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FINITE ELEMENT ANALYSIS OF IN-CONTACT SPHERES

FINITE ELEMENT ANALYSIS OF IN-CONTACT SPHERES. H. A. K HAWAJA (PhD Student, Dept. of Engineering) S. A. S COTT (Lecturer, Dept. of Engineering) K. P ARVEZ (Professor, Research Centre for Modelling & Simulation). 4 TH I NT. C ONFERENCE OF M ULTIPHYICS, L ILLE , F RANCE, 9-11 D EC 09.

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FINITE ELEMENT ANALYSIS OF IN-CONTACT SPHERES

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  1. FINITE ELEMENT ANALYSIS OF IN-CONTACT SPHERES H. A.KHAWAJA (PhD Student, Dept. of Engineering) S. A. SCOTT (Lecturer, Dept. of Engineering) K.PARVEZ (Professor, Research Centre for Modelling & Simulation) 4TH INT. CONFERENCEOF MULTIPHYICS, LILLE, FRANCE, 9-11DEC 09

  2. 2 H. A.KHAWAJAMULTIPHYSICS 2009, LILLE, FRANCE, 9-11 DEC 09 POINTSFOR DISCUSSION • BACKGROUND • INTRODUCTION • Normal Contact • Tangential Contact • FINITE ELEMENT ANALYSIS • Finite Element Modelling • Loading and Boundary Conditions • Finite Element Analysis Results • Comparison of Results with Available Models • SUMMARY & CONCLUSION • REFERNCES • ACKNOWLEDGEMENTS

  3. 3 H. A.KHAWAJAMULTIPHYSICS 2009, LILLE, FRANCE, 9-11 DEC 09 BACKGROUND • Particle-particle interaction is observed in many physical phenomena; fluidized beds, particle kiln, etc. • Fluidized Bed Video • Kiln Video • Particle sizes may vary and can be classified using Geldart Classifications; Geldart A (20-100 µm), Geldart B (40-500 µm), Geldart C (20-30 µm), Geldart D (>600 µm). • Available models for contact are quite old. Their basis of development were experiments. • This work addresses: • To understand the phenomenon of interaction between spherical particles. • Validation of available models • Re-modelling of contact models, if required. • Extension to cases for which models is not available

  4. 4 H. A.KHAWAJAMULTIPHYSICS 2009, LILLE, FRANCE, 9-11 DEC 09 INTRODUCTION • Normal Contact: SPHERE 1 CONTACT CIRCLE SPHERE 2 Caution: Exaggerated Animation for Understanding

  5. 5 H. A.KHAWAJAMULTIPHYSICS 2009, LILLE, FRANCE, 9-11 DEC 09 INTRODUCTION • Normal Contact: • Hertz Normal Contact Model (1882) DOES NOT CATER FRICTIONAL FORCE HERTZ, H. (1882). Journal der rennin und angewandeten Mathematik, 92, 136 JOHNSON, K., ed. (1984). Contact Mechanics. Cambridge University Press, Cambridge.

  6. 6 H. A.KHAWAJAMULTIPHYSICS 2009, LILLE, FRANCE, 9-11 DEC 09 INTRODUCTION • Tangential Contact: SPHERE 1 CONTACT CIRCLE SPHERE 2 Caution: Exaggerated Animation for Understanding

  7. 7 H. A.KHAWAJAMULTIPHYSICS 2009, LILLE, FRANCE, 9-11 DEC 09 INTRODUCTION • Tangential Contact Force: • Mindlin & Dresewicz (MD) Contact Model (1953) • Normal force and contact area is computed using Hertz (1882) model • Whenever there is change in normal traction it will bring change in tangential traction and if that change is more than the product of coefficient of friction and normal traction slip will occur. • There is annulus of slip that progresses concentrically inwards. • When slip occurs then the product of normal traction and coefficient of friction will be equal to tangential traction. • At the annulus of slip there is tangential displacement that can be calculated by mathematical relations. • Contact parameters are computable if every previous step of loading is known from the equilibrium state. HISTORY DEPENDENT !!!!!!!!!!!!!!!!!!!!!!!!! VERY VERY EXPENSIVE IN COMPUTATIONS MINDLIN, R. (1953). Journal of Applied Mechanics, 20, 327. JOHNSON, K., ed. (1984). Contact Mechanics. Cambridge University Press, Cambridge.

