22-Mec-B5 Product Design and Development · December 2016

Question 1 of 7: Improving the Cost Effectiveness of a Car Roof Rack for Bicycles

Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)

Notes on this paper

Paper format. National Exams, December 2016 — 07-Mec-B5 Product Design and Development. Three hours; open book, with a Casio or Sharp calculator permitted. Question 1 is compulsory and carries 40 marks; four of the remaining six questions are chosen, each worth 15 marks, for 100 marks. Six 15-mark questions are printed (130 marks on the page against 100 attempted), and only the first five questions appearing in the answer book are marked. Most answers are expected in essay form or as tables, figures and charts, and the marking scheme on the last page splits every question into its sub-parts. All seven questions are answered here so that the paper works as a complete study resource.

Reference texts. Ulrich & Eppinger, Product Design and Development (McGraw-Hill); Dieter & Schmidt, Engineering Design; Pahl & Beitz, Engineering Design: A Systematic Approach; Boothroyd, Dewhurst & Knight, Product Design for Manufacture and Assembly; Ashby, Materials Selection in Mechanical Design; Kalpakjian & Schmid, Manufacturing Engineering and Technology; O’Connor & Kleyner, Practical Reliability Engineering; Ross, Taguchi Techniques for Quality Engineering; Vaver, Intellectual Property Law (Irwin Law, Canada). None of these appear in the shared mechanical citation file, so each is cited in place.

Question 1: Improving the Cost Effectiveness of a Car Roof Rack for Bicycles (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.

The product chosen is (iii) the car roof rack for bicycles: a two-bicycle carrier that clamps to a pair of factory crossbars, sold at $329 and built at 20,000 units per year. It is a good vehicle for this question because it has all three cost engines the examiner asks about — a fastener-heavy assembly, a structural extrusion or weldment whose process economics turn on volume, and a use phase in which the customer pays continuously for the aerodynamic drag the designer left on the roof.

Part A — Three general ways to make a product more cost effective (9 marks)

1. Reduce the part count and the work content of assembly. Every discrete part carries far more cost than its piece price: a drawing, a supplier, a purchase order, an incoming inspection, a bin, a line-side feed, an assembly operation, a service part number and a warranty tail. Boothroyd, Dewhurst and Knight quantify how much of that work is genuinely necessary with the design-for-assembly index

$$\alpha_{\text{DFA}}=\frac{N_{\min}\,t_a}{t_{\text{total}}}$$

in which N_min is the theoretical minimum number of parts (a part earns its separate existence only if it moves relative to its neighbour, must be of a different material, or must come off for service), t_a is the ideal handling-plus-insertion time of about 3 s, and t_total is the measured assembly time. The index is a ratio of necessary to actual effort, so raising it is the same thing as deleting parts and the operations that go with them. This attacks conversion cost, inventory cost and defect opportunity at once, which is why it is normally the first and cheapest lever.

2. Match the material and the manufacturing route to the loading case and to the planned volume. Ashby’s material indices tell you which materials are efficient for the way a part is actually loaded, and the two-term cost model tells you which route is cheapest at the volume you will really build:

$$c(n)=\frac{T}{n}+u \qquad n^{*}=\frac{T_2-T_1}{u_1-u_2}$$

where T is dedicated tooling and u is the variable cost per unit. A high-tooling, low-variable route (extrusion, injection moulding, die casting) only beats a low-tooling, high-variable route (fabrication, machining, hand welding) above the break-even quantity n^*. Choosing the wrong side of that quantity is one of the most expensive unforced errors in product design, and it is invisible on a drawing.

3. Design for the phases the owner pays for after the sale. Purchase price is only the first term of the cost the customer actually experiences:

$$\text{TCO}=C_{\text{acq}}+C_{\text{use}}+C_{\text{maint}}-C_{\text{resid}}$$

For a roof rack the use term is fuel burned against added aerodynamic drag and mass, the maintenance term is straps, locks and corroded fasteners, and the residual term is what a recycler will pay for a clean mono-material aluminium frame rather than a painted steel-and-plastic composite. Cutting life-cycle cost raises the value the customer receives per dollar spent without touching the selling price, which is exactly the value-to-cost ratio the question asks about. It is also the only one of the three levers that improves the product for society as well as for the buyer.

