Member postings for John Haine

"extra force is needed to get a mass moving"...inertia?

Tony, nice! What is the tool called please?

I have used these which are adjustable and they work well.

**LINK**

If you insert a link using the "globe&link" icon and paste the text into the URL box you can hide all the superfluous characters, which I did with this link.

Edited By John Haine on 07/09/2023 11:48:35

"All models are wrong, but some are useful." https://en.wikipedia.org/wiki/All_models_are_wrong

Magnetic "reluctance" has a specific meaning, being the relationship between field (measured in amps/metre) and flux (tesla) in a magnetic circuit. It isn't a measure of the magnetic attraction or "reluctance to let go".

This is my mental picture of the arrangement. The rollers are two soft steel discs that form polepieces for a strong short cylindrical magnet mounted coaxially between them. If the contact is good virtually all the flux from the permanent magnet will flow through the polepieces, and establish a magnetic field in the space outside them, mainly concentrated in the air gap.

The lower picture shows this hanging from a flat soft magnetic plate. Since the plate and discs are in contact at the tangent point, most of the actual flux will flow through this point as that is the path of minimum reluctance. There will be some flux in the gap close to the contact point but it will fall off rapidly with distance. If there was any imbalance between the forces on each side of the contact point then the roller would move on its own - symmetry ensures it won't move.

In a real suspension the radius of the discs would be much larger and we will only need a small proportion of the circumference, but if we made sure that there was enough that the movement of the contact point is only a small proportion of the width I would guess there would still be no net magnetic force - given a suitable field analysis program we could compute this.

So I don't think that it's obvious that the system won't work at least from a magnetics point of view.

Edited By John Haine on 07/09/2023 11:43:50

So I only need to skip pendulum pulses, just seemed easier.

Ah, Joe, deeper waters here...

A pendulum's period depends on its amplitude, the fractional rate being given by (angle^2)/16 where angle is in radians. For small angles this is nearly negligible but gets more significant as the amplitude gets larger. Remember that 1s per day is nigh on 1 in 100,000. A pendulum designed for exactly 1 second period would lose 1 second per day at an amplitude of only 0.7 degrees. This is why we want to control the amplitude. Traditional "regulators" also use rather small swings because that also reduces the sensitivity because of the square law.  This is called "circular deviation" or sometimes "circular error". (CD)

If you impulse the pendulum exactly at the centre of its swing that has no effect on its period. If you apply the impulse early (or advance the phase of your sine wave drive) it makes the pendulum period slightly less; if late it makes it longer.  This is "escapement deviation". (ED)  Its magnitude depends on the phase shift and pendulum Q and for small errors the fractional change is (phase error)/2Q. (Strictly tan(phase error)/2Q.)

What one generally does is control the amplitude to keep it constant so the CD is constant and can be "adjusted out".  Likewise one tries to keep the impulse phase constant so ED can be adjusted out.

Many clocks have non-central impulses and when the impulse strength changes (for example because the spring unwinds), the amplitude reduces so it runs faster and the phase angle changes.  If the impulse lags and gets later it slows the pendulum down and if you're lucky the two will cancel out.  

The ultimate is Clock B which plays these effects off against Q changes due to varying barometric pressure to compensate for that too.

There have been designs that deliberately change the amplitude to adjust the clock, event to regulate it to an external reference.  A problem with this is that the amplitude, and hence period, responds only slowly to impulse changes so the loop is very slow.

What a few people (well certainly me and Dave I think) are proposing is to have the pendulum running as stably as possible with controlled amplitude (and in has case eventually in a vacuum), accumulate the phase of the pendulum then digitally correct this "post hoc" based on environmental observations before displaying the "time".

Edited By John Haine on 06/09/2023 15:44:59

Edited By John Haine on 06/09/2023 16:21:52

This is not a random error so not subject to the "root-n" type of averaging if that is what you mean Michael? Anyway 0.4us is one part in 2.5million compared to a second.

Extract from response from Tom.

"The PIC chip that I use has an internal four-phase architecture so a 10 MHz external clock becomes a 2.5 MHz internal clock and that translates to a 400 ns instruction cycle time. Thus any numerical result from a picPET is a multiple of 400 ns, which is 0.4 us. [1]

For mechanical timing, even for the best ever pendulum clock, 0.4 us is plenty good enough since measurements are usually limited by the sensor or the pendulum itself."

