# Thread: Gears: when base circle diameter less than the root circle/dedendum

1. ## Gears: when base circle diameter less than the root circle/dedendum

Hey guys,

Trying to design a spur gear but I am very confused as the root circle/dedendum ends up being greater than the base circle. What do I do in this case? The gear I'm trying to design has a 68.33mm pitch diameter, 60 teeth, the pressure angle a standard 20 degrees. What am I doing wrong here? Any help is appreciated!

-Sarah Anderson

2. You need to show your calculations... Unsure what the challenge is..

3. Originally Posted by Kelly Bramble
You need to show your calculations... Unsure what the challenge is..

desired pitch diameter: 68.330mm
desired teeth #: 60
pressure angle: 20deg
base circle diameter = cos(phi)*pitchdiameter =64.209mm
diameteral pitch = t/pitchdiameter= 0.878mm
addendum = module = 1/diametral pitch = 1.139mm
dedendum circle diameter = pitch diameter - 2*dedendum = 65.480mm

The problem is that the base circle must be greater than the dedendum circle, but with the given gear parameters, this is not the case (unless an assumption of mine has gone awry). I also dont really want to compromise the desired pitch diameter and number of teeth, unless that is the only solution.

If the calculations are correct, (which I think they are as they have been done few times) these are the pertinent values. So clearly the base circle is less than the dedendum circle diameter. I noticed that reducing pressure angle does fix this, but is that the only solution? Should I consider something else? Appreciate anybody who can help!

4. Interesting question..

Definition: "Base Diameter (Db) – is the diameter of the circle from which the involute form is generated."

So, this is a reference for calculations.. Not sure the "base circle diameter" has a requirement to be of less diameter..

5. Sarah,

The base circle is not larger than the root diameter. You have a sufficient number of teeth so that you do not need to undercut the flank at the bottom of the tooth.

Take the time to learn to how to construct the involute curve.

Also know that standard metric gear cutters are usually made in increments of 0.05 module. Expect the shop to use a 0.90. The mating gear must be cut with the same module although the exact cutter shape will vary with the number of teeth.

6. So basically what is being said is that it does not matter if the base circle is smaller than the dedendum circle diameter? I understand the involute curve, but now what I'm understanding from this post is that, in my case it starts below the root, which is still okay? ( meaning at the bottom of the tooth the involute curve has already been started?)

7. You are correct - with a 60 tooth gear the involute portion runs to the bottom where you add a small radius to blend into the dedendum circle. You can generate the involute curve section above and below the tooth on your drawing, it just doesn't happen in metal.

With about 14 or 15 teeth, depending upon the pressure angle, you get into a condition where the flank gets undercut and the tooth form is weakened at the root but, this will not happen with 60 teeth.

8. FYI - engineersedge.com gear design equations and calculators..

Spur Gear Design Tool

Gear Design Known Center Distance and Ratio

#### Posting Permissions

• You may not post new threads
• You may not post replies
• You may not post attachments
• You may not edit your posts
•