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MODELLING AND SIMULATION OF MANUFACTURING PROCESSES – 21ME64D3 Study Material Unit – I Compiled By Prof. Jinka Ranganayakulu MHRM, MS – IIT Madras, Ph.D. (Material is Prepared for Academic Purpose Only)...

MODELLING AND SIMULATION OF MANUFACTURING PROCESSES – 21ME64D3 Study Material Unit – I Compiled By Prof. Jinka Ranganayakulu MHRM, MS – IIT Madras, Ph.D. (Material is Prepared for Academic Purpose Only) Department of Mechanical Engineering RV College of Engineering® Bengaluru - 560059 (An autonomous institution affiliated to VTU, Belagavi)  Semester: VI MODELLING AND SIMULATION OF MANUFACTURING PROCESSES Category: Professional Elective (Theory) Course Code : 21ME64D3 CIE : 100 Marks Credits: L:T:P : 3:0:0 SEE : 100 Marks Total Hours : 45 L SEE Duration : 3.00 Hours Unit-I 09 Hrs Mathematical Modeling and Engineering Problem Solving – A Simple Mathematical Model and the engineering problem solving process, mathematical modelling process, Hierarchical vs. Concurrent approach, multi-scale models. Modelling of Sand-Casting and Fusion Welding: Casting: Mechanism of solidification – Rate of solidification, Solidification of large casting in an insulating mould; Fusion Welding: Heat Source – Emission and ionization of electric arc, arc structure and characteristics, modes of metal transfer in arc welding, Arc efficiency; Heat input to the weld, Relation between weld cross-section and energy input, Heat input rate, Width of the heat affected zone, Cooling rates, Numerical problems. Unit – II 09 Hrs Modelling of Forming Processes: Engineering and true stress-strain, Flow stress, Yield criteria; Slab method: Forging – Analysis of forging pressure for rectangular and circular disc. Numerical problems. Wire Drawing – Analysis of Drawing stress, Maximum reduction; Extrusion (Round bar/wire) – Extrusion workload & Stress analysis; Deep Drawing: Blank holding and drawing force analysis. Numerical problems. Unit –III 10 Hrs Modelling of Machining Processes: Review on Orthogonal cutting; Oblique Cutting: Direction of chip flow, Rake angles, cutting ratios, Velocity relationship, Shear angle; Mechanics of Turning Process: Analysis of chip flow direction, Effective rake angle, Power and forces, Specific cutting resistance. Numerical problems. Ultrasonic Machining: Grain throwing and grain hammering models, parametric analysis, and process Parameters; Electric Discharge Machining: Analysis of R-C circuits, Condition for maximum power generation, Material removal rate, Surface finish, Process parameters. Numerical problems. Unit –IV 08 Hrs Membership functions, Definitions in fuzzy sets, Standard operations in fuzzy sets and relations. Numerical problems. Measures of fuzziness and inaccuracy of fuzzy sets, Fuzzy Logic Controller: Mamdani approach, Takagi and Sugeno’s approach. Numerical problems. Unit –V 09 Hrs Fundamentals of Neural Networks: Artificial neuron, Transfer functions; Multi-Layer Feed-Forward Neural Network: Training of network using back-propagation algorithm, Types of training methods. (No problems) Neuro-Fuzzy System: Mamdani Approach – Tuning of the Neuro-Fuzzy System using a Back-Propagation algorithm; Adaptive Neuro-Fuzzy Inference System: Takagi and Sugeno’s approach. (No problems) Course Outcomes: After completing the course, the students will be able to CO1: Analyse models for metal casting and fusion welding processes. CO2: Apply models to analyse forces in forming processes. CO3: Analyse models for traditional and non-traditional machining processes. CO4: Apply the principles of soft computing tools to create models for the manufacturing process inputs and outputs. Reference Books 1 “Manufacturing Science”, Amitabha Ghosh, East-West Press Pvt Ltd, 2nd ed., 2010, ISBN-13: 978-81- 767-1063-3. 2 “Welding Science and Technology”, Md. Ibrahim Khan, New Age International (P) Limited, 2017, ISBN-13: 978-81-224-2621-5. 3  “Welding Processes and Technology”, R.S. Parmar, Khanna Publishers, 3rd Edition, 2020, ISBN-13: 978-81-7409-126-2. 4 “Principles of Metal Manufacturing Processes”, J. Beddoes & M. J. Bibby, Elsevier Butterworth- Heinemann, 2006, ISBN-13: 978-81-312-0133-6. 5 “Fundamentals of Metal Cutting and Machine Tools”, B.L Juneja, G.S. Sekhon & Nitin Seth, New Age International (P) Limited, 2003, 2nd Revised ed., 2003, ISBN-13: 978-81-224-1467-7. 6 “Unconventional Machining Processes”, Jagadeesha T, Dreamtech Press, Wiley India Pvt Ltd. 2021, ISBN-13: 978-9-389-97605-2. 7 “Soft Computing – Fundamentals and Applications”, Dilip K. Pratihar, Narosa Publishing House Compiled by Prof. Jinka Ranganayakulu, MHRM, MS – IIT Madras, Ph.D. Department of Mechanical Engineering, RV College of Engineering, Bengaluru -560 059  Pvt. Ltd. Revised Edition, 2015, ISBN-13: 978-81-8487-495-2. Mathematical Modeling and Engineering Problem Solving – A Simple Mathematical Model and the engineering problem solving process, mathematical modelling process, Hierarchical vs. Concurrent approach, multi-scale models. Modelling of Sand-Casting and Fusion Welding: Casting: Mechanism of solidification – Rate of solidification, Solidification of large casting in an insulating mould. Discuss about the importance of Mathematical modelling and engineering problem solving process. Knowledge and understanding are prerequisites for the effective implementation of any tool. No matter how impressive your tool chest, you will be hard-pressed to repair a car if you do not