In an effort to reduce the pendulum pivot friction for clock 4, I have decided to try setting the pivots on metal points rather than wood. The points and matching cups are cut from brass.
While a little hard to see, the pins mount in holes drilled in the end of the pendulum's hook-shaped protrusion. Once mounted, I marked where they sat on the hanger, and drilled holes to receive the cups. It sounds more complicated than it is; here is a zoom-in of the installation.
In the process of installing the pins, I snapped off the pendulum's hook. So that is now gluing. Once it's dry, I'll be able to tell if this helps to reduce the pendulum's running friction.
Update: after drying, for the unloaded pendulum, I get a median of 71 full periods for the amplitude to halve. That puts the unloaded Q = 320, which is a little bit better than before.
Continuing the thoughts from the previous post... How much power does the current Clock 4 pendulum and count wheel consume? Especially, how much weight is really necessary to drive it?
I'll treat the pendulum rod and bob as two separate weights...
Rod = 28.86 oz = 0.818 kg, centered at 24" = 0.61 m
Bob = 26.75 oz = 0.758 kg, centered at 45" = 1.14 m
Potential energy for a swinging weight = m g L (1-cos(angle))
The amount of energy at the top of the test swing (4.8 degrees) is
( 0.818 kg * 0.61 m + 0.758 kg * 1.14 m ) * 9.8 N/kg * ( 1 - cos (4.8 degrees) ) = 0.046850 J
At the bottom of the test swing (2.4 degrees), the energy is
( 0.818 kg * 0.61 m + 0.758 kg * 1.14 m ) * 9.8 N/kg * ( 1 - cos (2.4 degrees) ) = 0.011718 J.
Assuming one period of the pendulum is 2 seconds (it's not, but will eventually be):
The unloaded pendulum takes 65 periods to consume that energy = 0.270 mW
The pendulum driving the pulling pallet consumes this energy in 54 periods = 0.325 mW
The complete count wheel assembly consumes this energy in 50 periods = 0.351 mW
We can conclude that
The count wheel assembly consumes 0.081 mW,
of which 0.026 mW is due to the backstop.
These power figures are somewhat in line with my previous clocks. Clock 1 runs on 0.5 mW and Clock 3 runs on 0.8 mW. So thus far, Clock 3 is more efficient by a bit.
Assume that the escapement is triggered once per minute, is geared through a 10:1 gear mesh, and is driven by a 1" diameter barrel. How much weight is required for all of these power requirements?
The weight falls at an average speed of pi * 0.0254 m / (36000 s) = 2.216e-6 m/s.
Thus, it takes
12.4 kg = 27.4 lb to drive the unloaded pendulum,
3.7 kg = 8.2 lb to drive the count wheel (without the pendulum), and
16.1 kg = 35.5 lb to drive the pendulum and count wheel assembly.
Way too high, I think! I need to either improve the pendulum's Q or scrap the idea of the 10:1 gear mesh.
For testing purposes, if I were to drive the clock from the pin escape wheel directly, which has a 3/4" pinion, the weight falls at an average speed of pi * 0.75 in * 0.0254 m/in / (3600 s) = 1.6624e-05 m/s. The amount of weight necessary to drive the pendulum and count wheel assembly becomes 2.16 kg = 4.8 lb. (This may not be entirely safe since the pin escape wheel arbor isn't very strong.)
Here are some measurements of the clock 4 pendulum, trying to get a handle on its performance issues. Woodward is adamant that limiting count wheel friction was major concern in his designs. He employed a number of countermeasures, including anti-friction rollers, a polished acrylic count wheel, lightweight stainless steel pallets, and the merest hint of watch oil. I don't know that my situation calls for such measures, but I figured I ought to investigate.
The pendulum is a solid square black walnut rod about 2" on a side, and is 48" from knife edge to bottom. It weighs 28.86 oz, which is fairly uniformly distributed along its length. The pendulum was fitted with a crude bob constructed of short copper-clad steel rods bound together with a rubber band located 45" (on center) from the knife edge, weighing 26.75 oz.
