Machining of bevel gears

Hi guys,
Prepare for a long-winded post...

A couple questions here. More-so on derived values for the gear shape rather than the machining itself. I'm looking to reproduce some very old planetary gears for a good-sized rear differential. Let me give you some context: I was given values from Mark's Engineering Handbook, started drawing it in Solidworks to these dimensions, and some things weren't adding up. So I was double checking using the Machinery's Handbook, and this is when I discovered the discrepancies between the 2 references.

Also worth noting: a note here that these formulas (from Mark's) are based upon Gleason bevel-gear system which employs a basic pressure angle of 20 degrees. so maybe the formulas are slightly different for 14-1/2 degree pressure angle? not sure.

Also note: The Machinery's Handbook doesn't explicitly say (on the table) what pressure angle these formulas are geared towards (pun intended). The only reference I could find referring to pressure angle before or after the table is in regard to selecting a formed cutter. "For milling 14.5deg pressure angle bevel gears,..." But there is no reference to the table of formulas.

You'll also note the extra dimension in parenthesis in the root angle. This is per the note at the beginning of the table: "The formulas for milled bevel gears should be modified to make clearance at the bottom of the teeth uniform instead of tapering toward the vertex. If this recommendation is followed, then the cutting angle (root angle) should be determined by subtracting the addendum angle from the pitch cone angle instead of subtracting the dedendum angle as in the formula given in the table."

Here's some data...

Pinion (planetary gear): 16 teeth
Gear: 36 teeth
Shaft angle: 90deg

DP of 2.25 and 14-1/2 degree pressure angle.

Number of teeth: 16
Diametral pitch: 2.25
Pressure angle: 14-1/2 degree
Face width: 3.5
Working depth: 0.889
whole depth: 0.97
Pitch Dia: 7.111
Pitch Angle: 23.96 deg
Outer cone dist: 8.754
Circular pitch: 1.396
Addendum: 0.6086
Dedendum: 0.3638
Clearance: 0.081
Dedendum angle: 2.38 deg
Face angle of blank: 28.48 deg
Root angle: 21.58 deg
Outside Dia: 8.223
Pitch Apex to crown: 7.753
Bore: 1.950

The above parameters were calculated using Marks Engineering Handbook.

And where might these be?

A couple questions here

Click to expand...

Older info may possibly help. See page 267 and beyond

A treatise on milling and milling machines .. : Cincinnati Milling Machine Company : Free Download & Streaming : Internet Archive

i do not make gears.
.
i believe though now a days they have software usually on the cnc gear cutter that does what you are trying to do. they also cut so fast machines often have robot loader using one cart for blanks and one cart for finished gears. operator just wheels the carts into a compartment on machine and closes the door

Given the same data, here's what the Machinery's Handbook yields:
DP = 2.25
Teeth = 16
Pitch Cone Angle of Pinion = 23.96deg
Pitch Diameter = 7.111"
Addendum = .4444 (1/DP)
Dedendum = .5142 (1.157/DP)
Whole Depth of Tooth = .9587" (2.157/DP)
Thickness of Tooth at Pitch Line = .6982" (1.571/DP)
Pitch Cone Radius = 8.7553"
Addendum of Small End of Tooth = .265
Thickness of Tooth at Small End = .4163"
Addendum Angle = 2.906deg
Dedendum Angle = 3.361deg
Suggested MAX Face Width = 2.918"
Circular Pitch = 1.396
Face Angle = 26.866deg
Compound Rest Angle for Turning Blank = 63.134deg
Cutting Angle = 20.599deg (21.054deg going by suggestion at start of table in M.H.)
Angular Addendum = .4061
Outside Diameter = 7.9232"
Vertex/Apex Distance = 7.820"
Vertex/Apex Distance from Small End of Tooth = 4.662"
Number of Teeth For Which to Select a Cutter = 17.51 (number 6 cutter)

Something to note is the large difference between the addendum and dedendum values. I believe this is where a lot of the other values go awry from, compared to the values calculated from Mark's Engineering Handbook. The formulas in that handbook are also a little different for the same variable.

