Mechanical Engineering 2024 Paper I 50 marks Explain

Q8

(a) Explain the principle of electric discharge machining (EDM) using suitable diagram. Describe the effect of process parameters of electric discharge machining on process performance characteristics such as material removal rate, tolerance and surface characteristics. (20 marks) (b) XYZ corporation has given the following information on its capacity, sales and cost: (i) Current capacity = 100000 units (ii) At current level of operation, its margin of safety is 50% of its break-even point (iii) Contribution margin P/V ratio = 25% (iv) The unutilized capacity at present is 10000 units (v) Sales price is ₹ 40 per unit Based on the above information, determine the break-even point in sales volume, fixed costs, variable costs per unit and margin of safety in units. (20 marks) (c) A company is interested in locating a new facility in a target market and would like to know the most appropriate place in the target market to locate the facility. There are four supply points A, B, C and D in the locality which will provide key inputs to the new facility. A two-dimensional grid map of the target market in which we would like to locate a new facility along with the distance coordinates of four supply points is shown in the figure below. The annual supply from these four points to the proposed facility is 200, 450, 175 and 350 tons, respectively: (Distance coordinates are in brackets) | Supply Points | Coordinates (Units) | Annual Supply (tons) | |---------------|---------------------|----------------------| | A | (125, 550) | 200 | | B | (350, 400) | 450 | | C | (450, 125) | 175 | | D | (700, 300) | 350 | Identify the most appropriate point in the grid map to locate the new facility using centre of gravity model. (10 marks)

हिंदी में प्रश्न पढ़ें

(a) उपयुक्त आरेख की सहायता से विद्युत निस्सरण मशीन (EDM) के सिद्धांत की व्याख्या कीजिए। विद्युत निस्सरण मशीन की प्रक्रिया प्राचलों (पैरामीटर्स) का इसके प्रक्रिया प्रदर्शन अभिलक्षणों, जैसे कि पदार्थ पृथक्करण दर, उपेक्ष्य त्रुटि (टॉलरेंस) तथा सतही अभिलक्षण, पर पड़ने वाले प्रभावों का वर्णन कीजिए। (20 अंक) (b) XYZ निगम ने अपनी क्षमता, बिक्री तथा लागत की निम्नलिखित जानकारी प्रदान की है : (i) मौजूदा क्षमता = 100000 इकाई (ii) संचालन के वर्तमान स्तर पर, इसकी सुरक्षा का मार्जिन इसके ब्रेक-ईवेन बिंदु का 50% है (iii) योगदान मार्जिन P/V अनुपात = 25% (iv) मौजूदा समय में अप्रयुक्त क्षमता 10000 इकाई है (v) विक्रय मूल्य ₹ 40 प्रति इकाई है उपर्युक्त जानकारी के आधार पर, ब्रेक-ईवेन बिंदु बिक्री की मात्रा में, स्थिर लागत, परिवर्तनीय लागत प्रति इकाई तथा इकाई में सुरक्षा का मार्जिन ज्ञात कीजिए। (20 अंक) (c) एक कंपनी लक्षित बाजार में एक नई सुविधा (फैसिलिटी) स्थापित करने में रुचि रखती है और सुविधा का पता लगाने के लिए लक्षित बाजार में सबसे उपयुक्त स्थान जानना चाहती है। इलाके में चार आपूर्ति बिंदु हैं A, B, C और D, जो नई सुविधा के लिए मुख्य निवेश प्रदान करेंगे। लक्षित बाजार का एक दो-आयामी ग्रिड मानचित्र, जिसमें हम चार आपूर्ति बिंदुओं के दूरी निर्देशांक के साथ एक नई सुविधा का पता लगाना चाहते हैं, नीचे दिए गए चित्र में दर्शाया गया है। प्रस्तावित सुविधा के लिए इन चार बिंदुओं से वार्षिक आपूर्ति क्रमशः: 200, 450, 175 तथा 350 टन है : (दूरी निर्देशांक कोष्ठक में हैं) | आपूर्ति बिंदु | निर्देशांक (इकाई) | वार्षिक आपूर्ति (टन) | |---|---|---| | A | (125, 550) | 200 | | B | (350, 400) | 450 | | C | (450, 125) | 175 | | D | (700, 300) | 350 | गुरुत्वाकर्षण केंद्र मॉडल का प्रयोग करके नई सुविधा का पता लगाने के लिए ग्रिड मानचित्र में सबसे उपयुक्त बिंदु की पहचान कीजिए। (10 अंक)

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Directive word: Explain

This question asks you to explain. The directive word signals the depth of analysis expected, the structure of your answer, and the weight of evidence you must bring.

