Mechanical Engineering 2022 Paper I 50 marks Compulsory Solve

Q5

(a) An HSS drill during its life can drill 150 through holes in a 10 mm thick brass plate at a drill speed of 400 rpm. Another drill of same type can make only 75 holes when the drill speed is increased to 600 rpm. How many holes will be produced by another drill of same type if its speed is raised to 800 rpm ? Take the feed in all the cases as same. (10 marks) (b) Write the functions of coating on Shielded Metal Arc Welding (SMAW) electrode. (10 marks) (c) Discuss the Expansionist strategy and Wait-and-See strategy for capacity timing and sizing concerning the capacity planning. (10 marks) (d) A product is to be processed from its raw form to finished form through a number of workstations. The production lead time is given as 3 days. The daily demand requirement is 500 units. Safety stock is required for one day. Container's capacity is 400 units. Determine the number of Kanbans (containers) required. (10 marks) (e) Derive the expression for Reorder point when demand is variable and lead time is constant. Suppose the average demand is 18 units per week with a standard deviation of 5 units. The lead time is constant at 2 weeks. Determine the safety stock and reorder point if management wants a 95% customer service level. (Refer Standard Normal Distribution table given on the last page) (10 marks)

हिंदी में प्रश्न पढ़ें

(a) एक HSS ड्रिल अपने जीवन काल में 10 mm मोटी पीतल की प्लेट में 400 rpm ड्रिल चाल से 150 पारगामी छिद्र कर सकता है । दूसरा ड्रिल जो उसी प्रकार का है और जिसकी ड्रिल चाल बढ़ाकर 600 rpm की गई केवल 75 छिद्र कर सकता है । एक अन्य ड्रिल से, जो उसी प्रकार का है, यदि उसकी चाल बढ़ाकर 800 rpm कर दी जाए तो कितने छिद्रों का उत्पादन होगा ? सभी मामलों में प्रवरण समान लीजिए । (10 अंक) (b) परिरक्षित धातु आर्क वेल्डन (SMAW) इलेक्ट्रोड पर विलेपन के कार्य लिखिए । (10 अंक) (c) क्षमता प्लानिंग के संदर्भ में क्षमता काल समंजन व आमापन के लिए विस्तारवादी युक्ति व प्रतीक्षा व देखना युक्ति की विवेचना कीजिए । (10 अंक) (d) एक उत्पाद को उसके अपरिष्कृत रूप से परिष्कृत रूप तक कई क्रियक स्टेशनों से गुजारकर तैयार किया जाता है । उत्पादन अग्रता काल 3 दिन दिया गया है । प्रतिदिन की मांग आवश्यकता 500 इकाइयों की है । रक्षित स्टॉक की एक दिन की आवश्यकता है । कंटेनर की क्षमता 400 इकाइयों की है । आवश्यक कानबन (Kanbans) कंटेनरों की संख्या ज्ञात कीजिए । (10 अंक) (e) पुनरादेश बिन्दु के लिए व्यंजक व्युत्पन्न कीजिए जबकि मांग परिवर्ती है तथा अग्रता काल स्थिर है । मान लीजिए कि औसत मांग 18 इकाई प्रति सप्ताह है जबकि मानक विचलन 5 इकाई का है । अग्रता काल दो सप्ताह पर स्थिर है । यदि प्रबंधन 95% ग्राहक सेवा स्तर चाहता है तो सुरक्षा स्टॉक व पुनरादेश बिन्दु ज्ञात कीजिए । (अंतिम पृष्ठ पर दी गई मानक प्रसामान्य बंटन सारणी देखिए) (10 अंक)

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How this answer will be evaluated

Approach

Solve each sub-part systematically: for (a) apply Taylor's tool life equation to find tool life-speed relationship and predict holes at 800 rpm; for (b) enumerate SMAW coating functions with metallurgical reasoning; for (c) compare expansionist vs wait-and-see strategies with Indian industry examples; for (d) apply Kanban formula with given parameters; for (e) derive reorder point expression using normal distribution and calculate safety stock. Allocate approximately 15% time to (a), 15% to (b), 20% to (c), 15% to (d), and 35% to (e) due to derivation requirement.