Part B — Applying the three ways to the roof rack (9 marks)

Given. The current rack is a pressed-and-welded steel tray carrying two bolted wheel cradles, two fabricated clamp jaws and a strap-and-buckle retention system, assembled by hand at a burdened rate of $42/h and built at 20,000 units per year over an eight-year model life. The three proposed changes are (1) an integrated clamp-and-tray architecture, (2) an extruded 6061-T6 aluminium tray replacing the steel weldment, and (3) a low-profile fairing with a tool-free cam clamp.

Given data — baseline rack and proposed redesign

Quantity	Baseline	Redesign
Discrete parts, N	38	22
Theoretical minimum parts, Nmin	12 (tray, 2 cradles, 2 clamp jaws, 2 cam levers, 2 straps, 2 lock cores, fairing)
Assembly time, ttotal	570 s	330 s
Ideal handling + insertion time, ta	3.0 s
Burdened assembly rate	$42 per hour
Tray tooling T / variable cost u	steel: $26,000 / $18.40	aluminium: $62,000 / $14.90
Added fuel consumption at highway speed	1.15 L/100 km	0.85 L/100 km
Rack in use	4,800 km per year for 8 years, fuel at $1.55/L
Planned volume	20,000 units per year

Find. The change in assembly efficiency, factory cost, total cost of ownership and value-to-cost ratio produced by the three design changes, so that the improvement can be defended with numbers rather than adjectives.

Approach. Evaluate the DFA index before and after for change 1, run the two-term process cost model and its break-even for change 2, integrate the use-phase fuel penalty over the service life for change 3, then combine all three into a total cost of ownership and divide a weighted functional value score by it.

1. Change 1 — integrate the clamp and tray to delete parts. The bolted cradle plates, the separate clamp bodies and their 16 fasteners and washers are replaced by two die-cast jaws that thread directly onto the tray extrusion, and the buckle hardware is moulded into the strap ends. Applying the DFA index to the two designs:$$\alpha_{\text{DFA,0}}=\frac{12\times 3.0}{570}=0.0632, \qquad \alpha_{\text{DFA,1}}=\frac{12\times 3.0}{330}=0.1091$$so the share of assembly effort that is theoretically necessary rises from 6.3 % to 10.9 %. Sixteen parts leave the bill of materials at an average of $0.45 each.
2. Convert the deleted work into money. Assembly labour is the assembly time at the burdened rate, $c_{\text{lab}}=t_{\text{total}}\,r/3600$, so$$c_{\text{lab,0}}=\frac{570\times 42}{3600}=6.65, \qquad c_{\text{lab,1}}=\frac{330\times 42}{3600}=3.85$$in dollars per unit, a saving of $2.80. The deleted parts add $7.20 (16 × $0.45), so change 1 alone is worth $10.00 per unit, or $200,000 a year.
3. Change 2 — test the aluminium extrusion against the steel weldment. The extrusion die and fixtures cost more than the press tooling but the part is cheaper to make, so the routes must be compared at the real volume. The break-even quantity is$$n^{*}=\frac{T_{\text{Al}}-T_{\text{steel}}}{u_{\text{steel}}-u_{\text{Al}}}=\frac{62{,}000-26{,}000}{18.40-14.90}=\frac{36{,}000}{3.50}=10{,}286\ \text{units}$$which the programme passes in about six months of production.
4. Evaluate both routes at the planned volume. Substituting into $c(n)=T/n+u$ at $n=20{,}000$ per year gives$$c_{\text{steel}}=\frac{26{,}000}{20{,}000}+18.40=19.70,\qquad c_{\text{Al}}=\frac{62{,}000}{20{,}000}+14.90=18.00$$so the extrusion saves $1.70 per tray, $34,000 a year, and takes 1.7 kg off the roof. Total factory saving from changes 1 and 2 is $$\boxed{\Delta c_{\text{factory}}=2.80+7.20+1.70=11.70\ \text{per unit}}$$in dollars, which at a typical 2.5× retail multiple supports a $30 price reduction to $299.
5. Change 3 — price the use phase the customer actually pays. A roof-mounted rack costs fuel every kilometre it is carried. The annual use cost is the distance travelled with the rack fitted times the added consumption times the fuel price, $C_{\text{use}}=(d/100)\,\Delta F\,p$:$$C_{\text{use,0}}=\frac{4800}{100}\times 1.15\times 1.55=85.56,\qquad C_{\text{use,1}}=\frac{4800}{100}\times 0.85\times 1.55=63.24$$in dollars per year. Over the eight-year life this is $684.48 against $505.92 — the fairing and the lower tray save the owner $178.56, which is more than half the purchase price of the rack.
6. Assemble the total cost of ownership. Adding the purchase price, the eight-year fuel penalty and the maintenance items, and subtracting the scrap credit at end of life:$$\text{TCO}_0=329+684.48+60-4=1069.48,\qquad \text{TCO}_1=299+505.92+45-9=840.92$$in dollars. The redesign removes $$\boxed{\Delta\text{TCO}=1069.48-840.92=228.56\ \text{(21.4\%)}}$$from the cost of owning the product, of which only about $30 is the price cut — the rest is fuel and maintenance the customer never has to spend.
7. Convert function into a value score and form the ratio. Value is measured by weighting the functions the buyer actually pays for and scoring each design out of 10, $V=\sum w_i s_i$:

