Question 1 of 7: Redesigning a Product to Reduce Weight

Question 1: Redesigning a Product to Reduce Weight (40 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.

Product selected: the automobile — specifically a mid-size front-wheel-drive passenger car of 1,450 kg kerb mass, 8.6 L/100 km combined fuel consumption, built at 120,000 units per year. The automobile is chosen deliberately over the aircraft and the bicycle because it is the only one of the three in which mass drives a large downstream cost that the customer pays after the sale, so a weight reduction can be defended in money as well as in kilograms, and because its production volume is high enough to make the manufacturing consequences of a material change real rather than academic.

Part A — Three general ways to redesign a product to reduce weight (8 marks)

Weight is not a design variable in its own right. It is the consequence of a chain of decisions about what a part must do, what carries the load, and what the load-bearing material is. There are correspondingly only three general levers, and they act at three different levels of the design.

Lever 1 — substitute the material at equal function. Replace the incumbent material with one that delivers the same stiffness or the same strength at lower mass. The correct comparison is never density alone and never modulus alone: it is a material index, a combination of properties that follows from the loading mode and from which dimension is free to change. For a panel of fixed area whose thickness may be changed to hold bending stiffness, mass is minimised by maximising

while for a beam of free square section carrying the same duty the index becomes $E^{1/2}/\rho$, and for a strength-limited beam it becomes $\sigma_y^{2/3}/\rho$. Choosing the wrong index is the single commonest error in this lever, and it is not a small one: applying a beam exponent to a panel flatters the dense metals enough to reorder the shortlist.

Lever 2 — improve the efficiency of the shape and the load path. Hold the material and change where it sits. Material carries bending most efficiently when it is furthest from the neutral axis, so a solid section is almost always the wrong answer; hollow, ribbed and tailored sections raise the second moment of area far faster than they raise the cross-sectional area. At the assembly level, the same lever is topology optimisation and load-path rationalisation: route the load through the shortest triangulated path, remove material where the stress flux is low, and delete redundant structure that exists only because an earlier architecture put a joint in an awkward place.

Lever 3 — reduce the number of parts and let the system shrink around the saving. Function integration removes not only the deleted parts but their flanges, fasteners, sealing surfaces and assembly tolerances. More importantly, in any product whose subsystems are sized by the mass they must carry, accelerate, support or stop, a primary mass saving licenses a further secondary saving everywhere downstream. This is mass decompounding, and it is the lever most often left on the table, because it requires a designer to go back and re-specify subsystems that were already signed off.

The three levers are ordered by increasing organisational difficulty, not by increasing benefit. Lever 1 can be executed by one designer; Lever 2 needs analysis and manufacturing agreement; Lever 3 needs the whole programme to re-open decisions, and it is where the largest share of the total saving actually lives.

Part B — Applying the three levers to the automobile (8 marks)

Given. Baseline mid-size passenger car, kerb mass 1,450 kg, of which the body-in-white plus closures account for 340 kg, four cast-iron steering knuckles for 17.6 kg, and four seat structures for 84 kg. Baseline combined fuel consumption 8.6 L/100 km, design life 250,000 km, production volume 120,000 units per year. Candidate panel materials with modulus and density are listed in the figure below.

Find. The mass that each of the three levers removes from the critical components, and the vehicle mass that results once the secondary effects have been taken up.

Approach. Apply Lever 1 to the body panels through the panel index and convert the index ratio into a realisable mass; apply Lever 2 to a representative unsprung component through a section-efficiency calculation; apply Lever 3 by treating the secondary savings as a convergent geometric series driven by the primary saving.

