Question 1 of 7: The design process applied to a CNC machining centre

Question 1: The design process applied to a CNC machining centre (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 machine tool — specifically a three-axis vertical machining centre of about 15 kW spindle power, 800 × 500 × 500 mm travels and roughly 2.4 × 2.6 m floor plan, sold to Canadian job shops and small production shops. It is chosen because its user is a business rather than a consumer, which makes “value” something that can be written down as an equation instead of asserted, and because a machine tool is a capital good whose societal footprint is dominated by what it consumes and wastes over an eight-year life rather than by what it costs to build.

Part A — Establishing value in the market place (6 marks)

Value for a capital good is not the purchase price and it is not a list of features. It is what the buyer earns, or stops losing, per dollar of ownership. The method has four steps, and each one is a distinct piece of field work rather than an opinion.

Step 1 — identify who the end user actually is. For this machine there are three: the shop owner who signs the capital request, the programmer or setter who lives with the control, and the operator who loads parts. They value different things, and a design that pleases only the first is the standard way a machine tool loses a market.

Step 2 — gather needs directly and turn them into metrics. Following Ulrich and Eppinger, interview and observe in about a dozen shops, record raw need statements, organise them into a hierarchy, have customers rate their importance, and only then attach a measurable metric with a unit to each need. “It should not waste my day” becomes setup time per job, minutes; “it should not scrap my material” becomes scrap fraction, per cent of parts; “it should not eat my hydro bill” becomes average electrical demand over a representative cycle, kilowatts.

Step 3 — benchmark competitors against the same metrics so the target specification is set relative to what the market already offers, not relative to the previous internal model.

Step 4 — express value as a single economic figure of merit. For a machine tool the right one is the cost per good part: everything the machine costs the shop in a year, divided by the number of saleable parts it makes in that year. It captures purchase price, energy, maintenance, wasted material and lost spindle hours in one number, and it is the number a shop owner can check against the invoice book.

Given. A representative shop runs the machine 3,000 spindle hours a year over an eight-year life, making 12,000 parts from 4.6 kg aluminium billets across 420 job set-ups, and bills work at 95 CAD per spindle hour.

Find. The baseline cost per good part, to serve as the datum against which every design change in parts B to F is judged.

1. Annualise the capital. Straight-line over the life, $C/L = 180{,}000/8 = 22{,}500$ CAD per year.
2. Energy. $PH c_e = 9.5 \times 3{,}000 \times 0.13$; the machine draws $28{,}500$ kWh a year, costing $3{,}705$ CAD.
3. Wasted material. $sNmc_m = 0.032 \times 12{,}000 \times 4.6 \times 3.85$. That is $384$ scrapped parts, $1{,}766.4$ kg of billet and $6{,}800.64$ CAD thrown away each year.
4. Lost spindle hours. $Jtr = 420 \times (42/60) \times 95$; set-up consumes $294$ h of the 3,000 available, worth $27{,}930$ CAD of billable time.
5. Total and divide by good parts. The annual cost is $22{,}500 + 3{,}705 + 4{,}200 + 6{,}800.64 + 27{,}930 = 65{,}135.64$ CAD against $N(1-s) = 11{,}616$ saleable parts, so $$\boxed{\text{cost per good part} = \frac{65{,}135.64}{11{,}616} = 5.607\ \text{CAD}}$$

Two features of that figure decide the whole of the rest of this answer. Set-up time is worth 27,930 CAD a year and wasted material 6,801 CAD, together more than half the annual cost, while energy is only 3,705 CAD. Anything sold to this user has to move the first two numbers to be worth buying; moving only the third is a marketing claim rather than a value proposition. That is the answer to “how would you establish its value”: build the cost-per-good-part model from field data, and let it tell you which needs are worth engineering against.

Part B — Two design changes that enhance value to the end user (9 marks)

Change 1 — a regenerative main drive with managed auxiliary standby. The spindle and axis drives are put on a common DC bus with an active front end, so the kinetic energy recovered when a 15 kW spindle decelerates from 12,000 rev/min is returned to the bus instead of being burned in a braking resistor, and the controller sheds the coolant pump, chip conveyor, hydraulic power unit and enclosure lighting whenever the program is in a non-cutting state longer than a set dwell. Interaction with the rest of the machine is modest: the drive cabinet grows, the braking resistor and its fan disappear, and the control needs a state model of the auxiliaries. Effect on the value model: average demand falls from 9.5 kW to 6.8 kW.

Change 2 — on-machine probing with in-process adaptive compensation. A spindle-mounted touch probe and a tool-setting arm are made standard, and the control is given a compensation loop that measures the fixture and the first-off part in place, writes the work and tool offsets automatically, and re-measures at intervals to absorb thermal growth and tool wear. The operator stops dial-indicating fixtures and stops walking first-offs to the inspection bench. Interaction: the spindle taper, the probe interface and the coolant-through path all have to coexist, and the machine casting has to be thermally instrumented. Effect on the value model: set-up falls from 42 to 18 minutes per job and scrap from 3.2 to 1.1 per cent.

