Adrian Mariano wrote:

I tried the code in your post of Tue, Oct 29, 2024 12:35 AM at the time, but it didn’t work. I got a big fat red spot against line 22 [0,(-1+chamfer_bot)width,chamfer_bot], and the opening round bracket was marked, but i couldn’t find anything wrong. I am still using Version 2021.01**.**

Unfortunately, you cannot raise the cone by _conic  + _chamferHeight. The chamfer must (should?) radiate from the “origin” just like the ridge and grooves. I believe your code as written takes a constant chamfer off the teeth, but at the inner radius, that’s too much.

This code appears to be correct. I ran a lot of quick tests using this cone and my rotated cone. There’s a lot of noise in the results, but the rotate_extrude seems slightly faster. They are close enough, however, that I think the difference is not significant. F6 is around .35-.4 s and F5 is about .25 s. Oddly the time increased as _conic became larger. The number of facets and vertices did not change markedly so I don’t know how to explain that.

module _chamferF() {
up(_conic)
scale(1.5)
zcyl(h = _conic + _toothHeight/2 - _chamferHeight,
r1 = _or,
r2 = 0,
anchor = TOP);
}

The cone is easier to read and understand so I will keep it, but leave the other code as a comment.

• Bob

Jordan Brown wrote:

A conical face spline joint or conical Hirth joint is what Bob wants. A US patent https://patents.google.com/patent/US20080175526A1/en belonging to the German Schaeffler Group is very interesting in that it shows such a joint in great detail and in that “Hirth” does not appear anywhere in the text. The ridges of the splines appear to be rounded with the same radius along the whole length, as do the grooves. GKN https://web.eoltas.lv/en/trade/trade-news/gkn-face-spline-the-downsizing-does-stop-at-the-driveshaft/ also produces the joints in Germany and calls them face splines. Both companies supply the automotive industry, where “face spline” is evidently the official term - even in Germany. I first encountered it in a description of a US aero-engine (Pratt&Whitney or Curtis-Wright, i can’t remember).

I can’t get OP’s solution to work.

OP’s solution . . . simpler solution . . . simplest solution: Translate([]) cylinder(r1, r2, h); ?

In my code the chamfer is scaled to the height of the tooth, so it gets
smaller as you go towards the center.  It's a proportion of the tooth
height.  (I wanted to confirm that my code matched yours...but your code
was so slow to preview that I was not able to do that.)  I'll post a
revised version of my code at some point.  Right now I have an issue that
the parts don't mate properly---or at least I don't think they do.  It
looks ok when you have lots of teeth like 36 but with 5 teeth it becomes
apparent that something's not quite right, because the gap isn't even.  The
gap should be even, right?  There is a great deal of complication created
by the cone angle combined with the circular rather than polygonal
edge---give up either one of those and it gets a lot simpler.  And actually
some users might prefer a polygonal edge, so I wrote it to do both.
Another thing I like about my approach is that it allows rounding the
valleys (and tops), which is really the ideal thing to do.  (I haven't
implemented this, but it's possible.)  You can't create rounded teeth or
valleys by subtracting a cone.  And don't forget for BOSL2 inclusion we
have to assume that most users are running the "stable" version, 2021.01,
and cannot use manifold.

For the previously posted code, I think there is a trailing comma after the
definition of pts that is allowed in recent versions but not in 2021.01.
If you delete that it should work.

On Thu, Oct 31, 2024 at 5:07 PM Bob Carlson via Discuss <
discuss@lists.openscad.org> wrote:

I had the same experience. I found no mention of conical joints. But since my one and only real world example is conical, I know they exist and are used. Someone said early on that hirths are not standardized so maybe it’s not surprising that online sources are incomplete. An interesting problem is that if you have a conical hirth part and need to measure it to determine what the “conic” argument should be I have not figured out any way to do that precisely! The ridge angle is easily measured but a “hirth calculator” would be needed to go from ridge angle to conic.

As I worked with the code over the last month or so, I grew to mistrust the idea of a flat profile being projected away from the origin. I used that idea originally. But he more I thought about the situation at the outer radius, the more I suspected that my powers of visualization were not adequate. The tooth at the outer radius is the intersection of the tooth with a cylinder. In a flat joint that doesn’t seem too terrible, but then move the origin make a conical joint and it really gets hard to keep in my mind. Maybe that all doesn’t matter, but I wasn’t confident it didn't.