1. Lever 1: rank the panel candidates on the correct index. For a panel of area $A$ and free thickness $t$ held to a bending stiffness $S \propto E t^{3}$, equal stiffness requires $E_1 t_1^{3}=E_2 t_2^{3}$, so the thickness ratio and the resulting mass ratio are $$\begin{aligned}\frac{t_2}{t_1}&=\left(\frac{E_1}{E_2}\right)^{1/3} \\ \frac{m_2}{m_1}&=\frac{\rho_2}{\rho_1}\left(\frac{E_1}{E_2}\right)^{1/3}\end{aligned}$$ Substituting mild steel ($E=210$ GPa, $\rho=7{,}850$ kg/m³) and aluminium 6111-T4 ($E=70$ GPa, $\rho=2{,}700$ kg/m³) gives a thickness ratio of $(210/70)^{1/3}=1.4422$ and a mass ratio of $$\frac{m_{\text{Al}}}{m_{\text{steel}}}=\frac{2700}{7850}\times 1.4422=\boxed{0.4961}$$ so the index promises a 50.4 per cent saving on the panels.
2. Discount the index result to a realisable saving. The index assumes the panel is free to thicken and that nothing else changes. In a real body-in-white it is not: crash-energy management fixes some sections, the joining flanges do not scale, self-piercing rivets and structural adhesive add back mass that spot welds did not, and formability limits force larger radii and locally thicker blanks. Programme experience puts the realised saving on an aluminium-intensive body at roughly 40 per cent rather than 50, so on a 340 kg body-in-white and closure set $$\Delta m_{\text{BIW}} = 0.40 \times 340 = \boxed{136.0\ \text{kg}}$$ The gap between 50.4 and 40 per cent is not a failure of the method; it is the difference between a screening index and an executed design, and quoting the index without the discount is the mistake to avoid.
3. Lever 2: replace a solid section with an efficient one at equal bending stiffness. Take a representative solid square member of side $a=60$ mm in the knuckle or subframe, for which $$\begin{aligned}I_{\text{solid}}&=\frac{a^{4}}{12}=1.080\times 10^{6}\ \text{mm}^{4} \\ A_{\text{solid}}&=3{,}600\ \text{mm}^{2}\end{aligned}$$ Replace it with a square tube of outer width $b$ and wall $t$, held to the same $I$ but constrained against local buckling by a slenderness cap $b/t \le 40$. With $t=b/40$, $$I_{\text{tube}}=\frac{b^{4}-(0.95b)^{4}}{12}=0.015458\,b^{4}$$ Setting this equal to $I_{\text{solid}}$ gives $b=91.43$ mm, $t=2.286$ mm, and a section area of $A_{\text{tube}}=0.0975\,b^{2}=815.0$ mm², so $$\frac{A_{\text{tube}}}{A_{\text{solid}}}=\boxed{0.226}$$ a 77.4 per cent mass saving from shape alone, with no change of material. Applied to the four cast-iron knuckles, a topology-optimised aluminium replacement takes each from 4.4 kg to 2.6 kg, so $\Delta m_{\text{knuckle}}=4\times 1.8=7.2$ kg. The absolute number is small; the point of the calculation is that shape efficiency beats material substitution per unit of engineering effort, and it should therefore be exhausted first.
4. Lever 3: integrate functions, then take the decompounding tail. Integrating the seat back frame, recliner brackets and side-impact reinforcement into two stamped-and-welded assemblies takes each seat structure from 21.0 kg to 16.5 kg, so $\Delta m_{\text{seat}}=4\times 4.5=18.0$ kg. Summing the primary savings, $$\Delta m_{\text{primary}}=136.0+7.2+18.0=161.2\ \text{kg}$$ Every kilogram of primary saving now permits a fraction $k$ of a kilogram of secondary saving in the systems sized by vehicle mass, and each of those savings permits a further $k$ of itself, so the total is the geometric series $$\Delta m_{\text{total}}=\Delta m_{\text{primary}}\bigl(1+k+k^{2}+\cdots\bigr)=\frac{\Delta m_{\text{primary}}}{1-k}$$ Taking $k=0.30$, which is the ordinary range when the powertrain is allowed to be re-sized, $$\Delta m_{\text{total}}=\frac{161.2}{1-0.30}=\boxed{230.3\ \text{kg}}$$ of which 69.1 kg is secondary: a smaller engine, smaller brake rotors, softer springs and dampers, a lighter driveline and a smaller fuel tank for the same range.
5. Convert the mass saving into the benefit the customer actually buys. With the powertrain re-sized, the fuel reduction value is about 0.65 L/100 km per 100 kg, so $$\Delta FC = 0.65\times\frac{230.3}{100}=1.497\ \text{L/100 km}$$ taking the vehicle from 8.6 to $\boxed{7.10\ \text{L/100 km}}$, a 17.4 per cent improvement. Over a 250,000 km life that is 3,742 L of fuel and, at 2.31 kg of carbon dioxide per litre, 8.64 tonnes of tailpipe emissions.

Part C — Impact of the Part B changes on the manufacturing process (8 marks)

Every one of the three levers reaches into the plant, and the aluminium body reaches furthest. In the press shop, 6111-T4 has roughly two-thirds of the uniform elongation of a drawing-quality steel, so draw depths must be reduced, corner and hem radii opened out, and blank holder pressure re-tuned; springback is larger and less repeatable, which means die compensation loops that steel dies did not need, and it is common to move the most severe panels to warm forming. Tonnage falls, but die development time and die cost rise.

