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.

Question

(i) If the process is 90% efficient, determine the rate of material removal in mm³/minute.

(ii) If the resistivity of the electrolyte is 140 ohm-mm, determine the working gap.

(b) 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.

(c) Explain 'Coordinate system' and 'Motion control' with reference to NC machines.

UPSC Answer Check · Accepted Answer

Calculate the ECM material removal rate using Faraday's laws with efficiency correction for part (i), then determine working gap using Ohm's law and resistivity relationship for part (ii). For part (b), compute total material handling cost by summing individual load-distance products multiplied by unit cost. For part (c), explain coordinate systems (Cartesian, polar, cylindrical) and motion control types (point-to-point, continuous path) with NC machine context. Allocate approximately 35% time to numerical parts (a), 25% to cost calculation (b), and 40% to descriptive explanation (c).
- Part (i): Apply MRR = η × (C × I × t) with C = 3.42×10⁻² mm³/A-s, I = 1800 A, convert seconds to minutes; correct answer ≈ 3.32×10⁶ mm³/min
- Part (ii): Use V = I×R = I×(ρ×y/A) to solve for gap y = V×A/(I×ρ); correct answer ≈ 0.095 mm or 95 μm
- Part (b): Calculate cost = Σ(loads × distance × ₹1/m); incoming flows to area 6 total 4400 loads × 50m, outgoing 4400 × 100m; total cost = ₹6,60,000
- Part (c): Explain machine coordinate system (absolute vs. incremental), work coordinate system, and motion control types (PTP, continuous path, contouring) with NC applications
- Part (c): Describe interpolators (linear, circular) and control loops (open, closed, semi-closed) in CNC machines
- Correct unit conversions throughout (mm³/A-s to mm³/min, ohm-mm to consistent units)
- Recognition that total loads entering area 6 (4400) equal loads leaving to area 1 (4400), indicating system balance

Dimension	Weight	Max marks	Excellent	Average	Poor
Concept correctness	20%	10	Correctly applies Faraday's laws of electrolysis for ECM with efficiency factor; recognizes gap resistance as ρy/A; understands load-distance methodology for material handling; accurately describes absolute/incremental coordinate systems and PTP vs. continuous path motion control in NC machines.	Applies basic MRR formula but may miss efficiency application or confuse absolute/incremental coordinates; partial understanding of motion control types.	Confuses ECM with EDM or other NTM processes; treats gap calculation as parallel plate capacitor; misunderstands coordinate systems as purely geometric rather than machine-related.
Numerical accuracy	20%	10	Part (i): MRR = 0.9 × 3.42×10⁻² × 1800 × 60 = 3,323,640 mm³/min ≈ 3.32×10⁶ mm³/min; Part (ii): y = 12×2000/(1800×140) = 0.0952 mm; Part (b): Total cost = (4400×50 + 4400×100) = ₹6,60,000; all unit conversions correct.	Correct methodology but arithmetic slips in final values; minor unit conversion errors (e.g., seconds to minutes); partial summation in cost calculation.	Order of magnitude errors in MRR; confuses resistivity units leading to gap in meters; double-counts or misses flows in cost calculation; no unit consistency.
Diagram quality	15%	7.5	Clear schematic of ECM setup showing electrode, workpiece, electrolyte gap, and power supply; layout sketch for material flow showing areas 1-10 with distances; NC coordinate system diagram with machine axes (X,Y,Z,A,B,C) and origin conventions.	Basic ECM diagram without labels or incomplete material flow representation; mentions coordinate axes without showing machine orientation.	No diagrams despite question involving spatial layouts and coordinate systems; or completely incorrect schematics.
Step-by-step derivation	25%	12.5	Shows Faraday's law MRR = C×I×A×t with efficiency explicitly applied; derives gap from V=IR with R=ρL/A clearly stated; tabulates load-distance calculations; explains coordinate transformation from part to machine coordinates; describes interpolator algorithms for motion control.	States formulas correctly but skips intermediate algebraic steps; load-distance products shown but not tabulated; coordinate explanation descriptive rather than derived.	Final answers stated without derivation; no working shown for any numerical part; coordinate explanation lacks technical depth.
Practical interpretation	20%	10	Comments on ECM gap control significance for dimensional accuracy; discusses material handling cost reduction through layout optimization (e.g., relocating area 1 closer); relates NC coordinate systems to Indian manufacturing contexts (e.g., HMT machine tools); notes motion control impact on surface finish and accuracy.	Brief mention of practical importance without specific examples; generic statements about efficiency or cost savings.	No practical interpretation; treats all parts as purely theoretical exercises; no connection to manufacturing practice.

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