AEE Mechanical Engineering Core · Chapter 12

Machine Tools, Metrology, Production and Operations Management

What to remember

Cutting speed V = πDN/1000 (m/min). Tool life follows Taylor's equation V Tⁿ = C. Material removal rate in turning = V × f × d (speed × feed × depth of cut, in consistent units).
Metrology rests on accuracy, least count, limits and fits (hole basis), Taylor's principle of gauging (GO gauge checks full form, NO-GO checks one dimension) and standard tools like micrometer, vernier, slip gauges and sine bar.
Operations management gives formulas: EOQ = √(2DS/H), PERT time = (a + 4m + b)/6, Cp = (USL - LSL)/6σ, break-even = F/(p - v), line balancing cycle time = available time/demand.

1. Machine tools and cutting basics

Lathe operations: turning, facing, taper turning, threading, drilling, boring, knurling, parting.

Cutting speed V = π D N / 1000 m/min (D in mm, N in rpm).
Machining time for turning: T = L / (f N) minutes, where L is the length of cut and f is feed per revolution.
Material removal rate in turning: MRR = V f d (V in mm/min if f and d are in mm).
Taper turning: tailstock offset = (D - d) L / (2 l), where D and d are the large and small diameters of the taper, l is the length of the taper and L is the length of the job. Compound rest is set at half the taper angle: tan α = (D - d) / (2 l).
Drilling: twist drill, point angle about 118°. Milling: peripheral (slab) and face milling; up milling (conventional, cutter rotation opposes feed) and down milling (climb milling, cutter rotation with feed; better surface and needs backlash eliminator).
Simple indexing in a dividing head: index crank turns = 40 / N for N divisions (worm gear ratio 40:1).
Shaper uses a quick-return mechanism: the cutting stroke is slower than the return stroke. Planer: the work table moves and the tool is stationary. Slotter: vertical shaper. Broaching: a multi-tooth tool pushed or pulled through the workpiece.
Grinding: abrasives aluminium oxide (steel) and silicon carbide (cast iron, non-ferrous). Glazing: wheel becomes dull. Loading: chips clog the wheel. Dressing restores the wheel.
CNC (computer numerical control): G00 rapid positioning, G01 linear interpolation, G02 circular interpolation clockwise, G03 anticlockwise, M03 spindle clockwise, M05 spindle stop, M30 program end. CNC gives high accuracy and repeatability.
Non-traditional machining: EDM (spark erosion in dielectric fluid; works on any conductive material), ECM (electrochemical, no tool wear), USM (ultrasonic, for brittle materials), AJM, LBM, plasma arc machining.

2. Mechanics of metal cutting

Orthogonal cutting: the cutting edge is perpendicular to the cutting speed. Chip thickness ratio r = t / tc = (uncut thickness / chip thickness), always less than 1.
Shear angle: tan φ = r cos α / (1 - r sin α), where α is the rake angle.
Merchant's relation: φ = 45° + α/2 - β/2, where β is the friction angle.
Chip types: continuous (ductile metals, high speed), discontinuous (brittle metals), built-up edge (BUE, low speed on ductile metals; poor finish).
Tool signature (ASA): back rake, side rake, end relief, side relief, end cutting edge angle, side cutting edge angle, nose radius.
Tool materials: high speed steel (18% W, 4% Cr, 1% V), cemented carbide (tungsten carbide with cobalt binder), ceramics, cubic boron nitride and diamond. Hot hardness rises from HSS to carbide to ceramic.
Taylor's tool life equation: V Tⁿ = C. Typical n: about 0.1 to 0.2 for HSS, 0.2 to 0.4 for carbide, 0.4 to 0.6 for ceramic. Tool life drops quickly as speed increases.
Cutting fluids cool and lubricate and wash away chips.
Most of the energy in cutting becomes heat: major share is carried away in the chip.

Worked example. Taylor's n = 0.25 and tool life 60 min at 100 m/min. At 50 m/min the life becomes 60 × 2⁴ = 960 min (T is proportional to V^(-1/n)).