In the body shop the change is structural rather than incremental. Resistance spot welding, which is the entire economic basis of a steel body, is not viable at volume on aluminium: the oxide layer and the high thermal and electrical conductivity destroy electrode life. The joining strategy becomes self-piercing rivets plus structural adhesive, with laser brazing on visible joints, and that in turn changes flange design, access requirements for the rivet C-frames, and the fixture strategy, because an adhesive joint has to be clamped while it cures rather than tacked and released. Where aluminium meets the remaining steel structure, the galvanic couple must be broken with an adhesive layer and coated fasteners, and that isolation becomes a controlled characteristic, not a detail.

The paint shop constrains the alloy choice rather than the other way round: the panels arrive in the T4 condition and gain their final strength from the paint bake, so the bake schedule and the alloy's ageing response are now coupled, and any change to the oven is a change to the body's strength. In materials handling, aluminium and steel scrap must be segregated to retain the value of the aluminium, which changes press-line scrap conveyors and the recycling contract.

The knuckle change is a process-selection decision in its own right, and it is worth doing explicitly rather than asserting.

Given. Two candidate routes for the aluminium knuckle: machined from a forged blank, tooling and setup $T_1$ = CAD 60,000, variable cost $u_1$ = CAD 41.00 per part; high-pressure die cast and finish machined, $T_2$ = CAD 480,000, $u_2$ = CAD 17.50 per part. Volume 120,000 parts per year.

Find. The break-even volume between the two routes, and which route the programme volume selects.

Approach. Model each route with the standard process-cost relation $c(n)=T/n+u$ and equate them.

1. Locate the break-even volume. Setting $c_1(n)=c_2(n)$, $$\frac{T_1}{n}+u_1=\frac{T_2}{n}+u_2 \Longrightarrow n^{*}=\frac{T_2-T_1}{u_1-u_2}=\frac{480{,}000-60{,}000}{41.00-17.50}=\boxed{17{,}872\ \text{parts}}$$
2. Evaluate both routes at the programme volume. At $n=120{,}000$ the forged route costs $60{,}000/120{,}000+41.00=41.50$ per part and the die-cast route costs $480{,}000/120{,}000+17.50=21.50$ per part, so the casting route is right by CAD 20.00 per part, or CAD 2.40 million per year. The programme volume is nearly seven times the break-even, which is what makes the decision robust rather than marginal — it would survive a halving of demand.

Two manufacturing consequences follow that the cost model does not show. First, the die-cast route commits CAD 480,000 of tooling long before the design is validated, which is precisely the exposure that Question 7 will describe as the cost of compressing phases. Second, a die-cast wall thinner than about 1.2 mm cannot be filled reliably, so the mass credited to the casting in the index calculation is only achievable if the optimised topology respects that floor — a constraint the material index cannot see.

Part D — Converting weight-reduction ideas into engineering specifications (8 marks)

A high-level idea such as "use aluminium closures" is not a specification, because nobody can pass or fail it. Converting ideas into specifications is a cascade with four disciplines: allocate, translate, make verifiable, and reserve.

Allocate. The vehicle-level target of 230.3 kg is divided into a mass budget that names an owner and a number for every subsystem: 136.0 kg to body and closures, 7.2 kg to unsprung corners, 18.0 kg to seating, 69.1 kg to the powertrain, brake, suspension and fuel-system owners who benefit from decompounding. A mass budget with no named owner is a wish; the budget line is the specification's parent.

Translate. Each budget line becomes a part-level requirement expressed in the units the part is designed in, derived from the function the part must still perform. The door outer panel is the clean example.

Given. Steel door outer, thickness 0.70 mm, swept area 0.85 m², $\rho_{\text{steel}}=7{,}850$ kg/m³; aluminium replacement in 6111-T4, $E$ ratio as in Part B, four doors.

Find. The aluminium thickness that holds panel bending stiffness, the resulting part mass, and the mass specification to be written on the drawing.

