Some beginner questions on gear ratios and weights

Discussion in 'Clock Construction' started by Wallaby, Aug 27, 2018.

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  1. Wallaby

    Wallaby New Member

    Aug 27, 2018
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    Hello!

    I have some interest in clocks and automata and I'd like to try and build my own. One goal I'm hoping to achieve to have as long of a period between windings as possible and to create an entirely mechanical clock (no motors or electricity.)

    I was wondering if you could help with a few questions I have.

    1. If I use more teeth on the escapement gear, does that prolong the period I have between needing to wind the clock? For example, if I have 150 teeth vs 30.
    2. Does a longer pendulum mean more conserved energy? If my pendulum period is 2 seconds instead of the traditional 1 for grandfather clocks, does that mean longer running time? I know a 2 second pendulum is quite long, ~2.3 meters.
    3. Does a heavier weight increase the time between winding or does it just allow you to power more gears / features like a cuckoo?
    4. The barrel that the weight is wound on - does the circumference change anything about how power is distributed? For example, if the weight was wound up on a 1 cm rod (just as an example), it would unwind 3.14 cm per revolution (I think.) So a larger diameter - say 2 cm barrel, it would unwind 6.28 cm per revolution? Does this have an effect on anything?
    5. Can I conserve more energy in the weight by reducing the gear ratio between the main gear and the escapement?
    6. How do you re-wind the weight without affecting the pendulum?
    I think that's everything for now. I'm still unclear how to power the escapement and how the pendulum gets its energy from the weight but I think I mostly understand the mechanisms.

    Thank you!
     
  2. Paul Madden

    Paul Madden Registered User
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    Apr 24, 2017
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    Hi Wallaby,

    Welcome to the NAWCC!

    I'm also a relatively new member, and by no means an expert, but I will try and help you as best as I can.

    For your questions 1 - 3, my understanding it is the ratio between the center wheel pinion and the barrel (or great wheel) that initially determines the power reserve of the clock.

    In most clocks, the center wheel is what carries the minute hand.

    Therefore, if you imagine that a center wheel completes 192 revolutions in a single winding, the minute hand would have made 192 revolutions on the dial, i.e. 192 hours power reserve.

    Some clocks have a wheel placed in between the barrel (or great wheel) and the center wheel, and this further increases the power reserve (by increasing the number of turns of the center wheel relative to the turns of the barrel (or great wheel).

    Longer pendulums, heavier pendulums, and number of teeth of the escape wheel will not actually have an affect on power reserve.

    For question 4, the circumference of the barrel (or great wheel) relative to the center pinion does have an influence on power reserve, but also has an impact on torque output. All things being equal, a larger diameter barrel (or great wheel) will deliver more torque due to the lever affect.

    For question 5, there are many factors that influence how much energy is used to drive a gear train, and far more than could be listed here, but a general rule is that the more gears there are between the power source and the escapement, the more energy will be lost through friction.

    For question 6, maintaining power devices are used in higher quality clocks to allow energy to be supplied to the escapement during the winding process. A number of members in this forum have made clocks which feature a maintaining power device, so it would pay to check these posts out.

    For your last point, it is typically the escape wheel that impulses a pallet (which in turn impulses the pendulum via a crutch) that maintains the oscillations of the pendulum. The weights role is only to provide energy to the escape wheel via a train of gears (gear train).

    Please note that the statements above are all based on general principles, and there will always be exceptions.

    Wallaby, I hope this helps answer a few of your questions. It might be worth looking online for explanations of how mechanical timepieces work, especially in terms of energy transfer and escapements.

    Best wishes in the meantime,

    Paul.
     
  3. Wallaby

    Wallaby New Member

    Aug 27, 2018
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    Thank you for the reply.

    I was thinking that a longer pendulum period, while not actually adding energy to the system, would dissipate it slower because the escape wheel is moving half as often. (In the case of a 1 second vs 2 second pendulum.) I was curious how long the pendulum could be powered between windings without using a spring.

    Is there any reason why the anchor shouldn't be directly connected to the pendulum instead of using a crutch? I was thinking of something like a rod screwed into the base of the anchor mechanism. I am only speculating at this point. That might be considered exactly the same thing as a crutch and only a minor implementation detail.

    Thanks again!
     
  4. Allan Wolff

    Allan Wolff Moderator
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    Mar 17, 2005
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    Hi Wallaby,
    I don't see why you cannot use a longer pendulum. Achieving a practical case size is probably the main reason a long pendulum is not often used.

    You probably can connect the pendulum directly to the anchor if the case is really solid and the pendulum is not easily disturbed. the crutch is often the mechanism that isolates movement of the pendulum in undesired directions from the anchor. That is, the pendulum should naturally move from side to side, but any front to back movement will place stress on the anchor pivots, especially with a long pendulum like you are considering.
    Allan
     
  5. Wallaby

    Wallaby New Member

    Aug 27, 2018
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    That makes a lot of sense. The prototype I made definitely had unwanted forward and backward movement. I mounted it on a pillar and figured it was the lack of backing plate that was causing it.
     
  6. gmorse

    gmorse Registered User
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    Jan 7, 2011
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    Hi Wallaby,

    Just to be clear, a '1 second' pendulum takes 2 seconds to make a complete oscillation, that is, from the centre out to one side, back through the centre and out to the other side then back to the centre again. This is approximately 1 metre long. A '2 second' pendulum takes twice as long for a single oscillation, and is nearly 4 metres long, so the clock would have to be in a high room or have a hole cut in the floor! The Great Clock at Westminster, ('Big Ben'), has a '2 second' pendulum 4 metres long. A '3 second' pendulum would be nearly 9 metres long.