I measured pendulum amplitudes as deflections from equilibrium.
Provided the amplitude is greater than 2.5" (3 degrees) and less than 5" (6 degrees), the count wheel advances reliably. The count wheel does not advance at all when the amplitude is less than 2.25" (2.6 degrees). Double counting occurs when the amplitude is greater than 5.5" (6.6 degrees).
Here are counts of pendulum full periods starting at 4" (4.8 degrees) and ending at 2" (2.4 degrees), which is basically a half-time. Pendulum Q can be estimated from this by Q = 4.532 * number of periods to halve the amplitude.
Unloaded pendulum: 65, 72, 68. Median Q = 308
Pendulum driving pull pallet and count wheel, but no backstop: 58, 54, 54. Median Q = 245
This indicates a count wheel-only reliable run time of about 100 seconds, which I've confirmed approximately on previous days. If you push it a bit, you can sometimes do better on occasion.
There definitely is a noticeable change in loaded Q caused by driving the count wheel, as Woodward warns. But, the unloaded Q figures are probably the source of my trouble, though. The unloaded Q is around the same as a marine chronometer's balance (and not a good one at that), and that needs an impulse every period to keep running! (I already know that the clock can run if it impulses every second.... it's not supposed to do that, though!)
Although this is probably excessive for my needs, Woodward has a table that lists a "heavy seconds pendulum" at Q = 15 000. I think I need a better resonator!
Triggering the escapement certainly consumes energy, possibly a large amount of energy. But it's unclear how exactly to measure that accurately...
Short answer: no! Medium answer: adding more weight to the bob increases the per-period energy requirement of the clock, but only up to a limit. So once you have the clock running reliably, you can (and should) add more weight to the bob to improve its timekeeping stability.
When clock doesn't run because not enough energy is getting refreshed
into the pendulum (or other resonator), it's tempting to look for easy
fixes. Adding more weight to the pendulum bob certainly delays the inevitable, since the clock will run longer before stopping. But it has a certain futile feel to it... will you ever add enough so that it will never stop? Sadly, you cannot. Fixing the frictional losses (best) or increasing the drive power are the only solutions.
The reason is a straightforward derivation ending in a simple formula.
First of all, let the angular deflection of the pendulum be A = A(t), a function of time t. For small angles, this is governed by
A'' + (c/m) A' + (g/L) A = 0,
where m is the pendulum bob mass, g is the acceleration due to gravity, L is the length of the pendulum, and c is the frictional loss constant. By the usual process for solving such a differential equation, the envelope of the oscillations will naturally decay like
This expression is the one we're after, and really we want to know how it changes as we change m. Clearly at m = 0, the change in energy is zero. Taylor expanding in m, we have the behavior for large m is approximately
Here is a plot of the overall behavior
The takeaway is that as you increase the mass of the pendulum bob, you must supply more energy to sustain oscillations, but only up to a limit. For stable, reliable operation, you should ensure that the drive supplies at least that limiting amount of energy first first, before increasing bob weight. Minimizing frictional losses should be the first priority -- which decreases c -- before trying to increase drive weight. Only after the clock runs reliably should you attempt to increase the pendulum bob weight.
Since the pendulum on the La Duchesse clock is missing, I am attempting to replace it. I started by threading a length of 1/8" steel rod with 6-32 threads. That's at least a standard size for which I could either make a knurled nut or buy one.
I find it easiest to thread by hand on the lathe (with the power off). That way everything stays neatly aligned. There are markings on the movement saying "3 3/4", which I take to be roughly the length of the lower rod. At least, that makes the rod just longer than appears to fit nicely in the case. It's easier to shorten a rod in any event...
