JIS 2001D spline help required 2

[cambi0]

Hi all
I'm trying to create a spline model of a JIS D 2001 female spline.
Its 20 deg PA, 22tooth (1mod) side fit, 20.673 base dia, 22.0 mm pcd, 22.0 minor and 24.3 major dia. addendum modification 0.8
20.067/ 20.157 between dia 2 pins.
Ive drawn the involute form basics but the tooth width is massive, so i'm assuming i need to pull the involute intersection to the base circle down to match the 0.8 modification (ie run the intersection of the involute to the base dia minus 1.6?) but i'm not 100% sure.
I only really need a cad profile, so if anyone can help (or provide a wiring profile... i'd be very grateful
cheers
cam




ref thread406-280069

 

[gearguru]

I do not have that standard, but here are my 2 pennies:

1. If you do not know it yet you have to calculate the tooth thickness/space from the measurements between pins. Not simple calculation but not a rocket science either.
2. The tooth thickness/space is measured as an arc length on the pitch diameter, in your case 22(teeth)*1(module) = 22mm. Obviously it is just a theoretical value, but you have to model the teeth using these values. That's also the diameter where the pressure angle is measured.

 

[dinjin]

You might try these to see how close they fit the
max space width. You will have to mirror them about the vertical axis.

at point X=-1.09713293 Y=10.94514958
at point X=-1.09625777 Y=10.94858917
at point X=-1.09446577 Y=10.95557638
at point X=-1.09264878 Y=10.96260527
at point X=-1.09080657 Y=10.96967594
at point X=-1.08893890 Y=10.97678851
at point X=-1.08704554 Y=10.98394311
at point X=-1.08512625 Y=10.99113984
at point X=-1.08318079 Y=10.99837882
at point X=-1.08120892 Y=11.00566019
at point X=-1.07921039 Y=11.01298405
at point X=-1.07718497 Y=11.02035054
at point X=-1.07513241 Y=11.02775976
this assumes your input is correct.
You can rotate these to the right about 0,0
coordinates to get the mean one half space width.
The circular space width is about 2.140/2.197
You are responsible for checking these dimensions.
I do not have the JIS standard. These were generated in acad.

 

[gearguru]

Per my calculations the tooth space is:

For 20.067mm size between 2mm rolls: 2.1530189mm
For 20.157mm size between 2mm rolls: 2.1870009mm

As dinjin mentioned - "You are responsible for checking these dimensions."

 

[dinjin]

Thanks to Gearguru pointing out my error. I drew the involute
and then offset it 1mm. I drew the radius at the mean ball or roller radius. Where it intersected the offset involute, I drew
a line from that point tangent to the base diameter. I then extened that line to the original involute. Checking that extension was slightly greater than 1mm. So my layout was off by
that amount. Go with his tooth thicknesses and rotate the coordinates accordingly.

 

[gearguru]

Be sure that the involute starts at base diameter. Only the portion of the involute from minor to major diameter is used. Tooth space as I mentioned above is measured on the pitch diameter.

Dinjin, when you offset the involute you change the pressure angle at the pitch diameter, don't you?

 

[cambi0]

thanks all!
having had all you help and thinking about it in the shower (things always seems clear there, maybe i should move my desk!) i put in the 2mm ball circle, set the across balls radius and then made the involute curve tangent to it. having set the ball centre - rad line as the y axis then mirrored about this, set the limits of the root diameter to coincide with the angular spacing (360/44 degrees) either side, and finally rotated to get a lovely looking 3d model (attached).
final question.. the pressure angle seems arbitrary when i create the involute (create points and then curve through points for best fit approximation - only for the cad model), i.e. i dont seem to need it. is it a function of the base circle/ module?

