More Analysis… and a can of worms

So I was pretty confident that my initial guess for a 3/4″ drive shaft would be sufficient. I was wrong.

It turns out wood is HEAVY and with the sprockets mounted 5″ from the bearings you will pull the sprockets down about 1/8″ when you step on the wall (for a 250lb climber). Combined with some bending in the frame this would put us past our allowable total deformation. And the shaft will bow ~1/2″ in the center, not that you will be able to see it but that seems excessive to me. Also it means there is no way you could simply scale this design up if you wanted a 6′ wide wall, which I think would be a nice option.

By increasing the shaft to 1″ the bending at the sprockets will go down to ~1/32″ and 3/16″ at shaft center. Probably an acceptable amount. This led to a new problem: there is now no room for the previous bearings, with the stamped housing, to mount between where the planks run. After shopping around I found some cheap bearings in a chevron mount for around the same price, $12US. Though now the shaft needs to be longer and the gearbox hangs further out.

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Changing to a 1″ shaft also makes it very hard to find reasonably priced speed reducers with a hollow output shaft. Going to a solid output shaft will require a coupler (35$) and leave our gearbox hanging waaaayy out, but it should come out a little cheaper than the original gear box. As shown below. I suppose it doesn’t look crazy but I am not excited about it.

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If we are changing gear boxes anyway a new possibility opens up. The reason the drive sprocket was so small (below) was to keep torque down on the gearbox, allowing us to use a smaller cheaper gearbox. This choice necessitated the use of an extra idler sprocket next to the drive to spread the chains apart and leave room for the walls internal structure.

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But if we go to a bigger, higher torque gearbox and a correspondingly bigger drive sprocket we could skip the extra idler, saving a bit of money, and extra parts and messing around trying to line everything up. Like so:

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The catch is that the internal friction in a bigger gearbox might require a larger motor and larger motor driver circuit. Which would then be more expensive. The wall is largely driven by climber weight, so pretty much any motor will work, but it would be nice (but not necessary) if the motor could move the wall without someone on it. I am kind of torn on how to proceed. Any thoughts you might have would be helpful.

Wall Structure

While I was starting some structural checks on the wall I realized we have another unanswered question. How much flex is tolerable in a climbing wall? We have all seen this: a boulderer in the gym lunges to a jug and everyone cringes as they see the whole wall bow perceptibly. The climber has no idea the hold moved.

A steel frame, like the one for the prototype, will be able to flex a great deal before you are anywhere near permanently deforming or breaking the frame. So the main concern when designing the structure is how much flex should we allow. I believe that if the climber doesn’t notice the flex then it should be fine, and the less steel we use the better. How much do you think a climbing hold can move before it will become noticeable to the climber? Take the new survey and make your opinion heard. From some experimentation in Kyle’s garage I am taking 1/8″ as our maximum deflection.

All the images in this post represent an finite element analysis (FEA) of the entire steel wall frame. The first check I ran is shown below. This analysis shows the stress applied to the wall with loads representing the full ~300lbs of wood planks weighting on the wall, a 250lb climber hanging off the upper right corner of the frame, and a 30lb side load applied to that corner as well. This seemed like a reasonable but aggresive loading scenario to initially verify that the frame wouldn’t collapse under normal use, and looking closely we can see that there are no points of stress higher than ~5ksi. So we have a generous factor of safety against failure, roughly 9 assuming we will use 11ga, 44w steel. I had guessed that 10ga would be necessary but after some initial checks I reduced the thickness to 11ga. We could easily go thinner but 12ga saves surprisingly little in cost and 13ga just seems too thin.

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Stress in frame

The figure below shows the expected deformation with just the climbers weight and the side load applied. This provides an estimate of how much the climber will see the wall move if they suddenly grab the top corner, because the bending due to the weight of the planks and frame will already be present. In this case, with the structural bits being 11ga steel, we will see ~1/32″.

