Celestial Mechanica Series: Gearbox Design and Construction

Celestial Mechanica is a 16-ft tall kinetic steel sculpture of our solar system representing the majestic dance of the heavenly bodies. It was created by a team led by Jessika Welz for Burning Man 2014.
(Project facebook page: https://www.facebook.com/celestialmechanica2014)

The 4 gas giant planets, Saturn, Jupiter, Uranus, and Neptune are
cantilevered out on steel arms, the longest arm being about 20 feet. The arms rotate around and are driven by the gearbox that this Instructable talks about. The 4 rocky planets, Mercury, Venus, Earth, and Mars, are mounted on 6' diameter ring gears around the base that are also driven by the gearbox.

In this Instructable, I will talk about the design and construction process for the 400 pound machine in the center of the sculpture that drives the orbits of the planets. Because I doubt someone would want to build an exact copy of it, this Instructable will be less of a step by step howto and more of a walkthrough of what the thought process was, what it was like to create it, and what are some lessons that could be learned.

At first when you do something like this, there are endless choices and directions you can go. How did we want to drive the orbits of the planets on this piece? A motor for each planet, or one motor for all? Speeds controlled with gearing, motor controllers, or both? Other ways(Hydraulic motors??) Ac or Dc motors? Chains, gears, belts, friction wheels?

We knew that we wanted the speed of the orbits to be proportional to each other. Mercury's year is just 88 Earth days long, while Neptune's is 60190 Earth days long! So there is a big range of speeds that we were dealing with (Sorry kids, no Pluto here!). In addition, the arm of Neptune is 20 feet long and with the planet on the end, the torque from even a pretty mild wind would be significant. We also wanted computer control of the planet speeds, so that we could dial in planetary alignments of specific dates like people's birthdays.

We were on a pretty small budget for such a complex piece. The first thought was separate DC motors for each planet. In the past, I've used DC 1/6-1/4hp brushed gearmotors for art pieces. The motors themselves are pretty nice- well sealed, reliable, easy to mount, reduced down to a nice speed already. They run about $500 ea, which is getting pretty pricey already for 8 planets (or even just the 4 large planets). But the controllers (which cost another $100 or so) are awful. They blow out if you even think about looking at them wrong. They throw out so much electrical noise that it freezes up micros (even Arduinos, which are pretty tough little guys!) that are anywhere within a few feet. After using 6 of those on another Playa project (Helyx), I vowed to never use them again.

For DC motors, the price only went up from there if we wanted non-horrible controllers. Ac motors in a speed-controllable flavor are not any better. So it seemed like separate, speed-controllable motors for each planet weren't really practical for our budget.

I started thinking about ways to drive the planets from one, big, AC motor running at constant speed. Big AC motors are pretty cheap from surplus dealers, the one we ended up using cost around $200. One thought was to use hydraulic motors running off of a pump driven by the main motor- there are some cheap hydraulic components at surplus dealers too. But hydraulics would be messy, hard to precisely control without pricey proportional valves, and I could not find components that matched up in a way(taking into consideration speed, torque, hydraulic pressure, and hydraulic flow) that seemed to work.

Also, the vision of the piece was something very mechanical, tactile, dark-crystalley, and intricate. So that drew me more towards one mechanical thing driving all the planets. Also, I was in Europe for the summer designing the system to power the piece while the rest of the team was building the piece in San Francisco. So, a thing that was one unit that could easily just plug in to the rest of the sculpture to drive it seemed really attractive. I started thinking about clockwork and escapement mechanisms and different ways of controlling speed with them. I though about different ways that we could control speed by actuating a solenoid to connect or disconnect power to a planet one step at a time, in the same way that an old mechanical clock moves in a series of discrete steps.

Controlling speed by releasing the drive force and letting things slow down one little bit at a time seemed the most practical way forward- the torque would be significant and the motor would be running at a constant speed, so it seems easier to let the torque slip a little bit at a time than to have some mechanism to add torque a little bit at a time. I ended up going with a planetary gearset, where the cage that holds the planet gears would be held fixed by a solenoid-actuated brake, the ring gear would be driven by the motor, and the sun gear would drive the planet. There would be 8 of these in a chain, the speed of each step in the chain being from the previous one by the gear drive ratios. In this way, we could get the wide range of speeds we need without the jump in gear ratios being too big at any one point.