  8. 8 H. A.KHAWAJAMULTIPHYSICS 2009, LILLE, FRANCE, 9-11 DEC 09 FINITE ELEMENT MODELLING • Finite Element Mesh: • Part of sphere is modelled to reduce number of elements • Mesh sensitivity analysis is carried out to ensure the quality of results • Parameters taken for analysis are as follows:

  9. 9 H. A.KHAWAJAMULTIPHYSICS 2009, LILLE, FRANCE, 9-11 DEC 09 FINITE ELEMENT MODELLING • Loading and Boundary Conditions: • Loading Locations • Normal Loading Only • Normal and Tangential Loading Combined

  10. 10 H. A.KHAWAJAMULTIPHYSICS 2009, LILLE, FRANCE, 9-11 DEC 09 FINITE ELEMENT MODELLING • Finite Element Analysis Results: • Contact Pressure (Normal & Tangential Contact) In accordance with as defined by Hertz (1882)

  11. 11 H. A.KHAWAJAMULTIPHYSICS 2009, LILLE, FRANCE, 9-11 DEC 09 FINITE ELEMENT MODELLING • Finite Element Analysis Results: • Frictional Stress (Tangential Contact) Traction profile is not exactly depicted by MD (1953). It is axisymmetric in sliding region and non-axisymmetric in stick region, which conflicts with their theory.

  12. 12 H. A.KHAWAJAMULTIPHYSICS 2009, LILLE, FRANCE, 9-11 DEC 09 FINITE ELEMENT MODELLING • Finite Element Analysis Results: • Contact Status (Tangential Contact) In case of full sliding, Frictional force is Frictional Constant multiplied with Normal Force (μN). In case of partial sliding, Frictional Force has to be computed and cases could be very complicated.

  13. 13 H. A.KHAWAJAMULTIPHYSICS 2009, LILLE, FRANCE, 9-11 DEC 09 FLUIDIZED BED FINITE ELEMENT MODELLING • Comparison of Results with Available Models: • Normal Contact Force with Hertz Model (1882) • Tangential Contact Force with MD Model (1954)

  14. 14 H. A.KHAWAJAMULTIPHYSICS 2009, LILLE, FRANCE, 9-11 DEC 09 SUMMARY & CONCLUSION • Summary: • Normal Contact Model given by Hertz (1882) • Tangential Contact Force given by MD (1954) • Setting up FEM Contact Simulation • Comparison of results • Conclusion: • Contact Pressure and Normal Contact Force is in agreement with the Hertz (1882) Normal Contact Model • Frictional Stress Contour doesn't match with MD (1953). However, Frictional Force is in agreement with the model.

  15. 15 H. A.KHAWAJAMULTIPHYSICS 2009, LILLE, FRANCE, 9-11 DEC 09 FUTURE WORK • Tangential Contact Model needs to refined to support extensive computations • Removal of Historical Dependency • Simplification of mathematical process • FEA of contact model for 2-D Tangential Motion • Development of numerical model for 2-D Tangential Motion

  16. 16 H. A.KHAWAJAMULTIPHYSICS 2009, LILLE, FRANCE, 9-11 DEC 09 REFERENCES

  17. 17 H. A.KHAWAJAMULTIPHYSICS 2009, LILLE, FRANCE, 9-11 DEC 09 ACKNOWLEDGEMENTS • Institute of Space Technology (IST) – Pakistan • Cambridge Commonwealth Trust – Cambridge, UK • Research Centre for Modelling & Simulation, National University of Sciences & Technology (NUST) - Pakistan

  18. THANK YOU Trust me, I am not drunk!!!!!!!!!! CONTACT HASSAN KHAWAJA Email: hak23@cam.ac.uk Webpage: http://hassanabbaskhawaja.blogspot.com

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