understand how it works. This is particularly true when using computers to solve engineering problems. Although they have great potential utility, computers are practically useless without a fundamental understanding of how engineering systems work. This understanding is initially gained by empirical means—that is, by observation and experiment. Over years and years of observation and experiment, engineers and scientists have noticed that certain aspects of their empirical studies occur repeatedly. Such general behavior can then be expressed as fundamental laws that essentially embody the cumulative wisdom of past experience. Thus, most engineering problem solving employs the two-pronged approach of empiricism and theoretical analysis. Fig. The engineering problem- solving process. It must be stressed that the two prongs (empiricism and theoretical analysis) are closely coupled. Compiled by Prof. Jinka Ranganayakulu, MHRM, MS – IIT Madras, Ph.D. Department of Mechanical Engineering, RV College of Engineering, Bengaluru -560 059  As new measurements are taken, the generalizations may be modified or new ones developed. Similarly, the generalizations can have a strong influence on the experiments and observations. In particular, generalizations can serve as organizing principles that can be employed to synthesize observations and experimental results into a coherent and comprehensive framework from which conclusions can be drawn. From an engineering problem-solving perspective, such a framework is most useful when it is expressed in the form of a mathematical model. Discuss mathematical modelling aspects using a simple mathematical model. A mathematical model can be broadly defined as a formulation or equation that expresses the essential features of a physical system or process in mathematical terms. In a very general sense, it can be represented as a functional relationship of the form,  where the dependent variable is a characteristic that usually reflects the behavior or state of the system;  the independent variables are usually dimensions, such as time and space, along which the system’s behavior is being determined;  the parameters are reflective of the system’s properties or composition; and  the forcing functions are external influences acting upon the system.  The actual mathematical expression of Eq. (1) can range from a simple algebraic relationship to large complicated sets of differential equations.  For example, on the basis of his observations, Newton formulated his second law of motion, which states that the time rate of change of momentum of a body is equal to the resultant force acting on it.  The mathematical expression, or model, of the second law is the well known equation F = ma ------------------------ (2) where F = net force acting on the body (N, or kg m/s 2), m = mass of the object (kg), and a = its acceleration (m/s2). The second law can be recast in the format of Eq. (1) by merely dividing both sides by m to give a = F/m ________________________ (3) where a = the dependent variable reflecting the system’s behavior, F = the forcing function, and m = a parameter representing a property of the system. Compiled by Prof. Jinka Ranganayakulu, MHRM, MS – IIT Madras, Ph.D. Department of Mechanical Engineering, RV College of Engineering, Bengaluru -560 059  Note that for this simple case there is no independent variable because we are not yet predicting how acceleration varies in time or space. Equation (3) has several characteristics that are typical of mathematical models of the physical world: 1. It describes a natural process or system in mathematical terms. 2. It represents an idealization and simplification of reality. That is, the model ignores negligible details of the natural process and focuses on its essential manifestations. Thus, the second law does not include the effects of relativity that are of minimal importance when applied to objects and forces that interact on or about the earth’s surface at velocities and on scales visible to humans. 3. Finally, it yields reproducible results and, consequently, can be used for predictive purposes. For example, if the force on an object and the mass of an object are known, Eq. (3) can be used to compute acceleration.  Because of its simple algebraic form, the solution of Eq. (2) can be obtained easily.  To illustrate a more complex model of this kind, Newton’s second law can be used to determine the terminal velocity of a free falling body near the earth’s surface.  Our falling body will be a parachutist (Fig.).  A model for this case can be derived by expressing the acceleration as the time rate of change of the velocity (dv∕dt) and substituting it into Eq. (3) to yield where υ is velocity (m/s) and t is time (s). Thus, the mass multiplied by the rate of change of the velocity is equal to the net force acting on the body. If the net force is positive, the object will accelerate. If it is negative, the object will decelerate. If the net force is zero, the object’s velocity will remain at a constant level. Compiled by Prof. Jinka Ranganayakulu, MHRM, MS – IIT Madras, Ph.D. Department of Mechanical Engineering, RV College of Engineering, Bengaluru -560 059 Compiled by Prof. Jinka Ranganayakulu, MHRM, MS – IIT Madras, Ph.D. Department of Mechanical Engineering, RV College of Engineering, Bengaluru -560 059 Physics based modelling approach at different scale continuum to Nano  Equilibrium system– Form governing equations  