The pendulum rod is segmented. The upper portion is attached to the suspension spring and the crutch, and is also not missing. The lower half fits a hook on the upper half. Judging by how the Ansonia Crystal Regulator was made, the lower rod is flattened at the top and drilled to receive the hook. So, to that end, I heated and hammer the top of the now-threaded steel rod flat.
I center punched the flat, and tried to drill it with the appropriate size drill. Since I was using a hand drill (I don't have a drill press, and didn't try to set up the work in the lathe... probably should have), I had trouble with the bit slipping.
So I gave up, and bent a hook in the lower half as well. This was now easy since the steel was flat and annealed. However, it was too wind to receive the hook in the top rod. So I filled the hook in the lower rod to fit the upper hook nicely.
Once filed, I hardened and tempered the rod to blue.
I center drilled and turned a bob from a piece of lead (total weight around 1 oz).
I was initially concerned about turning lead being problematic, but it went nicely enough and the surface finish was good. Since the bob will be concealed inside the case, I didn't feel a need to attempt to polish it. Eye protection (as usual) was a must, but especially so since the chips were launched everywhere... messy clean-up.
I made a number of finishing touches to the gravity escapement timer. It now runs reliably!
First, I turned a thicker barrel on the lathe
Using a square file, I cut a keyway to engage with the metal teeth on the existing barrel.
Here's the finished barrel, ready for installation...
...and here it is installed.
Many of the wheels weren't running smoothly. To find where to file, I used a pencil to mark the pinion teeth...
... which transfered to the driving wheel. This could be filed down as needed.
Quite accidentally, I made the pinion teeth an integer multiple of their driving wheel teeth. This made debugging easier! Because I found certain pairs of teeth consistently binding. I marked them like so
which allowed me to track down the problems!
I made a 4 oz pendulum bob from two halves that friction fit to the pendulum.
The excess screws are for weight!
It's worth noting setting that a gravity escapement in beat is quite a bit more delicate than I expected. Here's a picture of the timer in action...
I made considerable progress on my timer over the past two weekends. I started with a pile of parts (after sanding)...
... and ended up with a nearly complete, partially functional timepiece!
Here is how it happened...
Since the design phase, I had left the spacing between the two plates as a yet-to-be determined variable. The key distance was the winding barrel, which had to rotate freely around the main wheel's arbor and engage with the ratchet and click assembly. I wasn't quite sure how much room I'd need, so I built the winding barrel first.
The winding barrel is hollow, and has two transverse pins to anchor the winding ribbon. First, I turned the outside of the winding barrel from 1/4" brass rod. Notice the thicker end (left) to receive the ratchet wheel.
I filed flats on the narrower portions...
And drilled holes to receive the pins in the flats.
I turned the pins from 1/8" brass rod, tapered to fit into the holes.
I pressed the pins into place with the vice.
This wasn't secure enough to keep the pins in place while center drilling, so I also soldered them.
I center drilled the assembled winding barrel in the lathe.
After it was drilled, it was fit friction-tight into the ratchet wheel.
Now that I knew the length of the winding barrel, I could estimate the distance between plates. Here are the two standoffs that hold the plates in place.
I also fabricated four pivots and two hollow bushings for the three arbors.
Here are the main wheel pivots drilled and fit into the frame.
Once that was all in place, I turned the main wheel arbor so that the winding barrel fit around it. I turned this out of a single piece of 1/4" brass rod, which took a while.
Then, I pressed the assembly together -- the winding barrel is permanently captive on the arbor.
With the main wheel assembled, I could align the main wheel pivot and bushing by aligning the two plates. This ensured that the arbor was installed perpendicular to the plates; if I had assembled the plates first, there was the risk that the pivot and bushing centers might be slightly out of alignment.
Next, I started to assemble the winding mechanism. Here is the click in place; I used a short nail with a broad head to attach the click so that it can move freely.