The speed of each planet would be controlled by the brake on the cage of each planetary gear. For the planet to go full speed, the brake would be applied fully, which would transmit all power to the planet. To slow the planet down, the brake would release, and friction would slow the orbit down. A helpful illustration of the principle is in the first video. There would be a microcontroller constantly applying and releasing the brake to achieve the desired speed- it would be a sort of really slow, mechanical pulse width modulation. The micro would also sense if wind was speeding up the planet when the brake was released instead of slowing it down, compensate for that, and use that to keep track of the prevailing wind direction. That was the idea at least.

The whole thing would be built with gears that we would cut ourselves out of 1/4" steel on a CNC plasma cutter. (We made some test gears before settling on this route, and they were promising).

With the basic strategy figured out, it was time to get down to specifics. I started a big spreadsheet for calculating the speeds and forces. It's attached if you want to look at it, though it may not be that exciting or easy to decipher. I put in the real orbit times of all the planets and established the ratios between them. I then put in a figure for how fast the orbit of the fastest planet, Mercury, would be on the sculpture. 1 RPM for mercury put Neptune's orbit time at 11.4 hours. That was a little long, so we ended up making it 4 times faster- Mercury would orbit once every 15 seconds. A little fast for something that is going around in a 6 foot diameter circle, but still reasonable, and then Neptune would go around once every 2.85 hours.

Since we were CNC plasma cutting the gears, and plasma cutting does not produce precise edges by any means, the teeth of the gears had to be pretty big. That way, the imprecision from the plasma cutting would be small in relation to the gear tooth size. We went with gears with a module of 0.5inch. A bit of gear theory: Pitch diameter refers to the diameter of an imaginary circle around the gear where the meshing between two gears theoretically occurs. The shape of gear teeth is actually quite complicated and takes a few obscure constants to calculate, but each tooth ends up being somewhere close to halfway inside and halfway outside this diameter. Module refers to units of pitch diameter per tooth. So if we have a gear of module 0.5in and 24 teeth, that means the gear has a diameter of 12". Gears have to have the same module to mesh, and the diameters must be in even increments of the module. So our gears all had to be made in increments of 0.5".

There would also be a worm drive gear reducer coming out of the main motor, a sprocket/chain link from the gear reducer to the gearbox, and additional stages of gearing from the gearbox to each planet. So it was a pretty complicated and interrelated set of things, and I had to adjust the ratios of all the components to achieve the final desired speed of each planet. This is where spreadsheets are your friend! I set up a series of formulas for the RPM of each component, each formula dependent on the result of the one before it in the powertrain. Even though the end result is complicated, it is just a collection of simple relationships. I played with the sizes of the gears and sprockets in the spreadsheet until the orbit speeds were close to what we wanted.

At this point, I also had to figure out how to handle the torque from wind. The piece is designed to withstand an 85 MPH wind, and that translates to a whole bunch of torque from the big planets that are on long arms. To avoid having to design the whole system to handle all that torque, I decided to instead allow the system to slip at a certain torque, which would let the arms weathervane away from the wind and reduce the force on the drive system. The slippage would come from the brakes used for speed control, which would be set up to grip just enough for normal operation. I then was able to use a reduced torque load on the system, and did some calculations on key components to make sure that they would hold the design torque.

With a spreadsheet full of numbers and a mental picture of the thing, I set out designing it in Solidworks and figuring out the details of how we would actually put it together. I felt a new understanding of what it must be like to be an automotive engineer after this. Everything I changed would make something else not fit or would compromise on some other aspect of the design. Comfortable space for the brakes made the gearbox not fit in the sculpture base; making the gears smaller so it would fit made some gears too small; making all the gears just a bit bigger in proportion made the gearbox not fit; driving one part of the planetary gear systems meant that you couldn't fit a gear in to connect to a different part; on and on like this for about weeks of tweaking the parts, trying new ratios on the spreadsheet, sourcing parts and then sourcing different parts.

