Gearify

Software helpfull to Gear makers.
Nate
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Re: Gearify

Post by Nate »

Gearify wrote: ...
HOWEVER! It is my hope that I can eventually find or produce a suitable generalization of the involute tooth concept for arbitrary non-circular gears. So far I have the following possible strategies:


1. Find some credible literature with a clear and reasonable approach to generalize involute teeth to non-ciruclar gears (no luck so far)
2. Devise my own generalization that at LEAST removes vibration (I have some ideas)
3. approximate the non-circular shape as a series of circular segments and use appropriate involute teeth per segment (meh.. I don't even yet know if this makes sense)
4. Allow the user to upload a "virtual hob" (which Artf mentioned) so that the portion cut away from the subtracion process can be larger than the tooth itself. This is a big feature on my TODO list. May not solve the issue but may get me closer.

So that's where I'm at with involute teeth. Its definitely my most requested, and desired feature, but as ArtF mentioned, it is very very hard to involute tooth a non-circular gear.

....

Feel free to ask me any questions or offer ideas for how you would like to see Gearify improved, or possible solutions for how to make the gears more suitable for application.
My impression is that gearify produces 'roller' profiles which (in the idealized case) have a continuous point of contact between the two rollers, rather than one that "jumps around" like the red dots in this youtube video:

https://www.youtube.com/watch?v=14yMFdgWM-A

Is that impression correct?

IMO Generalizing involutes to no non-circular profiles really isn't that hard. It's basically just like generating involute tooth flanks point-by-point.

I worked through the basics earlier this year: http://gearotic.com/ESW/FavIcons/index.php?topic=1313.0

For more advanced topics like how to use profile shifting I can't help you much.

I played with interpolating the roll line as a series of circular arcs and putting involute teeth on those, but that can have mechanically undesirable properties. For example, it won't work properly for non-circular gears with a fixed pivot.
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ArtF
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Re: Gearify

Post by ArtF »

Nate:

  :), you guys hurt my head, your math background is far advanced to mine. I struggle to do such things
as tooth a noncircular, and generalising it is something Ive spent many attempts at, including generation
point by point. While Ive gotten close, the virtual hob seems to be the only solution I can come up with
so far.
      Its a good discussion, and I agree with its direction, Ive always felt there is a formulaic generalization
of involution for any surface. Ive tried and tried to derive it, but its just over my head. When this happens
I just try to keep studying the subject till I understand. So your comments are helpful for what I can glean.
     
 
Art
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Re: Gearify

Post by Mooselake »

Hi, Michael!  Welcome to the Gearotic forum.

Guess it's time to cough up a few bucks and get rid of the wiggling in the Gearotic display :)  They're forecasting rain in Mooseville, so the outside project I got talked into (running antenna wiring in an old firehall) might get cancelled, which will free up the day for dinking around with the laser and Gearify/Gearotic.

I didn't see any provision for shafts, either sizes or locations, in Gearify gears, did I miss them?  Also, does the postmaster address on your site still work?

Kirk
Nate
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Re: Gearify

Post by Nate »

ArtF wrote: Nate:

 :), you guys hurt my head, your math background is far advanced to mine. I struggle to do such things
as tooth a noncircular, and generalising it is something Ive spent many attempts at, including generation
point by point. While Ive gotten close, the virtual hob seems to be the only solution I can come up with
so far.
...
Since Micheal was asking about it, I've been thinking about the best way to explain it.  So here's an attempt:

I'm going to assume that you can work out how to generate circular involute tooth profiles point-by point starting with the theory of involute gears.  So you know, for example, that there are two contact points on tooth flanks that correspond to every point on the pitch circle.   If that doesn't make sense then starting with a foundation of involute gear theory might be more productive.

The non-circular analogue of the pitch circle is called a roll line.  (I tend to call it a pitch line, or pitch profile, and there may be other terms, but I'll call it a roll line here.)  Similarly, let's call the analogue of the pitch point the roll point.

So let's say we want to make a set of involute non-circular gears, and let's suppose that we've produced two "nice" roll lines so that they'll roll against each other with fixed centers of rotation and with the point of contact - i.e. the roll point - always on the line between centers.

Then it's relatively straightforward to model the rolling action of one roll line against the other.  (For example, that's something that gearify already does.)

Now, to build involute tooth profiles from this action we need to pick some way to determine tooth phase, and a pressure line.  There are natural ways to do both of those:

The pressure line can be effectively the same as it would be for circular involutes:  It's the line that intersects the line between centers at the roll point, and is off perpendicular by the pressure angle.  (There are two of these pressure lines, one for the rising flank, and one for the falling flank that correspond to the two directions of the perpendicular.)

Similarly, the tooth phase is a linear sawtooth function of the arc length of the roll line.

