Question 6 of 7: Specifying a tolerance, and Design for Manufacture and Assembly

Question 6: Specifying a tolerance, and Design for Manufacture and Assembly (15 marks)

Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.

Given. The component under discussion is a moulded glass-filled nylon bearing boss on the toaster carriage of Question 3. The designer proposes ±0.10 mm on the bore, and the moulding process has a measured short-term standard deviation of σ = 0.035 mm. The assembly being improved in part B has 24 parts and takes 92 s, of which a theoretical-minimum analysis identifies 6 parts as genuinely necessary; the ideal handle-and-insert time for a well-designed part is 3 s, and burdened assembly cost is 45 CAD/h at 250 000 units a year.

Find. Three questions that would actually change the tolerance decision, and the DFMA concepts and metrics that turn the 24-part assembly into a better product.

Part A — Three questions for the manufacturing engineer (6 marks)

Question 1: “What is the short-term process capability of the intended process on this feature, and what tolerance would give me C_pk ≥ 1.33 without adding an operation?” This is the question that converts an opinion into a number. Capability compares the tolerance band with the process spread:

A capability below 1.0 means the process spread is wider than the tolerance band even when perfectly centred, so the proposed ±0.10 mm cannot be held. Turning the question round gives the actionable answer — the standard deviation the process would need to reach the customary 1.33 target is

so the moulding would have to improve by a factor of 1.4, or the tolerance must open to about ±0.14 mm, or a reaming operation must be added. Asking for capability rather than for “can you hold this?” also gets an answer that survives the transfer to a second supplier, because capability is a property of the process, not of the person answering.

Question 2: “What datum scheme and fixturing will you use, and can you measure to my datums with an acceptable gauge R&R?” A tolerance is meaningless without the datum it is measured from, and a drawing whose datums cannot be located in the fixture will be manufactured to different datums in practice. This question surfaces three things at once: whether the geometric dimensioning and tolerancing scheme matches how the part is actually held, whether the measurement system is capable (a gauge repeatability and reproducibility study consuming more than about 10 % of the tolerance band makes the tolerance unmeasurable regardless of the process), and whether a functional gauge would serve better than a coordinate measurement. It also opens the most valuable conversation available — whether a bonus tolerance under maximum-material condition would give the process the room it needs at no cost to function.

Question 3: “Where is the cost step, and what does the proposed limit do to scrap and cycle time?” Manufacturing cost against tolerance is not a smooth curve; it is a staircase, and each step is a change of process — as-moulded, to moulded-and-reamed, to ground. The useful information is where the next step sits, because a tolerance 0.01 mm inside a step boundary may cost 30 % more than one 0.01 mm outside it while delivering nothing the function needs. The same question should ask for the predicted fallout at the proposed limit: at C_p = 0.95 with a centred process the specification limits sit at 2.86σ, which is a defect rate of roughly 4 in 1 000 — and at 250 000 units a year that is a thousand rejected mouldings, a number that makes the case for opening the tolerance far better than an argument about principle.

The three questions are deliberately about capability, measurement and cost, because those are the three ways a tolerance can be wrong: unachievable, unverifiable, or achievable but not worth what it costs.

Part B — Design for Manufacture and Assembly (9 marks)

DFMA is the systematic evaluation of a design against the cost of making and assembling it, carried out early enough to change the design. Boothroyd, Dewhurst and Knight separate it into two halves that are often confused. Design for assembly (DFA) asks whether a part should exist at all and how easily it can be handled and inserted; design for manufacture (DFM) asks what each surviving part should be made of and by what process. The order matters: DFA runs first, because eliminating a part removes its manufacturing cost, its tooling, its inventory, its inspection and its assembly operation all at once, whereas optimising a part that should not exist achieves none of that.

Concept 1 — the three-question part-count test. For each part, moving through the assembly in sequence, ask: does it move relative to the parts already assembled? must it be of a different material for a fundamental physical reason? must it be separate to allow assembly or service of other parts? If all three answers are no, the part is a candidate for elimination or integration into a neighbour. Applied to a moulded assembly this typically removes fasteners, brackets, spacers and covers by replacing them with integral snap features, living hinges and self-locating bosses.

Concept 2 — design for handling and insertion. Assembly time is dominated by two things that have nothing to do with the part’s function: acquiring and orienting it, and inserting and securing it. The design rules follow directly — make parts symmetrical so orientation does not matter, or grossly asymmetrical so it cannot be got wrong; avoid parts that nest, tangle or are too flexible to handle; insert from a single direction, ideally vertically under gravity; provide chamfers and lead-ins so the part self-aligns; eliminate the need to hold a part while another is fitted; and prefer snap fits to screws, since every threaded fastener adds several seconds and a torque specification.

Concept 3 — the DFA index as a measurable target. The method is quantitative, which is what makes it a design tool rather than a checklist. The design efficiency is

where N_min is the theoretical minimum number of parts from the three-question test and t_a = 3 s the ideal handling-and-insertion time. For the toaster carriage as designed, with 24 parts assembled in 92 s and a theoretical minimum of 6:

after redesign to 11 parts and 41 s. The redesign removed 13 parts (54 %) and 51 s (55 %) of assembly time, and it did so by replacing eight screws and two brackets with snap features moulded into the existing panels, symmetrising the carriage guide so it cannot be fitted backwards, and consolidating two spacers into the boss of Part A.

Concept 4 — design for manufacture on the parts that survive. Once the part count is settled, each remaining part is matched to a process and then designed for it: uniform wall thickness, generous radii and adequate draft for mouldings; tolerances set from process capability as in part A rather than from habit; features oriented to avoid undercuts and side actions; and materials chosen so that a family of parts shares one grade. The tolerance discussion of part A is DFM in miniature — the cheapest tolerance is the loosest one the function permits.

How this improves the product, not just the cost. The saving is real: 51 s at 45 CAD/h is 0.64 CAD per unit, which is about 159 000 CAD a year at 250 000 units, before the tooling, inventory and purchasing cost of 13 deleted part numbers. But the more durable benefits are quality and reliability. Every part is a potential defect and every joint a potential failure; halving the part count roughly halves the opportunities for both. Fewer parts means shorter tolerance stacks, so the assembly is dimensionally better behaved. Symmetrical and self-locating parts cannot be assembled wrongly, so a whole class of field failures disappears. And a product that assembles in 41 s can be built to order in smaller batches, which is a business benefit the cost saving does not capture. The one genuine risk to state is that consolidation can work against serviceability and recycling — a moulded-in snap that cannot be released destroys the part on disassembly, which is precisely the tension identified at stage 5 of Question 3.