# VTU Syllabus Mechanical Engineering 4th Semester

**Engineering Mathematics Sem IV**

Module-1

Numerical Methods: Numerical solution of ordinary differential equations of first order and first degree, Picard’s method, Taylor’s series method, modified Euler’s method, Runge-Kutta method of fourth order. Milne’s and Adams-Bashforth predictor and corrector methods (No derivations of formulae). Numerical solution of simultaneous first order ordinary differential equations, Picard’s method, Runge-Kutta method of fourth order.

Module-2

Numerical Methods: Numerical solution of second order ordinary differential equations, Picard’s method, Runge-Kutta method and Milne’s method. Special Functions: Bessel’s functions- basic properties, recurrence relations, orthogonality and generating functions. Legendre’s functions – Legendre’s polynomial, Rodrigue’s formula, problems.

Module-3

Complex Variables: Function of a complex variable, limits, continuity, differentiability,.Analytic functions-Cauchy-Riemann equations in Cartesian and polar forms. Properties and construction of analytic functions. Complex line integrals-Cauchy’s theorem and Cauchy’s integral formula, Residue, poles, Cauchy’s Residue theorem with proof and problems. Transformations: Conformal transformations, discussion of transformations:w = z2 , w = e z , w = z + (a2 /z) and bilinear transformations.

Module-4

Probability Distributions: Random variables (discrete and continuous), probability functions. Poisson distributions, geometric distribution, uniform distribution, exponential and normal distributions, Problems. Joint probability distribution: Joint Probability distribution for two variables, expectation, covariance, correlation coefficient.

Module-5

Sampling Theory: Sampling, Sampling distributions, standard error, test of hypothesis

for means and proportions, confidence limits for means, student’s t-distribution, Chi- square distribution as a test of goodness of fit. Stochastic process: Stochastic process, probability vector, stochastic matrices, fixed points, regular stochastic matrices, Markov chains, higher transition probability.

Course Outcomes :

1. Use appropriate numerical methods to solve first and second order ordinary differential equations.

2. State and prove Cauchy’s theorem and its consequences including Cauchy’s integral formula.

3. Compute residues and apply the residue theorem to evaluate integrals.

4. Analyze, interpret, and evaluate scientific hypotheses and theories using rigorous statistical methods.

5. Use Bessel’s and Legendre’s function which often arises when a problem possesses axial and spherical symmetry, such as in quantum mechanics, electromagnetic theory, hydrodynamics and heat conduction.

Text Books :

- B.V.Ramana “Higher Engineering Mathematics” Tata McGraw-Hill, 2006.
- B. S. Grewal,” Higher Engineering Mathematics”, Khanna publishers, 42nd edition, 2013.

Reference Books :

- N P Bali and Manish Goyal, “A text book of Engineering mathematics” , Laxmi publications, latest edition.
- Kreyszig, “Advanced Engineering Mathematics ” – 9th edition, Wiley, 2013.
- H. K Dass and Er. RajnishVerma, “Higher Engineering Mathematics”, S. Chand, 1st ed, 2011.

**Fluid Mechanics Sem IV**

Module-1

1.1 Fluid Definition and properties, Newton’s law of viscosity concept of continuum, Classification of fluids

1.2 Fluid Statics: Definition of body and surface forces, Pascal’s law, Basic hydrostatic equation, Forces on surfaces due to hydrostatic pressure, Buoyancy and Archimedes’ principle

Module-2

2 Fluid Kinematics:

2.1 Eaulerian ancd Lagrangkian approatch to so.lutiocns; Velocoity andacceleration in an Eulerian flow field; Definition of streamlines, path lines and streak lines; Definition of steady/unsteady, uniform/non-uniform, one-two and three Understanding of differential and integral methods of analysis.

2.2 Definition and equations for stream function, velocity potential function in rectangular and cylindrical co-ordinates, rotational and irrotational flows; Definition and equations for source, sink, irrotational vortex, circulation.