So for every point on the roll line, we have a pressure line and a tooth phase, so we can work out the corresponding contact points, and this lets us generate the tooth flanks point-by-point.
Last edited by Nate on Thu Sep 24, 2015 8:28 am, edited 1 time in total.
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Re: Gearify

Post by ArtF »

Nate:

Very well explained, the problem Ive found is in the convexities.. that does work for me till the point where convexity causes a problem, been so long I cant say exactly what the problem was.. .. but you know, the one point you mentioned I hadnt tried was using a sawtooth phase on the arc length for flank position,...thats brilliant.. I may have to revisit
that code..

Art
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Re: Gearify

Post by Gearify »

Nate,

"Now, to build involute tooth profiles from this action we need to pick some way to determine tooth phase, and a pressure line."

Wow. This is essentially what I had in mind, only I was of the opinion that "picking" my own pressure line and tooth phase would not constitute something I could advertise as legitimate involute teeth, but rather my own personal bastardization of a precisely defined concept.  :D I have not had time to extensively review and understand in-volute tooth theory to know how much is good enough (I am involved in too many projects... )

This discussion is very motivating to me! If we can come up with a feasible definition I can definitely implement it in Gearify! :)

Here is my question for you though, Nate. By whatever definition you're working with, what is the pressure angle measured from on a non-circular gear? In circular gears, the line tangent to the roll lines at the point of contact is always perpendicular to the line through the centers of rotation (which gives us some nice properties). On non-circular gears (especially the more eccentric ones) the tangent line can be quite far from perpendicular to the line through the center. See the diagram below:

Image

If measured from (p1-p2) I feel that there would be severe disortions where t1-t2 differs significantly. But if from t1-t2, the gears may not "push" on eachother properly and the entire benefit of involute teeth is compromised.

Thoughts?

Last edited by Gearify on Fri Sep 25, 2015 4:23 am, edited 1 time in total.
Nate
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Re: Gearify

Post by Nate »

Gearify wrote: Here is my question for you though, Nate. By whatever definition you're working with, what is the pressure angle measured from on a non-circular gear? In circular gears, the line tangent to the roll lines at the point of contact is always perpendicular to the line through the centers of rotation (which gives us some nice properties). On non-circular gears (especially the more eccentric ones) the tangent line can be quite far from perpendicular to the line through the center.
I don't know what the official definition is or even if there is one for non-circular gears.  Art and I discussed the same question in the other thread.   As far as I'm concerned, the preferred usage is the angle off p1-p2.

If measured from (p1-p2) I feel that there would be severe disortions where t1-t2 differs significantly. But if from t1-t2, the gears may not "push" on eachother properly and the entire benefit of involute teeth is compromised.

Thoughts?
Mechanically speaking you probably want to measure the angle from p1-p2 and live with the distortions.   That's what I was trying to describe, and, mechanically, you want the action to be close to that line.  There's a lot of freedom in tooth profiles, so the roll line tangent line can somtimes also work.

In the illustration, if we imagine that we're turning the red gear clockwise as the master and the yellow gear is the slave and the gear flanks are roughly perpendicular to the t1-t2 line, then it's likely that the gears would just separate.

Nate
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Re: Gearify

Post by Nate »

Nate wrote:
Gearify wrote: Here is my question for you though, Nate. By whatever definition you're working with, what is the pressure angle measured from on a non-circular gear? In circular gears, the line tangent to the roll lines at the point of contact is always perpendicular to the line through the centers of rotation (which gives us some nice properties). On non-circular gears (especially the more eccentric ones) the tangent line can be quite far from perpendicular to the line through the center.
I don't know what the official definition is or even if there is one for non-circular gears.  Art and I discussed the same question in the other thread.   As far as I'm concerned, the preferred usage is the angle off p1-p2, but I worked this stuff out for myself.  Other people will have other notions.

If measured from (p1-p2) I feel that there would be severe disortions where t1-t2 differs significantly. But if from t1-t2, the gears may not "push" on eachother properly and the entire benefit of involute teeth is compromised.

Thoughts?
Mechanically speaking you probably want to measure the angle from p1-p2 and live with the distortions.   That's what I was trying to describe, and, mechanically, you want the action to be close to that line.  There's a lot of freedom in tooth profiles, so the roll line tangent line can somtimes also work.

In the illustration, if we imagine that we're turning the red gear clockwise as the master and the yellow gear is the slave and the gear flanks are roughly perpendicular to the t1-t2 line, then it's likely that the gears would just separate.

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Re: Gearify

Post by Gearify »

"so the roll line tangent line can somtimes also work."

Sounds like this could potentially be a user option!  :D

I do wonder how the distortions would appear when the roll-tangent line is significantly off-normal to the center-to-center line...

Here is another question.

