(a) (i) In an orthogonal cutting operation, the following data are obtained : Cutting force F_c = 1500 N Thrust force F_t = 900…

(a)(i) Orthogonal cutting analysis (15 marks)

Data: F_c = 1500 N, F_t = 900 N, α = 10° and chip thickness ratio r = t/t_c = 0.4.

(I) Shear angle. tan φ = r cos α/(1 − r sin α) = 0.4 × 0.9848/(1 − 0.4 × 0.1736) = 0.3939/0.9305 = 0.4233, so φ = 22.9°.

(II) Friction angle. Resolve the forces along and normal to the tool face:

• Friction force F = F_c sin α + F_t cos α = 1500 × 0.1736 + 900 × 0.9848 = 260.5 + 886.3 = 1146.8 N.
• Normal force N = F_c cos α − F_t sin α = 1477.2 − 156.3 = 1320.9 N.

tan β = F/N = 1146.8/1320.9 = 0.868, so β = 41.0°.

(III) Coefficient of friction. μ = tan β = F/N = 0.868.

(IV) Shear force. From Merchant's circle, F_s = F_c cos φ − F_t sin φ = 1500 × 0.9209 − 900 × 0.3899 = 1381.3 − 350.9 = 1030 N.

Check. The resultant is R = √(1500² + 900²) = 1749.3 N, and F_s = R cos(φ + β − α) = 1749.3 × cos 53.9° = 1749.3 × 0.5891 = 1030 N. This agrees.

(a)(ii) Limit gauges for a 25 ± 0.01 mm hole, by Taylor's principle (5 marks)

Work limits. The hole limits are 25.01 mm (maximum, least material) and 24.99 mm (minimum, maximum material), so the work tolerance is 0.02 mm.

Gauge allowances. Gauge tolerance = 10% of 0.02 = 0.002 mm. Wear allowance = 10% of 0.02 = 0.002 mm, applied to the GO gauge only, since only it wears in use. For a plug gauge, wear reduces the size, so the wear allowance is added above the minimum hole limit, and both gauge tolerance zones lie inside the work tolerance.

(I) GO plug gauge (checks the minimum hole limit, so it is the full-form gauge):

• Lower limit = 24.99 + 0.002 (wear allowance) = 24.992 mm.
• Upper limit = 24.992 + 0.002 (gauge tolerance) = 24.994 mm.
• Size: 24.992 mm to 24.994 mm, that is 24.992 (+0.002/0) mm.

(II) NO-GO plug gauge (checks the maximum hole limit, and has no wear allowance):

• Upper limit = 25.01 mm.
• Lower limit = 25.01 − 0.002 = 25.008 mm.
• Size: 25.008 mm to 25.010 mm, that is 25.010 (−0.002/0) mm.

By Taylor's principle, the GO gauge is a full-length plug that checks all the elements of the hole at once, and the NO-GO gauge checks only one dimension at a time, so it is a short plug.

(b) Flexibility, lean practices and agility (15 marks)

Roles.

• Flexibility is the capability of a manufacturing system to change or adapt to variety, in product mix, volume, routing, machines or process, quickly and at low cost. It is built through programmable machines, quick changeover, cross-trained workers and modular design.
• Lean practices aim to remove waste (muda) from the flow, and cover just-in-time and pull systems (kanban), continuous improvement (kaizen), 5S, standard work, poka-yoke, TPM and value-stream mapping. The role of lean is low cost, high quality and short lead time in a stable flow.
• Agility is an organisation-wide capability to sense unpredictable change in the market and respond quickly by reconfiguring products, processes, people and partners (for example virtual enterprises). Its role is competitive survival and opportunity capture in turbulent conditions.

How they are complementary.

• They work at different levels. Lean improves the efficiency of the existing flow, flexibility gives the operational room to vary that flow, and agility is the strategic ability to change direction. Each covers what the others do not.
• Lean needs flexibility. Levelled, small-batch pull production (heijunka) needs quick changeover (SMED) and multi-skilled workers, which are flexibility resources. Without them, lean would work only for a fixed, high-volume product.
• Agility rests on a lean base and flexibility. A firm that carries waste and rigid, slow processes cannot respond quickly, so lean removes the delay and cost that would hold back a response, and flexibility supplies the capacity to switch. Agility in turn tells the firm where to apply flexibility.
• Where they appear to conflict (lean removes buffers, while agility wants slack), firms resolve it with a decoupling point: lean upstream for standard components, and agile downstream for customer-specific assembly, together with modular design and postponement ("leagile").

Thus the three are complementary parts of one competitive system, and firms need all three, in different proportions, to give low cost, quality, variety and speed together.

(c) Predetermined time standards versus time study (15 marks)

(i) Conceptual basis of PTS. Any manual task can be broken down into a small set of basic motions, such as reach, move, grasp, position, release, turn and apply pressure, plus body and eye movements. PTS systems (MTM, MOST, Work-Factor) tabulate the time for each basic motion according to its type and the conditions that affect it, such as distance, weight, precision and difficulty. The time of a task is found by adding the tabulated times of its motions, in TMUs (1 TMU = 0.00001 h = 0.036 s), and then adding allowances.

Fundamental assumption. The time to perform a basic motion depends only on the characteristics of the motion itself (its type, distance, control and load), and not on the task it forms part of. It is also assumed that the motion times are additive, and that they refer to a qualified operator working at a normal pace, so no performance rating is needed. This allows the times to be pre-assigned and reused.

(ii) Situations for capacity planning.

PTS is preferred:

• When the line or workstation does not yet exist (design stage of a new assembly line), so no operator can be timed. Times can be set from the method on paper, and alternative layouts can be compared before building.
• For short-cycle, high-volume repetitive assembly work, where the standard must be consistent across stations and shifts and free of the rating bias of a stopwatch study, and where small method changes must be costed quickly.

PTS is inappropriate:

• For long-cycle, low-volume or non-repetitive work such as job-shop and maintenance tasks, where each job has different motions and the analysis costs more than the task is worth.
• For work dominated by mental activity, judgement or process (machine) time, such as inspection with decisions, or a task paced by a machine, because PTS covers only manual motion.