1/48 sajid ullah butt conception et modélisation d'un montage de fabrication pour le...

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1/48 Conception Fabrication Com m ande Conception Fabrication Com m ande Sajid Ullah BUTT Conception et modélisation d'un montage de fabrication pour le balançage optimisé d'une famille de pièces Arts et Métiers ParisTech - Centre de Metz Laboratoire de Conception Fabrication Commande EA 4495 Jury M. Cornel Mihai NICOLESCU, Professeur, KTH, Stockholm, Sweden Rapporteur M. Jean-François RIGAL, Professeur, LAMCOS, INSA Lyon, France Rapporteur M. Henri PARIS, Professeur, G.SCOP, Université Joseph Fourier, Grenoble, France Examinateur M. Jean-François ANTOINE, Maitre de conférences, IUT de Nancy Brabois, France Co-directeur de thèse M. Patrick MARTIN, Professeur, LCFC, Arts et Métiers ParisTech, Metz, France Directeur de thèse

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Page 1: 1/48 Sajid Ullah BUTT Conception et modélisation d'un montage de fabrication pour le balançage optimisé d'une famille de pièces Arts et Métiers ParisTech

1/48

Conception Fabrication CommandeConception Fabrication Commande

Sajid Ullah BUTT

Conception et modélisation d'un montage de fabrication pour le balançage optimisé d'une famille de pièces

Arts et Métiers ParisTech - Centre de MetzLaboratoire de Conception Fabrication Commande EA 4495

Jury M. Cornel Mihai NICOLESCU, Professeur, KTH, Stockholm, Sweden Rapporteur

M. Jean-François RIGAL, Professeur, LAMCOS, INSA Lyon, France Rapporteur

M. Henri PARIS, Professeur, G.SCOP, Université Joseph Fourier, Grenoble, France Examinateur

M. Jean-François ANTOINE, Maitre de conférences, IUT de Nancy Brabois, France Co-directeur de thèse

M. Patrick MARTIN, Professeur, LCFC, Arts et Métiers ParisTech, Metz, France Directeur de thèse

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Conception Fabrication CommandeConception Fabrication CommandePresentation layout

Sajid Ullah BUTT, PhD Defense 5 July 2012

• Context

• Positioning errors

• Compensation

• Objectives

• Workpiece repositioning through locators

• All the elements rigid

• Proposed fixturing system

• Analytical formulation

• Large displacements and Homogeneous Transformation Matrices

• Deformation of elastic elements and rigid body displacement of part on fixture under load

• Deformation of locators and contacts

• Lagrangian formulation

• Negligible friction, Small Displacements

• Convergence of non-linear contact deformation

• Work realized

• Conclusion

• Future work

Case Study

Context Kinematic Model Mechanical Model Conclusion and Perspectives

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Conception Fabrication CommandeConception Fabrication CommandePresentation layout

Sajid Ullah BUTT, PhD Defense 5 July 2012

• Context

• Positioning errors

• Compensation

• Objectives

• Workpiece repositioning through locators

• All the elements rigid

• Proposed fixturing system

• Analytical formulation

• Large displacements and Homogeneous Transformation Matrices

• Deformation of elastic elements and rigid body displacement of part on fixture under load

• Deformation of locators and contacts

• Lagrangian formulation

• Negligible friction, Small Displacements

• Convergence of non-linear contact deformation

• Work realized

• Conclusion

• Future work

Case Study

Context Kinematic Model Mechanical Model Conclusion and Perspectives

CONTEXT KINEMATIC MODEL MECHANICAL MODEL CONCLUSION

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Conception Fabrication CommandeConception Fabrication Commande

R

Initial surface

R

Context

Optimal balancing• The final product should have a minimum

allowance for better machining• In case of perfect positioning, minimum rough part

radius should have to be r + h• ∆ is the positioning error between the final product

and the rough part’s central axis• The minimum radius of the rough part has to be R

for a good machining operation• More positioning error will increase the material

waste

CONTEXT KINEMATIC MODEL MECHANICAL MODEL CONCLUSION

∆h

Allowance > Min chip thickness

h

Sajid Ullah BUTT, PhD Defense 5 July 2012

r

r

Final part

∆ L

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Conception Fabrication CommandeConception Fabrication Commande

