# Question about involute gear profile design calculation

• 08-04-2021, 07:16 PM
wpinboi
Question about involute gear profile design calculation
Hi all,

I'm new to this world but starting to get my head around CAD in OnShape.

Instead of using an automatic gear generator I am studying how to draw involute spur gear profiles from first principles. I am a hobbyist and there is no actual real world application to this outside my interest)

I came by this forum as I have been studying some of the excellent resources as I do the math first and begin to lay out my wheel designs (this is to be a clock that I had prior experience making out of wood from plans).

I am working on the assumption that I need a 94 Tooth gear with a specific tooth width/profile to mesh with a common sprocket design across my going train. This will actually be a 90T and a 94T with associated 12T Sprockets and a 30T Escape Wheel...

I start with a Pitch Diameter, Tooth count and (what is called in the clock world I'm familiar with) 'w' or section width of the tooth profile - typically one complete tooth and the connecting section to the next tooth.) This is in order to draw one tooth and then circular pattern repeat it another 93 times around the wheel.

So here is what I have to start with (working in mm and degrees):
(Much from here: [URL]https://www.engineersedge.com/gear_formula.htm[/URL])

N=94
D=194.49 (Pitch Diameter arrived at prior to commencing work)
P=0.48332 (Diametral Pitch: P=N/D)
p=6.50009 (Circular Pitch - what I believe I mean when I use the term 'w'; p=pi()/P)

I will use a standard pressure angle of 20'

b=2.5863 [Dedendum: b=1.25/P]
a=[COLOR=#ff0000]0.00514[/COLOR] [Addendum a=1/D][COLOR=#ff0000] *Seems very small*[/COLOR]
D(O)=198.628 [Outside Diameter D(O)=(N+2)/P]
D(R)=189.317 [Root Diameter D(R)=(N-2.5)/P]

OK so far so good - the original assumption I made about the Pitch Diameter and subsequent Addendum and Dedendum calculations confirmed the Root and Outside Diameters I had calculated previously by other simple formula you will all be aware of, so I was confident I was proceeding correctly.)

Now, I wanted to draw the involute curve correctly in OnShape and I understand I need to work with the Base Circle Diameter *(somewhere I see this listed as Base Circle Pitch):

D(B)=[COLOR=#ff0000]79.3679[/COLOR] [Base Diameter / Base Circle Pitch: D(B)=D cos(20) *as I am using 20' pressure angle)]

Now this seems like a completely wrong circle to work with as it is over 100mm smaller than the others I calculated.

Have I gone wrong?
I already found a thread here which discusses how the D(B) need not necessarily be larger than the Root Diameter but this seems to be an exceptionally large discrepancy