Much of the material I found about hirth joints was about how to machine them. It was clear that the groove angle was the critical number, because the groove is the path the cutter follows. I realized that I could trust the groove and ridge angles. Using spherical coordinates it was easy to create a tooth and easy to see why it worked correctly. Someone used to working with trig could probably come up with the angles for chamfer shoulders, but not me.

I may spend some more time understanding your method, but right now I’m concentrating on some other things.

• Bob

I feel your pain. I’ve been struggling to wrap my head around these for a while now. I decided to limit the number of teeth to 12 or more. That’s somewhat arbitrary but as you specify fewer teeth, things always get weird. If the radii are larger fewer teeth may work. I didn’t see much advantage in figuring out the limits.

I’m not sure what you mean by gap. My parts fit very snugly.

A rounded chamfer might be prettier but I don’t have a need for it and I suspect it will not print as well. I work exclusively with small things so far, so a rounded chamfer on a 60 tooth part with a radius of 20 mm doesn’t mean anything. I’ve spent time looking at the slices in the PrusaSlicer and they are not great when magnified. The tips of the teeth look kinda glopped on.

It’s purely selfish of me, but I am not willing to spend my time making stuff work on a 3 year old version of OpenSCAD. I see why you feel the need.

I feel pretty strongly about the chamfer being specified as a percentage. Like with gears the user cannot know the tooth height. A percentage is much more intuitive and you can have a default.

-Bob

There is a question that I've noted before about what is meant by "tooth
angle".  The wikipedia page suggests that it is measured relative to the
cylinder axis.  In gears tooth angle is measured relative to the ridge of
the tooth.  These two ideas produce a different result, and the steeper the
cone angle gets the bigger the difference.  Arguably it doesn't matter if
you're just trying to make parts that mate with each other as opposed to
mating with some manufactured standard part.  (You can change your tooth
angle if you don't like what happened when you specified a steep cone.)
Your method of using spherical coordinates is just a way of projecting
(scaling) a triangle.  The results should be the same.  (I did want to
confirm that.)  There is another question about what you consider the
"zero" conical angle.  I initially did it so that the base of the teeth was
at zero angle, but later thought this wasn't right: it should be the angle
that produces a part that mates with itself, which should occur if the line
through the center of the teeth is at angle zero.  At least, I think that's
right.

Note: it may not matter  in practice, but a rounded valley is STRONGER than
a chamfer.  Corners concentrate forces and are the places where parts
fail.  If the part is small printing will limit this, but what if someone
prints an 8" diameter part with 6 teeth?  There is nothing weird about this
joint that should limit the number of teeth to be more than 12.  It should
work with 3 teeth.  One might in fact want an 8 tooth version to provide
part alignment at 45 degree detents, so a 12 limit is...welll...limiting.

If you're machining a tooth you're surely going to have a constant
roundover at the bottom, not one that varies with tooth size.  At the top I
suppose other things are possible, but it does seem like the natural way to
machine it would also be with a constant with chamfer, not one that varies
with tooth size.  I didn't do it that way in my code for two reasons:  (1)
I was trying to match Bob's code and (2) the varying width chamfer was much
simpler to implement.  Of course, we aren't machining and we don't have to
limit ourselves to things that are easy to machine.

It can be a nuisance as a library author to have to write code that works
on the old version.  That's definitely the case.  Seeking efficiency in
general for library code is also a good goal, though.  When someone makes a
model with 45 hirth joints what happens?  I wonder if it's better to call
this "hirth" or "face_spline".

I see you just posted your code while I was typing so I'll take a look and
see if I can compare to mine.

On Thu, Oct 31, 2024 at 7:13 PM Bob Carlson bob@rjcarlson.com wrote:

Hi Bob,

Here's the basic code for a parametric Hirth Joint. Spring loaded often
use as a slip clutch in torque sensitive situations, e.g screw drivers,
tapping heads, etc. Larger scale high speed turbines for shaft
connections, since easy to balance, no windage, etc. I've tested as
saving as stl, and re-importing, gives no errors. Easy enough to cut out
the centre teeth if you don't want them.