For the spring, I used the drive spring from a broken toy car. (There are lots of toy cars around my house since Theodore loves cars! Whenever a car gets destroyed, I scavenge for useful parts, springs in particular.) The spring was easy to cut with diagonal cutters, and easy to bend to shape with tweezers.
Here is the spring installed with two small finishing nails. I put the nails in first...
... and then trimmed off their points flush with the back of the wheel.
In order to drill the other wheels, I realized that I was struggling to get perpendicular holes since I don't have a drill press. So, I made a clamp assembly for my lathe's flat faceplate. I started with a sheet of steel and drilled four mounting holes. I think that the steel was probably hardened, and I was unable to anneal it with my small propane torch. Anyway, I broke two drill bits. One was a carbide-tipped bit for drilling glass, which cracked -- thankfully after finishing the holes!
Then, came the job of cutting the clamps out. Again, much tool stress later (wore out the teeth on my hacksaw and two jeweler's saw blades), I had my clamps. I filed them neatly, so they wouldn't mark anything.
Here they are, holding the second wheel securely in place. I also made use of a wobble stick to get the center just right.
And with that, turned a simple arbor and fitted the wheel and pinion into the frame.
Now, on to the escape wheel. Again, it was important to get the size of the escape wheel before making its arbor. The escape wheel consists of two three-toothed wheels, held part by three brass pins. Here are the pins, turned from 1/8" brass rod.
The pins are pressed into holes on each of the wheels, forming the escape wheel.
Now, with the escape wheel sized, I was able to figure the length of the arbor. I learned my lesson with the main wheel: turning down a 1/4" brass rod to 1/8" over nearly its entire length so that you have a hub takes long time. To economize on time a bit, I turned the arbor from 1/8" rod brass, and made a separate hub from 1/4" brass rod.
These two items were soldered together, thereby avoiding waste of time and materials.
The escape pinion was pressed on, using my now-standard technique of pressing on the lathe.
As usually happens to me, the depthing for this wheel wasn't perfect. So I opened up the bushing and pivot holes a bit and shimmed them to fit.
Here, the escapement wheel is pressed into place on its arbor. This means that the escape wheel and its pinion are permanently attached to the outer plate.
Trial assembly; most everything seems to fit. The wheels turn (mostly) smoothly, with the escape pinion occasionally binding. That'll be a problem for later, but it will need to be managed... Anyhow, this was the end of the first weekend, probably about 10 hours in total.
The second weekend started with making lots of pins... There are (top to bottom) 2x locking pins, 2x pendulum crutch pins, 2x gravity arm pivots, and a pendulum support.
Here are the locking and crutch pins installed on the gravity arms.
Here are the gravity arm pivots. It turned out that I had made these too short, so I put washers in as a stop-gap measure. Will need to fix later.
The pendulum support rod was set up in the style of what's shown in Gary Mahoney's clock:
I slit my pendulum support rod with a jeweler's saw, filed two flats, and then drilled to receive a screw.
This allows the pendulum to be attached with a flexible hinge of some sort. For the moment, I'm using paper. Maybe I'll use a flat spring.
The whole mechanism is assembled and mounted!
It runs, somewhat intermittently, with 4lb 4oz of weight! It is noisy!
The key issues seem to be that
The escape pinion binds occasionally, stopping the clock
The escape wheel occasionally skips, in which it slips past its locking pin rather than being captured. This is kind of catastrophic since the pendulum receives an out-of-phase impulse; sometimes it can recover, sometimes it can't. I think the cause is the gravity arms slipping along their pivots.
Remaining tasks:
Cap off the ends of the gravity arm pivots. The arms tend to slip around and off the pivots
Fix the gravity arm pivots by either remaking them (preferable) or making custom washers so that they keep the gravity arms the correct distance away from the outer plate.
Fix the depthing of the escape pinion
Fabricate a pendulum bob. The current bob is attached with a rubber band
Replace the pendulum pivot with something a bit stiffer than paper -- the pendulum wobbles axially too much.
