Help Finding Beats per hour/min by formulas

Discussion in 'Clock Repair' started by bytes2doc, Apr 20, 2019.

1. bytes2doc Registered User NAWCC MemberSponsor

Aug 31, 2009
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#1
Time to get nerdy.

The ansonia movement pictured shows six wheels. This is different then what the book illustrates.

First is the barrel wheel with 83 teeth.

Second wheel directly above it has 60t and 8 p. It is attached to the third wheel directly above it, and the center wheel (minute wheel) to its right.

Third wheel directly above the 2nd wheel has 40t and 8p. It connects to the 4th wheel.

Fourth wheel (with the missing pinion on the arbor) is just right of the third wheel and has 42t and 7p.

The 5th wheel or escape wheel has 35t and 6p and sits directly above the 4W.

Most educational material I've come across show 5 wheels and this is what is used to determine number of vibrations per hour. This movement has six wheels, and I will discount the CW as it is not involved in driving the train.

Generally the 2nd wheel drives the center (The 3rd wheel) which drives the 4th wheel. This Ansonia movement has the 2nd wheel drive the 3W and the center. So the center wheel holding the minute hand would not be part of the equation to find bph=

(CWt x 3Wt x (2 x EWt)) /

(3p x Ep)

All multiplied by the number of turns of the CW.

Since the CW is being driven by the 2W, I will use the 2W to replace the CW.

That 2W rotates just under 1/2 turn for a complete revolution of the CW.

Plugging those numbers in I get

(60 x 40 x 42 x (2 x 35)) /
(7 x 6) = 168000 / 2 = 84000

Convert to bpm = 84000/3600 = 23.3

Since this movement is different from the book, are my assumptions of substituting the 2W for the CW correct?

Does this look even reasonable?

My Ansonia is ticking away at about 90 oscillation per min, or 180 vibrations per minute.

2. Dick Feldman Registered User

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When calculating BPM/BPH for a clock movement, one only needs to count teeth on wheels/pinions between the hands and the escapement, regardless of the number of total wheels/pinions in the clock.
If you think that through, you are only trying to find a ratio between the speed of the hand shaft wheels and the escapement. The speed or rpm of the wheels/pinions below the hands have nothing to do with proper timekeeping.
You will also find that counting teeth will only approximate good timekeeping. The true test will be to compare the travel of the hands with an accurate time standard and operating the movement. Good timekeeping is dependent on other factors.
Best,
Dick

3. shutterbug Moderator NAWCC Member

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And you are correct that the actual time wheels are eliminated because they are driven BY the train, but are not part of it.

4. dickstorer Registered User

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With all due respect to Mr. Feldman, I do not quite understand "counting teeth will only approximate good time keeping". Does that mean if I calculate the BPH/BPM to be 4800/80 and my timetrax indicates 4800 that the timekeeping will or will not be accurate? I am confused.

5. R. Croswell Registered User

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Last edited: Apr 21, 2019
Counting the teeth of wheels and pinions from the center shaft to the escape wheel and applying the formula will give you precisely the correct number of beats required per minute or hour for the hands to advance one minute or one hour. This is the number you need to look for on your Timetrax. To the extent that your Timetrax is accurate, your clock will keep time when that beat rate is set. It is not approximate, it is exact..

Where it becomes compromised is when one applies the tooth count formula to calculate the theoretical pendulum length required to produce that beat rate. The formula will give a pendulum length for a pendulum swinging free (no power applied) with a very small arc, in a vacuum. When a pendulum with this calculated length is put in a clock the actual rate of swinging of the pendulum will be influenced by the strength of the suspension spring, the size of the arc of the pendulum, barometric pressure, and other factors. Therefore the calculated pendulum length is approximate so the exact length will be slightly different and will ultimately need to be determined by trial and error.

RC

6. dickstorer Registered User

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Still confused.