See our UPSC directive words guide for a full breakdown of how to respond to each command word.

How this answer will be evaluated

Approach

Explain the EDM principle with a clear schematic diagram showing tool-workpiece gap, dielectric circulation, and pulse generator circuit, allocating ~40% time to part (a). For part (b), solve the break-even analysis stepwise using the given constraints, showing all formula derivations. For part (c), apply the centre of gravity formula with weighted coordinates, presenting calculations in tabular form. Conclude with practical implications for each part.

Key points expected

  • Part (a): EDM principle based on controlled spark erosion between tool (cathode) and workpiece (anode) in dielectric fluid; diagram showing servo system, power supply, dielectric pump, and gap
  • Part (a): Effect of parameters—pulse on-time (MRR↑, surface roughness↑), peak current (MRR↑, wear↑), gap voltage, flushing pressure; trade-off between MRR and surface finish
  • Part (b): Current sales = 90,000 units; MOS = 50% of BEP → Sales = 1.5 × BEP → BEP = 60,000 units; Fixed cost = ₹6,00,000; Variable cost = ₹30/unit; MOS = 30,000 units
  • Part (c): Centre of gravity coordinates X̄ = Σ(wi×xi)/Σwi = (200×125 + 450×350 + 175×450 + 350×700)/1175 = 407.45 units; Ȳ = (200×550 + 450×400 + 175×125 + 350×300)/1175 = 343.09 units
  • Part (c): Location approximately (407, 343) on grid; sensitivity to weight distribution noted

Evaluation rubric

DimensionWeightMax marksExcellentAveragePoor
Concept correctness20%10For (a), correctly explains thermal erosion mechanism, dielectric functions (ionization, flushing, cooling), and distinguishes RC vs transistorized pulse generators; for (b), correctly interprets MOS-BEP relationship and P/V ratio application; for (c), correctly applies weighted average principle recognizing centre of gravity minimizes ton-kilometersStates EDM uses sparks for material removal but confuses tool polarity effects; solves BEP with correct final answer but unclear on MOS derivation; applies centre of gravity formula correctly but treats it as simple averageDescribes EDM as electrochemical machining or confuses with ECM; fails to establish Sales = 1.5×BEP relationship or misapplies P/V ratio; calculates unweighted centroid or swaps x-y coordinates
Numerical accuracy20%10Part (b): BEP = 60,000 units, Fixed cost = ₹6,00,000, Variable cost = ₹30/unit, MOS = 30,000 units—all verified; part (c): X̄ = 407.45 (or ~407), Ȳ = 343.09 (or ~343) with proper rounding; all intermediate calculations shownCorrect final answers in (b) but arithmetic slip in intermediate step (e.g., FC calculation); part (c) correct method but arithmetic error in weighted sumFundamental errors: treats current capacity as sales, or computes BEP as 90,000; part (c) uses simple average or incorrect weighting; answers without units
Diagram quality15%7.5Clear EDM schematic with labelled components: DC pulse generator, tool holder with servo feed, workpiece tank, dielectric reservoir, pump, filter; shows spark gap with ionization and deionization phases; part (c) may include rough grid sketch showing supply points and computed locationEDM diagram present but missing key elements (no servo system, or dielectric flow not indicated); labels incomplete; part (c) has no diagramNo diagram for EDM, or diagram shows unrelated process (e.g., ECM, USM); hand-drawn sketch illegible with no labels
Step-by-step derivation25%12.5Part (a): Derives MRR ∝ (1/τ) from crater volume principles; part (b): Explicitly derives Sales = Capacity − Unutilized = 90,000; establishes MOS = Actual Sales − BEP = 0.5×BEP → 90,000 = 1.5×BEP; solves BEP = FC/PV ratio sequentially; part (c): Shows full weighted average formula, substitution table, and simplificationPart (b) jumps to BEP formula without showing MOS relationship derivation; part (c) shows formula and answer but skips intermediate multiplication stepsNo derivations; states final answers directly; or shows irrelevant derivations (e.g., graphical BEP method when data suits formula method)
Practical interpretation20%10Part (a): Discusses EDM applications (hardened die steels, complex cavities, aerospace superalloys) and parameter selection strategy (roughing vs finishing); part (b): Interprets 30,000 unit MOS as 33% cushion, assesses risk of current operations, suggests capacity expansion; part (c): Notes (407,343) is near supply point B, discusses transport cost minimization and sensitivity to volume changesMentions EDM used for hard materials; states MOS is 'safe' without quantification; part (c) states location without discussing why it mattersNo practical context; treats all parts as purely mathematical exercises; no mention of Indian manufacturing relevance (e.g., EDM in Bangalore precision industry, logistics hub location)

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