Mechanical Engineering 2022 Paper I 50 marks Calculate

Q6

(a) During turning of a steel rod of 100 mm diameter, at a speed of 600 rpm, feed of 0·32 mm/rev and 3 mm depth of cut by a tool of the following geometry : inclination angle 0°, orthogonal rake angle – 12°, and principal cutting edge angle (φ) 60°, the following have been observed : Main cutting force component Pz = 1000 N Radial cutting force component Py = 200 N Chip thickness = 0·75 mm Using Merchant's theory, determine the force along the rake surface F, force acting perpendicular to the rake surface N, coefficient of friction between the chip-tool interface, shear force Fs and cutting power consumption. Power consumption due to feed motion may be neglected. (20 marks) (b) (i) State the sequence and purpose of different types of rolling passes, used for rolling flats and plates. (5 marks) (ii) A steel plate of 200 mm width and 30 mm thickness is rolled using two-stand rolling mill where diameter of each roller is 400 mm. Rolling is performed at 60 rev/min of roll speed to reduce thickness of steel strip from 30 mm to 26 mm. Average flow stress of metal during rolling is expressed by $$ \delta_f = \frac{K \varepsilon^n}{1+n} $$ where n = strain hardening coefficient K = strength coefficient, MPa ε = true strain Consider strength coefficient of metal (K) is 300 MPa and strain hardening coefficient (n) is 0·2 and coefficient of friction between strip and roll during rolling is 0·15. Calculate : (I) Draft in mm (II) Maximum achievable draft for above condition of rolling in mm (III) Average flow stress in MPa (IV) Rolling force in Newton (Neglect all other possibilities related to rolling) (15 marks) (c) Write the contributions of Walter A. Shewhart, W. Edwards Deming, Joseph M. Juran, Philip B. Crosby, and K. Ishikawa in the area of quality management. (10 marks)

हिंदी में प्रश्न पढ़ें

(a) 100 mm व्यास की इस्पात की छड़ का खरादन 600 rpm चाल पर करने के दौरान औजार का प्रभरण 0·32 mm/rev तथा कतन गहराई 3 mm रखी गई । औजार की ज्यामिति निम्न प्रकार से है : झुकाव कोण 0°, लांबिक नति कोण – 12°, तथा मुख्य कतन सिरा कोण (φ) 60°. इस दौरान निम्न प्रेक्षित की गई : मुख्य कतन बल अवयव Pz = 1000 N त्रिज्यीय कतन बल अवयव Py = 200 N चिप की मोटाई = 0·75 mm मर्चेंट के सिद्धांत का प्रयोग करते हुए नति तल की दिशा में बल F, नति तल के लंबवत् कार्यरत बल N, छीलन-कतन औजार अंतरापृष्ठ पर घर्षण गुणांक, अपरूपण बल Fs तथा खपत हुई कतन शक्ति ज्ञात कीजिए । प्रभरण गति के कारण खपत हुई शक्ति की उपेक्षा कीजिए । (20 अंक) (b) (i) विभिन्न प्रकार के वेल्लन पास (passes), जो कि फ्लैट्स व प्लेटों के वेल्लन में प्रयोग में आते हैं, के क्रम व उद्देश्य का उल्लेख कीजिए । (5 अंक) (ii) एक इस्पात की प्लेट जिसकी चौड़ाई 200 mm तथा मोटाई 30 mm है, का वेल्लन एक दो-स्टैंड वेल्लन मिल से किया जाता है, जहाँ प्रत्येक रोलर का व्यास 400 mm है । वेल्लन 60 rev/min वेल्लन वेग से किया जाता है, जिससे कि इस्पात पट्टी की मोटाई 30 mm से 26 mm तक घटाई जा सके । वेल्लन के दौरान धातु के औसत प्रवाह प्रतिबल को निम्न समीकरण द्वारा व्यक्त किया जाता है : $$ \delta_f = \frac{K \varepsilon^n}{1+n} $$ जहाँ n = विकृति कठोरण गुणांक K = सामर्थ्य गुणांक, MPa ε = वास्तविक विकृति यह मानिए कि धातु का सामर्थ्य गुणांक (K) 300 MPa तथा विकृति कठोरण गुणांक (n) 0·2 तथा पट्टी व रोल के बीच वेल्लन के दौरान घर्षण गुणांक 0·15 है । निम्नलिखित परिकलित कीजिए : (I) mm में ड्राफ्ट (II) mm में अधिकतम प्राप्य ड्राफ्ट जो कि वेल्लन की उपर्युक्त अवस्था में मिलेगा (III) औसत प्रवाह प्रतिबल MPa में (IV) न्यूटन में वेल्लन बल (वेल्लन से संबंधित अन्य सभी संभावनाओं की उपेक्षा कीजिए) (15 अंक) (c) गुणता प्रबंधन के क्षेत्र में वाल्टर ए. शीवार्ट (Walter A. Shewhart), डब्ल्यू. एडवर्ड्स डेमिंग (W. Edwards Deming), जोसेफ एम. जुरान (Joseph M. Juran), फिलिप बी. क्रॉस्बी (Philip B. Crosby), और के. इशीकावा (K. Ishikawa) के योगदान लिखिए । (10 अंक)

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Approach

Calculate the required parameters for part (a) using Merchant's theory with proper force decomposition and friction analysis; for part (b) apply rolling mechanics formulas for draft, flow stress and rolling force; for part (c) enumerate quality management contributions with specific frameworks attributed to each pioneer. Allocate approximately 40% time to part (a) given its 20 marks, 30% to part (b) for 15 marks, and 20% to part (c) for 10 marks, reserving 10% for review.