1. Set the thickness from the stiffness requirement, not from the mass target. Equal panel bending stiffness requires $$t_{\text{Al}}=t_{\text{steel}}\left(\frac{E_{\text{steel}}}{E_{\text{Al}}}\right)^{1/3}=0.70\times 1.4422=1.01\ \text{mm}$$ so the drawing calls up 1.00 mm nominal, which is a rollable, formable and commercially stocked gauge.
2. Convert the gauge to the mass line in the budget. The steel panel weighs $0.85\times 0.00070\times 7850=4.671$ kg and the aluminium panel $0.85\times 0.00101\times 2700=2.318$ kg, a saving of 2.353 kg per panel and $$\Delta m_{\text{doors}}=4\times 2.353=\boxed{9.41\ \text{kg}}$$ against the 136.0 kg body budget. Only now does the idea become a specification: door outer panel, 6111-T4, 1.00 mm nominal, mass 2.32 kg maximum, panel stiffness not less than the carry-over steel panel measured by the standard centre-push test, dent resistance not less than the carry-over panel at the same test energy.

Make verifiable. Every specification is written with a value, a tolerance and a verification method drawn from the four standard classes — test, analysis, inspection or demonstration. "Light" becomes "2.32 kg maximum, verified by inspection of the first 30 production parts". "Stiff enough" becomes "not less than 42 Hz first body bending mode, verified by modal test on the second prototype body". Regulatory limits enter the same cascade as inviolable lines: static roof-crush strength-to-weight ratio not less than 4.0 to CMVSS 216, and torsional stiffness not below 22 kN·m/deg so that the weight saving does not quietly buy back a durability or noise problem.

Reserve. Mass grows through a programme; it never shrinks by accident. The cascade therefore carries an explicit contingency — typically 5 per cent of the target, here about 11 kg — held at vehicle level and released by the chief engineer, not distributed to the subsystems, where it would be spent immediately.

Part E — Establishing priorities when not all specifications can be met (8 marks)

The correct method is not to negotiate all the specifications at once. It is to sort them into classes that are traded differently, and then to trade only within the class that permits it.

Class 1, inviolable. Regulatory and safety requirements — CMVSS crash and roof-crush performance, emissions certification, functional-safety obligations. These are not prioritised against anything; a design that misses them is not a candidate design. Anything that competes with them loses by definition.

Class 2, contractual. Commitments already made to a customer, a fleet buyer or a regulator through a declared figure. These can be renegotiated, but only outside the engineering team and with a known commercial cost, so they behave like constraints during design.

Class 3, tradeable targets. Mass, cost, performance, refinement, and timing. These are traded against each other with an explicit weighted decision matrix in which the weights are agreed before the ratings are collected, because agreeing weights after seeing scores is how a decision matrix becomes a justification. The matrix is then tested for sensitivity: if a ten-point change in one weight inverts the ranking, the decision rests on the weight and not on the engineering, and more information is worth buying.

Two hard economic gates decide most of the Class 3 arguments on a weight programme, and both are worth computing rather than debating.

1. Gate 1: the cost of saved mass. The programme sets the maximum it will pay for a kilogram, here CAD 6.00 per kilogram saved. The aluminium body costs $204\times 4.20 = 856.80$ in material where the steel body cost $340\times 1.30 = 442.00$ (both CAD), so the premium is CAD 414.80 for 136.0 kg, that is $$\frac{414.80}{136.0}=\boxed{\text{CAD } 3.05\ \text{per kg saved}}$$ which passes the gate. Carbon-fibre closures at a realised 45 per cent saving cost $187\times 32 = 5{,}984$ CAD for 153.0 kg, that is CAD 36.22 per kilogram saved — six times the gate. The carbon option is refused, and refused on a number, even though it ranked first on the material index in Part B. This is the disciplined use of a screening index: it proposes candidates, it does not select them.
2. Gate 2: does the shortfall actually break a requirement? Suppose the programme can only realise 205 kg rather than 230.3 kg. The regulatory fuel-consumption target is 7.20 L/100 km, so the mass reduction required is $$\Delta m_{\text{req}}=\frac{8.6-7.20}{0.65}\times 100=215.4\ \text{kg}$$ and 205 kg misses it by 10.4 kg. That reframes the whole priority conversation: the argument is not about 25 kg of ambition, it is about the last 10.4 kg that separates a compliant vehicle from a non-compliant one. Everything above 215.4 kg is a Class 3 trade; everything below it has migrated into Class 1.

The remaining priority rules follow from those two calculations. Prioritise against the discontinuities in the cost and compliance functions rather than against the smooth targets in the specification table, because a target missed by a kilogram in the middle of a range costs nothing and a target missed by a kilogram at a compliance cliff costs the programme. Buy information before you buy mass: an extra analysis loop is cheaper than a material change. And record every accepted shortfall as a deviation with a named approver and a re-visit date, so that a decision made under time pressure in one phase does not silently become the specification in the next.