For example:
Whole Depth according to Mark's Engineering Handbook is 2.188/Pd + .002
Whereas in the Machinery's Handbook, it is 2.157/DP

In Mark's book, the Gear addendum is defined as (0.54/Pd) + 0.46/(Pd(N/n)^2
the pinion addendum is defined as Working depth - Gear addendum

In the Machinery's Handbook, Addendum is defined as 1/DP
Dedendum is defined as 1.157/DP

Any thoughts on these differences? Since the values are fairly different, we're getting pretty different values for root angle (cutting angle), outside diameter, etc. The outside diameter given by Mark's handbook is 8.223" and outside diameter given by Machinery's Handbook is 7.923", a sizeable difference. Would prefer to make them right the 1st time...

Granted, some small differences would be acceptable and still function fine in the application (very old piece of machinery), but these differences are rather large. Personally I'd stick to the Machinery's Handbook because that's always my go-to, but having not milled any bevel gears before, this is new ground for me.

Any thoughts/advice is welcome! Thanks

pianoman8t8 said:

Here's some data...

Pinion (planetary gear): 16 teeth
Gear: 36 teeth
Shaft angle: 90deg

DP of 2.25 and 14-1/2 degree pressure angle.

Number of teeth: 16
Diametral pitch: 2.25
Pressure angle: 14-1/2 degree
Face width: 3.5
Working depth: 0.889
whole depth: 0.97
Pitch Dia: 7.111
Pitch Angle: 23.96 deg
Outer cone dist: 8.754
Circular pitch: 1.396
Addendum: 0.6086
Dedendum: 0.3638
Clearance: 0.081
Dedendum angle: 2.38 deg
Face angle of blank: 28.48 deg
Root angle: 21.58 deg
Outside Dia: 8.223
Pitch Apex to crown: 7.753
Bore: 1.950

The above parameters were calculated using Marks Engineering Handbook.

Click to expand...

Something is out of range here because the ratio of addendum to dedendum is wacked. Check how you used the formula.

You do know that standard involute cutters are too thick to pass through the small end of the tooth?

Other than that, keep in mind that the tooth dimensions are proportional to the distance from the apex of the cone. So, you're comparing two different face widths of gears, so the addendum at the small end is going to differ in proportion to difference in face width. My WAG.

HuFlungDung said:

So, you're comparing two different face widths of gears, so the addendum at the small end is going to differ in proportion to difference in face width.

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That's the LEAST of it. You are comparing two different TYPES of manufacture of Bevel Gears, of which one is correct and the other a gross approximation. You need to do a lot more studying and determine which you actually have so you can determine what will work.

Milled Bevels were popular during The War due to the ease of manufacture, and suitable for less than stringent requirements. That does not make them interchangeable, most especially when combining two styles of one of the lesser method.

Frankly, you'd be best served spending the $35 - $75 ( whatever it is now ) to purchase the actual standards from AGMA, learn from them, and use that to get your base numbers. Adjust fire as necessary, after.

Another option that might be worth your time and money is to have them modeled for you, too. ( since you have SolidWorks but not the skill )

HuFlungDung,
Yes, I realized there were 2 different face widths used here, but only differ by .034". The 2.918" face width is the suggested max width calculated using the machinery's handbook. This is NOT the actual width of the face as measured. But, the calculations in the Machinery's Handbook to obtain the OD are independent of the face width. So this seems irrelevant.

Zahnrad Kopf,

These were most likely milled gears. These were made between approx. 1905 and 1915. They're a VERY low speed application (part of a rear differential on a machine whose top speed is less than 10mph).

While it would be advantageous to measure/verify everything on the original gear, this isn’t possible at this time, as the original one that dimensions were initially taken off of is now assembled in another machine. And a royal PITA to get at, understandably. The machine they go into is about 20tons in weight. This is not a high quantity, just need to make 4 of them.

I'll have to double check that the addendum/dedendum calculated by Mark's Handbook are correct, I was supplied these values. But they are quite different.

Again, in regard to the face width difference of .034" (not the difference of suggested max width based on the Machinery's Handbook), there are no other variables that control the shape of the gear profile on the OD end of the gear teeth. Yes, the face width is referenced in a couple other calculations in the Machinery's Handbook, but only to find tooth size at the SMALL end (addendum at small end, tooth width at small end, and vertex distance at small end, and that's it).

I should also note, these 4 pinion bevel gears will be mating with the original gears that drive the axles. FWIW...

"You do know that standard involute cutters are too thick to pass through the small end of the tooth?"

Yes, I'm aware of this. The Machinery's Handbook has a table to calculate the # of cutter needed to make this happen correctly.

"Selecting Formed Cutters for Milling Bevel Gears" in the Machinery's Handbook says it should be a #6 cutter, of the correct DP (2.25).

Without going and pulling out my Marks and reviewing your calcs in detail, I'm pretty sure the reason you are finding conflicting info on addendum and dedendum values is that Gleason introduced the long/short addendum concept in order to balance tooth strength based on the number of teeth in the gear and pinion, so essentially a gear set with the same number of teeth in the pinion and the gear would have equal tooth proportions. I'll look at the shop and see when this was introduced, but your gear set is probably old enough that it was based on the equal addendum system unless the gear sets were replaced along the way.

pianoman8t8 said:

These were most likely milled gears. These were made between approx. 1905 and 1915. They're a VERY low speed application (part of a rear differential on a machine whose top speed is less than 10mph).

Click to expand...

Ah. Okay. Then I would say that my esteemed colleague is spot on with his assessment that -

Dan from Oakland said:

... your gear set is probably old enough that it was based on the equal addendum system unless the gear sets were replaced along the way.

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This is something that can trip up even the most seasoned Gear Hand. I am betting that Dan is correct. Try the calculations based upon that, and I think you will find that they are reasonably close to what you have at hand.

Good luck.

( Good catch, Dan )

Dan from Oakland,
Thanks for your reply. I'd wager the gears were not re-made after the originals were put in place. These particular machines were made form about 1901 until about 1915, used until maybe 1930, and left abandoned or scrapped. These machines were initially steam powered, and later models (after about 1916, until about 1930) were powered by gasoline, with a similar rear end, some having a worm drive rear end. The gas models were used as late as maybe the 50's? Give or take.

Looking at the constant variables in the equations in the Machinery's Handbook, and the Cincinnati reference listed in post #3 (circa 1916), they are the same constants for finding addendum/dedendum. Does this mean that I should go by the calculations based off the Machinery's Handbook/Cincinnati reference?

That seems to be an interesting point. I have read several books on gear making, but none of them have contained a lot of historical information like this. I wonder if there is any go-to text for that as I would like to understand the evolution here.

Dan from Oakland said:

Without going and pulling out my Marks and reviewing your calcs in detail, I'm pretty sure the reason you are finding conflicting info on addendum and dedendum values is that Gleason introduced the long/short addendum concept in order to balance tooth strength based on the number of teeth in the gear and pinion, so essentially a gear set with the same number of teeth in the pinion and the gear would have equal tooth proportions. I'll look at the shop and see when this was introduced, but your gear set is probably old enough that it was based on the equal addendum system unless the gear sets were replaced along the way.

Click to expand...

FWIW, here's some photos of the machine, and of the differential gears inside it, minus the gears at the end of the axle shafts.

If you had a dollar, for each time someone asked what I am going to ask.....

Does it need to be historically accurate, or just work?

What's the ratio?

Any decent performance/hot rod shop can modify a rear end to the point of "Really? That was a 9 inch Ford rearend?"

Does that unit have a reverse gear?

Mechanical brakes for the tracks, right? Air brakes that use a "S-Cam" could be set up for cable operation, with not a lot of effort.


Will the engineer be dressed as Santa Claus?

SteveBausch,
-It just needs to work. Currently, we are missing the 4 planetary gears for this assembly.
-Ratio? What ratio? The planetary (pinion) gear is 16 teeth, the mating gear is 36 teeth
-Yeah, you won't be finding any parts for this on any shelf anywhere
-No reverse gear, but rather a reversing valve (steam)
-No brakes at all, actually
-The Engineer may in fact be dressed as Santa Claus...