Mechanical Engineering 2023 Paper I 50 marks Compulsory Solve

Q5

(a) In an electrochemical machining process of an iron surface using sodium chloride solution as electrolyte, following observations were made: Specific resistance of the electrolyte = 5 Ω cm (ohm-cm) Supply voltage = 15 V DC Cross-sectional area of iron surface = 20 mm × 20 mm Gap between the tool and workpiece = 0·3 mm Use the following data for iron: Valency = 2, Atomic weight = 55·85, and Density = 7860 kg/m³ Consider the current efficiency as 100% and Faraday's constant = 96540 Coulombs. Calculate the material removal rate and electrode feed rate in the above mentioned electrochemical machining process. (10 marks) (b) A laser beam with power intensity of 2 × 10⁵ W/mm² falls on a stainless steel sheet. Find out the time required for the stainless steel surface to reach melting temperature, assuming that only 10% of the beam power is absorbed. Use: Thermal conductivity = 0·27 W/cm-°C Volume specific heat = 3·36 J/cm³-°C Melting point temperature = 1455°C (10 marks) (c) Discuss the trade-off between cost and quality considering various costs of conformance and costs of non-conformance. (10 marks) (d) The corporation 'X' is designing its new assembly line. The line will produce 50 units per hour. The tasks, their times, and their predecessors are shown in the following table: | Task | Immediate Predecessor | Task Time (sec.) | |------|----------------------|------------------| | A | — | 55 | | B | A | 30 | | C | A | 22 | | D | B | 35 | | E | B, C | 50 | | F | C | 15 | | G | F | 5 | | H | G | 10 | (i) Draw the network diagram. (ii) Compute the cycle time with a desired output of 50 units/hour. (iii) Compute the theoretical number of work-stations and assign the task on the work-stations. Did you end up using more work-stations than the theoretical minimum? (iv) Compute the efficiency and balance delay of the line. (Use longest time method) (10 marks) (e) On the given data, perform regression analysis to forecast the demand for the 6th year, considering that the demand is increasing approximately exponentially. (y = aeᵇˣ; where a and b are constants, x is the number of the year and y is forecasted demand) | No. of the year | 1 | 2 | 3 | 4 | 5 | |-----------------|---|---|---|---|---| | Demand (units) | 40 | 60 | 200 | 700 | 1000 | (10 marks)

हिंदी में प्रश्न पढ़ें

(a) विद्युत-अपघट्य के रूप में सोडियम क्लोराइड विलयन का उपयोग करते हुए एक लोहे की सतह की विद्युत-रासायनिक मशीन प्रक्रिया की गई जिसमें निम्नलिखित प्रेक्षण पाए गए : विद्युत-अपघट्य का विशिष्ट प्रतिरोध = 5 Ω cm (ohm-cm) बोल्टेज आपूर्ति = 15 V दिष्ट धारा लोहे की सतह का अनुप्रस्थ-काट क्षेत्रफल = 20 mm × 20 mm औजार और कार्यखंड के बीच का अंतराल = 0·3 mm लोहे के लिए निम्नलिखित आँकड़ों का प्रयोग कीजिए : संयोजकता = 2, परमाणु भार = 55·85, तथा घनत्व = 7860 kg/m³ धारा की दक्षता को 100% तथा फैराडे स्थिरांक = 96540 कूलॉम मानिए । उपयुक्त विद्युत-रासायनिक मशीन प्रक्रिया में पदार्थ-पृथक्करण दर तथा इलेक्ट्रोड प्रभरण दर की गणना कीजिए । (10 अंक) (b) एक 2 × 10⁵ W/mm² शक्ति-क्षमता की लेजर किरण-पुंज एक जंगरोधी-इस्पात (स्टेनलेस स्टील) की चादर पर गिरती है । यदि केवल 10% किरण-पुंज की शक्ति अवशोषित होती है, तो यह ज्ञात कीजिए कि जंगरोधी-इस्पात की सतह कितने समय बाद गलनांक पर पहुँच जाएगी । निम्नलिखित का प्रयोग कीजिए : ऊष्मा चालकता = 0·27 W/cm-°C आयतनी विशिष्ट ऊष्मा = 3·36 J/cm³-°C गलन बिंदु तापमान = 1455°C (10 अंक) (c) अनुक्रुपता की विभिन्न लागतों और गैर-अनुक्रुपता की लागतों पर विचार करते हुए लागत और गुणवत्ता के बीच अदला-बदली (दुविधा) की विवेचना कीजिए । (10 अंक) (d) एक निगम 'X' अपनी नयी असेंबली लाइन की अभिकल्पना कर रहा है । यह लाइन 50 इकाई एक घंटे में उत्पादित करेगी । इसके कार्य, समय तथा पूर्ववर्तियों को निम्नांकित तालिका में दिखाया गया है : | कार्य | तात्कालिक पूर्ववर्ती | कार्य का समय (सेकंड) | |-------|---------------------|---------------------| | A | — | 55 | | B | A | 30 | | C | A | 22 | | D | B | 35 | | E | B, C | 50 | | F | C | 15 | | G | F | 5 | | H | G | 10 | (i) नेटवर्क आरेख खींचिए । (ii) अपेक्षित 50 इकाई/घंटा का चक्र समय परिकलित कीजिए । (iii) कार्य-स्थानों की सैद्धांतिक संख्या ज्ञात कीजिए तथा कार्य-स्थानों पर कार्य को निर्दिष्ट कीजिए । क्या आप सैद्धांतिक न्यूनतम से अधिक कार्य-स्थानों का उपयोग करके इसे प्राप्त किए हैं ? (iv) लाइन की दक्षता एवं बैलेंस डिले ज्ञात कीजिए । (सबसे लंबे समय विधि का उपयोग कीजिए) (10 अंक) (e) यह अनुमानित करते हुए कि माँग लगभग चरघातांकी विधि से बढ़ रही है, दिए गए आँकड़ों पर माँग का छठे साल में पूर्वानुमान लगाने के लिए समाश्रयण विश्लेषण कीजिए । (y = aeᵇˣ ; जहाँ a और b स्थिरांक हैं, x वर्षों की संख्या तथा y पूर्वानुमानित माँग है) | वर्षों की संख्या | 1 | 2 | 3 | 4 | 5 | |---------------|---|---|---|---|---| | माँग (इकाइयाँ) | 40 | 60 | 200 | 700 | 1000 | (10 अंक)

