v10 Grinding II

38
Modelling and Simulation in Manufacturing Technology Modeling and Simulation of Grinding processesProf. 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

Transcript of v10 Grinding II

Page 1: 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

Page 2: v10 Grinding II

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

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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

Page 4: v10 Grinding II

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

Page 5: v10 Grinding II

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

Page 6: v10 Grinding II

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

Page 7: v10 Grinding II

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

Page 8: v10 Grinding II

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

Page 9: v10 Grinding II

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

Page 10: v10 Grinding II

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

Page 11: v10 Grinding II

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

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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

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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

Page 14: v10 Grinding II

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

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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

Page 16: v10 Grinding II

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

Page 17: v10 Grinding II

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

Page 18: v10 Grinding II

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

Page 19: v10 Grinding II

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

Page 20: v10 Grinding II

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

Page 21: v10 Grinding II

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

Page 22: v10 Grinding II

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

Page 23: v10 Grinding II

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

Page 24: v10 Grinding II

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

Page 25: v10 Grinding II

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

Page 26: v10 Grinding II

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

Page 27: v10 Grinding II

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

Page 28: v10 Grinding II

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

Page 29: v10 Grinding II

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

Page 30: v10 Grinding II

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

Page 31: v10 Grinding II

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).

Page 32: v10 Grinding II

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

Page 33: v10 Grinding II

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

Page 34: v10 Grinding II

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

Page 35: v10 Grinding II

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

Page 36: v10 Grinding II

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

Page 37: v10 Grinding II

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

Page 38: v10 Grinding II

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?