In the end, it was designed- it would be a series of plates and gears that would stack up on a central shaft, the bottom layer driving Mercury and the top layer driving Neptune, each layer driving the one above it at a reduced speed via a stack of gears on a shaft that was parallel to the main one. A brake would hang off the side of each level and all the brakes would be controlled via steel cables that went to an assemblage of 8 linear actuators on the top of the unit. The gear stacks would be held in place by slotted plates that required only 4 bolts to lock the entire system together. The 3d modelling was done in Solidworks, and the pattern of the gear teeth was created in a Python program that would generate a DXF, which would then be imported into the 3D model. My poor computer with it's meager graphics card could barely handle a model of one gear, nevermind an assembly containing 83 of them.

When I was done, I got everything CNC ready and sent the files over to the rest of the crew working in San Francisco. I would get back from my summer away in Denmark about 2 weeks before the piece shipped, and the idea was that the pieces would be CNC cut and ready to go, and the whole thing would snap together like a steel lego kit in about a day when I got back. Heh. Optimism can be a funny thing.

The pieces all got CNC cut out and I was all set in my head for the planned magical one day assembly. I got back from Denmark and was faced with a massive pile of parts. People were grinding the plasma cutting slag off, I was trying to sort through them and match them to the different sizes that were on the spreadsheet, I was making piles, people were un-making the piles, there were gears of all sizes everywhere in the shop. It took awhile to tame the great gear diaspora and make sure everything was prepped and in an organized set of piles. If you've ever worked on a big Burning Man project a few weeks before it ships, you know the feeling of the intense working frenzy that takes over a shop at this time. Amazingly, no gears were lost!

Jessika did some of her amazing welding on the parts that needed welding. There may have been shims made from beer cans at some point.

I assembled some of the planetary gearsets to see how they worked and went together. Reality is a pain sometimes: They did not work as smoothly as I had hoped, or indeed in a way that the brake speed control mechanism would work at all.

One problem is that the parts were cut using some cheap imitation plasma cutter consumables from alibaba that we had around. Never use cheap imitation plasma cutter consumables except maybe to prop up small parts for painting. Rough edges on gear teeth and holes that weren't quite round plagued many of the gears and became a real problem for the gearbox that still isn't quite gone after a few upgrade cycles. Furthermore, our CNC plasma cutter was suffering from a slipping coupling on one of the stepper motors. It was not bad enough to be noticed, but bad enough to make all of the gears slightly oval.

Another problem was with the design of the planetary gears. The ring gear is driven, the cage is held fixed, and the sun gear drives the planet orbit. This means that the speed gets increased by the planetary gear system, which means that problems with friction and imprecision get multiplied. Early on in the design, I went back and forth a few times on which parts of the planetary gearset were the driving, driven, and fixed ones. Each variation had some compromise or something that made it not doable at all, so at the time this design seemed like the best way forward. But looking back, increasing the speed in the planetary gearset was probably a bad idea.

I fiddled with the planetary gears for a few days, and it just didn't seem hopeful that they would work. The planetary gears were there for controlling the planet speeds only. With about a week to go before the piece shipped, we decided to let go of the idea of speed control for now. The planets would still orbit with the right proportions of speed to each other due to the ratios in the rest of the gearbox, but the planetary gearsets would be locked together. We substituted the sun gear in each planetary gearset with a "sun-not-gear", which locked into the teeth of the planetary gears and made the whole gearset rotate as one. We left the brakes, brake actuators, and microcontroller system off.

Since the brakes were supposed to release excess torque in the event of serious wind, we had to find a new solution for that. That turned out to be fairly simple: The output connections that went from the gearbox to the planets were connected with a keyed shaft. So instead of a normal key which is supposed to be strong, we put in a brass key, which would shear and release the excess torque, allowing the planet arm to rotate away from the wind.

