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Sajid Ullah BUTT

Conception et modélisation d'un montage de fabrication pour le balançage optimisé d'une famille de pièces. Sajid Ullah BUTT. Jury M. Cornel Mihai NICOLESCU , Professeur, KTH, Stockholm, Sweden Rapporteur M. Jean-François RIGAL , Professeur, LAMCOS, INSA Lyon, France Rapporteur

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Sajid Ullah BUTT

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  1. Conception et modélisation d'un montage de fabrication pour le balançage optimisé d'une famille de pièces Sajid Ullah BUTT 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 Arts et Métiers ParisTech - Centre de Metz Laboratoire de Conception Fabrication Commande EA 4495

  2. Presentation layout Case Study Sajid Ullah BUTT, PhD Defense 5 July 2012

  3. Presentation layout Case Study Sajid Ullah BUTT, PhD Defense 5 July 2012

  4. Context Initial surface R ∆ Final part h r Allowance > Min chip thickness h ∆ r R ∆ L 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 Sajid Ullah BUTT, PhD Defense 5 July 2012

  5. Context Column Spindle Kinematics defects Tool Deformation due to forces Tool wear Effect of heat NC Code errors Part Locators placement Pallet Geometric/form defects Base 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 Sajid Ullah BUTT, PhD Defense 5 July 2012

  6. Positioning errors Z Y • 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) 3-2-1 Possible placement of locators 3-2-1C 0 -X X 4-1-1 -Z -Y (H. Paris, 1995) Sajid Ullah BUTT, PhD Defense 5 July 2012

  7. Positioning errors • 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) Sajid Ullah BUTT, PhD Defense 5 July 2012

  8. Positioning errors • 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 F F F F Including contact deformation Zero contact deformation Z Y X Sajid Ullah BUTT, PhD Defense 5 July 2012

  9. Positioning errors • Machine tool/kinematic chain defects • Machine tool position uncertainty • Kinematic chain • Kinematic defects increase with the increase the number of machine axes • OtherDefects • Defects due to heat generation • NC code defects • Tool wear How to Compensate these errors? Sajid Ullah BUTT, PhD Defense 5 July 2012

  10. Ideal position Error compensation Actual position Column Compensated position Tool Part program Tool orientation Part Part Pallet Base (Zhu et al. 2012) 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 Sajid Ullah BUTT, PhD Defense 5 July 2012

  11. Error compensation • 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 Column Tool Part 6 DOF repositioning Pallet Part Part Base Baseplate Baseplate

  12. Objective • 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 Column Production/Assembly line Tool Single machine unit Part Part Base Part Baseplate Part Baseplate Baseplate Pallet Reconfigurable Pallet Reconfigurable Pallet Baseplate Conveyor Previous Workstation Sajid Ullah BUTT, PhD Defense 5 July 2012

  13. Objective Sajid Ullah BUTT, PhD Defense 5 July 2012 Error compensation principle

  14. Presentation layout Case Study Sajid Ullah BUTT, PhD Defense 5 July 2012

  15. Kinematic model Z part X P Y Baseplate 5 Part 6 4 2 Baseplate 1 3 (Machine/Pallet reference) O Sajid Ullah BUTT, PhD Defense 5 July 2012 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

  16. Formulation ZP YP XP Error to be corrected [PPF] XF XP Baseplate Surface normals [Pb’F]=[PbP] [PPF] = [Pbb’] [PbP] Rigid link Xb’ Xb Correction [PPF ] [POb’] Z [POb] part X X3 Y3 P XO Y Baseplate Z3 Initial baseplate placement on the locators 5 Baseplate correction through locators 6 b 4 2 1 3 O (Machine/Pallet reference) Sajid Ullah BUTT, PhD Defense 5 July 2012

  17. Initial Position of the workpiece (2D Simulation) • Point P (intersection of two centerlines) • Definition of a plane • Simulation in 2D Neck Stem Y RMS CPT 12/14 Hip Prosthesis Zimmer P Min Material (Chebyshev) X Sajid Ullah BUTT, PhD Defense 5 July 2012