Dynamic system (Analyse the kinematics)– Form governing equations  May use constitutive equation  With essential and natural boundary conditions  Also need initial condition  Constitutive equation relates two different physical quantities  It does not directly follow physical laws  It can be combined with other equations such as equilibrium and kinematical equations which do represent physical laws The constitutive law parameter can be derived from experimental observation– called phenomenological modelling  The methodology is to explicitly include variables from physics as internal state variables  The other possibility is to determine the format of the constitutive equation based on knowledge about the physical mechanisms causing the deformation (For example, Failure mechanism)  An alternate to phenomenological modelling is to derive constitutive equations from low-scale where laws of physics is well understood  For example: parameters for grain size models for microstructural evolution Example: Determine the material property Young’s modulus from experiment and use it to develop mathematical continuum model that predicts material’s response.  Micromechanics model take into account more fine detail of the material’s structure at grain scale Compiled by Prof. Jinka Ranganayakulu, MHRM, MS – IIT Madras, Ph.D. Department of Mechanical Engineering, RV College of Engineering, Bengaluru -560 059   The properties at the micro scale are averaged and passed to the continuum model is through homogenization theory  Micromechanical models can provide local variation of material behavior than the simpler continuum model Discuss the Importance of Multiscale Methods? Limitations of industrial simulations today: a) Continuum models are good, but not always adequate Problems in fracture and failure of solids require improved constitutive models to describe material behavior Macroscopic material properties of new materials and composites are not readily available, while they are needed in simulation-based design Detailed atomistic information is required in regions of high deformation or discontinuity b) Molecular dynamics simulations Limited to small domains (~ 106- 108 atoms) and small time frames ( ~ nanoseconds) Experiments, even on nano-systems, involve much larger systems over longer times Discuss the difference between Hierarchical vs. Concurrent approach. Discuss various aspects of multi-scale modelling and Challenges in multi-scale modelling. Compiled by Prof. Jinka Ranganayakulu, MHRM, MS – IIT Madras, Ph.D. Department of Mechanical Engineering, RV College of Engineering, Bengaluru -560 059 Compiled by Prof. Jinka Ranganayakulu, MHRM, MS – IIT Madras, Ph.D. Department of Mechanical Engineering, RV College of Engineering, Bengaluru -560 059 COOLING AND SOLIDIFICATION of Casting A clear understanding of the mechanism of solidification and cooling of liquid metals and alloys is essential for the production of successful castings. During solidification, many important characteristics such as crystal structure and alloy composition at different parts of the casting are decided. Moreover, unless a proper care is taken, other defects, e.g., shrinkage cavity, cold shut, misrun, and hot tear, also occur. ______________________________________________________ MECHANISM OF SOLIDIFICATION Discuss the mechanism of solidification of casting with neat sketches. Pure Metals Liquids need to be cooled below their freezing points before the solidification begins. This is because energy is required to create surfaces for new crystals. The degree of supercooling necessary is reduced by the presence of other surfaces (particles) which serve as the initial nuclei for crystal growth. When a liquid metal is poured into a mould, initially (at time to in Fig. 1) the temperature everywhere is Ѳo. The mould face itself acts as the nucleus for crystal growth, and if the conductivity of the mould is high, randomly-oriented small crystals grow near the mould face. Subsequently, a temperature gradient results within the casting, as indicated in Fig. 1 for t1 and t2. As the solidification progresses Compiled by Prof. Jinka Ranganayakulu, MHRM, MS – IIT Madras, Ph.D. Department of Mechanical Engineering, RV College of Engineering, Bengaluru -560 059 gradually inwards, long columnar crystals, with their axes perpendicular to the mould face, grow. This orientation of crystal growth is desirable from the point of view of strength of the casting. Fig. 1 Development of columnar crystals. Alloy Metals Unlike a pure metal, alloys do not have a sharply defined freezing temperature. The solidification of an alloy takes place over a range of temperature. During this process, the solids separating out at different temperatures possess varying compositions. Due to all these facts, the direction of crystal growth in an alloy depends on various factors, such as (i) the composition gradient within the casting, (ii) the variation of solidus temperature with composition, and (iii) the thermal gradient within the mould. Consider a solid solution alloy whose phase diagram is shown in Fig. 2. Let the liquid alloy have the composition Co (of B in A). Also, let Ѳf be the freezing point of pure metal A, and Ѳo and Ѳ/o, respectively, be the liquidus and the solidus temperatures of the alloy of composition Co. As the liquid alloy is cooled down to the temperature Ѳo, solids start to separate out. The concentration of B in these solids is only C 1(