Posted by BillS on August 21, 2008 at 14:07:02:
In Reply to: Re: Face width of bevel gears posted by Stepan on August 20, 2008 at 20:53:14:
Are you wanting to know face width for strength and durability calculations? Or are you looking for face width to specify on a print?
If you want face width to determine load rating, consider the meshing member and minimum length of actual contact at a topland. Consider rolling contact near tooth roll out. This should be the theoretical worse-case beam load for a tooth.
This line of contact is generally taken as face width, but this only applies if the mating tooth faces are parallel (perpendicular to pitch line). As Stephen points out, your photo doesn't fit that description due to a flat face and large heel chamfer.
There are many variables that don't respect this theoretical line of contact load rating. Exceptions that concentrate load at narrowing lines of contact are shaft deflection and misalignment, mesh (mounting) misalignment, shock, etc. Common points of failure are at heel or toe OD where load is concentrated due to exceptions listed above.
Stephan gets the nod for getting this right, I just wanted to add some detail - Stephan, what do you think?
This looks like a "spider" pinion from a differential cage - is that the case? BTW, formulas for tooth proportions (working depth, addendum, clearance, etc.) are special for a differential pinion/gear set.
If you need face width for print specification leading to a summary calculation, you can use the length of the root line as Stephen says, which is close to pitch line length. Face width (used with pitch and cone distance) as a summary/print dimension primarily determines maximum cutter point width that will clear at toe tooth space. (Also, try to determine pitch at the heel at the imaginary tooth tip disregarding the chamfer. Determining pitch is a good topic for another thread :^) I say this assuming that you are reverse engineering from an existing pinion which has been load rated already.
For example Gleason recommends, as a general rule, that face width should be the lesser of 1/3 outer cone distance or 10/Pitch. Actually, it can be smaller if something in overall design requires it. Although you might think that Face Width is a physical measurement on your part, it really isn't. It's no more a "physical" measurement than OD is.
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