Sunday, August 29, 2021

The problem with string

 It is, of course, well known that everybody loves string, except when you are 3D printing. In the clocks that I've made recently, there is often a lot of stringing between gear teeth which are close together. It doesn't take much to clean it up: a few gentle swipes with a piece of sandpaper generally does the trick. However, there's always some residue left behind. The common advice is to lower the printing temperature, so I did a quick check to see if this helps. I selected a gear with 18 teeth, printed it at different temperatures and counted how many of the gaps between the teeth had significant stringing. "Significant" is a bit subjective here; roughly, I mean I would feel obliged to clean it up. Here's the results:

You probably can't make out too much in this picture. The counts of stringy teeth were:

  • 210C: 10
  • 205C: 10 or 11
  • 200C: 4 to 6
  • 195C: 3
  • 190C: 3
So this validates that a lower temperature helps. 210C is the Prusa default for PLA and I think they use it to ensure a good flow. I'll certainly consider lower temperatures in future.

Saturday, August 28, 2021

TheGoofy's clock, and a digression on balance wheels

 One of the oldest clock designs on thingiverse is this model by user TheGoofy. It has many makes and several remixes. I made this once before several years ago, and never got it to run reliably. At the time, I had a printer which was much less accurate and well-tuned than my current one. TheGoofy notes in his description that it was designed for older, more inaccurate printers. I think that I couldn't make it work as a combination of what my printer was able to produce and my ability to figure out what was going wrong and fix it.

I recently had another go, with some success. Here are some pictures and video:

The video was taken while I was still tuning it, and it's quite obvious that the beat and timing are off. Here is a later version that is a bit better:

It worked pretty much straight off with only a few changes. Some of  the parts came out undersized. In most cases this does not matter, but in the pentagonal connector between the escapement spring and the balance wheel, it is important to get a good fit. The original spring is 1mm thick, and I found that the coils flopped around too much. I found a remix with a 1.3mm spring. The end of the spring has a triangular piece which fits into the frame, and this was also far too loose. At first I held it in place with some tape, and then adjusted the model to make a tighter fit. One other adaptation I needed was to drill out the holes for the arbors in all the gears and moving parts, as they were too tight. My preferred way of doing this is with a drill bit in a pin vise. It allows you to go slowly and carefully control the drill so that you don't end up skewing the hole.

I used the v1 ratchet and no planetary drum. This gives the shortest running time in the sense that the weight falls a greater distance for a given run time. As I was regarding this a more of a clock demonstrator rather than something I intend to use as a real timepiece, I didn't worry about this too much. I like the idea of the servo driven version, and may try it out later. I found that the clock ran quite reliably with 600g of weight. I think 500g is also OK, but less than that wasn't enough. Note that TheGoofy recommends 1.2kg, and that may be needed for a different ratchet/drum combination: for a higher gear ratio you need more weight, and also get greater run time. With the version I used the weight dropped about 5 cm in 10 minutes (measured very approximately).

One issue I had is that the clock would sometimes stop dead. It took only a slight touch on the balance wheel to get it going again. After a while I realized that this was because I had some screws for setting the time on the balance wheel, and they protruded just enough to occasionally catch on one of the gears. Countersinking the holes on the balance wheel so I could screw them in a tiny amount further was all that was needed to fix this.

I also tried a variant version of the anchor in response to getting an occasional stall. I'm fairly sure that something about this throws the beat out (that is, the ticks and tocks are uneven), and I switched back to the original one.

There are two features of this clock which make it different from the Peterson and A26 clocks. It has a seconds hand, with a little extra mechanical complexity as a result. More importantly, the timing element is a spring/balance wheel combination, with an anchor between this and the escapement. I think this is called a Swiss or lever escapement. It's a much more compact arrangement than using a pendulum. In a 3D printed version, it's less practical as the spring will wear out over time. It's also harder to tune the period. I haven't found any very good guide on this, so here is my understanding of the physics and some observations about the practical reality.

