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

AI Thread Summary
When designing a spur gear, the base circle can indeed be less than the dedendum circle, which is a normal occurrence. The calculations provided indicate that the base circle diameter is 64.209mm, while the dedendum circle diameter is 65.480mm, aligning with expected gear nomenclature. Reducing the pressure angle can resolve the issue, but it is not the only solution; understanding the relationship between the base circle and dedendum is crucial. The involute curve begins at the base circle, and while the dedendum circle marks the tooth's bottom, it does not affect the gear's functionality. Proper comprehension of these parameters is essential for effective gear design.
bkhan10000
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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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Show us your workings please .

Is this a homework problem ?
 
Nidum said:
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!
 
bkhan10000 said:
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:
Baluncore said:
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?
 
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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