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Deformation of frame, with base stuck to floor

In this simulation the bottom of the frame is assumed to be stuck to the floor. This seemed to me like a reasonable assumption since the ~500lb weight of the thing should keep the base from sliding around. If the floor is assumed to be frictionless, the frame shifts on the floor as shown below and the top corner will move 1/4″ (twice our permissible limit) due to the side load, as shown below. (note that the deformation is not to scale, it is exaggerated for illustrative purposes) This is mainly due to the bottom of the frame deforming out a square.

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deformation of frame sliding on floor

The addition of a cross brace, below, will bring the deflection within the acceptable  range. However, I am inclined to leave the brace out and see if the prototype feels too wobbly and add it in if needed, because the unit will probably behave somewhere in between the fixed and the frictionless case. Spots like the top of the base frame might also require additional cross bracing when we finally get to pulling on a prototype and seeing how wobbly it feels.

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deformation of frame with brace added to base

 

From these simulations it also emerged the lower members tying the two halve of the lower frame together don’t need to be formed angles. We can get away with them just being flat bar without significantly changing the deflection. This would be ideal as your crashpad wouldn’t be sitting on the angle making the landing surface uneven. This will also be cheaper since it eliminates 2 parts that require box bends, during forming. A process that requires a change of tooling, making them much more expensive than they would be otherwise.

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Base frame without and with the unnecessary flange

The Drive

Project update: I am waiting for some quotes on the cost of steel for this thing. I work with these vendors regularly so I have some handle on what things should cost, but if it comes out at 2x what I expect I may have to scrap this project.

How do we make it go?

A up-close view of the drive assembly is shown below. From right to left we have the motor, coupler, and a right angle gearbox. Behind the gearbox you can see a sprocket on a shaft, the shaft is driven by the gearbox and the wall panels ride on a chain driven by the sprocket.

The motor does look relatively tiny. The idea is that by using a non-backdrivable gearbox (worm gear) the climbers weight will drive the wall and the motor will simply act as a governor, controlling the wall speed. So we don’t need a big motor, just big enough.

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Wall Drive System

In my experience walls that are driven by climber weight alone can feel “squishy”. When you really push with your legs, say for a dyno, the wall accelerates robbing energy from your movement, changing how you climb. A wall running at a constant speed doesn’t have this same feeling of give. This is the main reason I was inclined to go with a motor-driven wall.

It would be nice to have the wall driven by climber weight ’cause hey free energy. Ideally, we would simply have a brake that could maintain a constant speed regardless of load, but the worm gear seems like a cost effective solution. I am open to other ideas!

Using a stepper motor here should be ideal due to the high low-speed torque and ease of control. With the gearbox and the coupler, the climber won’t be able to feel the individual steps.

The flexible coupler lets you get away with the shaft of the motor and gearbox not being perfectly aligned. This means we can use a piece of formed steel to mount the two components easily without, potentially, destroying the bearings in the motor. For the extra 5$ it is likely worth using this over a rigid coupler.

Issues: We are just about maxing out the gearbox I dug up as far as it’s torque rating goes for a 200lb climber. It is still within its spec but if anyone has a lead on high torque (~300 in*lb), low speed (60rpm output), cheap (<200$usd) gear boxes let me know! Friction from the wood panels sliding in the channels will help reduce torque on the gear box. So if we can keep the friction high in the channels without adding undo wear to the channels or the wood that would be awesome. (I am still working on getting some science behind the wear in the channels)

How do we change the angle?

Based on our survey results (all 8 of them) I am inclined to leave the range of angles available right where they were in post 1, so around 0 to 30° overhanging. There are two options for how the angle can be adjusted. There is the cheap and simple method, where the wall frame is simply pinned in place in one of a series of holes as shown below. This is the approach I will be taking with the initial prototype.

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The easy way. Pin the wall in place.

There is also the deluxe option which I have been designing. In this design instead of the wall being pinned in place its angle is maintained by a small gear that runs on the curved plate.