3. Metrology

Accuracy: closeness to the true value. Precision: repeatability. Least count: smallest reading of the instrument. Sensitivity: change in output per change in measured value.
Vernier caliper: least count = 1 MSD - 1 VSD. Micrometer: least count = pitch / number of thimble divisions; 0.5 mm / 50 = 0.01 mm.
Limits, fits and tolerances: basic size, upper and lower deviation, tolerance = upper limit - lower limit. Types of fit: clearance (shaft always smaller than hole), interference (shaft always larger), transition (either). Hole basis system: hole has zero lower deviation (H); more common because holes are made with standard tools. Shaft basis: shaft has zero upper deviation (h). Standard tolerance grades IT01 to IT18.
Gauging: the GO gauge checks the maximum material limit and has full form; the NO-GO gauge checks the least material limit and checks one dimension at a time (Taylor's principle). Plug gauges check holes; ring and snap gauges check shafts.
Slip gauges (gauge blocks): very flat blocks that wring together to make any size; used for calibration.
Sine bar: sin θ = h / L, where h is the height of the slip gauge stack under one roller and L is the distance between roller centres. It is not suitable beyond about 45° because of error growth. For L = 200 mm and θ = 30°, h = 100 mm.
Comparators: mechanical (dial gauge), optical, pneumatic (air gauging) and electrical. They compare a part with a standard.
Optical flat and interference: each fringe represents a height difference of λ/2. Autocollimator measures small angles and straightness. Bevel protractor measures angles. Screw threads: three-wire method for effective diameter. Profile projector for contours. CMM (coordinate measuring machine) measures 3D coordinates.
Surface roughness: Ra (arithmetic average) and Rz (mean peak to valley height). Abbe's principle: the measuring axis should be in line with the axis of the scale. Calibration compares an instrument against a higher standard.

4. Production and operations management

Forecasting: moving average, exponential smoothing: F(t+1) = α A(t) + (1 - α) F(t), where α is the smoothing constant (0 to 1). Mean absolute deviation (MAD) measures forecast error. Delphi is a qualitative method.

Inventory control:

Economic order quantity EOQ = √(2 D S / H), where D = annual demand, S = ordering cost per order, H = holding cost per unit per year. At EOQ, the annual ordering cost equals the annual holding cost.
Reorder point = demand during lead time + safety stock.
ABC analysis: A items are few but of high value (about 70% of value from 10% of items); C items are many with low value. VED: vital, essential, desirable. FSN: fast, slow, non-moving.
Example: D = 1000 units, S = 50, H = 10 per unit/year: EOQ = √(2 × 1000 × 50 / 10) = 100 units.
In power plants, spare parts of high value, like turbine blades, are placed under tight control (A class), while nuts and bolts are C class.

Production systems and planning: job, batch, mass and continuous production. Layouts: product (line), process (functional), fixed position, cellular (group technology). MRP uses bill of materials, inventory status and master production schedule. JIT and Kanban (Toyota) aim to remove waste (lean). Productivity = output / input.

Line balancing: cycle time = available time / required output. Minimum number of workstations = (sum of task times) / cycle time, rounded up. Line efficiency = sum of task times / (number of stations × cycle time).

Work study: method study (improve methods) and work measurement (time study, work sampling). Normal time = observed time × rating factor. Standard time = normal time × (1 + allowance fraction).

Project management: CPM uses fixed times; PERT uses three estimates: optimistic a, most likely m, pessimistic b.

Expected time te = (a + 4m + b)/6; variance = ((b - a)/6)².
Critical path = longest path; activities on it have zero total float. Total float = LST - EST (or LFT - EFT).
A Gantt chart shows activities against time.

Scheduling and others: Johnson's rule gives the optimal sequence for n jobs on two machines. Shortest processing time (SPT) rule minimises average flow time. Assignment problems use the Hungarian method; transportation problems use the north-west corner, least cost and Vogel's approximation methods.

Quality: control charts: X-bar and R charts for variables; p and c charts for attributes. Process capability Cp = (USL - LSL) / 6σ; Cp of 1.33 or more is considered capable. Six Sigma targets 3.4 defects per million opportunities. TQM, ISO 9000 and Pareto analysis support quality improvement.

Break-even analysis: BEP quantity = fixed cost / (selling price per unit - variable cost per unit).

Maintenance: breakdown, preventive, predictive and total productive maintenance (TPM). Overhauls of power plant units are usually planned with CPM networks.

