Question 7 of 7: Material Selection for a Computer Case

Question 7: Material Selection for a Computer Case (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.

Part A — Three candidate materials and their challenges (3 marks)

1. Cold-rolled steel sheet, electrogalvanised (SECC). This is the incumbent for desktop and server chassis. It is stiff, strong, cheap per kilogram, inherently conductive so it forms an electromagnetic enclosure without any added treatment, and inherently a fire enclosure. The challenges are mass — roughly three times the density of aluminium, so a full tower is heavy to ship and to carry; corrosion, which requires the zinc coating and means every cut and pierced edge is an unprotected edge; sharp edges and burrs from blanking and piercing, which are a genuine injury hazard on a consumer product and drive a deburring or hemming operation; springback and formability limits on tight bends; and high tooling cost for the progressive dies, which commits the design to volume.

2. Injection-moulded polymer, flame-retardant PC/ABS. The standard choice for consumer-facing enclosures and bezels. It is light, needs no finishing to look good, and can carry snap-fits, standoffs, light pipes and ribs moulded in a single shot, so it collapses part count. The challenges are more numerous than the other two. Its modulus is roughly two per cent of steel’s, so the panel must be much thicker and heavily ribbed to be stiff enough not to drum against the fan noise. It is an insulator, so it provides no EMI shielding at all and must be given a conductive coating — vacuum metallising or conductive paint — which is an added process, an added cost, and a scrap risk. Fire performance requires a flame-retardant grade certified to UL 94 V-0, and the halogenated retardants that do this most cheaply are under regulatory pressure in Canada and the EU. Add the high tool cost and long lead time, the heat-deflection limit near a power supply, warpage and sink marks, and yellowing under ultraviolet exposure.

3. Aluminium alloy, 6063 extrusion or 5052 sheet (or ADC12 die casting). The premium choice, and the standard one where the product is carried. It is about a third the density of steel, conductive so it shields, an excellent thermal conductor so the chassis can serve as a heat spreader, corrosion-resistant, anodisable to a high-quality finish, and highly recyclable. The challenges are cost per kilogram, roughly three times that of steel; a modulus about a third of steel’s, so sections must be thicker for the same panel stiffness; poor thread performance, so threaded holes need inserts or self-tapping screws risk galling and stripping; anodising as an additional process with its own effluent handling; porosity in die castings, which limits their use where a sealing or structural face is required; and a high primary embodied energy, which recycling mitigates but does not eliminate.

Part B — How the material choice impacts the final use (3 marks)

The enclosure of a computer is not a cosmetic cover; it performs at least five functions in service, and the material sets the level of each. Mass and portability follow directly from density and from the thickness the modulus demands, and they determine whether the product can be carried, shipped economically, or wall-mounted. Stiffness governs acoustics and mechanical integrity: a floppy panel resonates with fan and drive excitation, so a low-modulus material must be ribbed or damped or the product will be measurably noisier, and it also determines whether the chassis protects the boards during shipping and handling. Thermal behaviour depends on conductivity: an aluminium chassis can be part of the heat path, spreading heat from a component to the outside surface and reducing or eliminating a fan, whereas a polymer case is a thermal insulator and forces all heat management onto forced convection. Electromagnetic compatibility is the constraint that most often decides the question, because a computer must meet the emissions limits of ISED ICES-003 in Canada and the equivalent FCC Part 15 Class B in the United States, and a conductive continuous enclosure with controlled apertures is the simplest way to get there — which is why a polymer case must be metallised and why a case that is nominally metal still fails if its seams and vents are wrong. Safety and regulatory performance follow: IEC 62368-1 requires a fire enclosure of defined performance, and metals satisfy it inherently while polymers must be qualified. And finally the material sets the perceived quality, the surface durability, the grounding path, and the end-of-life route — a mono-material steel or aluminium chassis is straightforwardly recyclable, whereas a metallised, flame-retardant polymer with moulded-in inserts is close to unrecyclable in practice.

Part C — How the material choice impacts the manufacturing process (3 marks)

Material and process are not independently selectable; choosing one narrows the other to a small family, and with it the geometry, the tooling investment, the joining method, the finishing route and the economic volume.

