Gear ratio with modified tooth addendums 2

[jeffcannon]

This question is probably mostly theoretical in nature but I couldn't find anyone that could give me a satisfactory answer. I work for a company that makes gearboxes and we routinely use gears with modified addendums. My question is how does this effect the gear ratio. I know the off the shelf answer is that the gear ratio is based purely on the number of teeth. But in reality isn't the ratio based on the test radius of the gears? I have always thought of gears as simply a system of rotating levers. By changing the distance between the levers I would alter the amount of torque I can transmit with a given force. By modifying the addendum I am changing the test radius and the center distance. Shouldn't this change the amount of torque I can transmit with a given input? I have calculated our geartrains both ways and the difference is generally only about 1%, but the question continues to bug me. Thanks in advance.

 

[israelkk]

You can not think of the teeth as levers. The gear ratio is basically the ratio of the two basic circles of the involutes which stays the same no matter how much addendum shifts you introduce into the gears. If you recall, the basic circle is the circle from which the involute profole is generated. the line of action of both gears is always tangent to the basic circles.

 

[tbuelna]

jeffcannon,

Addendum mods don't change the gear ratio. Gear ratio is based on tooth counts for most individual conventional gear meshes. However, there are some exceptions such as worm gears, harmonic drives, etc.

I would somewhat disagree with Israelkk's comment about thinking of gear teeth as levers. From a structural analysis standpoint, gear teeth are considered cantileverd beams in bending. As such, addendum mods are commonly used to help equalize tooth bending strengths between mating gears that have large differences in pitch diameter.

A gear with a small number of teeth will have gear tooth shapes that tend to be more "slender" at their root than a mating gear with a large number of teeth. So the smaller gear's teeth will tend to have higher root fillet stresses due to bending than the larger gear's teeth. Shifting the mesh line of contact towards the smaller gear's root by altering the gears addendums will help equalize the relative bending strength of the two mating gears.

Hope that helps.
Terry

 

[israelkk]

tbuelna

The "lever" term was used here for gear ratio calculation and not for strength. In modified gears the actual working pitch diameter'radius is larger or smallet than the standard. If you think of the actual pitch radius of a gear as a lever than you may think that the gear ratio will change. This is what jeffcannon meant in his post.

 

[tbuelna]

israelkk,

I agree with you. I was just trying to help jeffcannon understand the purpose for modifying addendum and how it affects the gear's performance. He seemed a little confused about the subject.

Of course, I would suggest that the conjugate action of an involute gear mesh is more akin to a cam and follower mechanism than a pair of levers.

Regards,
Terry

 

[jeffcannon]

Thanks for all the help guys. I am familiar with the use of the modified addendum for increasing tooth strength, or changing the center distance; but I forgot that the base circle would not be affected by this. Thanks again.