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Wall Angle Drive Gear

This gear is driven by a gear box tucked inside the wall frame behind the wood. This gearbox is just a smaller version of the one driving the wall. So when the motor on this gearbox isn’t running the wall will be locked in place. The gearbox and motor arrangement are shown below with the mounting bracket hidden (it hides the gearbox).

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Wall angle gearbox and motor

This is kind of an expensive upgrade, at around 300$US. But it would be cool to have the wall angle change automatically. You could have programs for different routes, that change angle, a program for interval training, or other options. I was thinking it would also be neat to make the controller program open-source so it could be readily “hacked”.

ParetoWorks Review & Ice Axe Design

Alright this is my first major diversion. I warned you that this was coming.

Aside from working on the mobius wall design I have also been playing around designing and building ice tools like the one below for a couple years. This one uses a purchased Grivel Pick.

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A homemade ice axe handle.

Recently, I had the opportunity to Beta test a software called ParetoWorks, a topology optimization software, which has led to a dramatic change in what my ice axe designs look like.  In this post I am going to discuss my experience using this software and how it affected my approach to designing a new ice tool. Having gone through this process I think that this software, and software like it, will lead to a fundamental shift in how many structural design problems are approached.

ParetoWorks is a plugin for Solidworks that helps you optimize the shape of structural parts. It was created by a research group from the University of Wisconsin, Madison and overall I think it is a very slick piece of software. When I started looking at it they did offer a trial version with somewhat limited functionality. Last time I visited their website the link to the trial version was gone, but if you can dig it up and have access to Solidworks you should definitely try it out.

The software is used much like Solidworks Simulation. You can assign material properties, boundary conditions, loads, and run FEA. It doesn’t have the nice design tree layout like Solidworks Simulation but it is easy enough to find all the buttons. There are only a few basic steps required to create an optimized part using ParetoWorks: initialization, set-up boundary conditions, finite element analysis (FEA), and Optimizing. All of which are neatly categorized in their menu.

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The ParetoWorks interface with all sub-menus collapsed

Boundary conditions are represented on your model using nice little icons representing your loads (arrows) and fixtures (black spheres for the one used below). It has a good selection of boundary conditions available, which should cover most any case you would need.

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Initial model to be optimized, with boundary conditions shown

During my trial period the icons did seem to go weird when using “English” units. This might be due to my using SW2014 still. I also couldn’t find a way to edit boundary conditions, you can clear them and make a new one but an edit tool would be nice. However, Sciart has been extremely responsive so far and I would expect they will be improving things rapidly over the next year or two.

For FEA you are presented with only two options: number of elements in your mesh and symmetry. After the FEA has run you can view a stress or deflection plot and get an idea of how your initial part performs. After this we get into optimizing the initial part.

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plot of stress in initial model
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deflection of initial model

I would like to have more options regarding how the FEA is setup, mesh is created, and results are viewed. It would help make this software a viable replacement for Solidworks Sim for some users and just give the user a little more control. The intended use of the software is, however, to provide a simple interface to guide you to a more optimal design at the beginning of the design process and fewer options may be better if that is your sole intent. But as a personal preference I always prefer the tools I use to be less of a black box wherever possible.

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The boundary condition and FEA menus

The optimization menu is really the core of this software. This will remove material selectively, minimizing either stress in the part or deflection, until one of your constraints is reached. The available constraints being: a material volume target, a max. deflection, and max. stress. I would love to know what optimization method they use, ’cause it is blindingly fast, but I would guess they are keeping it proprietary.

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The optimization menu

There are a few more options available here than in the FEA menu. You can optimize for either maximum strength (minimizes stress in the part) or maximum stiffness. You can also specify a draw direction. This is handy as it means you won’t have any features overhanging the selected plane so you could cast the part with a split line on the plane, or machine the part knowing there won’t be any pockets that would be difficult to mill. I know that more options are in the works for optimization, so that will be cool. I really like how you can view the stress and deflection in the resulting part immediately. This gives you the opportunity to make some decisions about it’s performance and tweak your optimization or applied loads and fixtures accordingly, without doing anything to your original part. The optimized part is presented, by default, as an orange blob like that shown below.

