Involute splines, how do you draw them

[pauluk]

Hi All
I have got a one off job that requires an involute spline cut on one end. I have a sample that i need to copy. my plan is to draw out the profile of the tooth, so i can m/c a cutter to produce the splines. the problem is i can't find the infomation to enable me to produce the drawing . Machinery's Handbook has a lot of info on splines, but not an idiots guide to drawing them out.

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[Climatepro]

An involute is the shape formed by a curve that is perpendicular to a line that at every point is tangent to the base circle. That's a pretty confusing thing, the easiest way to explain it is that it's the shape made if you do the following:

Wrap a string around a cylinder that has the diameter of the "base circle" (a circle which is roughly the root of the teeth). Now tie a knot in the string, and keeping the string taut, unwind it from the cylinder. The path taken by the knot is an involute. The involute shape is modified to contain a radius at the root of the tooth for strength, and it is chopped off at the tip (it would otherwise form a sharp point).

Is that enough to get your job done?

[Kiwi]

Paul
If you have CAD that can handle macros this may be of some use.
I wrote this for SW. You need to enter the Base Dia radius.

MACRO to GENERATE INVOLUTE PATH with SOLIDWORKS
===============================================
Sub main()
Set swApp = Application.SldWorks
Set Part = swApp.ActiveDoc
'----------
R = 71.6034 'ENTER BASE CIRCLE RADIUS
pi = 4 * Atn(1)
For Ang = 0 To 45 Step 2
X1 = Cos(Ang / 180 * pi) * R
Y1 = Sin(Ang / 180 * pi) * R
Opp = R * 2 * pi
Opp = Opp * (Ang / 360)
Hyp = Sqr(R ^ 2 + Opp ^ 2)
Ang2 = Atn(Opp / R)
Ang2 = Ang2 / pi * 180
Ang3 = Ang - Ang2
X2 = Hyp * Cos(Ang3 / 180 * pi)
X2 = Int(X2 * 10000 + 0.5) / 10000
Y2 = Hyp * Sin(Ang3 / 180 * pi)
Y2 = Int(Y2 * 10000 + 0.5) / 10000
XX = X2 / 1000
YY = Y2 / 1000
Part.CreateLine2 X, Y, 0, XX, YY, 0
X = XX
Y = YY
Next Ang
'----------
End Sub

[NC Cams]

I"m surprise that someone would even DRAW a spline anymore, even with CAD.

All the splines I"ve seen of late are merely psuedo splines that are called out on a "hatched" segment via the applicable ANSI standard note (flat root, side fit, involute, etc).

Once they are called out on the drawing, the spline cutter is/was responsible for meeting the form and tolerance call outs per the ANSI spec. We went thru the fiasco of having a designer "draw" the spline and it was a frigging tolerancing/dimensioning disaster. Consult/use the ANSI specs and type call outs and save yourself the nighmare.

You can order the ANSI standard handbook for splines and tolerances thereof from the Society of Automotive Engineers website. Worth the investment even for a 1 off job.

[HuFlungDung]

Make yourself an inexpensive female casting off the original spline. It only needs to encompass one tooth and two tooth spaces on the male shaft spline. Auto body filler seems to make a good enough stable casting media. When it hardens, remove it and form grind a flycutter to fit the space between teeth in the casting.

AFAIK, there is likely no really good drawing data for an involute since the shape is generated by the hob, which itself has a much simpler shape. But most of us don't have the luxery of a hobbing machine, so we make do with form ground cutters. I just grind them offhand on the bench grinder.

Then flycut the new spline out on the mill using the cutter.

The method that ClimatePro outlined, while I've heard of it, it does not really have any control over the pressure angle of the spline drawn. I'm not sure what the relationship is between this "string-generated involute" and the pressure angle. Does anyone?

[Kiwi]

>I'm not sure what the relationship is between this "string-generated involute" and the pressure angle. Does anyone?

The "Pressure Angle" and the "Involute" are calculated from the Base Circle.

[Climatepro]

I hope you didn't take my explanation to mean that you somehow mark the path a knot in a string takes! I figured you would get the physical explanation and then draw the curve in your CAD package perhaps using a 3 point curve.

An constant point on a line that is always tangent to a circle (the base circle) as the line is being swept around the circle (as if unreeling a string), IS THE DEFINITION of an involute. There's probably a nice mathematical definiton out there? Standard gear cutters are approximations of this shape, and as long as there's reasonable gear lash the inaccuracy doesn't matter much, but pauluk makes it sound as if he's going to either grind a cutter with data or mill the teeth with data.

[HuFlungDung]

Yes, I understood it was just a figurative method of drawing the involute , still, it seems as though one would obtain one single shape and that is it. Yet, gears with various pressure angles "look different", so is the curve for a 20 degree pressure angle face taken farther up the involute somehow, or is the center of the "unwrap focus" shifted somewhat relative to the pitch circle to achieve varying pressure angles?

