Question 7 of 7: Manufacturing Route Selection for a Bicycle Pedal

Question 7: Manufacturing Route Selection for a Bicycle Pedal (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.

The pedal considered is a conventional platform pedal: a body carrying the rider's foot, running on a bearing pair about a steel spindle that threads into the crank. Only the body is open to process choice; the spindle is a rolled-thread, heat-treated steel part in every case, and the bearings are bought in.

Part A — Three ways of manufacturing the pedal (3 marks)

(1) High-pressure die casting in aluminium. A hypoeutectic Al–Si alloy such as A380 or ADC12 is injected into a hardened steel die at high pressure and short cycle time, producing a thin-walled body with the cage ribs, the bearing bores and the pin bosses formed in one shot. Secondary operations are limited to trimming, boring and facing the bearing seats, tumbling or shot blasting, and anodising or powder coating. It gives good stiffness and strength, excellent surface detail, and cycle times of the order of a minute; against it are high die cost, porosity that limits fatigue performance in thin sections, and draft and section-thickness restrictions.

(2) Injection moulding in a glass-fibre-reinforced engineering thermoplastic. A 30 per cent glass-filled polyamide (PA66-GF30) or a filled polypropylene is moulded around brass or steel bearing inserts, sometimes as an insert-moulded assembly so that the bearing races are located in the mould. It gives the lowest piece cost at volume, integral colour requiring no finishing, excellent corrosion resistance, and the freedom to mould in the traction pins' bosses and the reflector mounts. Against it are lower stiffness and lower fatigue strength than metal, creep under sustained load, ultraviolet and temperature sensitivity, and a tool that must be multi-cavity and hardened to reach the volumes that justify it.

(3) CNC machining from wrought aluminium. The body is milled from 6061-T6 or 7075-T6 plate or extrusion on a three- or four-axis machining centre, with the bearing bores line-bored in the same setup. It gives full wrought mechanical properties with no porosity, the tightest tolerances, complete geometric freedom including undercuts, and negligible tooling cost, so it is the only viable route at low volume and the natural route for a premium or aftermarket product. Against it are long cycle times, high material removal and scrap, and a piece cost an order of magnitude above the moulded routes. A fourth route worth naming for completeness is the fabricated cage pedal — a stamped and welded steel or aluminium cage on a machined body — which dominated the market historically and survives at the lowest price points.

Part B — Factors governing the choice of process (6 marks)

The decision is driven by six families of factor. Production volume and production rate come first, because they determine whether a tooling investment can be amortised at all; this is the factor that most often settles the question by itself. Material and mechanical requirements follow: the pedal is a fatigue-critical component — ISO 4210-8 requires a pedal to survive of the order of one million cycles at an applied load near 1100 N — so the process must deliver the fatigue strength, and porosity, weld lines and fibre orientation are process attributes with direct structural consequences. Geometry, size and complexity govern feasibility: thin sections, undercuts, internal passages, draft, and the minimum radius the process can form. Tolerance and surface finish matter locally rather than globally — the bearing bores need a machining-grade tolerance and finish that no moulding process will hold, so the real question is not which process makes the part but which combination of primary process and secondary machining does. Cost structure — tooling, cycle time, material utilisation, secondary operations, scrap and rework — converts all of the above into money. Finally, lifecycle, supply-chain and sustainability factors: tooling lead time and its effect on time to market, supplier availability and location, recyclability at end of life, energy intensity of the process, and the ease of running product variants off the same tool.

Part C — A selection framework (6 marks)

The framework proposed has four stages: screen on the requirements the process must satisfy, rank the survivors on cost at the target volume, score them on the criteria cost does not capture, then test the answer for sensitivity to volume. Stages one and two are worked numerically below; stages three and four use the same weighted-matrix machinery as Question 1.

Given. Three candidate routes for the pedal body, with tooling cost $C_t$ and variable cost $c_v$ per pedal as follows: die casting, $C_t = 45\,000$ CAD and $c_v = 3.20$ CAD; injection moulding, $C_t = 60\,000$ CAD and $c_v = 1.60$ CAD; CNC machining, $C_t = 2\,500$ CAD and $c_v = 18.00$ CAD. The target market is a mass-market recreational bicycle, planned at $N = 60\,000$ pedals per year. The structural screen is ISO 4210-8: 1100 N applied at the pedal axle for $10^{6}$ cycles.

Find. Which routes survive the screen, the break-even volumes between them, the unit cost at the target volume, and the recommended route.

Approach. Apply the must-meet screen first, then model total cost as a straight line in volume, $C(N) = C_t + c_v N$, and find the crossings; the lowest line at the target volume is the cost-preferred route, after which the non-cost criteria are scored.

1. Screen on the must-meet requirements. The governing requirement is fatigue. Taking the 1100 N test load acting at an effective cantilever arm of 65 mm from the supported bearing, the bending moment at the critical section is $$M = FL = (1100)(0.065) = 71.5\ \text{N}\cdot\text{m}.$$ For the glass-filled polyamide, whose fatigue strength at $10^{6}$ cycles is of the order of 45 MPa, and with a factor of safety of 2.0 on a consumer product, the required section modulus is $$S = \frac{M\,n}{\sigma_f} = \frac{(71.5)(2.0)}{45\times10^{6}} = 3.18\times10^{-6}\ \text{m}^{3} = 3178\ \text{mm}^{3}.$$ That is achievable in a moulded body of the usual 100 mm by 70 mm platform envelope, so all three routes survive the screen for the recreational duty cycle. They would not all survive a competition or downhill duty cycle, where the test load and the impact requirement rise sharply and the moulded body is eliminated — which is exactly why the screen is stated in terms of the target market.
2. Model total cost and find the break-even volumes. With $C(N) = C_t + c_v N$, two routes break even where $$N^{*} = \frac{C_{t,1}-C_{t,2}}{c_{v,2}-c_{v,1}}.$$ Taking the pairs in turn, CNC machining against die casting breaks even at $N^{*} = (45\,000-2\,500)/(18.00-3.20) = 2872$ pedals; CNC machining against injection moulding at $N^{*} = (60\,000-2\,500)/(18.00-1.60) = 3507$; and die casting against injection moulding at $N^{*} = (60\,000-45\,000)/(3.20-1.60) = 9375$. The volume bands that follow are $$\boxed{\text{CNC below } 2872;\ \text{die casting } 2872\ \text{to } 9375;\ \text{injection moulding above } 9375}$$ pedals per year.
3. Evaluate at the target volume. At $N = 60\,000$ the total costs are 1 082 500 CAD for CNC machining, 237 000 CAD for die casting and 156 000 CAD for injection moulding, giving unit costs of 18.04, 3.95 and 2.60 CAD respectively. Injection moulding is 1.35 CAD per pedal cheaper than die casting, or 81 000 CAD a year — a difference far larger than the uncertainty in the estimates, so the cost ranking is decisive rather than marginal.
4. Score the criteria cost does not capture, then check sensitivity. Build the same weighted matrix as Question 1 over fatigue margin, stiffness and feel, corrosion and finish durability, tooling lead time, variant flexibility and recyclability, with weights agreed before rating. Then re-run the volume model at the pessimistic sales forecast: if the programme might realistically sell only 8000 pedals a year, that is below the 9375 break-even and die casting becomes the cheaper route, so the decision is sensitive to a forecast that is itself uncertain. The correct response is either to commit to the moulding tool only when the forecast is confirmed, or to start with a lower-cost single-cavity tool and add cavities as volume proves out.