Paper I — Q8
The frontal working area of the electrode is 2000 mm² in a certain ECM operation in which the applied current = 1800 amps and the…
The frontal working area of the electrode is 2000 mm² in a certain ECM operation in which the applied current = 1800 amps and the voltage = 12 volts. The material being cut is nickel (Valency = 2), whose specific removal rate is 3·42 × 10⁻² mm³/A-s.
If the process is 90% efficient, determine the rate of material removal in mm³/minute.
If the resistivity of the electrolyte is 140 ohm-mm, determine the working gap.
The layout of material storage section is given below. The material flow occurs between packing area (No. 6) and other 9 sections/areas. Loads are moved from packing area 6 to shipping/receiving area 1, while all other loads move from different sections/areas (2, 3, 4, 5, 7, 8, 9) to packing area No. 6. Average annual load movement/flow to/from sections is as under:
| Flow From – To | Average Annual Load (No.) | Distance Covered (m) |
|---|---|---|
| 2 to 6 | 200 | 50 |
| 3 to 6 | 300 | 50 |
| 4 to 6 | 400 | 50 |
| 5 to 6 | 500 | 50 |
| 7 to 6 | 600 | 50 |
| 8 to 6 | 700 | 50 |
| 9 to 6 | 800 | 50 |
| 10 to 6 | 900 | 50 |
| 6 to 1 | 4400 | 100 |
Assume cost of moving a load by unit distance (m) is ₹ 1/m. Determine the annual total cost of material handling.
Explain 'Coordinate system' and 'Motion control' with reference to NC machines.
हिंदी में प्रश्न पढ़ें
किसी ECM प्रक्रम में जिसमें प्रयुक्त विद्युत धारा = 1800 amps तथा वोल्टता = 12 volts है, में इलेक्ट्रोड का सम्मुख कार्य-क्षेत्र 2000 mm² है। जिस पदार्थ को काटा जाता है, वह निकेल (संयोजकता = 2) है, जिसकि विशिष्ट पृथक्करण दर 3·42 × 10⁻² mm³/A-s है।
यदि प्रक्रम 90% दक्ष है, तो mm³/minute में धातु पृथक्करण दर ज्ञात कीजिए।
यदि इलेक्ट्रोलाइट की प्रतिरोधकता 140 ohm-mm है, तो कार्यकारी रिक्ति ज्ञात कीजिए।
पदार्थ भंडारण विभाग का विन्यास नीचे दिया गया है। पदार्थ प्रवाह पैकिंग क्षेत्र (संख्या 6) व अन्य 9 विभाग/क्षेत्र के बीच हो रहा है। भार पैकिंग क्षेत्र 6 से शिपिंग/अभिग्रहण क्षेत्र 1 की ओर स्थानांतरित किए जा रहे हैं जबकि अन्य सभी भार विभिन्न विभागों/क्षेत्रों (2, 3, 4, 5, 7, 8, 9) से पैकिंग क्षेत्र 6 की तरफ स्थानांतरित किए जाते हैं। विभागों को/से औसत वार्षिक भार स्थानांतरण/प्रवाह निम्नवत है:
| प्रवाह से – तक | वार्षिक औसत भार (संख्या) | तय की गई दूरी (m) |
|---|---|---|
| 2 से 6 तक | 200 | 50 |
| 3 से 6 तक | 300 | 50 |
| 4 से 6 तक | 400 | 50 |
| 5 से 6 तक | 500 | 50 |
| 7 से 6 तक | 600 | 50 |
| 8 से 6 तक | 700 | 50 |
| 9 से 6 तक | 800 | 50 |
| 10 से 6 तक | 900 | 50 |
| 6 से 1 तक | 4400 | 100 |
मानिए कि एक भार की इकाई दूरी (m) स्थानांतरण करने की लागत ₹ 1/मी. है। पदार्थ प्रहस्तन की कुल वार्षिक लागत की गणना कीजिए।
NC मशीनों के संदर्भ में 'निर्देशांक प्रणाली' व 'गति नियंत्रण' की व्याख्या कीजिए।
The figure this question refers to, in words
The question paper is a scan and the diagram did not survive as text. This is the figure as read from the original page — every component, value and label — so the question can be worked from the text below.
(a) Table with columns: Jobs, Processing Time (in days), Due Date (from now) A, 6, 5 B, 4, 10 C, 5, 15 D, 8, 20 E, 7, 30
(b) Table with City as the major column header over Chennai, Delhi, and Kolkata: Head, Chennai, Delhi, Kolkata Fixed cost (Rupees), 800000, 600000, 500000 Variable cost per unit (Rupees), 30, 40, 50 Revenue per unit (Rupees), 60, 60, 60
(b) Layout diagram and flow table:
- Layout Diagram: A grid layout consisting of 10 square areas:
- Top row: section (2), section (3), section (4) from left to right.
- Middle row: section (1) on the far left, connected to section (5), which is to the left of 'Packing area (6)', followed by section (7) on the right.
- Bottom row: section (8) directly below (5), section (9) directly below (6), and section (10) directly below (7). Section (1) is attached only to the left side of section (5).