Part

Pallet

Col

umn

Base

Spindle

Kinematics defects

Locators placement

Geometric/form defects

Deformation due to forces

Context

Workpiece/machine tool Positioning error • Variation among the parts of the same part family cause the positioning error during

fixturing• Positioning error of the workpiece affects the quality of the final product

Tool wearEffect of heatNC Code errors

CONTEXT KINEMATIC MODEL MECHANICAL MODEL CONCLUSION

Tool

Sajid Ullah BUTT, PhD Defense 5 July 2012

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Conception Fabrication CommandeConception Fabrication Commande

Possible placement of

locators

Placement of locators• Block the 6-DOFs of the part

Placement procedure Choose the locating surfaces taking into account the

constraints of accessibility, load, external force and movements (Somashekar 2002)

Select the locators configurations (3-2-1, 3-2-1C, etc.) Choose the locators positions for the part stability (Roy

& Liao, 2002; Zirmi et al. 2009)

Positioning errors

3-2-1

3-2-1C

4-1-1

(H. Paris, 1995)

CONTEXT KINEMATIC MODEL MECHANICAL MODEL CONCLUSION

Y

-Y

Z

-X X

-Z

0

Sajid Ullah BUTT, PhD Defense 5 July 2012

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Conception Fabrication CommandeConception Fabrication Commande

Geometrical and form defects• When workpiece is placed directly on the locators• Local geometrical defects cause the orientation error • The orientation error have more effect on the final product quality than the

translation error (Asante, 2009)

Positioning errorsCONTEXT KINEMATIC MODEL MECHANICAL

MODEL CONCLUSION

Sajid Ullah BUTT, PhD Defense 5 July 2012

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Conception Fabrication CommandeConception Fabrication Commande

F

Deformation of locators under external load• The locators and their contacts deform under clamping and machining

forces• Deformation depends upon the stiffness of the locators• Hertz contact theory may be applied to calculate the contact deformation• Locators deformations induce the workpiece displacement

Zero contact deformation

sph

C

Including contact deformation

Positioning errorsCONTEXT KINEMATIC MODEL MECHANICAL

MODEL CONCLUSION

Z

Y

X

F FF

Sajid Ullah BUTT, PhD Defense 5 July 2012

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Conception Fabrication CommandeConception Fabrication CommandePositioning errors

Machine tool/kinematic chain defects• Machine tool position uncertainty • Kinematic chain • Kinematic defects increase with the increase the

number of machine axes

Other Defects• Defects due to heat generation• NC code defects• Tool wear

CONTEXT KINEMATIC MODEL MECHANICAL MODEL CONCLUSION

Sajid Ullah BUTT, PhD Defense 5 July 2012

How to Compensate these errors?

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Conception Fabrication CommandeConception Fabrication CommandeError compensation

Existing methods• Changing the part program

• Easiest way (Ramesh et al. 2000)

• Orientation of the machine tool

Disadvantages• Need 4 or 5 axis machines• Very expensive for the existing production

line

Actual position

Ideal position

Compensated position

(Zhu et al. 2012)

CONTEXT KINEMATIC MODEL MECHANICAL MODEL CONCLUSION

Sajid Ullah BUTT, PhD Defense 5 July 2012

Base

PartPart

Tool

Col

umn

Pallet

Part programTool orientation

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Conception Fabrication CommandeConception Fabrication Commande

Base

Tool

Col

umn

Part

Part

Baseplate

Part

Baseplate

Pallet

6 DOF repositioning

Error compensationCONTEXT KINEMATIC MODEL MECHANICAL

MODEL CONCLUSION

Our proposal• A 6-DOF workpiece repositioning

system is proposed

• A baseplate is introduced to avoid the positioning error caused by the geometrical defects

