl Length of the long grain axis
Grain model parameter:
Real grain form
NKF Number of grain faces
lAl
lAk
Analysis of the realgrain geometry
Inquiry of the statisticdispersion of the grain model
parameter
Analysis of the realgrain geometry
Determination of the ideal
basic-form and grain parameters
Analysis of the realgrain geometry
Determination of the ideal
basic-form and grain parameters
Generation of the ideal grain form
Finalization of the number and orientation of further grain layer
Generation of the final grain geometry
Analysis and modeling of the grain geometry
lAl = Length of the long grain axis
lAk= Length of the short grain axislAk
lAl
grain 1 grain 2
lAllAk
Model to specify the length of the short grain axis lAk
-560 80 100 120 140 160 180
Length of the short grain axis lAk [µm]
rela
tive
fre
qu
en
cy
[%]
0
5
10
15
20
25
0
quantifiedmodeleddifference
φ(x) =1
σ • (2π)0,5 • e-(x-µ)2
2 • σ2
Gaussian Distribution:
Analysis of the realgrain geometry
Inquiry of the statisticdispersion of the grain model
parameter
Analysis of the realgrain geometry
Determination of the ideal
basic-form and grain parameters
Analysis of the realgrain geometry
Determination of the ideal
basic-form and grain parameters
Generation of the ideal grain form
Finalization of the number and orientation of further grain layer
Generation of the final grain geometry
Analysis and modeling of the grain geometry
2,21,6 1,8 2,01,41,21,0
Model to specify thelongitudinal extension coefficient qm
-5
rela
tive
fre
qu
en
cy
[%]
0
5
10
15
20
25
longitudinal extension coefficient qm
0
Lorenz Distribution:
y = y0 +(2•A•W/ π)
(W2+4•(x-xc)2)
quantifiedmodeleddifference
lAl = Length of the long grain axis
lAk= Length of the short grain axislAk
lAl
grain 1 grain 2
lAllAk
Analysis of the realgrain geometry
Inquiry of the statisticdispersion of the grain model
parameter
Analysis of the realgrain geometry
Determination of the ideal
basic-form and grain parameters
Analysis of the realgrain geometry
Determination of the ideal
basic-form and grain parameters
Generation of the ideal grain form
Finalization of the number and orientation of further grain layer
Generation of the final grain geometry
Analysis and modeling of the grain geometry
Model to specify thenumber of grain surfaces NKF
-5
rela
tive
fre
qu
en
cy
[%]
0
5
10
15
20
25
quantifiedmodeleddifference
number of grain surfaces NKF
4 5 6 7 8 9 10 11 12
φ(x) = 1σ • (2π)0,5 • e
-(x-µ)2
2 • σ2
Gaussian Distribution :
lAl = Length of the long grain axis
lAk= Length of the short grain axislAk
lAl
grain 1 grain 2
lAllAk
Analysis of the realgrain geometry
Inquiry of the statisticdispersion of the grain model
parameter
Analysis of the realgrain geometry
Determination of the ideal
basic-form and grain parameters
Analysis of the realgrain geometry
Determination of the ideal
basic-form and grain parameters
Generation of the ideal grain form
Finalization of the number and orientation of further grain layer
Generation of the final grain geometry
Analysis and modeling of the grain geometryz
x
Hessesche normal form
n1yn1x n1z c1 = E1E1: n1 • x1 = c1
ci = distance from plane to the centre of the coordinates
ci = n0i • x ni
ni
ci = • x
y
ni
ci
E1
nix
niy
niz
ni = = normal vektorAnalysis of the real
grain geometry
Inquiry of the statisticdispersion of the grain model
parameter