  18. Initial Position of the workpiece (2D Simulation) • Point P (intersection of two centerlines) • Definition of a plane • Simulation in 2D Neck Stem Y RMS P Min Material (Chebyshev) X Sajid Ullah BUTT, PhD Defense 5 July 2012

  19. Compensation of errors Final calculated Position 2D Schematic explanation Calculating point of contact in axis 1* 1’ 2* 2’ 1 2 Z Position calculation in 3D X Sajid Ullah BUTT, PhD Defense 5 July 2012

  20. Simulation procedure: CAD Modeling Boolean Operation Workpiece Inverse impression of the workpiece for the simulation of cutting tool path D=3mm Baseplate Pallet Cavity with original workpiece dimensions Sajid Ullah BUTT, PhD Defense 5 July 2012

  21. Case study Initial Data Final required part position Gray: Machined surface Orange: Rough surface Calculated positions of locators Sajid Ullah BUTT, PhD Defense 5 July 2012

  22. Case study Simulated machining Calculated positions of locators Positioning error of workpiece after correction Positioning error of workpiece after second side correction Calculated positions of locators Final Product Sajid Ullah BUTT, PhD Defense 5 July 2012

  23. Robustness of model/Sensitivity Analysis Precision of locator Worst case 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 Sajid Ullah BUTT, PhD Defense 5 July 2012

  24. Presentation layout Case Study Sajid Ullah BUTT, PhD Defense 5 July 2012

  25. Mechanical 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 {XE}1 [KE]2 | T, F | [KE]1 f P [K]2 [K]1 [K]6 [K]5 [K]3 [K]4 Z Y X Sajid Ullah BUTT, PhD Defense 5 July 2012

  26. Formulation Machining forces and their displacement Error of the workpiece under load PFF* XF XF* Rigid link Pb’b*=PFF* Pb*F* =PbP Pb’F =PbP {XE}2 {XE}1 Clamping forces and their displacements [KE]2 Xb* Xb’ | T, F | Correction Pb*b’ [KE]1 f P POb’ Pob* [K]2 [K]1 [K]6 [K]5 [K]3 XO [K]4 Z Y X Initial baseplate locating under load Correction through locators Sajid Ullah BUTT, PhD Defense 5 July 2012

  27. F Formulation T XE2 Lagrangian Equation KE2 XE1 Part Baseplate KE1 ZP YP 6 P XP U: Potential energy of the system T: Kinetic energy of the system W:Work done by the external forces qi: Generalized coordinates K6 K1 K2 Work done by external force Machine/Pallet Reference K3 2 1 Z Y 3 X K5 K4 {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 4 5 Sajid Ullah BUTT, PhD Defense 5 July 2012

  28. F Formulation T XE2 Lagrangian Equation KE2 XE1 Part Baseplate KE1 ZP YP 6 P XP Potential Energy: U K6 Locators K1 K2 Machine/Pallet Reference K3 2 1 Z Clamps Y 3 X K5 K4 Kinetic Energy: T 4 5 (Lalanne et al. 1986) Sajid Ullah BUTT, PhD Defense 5 July 2012

  29. 20mm Locator model Locator Pin 20mm 68mm Perforated plate Pitch = 40mm Screw-nut Wedge-slop locator Rotation of knob causes axial movement of locator Slope 1:2 Screw M6x1 Locator diameter: 20mm Length of locator: 68mm Sphere radius: 20mm Sajid Ullah BUTT, PhD Defense 5 July 2012

  30. Formulation (Zero Friction) Locator axis Locator’s Stiffness Matrix Initial position of the surface 3 Final position of the surface 1 Compression 4 Deformed locator at the position having minimum potential energy 2 Bending + Shear Z Y Minimum energy (Menabrea’s theorem) Potential energy of locators X Sajid Ullah BUTT, PhD Defense 5 July 2012

  31. Formulation Final position of contact surface after only locator deformation Deformation of contact (Hertz contact theory) Z Final position of contact surface after locator and contact deformation Y Including contact deformation Zero contact deformation X Sajid Ullah BUTT, PhD Defense 5 July 2012