Exam traps

Cutting speed uses diameter in mm and gives m/min; feed is per revolution in turning.
Chip thickness ratio is below 1, because the chip is thicker than the uncut layer.
Go gauge checks maximum material and full form; no-go checks one dimension.
Hole basis: hole lower deviation is zero; shaft basis: shaft upper deviation is zero.
Precision is not accuracy.
EOQ: the holding cost H is per unit per year, not total.
PERT time has a factor 4 on the most likely time.
Critical path is the longest path, not the shortest.

One-liners

1. Cutting speed V = π D N / 1000.
2. Taylor's equation: V Tⁿ = C.
3. Carbide tools allow higher cutting speeds than HSS.
4. Up milling is conventional milling; down milling is climb milling.
5. Simple indexing uses 40/N turns of the crank.
6. A micrometer with 0.5 mm pitch and 50 divisions has least count 0.01 mm.
7. Sine bar relation: sin θ = h / L.
8. G01 means linear interpolation in CNC.
9. EOQ balances ordering cost and holding cost.
10. PERT expected time = (a + 4m + b)/6.
11. ABC analysis classifies items by value.
12. Six Sigma allows 3.4 defects per million opportunities.

Practice questions

The cutting speed in turning, in m/min, is given by (D in mm, N in rpm)
1. π D N
2. π D N / 1000
3. π D² N / 1000
4. D N / 1000
Answer
B. π D N / 1000
V = π D N / 1000 converts mm/min to m/min.
A job of 100 mm diameter is turned at 300 rpm. The cutting speed is about
1. 94 m/min
2. 9.4 m/min
3. 30 m/min
4. 300 m/min
Answer
A. 94 m/min
V = π × 100 × 300 / 1000 = 94.2 m/min.
A 300 mm long cut is made at feed 0.5 mm/rev and 300 rpm. The machining time is
1. 4 min
2. 0.5 min
3. 2 min
4. 1 min
Answer
C. 2 min
T = L / (f N) = 300 / (0.5 × 300) = 2 min.
At cutting speed 100 m/min, feed 0.2 mm/rev and depth of cut 2 mm, the material removal rate is
1. 400 mm³/min
2. 40,000 mm³/min
3. 20,000 mm³/min
4. 4000 mm³/min
Answer
B. 40,000 mm³/min
MRR = V f d = 100,000 × 0.2 × 2 = 40,000 mm³/min.
In Taylor's tool life equation V Tⁿ = C, the constant n is largest for
1. High speed steel tools
2. All tools equally
3. Carbon tool steel
4. Ceramic tools
Answer
D. Ceramic tools
n is about 0.1-0.2 for HSS, 0.2-0.4 for carbide and 0.4-0.6 for ceramics.
For Taylor's n = 0.25, if the cutting speed is halved, the tool life becomes
1. 8 times
2. 2 times
3. 16 times
4. 4 times
Answer
C. 16 times
T is proportional to V^(-1/n) = V⁻⁴; halving V gives 2⁴ = 16.
Chip thickness ratio r = t / tc in orthogonal cutting is generally
1. Less than 1
2. Greater than 1
3. Exactly 1
4. Equal to the shear angle
Answer
A. Less than 1
The chip is thicker than the uncut layer.
In orthogonal cutting the uncut thickness is 0.2 mm and the chip thickness is 0.4 mm. The chip thickness ratio is
1. 2
2. 0.2
3. 0.5
4. 0.8
Answer
C. 0.5
r = t / tc = 0.2 / 0.4.
Merchant's relation gives the shear angle φ as
1. 45° - α/2 + β/2
2. 90° - α - β
3. 45° + α + β
4. 45° + α/2 - β/2
Answer
D. 45° + α/2 - β/2
α is the rake angle and β is the friction angle.
With rake angle 10° and friction angle 30°, the shear angle from Merchant's relation is
1. 55°
2. 35°
3. 25°
4. 45°
Answer
B. 35°
φ = 45 + 5 - 15 = 35°.
Tailstock offset for turning a taper: total length of job 400 mm, taper length 200 mm, diameters 60 mm and 40 mm. The offset is
1. 5 mm
2. 10 mm
3. 40 mm
4. 20 mm
Answer
D. 20 mm
Offset = (D - d) L / (2 l) = 20 × 400 / 400 = 20 mm.
To mill 8 equal divisions using simple indexing, the index crank is turned by
1. 8 turns
2. 5 turns
3. 40 turns
4. 0.2 turn
Answer
B. 5 turns