• Repositioning is performed through the positioning of the 6 locators

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Conception Fabrication CommandeConception Fabrication Commande

• Develop a fixturing system which can– Hold custom single and complex parts– Perform 6-DOF Repositioning of the part at desired position – Added to Single machine unit or production/assembly line – Minimum modifications on existing production line

Part

Baseplate

Tool

Part

Baseplate

Conveyor

Previous Workstation

Reconfigurable Pallet

Base

Col

umn

Pallet

ObjectiveCONTEXT KINEMATIC MODEL MECHANICAL

MODEL CONCLUSION

Single machine unit Production/Assembly line

Sajid Ullah BUTT, PhD Defense 5 July 2012

Measure Calculate Compensate

Part

Baseplate

Reconfigurable Pallet

Part

Baseplate

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Conception Fabrication CommandeConception Fabrication Commande

MeasureWorkpiece geometrical errors• Offline: using CMM• Online: Integrated sensors

Calculate• The advancement of locators required to compensate the errors using

Homogeneous Transformation Matrices and Large displacements (Kinematic model)

• The errors due to deformation of elastic elements under load using Small Displacement hypothesis (Mechanical model)

CompensateThrough the axial advancement of 6 locators• Geometrical errors • Mechanical errors

ObjectiveCONTEXT KINEMATIC MODEL MECHANICAL

MODEL CONCLUSION

Sajid Ullah BUTT, PhD Defense 5 July 2012

Error compensation principle

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Conception Fabrication CommandeConception Fabrication CommandePresentation layout

Sajid Ullah BUTT, PhD Defense 5 July 2012

• Context

• Positioning errors

• Compensation

• Objectives

• Workpiece repositioning through locators

• All the elements rigid

• Proposed fixturing system

• Analytical formulation

• Large displacements and Homogeneous Transformation Matrices

• Deformation of elastic elements and rigid body displacement of part on fixture under load

• Deformation of locators and contacts

• Lagrangian formulation

• Negligible friction, Small Displacements

• Convergence of non-linear contact deformation

• Work realized

• Conclusion

• Future work

Case Study

Context Kinematic Model Mechanical Model Conclusion and Perspectives

CONTEXT KINEMATIC MODEL MECHANICAL MODEL CONCLUSION

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Conception Fabrication CommandeConception Fabrication Commande

Objective• Repositioning of a part of a part family placed roughly with a precision of

some millimeters

Components– Part (Hip prosthesis)– Baseplate (Cuboid)– 6-Locators (Axial movement)– Pallet

All the elements are rigid

XZ

YO

(Machine/Pallet reference)

P

6 4

5

2

31

Baseplate

part

Kinematic modelCONTEXT KINEMATIC MODEL MECHANICAL

MODEL CONCLUSION

Sajid Ullah BUTT, PhD Defense 5 July 2012

Part

Baseplate

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Conception Fabrication CommandeConception Fabrication Commande

[PPF

] = [P

bb’]

XF

Xb’

XO

Xb

XP

[PPF]

[PbP]

[Pb’F]=[PbP]

[POb’][POb]

Correction[PPF ]

Error to be corrected

Rigid link

Baseplate correction

through locators

Initial baseplate placement on the locators

Formulation

XZ

Y O(Machine/Pallet reference)

Y3

Z3

X3

b

P

XP

ZPYP

6 4

5

2

31

Baseplate

part

CONTEXT KINEMATIC MODEL MECHANICAL MODEL CONCLUSION

Sajid Ullah BUTT, PhD Defense 5 July 2012

Baseplate Surface normals

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Conception Fabrication CommandeConception Fabrication Commande

CPT 12/14 Hip Prosthesis Zimmer

-10.00 10.00 30.00 50.00 70.00 90.00 110.00 130.000.00

10.00

20.00

30.00

40.00

50.00

60.00

70.00

80.00

90.00

Initial Position of the workpiece (2D Simulation)

