ME685A

APPLIED NUMERICAL METHODS

Credits:

 

 

3L-0T-0L-0D (9 Credits)

 

Contents:


This course deals with how functions, derivatives, integrals, matrices and differential equations are evaluated as strings of numbers in the computer. It studies the speed of convergence of Taylor, Fourier, and other series expansions and their utility. Applications of these techniques in solving model engineering problems are included. Finally, it expects the students to write a computer program for several of the numerical techniques covered in the course.

Lecturewise Breakup (based on 50min per lecture)


I. Concepts of Algorithms and Programming; Revision of computer languages such as MATLAB, Fortran, and
    C++ (
2 Lectures)


II. Introduction to Mathematical Modelling (3 Lectures)


III. Taylor and Fourier series expansion (3 Lectures)


IV. Root finding (3 Lectures)


V. Interpolation, splines, extrapolation (3 Lectures)


VI. Regression and curve fitting (2 Lectures)


VII. Solution of simultaneous linear algebraic systems; nonlinear algebraic equations (5 Lectures)


VIII. Eigenvalues and eigenvectors (2 Lectures)


IX. Solution of simultaneous non-linear algebraic systems (1 Lecture)


X. Numerical integration, Simpson’s rule, Gaussian quadrature (3 Lectures)


XI. Solution of ODE: R. K. Methods; Predictor-Corrector methods; boundary-value problems (5 Lectures)


XII. Systems of ODE’s; convergence and error studies (4 Lectures)


XIII. Linear PDEs by finite differences (4 Lectures)


Programming projects based on mathematical modelling followed by an application of the numerical methods given above ( ~ 20% weightage)

References:

  1. Numerical Methods for Engineers; Steven C. Chapra and Raymond P. Canale, 7th edition, McGraw-Hill, 2014.

  2. Introduction to Numerical Analysis, S.S. Sastry; Prentice Hall of India,  2012.

  3. Numerical Methods for Engineers, Santhosh .K. Gupta, New Age International; 2012.

  4. Applied Numerical Methods for Digital Computation , M.L. James, G.M. Smith & J.C. Wolford, Harper- Collins College Division; 4th edition, 1993.

 

ME631A

Viscous Flow Theory

Credits:

 

 

 3L-0T-0L-0D (9 Credits)

 

Course Content:


Introduction: stress-deformation relation, vector and tensor, vorticity and circulation, derivation of Navier-Stokes equations; Exact solutions: Couette flow, Hagen-Poiseuille flow, Stokes problems; Complex variable and Potential flow, Two-dimensional boundary layer: Blassius solution, Kármán-Pohlhausen method, effect of pressure gradient, separation and control, Waltz’s-Quadrature formula; Flow instability: concept of small-perturbations, linearized stability of parallel viscous flows, Orr-Sommerfeld equation; Turbulent boundary layers: Reynolds stress tensor, energy cascade, mixing length hypothesis, universal law of wall, fully developed turbulent flow through a pipe and channel, power law and effect of wall roughness; Compressible flow: condition of compressibility, subsonic, supersonic and hypersonic flows, shock and Mach waves, shock-boundary layer interactions; Special topics: Transition and turbulence, fluid-solid interaction, free-surface flow, bio-fluids, non-Newtonian flows, CFD and Measurements (optional and limited to any one).

Lecturewise Breakup (based on 50min per lecture):


I. Introduction: (3 Lectures)

Fluid Properties, Definition of Continuum, Examples of Viscous Flow Phenomena, Laminar and Turbulent Flow, Vector and Tensor notation, Lagrangian/Eulerian Methods, Streamline, Path line, Streak line, Material Derivative and acceleration, Strain Rate, Translation, Rotation and Distortion of Fluid Element, Vorticity and Circulation.


II. Fundamental Equations of Viscous Flow: (5 Lectures)

Conservation of Mass, Momentum and Energy, Finite Volume Approach, Derivation of Continuity Equation: conservative and non conservative form, Derivation of Navier-Stokes (N-S) equations for Compressible Flow, Stokes Hypothesis. Incompressible form of N-S equations.


