(SEM VII) THEORY EXAMINATION 2022-23 MATHEMATICAL MODELING OF MANUFACTURING PROCESSES

SECTION A – Short Answers (2 Marks Each)

(a) Use of physics-based models in manufacturing

Physics-based models use fundamental laws of mechanics, heat transfer, and material science to predict behavior of materials and processes such as machining forces, heat generation, deformation, and tool wear.

(b) “Tool life is a random variable”

Tool life varies due to fluctuations in cutting conditions, material properties, temperature, vibration, and 

manufacturing defects. Hence, it cannot be predicted exactly and is treated as a random variable.

(c) Strain hardening and its use

Strain hardening is the increase in strength and hardness of a metal due to plastic deformation. It is used in cold working processes to improve strength without heat treatment.

(d) Centre-line Feeding Resistance (CFR)

CFR is the resistance offered to molten metal flow along the centre-line of a casting during mould filling, affecting filling time and defect formation.

(e) Thermit weld similarity with casting

In thermit welding, molten metal is poured into a mould cavity and allowed to solidify, similar to casting where molten metal fills a mould and solidifies into shape.

(f) Role of thermoplastic in P/M injection moulding

Thermoplastic acts as a binder to hold metal powder particles together, enabling easy injection into moulds and maintaining shape before sintering.

(g) Classification of additive manufacturing processes

Additive manufacturing processes are classified as material extrusion, material jetting, powder bed fusion, binder jetting, directed energy deposition, vat photopolymerization, and sheet lamination.

(h) Importance of chipless machining in future

Chipless machining reduces material waste, energy consumption, and environmental impact, making it important for sustainable and precision manufacturing.

(i) Microalloyed steels and their use

Microalloyed steels contain small amounts of alloying elements like Nb, V, or Ti. They are used in automotive parts, pipelines, and structural components due to high strength and toughness.

(j) Factors affecting suitability of casting operation

Material fluidity, melting temperature, shrinkage, solidification characteristics, chemical reactivity, and desired surface finish determine casting suitability.

SECTION B – Long Answers (10 Marks Each)

(Attempt any three in exam; answers provided for all)

(a) Methods to control properties of engineering materials

Material properties can be controlled through alloying, heat treatment, mechanical working, surface treatment, and microstructural control. Heat treatment alters hardness and toughness, while alloying improves strength, corrosion resistance, and wear properties.

(b) Orthogonal cutting vs oblique cutting

(c) Forming operations in manufacturing

Forming operations include rolling, forging, extrusion, drawing, bending, and deep drawing. These processes shape materials by plastic deformation without material removal, improving mechanical properties.

(d) Filling time of mould (Numerical – Method)

Filling time depends on molten metal head, gate area, gravitational acceleration, and mould volume.
For both gating designs, filling time is calculated using:

t=VA2ght = \frac{V}{A \sqrt{2gh}}t=A2gh​V​

Different gate positions affect head and hence filling time.

(e) TTT diagram and phase transformation in steel

TTT diagram shows time-temperature relationship for phase transformations. Slow cooling produces pearlite, moderate cooling produces bainite, and rapid quenching produces martensite in plain carbon steel.

SECTION C – Long Answers (10 Marks Each)

3(a) Effect of heat treatment on microstructure

Heat treatment changes grain size, phase composition, and dislocation density. Processes like annealing soften metals, quenching increases hardness, and tempering improves toughness.

3(b) Ceramic materials and processing

Ceramics are inorganic, non-metallic materials with high hardness and thermal resistance. Processing involves powder preparation, forming, drying, and sintering to achieve desired properties.

4(a) Orthogonal machining numerical (Solution outline)

Given cutting forces, chip thickness ratio is calculated.
Coefficient of friction:

μ=FTFC\mu = \frac{F_T}{F_C}μ=FC​FT​​

Shear stress is obtained using shear force and shear plane area based on Merchant’s analysis.

4(b) Abrasive Jet Machining (AJM)

AJM removes material by high-velocity abrasive particles.
Advantages include machining of brittle materials and no thermal damage.
Limitations include low material removal rate and nozzle wear.

5(a) Fusion welding and governing factors

Fusion welding joins metals by melting base material. Factors include heat input, welding speed, electrode type, shielding atmosphere, and material properties.

5(b) Modes of metal transfer in arc welding

Modes include short-circuiting, globular, spray, and pulsed spray transfer, each affecting weld quality and penetration.

6(a) Powder metallurgy process

Powder metallurgy involves powder production, blending, compaction, and sintering. It allows near-net shape manufacturing with minimal waste.

6(b) Advantages and applications of additive manufacturing

Advantages include design freedom, reduced waste, rapid prototyping, and complex geometry fabrication. Applications include aerospace, medical implants, tooling, and automotive parts.

7(a) Role of mathematical modeling in problem solving

Mathematical modeling represents real manufacturing problems using equations, enabling prediction, 

optimization, and control of processes.

7(b) Plastic deformation and residual stress removal

Plastic deformation occurs when stress exceeds yield strength. Residual stresses are removed using annealing, stress relieving, or controlled cooling.