500mm radius.

The resolution is 100ns because the thing is clocked at 10MHz. Tom quotes the "granularity" as 400ns and I have to admit I don't understand what that means! Here's a sequence of numbers from a run.

6725.56415040000
6727.55243760000
6729.54073600000
6731.52902880000
6733.51731360000
6735.50559720000
6737.49386360000
6739.48219080000
6741.47048760000
6743.45877480000
6745.44706960000
6747.43536440000
6749.42366040000
6751.41195520000
6753.40024800000

So far as I can tell the digits after the 6th decimal place are all even so multiples of 200ns, I'm not sure where the 400 comes from. I'll ask him. Whatever, it's at least an order of magnitude better than the resolution needed for my purposes!

Dickson type. RDG may stock?

Just like to remind you of the benefits of a picPET with an oxco...

I thought I'd try generating it in CamBam for CNC milling.

Assuming it would be milled from 2mm plate, the top shows the plan view and the bottom the toolpaths including 6 holding tabs, using a 3mm endmill. These not positioned on the "active" top left face as they have to be filed away after cutting. You can just about see that this face is slightly curved.

Though designed initially "flat", I rotated the design to avoid one of the axes having to reverse while cutting the curve which inevitably leaves a tiny mark due to even the smallest backlash.

Exactly.

Like this - not to scale. Upper surface 500mm radius, exaggerated width but ~40mm, thickness into page say 10mm. There would be a blind hole in the lower face for a pendulum rod to fit into, probably carbon fibre for minimum mass. Assume the bob is on the lower end of that rod so its CG is 100mm from the top face. Material has to be steel or iron so it can be attracted to the lower face of a strong magnet that will support the bob weight. Within the above limits the amount of material in this needs to be minimised so the pendulum approximates as closely as possible to "simple".

Just for information, the reason for the circular arc on the top is so the CG of the bob will swing in a cycloidal path at least up to +/- 10 degrees from vertical.

We don't need a 1 metre dia bit of metal, we need a small bit with a radiused face with 50cm radius of curvature on it, which would need to be about 4cm long. and maybe 6 to 10mm thick. Width behind the curved face wouldn't need to be large, less than 10mm I'd guess.

Cnc mill the profile. Polish by hand. Actually 1 metre approx outside diameter.

It would certainly be powerful if true but is demonstrably not! Michael's reductio ad absurdum is one demonstration.

I think this discussion got a bit sidetracked by the notion of "any point is cycloidal" - your original point about suspending a pendulum from a magnet is very valid and with the "shoe" would be a straightforward way to make a truly cycloidal pendulum. A bit of analysis needed to estimate the errors due to "compounding".

I have had another read through Woodward's analysis. He mainly looks at the case where the roller runs on the top of a flat plane (or knife edges in Dave's original proposal). The pendulum rod is fixed to a point on the roller so its axis passes through the roller centre, and the rod is significantly longer than the roller radius. He shows that for this case the circular deviation is increased by a factor (1+4r/L) compared to an ordinary suspension for small swing angles.

For the case where the roller is like a hoop suspended from the plane (by magnetism for example as Dave proposes) the same analysis applies, except that the circular deviation is reduced. Obviously you would want that to be reduced to zero, and he shows that for this to be true the bob mass has to be on the periphery of the hoop, when of course its motion is cycloidal. For longer rods I think it looks like the circular deviation will get larger the longer the rod and be possibly of opposite sign to its normal value.

I think the overall conclusion must be that roller suspension can only cancel CD for the case of a "suspended hoop" with the bob on its periphery, when the motion is cycloidal. This is only true for a simple pendulum anyway, all real pendulums are compound. But I guess Duncan's idea could be used.  Have a very light rod of carbon fibre with the bob at one end; and a steel "shoe" with a cylindrical "sole" at the other of radius equal to half the rod length and long enough to allow for the intended maximum angle.  Though the shoe would have significant weight it would not contribute much to the moment of inertia since the axis of rotation is on its upper surface.

Edited By John Haine on 04/09/2023 17:49:00