Analysis of the realgrain geometry
Determination of the ideal
basic-form and grain parameters
Analysis of the realgrain geometry
Determination of the ideal
basic-form and grain parameters
Generation of the ideal grain form
Finalization of the number and orientation of further grain layer
Generation of the final grain geometry
Analysis and modeling of the grain geometryz
E8
n8yn8x n8z c8 = E8
E5
n5yn5x n5z c5 = E5
E4
n4yn4x n4z c4 = E4
E1
l Al
lAk
y
base geometrie
n1yn1x n1z c1 = E1
E6
n6yn6x n6z c6 = E6
E2
n2yn2x n2z c2 = E2
E3
n3yn3x n3z c3 = E3
E7
n7yn7x n7z c7 = E7
Analysis of the realgrain geometry
Inquiry of the statisticdispersion of the grain model
parameter
Analysis of the realgrain geometry
Determination of the ideal
basic-form and grain parameters
Analysis of the realgrain geometry
Determination of the ideal
basic-form and grain parameters
Generation of the ideal grain form
Finalization of the number and orientation of further grain layer
Generation of the final grain geometry
Analysis and modeling of the grain geometry
n8yn8x n8z c8 = E8
n5yn5x n5z c5 = E5
n4yn4x n4z c4 = E4
n1yn1x n1z c1 = E1
n2yn2x n2z c2 = E2
n3yn3x n3z c3 = E3
n6yn6x n6z c6 = E6
n7yn7x n7z c7 = E7
z
y
E10
E12
E14
E9
E13
E11
base geometrie
n14yn14x n14z c14 = E14
n11yn11x n11z c11 = E11
n10yn10x n10z c10 = E10
n9yn9x n9z c9 = E9
n12yn12x n12z c12 = E12
n13yn13x n13z c13 = E13
x
Analysis of the realgrain geometry
Inquiry of the statisticdispersion of the grain model
parameter
Analysis of the realgrain geometry
Determination of the ideal
basic-form and grain parameters
Analysis of the realgrain geometry
Determination of the ideal
basic-form and grain parameters
Generation of the ideal grain form
Finalization of the number and orientation of further grain layer
Generation of the final grain geometry
Analysis and modeling of the grain geometryz modified geometrie
yn8yn8x n8z c8 = E8
n5yn5x n5z c5 = E5
n4yn4x n4z c4 = E4
n1yn1x n1z c1 = E1
n2yn2x n2z c2 = E2
n3yn3x n3z c3 = E3
n6yn6x n6z c6 = E6
n7yn7x n7z c7 = E7
n14yn14x n14zc14 = E14
n11yn11x n11zc11 = E11
n10yn10x n10zc10 = E10
n9yn9x n9z c9 = E9
n12yn12x n12zc12 = E12
n13yn13x n13zc13 = E13
x
Analysis of the realgrain geometry
Inquiry of the statisticdispersion of the grain model
parameter
Analysis of the realgrain geometry
Determination of the ideal
basic-form and grain parameters
Analysis of the realgrain geometry
Determination of the ideal
basic-form and grain parameters
Generation of the ideal grain form
Finalization of the number and orientation of further grain layer
Generation of the final grain geometry
Analysis and modeling of the grain geometry
z
y
modified geometry
x
n8yn8x n8z c8 = E8
n5yn5x n5z c5 = E5
n4yn4x n4z c4 = E4
n1yn1x n1z c1 = E1
n2yn2x n2z c2 = E2
n3yn3x n3z c3 = E3
n6yn6x n6z c6 = E6
n7yn7x n7z c7 = E7
n14yn14x n14z c14 = E14
n11yn11x n11z c11 = E11
n10yn10x n10z c10 = E10
n9yn9x n9z c9 = E9
n12yn12x n12z c12 = E12
n13yn13x n13z c13 = E13
Analysis of the realgrain geometry
Inquiry of the statisticdispersion of the grain model
parameter
Analysis of the realgrain geometry
Determination of the ideal
basic-form and grain parameters
Analysis of the realgrain geometry
Determination of the ideal
basic-form and grain parameters
Generation of the ideal grain form
Finalization of the number and orientation of further grain layer