[DICKEYBIRD]

Will this help? http://pergatory.mit.edu/2.007/Resou...-theory-bg.pdf

I ran across this in another forum...far more info than I can use right now but I saved it anyway. Filesize too big to post the .pdf directly.

[HuFlungDung]

That is a nice article, Dickeybird, and it does show how and why the involute varies in form for different diameter gears.

But, it does not explain how to geometrically generate an involute of a particular pressure angle. From the example, all one would get from generating an "unwound involute", is one unique pressure angle and no others would be possible. I'm not sure if 14.5° is the "natural pressure angle" of a drawn involute (I doubt it) but the question is interesting to ponder and imperative to answer before any gear tooth can be drawn with splines or whatever.

[pauluk]

Hi Guys
Thanks for the info so far. Just to clarify things I have a splined shaft which i need to copy for a customer, I can't get hold of the female part to check the fit of the part i make, so my intention was to draw the spline out, tweek the drawing very slightly to make sure it fits, and then use the drawing to cnc a tool to produce the splined shaft.

Thanks for the macro Kiwi, but i don't have solid works

It looks like I am going to have to grind up a tool by hand and give it a go.

Paul

[Bill Clark]

Since an involute curve is ever changing it cant simply be drawn like an arc or something. An involute spline is the same as an involute gear with the same specifications i.e number of teeth,pressure angle, and pitch. Generally speaking a spline is only shallower then a gear. If you want to draw a gear and generate a tool path use a cad-cam program like Bob-Cad or Master-cam. Use the gear program and fill in the blanks using your sample for the major and minor diameter to get the depth. Better yet send it to me and I will hob it for you.

[Kiwi]

Gears with the same number of Teeth and DP but different Pressure Angles have different Diameter Base Circles.
The Involute is generated from the Base Circle.

[HuFlungDung]

Okay, that makes sense. Thanks Kiwi, I now see the Base diameter listed in the chart that Dickeybird posted. It doesn't help me draw it but at least I understand where it begins from now

[Kiwi]

pauluk
Attached is the SW macro in a VB program which will generate the coords of a involute. Just enter the Base Circle Diameter and hit Generate

This web site has a program which you can download for splines and gears.
http://quickgear.bizland.com/index.html

[Ace12GA]

http://www.profilesmagazine.com/p33/marsalek.html

Found a very deatiled article on this very topic. It cleared it all up for me anyway.

[SplineGuy101]

I have worked with this macro in solidworks and I keep having to put in a fudge number depending on the spline is it possible to make this more accurate?

Paul
If you have CAD that can handle macros this may be of some use.
I wrote this for SW. You need to enter the Base Dia radius.

MACRO to GENERATE INVOLUTE PATH with SOLIDWORKS
===============================================
Sub main()
Set swApp = Application.SldWorks
Set Part = swApp.ActiveDoc
'----------
R = 71.6034 'ENTER BASE CIRCLE RADIUS
pi = 4 * Atn(1)
For Ang = 0 To 45 Step 2
X1 = Cos(Ang / 180 * pi) * R
Y1 = Sin(Ang / 180 * pi) * R
Opp = R * 2 * pi
Opp = Opp * (Ang / 360)
Hyp = Sqr(R ^ 2 + Opp ^ 2)
Ang2 = Atn(Opp / R)
Ang2 = Ang2 / pi * 180
Ang3 = Ang - Ang2
X2 = Hyp * Cos(Ang3 / 180 * pi)
X2 = Int(X2 * 10000 + 0.5) / 10000
Y2 = Hyp * Sin(Ang3 / 180 * pi)
Y2 = Int(Y2 * 10000 + 0.5) / 10000
XX = X2 / 1000
YY = Y2 / 1000
Part.CreateLine2 X, Y, 0, XX, YY, 0
X = XX
Y = YY
Next Ang
'----------
End Sub

[cam1]

Hi:
I'd recommend getting a copy of the ANSI B92.1 Involute Splines and inspection handbook. It lists the method of generating (CAD) involute spline profiles, along with the methods of Gaging the finished product (measurement over pins etc.). In my opinion the final requirement of the product ie. farm tractor (flat root major diamtere fit) or HS machinery (fillet root side fit) will ultimately dictate the need for an off the shelf cutter, or a home made cutter. Also try this link for some basic dimensional info.:http://www.omnigear.us/involute_spli..._diameter1.htm

regards

[cam1]

Hi: This topic was discussed a while back. Perhaps it may still be useful.

http://www.cnczone.com/forums/showthread.php?t=49445

[Kiwi]

I have worked with this macro in solidworks and I keep having to put in a fudge number depending on the spline is it possible to make this more accurate?

The macro doesn't draw a spline. It plots a Involute Curve from a given Radius.
If the math is not correct change the program in the Macro Edit.

To make more accurate change:

X2 = Int(X2 * 10000 + 0.5) / 10000 TO X2 = Int(X2 * 100000 + 0.5) / 100000

Y2 = Int(Y2 * 10000 + 0.5) / 10000 TO Y2 = Int(Y2 * 100000 + 0.5) / 100000