Both changes are aimed squarely at the two dominant terms found in part A, which is why they were chosen over the more obvious candidates (a bigger tool magazine, a faster rapid traverse) that move terms the model says are small.

Given. The two changes together carry an incremental manufacturing and engineering cost of 14,000 CAD per machine, raise maintenance to 4,400 CAD per year, and produce the demand, set-up and scrap improvements above.

Find. The revised cost per good part and the simple payback on the incremental price.

1. Recompute each operating term. Energy $6.8 \times 3{,}000 \times 0.13 = 2{,}652$ CAD; scrap $0.011 \times 12{,}000 \times 4.6 \times 3.85 = 2{,}337.72$ CAD; set-up $420 \times (18/60) \times 95 = 11{,}970$ CAD; maintenance $4{,}400$ CAD.
2. Annualised capital rises with the price. $(180{,}000 + 14{,}000)/8 = 24{,}250$ CAD per year.
3. New cost per good part. The annual total is $24{,}250 + 2{,}652 + 4{,}400 + 2{,}337.72 + 11{,}970 = 45{,}609.72$ CAD over $12{,}000 \times 0.989 = 11{,}868$ good parts, so $$\boxed{\text{cost per good part} = \frac{45{,}609.72}{11{,}868} = 3.843\ \text{CAD}}$$ a reduction of 31.5 per cent.
4. Payback on the incremental price. Operating cost falls from $42{,}635.64$ to $21{,}359.72$ CAD, a saving of $21{,}275.92$ CAD a year, giving $14{,}000/21{,}275.92 = 0.66$ year. That figure assumes every freed set-up hour is resold; if the shop only fills 45 per cent of the 168 freed hours, the saving is 12,497.92 CAD and the payback is 1.12 years, or about 13 months.

Part C — Societal impact, and should the change be implemented (9 marks)

Given. A Canada-average grid intensity of 0.130 kg CO₂e per kWh, an embodied burden of 8.2 kg CO₂e per kg of aluminium billet, and a shipping volume of 250 machines a year.

Find. The annual environmental effect of one machine and of a shipping year's fleet, as the quantitative half of the societal argument.

1. Energy saved per machine. $(9.5-6.8) \times 3{,}000 = 8{,}100$ kWh a year, which at 0.130 kg CO₂e per kWh is $1{,}053$ kg CO₂e.
2. Material saved per machine. The scrap reduction is $(0.032-0.011) \times 12{,}000 = 252$ parts, or $1{,}159.2$ kg of billet; at 8.2 kg CO₂e per kg that is $9{,}505.44$ kg CO₂e.
3. Total, and the fleet. $$\boxed{1{,}053 + 9{,}505 = 10{,}558\ \text{kg CO}_2\text{e per machine per year}}$$ and across 250 machines, $2{,}640$ t CO₂e a year, or about $21{,}100$ t over an eight-year life.

The arithmetic carries the first and least obvious part of the societal argument: the material saving is nine times the energy saving. Energy efficiency is what a machine tool brochure advertises, but on a Canadian grid that is roughly 82 per cent non-emitting, a kilowatt-hour saved at the machine is worth very little carbon, while a kilogram of primary aluminium not scrapped carries the smelting energy of a very different grid somewhere else. A designer who optimises only the plug load is optimising the small term. The second design change, which looked like a productivity feature, turns out to be the environmental one.

The impacts that do not appear in the arithmetic matter as much. Work. Adaptive compensation removes the indicating and first-off inspection that a skilled setter does today. Framed badly, that is a deskilling story and the shop floor will resist it; framed properly, the setter's time moves to process planning and fixture design, which is higher-value work, and the machine becomes usable by a shop that cannot currently hire a senior setter at all — a real constraint in smaller Canadian centres. The design should therefore ship with training material and a manual override, because a compensation loop the operator cannot inspect or switch off will be defeated in the first week. Safety. Fewer door openings for manual measurement means fewer interlock bypasses, the most common route to a machine-tool injury; the standby logic must not, however, be able to stop the chip conveyor or the mist extraction while an operator is inside, so the auxiliary state model has to be interlocked, not merely timed. Equity of access. A 14,000 CAD price rise on a 180,000 CAD machine is a genuine barrier for the smallest buyers, who are exactly the shops with the least ability to absorb scrap.

