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# Calculating External Spur Gear Inspection Data

## Calculating External Spur Gear Inspection Data

(OP)
Hello all.

I am fairly new to gear design so forgive me if my questions are overly simple, chances are I'm making this more complicated than it has to be.

The short story is that I am tasked with calculating new spur gear data and inspection data based on reducing the AGMA Quality Class of a set of gears from 12 to 11. I am specifically being asked to obtian new Maximum Total Composite Error (TTE) and Maximum Tooth-to-Tooth Error (TTE), Testing Radii, Dimension Across Pins (Or Measurement Over Wire, for now I'll call it MOW), and Circular Tooth Thickness.

I began by obtaining a copy of AGMA 2000-A88 and determining the new TCE and TTE using the appropriate equations for the gear in question (there are several individual gears I have to perform this on but I am only focusing on one for now).

I was told that from this data I could calculate the change in backlash that would result in increasing the TCE by assuming that 1/2 the change in TCE (delta TCE between Quality 12 and 11) is approximately equal to an equivalent change in centerline distance between gears (if I am understanding this correctly thus far). Multiplying this by 2tan(pressure angle) gives a change in backlash.

From here I am stuck on several points:

1. How do I use the change in backlash to calculate new circular tooth thicknesses?

2. Referencing Machinery's Handbook, I can't seem to figure out how to calculate new MOW for reduced tooth thickness. You use diametral pitch (Dp) and the appropriate table values to calculate the MOW but since Dp remains constant I don't see how MOW would change; any input would be greatly appreciated.

3. How does one go about calculating Test Radii? I understand what they are but referencing AGMA 2000-A88, Norton Machinery Design, Dudley Gear Design, and the Machinery Handbook, there is no mention of how to actually calculate these values.

Please let me konw if I am approaching this in the wrong way or if you need more information, thank you. Again, any input would be greatly appreciated.

### RE: Calculating External Spur Gear Inspection Data

AGMA 370.01 and/or AGMA 2002-B88.

### RE: Calculating External Spur Gear Inspection Data

(OP)
Thanks israelkk for the AGMA 370.01 reference, I obtained a copy and it was a great help. I also got my hands on an original copy of Dudley's Gear Design Handbook (not the Practical Gear Design book that I currently have) which explained the relationship between tooth thickness and backlash.

This text also provided the equations I was looking for to solve for measurement over wire for varying tooth thickness. I had to create a root finding program to solve for phiE but it worked out great!

As for calculating Test Radii, I am currently at this step and performing more research. I may have a few questions as I progress related to master gear selection.

Thanks again for the help, this website is always a valuable resource.

-Chris

### RE: Calculating External Spur Gear Inspection Data

(OP)
Just to follow up on this thread so that it can be closed and to answer my own questions above, this proved simpler than i suspected once I had appropriate reference materials.

I approached this problem in the wrong way with respect to question 1 that I had. Instead of using change in backlash to calculate new tooth thicknesses I changed the minimum test radius to accommodate the increase in total composite error that I calculated for a decreased AGMA quality of 11 (down from 12) for each gear in the assembly. From there I used the following equation to determine the reduced tooth thickness:

Tooth Thickness = Standard Tooth Thickness - 2tan(pressure angle)*abs(Testing Radius - Pitch Radius)

With respect to question 2 it helps to get an original copy of Dudley's "Gear Handbook", not the "Handbook of Practical Gear Designl." The equation that is used to solve for MOW is given and the only involved part is finding phiE which requires you to use a root finding method or solver. I used Newton-Raphson's method and used the pressure angle as an initial guess to solve for phiE and from there it's a matter of plugging in your values to obtain MOW. The upper and lower limit are found by using the max and min circular tooth thicknesses.

For my third question I can thank israelkk for the AGMA 370.01 reference, all you ever wanted to know about testing radii are included in this reference.

Thanks again for the guidance,

Chris

### RE: Calculating External Spur Gear Inspection Data

Hey, BCobra, if your interested, and have a TI89 Calc, I can send you the program I wrote for that. It may be of some help. It asks for Internal and External, Helix, Backlash, Tooth thinning or increasing, and spits out MOW. Or you can give it Test Radius and it gives MOW, or you can give it MOW, and it will give you Tooth Thickness.

Its helped me out at work allot, maybe it can do the same for you. Drop me an email, or respond to this post, and I would be glad to send you a copy.

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