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

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Discussion Overview

The discussion revolves around the design of a spur gear, specifically addressing the situation where the root circle (dedendum) appears to be greater than the base circle. Participants explore calculations related to gear dimensions, pressure angles, and the implications of these relationships in gear design.

Discussion Character

  • Technical explanation
  • Debate/contested

Main Points Raised

  • Bob Khan presents a scenario where the root circle is greater than the base circle and seeks clarification on the implications of this in gear design.
  • Some participants request detailed workings to understand the calculations involved.
  • Bob Khan provides specific calculations for pitch diameter, base circle diameter, dedendum, and addendum, indicating that the base circle is indeed less than the dedendum circle diameter.
  • One participant asserts that the relationship observed is expected and provides calculations to support this view, referencing gear nomenclature.
  • Another participant questions whether the involute curve's definition within the base circle affects the design, mentioning the strength of different tooth types.
  • There is a suggestion that reducing the pressure angle could resolve the issue, but it remains unclear if this is the only solution.

Areas of Agreement / Disagreement

Participants express differing views on the expected relationship between the base circle and dedendum circle, with some asserting it is typical while others reference diagrams that suggest otherwise. The discussion remains unresolved regarding the implications of these relationships and potential solutions.

Contextual Notes

Participants' calculations and assumptions about gear design parameters may vary, and there is uncertainty regarding the impact of the pressure angle on the relationship between the base circle and dedendum.

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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