Some noodling about balance wheels

In theory, the balance wheel acts as a harmonic oscillator. Wikipedia gives an expression for the period. The important factors are:

  • it is inversely proportional to the square root of the spring stiffness. So a thicker spring makes the period shorter, resulting in less time between ticks. It speeds up the clock, making it run faster.
  • it is proportional to the square root of the moment of inertia of the balance wheel. If you imagine the balance wheel as being made up of lots of tiny masses, the moment of inertia is then the sum of each mass times the square of its distance from the axis (mr^2). So a heavier balance wheel or moving some of the mass outwards makes the period longer and the clock runs slower.
The balance wheel has its own intrinsic mass, and also has eight holes round it which you can insert screws into. The screws can be moved in or out to a small degree and you can choose how many to use provided they are kept in pairs. So by adding or removing screws or adjusting their position, you have some control over the timing.

Now this is all for an idealized system, and in a clock there are at least a couple of things that might make it different. I don't have the skill to analyze this in detail, but my thoughts are:
  • gravity is acting on the screws attached to the balance wheel. The direction of the gravitational force relative to the balance wheel changes as the balance wheel moves. So the resulting moment on the balance wheel is also different. This implies you get different effects depending on which of the balance screws you use.
  • when the nub on the spring hits the anchor, it loses some energy, and it then gains some energy back as the trailing edge of the anchor hits it. It also interrupts the smooth motion. I've no idea how this would affect the period, if at all.
Note that you will find some descriptions on the web of adjusting the position and setting of certain balance screws having a special effect. I think this information needs to be taken carefully as it is often referring to a bimetallic balance wheel, which behaves differently from the kind we are using.

I did a few experiments to see how changing the weights on the balance wheel affected the period, by adding and removing screws. There are eight holes for screws round the balance wheel. If you imagine it vertically, I'll call the top pair A, the next one down B, the ones just below the midpoint C, and the pair at the bottom D. Note that this depends on exactly the orientation you choose for the balance wheel relative to the spring. You can also position it so that there is a screw at the top and bottom, and there are other orientations which are unbalanced.

I initially used M2.5x4 screws. I timed how long one rotation of the seconds hand took. The spring for these experiment is 1.3mm thick, though I think as a result of the slicing parameters it is probably more like 1.25mm. I noticed that with weight higher up, the movement of the spring was less regular. It looked in some cases as if it was about to tangle (one loop catching on the next one). Also, I doubt that I was setting the screws to a consistent depth in the experiments, and as noted this affect r in the mr^2 computation of the moment of inertia.

Here are some results:
  • screws in A, B and C: 92 seconds per revolution of the seconds hand (and somewhat uneven).
  • screws in B and C: 77s.
  • screws in C only: 71s.
  • screws in D only: 56s. Note that this case has the same theoretical moment of inertia as the previous one, and so supports some of my speculation above.
  • no screws at all: 75s. On a second run I got 68s.
The last reading is a bit odd. I think what is happening here is that the mass of the balance wheel is now so low that it can't transfer enough momentum to the anchor and hence to the escapement wheel. Some of the beats were noticeably uneven. I think the other results are somewhat consistent, in that I reran the timing for a couple of the cases and got the same result to within a second.

I now changed the spring to a thicker one, 1.5mm deep, with these results:
  • D: 56s.
  • C: 61s.
Another little bit of physics here. For a spring with a circular cross section, the stiffness varies as the diameter of the wire to the 4th power. The spring in this clock has a rectangular cross-section and we are changing only one dimension of it, so it's a reasonable guess that the stiffness should change as the square of the depth. The period varies as the inverse square root of the spring thickness, so it should be linear (inversely, that is) in the thickness. We went from 1.25mm thick (nominally 1.3mm) to 1.5, so a factor of 1.25/1 = 0.833. And in the D test, the change in period is 56/66 = 0.848. So it looks like physics is working.

The answer

The main reason for the analysis above is that I haven't understood how to tune balance wheels in the past and I wanted to work through the logic. The short summary is:
  • stiffer spring means slower.
  • more weights means slower.
  • position of the weights matters.
The actual configuration I ended up with was a 1.5mm spring, balance wheel oriented with screw holes on the vertical axis (different to the A/B/C/D configuration I described above), and no weights at all. This gave me pretty close to 1 minute per rotation of the seconds hand. I saw some variation across measurements at different times. Also, the clock sometimes runs smoothly and sometime stutters a bit. I think this is probably when I hit spots on the gears which I hadn't finished well - I didn't clean everything up very carefully.

This is another nice design - thanks TheGoofy (aka Christoph Laimer). Looking over the last three clocks, you might be able to see there is a progression, from an easy hours+minutes pendulum design, to a slightly harder hours+minutes horizontal pendulum design, and now to hours+minutes+seconds balance wheel. I have a few ideas for what I would like to try next.