Min Material (Chebyshev)

RMS

CONTEXT KINEMATIC MODEL MECHANICAL MODEL CONCLUSION

P

Sajid Ullah BUTT, PhD Defense 5 July 2012

Y

X

• Point P (intersection of two centerlines)• Definition of a plane• Simulation in 2D

Stem

Neck

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Conception Fabrication CommandeConception Fabrication Commande

-10.00 10.00 30.00 50.00 70.00 90.00 110.00 130.000.00

10.00

20.00

30.00

40.00

50.00

60.00

70.00

80.00

90.00

P

Min Material (Chebyshev)

RMS

• Point P (intersection of two centerlines)• Definition of a plane• Simulation in 2D

CONTEXT KINEMATIC MODEL MECHANICAL MODEL CONCLUSION

Sajid Ullah BUTT, PhD Defense 5 July 2012

Y

X

Initial Position of the workpiece (2D Simulation)

Stem

Neck

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Conception Fabrication CommandeConception Fabrication Commande

Z

X

1*2*

1’2’

1 2

Final calculated Position

Calculating point of contact in axis

Position calculation in 3D

Compensation of errorsCONTEXT KINEMATIC MODEL MECHANICAL

MODEL CONCLUSION

Sajid Ullah BUTT, PhD Defense 5 July 2012

2D Schematic explanation

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Conception Fabrication CommandeConception Fabrication CommandeSimulation procedure: CAD ModelingCONTEXT KINEMATIC MODEL MECHANICAL

MODEL CONCLUSION

Inverse impression of the workpiece for the simulation of

cutting tool path D=3mm

Cavity with original workpiece dimensions

Baseplate

Pallet

Workpiece

Sajid Ullah BUTT, PhD Defense 5 July 2012

Boolean Operation

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Conception Fabrication CommandeConception Fabrication CommandeCase study

Initial Data

Final required part position

Calculated positions of locators

CONTEXT KINEMATIC MODEL MECHANICAL MODEL CONCLUSION

Gray: Machined surfaceOrange: Rough surface

Sajid Ullah BUTT, PhD Defense 5 July 2012

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Conception Fabrication CommandeConception Fabrication Commande

Simulated machining

Positioning error of workpiece after correction

Case study

Calculated positions of locators

Final Product

CONTEXT KINEMATIC MODEL MECHANICAL MODEL CONCLUSION

Sajid Ullah BUTT, PhD Defense 5 July 2012

Calculated positions of locatorsPositioning error of workpiece after second side correction

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Conception Fabrication CommandeConception Fabrication CommandeRobustness of model/Sensitivity Analysis

• Use of Plucker matrix• Precision of workpiece displacement as a function of locators’ positioning precision• Position uncertainty = Geometrical uncertainty + uncertainty due to temperature

CONTEXT KINEMATIC MODEL MECHANICAL MODEL CONCLUSION

Sensitivity analysis

Sajid Ullah BUTT, PhD Defense 5 July 2012

Worst case

Precision of locator

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Conception Fabrication CommandeConception Fabrication CommandePresentation layout

Sajid Ullah BUTT, PhD Defense 5 July 2012

• Context

• Positioning errors

• Compensation

• Objectives

• Workpiece repositioning through locators

• All the elements rigid

• Proposed fixturing system

• Analytical formulation

• Large displacements and Homogeneous Transformation Matrices

• Deformation of elastic elements and rigid body displacement of part on fixture under load

• Deformation of locators and contacts

• Lagrangian formulation

• Negligible friction, Small Displacements

• Convergence of non-linear contact deformation

• Work realized

• Conclusion

• Future work

Case Study

Context Kinematic Model Mechanical Model Conclusion and Perspectives

CONTEXT KINEMATIC MODEL MECHANICAL MODEL CONCLUSION

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Conception Fabrication CommandeConception Fabrication CommandeMechanical model

