FINITE ELEMENT ANALYSIS OF IN-CONTACT SPHERES 4 TH I NT. C ONFERENCE OF M ULTIPHYICS, L ILLE, F...

FINITE ELEMENT ANALYSIS OF IN-CONTACT SPHERES

4TH INT. CONFERENCE OF MULTIPHYICS, LILLE, FRANCE, 9-11 DEC 09

H. A. KHAWAJA (PhD Student, Dept. of Engineering)

S. A. SCOTT (Lecturer, Dept. of Engineering)

K. PARVEZ

(Professor, Research Centre for Modelling & Simulation)

POINTS FOR 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

H. A. KHAWAJA MULTIPHYSICS 2009, LILLE, FRANCE, 9-11 DEC 09 2

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


INTRODUCTION

Normal Contact:

SPHERE 1

SPHERE 2

CONTACT CIRCLE


Caution: Exaggerated Animation for Understanding

INTRODUCTION

Normal Contact: Hertz Normal Contact Model (1882)

JOHNSON, K., ed. (1984). Contact Mechanics. Cambridge University Press, Cambridge.


DOES NOT CATER FRICTIONAL FORCE

HERTZ, H. (1882). Journal der rennin und angewandeten Mathematik, 92, 136

INTRODUCTION

Tangential Contact:

SPHERE 1

SPHERE 2

CONTACT CIRCLE


Caution: Exaggerated Animation for Understanding

INTRODUCTION

Tangential Contact Force: Mindlin & Dresewicz (MD) Contact Model (1953)


JOHNSON, K., ed. (1984). Contact Mechanics. Cambridge University Press, Cambridge.

MINDLIN, R. (1953). Journal of Applied Mechanics, 20, 327.

•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

FINITE ELEMENT MODELLING


1

JAN 22 200901:08:08

ELEMENTS

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:Parameter Values

Radius of Sphere 0.1m

Modulus of Elasticity 70GPa

Poisson Ratio 0.3

Coefficient of Friction 0.2

Solid Element Solid 186, 20-Noded Hexahedral Solid Element

Contact Element Contac 174, 8-Noded Surface to Surface Quadrilateral 3-D Contact Element

Target Element Targe 170, 8-Noded Surface to Surface Quadrilateral 3-D Target Element



Loading and Boundary Conditions: Loading Locations Normal Loading Only Normal and Tangential Loading Combined



Finite Element Analysis Results: Contact Pressure (Normal & Tangential Contact)

In accordance with as defined by Hertz (1882)



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.



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.

FLUIDIZED BED



Comparison of Results with Available Models:

Normal Contact Force with Hertz Model (1882) Tangential Contact Force with MD Model (1954)

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.

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

REFERENCES


•ANSYS® Multiphysics FEM Package, Release 11.0

•ANSYS® Technical Manuals, Release 11.0 Documentation for ANSYS®

•CUNDALL, P., STRACK, O. (1979). Geotechnique, 29,47.

•HERTZ, H. (1882). Journal der rennin und angewandeten Mathematik, 92, 136.

•JAEGER, J. (2205) New Solutions in Contact Mechanics, WIT Press Southampton, Boston.

•JOHNSON, K., ed. (1984). Contact Mechanics. Cambridge University Press, Cambridge.

•LIAN, G., THORNTON, C., KAFUI, D. (1998) TRUBAL, Aston University, Brimingham, UK.

•MINDLIN, R. (1953). Journal of Applied Mechanics, 20, 327.

•SCOTT, S., MUELLER, C., (2009) PONG3-D, University of Cambridge, UK.

•THORNTON, C., YIN, K., K. (1991) Powder Technology, 65, 155.

•TSUJI, Y., TANAKA, T., ISHIDA, T. (1992) Powder Technology, 71, 239.

•VU-QUOC, L., ZHANG, X. (2007). Mechanics of Materials, 31, 235-269.

•VU-QUOC, L., ZHANG, X., LESBURG, L. (2001). International Journal of Solids and Structures, 38, 6455-6489.

•WALTON, O., BRAUN, R. (1986). Journal of Rheology, 30, 949.

ACKNOWLEDGEMENTS

Institute of Space Technology (IST) – Pakistan

Cambridge Commonwealth Trust – Cambridge, UK

Research Centre for Modelling & Simulation, National University

of Sciences & Technology (NUST) - Pakistan


THANK YOUTrust me, I am not drunk!!!!!!!!!!

CONTACT

HASSAN KHAWAJA

Email: [email protected]

Webpage: http://hassanabbaskhawaja.blogspot.com

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