 

[dinjin]

Gearguru,

Offsetting the involute is not the way to go.
It was close obviously, but not close enough.
As to how the offset involute changed, it is not
clear to me other than it was wrong.
The original involute drawing that I have is for a 20 degree pressure angle but starts at the base diameter and goes out beyond any expected outside radius. It was also drawn at a 20 pitch diameter ie equal to a ten pitch radius that allows me to scale it easily to whatever pitch radius I need.
Some time back I rotated it to have the pitch line
contact point to be on the vertical axis. If the one half tooth thickness angle is known, it was easy for me to simply rotate it by that amount and
mirror it for a quick tooth form. I will try this for the mean tooth thickness that you have given and see how the coordinates changed.
I could not fully understand Cambrio's method so do not want to comment on it. From your dimensions, I got 1.08500495 as the mean on half tooth thickness.

 

[dinjin]

These are the coordinates of the mean tooth space.
Mirror these points about the vertical axis.
They start at the base diameter and go to the
major diameter.
at point X= 1.1716 Y= 10.2700
at point X= 1.1720 Y= 10.2744
at point X= 1.1729 Y= 10.2875
at point X= 1.1737 Y= 10.3096
at point X= 1.1741 Y= 10.3407
at point X= 1.1733 Y= 10.3811
at point X= 1.1709 Y= 10.4310
at point X= 1.1662 Y= 10.4906
at point X= 1.1586 Y= 10.5603
at point X= 1.1473 Y= 10.6405
at point X= 1.1316 Y= 10.7316
at point X= 1.1106 Y= 10.8340
at point X= 1.0833 Y= 10.9483
at point X= 1.0485 Y= 11.0750
at point X= 1.0050 Y= 11.2148
at point X= 0.9514 Y= 11.3684
at point X= 0.8859 Y= 11.5364
at point X= 0.8066 Y= 11.7197
at point X= 0.7114 Y= 11.9190
at point X= 0.5975 Y= 12.1353

 

[gearguru]

cambi0,
As I mentioned the pressure angle and tooth thickness/space are always defined on a pitch diameter.
Knowing it (and little bit of the involute geometry) one can find that:

d=z*m
db=d*cos(alpha)

d-pitch dia
z-no of teeth
m-module
db-basic dia (there the involute starts and pressure angle=0; involute does not exist on a smaller radius and the pressure angle is growing with the radius)
alpha-pressure angle (at d )

Something for your bath meditations: you modeled the tooth the "drafter's" way. I prefer to calculate the values and to use those for the model. I would do the same with the points on the involute. The involute is perfectly defined by math. data. In your case if you want to be very accurate you can use more precise data also for the basic diameter (see the formula), but in the praxis it is probably an overkill.

 

[cambi0]

Thanks gearguru, dug out my 'fundamentals of gearing' booklet and i'm back up to speed on gears profiles. But in the constraints of time and a relatively new cad system last week i drew it the old fashioned way and joined the dots.
As an aside, having drawn it all at mid limit, i measured tooth space as 2.17mm at 22.0 pcd, so accurate to within 2dp to what you calculated.
As a further question, do you know what the root radius to the major dia would likely be? guess as big as poss whilst avoiding interference, possibly provided in the JIS standard is the simple answer.
I might need to provide a profile to wire this so might be accurate enough to do that from the sketch, if i allow a little for heat treat movement.
I was thinking of using 300m as its for drive flange for a road application so needs a bit of give.

 

[Medeski]

Hello Cambi0,

I believe JIS D 2001 is outdated, JIS B 1603 is the new(er) standard for involute splines. Unlike some standards, you can view most JIS standards online, for free! The only caveat of not buying them is that you can't print them out and they are all in Japanese (There is an English version I think, but I don't know if these are free to view online). Here is the link for the page, it's broken up into multiple PDF's.

http://www.jisc.go.jp/app/pager?id=87316

I don't have time now to read through the whole thing, but if you have a specific question I could see if it's in there or not. You may be able to find what you need just by looking at the diagrams and charts.

Best,
Medeski

 

[gearguru]

cambi0
I do not know the root radius, I do not have the standard and I do not want to guess.
Perhaps Medeski can help.

 

[dinjin]

Like gears, I think it would be a minimum. In the case of gears because different backlash values necessitates cutting deeper to get the proper tooth thickness the depth would increase. I think your concern should be if you maintain the Form Diameter.