    The pendulums on early crown wheel clocks were indeed directly attached to the pallets which engaged with the crown (escape) wheel, but their pendulums were quite short, around 6", and had quite wide swings.

    Regards,

    Graham
     
  7. Wallaby

    Wallaby New Member

    Aug 27, 2018
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    Ah, I see. I've calculated that a 1.5 second pendulum (3 seconds total) would be about 2.3 meters. That's almost the full size of a standard wall height (2.4 meters, I think.) So it's doable, but not very practical.
     
  8. gmorse

    gmorse Registered User
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    Hi Wallaby,

    Yes it is, if the pendulum is suspended just under the ceiling. However, have you considered the possibilities of a compound pendulum?

    Regards,

    Graham
     
  9. dandydude

    dandydude Registered User

    Nov 30, 2014
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    Question 6. You can rewind the weight by using something called a 'maintaining power mechanism'. It keeps the clock ticking while you wind.
     
  10. dandydude

    dandydude Registered User

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    Questions 3. :
    Larger barrel = less driving weight. Smaller barrel = More driving weight.
    Larger barrel also ends up with a really long cable/rope. If the clock case has a limited space/height you may need to go with small barrel/ more weight. If it still doesn't work, you may need to compound the pulley.
    There are a lot of permutations and combinations.
     
  11. karlmansson

    karlmansson Registered User

    Apr 20, 2013
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    Hi Wallaby!
    You are right that a longer period of the pendulum means longer Power reserve. The 100 day torsion Clocks are a good example of this. They normally impulse every few seconds and some of them can actually stay running for a 100 Days on a single wind, if properly regulated and adjusted. They are however, in general, poor time keepers. If I understand it correctly, the longer the period of the pendulum, the more susceptible the pendulum is to errors during that time. Someone Walking on a floor through a room throwing the pendulum off ever so slighlty will potentially have an effect for one cycle. If that cycle is five seconds long instead of one, the impact on time keeping will be greater. I may have misunderstood this so if anyone can explain it better than me, please do. I Think that in watches at least a higher beat rate is to compensate for imperfections in the escapement. Or so Roger Smith says at least, who refuses to make watches with a beat rate over 18000 bph :).

    Best regards
    Karl
     
  12. gmorse

    gmorse Registered User
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    Hi Karl,

    There's also the issue of accelerated wear and maintenance of lubrication in higher beat escapements. I think Roger knows what he's talking about!

    Regards,

    Graham
     
  13. Phil Burman

    Phil Burman Registered User

    Mar 8, 2014
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    Hello Wallaby. Below is my input to your questions and is based on my current level of knowledge. Based on your current level of knowledge I think you would be far better served by adopting a known design rather than going of piste with a none typical/standard design.. A year duration regulator would be a good starting point.

    1. If I use more teeth on the escapement gear, does that prolong the period I have between needing to wind the clock? For example, if I have 150 teeth vs 30.

    The escape wheel is just another wheel in the gear train so increasing the number of teeth will increase the gear ratio and therefore the period between windings, but you will need to scale the diameter of the escape wheel to allow the pallets to function. You could achieve the same with a lot less trouble by increasing the gear ratio in the rest of the gear train. Small scape wheels work best as they use disproportionately less energy due to low inertia (during stop/start). This is actually the same for all gears in the train but I think most apparent with the escape wheel. You could calculate the energy lost due to the inertia of each wheel (if you have couple of weeks to spare).

    2. Does a longer pendulum mean more conserved energy? If my pendulum period is 2 seconds instead of the traditional 1 for grandfather clocks, does that mean longer running time? I know a 2 second pendulum is quite long, ~2.3 meters.

    Firstly the period of a grandfather clock is already 2 seconds (the beat is 1 second). A 2 second beat pendulum would have a length of 4 meters. Increasing the length of a pendulum increases the distance the bob travels between impulses so the energy lost to the air resistance and motion is greater and therefore the larger is the impulse necessary to keep the pendulum swinging.A lighter bob will require less energy but reduces the time precision of the clock and may require additional energy due to a disproportionate air effect. It all it the subtlety of the design. A good standard would be 30 tooth escape wheel with a 1 second (beat) pendulum and a heavy, aerodynamically slippery bob.

    3. Does a heavier weight increase the time between winding or does it just allow you to power more gears / features like a cuckoo?

    Increase drive weight multiplied by the drop is one of the fundamental parameters that determines the run time, together with a large gear train ratio. However a large gear train ratio needs lower tooth and pivot friction, there is a limit.

    4. The barrel that the weight is wound on - does the circumference change anything about how power is distributed? For example, if the weight was wound up on a 1 cm rod (just as an example), it would unwind 3.14 cm per revolution (I think.) So a larger diameter - say 2 cm barrel, it would unwind 6.28 cm per revolution? Does this have an effect on anything?

    The barrel is effectively just another gear in the gear train, see answer to question 1. The lower limit on diameter is dictated by the minimum bend radius of the cable.

    5. Can I conserve more energy in the weight by reducing the gear ratio between the main gear and the escapement?

    The reverse is actual true the greater the gear train ratio the less movement of the drive weight per beat. See the second sentence in answer to 3.

    6. How do you re-wind the weight without affecting the pendulum?

    Google maintaining power, Harrison, bolt and shutter and/or Arnold.
     

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