Robust, Lightweight, Cantilevered Lamp Post for Light Streak Machines
Orbit 2.5 Hub
Orbit 2 Machine
with simple tubular
Photo note: 1/4 second exposure, plus flash to show moving hub.
The first Orbit machine hub:
with single tubular stainless steel spoke
The cantilevered lamp posts of my fast spinning light-streak machines such as Orbit 2 (photo right) present unique and demanding design challenges. These components experience high stresses, chaotic in magnitude and directionality, as the machine whips them around in two axes. The mechanical torture (technically know as fatigue cycling) is especially severe towards their roots.
The cantilevered lamp posts, henceforth referred to as "spokes" , started out simple: a relatively thick wall stainless steel tubing (right and below). Later, a much better design evolved (above) using carbon fiber tubes and stainless steel sleeves. This new design is discussed below.
CANTILEVERS, BAD and BETTER
A CANTILEVER is simply a structure which is held on one end and free on the other. It may receive loading all over (like wind loading on a tower), or in a more concentrated form (like the weights in the diagram left top). In either case, the bending force or "bending moment" increases towards the held end, and if this cantilever is uniform throughout its length (as in both diagrams at left), the stress gets MUCH higher at the top and bottom of the inboard areas.
In fact, looking at the stress diagram we can see that the vast majority of that cantilever's material is wasted material... the blue and purple areas are doing almost nothing. Clearly, solid rectangular blocks are not good cantilever structures.
A better cantilever like the Eiffel Tower (right) gets wider towards the base so that the increased bending moment is more spread out there, limiting stress on the material. That's a step towards being an "ideal" structure, one which has the same stress throughout - so no part to doing too much or too little of the load bearing work. Also, you'll notice the Eiffel tower is tube-like: it has more air in the middle where the stress would be low anyway, and more material towards the outside where its needed.
Why don't we make every structure ideal? After all, this would save on material costs. The reason is that ideal structures are much more complex forms, and that increases design and fabrication costs.
In some fields, like spacecraft and robotics, materials costs are inconsequential but weight is the critical concern, so the quest for near-ideal structures is justified. And in the case of mother nature, design and fabrication costs are zero, so near-ideal structures are the norm.
horns: near-ideal cantilevers
In a perfect world, it would be practical to construct a gently tapered carbon fiber tube for this purpose, perhaps with increasing wall thickness towards the base. However, "constructability" needs to be balanced with ideals of form, so a 3 stepped structure was settled on.
2 sizes of "rigid carbon fiber" tube from McMaster-Carr form the basis for this design. These have a high percentage of parallel strands of carbon fiber running lengthwise, the balance being a polyester resin which holds everything together. Carbon fiber has a remarkably high stiffness to weight ratio (the highest of any available material) - ideal for this job.
Two practical considerations come into play working with this type of carbon fiber tube: First, it can be easily split - especially at the ends - so it needs to be constrained at the ends. Second, it is tricky to attach at the "held end" in a removable way (the round hub in this case). Both of these issues are solved in this design by epoxied-on stainless steel sleeves.
The innermost "Step" must be the strongest and also connect securely and removably into the hub (can't be adhesive joined). It is made of 2 layers: stainless steel tube outside and carbon fiber tube inside. They are joined with epoxy It seats into the hub in a closely fitting socket, and is secured by 2 cone-head set screws which seat in small holes in the stainless tube. The positive engagement of these set screws makes inadvertent disconnection impossible.
The middle step is made of 2 layers of carbon fiber tube, joined with injected urethane rubber (photo right). The rubber evenly spreads load - protecting the more delicate outer step from damage.
The outer step is made of slim, very light, carbon fiber tube.
At the end, a modified T1 LED is held in place by epoxy inside and a thin wall stainless steel tube outside.
A yellow Kevlar safety lanyard lives inside the spoke, along with the 2 wires which power the LED. If the spoke should break due to a collision or structural failure, the lanyard will prevent the spoke from becoming a projectile long enough for the machine to be halted.
trendy stairs version of bad cantilever
These tube sizes have substantial space between so they must be held concentric, this is done with the large black object and the white object at the bottom. A hole was drilled in advance to accept the hypodermic needle. Injection proceeds until overflow seen at junction. The rubber acts as an adhesive and as a cushion for the smaller tube.
Joining 2 sizes of carbon fiber tube with liquid rubber (PMC-780)
Nearly complete hub of Orbit 2.5.
Each of the 6 spokes is held to the hub by a pair of cone point set screws (aligned with spoke, on surface) which key into small holes in the spoke's outer stainless steel tube.
The Kevlar lanyards are anchored in the hub by knots which rest on small aluminum disks (4 installed in photo).
I was curious what would happen to the new "safe" spokes in a disaster.
Specifically, "how does carbon fiber break", and "will the Kevlar lanyard work?"
Sometimes failure testing is the only way to really understand something.
I set up a shield, and a long spoke was spun up to a high rpm, and a piece of cardboard was put in its path. WHAP! As anticipated, the spoke broke and flailed violently.
The machine was kept spinning for about 10 seconds then stopped.
The spoke broke where I anticipated it would (at the end of the thin section) and there lanyard worked as planned - keeping the spoke from coming apart (barely - getting chewed up by the sharp edges of the broken carbon fiber)).
Future lanyards will replace Kevlar with polyester or spectra which supposedly have better abrasion endurance.
The photos at right show more details of this test.