# GATE Production and Industrial Engineering Syllabus

## Subject Code: PI

### Course Structure

Sections/Units Topics
Section A Engineering Mathematics
Unit 1 Linear Algebra
Unit 2 Calculus
Unit 3 Differential Equations
Unit 4 Complex Variables
Unit 5 Probability and Statistics
Unit 6 Numerical Methods
Section B General Engineering
Unit 1 Engineering Materials
Unit 2 Applied Mechanics
Unit 3 Theory of Machines and Design
Unit 4 Thermal and FluidsEngineering
Section C Manufacturing Processes I
Unit 1 Casting
Unit 2 Metal Forming
Unit 3 Joining of materials
Unit 4 Powder processing
Unit 5 Polymers and Composites
Section D Manufacturing Processes II
Unit 1 Machine Tools and Machining
Unit 3 Computer Integrated Manufacturing
Section E Quality and Reliability
Unit 1 Metrology and Inspection
Unit 2 Quality management
Unit 3 Reliability and Maintenance
Section F Industrial Engineering
Unit 1 Industrial Engineering
Unit 2 Industrial Engineering
Unit 3 Facility Design
Section G Operations research and Operations management
Unit 1 Operation Research
Unit 2 Engineering Economy and Costing
Unit 3 Production control
Unit 4 Project management

### Course Syllabus

Section A: Engineering Mathematics

Unit 1: Linear Algebra

• Matrix algebra
• Systems of linear equations
• Eigen values and Eigen vectors

Unit 2: Calculus

• Functions of single variable, Limit, continuity and differentiability
• Mean value theorems
• Evaluation of definite and improper integrals
• Partial derivatives
• Total derivative
• Maxima and minima
• Divergence and Curl
• Vector identities
• Directional derivatives
• Line, Surface and Volume integrals
• Stokes, Gauss and Green’s theorems

Unit 3: Differential Equations

• First order equations (linear and nonlinear)
• Higher order linear differential equations with constant coefficients
• Cauchy’s and Euler’s equations
• Initial and boundary value problems
• Laplace transforms
• Solutions of one dimensional heat and wave equations and Laplace equation

Unit 4: Complex variables

• Analytic functions
• Cauchy’s integral theorem
• Taylor series

Unit 5: Probability and Statistics

• Definitions of probability and sampling theorems,
• Conditional probability, Mean, median, mode and standard deviation
• Random variables, Poisson, Normal and Binomial distributions

Unit 6: Numerical Methods

• Numerical solutions of linear and non-linear algebraic equations Integration by trapezoidal and Simpson’s rule

• Single and multi-step methods for differential equations

Section B: General Engineering

Unit 1: Engineering Materials

• Structure and properties correlation

• Engineering materials (metals, ceramics, polymers and composites) – properties and applications

• Stress strain behavior of metals and alloys

• Iron-carbon phase diagram, heat treatment of metals and alloys, its influence on mechanical properties

Unit 2: Applied Mechanics

• Engineering mechanics −

• Equivalent force systems

• Free body concepts

• Equations of equilibrium

• Trusses

• Strength of materials −

• Stress, strain and their relationship

• Failure theories, Mohr’s circle(stress), deflection of beams, bending and shear stress

• Euler’s theory of columns

Unit 3: Theory of Machines and Design

• Analysis of planar mechanisms, cams and followers
• Governors and fly wheels
• Design of bolted, riveted and welded joints
• Interference/shrink fit joints
• Design of shafts, keys, spur gears, belt drives, brakes and clutches
• Pressure vessels

Unit 4: Thermal and Fluids Engineering

• Fluid mechanics −
• Fluid statics
• Bernoulli’s equation
• Flow through pipes
• Equations of continuity and momentum
• Capillary action
• Contact angle and wetting
• Thermodynamics −
• Zeroth, first and second laws of thermodynamics
• Thermodynamic system and processes
• Calculation of work and heat for systems and control volumes
• Air standard cycles
• Heat transfer −
• Basic applications of conduction

Section C: Manufacturing Processes I

Unit 1: Casting

• Types of casting processes and applications
• Patterns – types and materials
• Allowances
• Moulds and cores – materials, making, and testing
• Casting techniques of cast iron, steels and nonferrous metals and alloys
• Analysis of solidification and microstructure development
• Design of gating and riser
• Origin of defects

Unit 2: Metal Forming

Stress-strain relations in elastic and plastic deformation; concept of flow stress; hot and cold working – forging, rolling, extrusion and wire drawing; sheet metal working processes – blanking, bending and deep drawing; ideal work and slab analysis; origin of metal working defects.