Generation of the final grain geometry
Analysis and modeling of the grain geometry
Analysis of the realgrain geometry
Inquiry of the statisticdispersion of the grain model
parameter
Analysis of the realgrain geometry
Determination of the ideal
basic-form and grain parameters
Analysis of the realgrain geometry
Determination of the ideal
basic-form and grain parameters
Generation of the ideal grain form
Finalization of the number and orientation of further grain layer
Generation of the final grain geometry
Part models for modelling the bond
grain
bond backside
vc
reality model
bond
Analysis and modeling of the grain dispersal in the grinding facing
lm
lm
14
12
10
8
6
4
2
0
rela
tive
fre
que
ncy
[%]
-140 140-120 -60 -20 20 60 100Distance from ideal position [µm]
Average grain distance lm=220 µm
120
∆x∆y
reality
model
∆ x = tangential grain offset∆ y = Axial grain offset
∆x∆y
Modeling of the grain orientation in the grinding facing
αk: angle of the grains rotation around the principal axis (0° < α < 360°)
βk: angle of the grains tilting aroundthe principal axis (0° < β < 30°)
χk: angle of the grains tilting around the principal plane (0° < χ < 45°)
x
y
z
αk
χk
βk
principal axis
principal plane
Numeric models in a grinding wheel
Zitt Kempa Hegeman
x
y12 1110
2
91
7
861415
16
1918
20
12
15
38
78
112827 26
25
2423 16
14
613
20
1918
2122
Model concept of the process kinematics and the penetration calculation
Kinematicmetal cutting-
parameters
cutting thickness,-width, -length,
-profile
process parameters
numeric modelof a workpiecemacro- micro-
geometry geometry
numeric modelof a grinding wheel
macro- micro-geometry geometry
prozess kinematicand
penetration-calculation
prozess kinematicand
penetration-calculation
process models
grindingforces/-power
single graingrinding wheel
thermal-flows
Model concept of the process kinematics and the penetration calculation
Assumptions:
1. workpiece stands fast
2. grinding wheel moves
around the workpiece
P
Kw
yw
xw
rw
rs βα
γ
∆x
∆y
∆z
V
zs
Ks xs
ys
workpiece
grinding wheel
Model concept of the process kinematics and the penetration calculation
coordinate systemKs ,Kw
rotation around x, y, z-axis α, β, γ
offset vector V
offset rate∆x, ∆y, ∆z
point P
position vector to point Prs , rw
rotation matrixD
P
Kw
yw
zw
xw
rw
rs βα
γ
∆x
∆y
∆z
V
zs
Ks xs
ys
rw = Ts,w • rs
=Ts, w = V0T
D1
cosβ cosγ sinα sinβ cosγ- cosα sinγ
cosα sinβ cosγ+ sinα sinγ
∆x
cosβ sinγ sinα sinβ sinγ+cosα cosγ
cosα sinβ sinγ- sinα cosγ
∆y
- sinβ sinα cosβ cosα cosβ ∆z
0 0 0 1
transformation matrix
Model concept of the process kinematics and the penetration calculation
rw = Ts,w • rs
=
cos γ 1 - sin γ 1 0 ∆x1,5 + x4(t)
Ts,wsin γ 1 cos γ 1 0 ∆y1,5 + y2(t)
∆z1,5 + z3(t) 10 0 0 0 0 1
= Ts,w
1
cos γ1 - sin γ1 0 ∆x1,2
sin γ1 cos γ1 0 ∆y1,2
∆z1,21 0 0
0 0 0 1
T1,2
2
1 0 0 ∆x4,5+ x4(t)
0 1 0 ∆y4,5
∆z4,51 0 0
0 0 0 1
T4,5
5
KS
KW
1 0 0 ∆x2,3
0 1 0 ∆y2,3 + y2(t)
∆z2,31 0 0
0 0 0 1
T2,3
3
1 0 0 ∆x3,4
0 1 0 ∆y3,4
∆z3,4+ z3(t)1 0 0
0 0 0 1
T3,4
4
feeding-inslide 2x y z
transversal feed-in slide 3x y z
longitudinal feed-in slide 4x y z
workpiece5
x y z
tool1
x y z α β γ α β γ α β γ α β γ α β γ
Model concept of the process kinematics and the penetration calculationexternalcylindrical grinding
internalcylindricalgrinding
surfacegrinding
rotarygrinding
peripheral-
plunge-
grinding
peripheral-