• Clamping and machining forces and moments• Elements designed to be rigid

– Workpiece baseplate assembly– Mass elements

• Elastic elements– Locators (body and contact)– Baseplate at contacts– Clamps with imposed external displacements

• Small displacement hypothesis• Friction neglected• Effects of heat neglected• No slippage of clamps at contact

{XE}2

Z

X

Y

P

[K]1

[K]2

[K]3[K]4

[K]5

[K]6

{XE}1

[KE]2

[KE]1f

| T, F |

CONTEXT KINEMATIC MODEL MECHANICAL MODEL CONCLUSION

Sajid Ullah BUTT, PhD Defense 5 July 2012

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Conception Fabrication CommandeConception Fabrication CommandeFormulation

XF*

Xb*

XF

Xb’

XO

P b’F =

P bP

Pob*

P b*F*

=P bP

POb’

Pb*b’

PFF*

Rigid link

Correction through locators

Error of the workpiece under load Machining forces and their displacement

P b’b*

=PFF

*

Clamping forces and their

displacements

Initial baseplate locating under load

Correction

{XE}2

Z

X

Y

P

[K]1

[K]2

[K]3[K]4

[K]5

[K]6

{XE}1

[KE]2

[KE]1f

| T, F |

CONTEXT KINEMATIC MODEL MECHANICAL MODEL CONCLUSION

Sajid Ullah BUTT, PhD Defense 5 July 2012

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Conception Fabrication CommandeConception Fabrication CommandeFormulation

Work done by external force

Lagrangian Equation

Z

X

Y21

3

K3

6

K6

P

ZP

XP

YP

5

K5

4

K4

K2K1

Baseplate KE1

XE1

KE2

XE2

Part

F

T

Machine/Pallet Reference

{ΔX,ΔY,ΔY}T: Linear displacement vector of point P{Δα,Δβ,Δγ}T: Angular displacement vector of point P{F}: Force vector{T}: Moment vector

CONTEXT KINEMATIC MODEL MECHANICAL MODEL CONCLUSION

U: Potential energy of the systemT: Kinetic energy of the systemW:Work done by the external forcesqi: Generalized coordinates

Sajid Ullah BUTT, PhD Defense 5 July 2012

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Conception Fabrication CommandeConception Fabrication CommandeFormulation

Potential Energy: U

Lagrangian Equation

Kinetic Energy: T t

ZV

t

YV

t

XV

z

y

x

tt

tt

tt

z

y

x

Z

X

Y21

3

K3

6

K6

P

ZP

XP

YP

5

K5

4

K4

K2K1

Baseplate KE1

XE1

KE2

XE2

Part

F

T

Machine/Pallet Reference

Locators

Clamps

CONTEXT KINEMATIC MODEL MECHANICAL MODEL CONCLUSION

(Lalanne et al. 1986)

Sajid Ullah BUTT, PhD Defense 5 July 2012

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Conception Fabrication CommandeConception Fabrication Commande

Locator Pin

68mm

20mm

20mm

Locator model

• Screw-nut Wedge-slop locator • Rotation of knob causes axial

movement of locatorSlope 1:2

Screw M6x1

Locator diameter: 20mm

Length of locator: 68mm

Sphere radius: 20mm

CONTEXT KINEMATIC MODEL MECHANICAL MODEL CONCLUSION

Perforated plate Pitch = 40mm

Sajid Ullah BUTT, PhD Defense 5 July 2012

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Conception Fabrication CommandeConception Fabrication Commande

1

2aL tLk k

Initial position of the surface

Final position of the surface

Locator axis

sph

ni

ZY

X

Deformed locator at the position having minimum potential energy

Formulation (Zero Friction)CONTEXT KINEMATIC MODEL MECHANICAL

MODEL CONCLUSION

3

aL tLk k

4

tL

aL

Bending + Shear

Compression

Minimum energy (Menabrea’s theorem) Potential energy of locators

Locator’s Stiffness Matrix

Sajid Ullah BUTT, PhD Defense 5 July 2012

sph

tL

aL

0U

tL

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Conception Fabrication CommandeConception Fabrication Commande

