Tradeoffs, Constraints, and Design Space in Engineering

Why Every Design Is a Compromise

We reviewed junior engineer design solutions on Wednesday. This was the first time he had presented a bracket design. The bracket was certainly strong enough, filled up the required space, and cost $8 to make when put into full production. The project manager congratulated him on a good job, but also asked him to make the bracket lighter. He was able to make it 30% lighter after about an hour of work on the design, returning with the thinner sections soon thereafter. The manufacturing team had this to say: "these thin walls are difficult to manufacture to dimensions with acceptable yield, and are therefore not a good design solution". The engineer thickened the bracket up again and the weight was back to where it started. The manufacturing team was happy with the solution.

However, the purchasing team then pointed out that the material cost had increased for this bracket. "Can we specify a less expensive alloy?" Yes, we can. However, it will have to be thicker to achieve the same strength. So, cost is down, weight is up, and manufacturability is worse.

Engineering is a never loosing battle: you cannot win, you can only choose which parts of the fight to lose most poorly. There are only four dimensions: make it stronger, make it lighter, make it cheaper, make it easier to make. Each improvement in one dimension comes at the expense of one of the others. The good engineer doesn't look for the best solution to a problem. The good engineer looks for a solution that has a bad flaw, and tries to determine whether that flaw will matter for his particular use case.

Students in engineering courses often think about engineering design from the perspective of seeking "the right answer", while experienced engineers think about the engineering design task as finding "the answer that best balances the things that actually matter here". On a strength-to-weight basis, based on historical data, titanium is objectively better than steel. However, for a stationary industrial machine, weight is not an issue, and steel is 1/10th the cost of titanium. Who cares about weight here? Context profoundly affects what we consider to be "better".

Design Space: What's Possible vs. What's Allowed

When designing, one should think of the available solution space as a map with hard constraints (some areas are off-limits), a soft constraint (a preferred path through the space), an overall objective (e.g. "this thing should be awesome") and sometimes even a desired aesthetic. In the part I'm designing, the form can vary significantly so long as the part is no larger than 4" x 4" x 4", it can weigh as much as 2 pounds, and it costs no more than $50. The comfortable path through solution space is a major constraint as well.

Inside these boundaries the usual preferences rule, lighter is better than heavier, cheaper is better than expensive, easier to manufacture is better than complicated. But "better" is a relative term. Sometimes heavier for less expense is a good tradeoff, and sometimes more expense for easier manufacturing is a good tradeoff. Such decisions are up to you based on the particular circumstances of the design project you are working on.

This design space is powerful. Within it there are many good answers; the problem is picking the answer that is best for your specific situation given your specific constraints and priorities.

Conflicting Requirements Across Teams

In real life a part is designed. As Manufacturing works up the fabrication process they realize that the internal corners of some features are hard or impossible to machine and larger radii are needed. These are then added to the part design. Stress analysts then point out that the bigger radii create stress concentrations not accounted for elsewhere in the part design and more material is needed to reinforce those critical areas. The procurement organization is delighted as the weight of the part has increased by 200 grams; for a part that is making up 1% of the overall assembly weight this translates to 200 grams x 50,000 parts per year = 10,000 pounds per year of additional aluminum. This translates to $30,000 per year in additional cost. The organization then clamors for a less expensive material to reduce these costs. The reliability organization soon chimes in pointing out that this new material has a lower fatigue strength and a reduced safety factor will be required. More material. More cost. The circle is never ended.

Nobody's wrong here. Manufacturing will tell you that typically manufacturing processes are not capable of producing tight radii with standard tooling. The stress analyst is right that changes in geometry will affect the stress distribution. Procurement will tell you that they have a budget target for the part. Reliability will tell you that you need to design a part that will last. The reality is that all of these requirements conflict with each other and the job of the design engineer is to design a part that violates the fewest important requirements.

As you review the list of requirements, keep in mind that some are hard and fast, and others are merely preferences that have been cast into the requirement mold. For example, the requirement "Must be under 500 grams" might actually translate to "We prefer something lighter because of shipping costs", and you must determine how important shipping costs are versus the increase in manufacturing cost to ship a slightly heavier product. In this example, saving 50 grams might reduce shipping costs by $0.30, but increase manufacturing costs by $2.00.

