# Gears: when Base circle less than the root circle/dedendum

#### bkhan10000

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!

-Bob Khan

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#### Nidum

Science Advisor
Gold Member
Show us your workings please .

Is this a homework problem ?

#### bkhan10000

Show us your workings please .

Is this a homework problem ?
Thanks for the reply. Not a homework problem though.

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 = addendum*1.25 = 1.424mm
Addendum circle diameter = pitch diameter + 2*addendum = 70.610mm
dedendum circle diameter = pitch diameter - 2*dedendum = 65.480mm

If the calculations are correct, (which I think they are as they 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!

#### Baluncore

Science Advisor
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?
That is exactly what you should expect. Moving out along a radius ...

Base circle diameter = cos(phi)*pitchdiameter = 64.209mm
Dedendum circle diameter = pitch diameter - 2*dedendum = 65.480mm = Root circle
Desired pitch diameter: = 68.330mm
Addendum circle diameter = pitch diameter + 2*addendum = 70.610mm

They are in the correct order,
https://en.wikipedia.org/wiki/List_of_gear_nomenclature#Base_circle
https://en.wikipedia.org/wiki/List_of_gear_nomenclature#Root_circle

Last edited:

#### bkhan10000

That is exactly what you should expect. Moving out along a radius ...

Base circle diameter = cos(phi)*pitchdiameter = 64.209mm
Dedendum circle diameter = pitch diameter - 2*dedendum = 65.480mm = Root circle
Desired pitch diameter: = 68.330mm
Addendum circle diameter = pitch diameter + 2*addendum = 70.610mm

They are in the correct order,
https://en.wikipedia.org/wiki/List_of_gear_nomenclature#Base_circle
https://en.wikipedia.org/wiki/List_of_gear_nomenclature#Root_circle
Well in most cases, the base circle is larger than the dedendum circle in diagrams I have seen:

http://images.slideplayer.com/32/10033503/slides/slide_39.jpg

Either way, what I am understanding is that it doesn't matter? Like the involute line starts from the base circle but it doesn't matter that the bottom of the gear tooth still starts at the dedendum circle?

#### Baluncore

Science Advisor
How is the involute curve defined inside the base circle ?
Involute teeth have a 0° contact face at the base circle. Undercut teeth are weaker than stub teeth.

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