Module-3

3 Fluid Dynamics:

3.1 Integral equations for the control volume: Reynold’s Transport theorem( with proof), equations for conservation of mass, energy and momentum, Bernoulli’s equation and its application in flow measurement, pitot tube, venture, orifice and nozzle meters.

3.2 Differential equations for the control volume: Mass conservation in 2 and 3 dimension in rectangular and cylindrical co-ordinates, Euler’s equations in 2,3 dimensions and subsequent derivation of Bernoulli’s equation; Navier-Stokes equations( without proof) in rectangular cartesian co-ordinates; Exact solutions of Navier-Stokes Equations to viscous laminar flow between two parallel planes ( Couette flow and plane Poiseuille flow)

Module-4

4 Real fluid flows:

4.1 Definition of Reynold’s number, Laminar flow through a pipe ( Hagen- Poiseuille flow), velocity profile and head loss; Turbulent flows and theories of turbulence-Statistical theory, Eddy viscosity theory and Prandtl mixing length theory; velocity profiles for turbulent flows- universal velocity profile, 1/7th power law; Velocity profiles for smooth and rough pipes

4.2 Darcy’s equation for head loss in pipe( no derivation),Moody’s diagram, pipes in series and parallel, major and minor losses in pipes

Module-5

5 Boundary Layer Flows:

5.1 Concept of boundary layer and definition of boundary layer thickness, displacement, momentum and energy thickness; Growth of boundary layer,laminar and turbulent boundary layers, laminar sub-layer; Von Karman Momentum Integral equation for boundary layers, analysis of laminar and turbulent boundary layers, drag, boundary layer separation and methods to control it, streamlined and bluff bodies

5.2 Aerofoil theory: Definition of aerofoil, lift and drag, stalling of aerofoils, induced drag.

Module-6

6 Compressible Fluid flow:

6.1 Propagation of sound waves through compressible fluids, Sonic velocity and Mach number; Application of continuity , momentum and energy equations for steady state conditions; steady flow through nozzle, isentropic flow through ducts of varying cross-sectional area, Effect of varying back pressure on nozzle performance, Critical pressure ratio

6.2 Normal shocks, basic equations of normal shock, change of properties across normal shock

List of Experiments:

1. Calibration of pressure gauge

2. Determination of pressure surge in pipes

3. Measurement of hydrostatic force on bodies/surfaces

4. Verific tion of Ar himedes’ Principle

5. Verification of Pascal’s law

6. Calibration of venture meter / orificemeter / nozzlemeter / pitot tube

7. Determination of friction factor for pipes

8. Determination of major and minor losses in piping systems

9. Verification of energy equation

10. Verification of momentum principle

11. Verification of Bernoulli’s equation

12. Calculation of lift and drag in aerofoils

13. Determination of pressure profile over an aerofoil

14. Mini Project along with brief report in which a group of students (Max 4) will

Reference Books:

1. Fluid Mechanics : Streeter and Wylie, McGraw Hill

2. Fluid Mechanics : F.M.White, McGraw Hill

3. Fluid Mechanics: K.L.Kumar

4. Introduction to Fluid Mechanics: Fox and McDonald

5. Introduction to Fluid Mechanics: James.A.Fay

6. Prandtl Essentials of Fluid Mechanics :Herbert Oertel(Ed)

7. Fluid Mechanics: B.M.Massey

8. Fluid Mechanics: Cengel and Cimbala

9. Mechanics of Fluids: Irving Shames

10. Advanced Fluid Dynamics: Muralidhar and Biswas P11.rFluid Maechanics acnd Hydrakulics, S. K. tUkaran.de, Acne BooksoPvt.Ltd

**Theory of Machines-I Sem IV**

Module-1

1.1 Kinetics of rigid bodies

Mass M.I. about centroidal axis and about any other axis. Radius of Gyration. D’Alemberts Principle of Bodies under rotational motion about a fixed axis and plane motion. Application of motion of bars, Cylinders and spheres only.