7. R. Croswell Registered User

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Ok, lets look at it a bit differently. Between the center shaft and the escape wheel is a train of gears and pinions. Every time the minute hand turns one revolution (one minute) the escape wheel must turn a certain number of turns and this cannot change because the number of teeth on the wheels and pinions cannot change. Now the escape wheel also has a fixed number of teeth, lets say 38 teeth as an example. The clock will "tick-tock" each time a tooth passes through the escapement. Because these gear ratios are fixed and cannot change for a given clock, each time the center shaft (minute hand) rotates one time it will produce exactly the same number of ticks and tocks. That number can be calculated using the mathematic formula. The number of beats per minute (or per hour) is the only number of beats that will result in the clock keeping time. Doesn't matter if one is using a Microset, Timetrax, or pencil and note pad and counting ticks, each time the minute hand rotates one revolution it will produce that number of ticks. Now if it takes longer than one minute actual time to achieve that count the clock is running slow. If it reaches that count before one minute actual time the clock is running fast. Now the Microset and Timetrax not only count the number of beats but they calculate electronically and display beats per hour (BPH) Only when the clock is running and producing the exact number of beats per hour calculated for that clocks gear ratios will it be keeping time.

You said earlier, " Does that mean if I calculate the BPH/BPM to be 4800/80 and my timetrax indicates 4800 that the timekeeping will or will not be accurate?" The short answer is that if your Timetrax indicates any number that is not exactly identical to the calculated number then the clock is not running at the correct rate. Whether the "timekeeping" will be accurate is another question. The Timetrax only indicates how the clock is running right now over the sample period of just a minute or so. There are several factors that influence the accuracy of the Timetrax or Microset devices. There may be slight differences in the teeth of the escape wheel that can produce a slight error. If you have an escape wheel with a large number of teeth, the sample period may actually be less than one revolution or the escape wheel. You may even notice that each subsequent display on the Microset or Timetrax is very slightly different. I don't have a Timetrax, but my Microset suggests setting the sample period equal to the number of teeth on the escape wheel (or some interger multiple of that number). If you set the meter to "average" over a longer period of time you will get a better picture of exactly how fast the clock is running. Keep in mind that any condition issues in the clock can cause variations in the clock's beat rate as it runs. Striking clocks typically slow a little as the strike train is being unlocked. Spring powered clocks tend to slow a bit as the springs run down. A bent pivot or wheel or anything else that occurs periodically over the course of a week will cause little variations in the clocks beat rate. Keep in mind that the Timetrax is probably sampling for perhaps 1 minute. even the very smallest error will be multiplied x 10,080 minutes in a week.

So will the timekeeping be accurate if your Timetrax displays the precise number calculated by the formula? The only thing that can tell you is that the clock is keeping perfect time at that exact moment (within the limits of the accuracy of the quartz clock inside the device). It will probably NOT be precisely accurate over a full week for most clocks because of temperature changes, variations in power, slowing to unlock time/strike trains, and any other little irregularities that occur in the movement over time. It is still the best place to start in the process of regulating a clock.

If this still isn't clear, please try to be more specific about just what is confusing.

RC

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8. shutterbug Moderator NAWCC Member

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There's an easier way too. Your Timetrax has a count feature that just counts beats. Use that, and set your minute hand at a precise point on the dial. Let it run until the minute hand touches that spot again. The number of beats counted by the Timetrax will be your BPH. For more accuracy, run it 3 or 4 revolutions of the minute hand and divide the count by the number of revolutions.
You can do this with any kind of pendulum, or even without one, and get the same number.

9. R. Croswell Registered User

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That works but kinda hard to split hairs to get exactly one minute. It will get you close enough to start, just remember that any error will be multiplied by ten thousand over a week run. Notice in the beat book many of the beats are not whole numbers and are specified to two decimal places

RC

10. dickstorer Registered User

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Mr. Croswell
Re--post 7
Thanks, I will print and keep this.