Recommendation: implement both changes, with conditions. The economics clear any reasonable capital hurdle (payback between eight and thirteen months depending on how much of the freed capacity is resold), the environmental case is real and is dominated by the material term rather than the energy term, and the labour effect is manageable and can be made positive. The conditions are the three above: interlocked rather than timed auxiliary shedding, an operator-visible and operator-defeatable compensation loop with training, and a pricing structure — the probing package offered as a retrofittable option on the base machine — that keeps the entry price within reach of the small shop.

Part D — Realistic engineering specifications (6 marks)

Each customer need from part A is carried by one or more metrics with a unit, a marginal value that must be met for the product to be viable, and an ideal value that the design team aims at. Verification method is given for every line, because a specification that cannot be measured is a wish.

Lines 1 to 4 implement change 1, lines 5 to 9 implement change 2, and lines 10 to 13 are the constraints that stop either change damaging the base machine — the accuracy the machine already sells on, the floor plan the customer already has, and the certification without which it cannot be sold in Canada at all. Marginal values are set from the value model: 7.0 kW and 20 minutes are the worst values that still deliver a payback under two years, so they are the true viability threshold rather than round numbers.

Part E — A methodology for comparing the design alternatives (4 marks)

The comparison is done in four steps, and their order is what makes the result defensible.

1. Screen with a Pugh matrix. Take the existing machine as the datum, score each concept on each selection criterion as better, same or worse, and compute the net score. Screening is coarse on purpose: it eliminates the unviable cheaply and, because every score is relative to a real product, it needs no data the team does not yet have.
2. Fix the weights before looking at any ratings. The weights come from the customer-importance ratings gathered in part A and from the business objectives, and they are agreed and written down first. Deciding weights after seeing scores is how a decision matrix is used to justify a conclusion already reached.
3. Score with a weighted objectives matrix. Rate each surviving concept 1 to 5 against each criterion and compute $S_j=\sum_i w_i r_{ij}$ with $\sum_i w_i = 1$. Ratings are evidence — test data, cost estimates, supplier quotations — and the weights are values; keeping them in separate columns is what stops one being used to smuggle in the other.
4. Run a sensitivity pass. Recompute the totals with the weights that a reasonable person might disagree about pushed to their plausible extreme. If the ranking holds, report a result; if it flips, the honest report is that the choice is a business decision and the engineering does not settle it.

Part F — Ranking and selection (6 marks)

Three concepts are carried forward: C1, the regenerative drive with managed standby alone; C2, on-machine probing with adaptive compensation alone; and C3, both changes released together on a shared power and control platform.

All three beat or match the datum closely enough to survive screening, and C3's negative net score is a warning rather than an elimination: it is worse than the datum on three counts precisely because it does two things at once. Screening has done its job, which is to tell us that nothing here can be dismissed without data.

Given. Agreed weights of 0.30 on value to the end user, 0.20 on societal and environmental impact, 0.15 on low technical risk, 0.20 on incremental cost and 0.15 on time to market, and ratings from 1 (poor) to 5 (excellent).

Find. The weighted score of each concept, the ranking, and whether that ranking survives a sensitivity pass.

1. Compute the totals. $S_{C1}=0.30(3)+0.20(4)+0.15(4)+0.20(4)+0.15(4)=3.70$; $S_{C2}=0.30(5)+0.20(3)+0.15(3)+0.20(3)+0.15(3)=3.60$; $S_{C3}=0.30(5)+0.20(5)+0.15(2)+0.20(2)+0.15(2)=3.50$. The ranking is $$\boxed{C1\ (3.70) \succ C2\ (3.60) \succ C3\ (3.50)}$$ but the whole spread is 0.20 on a five-point scale, which is well inside the resolution of the ratings.
2. Sensitivity pass. The one weight a reasonable person would dispute is the 0.30 on value to the end user — the question itself is about enhancing value, so push it to 0.50 and rescale the rest by $0.50/0.70$, giving 0.1429 on impact and cost and 0.1071 on risk and time to market. Then $S_{C1}=3.50$, $S_{C2}=4.00$ and $S_{C3}=3.93$: $$\boxed{\text{the ranking inverts to } C2 \succ C3 \succ C1}$$

Selection. The matrix does not settle the choice, and saying so is the honest report. What settles it is the question asked: the brief is to enhance value to the end user, which is the criterion whose weight causes the inversion, and under any weighting that takes that brief seriously C2 — on-machine probing with adaptive compensation — is selected. It carries almost all of the cost-per-good-part reduction found in part B, it carries nine tenths of the environmental benefit found in part C through the material term, it is retrofittable so it does not raise the entry price of the base machine, and it is the change the user notices every single set-up.

C1 is not discarded but deferred: it is scheduled as the following release on the same control platform, which reaches the C3 configuration in two steps while retiring the development risk that made C3 the worst concept on Pugh screening. That staging is available only because the sensitivity pass exposed how thin the original margin was; a team that had read 3.70 against 3.60 as a result would have shipped the wrong machine.