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How this answer will be evaluated

Approach

Solve all five sub-parts systematically, allocating approximately 20% time each. For (a) and (b), apply manufacturing process formulas with unit conversions; for (c), structure the discussion with cost categories and Indian industry examples; for (d), draw the precedence diagram before calculations; for (e), transform to linear form using logarithms. Present derivations stepwise with final answers boxed.

Key points expected

  • (a) ECM: Current I = V/R = 15/(5×0.03) = 100 A; MRR = (I×A×η)/(ρ×Z×F) = 100×55.85/(7860×2×96540×10^-6) mm³/s; Feed rate = MRR/Area
  • (b) Laser: Use q = k(Tm-T0)/√(παt) with α = k/(ρc); solve for t = πk²(Tm-T0)²/(4αq²) with q = 0.1×2×10⁵ W/mm² converted properly
  • (c) Quality costs: Prevention, appraisal (conformance) vs internal/external failure (non-conformance); cite TQM in Indian auto sector (Maruti, Tata)
  • (d) Assembly line: Network with A→(B,C), B→(D,E), C→(E,F), F→G→H; Cycle time = 3600/50 = 72 sec; Theoretical stations = 202/72 ≈ 3; Longest task rule assignment
  • (e) Exponential regression: ln(y) = ln(a) + bx; compute Σx, Σln(y), Σxln(y), Σx²; solve normal equations for a, b; forecast y₆ = ae^(6b)

Evaluation rubric

DimensionWeightMax marksExcellentAveragePoor
Concept correctness20%10Correctly applies Faraday's laws for ECM, heat conduction theory for laser melting, distinguishes all four quality cost categories, understands precedence constraints in line balancing, and transforms exponential to linear regression properly.Uses correct basic formulas but confuses thermal diffusivity with conductivity or misclassifies quality costs; understands line balancing but applies heuristic incorrectly.Confuses ECM with EDM principles, treats laser problem as steady-state conduction, describes quality costs vaguely without conformance/non-conformance distinction, fails to recognize precedence relationships.
Numerical accuracy20%10All five sub-parts computed correctly: (a) MRR ≈ 3.68 mm³/s, feed ≈ 0.0092 mm/s; (b) t ≈ 0.12 ms; (d) efficiency ≈ 93%; (e) forecast ≈ 2800 units with proper regression coefficients.Correct final answers for 3-4 sub-parts with minor unit conversion errors (e.g., Ω-cm to Ω-mm, W/mm² to W/cm²); one significant calculation error.Multiple incorrect answers due to unit confusion (Ω-cm vs Ω-m, mm vs cm), arithmetic errors in regression summations, or wrong cycle time calculation.
Diagram quality20%10Clear precedence diagram for (d) with nodes, arrows, and task times labelled; ECM and laser schematics drawn if helpful; regression plot showing data points and fitted curve.Precedence diagram drawn but missing some arrows or times; no diagrams for other parts where they could aid explanation.No network diagram for (d) or incorrect diagram showing wrong precedence (e.g., C before B, missing H); no visual aids for any part.
Step-by-step derivation20%10Shows all intermediate steps: ECM current calculation with gap resistance, thermal penetration depth derivation, quality cost formula application, longest-task heuristic application with table, regression normal equations setup and solution.Shows key steps but skips some algebraic manipulation or jumps from formula to answer; regression steps shown but with minor computational shortcuts.Final answers stated without derivation; no working for regression coefficients; line balancing done by inspection without systematic heuristic application.
Practical interpretation20%10Relates ECM parameters to surface finish and accuracy; discusses laser heating limitations for thick sections; cites Indian manufacturing examples (ISRO precision ECM, SAIL quality programs); interprets line efficiency for capacity planning; discusses regression forecast reliability.Brief practical comments for 2-3 sub-parts; mentions applications without specific Indian context.No practical interpretation; treats all parts as pure mathematical exercises; no discussion of result validity or real-world constraints.

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