- Data Table: Flow From - To | Average Annual Load (No.) | Distance Covered (m) 2 to 6 | 200 | 50 3 to 6 | 300 | 50 4 to 6 | 400 | 50 5 to 6 | 500 | 50 7 to 6 | 600 | 50 8 to 6 | 700 | 50 9 to 6 | 800 | 50 10 to 6 | 900 | 50 6 to 1 | 4400 | 100
Model answer
Drafted with AI by UPSC Answer Check against this question's marking rubric, to the expected length. UPSC does not publish answers for Mains — this is one way to score well, not an official key. How we build rubrics and answers.
(a) Electrochemical machining
(i) Material removal rate = η × (specific removal rate) × I = 0.90 × 3.42 × 10⁻² × 1800 = 55.4 mm³/s. In mm³/min this is 55.4 × 60 = 3324 mm³/min.
(ii) The electrolyte in the gap behaves as a resistance R = ρh/A. By Ohm's law R = V/I = 12/1800 = 1/150 Ω. Hence the working gap is
h = RA/ρ = (1/150) × 2000/140 = 0.0952 mm ≈ 0.095 mm.
(b) Annual material-handling cost
Cost = Σ (number of loads × distance × ₹1/m).
Loads from sections 2, 3, 4, 5, 7, 8, 9 and 10 to the packing area 6 total 200 + 300 + … + 900 = 4400, each moved 50 m: 4400 × 50 = ₹2 20 000.
Loads from 6 to shipping area 1: 4400 × 100 = ₹4 40 000.
Total annual cost = ₹6 60 000.
(c) Coordinate system and motion control in NC machines
Coordinate system: this is the reference frame that defines positions of the tool relative to the workpiece. NC machines use a right-handed Cartesian system, with X, Y and Z mutually perpendicular. The Z axis is parallel to the spindle axis, and A, B and C are rotations about X, Y and Z. Positions are given either in absolute coordinates, measured from a fixed zero, or in incremental coordinates, measured from the previous position (G90 and G91). Several origins are used: the machine zero, the workpiece (program) zero and the tool offsets that relate them. Every programmed move is a coordinate pair or triple in this frame, so the system gives an unambiguous numerical description of the tool path.
Motion control: this is how the controller drives the axes to the programmed positions and speeds. The controller reads each block of the part program, works out displacement, direction and feed, and sends signals to the axis drives. The types of motion are:
- Point-to-point (positioning): only the end point matters and the path is irrelevant, as in drilling and spot welding.
- Straight-cut (linear): motion along one axis at a controlled feed, as in simple milling.
- Contouring (continuous path): two or more axes are coordinated by interpolation (linear G01, circular G02/G03) to produce slopes and curves.
The control may be open loop, using stepper motors without feedback, or closed loop, using servo drives with encoder or tacho feedback to correct error. Accurate motion control gives dimensional accuracy, surface finish and repeatability, with backlash and pitch-error compensation included.
How this answer will be evaluated
What earns full marks: All parts show complete working, correct formulas, and clear interpretation.
Evaluation rubric
Each sub-part is marked on its own, against the marks and word limit printed on the paper.
- (a) Find the ECM material removal rate in mm³/min and the working gap 15 marks
calculate— given → formula → substitution → result with units → interpretation
Must cover
- MRR = η × specific rate × I = 55.4 mm³/s = 3324 mm³/min
- Gap resistance R = V/I = 1/150 Ω
- Working gap h = RA/ρ ≈ 0.095 mm
Loses marks
- Forgetting to convert seconds to minutes
- Using resistivity in the wrong units
Earns more
- Efficiency applied to the removal rate
- Resistance relation R = ρh/A used
Extra mark
- Cross-checks with Faraday's law
- (b) Find the annual total material-handling cost 15 marks
calculate— given → formula → substitution → result with units → interpretation
Must cover
- Cost = load × distance × ₹1/m for each flow
- Flows into area 6 give ₹2 20 000
- Total cost ₹6 60 000
Loses marks
- Omitting the 6 to 1 flow
- Arithmetic error in the sum
Earns more
- All nine flows included
- 6 to 1 flow of 4400 loads over 100 m included
Extra mark
- Notes that the 6–1 flow dominates the cost
- (c) Explain the coordinate system and motion control in NC machines 20 marks
explain— definition/context → points in order → small example → short close
Must cover
- Right-handed Cartesian X, Y, Z axes with Z along the spindle and absolute and incremental modes
- Point-to-point, straight-cut and contouring motion control
- Open-loop and closed-loop control
Loses marks
- Confusing coordinate system with motion types
- Not distinguishing positioning from contouring
Earns more
- Machine zero, work zero and offsets
- Interpolation G01, G02/G03
- Compensations for backlash and tool
Extra mark
- Links accuracy and repeatability to motion control
What "Calculate" is asking you to do
Apply the standard formula or schedule to data the question has already supplied — a table of readings, cost records, a balance sheet — and produce the number. The method is rarely in doubt; the marks sit in the named intermediate quantities, each of which has to appear as a labelled line.
Structure that answers it
Data as given → formula or standard treatment, named → substitution → each intermediate, labelled → result with units
Where marks are lost
Omitting an intermediate the marking scheme pays for separately, or rounding at an intermediate line so the final figure drifts. In commerce and accountancy, any figure in a statement that no numbered working note supports is treated as unearned.
Practice this exact question
Write your answer and it is marked point by point against the model answer above — what you covered, what you missed, what you got wrong.
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