Apr 18, 2017

[2.70] Seek and Geek #9: U8 Outrunner BLDC Motor

This post is about bearing placement, shaft alignment, and hi-speed cantilever moment stiffness in outrunner brushless motors!

A disassembled U8 brushless motor

The point of a motor is to transmit torque, so motor bearings play an integral role in taking on load and minimizing friction losses. This particular motor supports a max thrust of 2.6kg using two bearings with load ratings of 2070N.

Guesstimating at moment resisted by the bearings...
Max stall torque from the motor is 0.912 Nm, and the rotor shaft is pressed on with probably a 5┬Ám tolerance. Assuming no axial loading on the bearings, each bearing experiences half this torque as a radial force = approx. 50N.

We call the distance between bearings $a = 18mm$. F_bearing is the load on each bearing, which includes both applied loads and misalignment loads. By treating this shaft like a cantilever beam, we can calculate forces on the bearings due to misalignment:

$F = kx$, 
 $F_{bearing}\cdot a = K_{moment}\cdot\alpha = \frac{2EI}{L}\cdot \frac{\delta_{tol}}{L}$.
$F_{bearing} = \frac{2EI\delta_{tol}}{aL^2} + F_{applied}$

For this motor, L = 25mm, E = 69 GPa (material assumed to be 6061 AL), and I = 4019mm^4
$F_{misalignment}$ = 247N worst case.

So each bearing experiences 300N at max. torque of the motor, or nominally 15% of load rating.

Apr 17, 2017

[2.70] Cardboard Concept Desk

Modeling a concept desk out of cardboard, just as a quick stupid-check before designing components in detail.

The goal here was to see what this desk idea would look and feel like, without worrying about geometrical tolerances. I also played around with adding trusses to the interior of the desk (and added a drawer!)

Construction was all hot-glued corrugated cardboard, with the exception of the simple linear axis which makes a final reappearance here. So, the vertical column was assumed to have substantially higher stiffness than the rest of the cardboard desk.

Adding more thickness (box drawer) to the desk significantly helped improve moment of inertia and reduce deflections, but I don't think the interior trusses contributed much. I think future desk might scrap the truss idea in favor of having just clean box walls.

Derp-cardboard desk's only attachment to the carriage was via hot-glued foamcore, and clearly future desk will need a more load-bearing attachment system. Surprisingly, hotglue held the desk and 200g of motor components just fine.

Real desk will also likely be a wall-mounted desk, for simplicity.

Apr 9, 2017

[2.70] Seek and Geek #8: Stiletto Heels

National Geographic has a 2014 article about Hugh Turvey, a British photographer who uses a fusion of x-rays and visible light to create art. In particular, a photo of his wife's foot in a stiletto heel caught my eye.

"Femme Fatale", Hugh Turvey
What's with that heel?

After some internet searching, it's not a fancy flexure that allows the heel shank to snap off before the ankle twists...
It's actually the five nails used to attach the shank to the shoe!

Pressure under one of these stiletto heels can be more than 3000 kPa!

[2.70] Seek and Geek #7: Truss Geometries

2.70 coursework is pivoting towards specific components of the desk, so this seek&geek is about possible truss geometries for the desktop. I expect a constant distributed load (from desk weight and stuff placed on top) as well as a worst case point-load on the end (elbows and bodyweight). So how do other real-life objects achieve lightweight rigid planar structures?

Trusses are statically determinate structures solely consisting of two-force members, so basically assemblies of pinned beams. Trusses are most commonly seen in bridges, where the top beams "top chords" are typically under compression and the bottom chords are under tension.

Warren truss bridge

In my case, a desktop with a truss frame would experience tension on top and compression on the bottom. This design problem is similar to overhead cantilever road signs seen on the highway! Therefore, my desktop design can draw from a wealth of experience and calculations.

Highway signs also have to deal with significantly higher lateral loads than my desk does
Highway signs typically use a Pratt truss geometry to minimize sensitivity to buckling

Drawings and calculations for a highway overhead sign in I-85 Atlanta, GA

[2.70] Seek and Geek #6: Disposable Lighter

I signed up for a bunch of grill shifts this weekend, so now I have a lighter on my desk.

A very standard disposable lighter

Butane lighters like this one work by releasing compressed liquid butane as a narrow stream of gas. When this stream of gas meets a spark, it ignites and produces a flame. Holding open the valve continues to draw fuel out of the reservoir to support the flame and the outrush of gas prevents the flame from traveling inside the canister irrespective of orientation.

Lighters are dirt cheap, yet have a seemingly long working lifetime (it runs out of fuel long before it breaks) They do well on the cost/performance curve because they have very few moving parts - just the thumb-lever fork and the rotating spark wheel. They are also fairly idiot-proof - one swipe of the thumb rotates the sparkwheel with enough force to strike the flint and produce sparks, and that same motion lands the thumb on the fork lever to open the gas valve.

Parts of a lighter
An interesting note: the "flint" used in lighters and other modern firestarters is not the true sedimentary rock. "Flint" is actually the synthetic alloy "Ferrocerium" invented in 1903, which has an ignition temperature below 180 °C (easily generated by thumb friction) and produces sparks reaching temperatures up to 3,000 °C.