Kinetics of Rigid Bodies: Work and Energy. Kinetic energy in translating motion, Rotation about fixed axis and in general plane motion, Work Energy Principle and Conservation of a Energy. ckt.co

1.2 Basic Kinematics:

Kinematic link, Types of links, Kinematic pair, Types of constrained motions, Types of Kinematic pairs, Kinematic chain, Types of joints, Mechanism, Machine, Degree of freedom (Mobility), Kutzbachcrieterion, Grubler’s criterion. Four bar chain and its inversions, Grashoff’s law, Slider crank chain and its inversions, Double slider crank chain and its inversions.

Module-2

2.1 Special Mechanisms:

Straight line generating Mechanisms: Exact Straight Line Generating Mechanisms – Peaucellier’s and Hart’s Approximate Straight Line Generating Mechanisms – Watt’s, Grasshopper and Tchebicheff’s.

Offset slider crank mechanisms, Pantograph. Hook joint- single and double

Steering gear mechanisms – Ackerman, Davis

Module-3

3.1 Velocity Analysis of mechanisms (mechanisms up to 6 links). Velocity analysis by instantaneous center of rotation method (Graphical approach) Velocity analysis by relative velocity method (Graphical approach)Analysis is extended to find rubbing velocities at joints, mechanical advantage (Graphical approach). Velocity analysis of low degree complexity mechanisms (Graphical approach). Auxiliary point method

3.2 Velocity and Acceleration analysis of mechanism. Velocity and Acceleration – analysis by relative method (mechanismsup to 6 link) including pairs involving Coriolis acceleration (Graphical Approach).

Module-4

4. Cam Mechanisms:

4.1 Cam and its Classifications.

4.2 Followers and its Classification.

4.3Motion analysis and plotting of displacement-time, velocity- time,acceleration- time, jerk-time graphs for uniform velocity. UARM, SHM and Cycloid motions (combined motions during one stroke excluded).

4.4 Motion analysis of simple cams – R-R cam, D-R-R and D-R-D-R camoperating radial translating follower.

4.5 Pressure angle and method to control pressure angle

4.6 Layout of cam profiles.

Module-5

5. Flexible Connectors:

5.1 Belt – Types of belts, velocity ratio, slip & creep, length of belt for open & cross system. Law of belting, Dynamic analysis- driving tensions, centrifugal tension, initial tension, condition of maximum power transmission.

5.2 Chains – types of chains, chordal action, variation in velocity ratio, Length of chain

Module-6

6. Gears

6.1 Law of gearing, Involute and Cycloid gear tooth profile, Construction of Involute profile.

6.2 Path of contact, arc of contact, contact ratio for involutes and cycloidal tooth profile, Interference in involutes gears. Critical Numbers of teeth for interference free motion.Methods to control interference in involutes gears.

6.3 Static force analysis in gears- spur, helical, worm & worm wheel.

Reference Books :

1. Theory or Mechanisms and Machines by Amitabh Ghosh and A. Kumar Mallik.

2. Theory of Machines and Mechanism by John Uiker, Garden Pennock& Late. J. F. shigley

3. Theory of Machines – P. L. Ballaney

4. Theory of Machines by S. S. Rattan

5. Kinematics of Machines by R T Hinckle (Prentice Hall Inc.)

6. Kinematics By V.M. Fairs (McGraw Hill)

7. Mechanism Design: Analysis and Synthesis Vol. I by A. Erdman and G.N. Sander (Prentice Hall)

8. Kinematics and Dynamics of Planer Mechanisms by Jeremy Hirsihham (McGraw Hill).

**Production Process-II Sem IV**

Module-1

Classification, Selection and application of Machine Tools:

1.1 Lathe Machines, Milling Machines, Drilling Machines, Grinding Machines, Broaching machines, Lapping/Honing machines and shaping/ slotting/planning Machines.

