The value of balance wheel moment of inertia
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Thread: The value of balance wheel moment of inertia

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  1. #1
    Member edeag3's Avatar
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    The value of balance wheel moment of inertia

    Recently I noticed that when the inertia value of a balance wheel is high (i.e. >10 mg/cm^2), it is often used as a marketing tool. Not all marketing tools are a scam, of course, an I'm just wondering how much value this has.
    I know all other things being equal, a larger diameter and heavier balance wheel (hence more inertial since the moment of inertia of a circle is mr^2) will be more shock stable. Other than that I *believe* that it may use more energy since each oscillation will require more energy to change direction or stop and turn around.
    Anyone more technical want to help me with this?
    Here are a few values of some movements for which the moment of inertia is known (all units in mg/cm^2) in descending order:

    Omega 8500 (in-house co-axial hour vision) - 21
    IWC 80110 - 18
    Rolex 3135 - 16
    JLC 975 "autotractor" - 14.95
    Valjoux 7750 - 12
    JLC MC Lab 2 (first watch with no lubrication)- 11.5
    ETA 2892 (and thus 2893 and 2894 + other derivatives) - 10.1
    Omega 2500 (Co-axial 2892)- 9.4
    JLC 899 (and derivatives such as VC 1124 and many others)- 3.8
    Eta 2004 - 2.7
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  2. #2
    Member lysanderxiii's Avatar
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    Re: The value of balance wheel moment of inertia

    A higher moment of inertia also means 1) a higher balance wheel weight or 2) weaker structure of the wheel. Both of which lead to reduced shock resistance due to higher loads on the balance staff. To counter this, a heavier staff is required, and this introduces drawbacks of its own.

    Further, the manner in which shock resistance (Incabloc) works, a heavier wheel will return to normal running position slower. Since during the shock event, balance operation is interrupted and timing is altered until normal running is resumed, a heavier wheel may see higher errors due to jarring.

    A heavier balance need a stiffer mainspring to handle its increased power requirements. A stiffer mainspring will require a larger barrel.

    In short, the size of the balance does what is is advertised as doing (although, by shock stability, they mean variations in the impulse energy, not so much dropping it), but like any other engineering design issue, there will be tradeoffs, and the end result will be a optimization.
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  3. #3
    Member CitizenM's Avatar
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    Re: The value of balance wheel moment of inertia

    I for one love the balance wheel moment of inertia and I'm not afraid to say it anymore. That's right, I love the balance wheel moment of inertia. No more hiding.
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  5. #4
    Vintage & NAWCC Forum moderator Ben_hutcherson's Avatar
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    Re: The value of balance wheel moment of inertia

    In general, a higher moment of inertia means that the oscillation frequency is less susceptible to alteration by external influences. This means that, at least in theory, it should offer better timekeeping in service.

    Usually, a greater moment of inertia also comes with a more massive balance. The more massive balance means that if the watch is dropped, the balance pivots are more likely to be damaged or break. Of course, this is less of a problem with shock protection, but none the less under the right conditions can still present a problem.

    I'm less familiar with modern balance design. In the old days, it was relatively easy to increase the moment of inertia of the balance wheel by adding more balance screws, or switching from brass to gold screws. Of course, this also requires a stiffer hairspring to maintain the correct frequency and a stronger mainspring to get the amplitude correct.

    Now, though, the most obvious way to increase the moment of inertia is to increase the diameter of the balance-something that has its practical limits.

    As you've correctly identified, also, a higher moment of inertia does come with greater power demands in order to maintain satisfactory amplitude. If the mainspring barrel is kept the same size, a thicker mainspring must be used. This brings with it a decrease in power reserve. A wider spring can be used, or a thicker spring combined with a larger diameter barrel to maintain the power reserve.

    If I get a chance later this evening, I'll post some photos of the balance wheels and mainsprings from two Elgin pocket watch movements-an 18 size model 4 and an 18 size model 8. The model 8 is noted for having an especially high moment of inertia(and is regarded as an excellent timekeeper as a result). The difference in mainspring size between the two movements is quite striking.
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    Serious collector of American pocket watches-Waltham(and the predecessor companies) is my specialty.

  6. #5
    Member edeag3's Avatar
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    Re: The value of balance wheel moment of inertia

    Thanks a lot for the information, looking forwards to the photos if you have time to get them up.
    Thanks

    Quote Originally Posted by Ben_hutcherson View Post
    In general, a higher moment of inertia means that the oscillation frequency is less susceptible to alteration by external influences. This means that, at least in theory, it should offer better timekeeping in service.

    Usually, a greater moment of inertia also comes with a more massive balance. The more massive balance means that if the watch is dropped, the balance pivots are more likely to be damaged or break. Of course, this is less of a problem with shock protection, but none the less under the right conditions can still present a problem.

    I'm less familiar with modern balance design. In the old days, it was relatively easy to increase the moment of inertia of the balance wheel by adding more balance screws, or switching from brass to gold screws. Of course, this also requires a stiffer hairspring to maintain the correct frequency and a stronger mainspring to get the amplitude correct.

    Now, though, the most obvious way to increase the moment of inertia is to increase the diameter of the balance-something that has its practical limits.

    As you've correctly identified, also, a higher moment of inertia does come with greater power demands in order to maintain satisfactory amplitude. If the mainspring barrel is kept the same size, a thicker mainspring must be used. This brings with it a decrease in power reserve. A wider spring can be used, or a thicker spring combined with a larger diameter barrel to maintain the power reserve.

    If I get a chance later this evening, I'll post some photos of the balance wheels and mainsprings from two Elgin pocket watch movements-an 18 size model 4 and an 18 size model 8. The model 8 is noted for having an especially high moment of inertia(and is regarded as an excellent timekeeper as a result). The difference in mainspring size between the two movements is quite striking.

  7. #6
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    Re: The value of balance wheel moment of inertia

    Wonderful thread. Thanks for all the info to all of you. I think this is what makes the hobby very fascinating. So here's my question: Are the accepted inertia values that can be seen as optimal compronises between accuracy and shock resistance and size of movement? I could imagine that given the size of the movement, Rolex can use a bigger balance wheel, same for Omega 8500.

    Also, what's the value for an ETA 2824? Anyone know?

  8. #7
    Member lysanderxiii's Avatar
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    Re: The value of balance wheel moment of inertia

    Quote Originally Posted by Watchalex View Post
    Wonderful thread. Thanks for all the info to all of you. I think this is what makes the hobby very fascinating. So here's my question: Are the accepted inertia values that can be seen as optimal compronises between accuracy and shock resistance and size of movement? I could imagine that given the size of the movement, Rolex can use a bigger balance wheel, same for Omega 8500.

    Also, what's the value for an ETA 2824? Anyone know?
    They can use whatever size balance they what, provided they are willing to accept the drawbacks of that size to get the benefits....

    The balance of a 2824 is around the same diameter as a 7750, so I guess the moment of inertia is about the same.....
    familiaritas parit contemptum; raritate admiratione wins.- Lucius Apuleius
    est necessry, accurate ad secundo? - Lysander magna
    iustum est horologium - Obscurus Genius

  9. #8
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    Quote Originally Posted by CitizenM View Post
    I for one love the balance wheel moment of inertia and I'm not afraid to say it anymore. That's right, I love the balance wheel moment of inertia. No more hiding.
    Anything else you need to get off your chest? ;)
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