Does a thicker shaft give more time per winding?

[dmarlen]

In my sample wall art, I've got a pendulum ticking well with me just applying some "weight" by turning the shaft of the deadbeat gear.  Now I'm ready to add a weight.  Here's my question:

What's the tradeoff between winding a string around the 1/4" shaft, or putting a thicker "spool" on the shaft and winding around it?  So I'll either wind around a 1/4" or a 1" shaft.  The weight only has about 8 inches to drop before it hits the desk.  What diameter will give me the longer running time?

Does it affect how much weight I use?  It seems that physics is in play here, but I can't seem to think it through.  I might guess that a shaft of thicker diameter will run longer, but will need more weight.

Do I get a C-? 



Also, is there a trick to getting the shaft to stay tight in the bearing with the deadbeat gear?  I can see it wants to "skip" and turn faster.

David.

[Steve Fox]

Torque equals mass times distance.

If you have a 3 pound weight on a cable wrapped around your 1/4" shaft, the force is .125 (the radius) x 3.
That equals .375 inch pounds of force.

If you make a 1" spool, you get .5 x 3.
That equals 1.5 inch pounds of force or four times as much.

With a 1/4" shaft, the weight falls .25 x pi(3.14159) inches per revolutio n or .78".
With a 1" spool, the weight falls 1 x pi or 3.14159", which is four times as far.

So that means the larger you make the spool, the more torque you get, so the smaller the weight needs to be and the faster the weight drops.

Your problem is to balance the size of the weight with the size of the spool to get the amount of torque you need.

I hope that's is correct and it makes sense.

I have no idea what you are talking about with the deadbeat gear.

[ArtF]

Agreed. I also have no idea of whats meant by the bearing.

  Do you mean your getting flex on the shaft?

Art

[BobL]

Hi;

 Maybe I'm also misunders tanding the question, but shouldn't the deadbeat gear be attached directly to shaft? I don't see why you'd need the bearing in the first place?



Bob

[Brian Decker]

What diameter will give me the longer running time?

Everythin g Steve said is correct - but the amount of weight should not affect the run time of an escapemen t set up like you have described .  The rotation speed of the weight bearing shaft and the escapemen t are locked by the gearing so each turn of the weight "spool" will equal the same number of turns of the escapemen t regardles s of the weight or size of the "spool".  A larger diameter spool increases torque, but the input torque of an escapemen t does not change the run time - the run time is determine d by the oscillati on of the pendulum which is determine d by it's length.  The two condition s in which drive torque does affect run time are when there is too little input torque to overcome friction or when there is so much input torque the pendulum is "over driven" and swung faster than it's natural oscillati on frequency . 

In other words the amount of weight needed to run your escapemen t - regardles s of clock or sculpture - should be enough to overcome the friction of the mechanism but not so much that the pendulum is being driven by the movement except when the pallet is being impulsed (pushed) by the escape wheel as it unlocks from a tooth.  Increasin g run time is achieved by lengtheni ng the pendulum and slowing its oscillati ons or adding additiona l gears between the weight bearing input shaft and the escapemen t to require more turns of the escapemen t shaft per turn of the weight shaft. The key point is that run time is determine d by pendulum length and not input weight

[dmarlen]

Thank you everyone.  The math clears it up.  I meant to say escapemen t.  So I have the weight on the escapemen t gear.  So my other question was if there was a trick to getting the shaft of the escapemen t gear in the bearings so the shaft doesn't just spin.  I think that is the only shaft that is actually under much more pressure and so it needs to be snug.  (As I understan d it.)

Does the pendulum itself have to be a certain weight?  I cut one out of acrylic and it didn't seem heavy enough.  So I've attached some quarters to give it weight.  Is it a case of not too much, not too little, but something like just right?

David.

[ArtF]

Hi:

   Hmm, OK, lets clear up the terminolo gy so we can understan d. An Escapemen t, is comprised of a DeadBeat gear, and a pawl system. The pawl shaft is what the pendulum hangs from. Many way to hang them. The DeadBeat gear, ( that gear with all  the pins ) is usually
tight on its arbor, and shares that arbor with another gear and perhaps a second hand. That arbor is usually on bearings in the casing or front/back plates. But the geaqr itself is simply tightly fit to the arbor, as is the spur or cycloidic gear that runs into the rest of the gear train.
  For me, I use several small disks of plastic tightly pressed on the arbor and glued to the deadbeat, also pressed onto the arbor, this gives me lots of frictiona l surface area to hold things tight. ( see Clockmaki ng video #2 for details on how I do it.).

  With wooded gears, the same can be done to make sure the deadbeat doesnt spin on its shaft. That usuallly isnt an issue as the deadbeat has very very little torque on it, the high torque is further down a clocks chain. If your just building  an art jig to show an escapemen t working, then it shouldnt take much weight to run it.. not much torque. My clock runs with just the weight of a fnger resting on a deadbeat tooth for example.. The disks I use have a secondary purpose, they make the gear set straight on the shaft by forcing the trueness of the gear to the average trueness of the disks, this removes the bevel a laser cutter makes in a hole..

  The pendulum weight has to be enough that that the pendulum swings to the bottom when moved slihly one way and released. That means it only has to overcome friction of the hanging method. I use 3 , 1 dollar coins on mine as a weigth for example.. as in the video.

Good luck, show us pictures. .

Art

[dmarlen]

Ah, always good to review terminolo goy.  So in my first comment, I made reference to the deadbeat gear.  Apparentl y I was correct in that, but not in referring to the bearing in that gear.  I had -meant- that the bearing that was sharing the shaft of the deadbeat was in the front plate and the shaft was not tight enough in the bearing itself.  Maybe I'm not being clearer now; it can be hard sometimes to express without pictures. 

I'll throw a weight on it to see how it goes and then take a video.  I hope everyone can learn from my early steps as I always enjoying learning from others.

David.

[ArtF]

David:

  Ahhh...no w I understan d. :-)

  So basically your arbor ( shaft) is not large enough for the bearing inside diameter.?
The only real solution for that is to get an arbour that fits the bearing. . Of course, as long as it isnt so loose that it actually moves up and down its ok.. the centering IS important, so you dont want too much shivering up and down, but as to if its tight in the center, it doesnt matter. A semi snug fit is fine..

Art

[dmarlen]

Right, Art.  My arbor shaft wasn't quite bit enough to fill the ID of the bearing.  I mean it was pretty good at a friction fit, but too much weight and it would spin.

I've ordered several different types of bearings off Ebay.  When they arrive I'll have to play around with what supplies I'll need for better fits.

David.