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Author Topic: 3D Printed Top  (Read 12441 times)

Jeremy McCreary

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Re: 3D Printed Top
« Reply #60 on: October 28, 2016, 01:08:42 PM »

NB:  Edited the text below to make it clearer and add the effect on AMI.

I have no experience with throwing tops. How does the top's curvature affect its play -- not just in theory, but in practice? (By "curvature" here, I mean the curvature of the top's silhouette in a plane containing its "axis" of symmetry.)

For example, let z track "height" along the axis, and r(z), the perpendicular "radius" from the axis to the silhouette at height z. Then the silhouette is just a graph of r(z) vs. z. If T(z) tracks string tension at the top as the string leaves height z, then the driving axial torque Qd(z) applied to the top grows with radius:

Qd(z) = T(z) r(z)

Hence the silhouette shapes the driving torque curve Qd(z), which in turn limits release speed. The aerodynamic braking torque Qa(z) opposing the driving torque also grows with r(z), but at an even faster rate. Hence the net axial torque (ignoring tip friction) at height z during spin-up is

Q(z) = Qd(z) - Qa(r(z)) = T(z) R(z) - Qa(z)

To accelerate the top to release speed, this net torque has to work against the top's axial moment of inertia (AMI), which depends on the shape of r(z) and grows very roughly with the square of mean radius.

When integrated over the appropriate height range, are any of the net effects noticeable in play?
« Last Edit: October 28, 2016, 06:30:20 PM by Jeremy McCreary »
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Playing with the physical world through LEGO

Jack

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Re: 3D Printed Top
« Reply #61 on: October 28, 2016, 04:52:33 PM »

NB:  Edited the text below to make it clearer and add the effect on AMI.

I have no experience with throwing tops. How does the top's curvature affect its play -- not just in theory, but in practice? (By "curvature" here, I mean the curvature of the top's silhouette in a plane containing its "axis" of symmetry.)

For example, let z track "height" along the axis, and r(z), the perpendicular "radius" from the axis to the silhouette at height z. Then the silhouette is just a graph of r(z) vs. z. If T(z) tracks string tension at the top as the string leaves height z, then the driving axial torque Qd(z) applied to the top grows with radius:

Qd(z) = T(z) r(z)

Hence the silhouette shapes the driving torque curve Qd(z), which in turn limits release speed. The aerodynamic braking torque Qa(z) opposing the driving torque also grows with r(z), but at an even faster rate. Hence the net axial torque (ignoring tip friction) at height z during spin-up is

Q(z) = Qd(z) - Qa(r(z)) = T(z) R(z) - Qa(z)

At the same time, the axial moment of inertia (AMI) resisting the net axial torque depends on the height and shape of r(z) and grows roughly with mean radius.

When integrated over the appropriate height range, are any of the net effects noticeable in play?

« Last Edit: October 29, 2016, 10:51:26 AM by ta0 »
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Jeremy McCreary

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Re: 3D Printed Top
« Reply #62 on: October 28, 2016, 06:23:37 PM »

Ah, my evil scheme is working! So Jack, apart from top size, how does throwing top shape affect play in your experience? I'm particularly interested in the curvature of the silhouette below the widest part.
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jmadrigal

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Re: 3D Printed Top
« Reply #63 on: October 28, 2016, 09:21:20 PM »

Cecil- Making different shapes and trying new things is what is so fun about making tops. I think the straight sides allow certain tricks to be more accessible. With Stormy I was able to do a staircase to heaven with 3 wraps. I wasn't with the larger tops since they require thicker string. I am happy with this shape for play but I am sure I will continue experimenting with other shapes.
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jmadrigal

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Re: 3D Printed Top
« Reply #64 on: October 28, 2016, 09:25:11 PM »

I drew up the tip to send out for purchase through an online machine shop. I wanted opinions on material for the tip. I was thinking 7075 aluminum would be good for strength, cost and machinability. 
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ta0

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Re: 3D Printed Top
« Reply #65 on: October 29, 2016, 11:19:40 AM »

Jeremy: changes in air drag have no effect on play. The shape of the conical part has little effect during play, except for the following:

1. It may affect the stability of the wrap and how hard you can throw it.
2. If you land on the string with the side of the body, a more convex shape will help the string slide towards the tip instead of killing the spin.
3. A more convex shape will result in a lower center of mass, with slower precession and more stability/less response.
4. A convex shape may make it more difficult for the top to go around the string without touching it.

A straight shape (cone) works well, as do convex shapes. On the other hand, a concave shape like the one of the YYJ Chihuahua has big issues with 1 and 2:



José: how much are they charging you for a tip? Aluminum is ok, but of course steel would be better (but more expensive to machine).
« Last Edit: October 29, 2016, 12:51:47 PM by ta0 »
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Jeremy McCreary

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Re: 3D Printed Top
« Reply #66 on: October 29, 2016, 11:47:34 AM »

Jeremy: changes in air drag have no effect on play. The shape of the conical part has little effect during play, expect for the following...

Thanks, ta0 -- just what I was looking for.
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Jeremy McCreary

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Re: 3D Printed Top
« Reply #67 on: October 29, 2016, 11:54:17 AM »

I think the straight sides allow certain tricks to be more accessible.

Is this mainly the string clearance issue ta0 mentioned?
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jmadrigal

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Re: 3D Printed Top
« Reply #68 on: October 29, 2016, 01:07:03 PM »

José: how much are they charging you for a tip? Aluminum is ok, but of course steel would be better (but more expensive to machine).

They have many options for material and the price depends heavily on quantity. Comparing aluminum 7075 to steel 4140 for 10 tips the price is ~21ea. If you kick up the quantity to 50 the price comes down to about 7 to 8 ea. If you get stainless the price is about 2 more per tip.
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Jack

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Re: 3D Printed Top
« Reply #69 on: October 29, 2016, 07:20:24 PM »

So Jack, apart from top size, how does throwing top shape affect play in your experience? I'm particularly interested in the curvature of the silhouette below the widest part.

makes no difference.............you just make it work  ;D
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cecil

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Re: 3D Printed Top
« Reply #70 on: October 30, 2016, 02:02:53 AM »

Is that $21.00 each for steal?
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jmadrigal

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Re: 3D Printed Top
« Reply #71 on: October 30, 2016, 08:51:12 AM »

Is that $21.00 each for steal?
Yes, at the lower quantity but even steel drops to about 8 at the higher quantity.
Stainless is more though, about a couple bucks more per tip on average. 
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cecil

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Re: 3D Printed Top
« Reply #72 on: October 30, 2016, 01:23:05 PM »

I think that's a great price. I have to make mine on a big manual lathe. The first one takes about 45 minutes then I can make them in about 30 minutes. I drill and tap 8 - 32 where I can pull the tip in. I'm lucky to get in the shop twice a month. At $ 21.00 a piece they are making them on a C.N.C lathe.
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jmadrigal

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Re: 3D Printed Top
« Reply #73 on: October 30, 2016, 05:21:45 PM »

What type of steel do you recommend?
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Jack

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Re: 3D Printed Top
« Reply #74 on: October 30, 2016, 05:23:56 PM »

What type of steel do you recommend?

« Last Edit: October 31, 2016, 10:37:59 AM by ta0 »
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