Unit 3: Joining of materials

Principles of fusion welding processes (manual metal arc, MIG, TIG, plasma arc, submerged arc welding processes)–different heat sources (flame, arc, resistive, laser, electron beam), and heat transfer and associated losses, flux application, feeding of filler rod; Principles of solid state welding processes (friction, explosive welding, ultrasonic welding processes); Principles of adhesive, brazing and soldering processes; Origins of welding defects.

Unit 4: Powder processing

• Production of metal/ceramic powders
• Compaction and sintering of metals and ceramic powders

Unit 5: Polymers and Composites

• Plastic processing −
• Injection, compression and blow molding
• Extrusion, calendaring and thermoforming
• Molding of composites

Section D: Manufacturing Processes II

Unit 1: Machine Tools and Machining

• Basic machine tools like centre lathe, milling machine, and drilling machine – construction and kinematics

• Machining processes −

• Turning

• Taper turning

• Drilling

• Boring

• Milling

• Gear cutting

• Grinding

• Geometry of single point cutting tools, chip formation, cutting forces, specific cutting energy and power requirements, merchant’s analysis

• Basis of selection of machining parameters

• Tool materials, tool wear and tool life, economics of machining, thermal aspects of machining, cutting fluids, machinability

• Jigs and fixtures – principles, applications, and design

• Principles, applications, effect of process parameters on MRR and product quality of non-traditional machining processes – USM, AJM, WJM, AWJM, EDM and Wire cut EDM, LBM, EBM, PAM, CHM, ECM

Unit 3: Computer Integrated Manufacturing

• Basic concepts of CAD – geometric modeling
• CAM – CNC and robotics – configurations
• Drives and controls
• Group Technology and its applications – CAPP
• Cellular manufacturing and FMS

Section E: Quality and Reliability

Unit 1: Metrology and Inspection

• Limits, fits, and tolerances, gauge design, interchangeability, selective assembly

• Linear, angular, and form measurements (straightness, squareness, flatness, roundness, and cylindricity) by mechanical and optical methods

• Inspection of screw threads and gears

• Surface finish measurement by contact and non-contact methods

• Tolerance analysis in manufacturing and assembly

Unit 2: Quality management

• Quality – concept and costs
• Quality assurance
• Statistical quality control, acceptance sampling, zero defects, six sigma
• Total quality management
• ISO 9000

Unit 3: Reliability and Maintenance

• Reliability, availability and maintainability
• Distribution of failure and repair times
• Determination of MTBF and MTTR
• Reliability models
• Determination of system reliability
• Preventive maintenance and replacement

Section F: Industrial Engineering

Unit 1: Product Design and Development

Principles of good product design, tolerance design; quality and cost considerations; product life cycle; standardization, simplification, diversification, value engineering and analysis, concurrent engineering; comparison of production alternatives.

Unit 2: Work System Design

• Taylor’s scientific management, Gilbreths’s contributions
• Productivity – concepts and measurements
• Method study, micro-motion study, principles of motion economy
• Work measurement −
• Time study
• Work sampling
• Standard data
• PMTS
• Ergonomics
• Job evaluation, merit rating, incentive schemes, and wage administration

Unit 3: Facility Design

• Facility location factors and evaluation of alternate locations
• Types of plant layout and their evaluation
• Computer aided layout design techniques
• Assembly line balancing
• Materials handling systems

Section G: Operations research and Operations management

Unit 1: Operation Research

• Linear programming −
• Problem formulation
• Simplex method
• Duality and sensitivity analysis
• Transportation and assignment models
• Network flow models, constrained optimization and Lagrange multipliers
• Markovian queuing models
• Dynamic programming
• Simulation – manufacturing applications

Unit 2: Engineering Economy and Costing

• Elementary cost accounting and methods of depreciation

• Break-even analysis, techniques for evaluation of capital investments, financial statements, time-cost trade-off, resource leveling

Unit 3: Production Control

• Forecasting techniques −
• Causal and time series models
• Moving average
• Exponential smoothing
• Trend
• Seasonality
• Aggregate production planning
• Master production scheduling
• MRP and MRP-II
• Routing, scheduling and priority dispatching
• Push and pull production systems, concept of JIT manufacturing system
• Logistics, distribution, and supply chain management
• Inventory −
• Functions
• Costs
• Classifications
• Deterministic inventory models
• Quantity discount
• Perpetual and periodic inventory control systems

Unit 4: Project management

• PERT
• CPM