Final position of contact surface after only locator deformation

C

ni

Final position of contact surface after locator and contact deformation

ni

Z

Y

X Zero contact deformation

Including contact deformation

Formulation

Deformation of contact (Hertz contact theory)CONTEXT KINEMATIC MODEL MECHANICAL

MODEL CONCLUSION

Sajid Ullah BUTT, PhD Defense 5 July 2012

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Conception Fabrication CommandeConception Fabrication CommandeFormulation (Iterations procedure)

New stiffness matrices of each locator [K]i

Stiffness matrix [K] , overall displacement vector {∆X} and natural frequencies of the system using Lagrangian

Deformation of each locator{δ}i

Potential energy calculations

Deformation and stiffness of ith

locator body (δL, KL) i

Deformation and stiffness of ith contact (δC, KC) i

Overall stiffness of each locator and displacement vector of the workpiece ({∆Xnew} ) using inverse Plucker

[KNew]i = {F}i /{δNew}iT

{∆XNew}=[Plu]-1{δPlu}

Limite1001

X

XMAX New

iii KF

Final deformation/displacement vector and stiffness matrix of each locator and the

fixturing system

No

Yes/STOP

Kinetic energy and Work done

[K]i =[KNew]i

{∆X}= {∆XNew} +gain*({∆X} - {∆Xnew} )

{δNew}i= {δC}i +{δL}i

{∆XNew}

{∆XNew}

[K]i

CONTEXT KINEMATIC MODEL MECHANICAL MODEL CONCLUSION

ni

Z

Y

X

3D stiffness matrix of the locator body

[KL] i

[KC] i

{F}i

3D stiffness matrix of the contact

3D equivalent stiffness matrix

{F}i

[KNew] i

Force vector on the ith locator

{F}i

Sajid Ullah BUTT, PhD Defense 5 July 2012

Gain

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Conception Fabrication CommandeConception Fabrication Commande

Y

X

Z

1

2

3

4

5 6

P

70

110

70

110

14

1008

60

23

21

60

6060

100

22

10

12040

O

{XE}2

Z

X

Y

P

[K]1

[K]2

[K]3[K]4

[K]5

[K]6

{XE}1

[KE]2

[KE]1f

Case study

oB

oB

oB

494.0

485.1

039.1

| T, F |

CONTEXT KINEMATIC MODEL MECHANICAL MODEL CONCLUSION

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Conception Fabrication CommandeConception Fabrication Commande

Clamps

Baseplate (made of steel)

{XE}2

Z

X

Y

P

[K]1

[K]2

[K]3[K]4

[K]5

[K]6

{XE}1

[KE]2

[KE]1f

locators-baseplate contacting points

Contacting points of clamps

Case study (Input)

Locator stiffness| T, F |

68mm

20mm

20mm

CONTEXT KINEMATIC MODEL MECHANICAL MODEL CONCLUSION

Sajid Ullah BUTT, PhD Defense 5 July 2012

Ext

ract

ed

from

C

AD

mod

el

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Conception Fabrication CommandeConception Fabrication Commande

Processed material• Prosthesis material : M30NW (X4CrNiMoN21)• ISO equivalent material: M3.2.C.AQ (Stainless steel Cast, Annealed quenched)

– Stainless steel 316LN (X2CrNiMoN18-13, Sandvik technical guide 2011)– σ = 880MPa

Cutting condition– Tool : CoroMill 216 ball nose endmill of 3 mm in diameter (2 teeth)– DOC, ap : 0.5 mm, Feed per tooth, Fz : 0.03 mm

– Cutting speed, Vc: 75 m/min, Spindle speed, N : 8000 RPM

Machining forces– Tangential force (Sandvik technical guide 2011)– Repulsive forces (Pruvot, 1993)

