gary's clocks

tolerance analysis


Here is how we'd like to arrange a set of gears.

The ideal distance between a pair of gears should be equal to the sum of the pitch diameters divided by 2.

The goal is to have the gears in contact as much as possible at the pitch diameters to minimize sliding between the teeth.

Easier said than done I'm afraid.

There are a number of factors working against us:

  • The gears are cut by hand on a scrollsaw and are not perfect
  • The gears most likely won't run true because of eccentricity in the shaft or if the center hole is not dead center
  • Wood moves, warps and bends through the year as the weather changes


    In this tight example the gear centers are closer together than they should be.

    There is a danger that the wheel can foul at the root diameter of the pinion


    In this example the gear centers are farther apart than they should be.

    There is the danger that the gears can slip by each other.

    Let's take a look at these gears in action.......







    Ok so just how tight is tight?

    The technical details:

  • The big wheel has 100 teeth and a pitch diameter of 7.14 inches.
  • The pinion has just 8 teeth and a pitch diameter of .57 inches.
  • So the ideal distance between gear centers would be (7.140+.570)/2= 3.855 inches
  • In the tight example the gear centers are moved closer together by .015 inches
  • In the loose example the gear centers are moved further apart by .015 inches.

    Wow!! .015"

    +/- .015" inches isn't a whole lot of room to play with. A typical human hair is about .005" thick. Talk about splitting hairs.

    But it isn't really as bad as all that. Read on..........

    The large gear is the size it is in order to fit on an 8.5x11 sheet of paper for printing.

    If you made the gear larger or kept the gear the same diameter but reduced the number of teeth you'd get more room to play with.

    Look close at the tight animation. The pinion root diamater could be reduced to give more clearance.

    It looks like the loose example has some room to move further out too.

    The true order of tolerance is more like +/- .030". Or about the thickness of the lines on the printed plans.

    Some gears to print

    The best way to see how you have more tolerance between gears with smaller diametral pitches is to print them full scale.

    Diametral pitch is the ratio between the number of teeth and the pitch diameter. P= N/D. So gears with smaller diametral pitch have larger teeth.

    Here is a PDF file that you can print out to compare a 50 tooth 7 dp wheel to a 100 tooth 14 dp wheel.

    Note that both gears have the same pitch diameters and just fit onto an a4 sheet.

    It is important that you print these two sheets out on your printer to see the gears truly full scale. There is no way for me to show you the gears full scale on your computer screen due to differences in screen resolution and monitor size.

    comp14-7 comp-7-14dp.pdf (148kb)

    Once again-TINSTAAFL

    There Is No Such Thing As A Free Lunch.

    If you are looking for an easier time cutting the gears out you'd have to use gears with the larger teeth.

    Larger teeth naturally lead to larger gears, increased inertias and a larger clock.

    I think this partially explains why so many wooden clocks are as large as they are.

    It's just easier to make gears with bigger teeth.

    The big gears look good too!

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