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

• bkhan10000
In summary, when the base circle of a gear is smaller than the root circle or dedendum, it results in a gear with a smaller overall size and a lower tooth strength. This can be beneficial in certain applications where space is limited, but it may also affect the durability and load-bearing capabilities of the gear. Careful consideration and calculation is necessary when designing gears with a smaller base circle to ensure they can withstand the intended use.
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

Is this a homework problem ?

Nidum said:

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 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

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

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.

1. What is the base circle and root circle of a gear?

The base circle is the theoretical circle from which the involute curve of a gear is generated. It is the circle that touches the involute curve at its base point. The root circle, also known as the dedendum circle, is the circle that defines the bottom of the gear teeth.

2. Why would the base circle be smaller than the root circle/dedendum?

This occurs when the gear has a smaller number of teeth or when the pressure angle is larger. In these cases, the involute curve will have a steeper slope, resulting in a smaller base circle.

3. What is the significance of the base circle being smaller than the root circle/dedendum?

Having a smaller base circle allows for a smaller gear size and weight, making it more efficient for certain applications. However, it can also result in a weaker gear with a lower load-carrying capacity.

4. How does the base circle affect the gear's meshing with another gear?

A smaller base circle means the gear will have a smaller pitch diameter, which can affect the gear's meshing with another gear. It may require a different gear ratio or have a higher risk of interference with the mating gear.

5. Are there any other factors that can influence the size of the base circle in comparison to the root circle/dedendum?

Yes, the pressure angle, module, and tooth profile all play a role in determining the size of the base circle. Additionally, the manufacturing process and desired gear performance can also impact the size of the base circle.

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