Steel sheet routes to blanking, piercing, bending and drawing on a progressive die, joined by spot welding, riveting or self-clinching fasteners, and finished by powder coating or by relying on the zinc. The tooling is expensive and the cycle time is very short, so the unit cost is low but only at volume; the design must respect minimum bend radii, the bend-relief and springback rules, and a minimum flange length, and it must plan the deburring of every cut edge.

Polymer routes to injection moulding, which carries the highest tool cost of the three and a lead time of months, but the lowest incremental cost for complexity — features that would be separate parts in steel are free in a moulding, which is why the polymer route usually wins on assembly cost even when it loses on material cost. It imposes its own geometric rules absolutely: draft on every wall, uniform wall thickness to avoid sink and warpage, generous radii, ribs no more than about 60 per cent of the wall thickness, and no undercut that cannot be released or bought with a side action. It then adds the metallising or painting operation the other two do not need.

Aluminium splits. Extrusion plus CNC machining has very low tooling cost and a lead time of weeks, so it suits low volumes and premium products, but the machining time makes the unit cost high and roughly volume-independent. Die casting inverts that, with high tool cost and low unit cost, and imposes draft, uniform wall and porosity constraints similar in kind to moulding. Joining moves to threaded inserts or self-tapping screws because aluminium threads poorly, and anodising is a batch chemical process with its own fixturing and effluent requirements.

The general statement is that the material fixes the shape of the cost curve, not just its level: steel and moulding are high-fixed-cost, low-variable-cost routes, while extrusion and machining are low-fixed, high-variable. Which is cheapest is therefore a question about volume, and it is answered quantitatively in Part D.

Part D — A material-selection framework, applied (6 marks)

The framework used is Ashby’s four-step method — translate, screen, rank, document — extended with a process-economics step, because for an enclosure the manufacturing route dominates the decision as much as the material property does.

Given. A mid-tower desktop computer case, produced at 200,000 units per year, must enclose the electronics, hold the panel deflection under a 100 N hand load to 1 mm, provide at least 40 dB of shielding at 1 GHz, satisfy the fire-enclosure requirement of IEC 62368-1, and survive 60 °C internal air. Candidate properties and costs are tabulated below.

Find. The material and process route that minimises unit cost at the stated volume while satisfying the constraints, and the volume at which that answer changes.

