| Course Unit Code | 633-3007/03 |
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| Number of ECTS Credits Allocated | 6 ECTS credits |
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| Type of Course Unit * | Compulsory |
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| Level of Course Unit * | Second Cycle |
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| Year of Study * | Second Year |
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| Semester when the Course Unit is delivered | Winter Semester |
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| Mode of Delivery | Face-to-face |
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| Language of Instruction | Czech |
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| Prerequisites and Co-Requisites | Course succeeds to compulsory courses of previous semester |
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| Name of Lecturer(s) | Personal ID | Name |
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| FAB37 | doc. Ing. Richard Fabík, Ph.D. |
| Summary |
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| The subject deals with the mathematical modeling of forming processes. The aim is to clarify the mathematical background of the finite element method, using practical examples explain the engineering approach to the mathematical modeling. |
| Learning Outcomes of the Course Unit |
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- Student will be able to explain the finite element method
- Student will be able to define and establish initial and boundary conditions in mathematical modeling of forming processes
- Student will be able to discuss the possibilities and difficulties of using the finite element method for modeling of selected forming processes
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| Course Contents |
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1. Introduction to mathematical modeling, principles of mathematical model
2. Analytical solution of Poisson's and Laplace's equation
3. The finite element method, a variation of a functional, properties of basis functions.
4. Patterns of creating finite element mesh (accuracy vs. computation speed).
5. Boundary and initial conditions for modeling of forming processes - an overview.
6. Thermo-mechanical analysis in forming.
7. Tribology and friction during forming.
8. Model of heat transfer to the surroundings and the tools.
9. Mathematical modeling temperature fields of rolled products and forging.
10. Mathematical modeling of forging (upsetting, extension).
11. Mathematical modeling of microstructure evolution during forming.
12. Mathematical modeling of rolling of asymmetrical shapes.
13. Use of mathematical modeling in the evaluation of technological formability.
14. Mathematical modeling of wire drawing
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| Recommended or Required Reading |
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| Required Reading: |
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[1] WAGONER, R.H. and J.L. CHENOT. Metal Forming Analysis. Cambridge: Cambridge University Press, 2001. ISBN 0-521-64267-1.
[2] KOBAYASHI, S., S. OH and T. ALTAN. Metal Forming and the Finite-Element Method. Oxford: Oxford University Press, 1989. ISBN 0-19-504402-9.
[3] LENARD, J.G., M. PIETRZYK and L. CSER. Mathematical and Physical Simulation of the Properties of Hot Rolled Products. Elsevier Science Ltd, 1999. ISBN 0-08-042701-4.
[4] ALTAN. T., S. OH and H. GEGEL. Metal forming – fundamentals and applications. Metals park: ASM, 1983.
[5] LENARD, J. G. Primer on Flat rolling. Elsevier. 2007.
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[1]http://katedry.fmmi.vsb.cz/Modin_Animace/Opory/02_Metalurgicke_inze-nyrstvi/14_Modelovani_tvarecich_procesu/Fabik_Modelovani_tvarecich_procesu.pdf
[2] ŽÍDEK, M., DĚDEK, V., SOMMER, B. Tváření oceli. Praha: SNTL, 1988.
[3] WAGONER, R.H. and J.L. CHENOT. Metal Forming Analysis. Cambridge: Cambridge University Press, 2001. ISBN 0-521-64267-1.
[4] KOBAYASHI, S., S. OH and T. ALTAN. Metal Forming and the Finite-Element Method. Oxford: Oxford University Press, 1989. ISBN 0-19-504402-9.
[5] LENARD, J.G., M. PIETRZYK and L. CSER. Mathematical and Physical Simulation of the Properties of Hot Rolled Products. Elsevier Science Ltd, 1999. ISBN 0-08-042701-4. |
| Recommended Reading: |
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[1] GINZBURG, V., B., Steel-Rolling Technology,Theory and Praktice. New York and Basel: Marcel Dekker, Inc., 1989. ISBN 0-8247-8124-4.
[2] NAUJOKS, Waldemar, FABEL, Donald C. Forging Handbook. 4th edition. Cleveland, Ohio: The American Society for Metals, 1948.
[3] ENGHANG, P., Steel wire technology, Applied Materials Technology. Örebro: Repro Örebro University, 2008. ISBN 91-631-1962-5.
[4] CALLISTER, W.D. Fundamentals of Materials Science and Engineering: An Interactive E-text. Wayne Anderson. 5th edition. New York: John Wiley & Sons, 2001. ISBN 0-471-39551-X.
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[1] DYJA, H., et al, Modelowanie procesów kucia swobodnego, Wydawnictwo wipmifs, Częstochowa 2004, ISBN 83-87745-52-9
[2] REKTORYS, K. Variační metody v inženýrských problémech a v problémech matematické fyziky. Praha: Academia, 1999. ISBN 80-200-0714-8.
[3] BLAHETA, R., K. Matematické modelování a metoda konečných prvků. Studijní opora k předmětu. 2012, 117s.
[4] HAŠEK, V., aj. Kování. Praha: SNTL, 1965. ISBN 04-233-65.
[5] RÉDR, M. a M. PŘÍHODA. Základy tepelné techniky. Praha: SNTL, 1991. ISBN 04-413-91.
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| Planned learning activities and teaching methods |
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| Lectures, Individual consultations, Tutorials, Experimental work in labs, Project work |
| Assesment methods and criteria |
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| Task Title | Task Type | Maximum Number of Points
(Act. for Subtasks) | Minimum Number of Points for Task Passing |
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| Credit and Examination | Credit and Examination | 100 (100) | 51 |
| Credit | Credit | 30 | 16 |
| Examination | Examination | 70 | 35 |