Mechanical Engineering 2021 Paper I 50 marks Solve

Q3

(a) What is the purpose of tempering of hardened steel? Explain the principle of tempering using suitable schematics including heating temperature requirement and microstructural changes. (15 marks) (b) A solid circular shaft is subjected to a bending moment of 2500 N-m and a torque of 8000 N-m. The ultimate tensile stress and ultimate shear stress of the shaft material are 700 MPa and 500 MPa respectively. Assuming a factor of safety as 6, determine the diameter of the shaft. (15 marks) (c) A single cylinder, four-stroke engine develops 20 kW at 250 rpm. The work done by the gases during the expansion stroke is 3 times the work done on the gases during the compression stroke. The work done during the suction and exhaust strokes may be neglected. During expansion and compression strokes the turning moment curve is assumed to be triangular. If the flywheel has a mass of 1500 kg and has a radius of gyration of 0.6 m, find the coefficient of fluctuation of speed. (20 marks)

हिंदी में प्रश्न पढ़ें

(a) कठोरीकृत इस्पात के पायन (टेम्परिंग) का क्या प्रयोजन है? तापक तापमान की आवश्यकता तथा सूक्ष्म संरचनागत परिवर्तनों को समाहित करते हुए उपयुक्त योजनाबद्ध आरेख के माध्यम से पायन के सिद्धांत को समझाइए। (15 अंक) (b) एक ठोस वृत्तीय शैफ्ट पर 2500 N-m का बंकन आघूर्ण और 8000 N-m का बल-आघूर्ण लगाया जाता है। शैफ्ट के पदार्थ का चरम तनन प्रतिबल तथा चरम अपरूपण प्रतिबल क्रमशः 700 MPa और 500 MPa है। सुरक्षा गुणक को 6 मानते हुए शैफ्ट के व्यास की गणना कीजिए। (15 अंक) (c) एक एकल सिलिंडर, चार-स्ट्रोक इंजन 250 rpm पर 20 kW विकसित करता है। गैसों द्वारा प्रसरण स्ट्रोक में किया गया कार्य गैसों पर संपीडन स्ट्रोक में किए गए कार्य का 3 गुना है। चूषण तथा रेचक स्ट्रोकों में किए गए कार्यों को नगण्य मान सकते हैं। प्रसरण और संपीडन स्ट्रोकों के दौरान टर्निंग आघूर्ण वक्र को त्रिभुजीय मान लिया गया है। यदि गतिपालक चक्र का द्रव्यमान 1500 kg तथा परिभ्रमण त्रिज्या 0.6 m है, तो गति के उच्चावचन का गुणांक ज्ञात कीजिए। (20 अंक)

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Approach

Solve all three sub-parts systematically, allocating time proportional to marks: spend ~30% on (a) for conceptual explanation with diagrams, ~30% on (b) for shaft diameter calculation using combined loading theories, and ~40% on (c) for flywheel fluctuation analysis with energy and speed variation calculations. Begin each part with stated assumptions and end with clearly boxed final answers.

Key points expected

  • Part (a): Purpose of tempering (reduce brittleness, relieve internal stresses, improve toughness); tempering temperature ranges (150-250°C low, 350-500°C medium, 500-650°C high) with corresponding microstructures (martensite → tempered martensite/ferrite + cementite)
  • Part (a): Schematic showing hardness vs tempering temperature curve, and microstructural transformation diagram with time-temperature parameters
  • Part (b): Application of maximum shear stress theory or distortion energy theory for combined bending and torsion; equivalent torque Te = √(M² + T²) or equivalent moment Me = ½[M + √(M² + T²)]
  • Part (b): Correct shaft diameter calculation: d = [16Te/(πτ_allowable)]^(1/3) or using allowable bending stress; τ_allowable = 500/6 = 83.33 MPa, σ_allowable = 700/6 = 116.67 MPa
  • Part (c): Work done per cycle = 20,000 × (60/125) = 9600 J; expansion work = 3× compression work, so W_exp = 7200 J, W_comp = 2400 J
  • Part (c): Maximum fluctuation of energy ΔE = ½ × base × height of triangle = ½ × (π/2) × (T_max - T_mean) × (π/2) for triangular TM diagram; or ΔE = ½ × W_exp = 3600 J
  • Part (c): Coefficient of fluctuation of speed Cs = ΔE/(Iω²) = ΔE/(mk²ω²) where ω = 2π×250/60 = 26.18 rad/s; I = 1500 × (0.6)² = 540 kg.m²