longitudinal-
grinding
face-
plunge-
grinding
face-
longitudinal-
grinding
Model concept of the process kinematics and the penetration calculation
grains cladding profile
grinding direction
bk
10
µm30
0
gra
in h
eig
ht
h k
grain width bk
maximal grain profilerighted to grinding direction
grinding direction
likin,3D
cutting length
cutting width
cutting thickness
cuttingprofile
Results of the penetration calculation
Process kinematicand
penetration-calculation
Prozessparameter
numeric modelof a workpiecemacro- mikro-
geometry geometry
numeric modelof a grinding wheel
macro- micro-geometry geometry
prozess modelsprozess models
grindingforces/-power
single graingrinding wheel
grindingforces/-power
single graingrinding wheel
thermalflows
thermalflows
Kinematicmetall cutting-
parameters
cutting thickness,-width, -length,
-profile
Kinematicmetall cutting-
parameters
cutting thickness,-width, -length,
-profilemicro-
geometry
Simulated 3D-work piece surfaces
Hegeman
010
µm
30
Kempa
Zitt
Results of the penetration calculation
cuttinglength
cuttingwidth
cuttingthickness
cutting profile
angle of the grinding wheelcu
rre
nt c
utti
ng p
rofil
e0° 180° 360°
0
50
100
µm²
200current cutting profile
angle of the grinding wheel
curr
en
t cu
tting
pro
file
0° 180° 360°0
50
100
µm²
200current cutting profile
Results of the penetration calculation
cuttinglength
cuttingwidth
cuttingthickness
cutting profile
0 2 4 µm 8
rel.
fre
que
ncy
0
2
4
%
8maximal cutting thickness
maximal cutting thickness
angkle of the grinding wheell
curr
en
t cu
tting
pro
file
0° 180° 360°0
50
100
µm²
200current cutting profile
0 2 4 µm 8
rel.
fre
quen
cy
0
2
4
%
8
maximal cutting thickness
maximal cutting thickness
Results of the penetration calculation
tangential grinding force
cuttinglength
cuttingwidth
cuttingthickness
cutting profile
angle of the grinding wheel
500
250
0
125
N
tang
ent
ialg
rind
ing
fo
rce
Ft
0° 180° 360°
Ft (simulation)
Ft (experiment)
Ft,stat.
angle of the grinding wheel
curr
en
t cu
tting
pro
file
0° 180° 360°0
50
100
µm²
200current cutting profile
0 2 4 µm 8
rel.
fre
quen
cy
0
2
4
%
8
maximal cutting thickness
max. cutting thickness angle of the grinding wheel
500
250
0
125
NFt (simulation)
Ft (experiment)
Ft,stat.
tang
entia
lgrin
diin
g fo
rce
Ft
0° 180° 360°
tangential grinding force
Model concept of the kinematic simulation of grinding processes
models to calculate theelastic-mechanic deformation
spindle tool
model to generate the abrasionof the grinding wheel
models to calculate the thermal-elastic deformation
models to calculate the thermal stress
superpositioning andcalculating of the
resultingform- and size-
deviation
prozess modells
grindingforces/-power
single graingrinding wheel
thermalflows
kinematicmetal cutting-
parameters
cutting thickness,-width, -length,
-profile
process kinematicand
penetration-calculation
numeric modelof the grinding wheel
macro- micro-geometry geometry
numeric modellof the workpiecemacro- micro-
geometry geometry
process parameters
Conclusion in between - Kinematic penetration calculation
closed simulation of the grinding process
adjustment of the complexity of the model by integrationof sub models
close to reality numeric model of the grinding wheel
modelling of a multitude of grinding grains
but:
Elastic-plastic workpiece behaviour is not considered.