Turns = 40 / N = 40 / 8 = 5.
In climb (down) milling
1. The cutter rotation is in the direction of feed at cut entry
2. The work is clamped loosely
3. The cutter rotation opposes the feed
4. The chip thickness is zero at start always
Answer
A. The cutter rotation is in the direction of feed at cut entry
It gives better surface but needs a backlash eliminator.
A quick-return mechanism is used in a
1. Shaper
2. Drilling machine
3. Lathe
4. Grinder
Answer
A. Shaper
The return stroke is faster than the cutting stroke.
In CNC programming G01 means
1. Spindle stop
2. Circular interpolation clockwise
3. Linear interpolation
4. Rapid positioning
Answer
C. Linear interpolation
G00 is rapid positioning; G02 is clockwise arc; M05 stops the spindle.
Electrical discharge machining (EDM) can machine materials that are
1. Electrically conductive
2. Only brittle non-metals
3. Only soft plastics
4. Only ceramics
Answer
A. Electrically conductive
Spark erosion needs a conductive workpiece in a dielectric fluid.
The least count of a micrometer with pitch 0.5 mm and 50 thimble divisions is
1. 0.02 mm
2. 0.1 mm
3. 0.05 mm
4. 0.01 mm
Answer
D. 0.01 mm
LC = pitch / divisions = 0.5 / 50.
A vernier has 10 divisions equal to 9 main scale divisions of 1 mm each. The least count is
1. 0.01 mm
2. 0.1 mm
3. 0.9 mm
4. 1 mm
Answer
B. 0.1 mm
LC = 1 MSD - 1 VSD = 1 - 0.9 = 0.1 mm.
Repeatability of measurement is called
1. Sensitivity
2. Accuracy
3. Range
4. Precision
Answer
D. Precision
Accuracy is closeness to the true value.
In the hole basis system, the hole has
1. Zero upper deviation
2. Zero lower deviation
3. Negative tolerance only
4. Maximum interference
Answer
B. Zero lower deviation
Hole is designated H; shaft deviations vary to give the fit.
Hole: 50.00 to 50.05 mm; shaft: 49.90 to 49.95 mm. The minimum clearance is
1. 0.10 mm
2. 0.15 mm
3. 0.05 mm
4. 0
Answer
C. 0.05 mm
Min clearance = hole min - shaft max = 50.00 - 49.95 = 0.05 mm.
According to Taylor's principle, the GO gauge
1. Checks the maximum material limit with full form
2. Checks the least material limit
3. Checks only one dimension
4. Is always the shorter gauge
Answer
A. Checks the maximum material limit with full form
The NO-GO gauge checks the least material limit, one dimension at a time.
A sine bar of centre distance 100 mm is set to 30°. The height of the slip gauge stack is
1. 30 mm
2. 100 mm
3. 50 mm
4. 86.6 mm
Answer
C. 50 mm
h = L sin θ = 100 × 0.5.
Each interference fringe seen with an optical flat shows a height difference of
1. λ / 4
2. λ
3. 2λ
4. λ / 2
Answer
D. λ / 2
Light travels the gap twice, so a fringe represents half a wavelength.
Ten fringes are seen with light of wavelength 0.6 μm. The height difference is
1. 6 μm
2. 3 μm
3. 1.2 μm
4. 0.3 μm
Answer
B. 3 μm
Height = 10 × λ/2 = 10 × 0.3 = 3 μm.
Economic order quantity is given by
1. √(2 H / D S)
2. 2 D S / H
3. √(2 D S / H)
4. √(D S / 2H)
Answer
C. √(2 D S / H)
D = annual demand, S = ordering cost per order, H = holding cost per unit per year.
Annual demand 800 units, ordering cost 25 per order, holding cost 4 per unit per year. The EOQ is
1. 200 units
2. 50 units
3. 400 units
4. 100 units
Answer
D. 100 units
EOQ = √(2 × 800 × 25 / 4) = √10,000 = 100.
At the economic order quantity
1. Ordering cost equals holding cost
2. Holding cost is zero
3. Total cost is maximum
4. Ordering cost is zero
Answer
A. Ordering cost equals holding cost
Total cost is minimum where the two annual costs are equal.
In ABC analysis, class A items are