1.2 Gear Manufacturing -Gear milling, standard cutters and limitations, gear hobbing, gear shaping, gear shaving and gear grinding processes.

Module-2

CNC machines: Introduction, principles of operation, Types – Vertical machining centers and horizontal machining centers, major elements, functions, applications, controllers, open loop and closed loop systems, coordinate measuring machines, maintenance of CNC machines, G, M Codes, Basic CNC programming.

Module-3

Meatal Cuttincg & Tokol Engineetring: .Featucres of moachining processes, concept of speed and cutting, mechanism of chip formation, concept of shear plane, chip reduction coefficient force analysis. Merchants circle of cutting cutting forces and tool angles. Merchants theory-original and modified cutting force and power calculation in machining processes, gross power , efficiency of machine tools, effect of various parameters on cutting forces, methods of estimating of cutting forces.

Module-4

Measurement of Tool Forces and Economics of metal cutting: Different types of dynamometers and their operations. Tool life definition, mechanism of tool wear and measurement, preliminary and ultimate feature, factors Influencing tool life such as speed, feed, depth of cut, tool material, cutting fluids etc. Machinability, Economics of metal cutting:-parameters affecting machining cost. Tool life for minimum cost and for maximum productivity

Module-5

Surface Finish, Cutting Tool Materials, Coolants: Surface finish-influence of various parameters cutting tool materials-composition, field of application and manufacture.(carbon tool steel, high speed steel, non-ferrous alloys, carbides and ceramics), Selection of grinding wheel and dressing & truing of grinding wheels, coolants –function of coolants, effects on cutting force, tool life and surface finish, Types of coolants, Choice of coolants.

Module-6

Design of Cutting Tools or Tool design: Tool geometry and definition of principles tool angles of single point cutting tools, Design of single point cutting tools, Form tools, Drills, Milling cutters, Inserted type cutters, Broach tools, Standard inserts and Holders for Turning.

Reference Books:

1. Tool Design by Donaldson.

2. Machining Process by H.L. Juneja

3. Production Technology – HMT

4. Manufacturing, Engineering and Technology SI by SeropeKalpakjian, Steven R. Schmid, published by Prentice Hall

5. Fundamentals of Tool Design by ASTME

6. Metal cutting Theory & Cutting Tool Designing by V. Arshinov, G Alekseev

7. Principle of Metal cutting by Sen& Bhattacharya

8. Fundamentals of Metal Machining by GeofferyBoothroyd

9. Manuf cturing science by Ghosh and Mallick

**Material Technology Sem IV**

Module-1

Classification of Materials: Metallic materials, Polymeric Materials,Ceramics and Composites: Definition, general properties, applications with examples.

Lattice Imperfections: Definition, classification and significance of Imperfections Point defects: vacancy, interstitial and impurity atom defects. Their formation and effects.

Dislocation: Edge and screw dislocations Burger’s vector. Motion of dislocations and their significance.

Suraface defeccts: Grainkboundary,tsub- a.nglecgrain booundary and stacking conditions of multiplication and significance.

Deformation: Definition, elastic and plastic deformation, Mechanism of deformation and its significance in design and shaping, Critical Resolved shear stress. Deformation in single crystal and polycrystalline materials Slip systems and deformability of FCC, BCC and HCP lattice systems.

Strain Hardening: Definition importance of strain hardening. Dislocation theory of strain hardening, Effect of strain hardening on engineering behaviour of materials. Recrystallization Annealing: stages of recrystallization annealing and factors affecting it

Module-2

Failure mechanisms: Fracture: Definition and types of facture, Brittle fracture: Griffith’s theory of facture. Orowan’s modification. Dislocation theory of facture. Critical stress and crack propagation velocity for brittle fracture. Ductile fracture: Notch effect on fracture. Fracture toughness. Ductility transition. Definition and signification. Conditions of ductility transition factors affecting it.

