Building the pendulum demonstrator

I'm not sure why anyone would care if the period is shorter. The important part of a clock is not the period of the pendulum (which can easily be adjusted by moving the weight on the pendulum arm) but the precision with which the period is maintained. If the effect of the spring on the period is constant over time and temperature and is linear over angle then it is ideal. If the second order effect of gravity on the period is compensated for, small temperature effects don't matter either.

Your "pretty close" for small angles is the difference between good clocks and great clocks. The battle is to either compensate for the error term, or maintain the amplitude of the pendulum swing as precisely as possible. The Shortt clock does the latter and at least one other "great" clock does the former. Both use spring suspensions.

Fun! (much better than boring stability stuff :^) We make a torsional oscillator, a colleague claims to have turned it into a clock with the a negative resistance opamp circuit, but I have not seen it in operation. (I think he had issues with AGC)

A torsional oscillator may have low enough friction that it would not have your low amplitude limit cycle. (am I using limit cycle in the correct way?)

George H.

I still think suspending a hollow steel ball would be very instructive. Give it a perturbation one way or the other and it crashes (up or down) depending on the reaction of the system. It would be fun to lift the ball up or push it down and see the results on a 'scope. Maybe lift it and then let it go to see the bouncing (or not when properly PID'd).

Damn! That sounds like educational fun.

Because (a) it's far less predictable than a gravity pendulum; (b) it has a huge tempco, as I said (unless it's Alloy 42 or the equivalent); and (c) If you're happy with springs providing the restoring force, use an alarm clock!

The

We were talking about the effect of spring constant on pendulum period, of which you denied the existence. No biggie. I'm quite unlikely to be designing a mechanical clock any time soon, but the performance of flexures is important in my work.

I learned about the Alloy-42 thing working with a company that made ultrastable gravimeters and gravity gradiometers for downhole use. They used a mass and spring, measured with an interferometer based on an ultrastable laser that I built for them.

Industry know-it-alls wanted them to use fused silica suspensions, but the zero tempco of Young's modulus made the Alloy 42 suspension a clear winner.

Cheers

Phil Hobbs

Only if you lack the imagination and resources to make a really long, really heavy pendulum, Phil. The cliffs in Oregon City are some 40 meters high, and a truck spring would probably suspend a pendulum of several tons.

I wonder if they want a municipal clock. Timed with a pendulum. With a period of ten seconds or so...

The problem with the bearings is that the limit cycle ended up being hard rather than soft -- in other words, my oscillator won't start on its own. The problem is that the bearing shows stiction, which effectively increases the damping for small motion.

If the resonator is made by suspending an inertia wheel on a torsion spring, then that problem should go away.

Show him my circuit -- no AGC!

dulum (that used to be?) at Griffith Park Observatory. The guide touted the knife-edge (which that pendulum didn't use) as having the lowest possible friction and damping available. Easiest to maintain and repair, too.

Balances of yesteryear frequently used a 60 degree steel edge on a hard mineral (agate? sapphire? jade?) table. They've held up rather well. S ome provision is made for unloading the edge during shipping, so nothing rattles.

For a long-duration timekeeper, fused silica has advantages (no corrosion, large elastic range of deformation) that might be important. Isn't Alloy 42 kinda weak? Does it creep?

This one kind of turned into an unhealthy obsession.

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It's basically stainless steel minus the carbon, so it ought to be pretty s trong. These folks

say 85kpsi annealed / >120kpsi hard, which is about twice that of 6061-T6 a luminum. Plus it won't corrode readily unless you dunk it in an alkali. (Ch loride ion might be bad for it too, but then water itself is really bad for fused silica that's under tensile stress.)

That will depend on its previous history. I don't know whether the zero TC of stiffness requires fancy tempering the way Invar does.

Cheers

Phil Hobbs

I'm not denying the existence of anything. The issue is how significant it is. Clearly the amount of resistance provided by the suspension spring is not enough to cause problems in a laboratory clock. In the case of the Fedchenko clock the spring is specially designed to offset the second order effects of gravity on the pendulum. I'm not sure exactly what your point is. Clearly spring suspensions are some of the best in the world as they appear in the best pendulum clocks.

n, large

strong. These folks

aluminum. Plus it won't corrode readily unless you dunk it in an alkali. ( Chloride ion might be bad for it too, but then water itself is really bad f or fused silica that's under tensile stress.)

C of stiffness requires fancy tempering the way Invar does.

Phil, do you use alloy-42 to make flexures? Or are you just suggesting it would work and has a small TCE.

I make flexure's from 7075 Al, which I think I choose as the stiffest piece of Al in the McMaster-C catalog. I don't care about TCE in my flexures.

George H.

The gravimeter folks I was working with made all of their instruments using dual flexures laser-cut from Alloy 42 sheet. The two were arranged parallel to each other, so that the mirror (which was also the test mass) couldn't get misaligned.

They worked like the bomb, far better than fused silica. Because the flexure was approximately radially symmetric, the CTE didn't matter much, though Alloy 42's is quite low--it's not far off the Invar composition (36% Ni).

Most of the flexures I've used have been aluminum as well. I still have a very nice 2D scan stage made by Wye Creek Instruments way back in the day (like 1988). It was a side operation of a couple of NIST greats, Fred Scire and Clayton Teague.

The nice thing about aluminum flexures is that you can EDM them from solid, so they don't squirm around the way built-up flexures do. EDMing a plate of Alloy 42 would make much stiffer and much heavier flexures, with about the same resonant frequency (twice the mass and twice the spring constant). I don't know what their comparative range of motions would be.

If you have a positive drive, such as a preloaded micrometer or piezo, you don't care about the tempco of stiffness either. It's situations like super-accurate pendulums and especially mass-and-spring devices like gravimeters and accelerometers, where you care.

Cheers

Phil Hobbs

Heigh-ho, 'tis true, 'tis true. ;)

The cliffs in Oregon City are some 40

Maybe suggest an Edgar Allan Poe festival? Sort of like Burning Man only different.

Cheers

Phil Hobbs

Moldering Man.

Mark L. Fergerson

sion, large

tty strong. These folks

-T6 aluminum. Plus it won't corrode readily unless you dunk it in an alkali . (Chloride ion might be bad for it too, but then water itself is really ba d for fused silica that's under tensile stress.)

o TC of stiffness requires fancy tempering the way Invar does.

it would

Bill Wether? I was excited for a moment.. who is this new guy Bill Wether that's hung out at nist?

Are you changing nims? Becoming a Bellwether? :^)

As always, thanks Phil.

George H.

Nah, the Eternal September account on one of my computers was set up for other purposes.

Plausible deniability works except when it isn't plausible. ;)

Cheers

Phil Hobbs

It's impacts, rather that rattles, that are the problem. There's a big difference between supporting the pendulum mass at 1G vs a shock force of >100G.

Clocks like my 1870's French one *require* the pendulum to be unhooked for transport.

I strongly disagree! I think you learn the MOST on "pet projects" where you aren't arbitrarily constrained by a client's notion of what it should do, how it should work, what it should cost, when it should be finished, etc.

Your money, your time, your imagination! Nothing to get in the way...