Case study (Input)CONTEXT KINEMATIC MODEL MECHANICAL

MODEL CONCLUSION

Sajid Ullah BUTT, PhD Defense 5 July 2012

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Conception Fabrication CommandeConception Fabrication Commande

Results without considering contact deformation

Case study (Results)

Results with considering contact deformation

Natural frequencies of the system Error compensation

CONTEXT KINEMATIC MODEL MECHANICAL MODEL CONCLUSION

Sajid Ullah BUTT, PhD Defense 5 July 2012

Tool Excitation frequency=837 rad/sec

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Conception Fabrication CommandeConception Fabrication Commande

1 10 100 10001E-02

1E-01

1E+00

1E+01

1E+02

1E+03

∆X

∆Y

∆Z

∆β

∆γ

∆α

1 10 100 1000-70

-20

30

80

130

∆X

∆Y

∆Z

∆β

∆γ

∆α

Convergence of displacement vectorμ

Rad

, μm

No of iterations

No of iterations

% E

rror

CONTEXT KINEMATIC MODEL MECHANICAL MODEL CONCLUSION

Sajid Ullah BUTT, PhD Defense 5 July 2012

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Conception Fabrication CommandeConception Fabrication Commande

1 10 100-60

-40

-20

0

20

40

60

80

100

120

140

0.33

0.41

0.51

0.64

0.80

1.00

GAIN

Effect of gain on convergence μ

Rad

No of iterations

CONTEXT KINEMATIC MODEL MECHANICAL MODEL CONCLUSION

Convergence of parameter slowest parameter ∆γ

Sajid Ullah BUTT, PhD Defense 5 July 2012

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Conception Fabrication CommandeConception Fabrication CommandeRough contactsCONTEXT KINEMATIC MODEL MECHANICAL

MODEL CONCLUSION

Baseplate-locator equivalent RMS roughness = 0.8 E-6 m

kC/k

H

RMS Roughness (m)

1N

10N

100N

1kN

Comparison between ideal and rough surface contacts

(Bahrami et al. 2005)

Sajid Ullah BUTT, PhD Defense 5 July 2012

6.6% decrease

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Conception Fabrication CommandeConception Fabrication Commande4-2-2 locator configuration

{XE}2

Z

X

Y

P

[K]1

[K]2

[K]3[K]4

[K]5

[K]6

{XE}1

[KE]2

[KE]1

f

| T, F |

{XE}2

Z

X

Y

P

[K]1

[K]2

[K]3

[K]4

[K]5

[K]6

{XE}1

[KE]2

[KE]1

f[K]7

[K]8

| T, F |System stiffness

Comparison between 3-2-1 and 4-2-2

CONTEXT KINEMATIC MODEL MECHANICAL MODEL CONCLUSION

Sajid Ullah BUTT, PhD Defense 5 July 2012

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Conception Fabrication CommandeConception Fabrication CommandePresentation layout

Sajid Ullah BUTT, PhD Defense 5 July 2012

• Context

• Positioning errors

• Compensation

• Objectives

• Workpiece repositioning through locators

• All the elements rigid

• Proposed fixturing system

• Analytical formulation

• Large displacements and Homogeneous Transformation Matrices

• Deformation of elastic elements and rigid body displacement of part on fixture under load

• Deformation of locators and contacts

• Lagrangian formulation

• Negligible friction, Small Displacements

• Convergence of non-linear contact deformation

• Work realized

• Conclusion

• Future work

Case Study

Context Kinematic Model Mechanical Model Conclusion and Perspectives

CONTEXT KINEMATIC MODEL MECHANICAL MODEL CONCLUSION

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Conception Fabrication CommandeConception Fabrication CommandeConclusion

• High quality baseplate is introduced• Compensation is performed through advancement of locators (kinematic model)• Deformation of each locator is calculated and its contact with baseplate under load (mechanical model)• Also its resultant rigid body displacement of the workpiece is calculated (positioning error)• Compensation is performed using kinematic model