Fatigue Failure: Definition of fatigue and significance of cyclic stress. Mechanism of fatigue and theories of fatigue failure, Fatigue testing. Test data presentation and statistical evolution. S-N Curve and its interpretation. Influence of important factors on fatigue. Notch effect,surface effect,Effect of pre-stressing, corrosion fatigue, Thermal fatigue.

Creep: Definition and significance of creep. Effect of temperature and creep on mechanical behaviors of materials. Creep testing and data presentation & analysis.Mechanism and types of creep. Analysis of classical creep curve and use of creep rate in designing of products for load bearing applications. Creep Resistant materials.

Module-3

Theory of Alloys& Alloys Diagrams : Significance of alloying, Definition, Classification and properties of different types of alloys. Different types of phase diagrams (Isomorphous, Eutectic, Peritectic, Eutectoid, Peritectoid) and their analysis. Importance of Iron as engineering material, Allotropic forms of Iron, Influence of carbon in Iron- Carbon alloying

Iron-Iron carbide diagram and its analysis,TTT diagram,Hardenability concepts and tests, Graphitization of Iron- Grey iron, white iron, Nodular and malleable irons. Their microstructures, properties and applications.

Module-4

Heat treatment Process: Technology of heat treatment. Classification of heat treatment process. Annealing- Principle process, properties and applications of full annealing, Diffusion annealing, process annealing and Cyclic annealing, Normalizing, Hardening heat treatment. Tempering, Subzero treatment, Austempering, Martempering, Maraging and Ausforming process.

Surface hardening: Hardening and surface Hardening methods. Their significance and applications. Carburizing, Nitriding, Cyaniding, Carbonitriding, induction hardening and flame hardening processes.

Module-5

Effect of Alloying Elements in Steels: Limitation of plain carbon steels. Significance of alloying elements.Effects of major and minor constituents, Effect of alloying elements on ferrite, carbide, austenite, Effect of alloying elements on phase transformation Classification of tool steels and metallurgy of tool steels and special steels

Module-6

Introduction to New materials: Composites: Basic concepts of composites, Processing of composites, advantages over metallic materials,various types of composites and their applications.

Nano Materials: Introduction, Concepts, synthesis of nanomaterials, examples, applications and nano composites.

Polymers: Basic concepts, Processing methods, advantages and disadvantages over metallic materials, examples and applications.

List of Experiment: Minimum eight experiments

1. Study of metallurgical microscope.

2. Metallographic sample preparation and etching.

3. Microstructures of plain carbon steels.

4. Microstructures of cast irons.

5. Fatigue test – To determine number of cycles to failure of a given material at a given stress.

6. Annealing, Normalising and Hardening of medium carbon steel and observation of microstructures.

7. Study of tempering characteristics of hardened steel.

8. Determination of hardenability of steel using Jominy end Quench Test.

9. Corrosion rate test

Reference Books :

1. Materials Science and Engineering by William D. Callister, Jr. – Adapted by R. Balasubramaniam. Wiley India (P) Ltd.

2. The Structure and Properties of Materials Vol I: M. G. Moffet, G. T. W. Pearsall & J. Wulff.

3. Material Science and Metallurgy, By V.D. Kodgire.

4. Metallurgy for Engineer- E.C. Rollason – ELBS SOC. And Edward Arnold, London.

5. Mechanical Behaviour of Materials- Courtney- McGraw Hill International New Delhi.

6. Introduction of Engineering Materials, By B.K. Agrawal, McGraw Hill Pub. Co. ltd

7. Mechanical Metallurgy: G.E. Dieter , McGraw Hill International New Delhi.

8. Metallurgy Engineering Part I&II-R. A. Higgins &HodderStoughlon, London.

9. A text book of Metallurgy- A.R.Bailey – Macmillan & Co. Ltd., London.

10. Introduction to solids- L.V.Azaroff- McGraw Hill International New Delhi.

**Industrial Electronics Sem IV**

Module-1

Semiconductor Devices: Review of diodes: rectifier diode , zener diode, LED, photodiode SCR V-I characteristics , R,R-C,UJT triggering circuits, turning-off of a SCR (preliminary discussion), basics of Gate Turn Off ( GTO ) Structure and V-I characteristics of Triac (modes of operation not needed) and Diac , Applications of Triac-Diac circuit, Characteristics and principle of Power BJT, power MOSFET,IGBT,

comparison of devices.

