Member postings for John Haine

7.79mm would probably be within tolerance for an m8 thread - they are always smaller than the nominal diameter. What is its pitch? Maybe it's M8 fine?

I thought it would be interesting to directly compare the normal distribution curve with a resonance curve according to the equation Dave quoted above.

In this picture the normal (blue) curve is plotted using Excel's normal distribution function normalised so the peak is unity. I've normalised the mean to unity and the standard deviation to the value that Dave measured divided by his period, to give 0.001194. I've plotted the vertical axis in dB to make it easy to compare the 3dB points. I wasn't quite sure how to render the vertical probability axis in dB since it doesn't really have a meaning but I chose 20*log10 to match what I did with the resonance formula. The resonance curve (orange) used the same centre frequency of 1Hz and I twiddled the Q to to get the -3dB points to match the normal curve, which needed a Q of ~500.

What's obvious is that though the curves are similar around the peak they diverge hugely as one moves away, by 10s of dB.

It seems to me that the period error must depend on the Q, obviously, but also on the "noisiness" of the whole oscillator, and the amplitude of the oscillation which the noise is perturbing. Those factors are captured in the equation I posted. Clock B is a nice example - the pendulum has a rather low Q compared to most regulators, but it swings with about 4 - 6x the amplitude, the drive torque is very accurately controlled with a remontoire, the escapement minimises frictional variation of force, the whole thing is extremely massive and (for the critical tests) was mounted on a masonry column embedded in boulder clay; and finally the pendulum is temperature and barometrically compensated.

I think Dave's distribution looks very gaussian (normal) and is actually a very useful measure though not of Q! It tells us I think that the systematic variations are pretty small and most of the fluctuations are random, though they could be due either to the oscillator or the measurement system.

Though chest deep in doubt, I still think Decay and Bandwidth are both valid ways of measuring pendulum Q.

Absolutely they are - but I don't think your probability distribution of period is a bandwidth measure.

Wikipedia has a good collection of information on Q. Includes a couple of useful formulae.

Time constant of decay T = 2Q/Wo where Wo = 2pi/To (To is the full period).

Then amplitude decays at A = Ao.exp(-t/To).

Setting A/Ao to various convenient values such as 0.5 or 1/e then gives the various formulas for Q in terms of number of cycles that have been quoted.

Have to get our ChatGPT subs so we can autoreply in the same vein. Should be fun to watch...

**LINK**

All the information in that thread Joe.

Nice!

I thought that the following example of a run-down test might be useful. I took this from my new pendulum just after replacing the spring and rod. Essentially allowed the amplitude to stabilise at just above the intended operating point, then switched off the impulsing and logged amplitude as it decayed, measuring it basically by the photogate time.

The plot shows the natural log of amplitude against beat time (essentially seconds). Nearly a straight line with a barely visible "kink" after about 15000 seconds. The first part of the run (around the eventual operating point) yields a Q of about 22,500. Andrew Millington pointed out that the Q improves at lower amplitude to about 24,500. There are essentially two flow regimes around the bob it would seem, at larger amplitudes there is an increasing square-law dependence of drag on velocity whereas at lower amplitude it is essentially linear. Note that the curve is very clean with very little scatter of the points about the trend line.

Oops! Quite correct Duncan. Told you to trust Woodward.

By the way Joe, I love your angle sensor!

If I may I'd like to comment on Dave's method. It seems to me that the resemblance of the normal distribution curve to a resonance curve is tempting but unfortunate. Assuming that Dave's period distribution is normal, its width is characterised by just one parameter, the standard deviation. The "-3dB" points are related to this but superfluous.

In practice the width of the period distribution must depend on the amplitude and noise level (i.e. the "signal to noise ratio" as well as on Q. So buried in Dave's computation is this SNR, which itself is also determined by Q (as this determines the bandwidth of the noise which is affecting the period). So one can't take the width of the distribution compared to the mean as the Q since actually if the noise was zero Q would apparently be infinite! Some time back I looked at this and I think this equation for the rms period variation is accurate for a pendulum with small swing, in equilibrium amplitude, at frequency Fo, Q, amplitude a, and mass m, where N is the spectral density of the noise force component of the impulse.

To compute Q from this you would need to know N. Pendulum Q can be measured most directly by a run-down test. Electronics Q is generally best measured as bandwidth or sometimes magnification factor.

Well Philip Woodward was a respected mathematician as well as horologist and I think we can trust him!

If you take my expression:

An/A0 = exp(-n*pi/Q)

If An/A0 = 1/2 then exp(n*pi/Q) = 2

Or n*pi/Q = ln(2)

Q = n*pi/ln(2) which is Woodward's formula.

Edited By John Haine on 16/08/2023 17:08:47

Edited By John Haine on 16/08/2023 17:34:08

An/A0 = exp(-n*pi/Q), where n is number of periods. So if ln(An/A0) = -1, then Q = n*pi.

So An/Ao = exp(-1) = 0.6321. Count cycles until amplitude is 63.2%, multiply by pi.

Very interesting approach Joe!

Sinusoidal drive was used in a couple of clocks by Ned Bigelow in the US. He used a moving magnet design with a large number of turns on his coils. This gave a high transduction coefficient "K" which allowed him to connect the pendulum as the resonator in a simple oscillator circuit - in effect he had a resonant circuit with the Q of the pendulum. IIRC "K" is the volts/m/s as well as newtons/ampere - same value different units. I looked at using a similar approach with my design but K is very small so the impedance would be swamped by the circuit parasitics. Do you have any measurements for your drive arrangement? I did consider using sinusoidal drive in the way you are proposing and still might, so looking forward to seeing your results.

On the suspension, the arrangement you have for the trunnion bearing makes it hard for the pendulum to hang truly vertical "back and forth" as there will be some friction between the bar and vees (yes, I know I use a similar arrangement!). IIRC the maximum hanging angle is something like arcsin(coefficient of friction), it's in Matthys' book. Doug Bateman simply has a flat surface on the "brackets" so the pendulum can roll to verticality. Or one could use ball bearings to reduce friction but also constrain the pendulum back-and-forth.

I'm sure that's right Michael - from memory when looking for it, at the price it could only be "brick wall lowpass". At 2mm thick it cant be dichroic anyway.

Dave, perhaps time to start taking some ADev plots to get a feel for what sort of noise you have?

Michael said:

"Therefore … Stray light problems might be considerably reduced by inserting a suitable narrow-band-pass filter in the beam path."

This I have done by inserting a strip of 2mm filter material (made for IR videoing to put in front of a light source) in front of the detector side of the sensor. Visually it's dead black but seems to have zero effect on the sensitivity of the Sharp but does get rid of the non-IR content of ambient illumination. Still a problem with sunlight that has a lot of IR which is why I plan to put some 3M solar film over the glass door of the case.

What's the spindle bore? I got ER40 for my big bore Super 7 to accommodate the maximum diameter the bore could but otherwise ER32 would have been fine.

Look at Arc Eurotrade for ER collet chucks and backplates. You'll have to turn the latter to fit your chuck.

Don't even think about the MT2 type for use in the lathe - too much overhang and you loose the ability to put material through the bore.

No contest, fit a decent 3 phase and a VFD.

On its way to you Michael, together with a write-up, by email.