III. Exact Solutions: (7 Lectures)

Parallel Flow in a Straight Channel, Couette Flow,  Lubrication Theory, Hagen-Poiseuille Flow, Unsteady Parallel Flow, Stokes Problems, Similarity Solution and Creeping Flow, Complex variable and Potential flow.


IV. Boundary Layer Theory: (6 Lectures)

Derivation of 2-D Boundary Layer Equations, Displacement, Momentum and Energy Thickness, Order of Magnitude Analysis, Shape Factor, Momentum-Integral Approach, Boundary Layer Separation, Effect of Pressure Gradient, Boundary Layer Control by Suction and Blowing, Blassius Solution of Boundary Layer Equation, Kármán-Pohlhausen Method for Non-Zero Pressure Gradient, Holsten and Bohlen Method (Modified Pohlhausen Method), Waltz’s-Quadrature Formula and Example Problems.


V. Flow Instability: (4 Lectures)

Instability, Concept of Small-Perturbations, Linearized Stability of Parallel Viscous Flows, Orr-Sommerfeld Equation, Neutral Stability Curve, Boundary Layer Transition qver a Flat Plate.


VI. Turbulent Boundary Layers: (6 Lectures)

Introduction to Turbulent Flows, Features of Turbulence, Energy Cascade, Mean and Fluctuating Components, Derivations of Reynolds Averaged Navier-Stokes Equations, Reynolds Stress Tensor, Turbulent Boundary Layer Equations, Eddy Viscosity and Mixing Length Hypothesis, Universal Law of Wall, Laminar Sublayer, Power Law for Turbulent Boundary Layer, Skin Friction Coefficient, Turbulent Boundary Layer with Pressure Gradient, Quadrature Formula and Example Problems.


VII. Internal Flows: (3 Lectures)

Fully Developed Turbulent Flow through a Pipe and Channel, Use of Log Law and Power Law, Derivation of Coefficient of Friction for Turbulent Pipe Flow, Moody Diagram, Hydrodynamic Smooth and Rough Pipe and Example Problems.


VIII. Compressible Flows: (5 Lectures)

Introduction and Definition, Limiting Condition of Compressibility, Subsonic, Supersonic and Hypersonic Flows, Mach Angle, Propagation of Small Disturbances, Formation of Shock, Shock Waves, Normal Shock Relations, Oblique Shock, Compression and Expansion Waves, Reflection and Interaction of Shocks, Expansion Waves, Shock-Boundary Layer Interactions and Example Problems.


IX. Special Topics: (3 Lectures)

Transition and turbulence, fluid-solid interaction, free-surface flow, bio-fluids and non-Newtonian flows, CFD and Measurements (optional and limited to any one topic).

References:

  1. Fluid Mechanics by Pijush K. Kundu, Ira M. Cohen, David R Dowling (Academic Press)

  2. Fluid Mechanics by Frank M White (McGraw-Hill)

  3. Viscous Fluid Flow by Frank M White (McGraw-Hill)

  4. Boundary Layer Theory by H Sctllichting (McGraw-Hill)

 

ME662A

Machining Science – II

Credits:

 

 

3L-0T-0L-0D (9 Credits)

 

Course Content:


General classification of unconventional machining, chemical machining, electric discharge machining, Abrasive Jet and Ultrasonic Machining, electron beam machining, laser beam machining, ion beam machining, plasma arc machining; Comparative evaluation of different processes; Conventional machining with modifications.

Lecturewise Breakup(based on 50min per lecture)


I. Introduction to Advanced Manufacturing Processes (4 Lectures)

Introduction to manufacturing processes.
Overview of non conventional machining processes with (AJM, USM, ECM, EDM, EBM, LBM, AFM, MRF, MAF, MFP and MRAFF etc.)
Introduction to use of non conventional processes for micro-machining.