Sunday, August 22, 2021

Short notes on clock calibration

Here are some notes from calibrating and comparing the two clocks.

The A26 clock is supposed to run at 3600bph. I calibrated it to this value when I set it up. After leaving the clock without running it for a few days, I then set it going and found that it was gaining about 30 seconds in 5 hours (6 seconds per hour). Just before I stopped the run, I measured it 3640 bph. It's probably quite temperature sensitive due to the use of a brass rod for the pendulum.

The Peterson clock is intended to run at 5850bph. I set it that way originally and it has run continuously for around 10 days since then. On a test over 30 hours or so, it gained around 2 minutes (4 seconds per hour), and I measured it at 5870bph.

Both measurements of how fast the clocks ran could be very inaccurate as they rely on judging the time by eye.

Another data point. In one hour, the weight on the A26 clock fell 120mm. So you would need a lot of height or to double up the weight chain to get a good run time. The weight was about 300g with a 30g counterweight.

The weight for the Peterson fell about 5mm in one hour. So with a four foot drop, you should be able to get 10 days from it. The weight is 7 pounds 12 ounces, with a doubled weight cord.

Sunday, August 15, 2021

Printing and Remixing the A26 Clock

Several years ago, thingiverse user A26 published a model for a simple clock. I made one version of this in 2019, and was never very satisfied with it. Following from making Steve Peterson's clock recently, I decided to have another go at it, and to make some design changes to improve it. The first change I made was to adjust the tolerances on some of the parts. Several of them fitted together very loosely so that, for example, gears would slip on their shafts, and bearings come loose. I think this is likely due to variation between prints and slicers.

The most serious problem was in the design of the anchor. It uses a knife edge: basically a V-shaped pivot which rests in a groove. A gust of wind can make the pendulum swing about the vertical axis (if you see what I mean), and as I found with my original build, if you are clumsy as I am, you can easily knock it out of place entirely. I therefore redesigned the anchor somewhat along the lines of the Peterson clock, so that it is mounted on a 3mm shaft. This entailed extending the frame of the clock to allow extra room. The result is much more stable. I haven't yet tuned the timing of the clock or allowed it to run for a long time, but so far it seems to be working well.

Here's some pictures and video:

The filament is PLA throughout. Most of the parts are directly from the original design or my modifications of them (thingiverse remix), with the drum and ratchet from the self-winding version. (I started on adding the self winding mechanism, but got frustrated with it and gave up). The face also comes from this design, held on with some clips that I knocked together. I added a couple of small clips that slide tightly onto the pendulum shaft and help stop it from slipping. The main shaft and pendulum shaft are stainless steel, as I had pieces about the right length. All the other shafts are brass. I much prefer brass as I can cut it without power tools. I've been using this saw, which allows very clean and precise cuts with minimal effort.

To set the hour, the best approach is to hold the part called Wheel 4A stationary (see the original design for which this is), and turn Wheel 5. The shaft that connects Wheel 4A and 4B is snug but not so tight it can't turn. I glued the 4B end of the shaft in place. For the minutes hand, I hold Wheel 3 stationary and rotate the minutes hand on the shaft. The first time I did this, the hand broke, so I made a new version which is stronger. I am using about 200g weight.

Adjusting the beat (that is making the ticks and tocks of equal duration) and the timing (beats per hour) is difficult. For the beat you have to have the pendulum shaft exactly centered and the weights at exactly the same distance from each end. For the timing, you have to move the weights in or out on the shaft. Fine adjustment is tricky; the designer of the self winding version addressed this by threading the pendulum shaft and weights, but I am not able to do this.

Note that my change to the anchor means that you can't get the timing right. The clock needs to tick at 3600bph, and the slowest I could get was around 4400bph. This can be fixed by either using a longer pendulum shaft or modifying the pen weights so that they have a longer stem. I used both: the shaft is 250mm, and the longer stem pen weights allow for a bit more range of adjustment (not shown in the pictures above). The fine adjustment is tricky. What worked for me was to measure the beat rate with the Cuckoo Clock Calibration app, move the weight on one side to make the clock faster or slower, then move the weight on the other size until the pendulum shaft was horizontal. Towards the end of the adjustment, you may need to move the pen weights as little as 0.5 or 1mm, which can be hard to do precisely.

Another nice design - many thanks to A26.

