(SEM VII) THEORY EXAMINATION 2024-25 MATHEMATICAL MODELING OF MANUFACTURING PROCESSES

SECTION A

(2 × 10 = 20 marks | Very Short Answers)

a) Causes of residual stresses

Residual stresses are caused due to non-uniform plastic deformation, thermal gradients during cooling, phase transformation, welding, casting, forging, and machining operations.

b) Modes of heat transfer in welding

Heat transfer in welding occurs by:                        Conduction (major mode within metal)

Convection (molten pool movement)                   Radiation (heat loss from surface)

c) Centre-line Feeding Resistance (CFR)

CFR is the resistance offered to molten metal flow along the center line of a casting during solidification, which affects feeding efficiency and shrinkage defects.

d) Advantages of additive manufacturing

Complex geometry possible                                   Reduced material waste

Rapid prototyping                                                   Customization

Shorter production time

e) Role of thermoplastic material in P/M injection moulding

Thermoplastics act as binders, providing flowability during injection and holding powder particles together before debinding and sintering.

f) Principles of plastic processing

Plastic processing is based on:                                Heating to soften

Shaping under pressure                                        Cooling to retain shape

g) Importance of chipless machining in future

Chipless machining reduces material waste, energy consumption, and finishing operations, making it environmentally friendly and cost-effective.

h) Principle of powder metallurgy

Powder metallurgy involves powder production, compaction, and sintering to produce components without melting the material completely.

i) Bio-materials

Bio-materials are materials used in medical applications to replace or support body tissues, such as titanium implants and polymeric prosthetics.

j) Factors affecting suitability of casting

Melting temperature                                                Fluidity

Shrinkage tendency                                                  Chemical reactivity

Cost and availability

SECTION B

(Attempt any 3 | 10 marks each)

a) Relation of mathematical modeling with problem solving

Mathematical modeling converts real manufacturing problems into mathematical equations. It helps in prediction, optimization, cost reduction, and understanding process behavior, thus improving decision-making.

b) Orthogonal vs Oblique cutting (Comparison)

c) Solid-state welding and its types

Solid-state welding joins materials without melting.
Types include:                                             Friction welding

Diffusion bonding                                      Ultrasonic welding

Explosive welding                                       Advantages include minimal distortion and high joint strength.

d) Powder metallurgy process

Steps:                                                          Powder production

Blending                                                     Compaction

Sintering

Applications: gears, bearings, filters
Advantages: high precision, minimal waste, mass production

e) Finishing and packaging in micro/nano manufacturing

Finishing improves surface quality and functionality, while packaging protects devices from moisture, vibration, and contamination, ensuring long-term reliability.

SECTION C

Q3 (Attempt any one)

a) Effect of friction in forging and extrusion

Friction increases energy consumption, tool wear, and heat generation. Controlled friction improves material flow, while excessive friction reduces surface quality and causes defects.

b) Driving forces behind phase transformation

Phase transformations occur due to:                             Change in temperature

Reduction in free energy                                                Diffusion of atoms

Examples include austenite to martensite transformation during heat treatment.

Q4 (Attempt any one)

a) Tool life calculation

Given:
V = 100 m/min, n = 0.25, C = 300

VTn=CVT^n = CVTn=C 100×T0.25=300100 \times T^{0.25} = 300100×T0.25=300 T0.25=3⇒T=81 minutesT^{0.25} = 3 \Rightarrow T = 81 \text{ minutes}T0.25=3⇒T=81 minutes 

b) Importance of parameter identification

Correct identification of parameters improves model accuracy, process optimization, prediction of tool wear, and product quality.

Q5 (Attempt any one)

a) Mechanics of deep drawing

Deep drawing involves pulling sheet metal into a die using a punch.
Key parameters:                                                            Blank holder force

Material properties                                                       Die radius

Friction                                                                          Proper control prevents wrinkling and tearing.

b) Heat source modeling in welding

Heat source models (Gaussian, double ellipsoid) help predict temperature distribution, weld penetration, and cooling rates using mathematical equations.

Q6 (Attempt any one)

a) Shrinkage in casting

Shrinkage occurs during solidification and cooling.
Minimization methods:                                                Risers

Chills                                                                            Directional solidification

b) Powder metallurgy vs traditional manufacturing

Powder metallurgy uses solid-state processing, while traditional methods involve melting. PM offers higher precision and less waste.

Q7 (Attempt any one)

a) Role of microstructure and residual stress evaluation

They help predict strength, fatigue life, distortion, and failure, ensuring better performance of welded and cast components.

b) Micro and nano joining techniques

Laser welding: precise, minimal heat affected zone

Diffusion bonding: high-strength joints

Applications include electronics, MEMS, and biomedical implants.