Structure
Introduction and motivation
The Grinding process - important aspects for process modeling
Classification of the process models
Kinematic penetration calculation
Simulation of the grinding process with FEM- macroscopic layer- microscopic layer, physical cutting simulation
Summarization
Principle of the FEM
object
material- and process parameters of the
grinding process are often not available or
can only be acquired very inaccurate
linking-up
linked-up object
numeric calculation of:
offset v
expansion εstress σdeformation ϕspeed of deformation ϕtemperature ϑ
.
material parameters:
flow sheets
thermal expansion coefficient
grade of emissions
process parameters:
thermal distribution factor kw
2D
3D
Example: Thermal dispersal factor kw
thermal flow during grinding
determination of kw during grinding is difficult
temperature in the contact zone can not be
measured directlythermal distribution factor depend on
process parameters
estimation of kw
change kw iterative until the temperatureat the measuring points in the model
and in reality nearly match
gauging of the temperature close to the contact zone
thermal elements thermal cameras
estimation of kw
Qw = kw • Pc = kw • Ft • vc
Fn
5 - 84 %
3 - 38 %9 - 52 %
2 - 12 %
Ft
vc
Qw
Model for temerature calculation in the grinding process
q
onside definedsemi-infinite solid
adiabaticsurface
z
x
∞ ∞
bk»lk
lk=2l
V
workpiece
speed of theheat source
v
x
y
z
q
model by Carslaw and Jaeger
heat source has a constant anduniformly distributed heat flow density
heat source moves straight-line andwith constant speed over the surface
heat source has an unlimited expansion vertical to the direction of movement
the heated solid is semi-infinite that means it is only limited at one side
the surface of the solid is adiabatic
quasi-stationary circumstances, t.m.that the residence time of the heat was long enough
From the real process to the FEM model
contact length lg
seat υ0 = +20 ° C
cooling lubricant
fixin
g
grinding wheel
cla
mp
ing
forc
ep
s
lg
cla
mp
ing
fo
rce
ps
cooling
heat source qw
cooling
const. temperature level υ0 = + 20°C
surface-pressure pr
workpiece vf g
specification of the abstraction level
How are the thermal and mechanicalencumbrances specified?
Where do the mechanical and thermalencumbrances take effect?
f.e. heat sources
triangularrectangular
parabolicallytrapezoid-shaped
FEM - simulation in the grinding process - example
grinding wheel/ workpiece:grinding wheel: 89A60-219AV2workpiece: nickel basis alloy
process parameters:cutting speed vc: 26 m/sfeed rate vft: 300 mm/minspecific removal rate Q‘ : 5 mm³/mm sradial feed in fr: 1 mmcontact depth ap: 12,5 mm
process-/simulations parameters:tangential force Ft: 116 Ncutting performance Pc: 3016 W
heat distribution factor : kw = 22%temperature measured 520 °Cat measuring point simulated 529 °C
vf
Conclusion in between - FEM simulation
FEM allows the arial and timed simulation of physicalprocedures during the grinding process
FEM is a proper device in order to analyse andoptimise the grinding process
but:
quality of the simulation depends on the predefined simplifications
exact knowledge of the material- and process parameters is necessary
level of detailing of the FE-model is limited by the present computer performance
Results of the penetration calculation
Introduction and motivation
The Grinding process - important aspects for process modeling
Classification of the process models
Kinematic penetration calculation
Simulation of the grinding process with FEM- macroscopic layer- microscopic layer, physical cutting simulation
Summarization
Physical cutting simulation with FEM
potential
exact simulation of the physical procedures at the grain cutting edge is possible
the elasto-plastic material behaviour will be considered
challenge
exacte knowledge of the material is required
material flow curves for high deformation speeds and high temperaturesare necessary
Split-Hopkinson-Bar-Test
projectile tempered chamber
front-end staff output staff
probe
v >> 50m/s .ϕ bis 104 s-1≈
Split-Hopkinson-Bar-Test
2600
[MPa]
2200
2000
1800
1600
1400
1200
1000
flow
str
ess
grade of deformation
deformation speed
.
projectile tempered chamber
front-end staff output staff
RT 600 [C°] 900
100
[%]
60
40
20
0
ϕ = 0,1
temperature
ψ
thermal coefficient
1
2
σ (T, ϕ = 0,1)σ (T = RT,ϕ = 0,1)
ψ =kf = σ (ϕ, ϕ )
kf = f (ϕ, ϕ , ψ).
