• You can now help support WorldwideDX when you shop on Amazon at no additional cost to you! Simply follow this Shop on Amazon link first and a portion of any purchase is sent to WorldwideDX to help with site costs.
  • The Retevis Holidays giveaway winner has been selected! Check Here to see who won!

Critical Neanderthal Cognition

kopcicle

Sr. Member
Feb 17, 2016
2,156
3,512
273
A long time ago in a basement far, far away.....


4th_5th_front.jpg


All things evolve stagnate or die. In this case the original 3018 was used as a model for a 4th and 5th axis machine.
I had a bit of an engineering challenge.

Crown-Gear_example.png


https://www.mdpi.com/2075-1702/12/8/496 ugh, a bit out of my wheelhouse but there's a bit of an idea showing itself.

https://academic.oup.com/jcde/article/11/4/184/7716037 And you thought I obsessed on, well , anything. So about everything you could ever want to know about a (Face) crown gear is contained there, but what we have here is a Timex, not a Rolex. What I need is a best, most bang for the buck approximation of a face gear.

First things first.

Requirements. These gears are small, 64 diametrical pitch or .3969 module (close enough to .4 it doesn't matter)
At some point quit thinking about it and make the gears.
On the way to a finished product always keep in mind that there could be a path to mass production.
On the other hand $100,000 equipment for a $10 gear makes no sense in quantities below 50,000.
On the gripping hand, a cost efficient method with little time and materials wasted could easily produce tens of thousands at not much more than the mass produced product.

Next up. The math.
 

Here you can find the set of calculators related to circular segment: segment area calculator, arc length calculator, chord length calculator, height and perimeter of circular segment by radius and angle calculator.




Circular segment
Circular segment


Circular segment - is an area of a "cut off" circle from the rest of the circle by a secant (chord).
On the picture:
L - arc length
h - height
c - chord
R - radius
a - angle
If you know the radius and the angle, you may use the following formulas to calculate the remaining segment values:

Circular segment formulas​

Segment area:
A=\frac{1}{2}R^2(\alpha-\sin{\alpha})
[1]
Arc length:
L={\alpha}R

Chord length:
c=2{R}{\sin{\frac{\alpha}{2}}}

Segment height:
h={R}\left(1-{\cos{\frac{\alpha}{2}}}\right)
 
R=52
Height=3.1360
Chord length=35.5701 1/2 Chord length=17.78505
Arc length=36.3028 1/2 Arc length=18.1514

I'm using an angle of 40 degrees because I will have to start at X0,Y0, Z52 (R) and move clockwise from Top Dead Center (for lack of a better description) to the end point of the radius.

I'm assuming I can do this in incremental as well as absolute and the syntax would be nearly the same save for G98 (absolute) G91 (incremental) modes. Still the syntax escapes me.

Using G19 , from TDC the start point, Y0 Z0, the end point would be 1/2 the chord length, 17.78505 and the height, -3.1360, while assuming (yeah, yeah , I know) the offset is 52 for the radius.

But wait, that's not all. I have an X move I need to add. That is relatively simple math that finds a common denominator between 1/2 the arc length, 18.1514 and the X path length between 1 and 1,8. I can do triangles but.

So the above was the question

and with a few tweaks this may be the answer.

CW MoveG01 Y0.000 Z0.000G19 G02 Y17.785 Z-3.136 J0.000 K-52.000 X1.5 A20
CCW MoveG01 Y0.000 Z0.000G19 G03 Y-17.785 Z-3.136 J0.000 K-52.000 X-1.5 A-20
or something like that.still not quite right I keep messing up the machine/firmware specific headers and feeds. all will have to start at Top Dead Center for lack of a better terminology and end at the end point, at the same time. So all of this will be dictated by the cutting tool's best feed in the X axis.

 

dxChat
Help Users
  • No one is chatting at the moment.