After we decided to forgo the operation of the planetary gears, assembly proceeded and went fairly well, though with lots of extra die-grinding due to the plasma cutting issues. One issue that came up was that the sun not-gears, which I had rushed through in designing since we only had a few days left, could not be assembled with all three planetary gears in place due to the angle of one of the "claws". But I figured that it would be OK to just leave one of the gears out, since everything would still be locked in place and was held in place by the gear cages. We connected it up and turned it on for the first time, and it worked! There was some kerchunking from areas that still needed to be ground down, but it was mostly pretty easy to fix. We got it running smoothly, and sent it off to the desert!

So, with a (mostly) complete sculpture and a working gearbox, we headed off to Burning Man! The construction of the whole piece took a little less than a week. With it all assembled, we turned it on and hoped for the best! It all started to turn and seemed to be working, but then a big CLUNK! happened. Oh no!!

Some of the gears had slipped into misalignment, and it would not work again. Over the next few days, Jessika disassembled the gearbox while it was still inside the sculpture. No fun task, considering the inside of the thing looks like a meat grinder and there are trusses, drive chains, hoses and all kinds of other stuff in the way. There were some gears jammed into a misaligned position, and she un-jammed them and reassembled it.

We disconnected all of the planets from the gearbox and turned it on, and it worked again. But if we connected too many of them, problems would happen and it would want to break. We tinkered with it, adding collars to shafts and adjusting things and un-jamming it again for probably the whole week. It ran at points with just the 4 gas giants connected, but never that consistently.

It took awhile to figure out all the things that kept it from working well and how to fix them. It would be about 8 months until the next show, which was Maker Faire 2015. In that time, we worked on fixing the sculpture at a relaxed pace. Things that were broken, and how we fixed them:

• The 6 foot ring gears that the 4 inner planets were mounted on had problems with jamming and lots of friction. These parts and how we fixed them will be the subject of a different Instructable in this collection!

• The gears in the gearbox were too free to move up and down. The whole gearbox is fairly loose and flexible, most of it is just locked in place by how it is assembled and has no bolts to fully constrain it. This is by design. There are a few different ways to approach precision, fit, and alignment in mechanisms. One way is to make everything very precisely, and constrain it in place tightly. In many cases such as high speed mechanisms, this is really the only way. But plasma cutting and welding finished parts together are not precise operations, so we have to make the mechanism be able to deal with it's inherent imprecision. To make something imprecise work, you have to build in adjustability and strategic flexibility, otherwise overconstrained parts will produce huge forces in unintended ways and break or jam. But we went too far at first in allowing the gears flexibility to move up and down, and they would jump out of alignment with each other. So we welded on additional 1/8" steel rings to the top and bottom of some gears. These ensure that the gear can't move up or down relative to the gear it meshes with.

• I calculated out the spacing of everything in the gear stacks precisely and, in the original build, added shims to match those calculations. But reality just didn't jive with those calculations for reasons I'm still not quite sure of. So to get gears towards the top of the gearbox to align well in the vertical direction, the ones toward the bottom had to be pulled more out of alignment and vice-verse. The gears will tolerate some misalignment due to the aforementioned flexibility, but being misaligned makes them more likely to skip if there are other problems at play too. When I rebuilt the gearbox, I tossed the precise calculations aside, and just added shims to each level one at a time to make it mesh well with it's counterpart. It was more tedious than adding in a predetermined amount of shims, but the alignment of everything in the gearbox turned out much, much better.

• We made replacements for some of the most poorly cut gears

With the rebuilt gearbox and the other changes we implemented, we ran for three days at Maker Faire! Towards the end of day two, our motor did start to die. The inner planets move the fastest and still had a lot of friction. Power required equals speed times force, and our 1/2hp motor was just not powerful enough and started to cook some windings. But it was not completely gone, and it still ran fine when we disconnected the 4 inner planets.

We hope to show Celestial many more times in the future! I really would like to get the full controllability of the planets implemented. But I think that we would need to make a new gearbox with more precisely made gears and lower friction. My dream is to waterjet cut a new set of gears, complete with beautiful patterns on them, and make some changes to the planetary gearset design so that it is not incurring a friction penalty by increasing the speed.