Another silly question I'm sure 3

[PhilipFry]

Okay, I've searched high and low here, but have come up scratching my head. I know you can determine that point of initial contact between spur gears based on the addendum circle and the line of action. But how do you determinem where the contact zones are? I know the contact ratio gives you the average number of teeth in contact over the entire arc of action. Is there a simple method of finding where two pair are in contact as opposed to a single pair?

 

[diamondjim]

The highest point of single tooth contact
sometimes called the HPSTC to the tip of
the tooth will have two teeth in action
and the remainder of the profile will have
only one tooth in contact. That is why
some use the HPSTC to calculate the max
bending strength instead of using the tip
loading factors.

 

[PhilipFry]

Oh, I'm sorry, there may be some confusion here. If I understand correctly, the HPSTC tells which part of the tooth profile sees multiple pair contact, but what I'm looking for is the angle where multiple teeth contact begins and ends. Using the pitch point as an origin for a reference axis pointing along the line of centers, how do I determine which angles that see two teeth in action and which angles only see one?

 

[diamondjim]

Mae,
The base diameter divided by the
HPSTC will be the cosine of the
angle at that diameter.
Likewise the base diameter divided
by the od will be the cosine of the
angle at the od.
Are you asking for the roll angle
values instead?
Are you trying to rotate the HPSTC
to be inline with the line of action?
I think you know that the 20 degree
angle is unique at the pitch line.
Do you have an unique problem or
gear pinion combination that can
be illustrated or calculated to
be used as an example?
Do you have a copy of Earl Buckingham's
book "Analytical Mechanics of Gears"?
If so, Fig 5-5 on page 84 shows the
line of contact of two gears.
I could not find a good illustration
in Dudley's book that shows the same.

 

[PhilipFry]

Well, I'm trying to develope a dynamic model to help show lateral and torsional coupling effects. As much as I would like to assume one gair pair in action to simplify my problem, I think it is worth looking at the effects of more than one gear pair in contact as well. Therefore, I need to know when two pair are in contact, and when only one pair are.

I am not necessarily trying to rotate the HPSTC into the line of action, but I kind of assumed that it would be in the line of action anyway...

Maybe I'm mistaken, but I figured that two teeth action would be some function related to the circular pitch in some way.

 

[diamondjim]

Mae,
It is related to the base pitch but also
dependent on the pinion gear combination.
Basically the active profile is from the
SAP diameter to the OD. Two teeth are not
in contact when the pitchline is on the
line of contact. You almost need a working
model to see how the contact points progress
along the line of contact. If the pinion is
undercut, you must know exactly where the
undercut starts. You may call me at
330-678-0226 if you need more help.
Sorry that I cannot make this easy to grasp
but you do need to know about roll angles
and to see that all active profile radii
pass thru the line of contact. Its
tangent point with the base diameter is
in the same plane as the line of contact.

 

[PhilipFry]

Wow. Okay. Let me digest what you just said and head over to the library before I bother you on the phone.

Thanks for the help!
mae1778

 

[Dennyd]

mae1778,

Try this web site:

http://www.mech.uwa.edu.au/DANotes/gears/meshing/meshing.html#top

It will give a lot of insight into how gears work. There are several links to other information at this site that should also be helpful.

- - -Dennyd, P.E.

 

[diamondjim]

Dennyd,
You are right, a great site!
Thanks for sharing!
I'm giving you a star for this one.

 

[PhilipFry]

Oh boy. I figured it out. The solution wasn't nearly as clean cut as I thought it would be. Now that I've familiarized myself with what you were talking about...

No, I am/was not looking for roll angles. I really should have phrased my question better.

Yes, I am rotating the HPSTC into the line of action. From there, the solution is wholely trigonomic.

Thanks for the help!
mae1778