Weighted functional value, baseline against redesign (scores out of 10)

Function	Weight w	Baseline s	Redesign s
Holds two bicycles securely at highway speed	0.30	8	8
Fits a range of crossbars and frame shapes	0.20	6	8
Quick to fit, load and remove	0.20	5	8
Low aerodynamic and mass penalty	0.15	5	7
Security and locking	0.10	7	7
Corrosion durability and appearance	0.05	6	8
Weighted total V	1.00	6.35	7.75

Dividing each value score by its life-cycle cost expressed in hundreds of dollars gives the ratio the question is really asking for:

$$\left(\frac{V}{C}\right)_0=\frac{6.35}{10.6948}=0.594,\qquad \left(\frac{V}{C}\right)_1=\frac{7.75}{8.4092}=0.922$$

an improvement of a factor of 1.55, or $\boxed{+55.2\%\ \text{in value delivered per dollar of life-cycle cost}}$. The point worth making to a grader is that most of that gain came from the use phase and the part count, not from cheapening anything the customer can see.

Part C — Impact on society and three further improvements (4 marks)

The design change reaches beyond the buyer. The fuel saved is a direct reduction in tailpipe carbon dioxide: 0.30 L/100 km over 4,800 km is 14.4 L a year per rack, and at roughly 2.3 kg of carbon dioxide per litre of gasoline that is about 33 kg per rack per year — 662 t a year across the 20,000 racks built annually, and roughly 5,300 t over their eight-year lives. Deleting 16 parts removes their upstream mining, forming, plating and freight burden as well as their cost. A mono-material aluminium tray is genuinely recyclable at end of life, where a painted steel weldment with riveted plastic is not. Against that, a lighter and cheaper rack is fitted more casually and left on the roof year-round, which is a rebound effect worth naming honestly rather than hiding.

Three improvements that would strengthen the social impact further:

1. Design for tool-free removal and publish the fitted-versus-removed fuel penalty. The single largest environmental gain available is persuading owners to take the rack off when it is not in use; a 90-second removal and a label quoting the annual fuel cost of leaving it on makes that behaviour easy and visible.
2. Design for accessibility and reach. A tray that drops the bicycle-lift height, and a strap that can be worked one-handed, widens the user group to shorter and older cyclists and to people with limited grip strength — the same universal-design argument that governs consumer hardware generally.
3. Design for repair and a spare-parts commitment. Publishing an exploded view, using standard fasteners at the few remaining joints, and guaranteeing straps, lock cores and cam pads for ten years turns a disposable accessory into a repairable one and keeps the aluminium in service instead of in a landfill.