1. Translate the requirement into function, constraints, objective and free variable. The function is a panel of specified stiffness; the constraints are the shielding, fire, temperature and dimensional requirements; the objective is minimum cost, with mass as a secondary objective; the free variable is the panel thickness. The idealisation is the single most consequential decision in the whole framework, and it must be stated explicitly: the side of a computer case is a panel of fixed area and free thickness, not a beam of free section.
2. Screen on the attribute limits. Anything that cannot meet a constraint is removed before ranking, whatever its index. Unfilled and non-flame-retardant polymers fail the fire-enclosure requirement outright; any non-conductive material fails the 40 dB shielding requirement unless a conductive coating is added, which is why the PC/ABS route in the table carries the coating in its unit cost rather than being screened out; and materials with a heat-deflection temperature below about 90 °C fail the thermal constraint. Screening is not ranking: a material that fails a constraint is not merely worse, it is ineligible.
3. Rank on the material index for the idealisation chosen. For a panel of given bending stiffness, fixed area and free thickness, minimising mass gives the index $M_1 = E^{1/3}/\rho$; the derivation is that the stiffness of a panel goes as $Et^3$, so the thickness needed varies as $E^{-1/3}$ and the mass as $\rho E^{-1/3}$. Evaluating with $E$ in GPa and $\rho$ in Mg/m$^3$: $$\begin{aligned} M_1(\text{steel}) &= \frac{210^{1/3}}{7.85} = \frac{5.94}{7.85} = 0.757 \\ M_1(\text{Al}) &= \frac{69^{1/3}}{2.70} = \frac{4.10}{2.70} = 1.519 \\ M_1(\text{PC/ABS}) &= \frac{2.4^{1/3}}{1.05} = \frac{1.34}{1.05} = 1.275 \\ M_1(\text{Mg}) &= \frac{45^{1/3}}{1.81} = \frac{3.56}{1.81} = \boxed{1.965} \end{aligned}$$ so on a mass basis the order is magnesium, then aluminium, then the polymer, and steel is last by a wide margin.
4. Check the idealisation, because the exponent decides the answer. Had the panel been idealised as a beam of free section, the index would be $M_2 = E^{1/2}/\rho$, giving 1.846 for steel, 3.077 for aluminium, 1.475 for PC/ABS and 3.706 for magnesium. The polymer and the steel change places: the polymer leads steel comfortably on the panel index and trails it on the beam index, because the higher exponent rewards stiffness more heavily and the polymer’s modulus is two orders of magnitude down. Using the beam exponent on a panel would therefore delete the polymer from the shortlist and put the wrong material into the cost comparison — which is why the idealisation is stated in Step 1 and not assumed.
5. Re-rank against the actual objective, which is cost and not mass. Dividing the mass index by the material price gives stiffness per dollar for the same panel, $M_3 = E^{1/3}/(\rho\, C_m)$: $$\begin{aligned} M_3(\text{steel}) &= \frac{0.757}{1.10} = \boxed{0.688} \\ M_3(\text{Al}) &= \frac{1.519}{3.50} = 0.434 \\ M_3(\text{PC/ABS}) &= \frac{1.275}{3.20} = 0.399 \end{aligned}$$ and the ranking inverts completely: steel is the cheapest way to buy panel stiffness, by more than half again over its nearest rival. The two rankings disagreeing is the whole content of the selection problem — it means the answer depends entirely on which objective the product is actually being designed to, and for a desktop tower that objective is cost, not mass.
6. Add the process economics, since the route dominates at this volume. Material price alone omits tooling and conversion. With unit cost $c(n) = T/n + u$ evaluated at $n = 200{,}000$: $$\begin{aligned} c_{\text{steel}} &= \frac{85{,}000}{200{,}000} + 4.20 = 4.63 \\ c_{\text{PC/ABS}} &= \frac{180{,}000}{200{,}000} + 3.55 = 4.45 \\ c_{\text{Al}} &= \frac{12{,}000}{200{,}000} + 16.00 = 16.06 \end{aligned}$$ in CAD per unit. Aluminium is eliminated on cost at this volume — the machining time is the whole of its unit cost and volume does not help it. Steel and the coated polymer are within four per cent of one another, which is inside the error of a should-cost model at this stage.
7. Find the volume at which the two survivors change places. Equating the two cost lines and solving for the crossover, $$n^* = \frac{T_{PC/ABS} - T_{steel}}{u_{steel} - u_{PC/ABS}} = \frac{180{,}000 - 85{,}000}{4.20 - 3.55} = \frac{95{,}000}{0.65} = \boxed{146{,}000\ \text{units per year}}$$ so steel is cheaper below about 146,000 units a year and the polymer above it. The programme volume of 200,000 sits only a third above the crossover, which means the cost advantage of the polymer is not robust: a twenty per cent volume shortfall or a small rise in the coating cost erases it entirely. Note also how much of that crossover the conductive coating is responsible for — without it the polymer’s unit cost would be 2.60 and the crossover would fall to 59,400 units.
8. Select, and document the reasoning and its sensitivity. Select electrogalvanised cold-rolled steel for the chassis and structural panels, with a moulded PC/ABS front bezel where appearance and feature integration matter and neither shielding nor fire performance is at stake. Steel wins the cost index outright, is within four per cent of the polymer on delivered unit cost at a volume where that gap is inside the modelling error, and — the decisive point — satisfies the shielding and fire constraints inherently rather than through a coating operation that carries its own yield risk and its own regulatory exposure on flame retardants. The mass penalty is real and is accepted because a desktop tower is not carried. The sensitivity is stated for the record: if the product were portable, mass would become the objective, the ranking of Step 3 would govern, and aluminium or magnesium would win; and if the volume were to exceed roughly 300,000 units with a proven coating process, the polymer route would become the cost leader.