1. Many in number and low in value
2. Non-moving items
3. Only perishable items
4. Few in number but high in value
Answer
D. Few in number but high in value
A items need tight control.
Using exponential smoothing with α = 0.2, last actual 100 and last forecast 80, the next forecast is
1. 80
2. 84
3. 88
4. 90
Answer
B. 84
F = 0.2 × 100 + 0.8 × 80 = 20 + 64 = 84.
PERT optimistic, most likely and pessimistic times are 2, 5 and 14 days. The expected time is
1. 6 days
2. 8 days
3. 5 days
4. 7 days
Answer
A. 6 days
te = (2 + 4 × 5 + 14) / 6 = 36/6.
For the same activity (a = 2, b = 14), the variance is
1. 4
2. 2
3. 12
4. 36
Answer
A. 4
((b - a)/6)² = (12/6)² = 4.
The critical path in a network is
1. The shortest path
2. The path with most activities
3. The longest path
4. The path with the largest float
Answer
C. The longest path
It determines the project duration; its activities have zero total float.
Total task time on an assembly line is 120 s and the cycle time is 30 s. The minimum number of workstations is
1. 3
2. 5
3. 6
4. 4
Answer
D. 4
N = 120 / 30 = 4.
With 5 stations and cycle time 30 s, total task time of 120 s gives a line efficiency of
1. 100%
2. 80%
3. 60%
4. 96%
Answer
B. 80%
Efficiency = 120 / (5 × 30) = 0.8.
Observed time 2 min, rating factor 110% and allowance 10% of normal time. The standard time is
1. 2.0 min
2. 2.62 min
3. 2.42 min
4. 2.2 min
Answer
C. 2.42 min
Normal = 2 × 1.1 = 2.2; standard = 2.2 × 1.1 = 2.42 min.
Fixed cost 60,000, selling price 50 and variable cost 30 per unit. The break-even quantity is
1. 6000 units
2. 3000 units
3. 2000 units
4. 1200 units
Answer
B. 3000 units
BEP = 60,000 / (50 - 30) = 3000.
A process has USL - LSL = 12 and σ = 1.5. Cp is
1. 8
2. 1.33
3. 0.8
4. 0.67
Answer
B. 1.33
Cp = 12 / (6 × 1.5) = 1.33.
An activity has earliest start 3 days and latest start 7 days. Its total float is
1. 4 days
2. 3 days
3. 0
4. 10 days
Answer
A. 4 days
Float = LST - EST = 7 - 3.
Consider: 1. CPM uses three time estimates for each activity. 2. In a network, the critical path is the longest path. Which is/are correct?
1. 1 only
2. 2 only
3. Both 1 and 2
4. Neither 1 nor 2
Answer
B. 2 only
CPM uses one time; PERT uses three estimates. So 1 is wrong.
Johnson's rule is used to find the optimal sequence for
1. Transportation costs
2. Inventory levels
3. One job on n machines
4. n jobs on two machines
Answer
D. n jobs on two machines
It minimises total makespan on two machines in series.
Consider: 1. Precision means closeness to the true value. 2. Least count is the smallest reading an instrument can give. Which is/are correct?
1. 1 only
2. 2 only
3. Both 1 and 2
4. Neither 1 nor 2
Answer
B. 2 only
Precision is repeatability, not closeness to the true value (accuracy), so 1 is wrong.
Six Sigma quality aims at about
1. 34 defects per million
2. 3400 defects per million
3. 3.4 defects per million opportunities
4. 0.34 defects per million
Answer
C. 3.4 defects per million opportunities
This is the standard Six Sigma target.
Consider: 1. In turning, the feed is expressed per revolution. 2. In the hole basis system the hole is designated H. Which is/are correct?
1. 1 only
2. 2 only
3. Both 1 and 2
4. Neither 1 nor 2
Answer
C. Both 1 and 2
Both statements are correct.
Which gauge is generally used to check a hole of fixed size?
1. Plug gauge
2. Sine bar
3. Snap gauge
4. Ring gauge
Answer
A. Plug gauge
Plug gauges check holes; ring and snap gauges check shafts.

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