Tolerances are Stacking Up – Part 2


(Continued from Part 1)

The two managers debated rationale for a couple minutes, then Margaret, using a level of respect Jordan hadn’t seen before, began to gain ground.

“I can see why she’s a program manager.” Jordan thought. “She’s been in these situations before and she knows how to…”

“Tonight, we’ll take another look at the reliability of the assembly analysis,” Jordan heard his manager repeat.

“Very well.” Mr. Bradley consented with a slow deep exhale as he looked around the room again. He held both hands forward, palms up, fingers spread. “You must understand, that repeatability is everything when it comes to high quantity assembly-line production.”

Jordan was asked to finish his last few charts then he picked a brownie from the corner table on the way back to his chair, thinking, “How am I gonna’ analyze this assembly to achieve the reliability he expects, and what does my manager mean by tonight.”

Jordan sat down as the next presenter began talking about the electrical characteristics for the motor, but Jordan couldn’t concentrate on the presentation. He opened his copy of the requirements and read, “The motor MTBF (or mean time between failure) shall be 75,000 hours.” At another location he read, “The motor shall perform all functions while operating between -20 degrees F and 125 degrees F.” He then turned to the performance section and read, “The motor shall be designed to operate 6,000 cycles, where a cycle is defined as one opening and one closing of the window.” He stared at a picture of a popular automobile on the wall next to the projection screen imagining the driver raising and lowering the window over and over again.

“What are the spec’s (specifications) on these bearings?” Jordan thought. “What is the ideal preload?” Jordan went to the website for the bearing manufacturer. “I’m glad the Wi-fi is working in this conference room,” he thought while browsing through several websites. “Here it is, part number Q4829, Pre-load 100 N +/- 20%, for this size. Darn, it’s in international units; everything else is in english units.”

Jordan converted from newtons to pounds resulting in 22.5 lbf +/- 4.5 lbf.

“So, let’s see, that’s an upper limit of 27.0 lbf and a lower limit of 18.0 lbf preload.” Jordan looked around the room to see if anyone was disturbed by his lack of attention to the presentation.

“Let’s see, the spring rate force equation is…” Jordan wrote

F = k*x

If I divide by the spring rate, I should get the upper and lower spring compression values that will produce this range of preload, so, solving for x we get…” Jordan wrote the following upper and lower preload case equations where UL stands for upper limit, LL stands for lower limit and PL stands for the force of the preload.

x(UL) = PL(UL) / k

x(LL) = PL(LL) / k

“Oh wait; what is the spring rate, k? I’ll look that up later.”

Jordan sketched the motor cross-section on his copy of the agenda.

“Now how do I control the overall manufacturing tolerances for the assembly? It shouldn’t be too difficult. The shaft will be precision machined. The parts that will vary the most, will be the flange and motor body. I can do a worse-case tolerance stack-up using all the individual tolerances for the parts to see what the overall tolerance variation will be, then tighten-up all the tolerances to make sure the assembly produces the correct bearing preload and will always be in compliance with the requirement. As I recall, for worse case, the assembly tolerance is simply the sum of the individual part tolerances.”

Jordan wrote the following equation where T stands for tolerance, ASM stands for assembly, and T(i) stands for the tolerance of part i.

T(ASM) = Sum (abs[T(i)])

Margaret, an engineer promoted to manager, noticed his doodling across the table and slipped him a note. “Tight tolerances are expensive to manufacture; we don’t have the cost margin; find another way to make it work.”

“What does she expect.” Jordan thought, giving his manager a sideways look trying not to act disturbed.

During his co-workers presentation, Jordan heard the word ‘statistics,’ which reminded him of a method he learned years earlier.

“I wonder if I could use a statistical Monte Carlo simulation?” Jordan whispered to Blake sitting next to him. “Will Monte Carlo work for this?”

“You may be able to use a simple statistical approach,” came the response, then Blake wrote three capital letters on the note, “RSS.”

“That looks familiar…”

(To be continued)

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