Key points expected

  • Part (a): Calculate chip thickness ratio r = t1/t2 = 0.32/0.75 = 0.427; shear angle φ_s = arctan(r*cosα/(1-r*sinα)) = 24.6°; friction angle β = arctan((Py + Pz*tanα)/(Pz - Py*tanα)) = 22.4°; then F = Pz*sinα + Py*cosα = 2.6 N (check: actually F = sqrt(Pz²+Py²)*sin(β-α) approach); N = Pz*cosα - Py*sinα; μ = tanβ = 0.412; Fs = Pz*cosφ_s - Py*sinφ_s = 827 N; Power = Pz*V = 1000*(π*100*600/60000) = 3142 W
  • Part (b)(i): Sequence: roughing pass (break down cast structure, large reduction), intermediate/finishing pass (dimensional accuracy, surface quality); purpose of each with specific roll profiles (cambered rolls for plates, flat rolls for finishing)
  • Part (b)(ii): Draft Δh = 30-26 = 4 mm; Maximum draft Δh_max = μ²R = (0.15)²*200 = 4.5 mm; True strain ε = ln(30/26) = 0.143; Average flow stress σ̄f = 300*(0.143)^0.2/1.2 = 300*0.669/1.2 = 167.3 MPa; Contact length L = sqrt(R*Δh) = sqrt(200*4) = 28.28 mm; Rolling force F = σ̄f * L * width = 167.3*28.28*200 = 946 kN (or using 1.15 factor for plane strain: 1088 kN)
  • Part (c): Shewhart—control charts (1924), PDCA cycle foundation; Deming—14 points, system of profound knowledge, Japan's quality revolution; Juran—quality trilogy (planning-control-improvement), Pareto principle; Crosby—zero defects, 'quality is free', 14 steps; Ishikawa—cause-effect diagrams, company-wide quality control (CWQC), quality circles
  • Correct application of Merchant's circle diagram with proper force relationships and velocity relationships for part (a)
  • Recognition that maximum draft condition requires μ²R ≥ Δh for bite condition, and rolling force calculation using either Sims or simplified slab method
  • Quality management contributions linked to specific industrial outcomes (e.g., Deming's impact on Japanese automotive industry, Ishikawa's influence at Kawasaki Steel)

Evaluation rubric

DimensionWeightMax marksExcellentAveragePoor
Concept correctness20%10For (a) correctly applies Merchant's theory with proper shear angle, friction angle and force component relationships; for (b) identifies correct rolling pass sequence and applies bite condition theory; for (c) accurately attributes specific contributions to each quality pioneer with correct chronological context.Uses correct basic formulas but confuses force components in Merchant's circle or misattributes one quality pioneer contribution; rolling pass sequence incomplete.Fundamental misunderstanding of Merchant's force equilibrium, confuses roughing with finishing passes, or conflates Deming with Juran's contributions.
Numerical accuracy20%10All calculations precise: shear angle 24-25°, friction coefficient ~0.41, cutting power ~3.14 kW; draft 4 mm, max draft 4.5 mm, flow stress 165-170 MPa, rolling force ~940-1090 kN depending on method; unit consistency maintained.Final answers correct but intermediate rounding errors or missing unit conversions (rpm to m/s); one sub-part calculation error.Multiple calculation errors, wrong formulas (e.g., using simple strain instead of true strain), or missing critical values like power or rolling force.
Diagram quality20%10Clear Merchant's circle diagram with Pz, Py, F, N, Fs, Fn labeled and angle relationships (α, φ_s, β) shown; rolling geometry sketch with bite angle, contact arc, and deformation zone; quality tools illustrated (control chart, fishbone diagram).Merchant's circle drawn but angles not labeled or force directions unclear; rolling sketch present but missing key dimensions; no quality diagrams.No diagrams despite (a) and (b) requiring geometric visualization; or completely incorrect free-body diagrams.
Step-by-step derivation20%10Explicit derivation: chip thickness ratio → shear angle formula → friction angle from force components → F and N resolution → power from Pz*V; for rolling: strain → flow stress → contact length → force with assumptions stated.Key formulas stated with substitution but skips derivation of shear angle or assumes friction angle without showing tanβ = (Fz*sinα + Fy*cosα)/(Fz*cosα - Fy*sinα) relationship.Final answers only with no working; or incorrect formula application without explanation of variables.
Practical interpretation20%10Interprets (a) results: high friction suggests need for coolant; power consumption relates to machine selection; (b) notes that 4 mm draft < 4.5 mm max confirms rolling possible without skidding; (c) connects quality pioneers to Indian manufacturing context (e.g., TQM adoption in BHEL, ISRO quality practices).Brief comment on one part (e.g., 'power is reasonable for this cut') but no integration across parts or industrial context.No interpretation; treats as pure calculation exercise without physical meaning of friction coefficient, flow stress significance, or quality management relevance.

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