We can define the pressure lines as a series of "snap shots" where the line is chosen to pass through the contact point at a particular point in time. So there is in a sense a "jump" from one pressure line to the next as the position of the line switches for each tooth, to pass through the varying point of contact of the roll lines. This jump may produce some abrupt changes in stress and pressure that may be undesirable (am I wrong?).

One could, however, define a MOVING pressure line.  Such a pressure line would always be intersecting the point of contact between the roll lines, and the point of contact would linearly travel along this "floating" pressure line.

This is similar to how a Cubic Bezier curve is generated. Imagine the green line below is our "floating" pressure line. The orientation of the line is defined by either of the two "pressure angle" notions we defined (this is constant if measured from (p2-p1) as described earlier, and continuous if measured from (t2-t1)), and the position of the line would be continuously defined by the point of contact on the roll lines...

What do you guys think?  
Image
Last edited by Gearify on Fri Sep 25, 2015 6:16 am, edited 1 time in total.
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Re: Gearify

Post by ArtF »

I think youll find the pressure angle is measured not from the pitch circle, but from the base circle, so if we shrink the ellipse by the base circle amount,
then compute a tangent between the two offset base ellipses, that would be the pressure angle Id use ( and do currently) in computing the involutes.

I think Nates idea is a really good one. Ill probably play with it in the coming months to see if it improves on hobbing, but I have read papers
on the hobbing being superiour simply because it deals with degenerate solutions to Nates idea. Its like the tips of the teeth on high K areas
of the curve, the hob finds it naturally, the involute equations start to produce some nasty overlap that needs to be dealt with.. at least thats
what Ive experienced so far.

Art

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Re: Gearify

Post by ArtF »

Michael:

As an example, in your drawing, Id imagine the proper line of action is if you moved T1 to a 1/4 inch inside the red on a line from
c1 to p1, and then places t2 at a line crossing pitchpoint to a point 1/4" inside the yellow...that woudl be the proper line for that gear.

Art
Nate
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Re: Gearify

Post by Nate »

ArtF wrote: ...
I think Nates idea is a really good one. Ill probably play with it in the coming months to see if it improves on hobbing, but I have read papers
on the hobbing being superiour simply because it deals with degenerate solutions to Nates idea. Its like the tips of the teeth on high K areas
of the curve, the hob finds it naturally, the involute equations start to produce some nasty overlap that needs to be dealt with.. at least thats
what Ive experienced so far.
...
Right, the hob is good for finding clearances, but if the profiles are degenerate, then 'virtual hobbing' will produce bad gears.  (I.e. gears that lose mesh or with rotational ratios that are inconsistent with the roll lines.)
Nate
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Re: Gearify

Post by Nate »

Gearify wrote: ...
We can define the pressure lines as a series of "snap shots" where the line is chosen to pass through the contact point at a particular point in time. So there is in a sense a "jump" from one pressure line to the next as the position of the line switches for each tooth, to pass through the varying point of contact of the roll lines. This jump may produce some abrupt changes in stress and pressure that may be undesirable (am I wrong?).

One could, however, define a MOVING pressure line.  Such a pressure line would always be intersecting the point of contact between the roll lines, and the point of contact would linearly travel along this "floating" pressure line.
...
The pressure line is stationary in the reference frame of the pitch point. In any reference frame where the pitch point is moving the pressure line will be moving as well.

In this video the pressure line is the red line, and the red dots are points of contact.  Can you explain what time in the cycle the "jump" you're concerned about occurs?

https://www.youtube.com/watch?v=14yMFdgWM-A
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Re: Gearify

Post by Gearify »

Let's say that P(t) is the point of contact between the roll lines at time t. The line of action (as you defined it) passes through P(t), and is oriented based on the pressure angle.

Suppose the pitch point begins contact at time t0 and moves smoothly along the line of action until the next tooth is engaged at time t1. Now a new line of action is engaged and will pass through point P(t1).

For a circular gear, P(t0) = P(t1). for a non-circular gear, they are most likely not equal.

So imagine in the video you posted, imagine that the height of the red line would instantaneously jump to a different vertical height every time a new tooth engaged.
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Re: Gearify

Post by Nate »

Gearify wrote:...
So imagine in the video you posted, imagine that the height of the red line would instantaneously jump to a different vertical height every time a new tooth engaged.
The pitch point is moving continuously along a continuous path.  There's also a continuous rotation.  What does your math education tell you about the composition of continuous things?  Also, does continuous motion 'instantaneously jump'?

The "dots" do jump back to the start of the line of action - that's the sawtooth phase I described - but the motion of the line of action as a whole is going to be continuous in any setting where the motion of the gears is continuous.

...

BTW:  If we imagine that the gear in the video is rolling along a stationary rack, then the only way that P(t0) = P(t1) is if t0=t1.  You're not thinking in terms of the reference frame of the pitch point.
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