Constraints Define the Problem

I like to bring this up with my students because they almost always react negatively to the concept of constraints. I might present a challenge and they say something like: "Well, if only I didn't have to worry about the cost of the part, or the manufacturing process, or the envelope constraints of the space where it will live, then I could make something really cool." And I stop them right there. I say something like: "Constraints are not something that stifle design, they are what make design possible." With an infinite number of solutions to any given problem, there is no way to begin. With some constraints in place, you can start to make design decisions and actually make progress.

"Design the best bracket possible" is an impossible problem to solve, because it is impossible to define "best". Is it lightest, strongest, cheapest, most reliable, or easiest to install? You can't make all of those factors optimise at the same time. By imposing some simple constraints, the problem is turned into a real design task: "Design a bracket that fits within 200 × 100 mm, which carries a load of 5000 N, costs under $50, and can be manufactured on our current facilities".

Challenge every "must" in specs, design to meet actual technical requirements not to uphold assumptions disguised as requirements. "It must be stainless steel." Is that because "we worry about corrosion"? Indoor use, occasional exposure to water? That may be coated carbon steel at 1/3 cost. Outdoor, marine, subject to salt spray? Stainless steel is probably correct.

Here's what constraints you're actually navigating:

Physics: (left to right) The properties of materials will not compromise for you; steel always yeilds at its yield strength, the amount of deflection of a beam is controlled by physical equations, and the laws of thermodynamics cannot be bypassed by good design.

Manufacturing - What tools are available? What tolerances can be achieved? Can your supplier actually produce the geometries shown in your design, or is what you've created optimized for CAD but unsuitable for manufacturing?

When you have money on the line, it's real. This means that simply saying that using titanium instead of steel would be a good idea is not enough; that idea has to return enough to invest. Development cost, tooling cost, everything has to be balanced. Sometimes, "good enough" and cheap is better than "superior" and expensive.

Time: By deadline, we mean the point at which the customer needs to receive the design, the date of the trade show, or when the client's company runs out of money. A perfectly-designed product that launches six months late is inferior to a good enough design that hits its target launch date on time.

Regulations: The safety codes were written in blood. The requirements set forth by OSHA, the pressure vessel codes, the electrical standards, to name a few, cannot be ignored in the name of expediency.

I am too limited by my current materials and resources. Instead of wasting time wishing I had more freedom to create in an ideal design space, I should direct my ingenuity towards crafting the best design I can within the constraints I have.

When to Stop Optimizing and Commit

At some point in the design process you have to decide that you like what you have and move on. The hardest skill in engineering isn't the hardest programming trick, or the most powerful simulation tool, or the best analytical technique. The hardest skill in engineering is knowing when something is good enough. Over-optimizing is a real problem.

Optimizing is hard and expensive. Before you start, ask yourself: Is this going to matter? Optimizing for minimum weight of a stationary piece of metal is silly, it is something you do to amuse yourself, it is performance engineering rather than real engineering and not worth your time. But if you are building a satellite payload, every gram counts and weight optimization is an incredible amount of work for which you will get an incredible amount of return.

Okay, here's how to make some actual design decisions while you're still in the Analysis Phase.

As we embark on the design process, it is important to define what success looks like before we generate a single part file. I like to write down success criteria at the beginning of the design process. Success criteria are quantifiable targets that define what it means for the design to be successful. "Part must carry 5000 N with FOS ≥ 2, cost under $50, and can be manufactured in our facility" for example. Now I know when I am done designing.

Optimize for the right parameters. Second, once you have a decent model, identify the 2-3 variables that actually drive the differences you care about. Don't try to optimize for 15 parameters. Most designs have a small number of drivers. Thickness vs. split? Thickness wins. Strength is the limit. Simplify the geometry to cost down.

Third, justify the design choice to future-you. " Chose steel over aluminum because stiffness was a priority in this design, and using aluminum would require inflating the tube ID by an extra 1/2" to stay within deflection limits, which would likely add enough weight to erase any weight savings while increasing the cost as well." This note has a lot of utility as future-you will be able to see that aluminum was considered but it didn't add any benefits. A competing design choice would be even less valuable.

4. Verify key assumptions early: Verify assumptions like "the customer won't ever see loads above 5000 N" before you finish the detailed design. These assumptions can be sneaky and costly if not validated early on. A quick test or prototype test can expose incorrect assumptions before too much time is spent on a false path.

Our goal is not to design an excellent product – it is to design a product that works, meets its specified requirements, was delivered on time, and cost the right amount of money. Good enough is always better than good if good enough is delivered on time.