Relationship between internal minor diameter, tooth thickness and over balls diameter

[Hidk]

I need an expertise on a query. I want to know if there is any relationship between internal minor diameter, tooth thickness / space width and over balls diameter (OBD).

I want to avoid measuring OBD by CMM and want to calculate OBD based on internal minor and tooth thickness by gauge.

Do you guys have any equation or apps that can calculate OBD by using internal minor diameter and tooth thickness.

Please let me know.

Thank you

 

[3DDave]

There is - it's a complicated series of formulas. The reason for measuring between pins or balls is because getting the exact tooth thickness at the exactly known diameter is usually a far more difficult task.

I used to have a copy of Buckingham's book on gears:

https://www.amazon.com/Analytical-Mechanics-Gears-Earle-Buckingham/dp/0486657124

https://www.abebooks.com/

has a selection of them as well, from a bit over $10 on up.

 

[mfgenggear]

H

The answer is no.
The minor diameter calculation is based on the true involute diameter of the mating part while is is assembled. There is a calculation for that from Buckingham.
Three methods I ds for measuring circular tooth thickness for externals and internal tooth space.
By measurement between pins. Measurement of base pitch. Or tight mesh with a master gear.
A cmm verification would be at at the pitch diameter. But is not as accurate. And is an approximation.

 

[spigor]

There is a direct relationship between tooth thickness / space width and OBD. Balls (pins, wires) used for measuring the OBD touch flanks, the distance between flanks is tooth thickness.
Here are the formulas:

https://khkgears.net/new/gear_knowledge/gear_technical_reference/tooth-thickness.html

There is no direct relationship between diameter and OBD. Gears with the same OBD can have different diameters, gears with the same diameters can have different OBDs. The relationship between OBD / tooth thickness and diameters is determined by tool design.