Key points expected

  • Part (a): Apply Taylor's equation VT^n = C; establish relationship between cutting speed and tool life; calculate holes at 800 rpm = 50 holes (or equivalent based on derived n value)
  • Part (b): List 6-8 coating functions: arc stability, gas shielding, slag formation, alloying, deoxidation, metal transfer improvement, cooling rate control, mechanical protection
  • Part (c): Define expansionist strategy (preemptive capacity ahead of demand) and wait-and-see strategy (reactive capacity after demand confirmation); compare risks, costs, and flexibility; cite Indian examples like Maruti Suzuki vs Tata Motors approaches
  • Part (d): Apply Kanban formula N = (DL(1+S))/C; with D=500, L=3, S=1/3 (safety stock 1 day vs lead time 3 days), C=400; calculate N = 5 containers
  • Part (e): Derive ROP = d̄L + zσ_d√L for variable demand, constant lead time; calculate safety stock = zσ_d√L = 1.645×5×√2 ≈ 11.62 ≈ 12 units; ROP = 36+12 = 48 units
  • Part (e) continued: Show standard normal table usage, identify z=1.645 for 95% service level, explain √L factor for demand variability over lead time

Evaluation rubric

DimensionWeightMax marksExcellentAveragePoor
Concept correctness20%10Correctly applies Taylor's tool life equation in (a); comprehensively covers metallurgical and operational functions of SMAW coating in (b); accurately distinguishes strategic trade-offs between expansionist (aggressive, high risk, economies of scale) and wait-and-see (conservative, flexible, higher unit costs) approaches with relevant Indian manufacturing examples in (c); proper Kanban variables identification in (d); correct statistical inventory model with z-score application in (e).Taylor's equation applied with minor errors; 4-5 coating functions listed; strategies described but comparison superficial; Kanban formula correct but variable interpretation shaky; derivation structure present but statistical reasoning weak.Wrong tool life relationship (linear instead of logarithmic); coating functions confused with flux-core functions; strategies muddled or reversed; Kanban formula completely wrong; no understanding of why √L appears in safety stock formula.
Numerical accuracy20%10Part (a): Correct n ≈ 0.5-0.6 from given data, final answer 50 holes (or consistent calculation); Part (d): N = 5 containers exact; Part (e): z = 1.645, safety stock ≈ 12 units, ROP = 48 units; all arithmetic traceable, unit handling consistent.One sub-part has calculation error (e.g., wrong z-value 1.96 used, or safety stock rounded excessively); intermediate steps shown but final answer off by small margin; Kanban calculation uses wrong safety stock interpretation.Multiple numerical errors; no working shown for calculations; orders of magnitude wrong (e.g., 500 containers instead of 5); z-score completely misapplied.
Diagram quality15%7.5Clear schematic of SMAW electrode cross-section showing coating, core wire, and functions labeled in (b); capacity strategy comparison matrix or timeline diagram in (c); inventory level vs time diagram showing ROP, safety stock, and lead time in (e); all diagrams properly labeled with axes and annotations.One relevant diagram present (either SMAW or inventory), adequately labeled; or text descriptions substitute for diagrams adequately.No diagrams despite clear opportunities in (b), (c), (e); or diagrams drawn without labels, making them uninterpretable.
Step-by-step derivation25%12.5Part (a): Shows logarithmic transformation of Taylor's equation, solves for n using two data points, then predicts third; Part (e): Complete derivation from service level → z-score → safety stock formula → ROP expression, with clear probabilistic reasoning for why σ_d√L represents demand uncertainty over lead time.Derivation structure present but skips key steps (e.g., jumps to final formula without showing logarithmic steps in Taylor's equation, or states safety stock formula without explaining √L origin); final formulas correct but reasoning thin.No derivations—only final formulas stated; or incorrect derivations with algebraic errors; confuses derivation with example calculation.
Practical interpretation15%7.5Part (a): Interprets result as speed-productivity trade-off for HSS tools in Indian MSME machining contexts; Part (b): Links coating functions to weld quality defects (porosity, cracking) and electrode selection for structural steel; Part (c): Applies to Make in India capacity decisions, citing sector-specific examples (automotive, textiles); Part (e): Discusses cost of service level choice and implications for working capital.Brief practical mention for 2-3 sub-parts without depth; generic statements about 'industry application' without specificity.No practical interpretation; treats all parts as pure mathematics; or irrelevant applications (e.g., discussing drilling in agriculture for part a).

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