Course detail
Mathematical Modelling
FSI-PMM Acad. year: 2025/2026 Summer semester
Due to the development of computer technology, the numerical simulation has become helpful in designing and optimising foundry processes. Mathematical simulation is aimed at the tuning of the designed technology in the phase of production preparation in order to avoid expensive experimental testing. The simulation of foundry processes connects numerical methods, physics and computer technology. It enables the study of processes during melt flow, solidification and cooling of castings.
Language of instruction
Czech
Number of ECTS credits
4
Supervisor
Department
Entry knowledge
Basic knowledge of Foundry technology, knowledge of liquid flows and heat transfer, basic computer skills
Rules for evaluation and completion of the course
Course – unit credit requirements-optimisation of real casting technology, participation in the lessons
Exam – written and oral parts
Participation in seminars is required. An apologized absence from seminars may be compensated by individual work.
Aims
The aim of the course is to explain all the stages of simulation preparation and to give a compact view of the possibilities of computer assisted systems in the area of foundry processes.
Student will acquire the knowledge of 3D modelling of castings, definition of initial and boundary conditions of numerical simulation, evaluation of simulation results. The optimisation of gating and feeding systems is done using real castings and is performed for all foundry processes (gravity sand and die casting, high pressure die casting, investment casting, semi-solid processes). Calculation of production costs and sale price of castings together with Pacyna’s classification of castings is described. Relationships between other modules for thermo-mechanical calculation of castings are shown. The calculations are carried out with the support of modern software products.
Study aids
The materials will be accessible via e-learning.
The study programmes with the given course
Programme N-SLE-P: Foundry Technology, Master's, compulsory
Type of course unit
Lecture
13 hours, compulsory
Syllabus
1. Introduction to numerical simulation of foundry processes.
2. Application of CAD system in foundry processes.
3. Methods of numerical simulation.
4. Basic knowledge of heat transfer.
5. Initial condition definition.
6. Boundary condition definition.
7. Thermo-physical properties.
8. Calculation of porosity defects in casting.
9. Simulation of gravity sand casting technology.
10. Simulation of high and low pressure die casting technology.
11. Investment casting technology.
12. Special processes; semi-solid processes.
13. Post-processing and industrial cases.
Computer-assisted exercise
26 hours, compulsory
Syllabus
1. Geometry design – data import and export.
2. Preparation of surface and volume meshes.
3. Repairing of bad meshes.
4. Definition of initial and boundary conditions.
5. Calculation definition; modules, calculation steps.
6. Examples of gravity casting calculation.
7. Examples of pressure casting calculation.
8. Examples of investment casting calculation.
9. Calculation of special processes.
10. Porosity calculation.
11. Optimisation of gating and feeding systems.
12. Post-processing.
13. Results validation.