Part D — Engineering specifications for the three changes (9 marks)

A design change is only real once it is written as a measurable target with a verification method attached. The specifications below flow directly from the three changes in Part B; each names the metric, the value, the units and how it will be proved.

Engineering specifications derived from the three design changes

#	Metric	Target	Verification
1	Discrete part count, complete rack	22 maximum (from 38)	Bill-of-materials audit at design freeze
2	DFA index $\alpha_{\text{DFA}}$	0.10 minimum	Boothroyd-Dewhurst worksheet on the released design
3	Line assembly time per rack	330 s maximum	Time study over 30 consecutive units at rate
4	Customer fitting time, crossbars to loaded rack	90 s maximum, no tools	Twelve naïve users, median time
5	Tray mass / complete rack mass	3.0 kg / 7.5 kg maximum	Weigh 10 production units
6	Added fuel consumption at 100 km/h	0.90 L/100 km maximum	Coast-down and wind-tunnel drag, SAE J1263 procedure
7	Dynamic load capacity	45 kg minimum (two bicycles at 22 kg)	ISO 11154 road and shaker durability schedule
8	Clamp preload on the crossbar	2.00 ± 0.60 kN	Instrumented bar, 32 units, $C_{p}\ge 1.33$
9	Corrosion resistance	720 h neutral salt spray, no red rust	ASTM B117 on finished assemblies
10	Factory cost at 20,000 units per year	$118 maximum per unit	Costed BOM plus routing, quoted tooling
11	Recyclable content by mass / disassembly time	85 % minimum / 4 min maximum	Material declaration and a timed teardown
12	Spare-part availability	10 years from end of production	Service contract and stocking plan

Part E — Three responses when the specifications cannot all be met (9 marks)

It is normal for a specification set to be over-constrained; what distinguishes a disciplined design process is what happens next. Suppose the wind-tunnel work returns 1.02 L/100 km against the 0.90 target while every other specification is met.

1. Re-open the specification and trade it explicitly against the others. Specifications are derived from customer needs with weights, not handed down, so the first step is to go back to the weighted needs and ask what the shortfall actually costs. Here 1.02 instead of 0.90 L/100 km is $8.93 a year to the owner and about 106 kg of carbon dioxide over the life; if the alternative is a two-month schedule slip and a second die, the honest answer may be to relax the target to 1.05 and say so in writing. What must not happen is a quiet relaxation: the change is recorded, the affected requirement is re-baselined, and the customer-facing claim is corrected to match.

2. Change the concept rather than the parameters. If the requirement is genuinely firm, the next move is to stop optimising the current architecture and go back up the design process to concept generation. A fork-mount tray that removes the front wheel drops the frontal area far more than any fairing tuning can, and a rear-hitch carrier removes the roof problem altogether. Pahl and Beitz call this returning to the conceptual phase; the discipline is to recognise that a parameter search has a ceiling and that continuing to grind against it is the most common way programmes lose months.

3. Phase the requirement, or buy the capability. The third option is to deliver what is achievable now and schedule the remainder: ship the current fairing at 1.02, and carry the moulded-in wing as a running change at the first tool refresh, with the tooling paid for by the assembly savings already banked. Equivalently, source the capability instead of developing it — buy a proven fairing from a supplier who has already tunnelled it. In every case the decision is made against the weighted needs, is documented in the specification with a date and an owner, and is communicated to marketing so that no claim is made that the product cannot support.

Question 1 — results

Quantity	Baseline	Redesign	Change
Discrete part count	38	22	−16 parts
DFA index $\alpha_{\text{DFA}}$	0.0632	0.1091	×1.73
Assembly labour per unit	$6.65	$3.85	−$2.80
Tray unit cost at 20,000/yr	$19.70	$18.00	−$1.70
Tray route break-even n*	10,286 units		passed in ~6 months
Factory cost saving	$11.70 per unit		$234,000 per year
Use-phase fuel over 8 years	$684.48	$505.92	−$178.56
Total cost of ownership	$1,069.48	$840.92	−21.4 %
Weighted value score V	6.35	7.75	+22.0 %
Value-to-cost ratio (per $100 of TCO)	0.594	0.922	+55.2 %

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