Sunday, August 08, 2021

Steve Peterson's 3D Printed Clock

I have made several attempts at making clocks using a 3D printer, always ending in a clock that didn't run at all or that would only run for a short time. Some of this is attributable to the quality of the prints. My first two printers really weren't up to the level of precision that is needed. Another source of problems is my inexperience with debugging clocks, and mechanisms in general. I know how to think about solving software problems, but I don't have a good feel for where to start with mechanical ones. I've gotten better at this over time, and in the case of clocks I have a better understanding of them as physical systems than I did at first; I mean things like how power is transmitted through the system and how it interacts with the elements that control the timing. And finally, some of the designs that I tried just weren't as good as they might be. I don't mean that the designer was negligent, just that you find many objects on 3D printing sites which worked when the designer made then and so they generously shared the design with the community, but they didn't test them to allow for variation in printers, materials and the abilities of the person making the clock.

I recently came across a design by Steve Peterson for a clock intended to be easy to make and get going. He accompanies the design with detailed videos on assembling and debugging the clock. It has variants for different run times, from 7 days up to 32 days, with 10 days being the recommended starting point. (Strictly speaking, the run time depends on how long it takes the weights that drive the clock to reach the ground; if hung in a deep stairwell, it would run for longer.) I successfully built this clock and have it running, and enjoyed the process.

Here are some pictures and a video of my build of it:

One element which is not complete is the weight shell. I am waiting for Amazon to deliver the BBs to fill it and will then fit it.

In the mean time, metal water bottles provide the weight:

The dog bed provides a convenient soft landing in case something should break.

The frame and weight shell are printed at 0.3mm instead of the recommended 0.15mm to make the print time more manageable. Most of the parts are printed in regular or silk PLA. The weight shell is rainbow PETG; it's a bit rough due to the 0.3mm layers and because I upped the print speed for it. I made one modification to the original design. There is a gear that has to be slid to the right position on its arbor, and also has to be so tight on the arbor that it it won't rotate. I replaced this with a version that could be held in place with two M2x6 machine screws like this:

The screws would be better as M2x4, but they were just too short. This change makes it easier to position, while giving some confidence that it won't slip.

The debugging procedure recommended by Steve starts with checking the pendulum will swing freely for about 10-12 minutes. He recommends cleaning the factory grease out the bearings to reduce friction. At first, I got it to run for just under 10 minutes, this was because I had put the wrong bearing on, so that only one of them was clean. The clock as a whole ran initially for 20 minutes and then 40 minutes. At this point, I disassembled it, fixed the bearing and visually inspected everything. One of the gears has some distorted teeth due to first layer adhesion and two others had minor amounts of elephant's footing. I reprinted all of these. With 2 pounds 15 ounces of weight, it ran for 7 hours and then on a second run for almost 28 hours. I increased the weight to 4 pounds 7 ounces, and and time of writing it is just coming up to 60 hours, with one rewind.

I think when it stopped after 7 hours, it was probably because I didn't have the beat right. Steve discusses this at length in the debugging video. I found an app called Cuckoo Clock Calibration which really helped in checking it, as well as setting the beats per hour by adjusting the pendulum length. The app uses the phone's microphone to listen to the ticking and reports the time between ticks, whether the clock is level and the overall rate. One other thing I noticed is that the tick sometimes has a slight double-click sound to it. Perhaps the pallet is bouncing off the escape wheel tooth for a moment. The app confirms this: you can see an occasional double spike in its display of the sound waves (I've tried to take a screenshot, but the noise of pressing the button to do it swamps the sound of the clock).

I also noticed that the ratchet was not completely in position after rewinding, like this:

I'm planning to lightly sand the inside of the ratchet drum and make the springs a little weaker. This could be the source of the stoppage after 28 hours, as if the ratchet then slips, it might interrupt the operation of the clock.

A couple of other build notes. I used brass for the 3mm arbors, as it's easy to cut. For the 1.5mm ones, I already had some 1.4mm steel axles of about the right length, and then seem to have worked fine. Several ballpoint pens gave up their lives in order to supply me with springs. There's a little finish work I still intent to do, for example the minute hand has a small blob of filament on the edging.

Huge credit goes to Steve Peterson. It's a good design with good supporting information. There are many thoughtful decisions, such as using gear teeth with a profile that makes them easier to print. I'm really happy with it, and plan to move on to some more challenging clock models next.