// clutch.scad

ind= 50;  // overall diameter
num= 20;  // number of teeth
back = 6; //thickness of back
////////////////////////////////////////////

diam= ind/cos (180/num);   // bigger to allow for chords
chord = diam*sin(180/num);

ridge= chord *sqrt(3)/3;  // or set to whatever (denominator = 2 for 60
degrees.)

points=[
 [0,0,ridge/2],
 [diam/2,-chord/2,0],
 [diam/2,+chord/2,0],
 [diam/2,0,ridge]
 ];
 faces=[
 [0,1,2],
 [0,1,3],
 [0,2,3],
 [1,2,3]
 ];

 module wedge(){
   polyhedron(points,faces,convexity=10);
 }

 //rotate wedge

 intersection(){
     translate([0,0,-back])
       cylinder(d=ind,h=200,$fn=100);
        union(){
             for (j=[0:1:+1+360/num])
              rotate([0,0,j360/num+0.5360/num]) wedge();
                    cylinder(d1=diam,d2=0,h=ridge/2,$fn=num);
                     translate([0,0,-back])
                     cylinder(d=diam,h=back,$fn=num);
      }
 }

//save as stl, then import to check for valid stl. (remove comments
below and run again)

/*
 translate([0,0,6])
 rotate([0,180,360/(num*2)])
 import("P:/Docs/openscad/clutch.stl");
*/

On 26/10/2024 00:44, Bob Carlson via Discuss wrote:

Here is the python code for creating the hirth_coupling with no limitation
of teeth, cone angle,teeth angle, chamfer etc.

from openscad2 import *

hirth coupling

n=36 # number of teeths
ta=60 # teeth angle
ca=20 # for straight 360/42.232 # cone angle
i_r=30 # inner radius
o_r=50 # outer radius
ch=1 # chamfer height
l1=[[i_r,0],[o_r,0]]
l2=[ q_rot([f'z{i}'],l1)  for i in linspace(0,360,n+1)[:-1]]

l3=axis_rot_1(l1,ax1=[0,1,0],loc1=[o_r,0],theta=ca)
l3= line2length(flip(line2length(l3,(o_r-i_r)+5)),(o_r-i_r)+10)
cone1=[ q_rot([f'z{i}'],l3) for i in linspace(0,360,n)]
l2=psos(cone1,l2,[0,0,1])
l1=[l2[0][0],l2[1][0]]
d1=l_len(l1)/2/cos(d2r(ta))
l1=axis_rot_1(l1,line_as_axis(l2[0]),l2[0][0],ta)
l1=line2length(l1,d1)
l3=[l2[0][1],l2[1][1]]
d2=l_len(l3)/2/cos(d2r(ta))
l3=axis_rot_1(l3,line_as_axis(l2[0]),l2[0][1],ta)
l3=line2length(l3,d2)
l4=[l1[1],l3[1]]
a,b=l4
l4=line2length(flip(line2length(l4,25)),30)
cone2=[ q_rot([f'z{i}'],l4) for i in linspace(0,360,n)]
l3=psos(cone2,l2,[0,0,1])
l3=q_rot([f'z{360/n/2}'],l3)
s1=l_(a_([l2,l3]).transpose(1,0,2,3).reshape(n*2,2,3))
s1=s1+[s1[0]]
s1=l_(a_(s1).transpose(1,0,2))
sol1=flip(surf_base(s1,s1[0][1][2]+10))
s2=l_(a_(cone1).transpose(1,0,2))
s2=surface_offset(s2,-ch)
sol2=surf_base(s2,s1[1][0][2]-10)
sol2=sol2+[sol2[0]]
sol3=surf_base(flip(s1),s1[1][0][2]-10)
s3=q_rot(['z5'],l_(a_(cone2[:-1]).transpose(1,0,2)))
s3=surface_offset(s3,ch)
sol4=surf_base(s3,s1[0][1][2]+10)
sol4=sol4+[sol4[0]]
with open('trial.scad','w+') as f:
f.write(f'''

translate([0,0,25])

// color([.13,.81,.37])
difference(){{
{swp_c(sol1)}
{swp_c(sol2)}
}}
difference(){{
{swp_c(sol3)}
{swp_c(sol4)}
}}
''')

On Fri, 1 Nov 2024 at 05:31, Raymond West via Discuss <
discuss@lists.openscad.org> wrote: