root fillets of gears 1

[mfgenggear]

I seemed to misplace my equation for the max root radii fillet possible for a specific gear data.
And I am unable to retrieve it from my old HP 42 card reader. This was given to me about 30 years ago.

How ever In reviewing Gear Handbook by Dudley
Chapter 5 pages 5-24, 5-31 & 5-40
5-24
It depicts Eq. 5-33
Root Fillets

rf=0.7[rT+ (ht-a-rT) /(d/2cos2 helix)+ht-(a+rT)]
(super & sub scrpits formated correctly in word but does not format correctly here)



rs = mim calc fillet radius produced by hobbing or generating grinding
rT = edge radius of generating rack, hob or grinding wheel
a= addendum of gear
ht=whole depth of gear
d= pitch diameter of gear
helix=helix angle (use 0 degrees for spur gears)
then

easiest equation for fillet radius as shown 5-31 & 5-34
reprint from AGMA rf =fillet radius (in basic rack ) coarse pitch
.300/P = rf (20 & 25 deg Pressure Angle)

obsolete system
.157/P= rf (for brown & sharp, AGMA 14.5 deg), & 1.33 x clearance (for full depth AGMA) will add more as time permits
Please comment for any suggestions or additions.

 

[dimjim]

You will find equations for the suggested minimum fillet
radius. Machineries handbook used 1.333xclearance for 14.5 degree and 1.50xclearance for 20 degree teeth.
Each number of teeth will have fillet radii exceeding this
general guideline. The fewer teeth, the greater the radii that the hob radius will generate. As the number of teeth
approaches infinity, the closer will the part radii equal the hob radii. These general rules applied to full depth
teeth. I think FMC decided on using .295 for the clearance
as it would allow the maxiumum radius for a full fillet radius to be formed and it approached .44847 divided by the
diametral pitch which nearly matches the 1.5 x the clearance rule.
A theoretical approach for the max radius on the hob would be (C/CosAlpha) times the Tan((90 plus Alpha)/2) where
Alpha is the pressure angle of the gear or hob. This gives a value of almost 1.52 times the clearance for a 20 degree pressure angle gear. Does this sound familiar?

 

[mfgenggear]

DimJim

Thanks for your reply

The equation I had, use the following gear data:

# Teeth
Diametral pitch
Pressure Angle
Major & Minor Diameter
True/start of Involute (TIF)
Actual circular tooth thickness

I may be able to purchased a used card reader
and reload the program & decipher the equation.

 

[dimjim]

If you check out my formula, the result for 14.5degrees
is 1.33 x the clearance, and for 20degrees is 1.519 x the clearance. This was in agreement with the past Machineries handbook for external gears.

Internal gears cannot be hobbed and the radius is somewhat dependent on the number of teeth in the gear shaper cutter.

When you find your magic formula from your HP42 module, please post it here. Do you think it came from the AGMA formulas for calculating the max bending strength? I do remember a formula there in one of the AGMA standards.