  32. Formulation (Iterations procedure) {∆XNew} New stiffness matrices of each locator [K]i Kinetic energy and Work done [K]i {F}i {F}i {F}i Force vector on the ith locator Potential energy calculations 3D equivalent stiffness matrix [KC] i Stiffness matrix [K] , overall displacement vector {∆X} and natural frequencies of the system using Lagrangian 3D stiffness matrix of the contact Gain [KNew] i {∆X}= {∆XNew}+gain*({∆X}- {∆Xnew}) Deformation of each locator{δ}i [KL] i 3D stiffness matrix of the locator body Deformation and stiffness of ithlocator body (δL, KL)i Deformation and stiffness of ith contact (δC, KC)i {δNew}i= {δC}i+{δL}i Z 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} Y [K]i =[KNew]i X No {∆XNew} Yes/STOP Final deformation/displacement vector and stiffness matrix of each locator and the fixturing system Sajid Ullah BUTT, PhD Defense 5 July 2012

  33. Z 4 Case study 70 60 8 110 5 6 10 | T, F | 60 14 O 60 P 60 120 21 X 40 {XE}2 100 {XE}1 3 23 [KE]2 100 70 Y 1 [KE]1 22 f 110 P [K]2 2 [K]1 [K]6 [K]5 [K]3 [K]4 Z Y X Sajid Ullah BUTT, PhD Defense 5 July 2012

  34. 20mm Case study (Input) 20mm Locator stiffness 68mm | T, F | Baseplate (made of steel) Extracted from CAD model {XE}2 {XE}1 [KE]2 [KE]1 Clamps f P [K]2 locators-baseplate contacting points [K]1 [K]6 [K]5 [K]3 [K]4 Z Y Contacting points of clamps X Sajid Ullah BUTT, PhD Defense 5 July 2012

  35. Case study (Input) 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) Sajid Ullah BUTT, PhD Defense 5 July 2012

  36. Case study (Results) Results without considering contact deformation Results with considering contact deformation Natural frequencies of the system Error compensation Tool Excitation frequency=837 rad/sec Sajid Ullah BUTT, PhD Defense 5 July 2012

  37. Convergence of displacement vector μRad, μm No of iterations % Error No of iterations Sajid Ullah BUTT, PhD Defense 5 July 2012

  38. Effect of gain on convergence Convergence of parameter slowest parameter ∆γ μRad No of iterations Sajid Ullah BUTT, PhD Defense 5 July 2012

  39. Rough contacts (Bahrami et al. 2005) • Baseplate-locator equivalent RMS roughness = 0.8E-6 m kC/kH 1kN 100N 10N 1N 6.6% decrease Comparison between ideal and rough surface contacts RMS Roughness (m) Sajid Ullah BUTT, PhD Defense 5 July 2012

  40. 4-2-2 locator configuration {XE}2 {XE}1 [KE]2 | T, F | | T, F | System stiffness [KE]1 f [K]7 P [K]2 [K]5 [K]1 [K]8 {XE}2 [K]6 {XE}1 [K]4 Z [KE]2 Y [K]3 X [KE]1 Comparison between 3-2-1 and 4-2-2 f P [K]2 [K]1 [K]6 [K]5 [K]3 [K]4 Z Y X Sajid Ullah BUTT, PhD Defense 5 July 2012

  41. Presentation layout Case Study Sajid Ullah BUTT, PhD Defense 5 July 2012

  42. Conclusion Column Kinematics defects Tool 6 DOF part repositioning Part Locators placement Part Part Pallet Baseplate Baseplate Deformation due to forces Geometric/form defects Base Sajid Ullah BUTT, PhD Defense 5 July 2012 • 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

  43. Conclusion 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 Sajid Ullah BUTT, PhD Defense 5 July 2012

  44. Conclusion 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 Sajid Ullah BUTT, PhD Defense 5 July 2012

  45. Conclusion • 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 Sajid Ullah BUTT, PhD Defense 5 July 2012

  46. Limitations and Future work 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 Sajid Ullah BUTT, PhD Defense 5 July 2012

  47. Scientific activities Poster Presentation • “Conception, Modélisation et Réalisation d'un montage modulairerapide 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

  48. Thanks for your attention f

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