II. Mechanical Material Removal Processes (AJM, USM and WAJM) (8 Lectures)

Abrasive Jet Machining (AJM):
Introduction to abrasive jet machining (AJM), Mechanics of AJM, AJM process parameters Components of AJM (Abrasive, Gas, Setup), Mixing and Mass ratio and Material removal rate, Numerical approach to AJM, Modelling of Material Removal Rate (MRR). Ultrasonic Machining (USM):
Basics of USM processes, Mechanics of USM,  Process parameters of USM, Shaw’s model of USM mechanics, Compressed grain modelling and direct throw modelling and comparison,  Dependence of process parameters in estimation of MRR, Numerical approach to USM, Ultrasonic machining setup, Design of acoustic ultrasonic head and feed mechanism in USM.
Water Abrasive jet machining (WAJM): 
Introduction to WAJM (Basic principle and MRR estimation), WAJM process video.


III. Nano-finishing processes (6 Lectures)

Introduction to nanofinishing and need of nanofinishing, Abrasive Flow Finishing (AFF),
Introduction to AFF and self deformable feature, AFF machine elements, Magnetic Abrasive Finishing (MAF), Introduction to MAF, Elements of MAF, Setup and process parameters for AFF and MAF, Parametric analysis and applications of MAF and AFF.


III. Electrochemical Machining Process (ECM) (8 Lectures)

Electrochemistry basics, Basic Principle of Electrochemical Machining, Estimation of MRR in ECM, MRR in multiphase alloys, Modelling of Kinematics and Dynamics for ECM process, Numerical approach to ECM, Tool design in ECM, Electrolyte flow dynamics and design of electrode for electrolyte flow, Insulation design in ECM, Surface Finish in ECM of alloys, Basics of Electrochemical drilling, Basics of Electrochemical Grinding , Basics of Electro stream drilling, Process parameters from Electro-stream drilling and Electrochemical Grinding, Allied Processes, Electrochemical turning, Electrochemical Milling, Electrochemical deburring, Electrocemical boring etc.


IV. Thermal Matersial Removal Processes (EDM, EBM, LBM) (12 Lectures)

Electro-discharge machining:

Electro-discharge machining (EDM), Process parameters of EDM, Mechanics of EDM, Theoretical estimation of MRR in EDM, Modelling of depth of melting temperature, Role of cavitation in material removal in EDM, Role of melting temperature of the work-piece material, EDM circuits  and operating principles, Surface finishing and machining accuracy in EDM,  Taper and overcut in EDM, Effect of EDM on surface hardness, Electrode and dielectric fluid, EDM allied processes, ED turning, Wire EDM.

Electron Beam Machining (EBM): 

Introduction to electron beam machining, Comparison of E-beam machining with other thermal processes, Setup for EBM, Power requirement in E-Beam, Mechanics of EBM process, Derivation of functional characteristics in EBM by using Buckingham’s Pie theorem, Comparison of outcome of functional characteristics with empirical model, Power requirements for different work-piece materials in EBM

Laser Beam Machining (LBM): 

Introduction to Lasers and Laser beam machining, Types of lasers and feedback mechanisms in Lasers, Mechanics of material removal in Laser machining, Numerical modelling of LBM on semi-infinite surface and LBM with circular beams, Numerical estimation of time of machining in both the semi-infinite and circular beam cases, Steady state hole penetration model in LBM, Dependence of heat input in cutting speed of laser beam.


Videos of Lithograhy, EDM, LBM, Vacuum forming with process basics. (2-Hours)


PS: Three experimental demonstrations of 01 hour each in the area of LBM, EDM and MAF to be made in the manufacturing laboratory and 4i laboratory respectively.

References:

  1. Advanced manufacturing processes, Hassan Abdel, Gabad El Hoffy, McGraw Hill.

  2. V.K.Jain, Advance Machining Processes, Allied Publisher Bombay.

  3. Ghosh and Mallik, Manufacturing Science, EWP Private Ltd. 

  4. Pandey P.C., Shan H.S., Modern machining processes, Tata McGraw-Hill Education.

  5. Weller E.J., Non traditional machining processes, Society of Manufacturing Engineers, Publications.

  6. The Science and Engineering of Micro-fabrication, Stephen P. Campbell, Oxford university press.

 

ME661A

Machining Science – I

Credits:

 

 

 3L-0T-0P-1D (9C)

 

Course Content:


Mechanics of chip formation, chip curl. Bluntness and cutting forces. Thermal aspects of machining. Tool wear, tool life and economics of machining. Mechanics of grinding, forces and specific energy, temperature. wheel wear and surface finish.