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An ice axe optimized for a given set of constraints

Results can be saved out as an STL file. Which can then be imported into your part or assembly for reference. This process is a little onerous. It would be awesome if Paretoworks had a single button to import the STL into the active part as a feature. From here you then remove material from your original part using standard SW tools to create a design like that suggested by ParetoWorks. You could, potentially, simply manufacture a part based on the resultant STL file but I can’t imagine many instances where that will be practical. The typical user will likely want to tweak the output before manufacturing. Using “english” units also seemed to mess up the scale of saved STL files.

What is really interesting about topology optimization software is how it changes the design process for complex, structural parts. In my normal work flow, I would do some rough hand calc’s and sketch out a design that should work. From there I would check it’s performance using an FEA tool and modify my design to improve it based on those results. I would then repeat this process until I was happy with the result. With software like ParetoWorks you can simply start with a shape that simply captures your required boundary conditions and maximum available envelope and let it generate a part that is very close to optimal right from the start. No hand sketches or calculations required. As an example you could start with a giant blob of an ice tool and get results that might be counter-intuitive but would meet whatever criteria you put into the software, like the battle axe shown below.

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An absurd ice tool design

I have probably run about 20 different optimization cases on my basic ice tool, playing with different FEA and optimization settings in ParetoWorks. Just to get a feel for the software. During this process I was fascinated to see that the optimization algorithm can converge to distinct local minima (I think). In this case one minimum looks like the example shown above (the normal one) with the reinforcing ribs all lying along the central plane of the ice tool, like an I-beam, making the tool symmetric. The other becomes asymmetric toward the handle, with ribs on alternating sides of the tool:

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A bitchin’ ice tool! Designed using ParetoWorks

In both solutions the tool design comes out absurdly light, under 500g. (I’m not really sure which is the global min.) Either should still pass the standard strength tests (barely by my quick checks but that is the point) as a T-rated ice tool. It probably wouldn’t have the heft to even stick into ice! And it only took a couple hours to arrive at this solution. I could have spent hundreds of hours optimizing my design the traditional way and never have arrived at a comparable solution.

I should note that a single run, from when you hit go till it converges at a solution, took anywhere from 20 to 30min. for this part. Considering that this is conducting FEA with 60,000 to 80,000 nodes at each iteration and running an opto. algorithm, this seemed blindingly fast to me. I was super impressed with this having played with other optimization software.

My take away from this has been that if you are in an organization where any time is spent trying to optimize structural parts, to reduce weight or save on material costs, a tool like this could prove invaluable. It will reduce the time taken to reach a solution and produce better results than a manual approach ever could. I have read a lot of buzz around topology optimization being a great design tool for 3D printed parts, but as this design (which I am machining in my garage) shows it can be readily applied to conventional manufacturing techniques as well.

A few more hours in the garage and we will be able to see how well this actually works!

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Brainstorming: Follow-Up

Thanks for everyone’s help so far.

A few interesting points have come out of the discussion regarding the first post:

1. Help me out, I need some input:

A helpful co-worker prompted this by saying “he would want the wall to go slabbier”. How slabby should it go? How fast should it go is another valid question. And taller is obviously better but how tall is too tall? What would you have room for? In the current design these decisions were just based on my opinion. Please help me out and take this 3 question survey, or leave a comment to let me know what you think.

2. Research needed:

Trent, of The Climbing Life, suggested putting a PE bearing material in the channels. Which is a good idea but might not be necessary. This has led me to do a little reading regarding wear rates in wood bearings (another place where wood rubs on another material for extended periods). Now tribology isn’t my favorite subject but a little work here seems like a good idea, just to make sure things don’t wear out unexpectedly fast. So you can expect a post including math, if anyone wants to see it, in the not too distant future.

3. Gearbox mounting

The co-worker from 1. also pointed out an issue with the gearbox mounting. So I will be fixing that before bothering to show more details.