Module-2

Operational amplifiers and 555 Timer: Operational amplifier circuits, Ideal OPAMP behavior , common OPAMP ICs, Basic OPAMP circuits- Inverting amplifier, Noninverting amplifier ,Voltage follower (Buffer), Instrumentation Amplifier, Summing amplifier, Schmitt triggers Active first order filter: Low pass and high pass filter Power Op Amps, Optical Isolation amplifier

555 timer-Operating modes: monostable, astablemultivibrator.

Module-3

Digital logic and logic families: Digital signals, combinational and sequential logic circuits, clock signals, Boolean algebra and logic gates

Integrated circuits and logic families : Logic Levels, Noise Immunity, Fan Out, Power Dissipation, Propagation Delay,

TTL logic family : TTL Designations, TTL Versions, Output Configuration, TTL characteristic, The CMOS family,, comparison with TTL family

Flip flops: Set Reset(SR),Trigger(T),clocked D F/Fs; Buffer and drivers Registers, decoders and encoders, Multiplexer and Demultiplexer

Module-4

Overview of generic microprocessor, architecture and functional block diagram, Comparison of microprocessor and microcontroller, MSP430Functional block diagram and architecture, assembly language programming, C compiler programming, basics of interfacing with external input / output devices (like reading external analog voltages, digital input output)

Module-5

Motors: Review and comparison of Torque–speed characteristics of DC motors and AC induction motors. Basic principles of speed control of AC/DC motors.

Basics of BLDC motor, Linear Actuator motor, Servo Motor Suitability of each motor for various industrial applications, Selection and sizing of motors for different applications. Applications for pumps, conveyors, machine tools etc.

List of Experiment:

1. BJT as a switch

2. V-I characteristics of SCR

3. Triggering circuit of SCR (R,RC,UJT)

4. Full wave Rectifier using SCR

5. Single phase Bridge inverter with rectifier load

6. OPAMP as integrator

7. 555 timer as astablemultivibrator

8. Implementing study of gates and Logic Operations like , NOT, AND, OR,

9. Realization of basic gates using universal gates

10. Light dimmer circuit using Diac-Triac

11. Characteristics of DC shunt motor

12. Speed control of DC motor

13. Speed control of induction motor

14. Simple programs using microcontroller

15. Simple programs for microcontroller based applications

Reference Books:

1. Power Electronics M.H.Rashid, Prentice-Hall of India

2. Power Electronics, P S Bhimbra

3. Power Electronics VedamSubramanyam, New Age International

4. Jain R.P., “Modern Digitals Electronic “Tata McGraw Hill, 1984.

5. Fundamentals of Microcontrollers and Embedded System, Ramesh Gaonkar, PENRAM

6. Electrical drives by G K Dubey, Narosapublications

7. Power Electronics, Ned Mohan, Undeland, Robbins, John Wiley Publication

8. Digital principal and Application, Malvino& Leach, Tata McGraw Hill, 1991.

9. Digital design, Morris M. Mano, Prentice Hall International – 1984.

10. Electronic Devices and Circuits, Robert Boylestad and Louis Nashelsky, Prentice-Hall of India.

**Machine Shop Practice Sem IV**

Module-1

One composite job consisting minimum four parts employing operations on lathe like precision turning screw cutting, boring etc. This job shall involve use of shaping, milling and grinding operations.