Evaluation rubric

DimensionWeightMax marksExcellentAveragePoor
Concept correctness20%10For (a), correctly identifies tempering as sub-critical heat treatment to transform martensite to tempered martensite, with accurate temperature ranges and microstructural outcomes; for (b), selects appropriate failure theory (Tresca or von Mises) with clear justification; for (c), correctly models triangular turning moment diagram and identifies mean torque position.States tempering purpose correctly but confuses temperature ranges or microstructures; uses correct failure theory for (b) but without justification; for (c), identifies work ratio but makes errors in energy fluctuation geometry.Confuses tempering with annealing or normalizing; applies simple bending theory ignoring torsion for (b); treats turning moment as rectangular rather than triangular for (c).
Numerical accuracy20%10All calculations precise: (b) diameter ≈ 97-98 mm (using Tresca) or ≈ 94-95 mm (von Mises) with clear theory stated; (c) Cs ≈ 0.02-0.025 or 2-2.5%; intermediate values (ω = 26.18 rad/s, I = 540 kg.m², ΔE = 3600 J) all correct; unit consistency maintained throughout.Final answers approximately correct but with minor arithmetic errors (e.g., factor of 2 error in ΔE, or ω calculation slip); units mostly consistent but occasional mixing of N-mm and N-m.Major computational errors: wrong formula for equivalent torque, incorrect angular velocity conversion, or energy calculation treating four-stroke as two-stroke; final answers orders of magnitude wrong.
Diagram quality20%10For (a), provides two clear schematics: (i) hardness vs tempering temperature curve with three zones labelled, and (ii) microstructural transformation showing martensite laths evolving to tempered structure with cementite particles; for (c), draws accurate triangular turning moment diagram for four-stroke cycle with expansion, compression, suction, exhaust strokes labelled and mean torque line shown.One good diagram for (a) but missing the second; or diagrams present but poorly labelled; TM diagram for (c) drawn but missing key features like mean line or stroke identification.No diagrams for (a) despite explicit requirement; or diagrams drawn without any labels; TM diagram completely wrong shape or missing.
Step-by-step derivation20%10For (a), derives tempering kinetics with Arrhenius-type temperature dependence; for (b), shows complete derivation from stress elements: σ_b = 32M/(πd³), τ = 16T/(πd³), then combines using τ_max = √((σ/2)² + τ²) ≤ τ_allowable; for (c), derives ΔE from triangular area geometry explicitly, then substitutes into Cs formula with all intermediate steps.Uses standard formulae with some derivation shown but skips key steps (e.g., jumps to Te formula without showing stress combination); for (c), states ΔE result without deriving from triangle geometry.No derivations shown; formulae quoted without context; final answers appear without any working; or completely wrong formulae used throughout.
Practical interpretation20%10For (a), relates tempering to Indian industrial practice (e.g., IS 1570 standard for tool steels, or TISCO/Ahmedabad heat treatment practices); for (b), comments on shaft sizing for automotive or turbine applications and checks for rigidity if mentioned; for (c), interprets Cs value: if <0.05 acceptable for stationary engines, suggests flywheel mass adjustment if too high, relates to engine mounting and vibration isolation.Brief practical mention for one part (e.g., 'tempering is used in springs') but no depth; or generic statements without specific application context.No practical interpretation whatsoever; treats all parts as pure examination exercises with no connection to engineering reality or Indian manufacturing context.

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