# The Gregs Pendulum

#### GregS

##### Registered User
First off let me say that I do not have an engineering background, a math background or any metal working experience aside from general clock repair. I have the usual clock repair tools, my trusty Sherline 4400 lathe, a drill press and assorted hand tools of every shape and size. In the summer of 2020 I finally added a small table top mill and the possibilities exploded. It was during the start of the COVID pandemic I decided it would be fun to design and build my own clock, mechanism and all. To this end I am doing everything backwards. I've built the pendulum first. Then the escapement, (more on that in the next post). I did it this way because I wanted to make sure I could make the escapement work before I under took the process of cutting gears.

I wanted to build the most accurate clock I could. Let me emphasize the "I" here. Not the most accurate clock ever built, but the best I could build. Thus it seemed a temperature compensated pendulum would be the first logical step. This quickly turned into a lot of formula seeking and materials science that I would not have dreamed of previously. Not wanting to build a typical grid iron pendulum and not wanting to deal with glass vials of mercury, I felt a simple pendulum of INVAR 36 and some compensation material would be easiest. Many examples exists that show the compensation tube inside the bob which shielded it from temperature changes. I decided that my entire bob would be the compensation "tube".

When I purchased the INVAR, I received the mill's spec sheet which stated the coefficient of linear thermal expansion was 2.2 to the 10[SUP]-6[/SUP]/°C. So how do you know how much material you will need to offset or overcome this expansion/contraction as the temperature changes? In order to solve that we need to know how long the rod will actually be. I spent a long time researching the formula for determining the period of a pendulum for any given length as shown here:

Period = 2PI * sqrt( Inertia / (Mass * gravity * d) )
d being the distance to center of mass.

The problem I had was I knew what period I wanted (one second), I just needed the formula to determine the length from the period. As far as I can tell no such formula exists for this. In the end I wrote a small computer program that ran in a loop to ever so slightly change the length, recalculate the center of mass, recalculate inertia, then calculate the period. Compare the results to 1 second and repeat until I got a length close to 1 second.

Of course to do this assumed that the pendulum bob's size and weight was already known. It wasn't and so I started with arbitrary values I thought were reasonable. The largest bob I could machine using the tools I have is 8 inches in diameter and that was the base value I used initially. Once I knew the length, I needed to determine how much the rod's length would change from one temperature to another. I chose 60°F to 80°F as my upper and lower temperature limits. Thus:

growth = Rod Length * (Coefficient * 0.000001) * (Upper Temp - Lower Temp)
(formula modified for Imperial units)

As a starting point I needed a bob that would expand the same amount. I chose 6061 aluminum because its coefficient of linear thermal expansion of 23.6 to the 10[SUP]-6[/SUP]/°C was enough to cancel out the rods change in length due to temperature. One problem with all of this is that changing the bob's diameter, changes the pendulums center of mass, which of course changes the period. Placing the pendulums rating nut at the bottom of the bob as is traditional would mean there would be no way to tune the temperature compensation. My pendulum has a tunable rating nut hidden inside the bob and a rough adjustment stem doubling as the pendulums pointer protruding from the bottom of the bob.

The below image (the aluminum was anodized) shows the interior of the bob. Seen are the pendulum rod and the tunable rating nut. The sections of the bob marked A & B cancel each other out as the bob expands and contracts with changing temperature. Section A grows downward, section B grows upward and vice-versa. The section marked C is that part of the bob that offsets the change in length of the pendulum rod as temperature changes. As you can see this is a relatively small section of aluminum to offset the entire length of the INVAR rod from the center of the suspension spring to the center of the tunable rating nut.

My plan to tune this is to adjust the pendulum to one second using the rough adjustment stem while the pendulum is at the lower temperature limit, then later when the pendulum is at the upper temperature limit re-adjust the pendulum to one second using the internal rating nut. The result will be a temperature compensated pendulum as best as I can make it.

About twelve inches below the top of the rod is two inches of 7/16 x 40 tpi thread to which a brass disk with 30 divisions threads onto. This is used for fine adjustment. This is handy when my Microset says the length needs to change about 1 or 2 ten-thousands of an inch.

So there you have it. This is my pendulum as it exists today.

Cheers

Bernhard J.

#### bruce linde

NAWCC Member
Donor
very impressive... do you have a quality regulator movement you can test/monitor it in over time while you're building the rest of your clock?

#### John MacArthur

NAWCC Member
Gregs - We'll be very interested in how it works out. I too have been working up an invar pendulum, as mercury has gotten impossible to acquire. That said, a mercury bob has a pretty substantial thermal lag due to it's mass. I've been making a pendulum along the lines of the Strasser and Rohde ones, with the compensating tube exposed between the double bob. I'm almost done with it, and will post some pics when I get there. If you can find a copy of Mathys "Precision Clock Pendulums" it has a huge amount of information and experimental data. Copies are hard to come by, but you might luck out.
Johnny

#### svenedin

NAWCC Member
Years ago I replaced the standard thin steel pendulum rod with an invar rod on one of my British longcase clocks. The old rod had been badly bent when the clock was moved. The new Invar road was supplied by a clock material house. Although I did not keep records, the timekeeping was very significantly improved and I felt it was definitely worth doing.

#### GregS

##### Registered User
very impressive... do you have a quality regulator movement you can test/monitor it in over time while you're building the rest of your clock?
Bruce, Thanks for the kind words. The clock will be driven by my rendition of a gravity escapement. This escapement is largely finished and I will use it to drive the pendulum during testing/tuning. The pendulum and escapement were largely created similtaniously but the pendulum was finished first.

bruce linde
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