Single-grit-tests
L
hcu,max
vcvf
single-grit test
FEM-simulation
∆x
x
y
z
basic kinematics:longitudinal-pheripheral-surfacegrinding
vcvf
vf
L
hcu,max
vc
Optimized lay-out of the FEM - model
fortunate model
symmetry plane
characteristics
elasto-plastic workpiecehigher grid density nearby the grain,to reproduce elasto-plastical materialbehaviour
symmetry planes
grit optimisation
Optimized lay-out of the FEM - model
hcu, max
vx
vy
vx
vy
max. in-feed depth
eraser windowallowance area
vx
vy
end
vx
vy
eraser window
start
hcu, max
the whole componentmust be linked-up
grain moves on the contact track
long simulation duration
partiel linking-up around the grain
grain moves in in-feeddirection, workpiece in form feed direction
shorter simulation duration
Single-grit-tests with the FEM - model
crenation depth: 5 µmspeed : 1,26 m/s spike radius : 2,5 µmmaterial : 16MnCr5, carburised, tempered
Results of the physical cutting simulation
appliance to analyse andoptimise of the metal removalmechanisms
shaping of the elasto-plasticmaterial behaviour in the model
Results of the physical cutting simulation
speed vector
residual stresstemperature
model
Results of the physical cutting simulation
de
form
atio
n sp
ee
d
1 2 3 4 5 6 7spot
123
45
67
vc = 1,26 m/s
vc = 0,63 m/s
600
300
150
x10³1/s
0
workpiece: 16MnCr5
grain: inelastic
in-feed: 2µm
chipping length: 200µm
friction coefficient: 0,2µ
deformation speed
Results of the physical cutting simulation
1 2 3 4 5 µm 7
workpiece: 16MnCr5
grain: starr
feed-in: 2µm
chipping length : 200µm
friction coefficient : 0,2µ
123
4
vc = 1,26 m/s
vc = 0,63 m/s
400
200
100
°C
0
tem
pe
ratu
re
temperature
Conclusion in between - physical cutting simulation
physical friction simulation enabled the proper simulation of physical procedures at the grain cutting edge
physical machining simulation is a qualified tool to analyse and optimise the grinding process
but:
at the moment, physical machining simulation has only been realised for low cutting speed spheres
exact knowledge of material- and process parameters are requiered
because of the fact that high computer power is needed, the physical machining simulation is currently confined to the modelling of a single grain
Structure
Introduction and motivation
The Grinding process - important aspects for process modeling
Classification of the process models
Kinematic penetration calculation
Simulation of the grinding process with FEM- macroscopic layer- microscopic layer, physical cutting simulation
Summarization
Summarization
the physical simulation of the grinding process using numeric operations gains in importance.
kinematic penetration computation:
any complex, closed simulation by integrationof part models
good approximation of the geometric undefined form of the grinding grain
close to reality modelling of the grinding wheel
simulation and penetration calculation of many cutting edges
no consideration of the elasto-plastic material dehaviour
qualitative statement about the grinding process
Summarization
FEM-simulation (macro- und microscopic):
consideration of the elasto-plastic material behaviour
exact knowledge of the needed material- and processparameters
determination of the needed parameters in the spheres that are interesting for grinding is not easy
mainly the level of detail is limited by the computer power
qualitative and quantitative results
potential is in the combination of different rudiments
the models are at the moment not nicht compatible
Questions I1) What is the material removal-rate a quantum for?
2) How do you assign the material romoval volume?
3) In which procedures for generating a rationally symmetric geometry is the tool feed a) radial b) axial?
4) What is the difference between down-grinding / up-grinding?
5) Name four common grinding procedures!
6) How can you avoid workpiece deflection in the process of external cylindrical grinding?
7) What problems can occur in the internal cylindrical grinding process andhow are they caused?
8) What are the advantages and disadvantages in deep- and pendulum-grinding?
9) What are the typical devices, which are machined in centreless grinding?
10) What are the four active principles of the cutting edge engagement in machining with geometrically undefined cutting edges?