CONTEXT KINEMATIC MODEL MECHANICAL MODEL CONCLUSION

Base

Tool

Col

umn

Part

Part

Baseplate

Part

Baseplate

Pallet

Kinematics defects

Locators placement

Geometric/form defectsDeformation due to forces

Sajid Ullah BUTT, PhD Defense 5 July 2012

6 DOF part repositioning

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Conception Fabrication CommandeConception Fabrication CommandeConclusion

6 DOF positioning using kinematic model– 3-2-1 locating configuration is used– All elements are considered rigid– Error compensation is performed through the axial translation of 6-locators

using HTM and LD– Validated on a case study of repositioning the hip prosthesis– Sensitivity analysis are carried out

CONTEXT KINEMATIC MODEL MECHANICAL MODEL CONCLUSION

Sajid Ullah BUTT, PhD Defense 5 July 2012

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Conception Fabrication CommandeConception Fabrication CommandeConclusion

Mechanical modeling of the fixturing system– The analytical model is developed– Deformation of locators under load is calculated – Workpiece-baseplate assembly is designed to be rigid– Locators, clamps and locator-baseplate contacts are assumed deformable– Small displacement hypothesis are used– Lagrangian formulation is used to calculate the mass & stiffness matrices and workpiece

displacement vector– Non-linear behavior of locator-baseplate contact is linearized– Demonstrated on a case study of 3-2-1 locating configuration and compared with 4-2-2

configuration of locators

CONTEXT KINEMATIC MODEL MECHANICAL MODEL CONCLUSION

Sajid Ullah BUTT, PhD Defense 5 July 2012

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Conception Fabrication CommandeConception Fabrication Commande

• Analytical modeling gives very quick result as compared to numerical modeling

• The proposed mechanical model can easily be applied to more complex problems with multiple loads, different orientations and stiffness of locators and clamps

• The proposed fixturing system allows precise positioning of the workpiece at each workstation without the need of 4 or 5 axis machines or modifying the existing workstations

• Reduce dimensional errors, machining allowances and thus the material removal by uniformly centering the rough part to the required part• Consequently, it reduces the material waste

• Large parts could also be repositioned during assembling

ConclusionCONTEXT KINEMATIC MODEL MECHANICAL

MODEL CONCLUSION

Sajid Ullah BUTT, PhD Defense 5 July 2012

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Conception Fabrication CommandeConception Fabrication Commande

• The positioning error due to heat/temperature change can be introduced

• Construction of the fixturing system for validating the analytical model. We could not construct the model because of time and cost associated with precise part production

• The mechanical model calculates the deformation of locators as the result of an instantaneous force at a point. The model should be developed to simulate the whole tool path

Limitations and Future workCONTEXT KINEMATIC MODEL MECHANICAL

MODEL CONCLUSION

Sajid Ullah BUTT, PhD Defense 5 July 2012

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Conception Fabrication CommandeConception Fabrication CommandeScientific activities

Poster Presentation

• “Conception, Modélisation et Réalisation d'un montage modulaire rapide destine a la Fabrication Mécanique” J2A Arts et Métiers ParisTech, 8th-9th June 2010 (Poster Presentation)

National Colloquium

• S. U. Butt, J. F. Antoine, P. Martin, “Mechanical model for control of 6 DOF repositioning system”, 12th National Colloquium, AIP Primeca, Mont-Dore 29th March to 1st April 2011

Scientific Publications

• S. U. Butt, J. F. Antoine, P. Martin, “An analytical model for the repositioning of 6 DOF repositioning system”, Journal of Mechanics and Industry (Accepted June 2012 )

• S. U. Butt, J. F. Antoine, P. Martin, “An analytical stiffness model for spherical rough contacts”, Asian International Journal of Science and Technology in Production and Manufacturing Engineering (Submitted June 2012)

Sajid Ullah BUTT, PhD Defense 5 July 2012

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Conception Fabrication CommandeConception Fabrication Commande

f

Thanks for your attention