Understanding of relation between different gears

[asong]

Gear transmission is the transmission of two partial spheres which have their own centers and axles.

I believe the spur gear is the particular condition of bevel gear, when the apex is at the infinite distance and the shaft angle is 0. So equations for bevel gear can be used for spur gear.
So I can say there must be certain equations or formulas which can be used for all kinds gear (including spur, helix, bevel, hypoid, worm).
Am I right?

 

[ERT]

Hi asong,

Your question sounds very theoretical and may make for an interesting university thesis topic. In industry, spur gears are often presented in formulas as a helical gear with zero degree helix angle; and the same for spiral bevel vs straight bevel, etc.

I am not aware of general formulas that cover spur, bevel, hypoid and worm. The basic theory of conjugate geometry can be applied to all, but only at a theoretical level. You should not forget that manufacturing methods influence the geometry of the contact and non-contact areas of gear geometry - try to compare a double-enveloping worm and wheel geometry to a spiral hypoid gear and you will soon see the exercise is not very efficient use of your time.

What aspect of gearing are you interested in? Geometry only? or lubrication? vibration? manufacturing? strength? efficiency? design?

Regards,
ERT

http://www.akeng.com

 

[asong]

Hi, ERT
Thanks for your concern, and your advice.
I am an assembly processsing engineer, designing tools to assemble gear boxes. Our factory makes spur and helical gears. I think to understand gear by geometry is the base of all other respects.
And all respects of gear are associated: too thin housing may cause more vibration; bad designed cutting tools may make a good design gear set worthless; too accurate dimension design wastes manufacture cost.....
Our factory purchased a bad designed shaper cut tool: a "fixed tip relief angle (6 degrees)" by text book, caused a mass scrap. Although it is not my job, but I figured it out.

Regards
asong

 

[gearman1234]

Hello Asong,

I think that understanding gear geometry, gear strength, gear manufacturing, cutter design, materials for cutter and gear are essential for analysing the problem at hand.

I ws wondering what was the defect in the gear you observed.
Was the gear under consideration external or internal, was it helical or spur?
Generally -- A shaper cutter is similar to a cyl. gear whose adendum modification changes continually along the facewidth from a positive value to a negative value.

Basic rack tooth profile of the cutter enveloping surface must correspond to the gear basic rack toth profile in the same plane. All the angles of shaper cutter are interrelated based on the earlier principle.

 

[asong]

Hi, Gearman
The gear we cut with shaper was an internal ring gear, after resharpening (like you said, it was to certain nagative value), the root diameter got smaller, the tip of planetry gear hit the root.
The shaper cutter had a too big tip relief angle. here below is my post about this:

http://www.eng-tips.com/viewthread.cfm?qid=147646&page=1

Thanks
asong

 

[diamondjim]

Asong,
The tip relief on a shaper cutter is for external
gears and it is used to minimize the effects
of undercutting. I have not seen it used to cut
internal gears. Normally a full fillet is
recommended for the internal gears. I think the
interference that you would see on the internal
gear is involute interference in the fillet and
not directly the result of shortening the root
radius. You should have sufficient clearance
designed in a shaper cutter something of the
magnitude of .25/DP as a minimum.