Lecturewise Breakup (based on 50min per lecture)


I. Introduction: (2 Lectures)

Machining; Plastic Deformation, Tensile Test, Stress and Strain; Mechanism of Plastic Deformation: Slips, defects, plastic deformation on atomic scale.


II. Machining Process: (2.5 Lectures)

Types of machining processes; Chip formation; Orthogonal and Oblique Cutting; Types of Chips; Built-up edge formation.


III. Tool Geometry: (4 Lectures)

Reference planes; Tool specification: American System (ASA), continental or Orthogonal System (ORS), International or Normal Rake system (NRS); Tool angle relationships in ORS, ASA and NRS; Selection of Tool Angles; Multiple-point cutting tools: twist drill, helical milling cutter.


IV. Mechanics of Metal Cutting: (4.5 Lectures)

Merchant's Circle Diagram; Co-efficient of Friction: Determination of stress, strain and strain rate; Measurement of shear angle; Thin Zone model: Lee and Shaffer's Relationship; Thick Zone model: Okushima and Hitomi Analysisc.


V. Friction in Metal Cutting: (3 Lectures)

Nature of sliding friction; Friction in Metal Cutting: Sticking and Sliding Zones, Analysis of Stress Distribution on the tool face: Zorev’s model; Determination of mean angle of friction.


VI. Mechanism of Oblique cutting: (5 Lectures)

Rake angles in oblique cutting: Analytical determination of Normal Rake angle, velocity rake angle and effective rake angle; their relationship; shear angles in oblique cutting; velocity relationship; Force relationships in oblique cutting.


VII. Practical Machining Operations: (3.5 Lectures)

Turning, shaping and planning, Slab milling, Drilling: Machining Parameters, force magnitudes, power consumption, material removal rate, time per pass.


VIII. Measurement of cutting Forces: (2 Lectures)

Basic methods of measurement: Axially Loaded members, Cantilever Beam, Rings and Octagon, dynamometer requirements; machine tool dynamometers.


IX. Laboratory experiments on turning and grinding: (3 Lectures)

Tool angles; Measurement of cutting forces in turning and grinding; Measurement of temperature; chip thickness ratio; grain concentration in grinding.


IX. Tool Material, Tool Wear and Tool Life: (4 Lectures)

Types of tool wear; Mechanisms of wear: Abrasion, Adhesion and Diffusion. Progressive tool wear: flank and crater wear. Tool Life: variables affecting tool life - cutting conditions, tool geometry, Types of tool materials, fabrication of cutting inserts, coatings, work material and cutting fluid; Machinability and their criteria.


X. Economic of Machining: (2.5 Lectures)

Minimum Production Cost Criterion; Maximum Production Rate Criterion, and Maximum Profit Rate Criterion. Restrictions on cutting conditions: maximum power restriction, speed restriction, force and vibration restriction, surface finish restriction.


XI. Thermal Aspects of Machining: (2 Lectures)


Distinct regions of heat generation; Equations of Heat Flow: heat Flow due to conduction, heat flow due to transportation, heat absorbed and heat generated; Average Shear Plane temperature; Average Chip-tool interface Temperature; Experimental determination of cutting temperatures.


XII. Abrasive Machining Process: (3.5 Lectures)

Introduction: Types of abrasive machining processes; Grinding; types and characteristics; characteristics and specification of grinding wheels; Mechanics of Grinding Process; Determination of chip length in Grinding; Size effect; Wheel wear; Thermal Analysis; Honing and Lapping.


XIII. Term Paper:

Submission of soft and hard copies: presentation.

References:

  1. E.J.A. Armarego and R.H.Brown-The machining of Metals

  2. G Boothroyd-Fundamentals of Metal Machining and Machine  tools

  3. A.Ghosh and Asok Mallik- Machining Science

  4. G.K.Lal and S.K.Choudhury-Fundamental of Manufacturing Processes

  5. M.C.Shaw-Metal Cuttting Principle