Author Topic: Shay gears (parallel depth bevel gears graphical tutorial)  (Read 3973 times)

Online Dan Rowe

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Shay gears (parallel depth bevel gears graphical tutorial)
« on: September 07, 2020, 08:11:10 PM »
Years of searching has never led to finding a sutiable bevel gear set for a 7/8" Shay. The face length is always to short and to make matters worse I can not even find a good compromise. The stock gears always stick out one end or the other not in the middle of a proper Shay gear.

I know at least three ways to make a bevel gear set in my shop. Two of them require me to make an attachment to one of my machines. I plan to start with the parallel depth method Kozo used but slightly different. I will describe all three methods in this topic so ask any questions as I go through the explanition.

A question came to me by PM asking if Shay gears were ever used as cast without machining as was common in early farm machinery. I know in later years they were machined as there is a photo of a Shay bull gear being machined. The photo was not taken in the original Lima Machine Works but in a much later version of the company.

I can not say for sure but Lima was really back in the woods when the early Shays were made and the only bevel gear machine that was avaible at the time to machine gears was the bevel gear template planer invented by William Gleason in 1874. This was 6 years before the first Shays but I find it unlikely that one would have been in a small shop in Lima Ohio making saw mills and farm equipment. It is my opinion that the early gears were used as cast and as sales picked up new machinery was added to the shop.

Here is a sketch of the operating principal of the early Gleason bevel gear planer.


I have thoughts of making a small version of this machine so I can cut teeth in wax blanks. It is the simplest way I could make an accurate true bevel gear. Cast in nickel silver and covered in black grease would make a very convincing Shay gear.

The next mathod to be avaible in the US was invented by Hugo Bilgram in 1884. This was a modified shaper with an attachment to roll the gear blank on a master cone that matched the pitch cone of the gear being cut. The shaper had a single tooth rack that cuts the gap. This ia a version from about 1900 with added automatic indexing. The first models had manual indexing and operation. This machine was designed for gears for chainless bicycles as this was all the rage at the time. I am not sure if these machines were ever made large enough for Shay gears.



I have considered making one of the attachments for my shaper but I soon sober up.

The final method was most likely not used at the Lima works but it could have been used by back shops near working Shays especially ones used in distant locations like Queensland.

The earliest mention of the parallel depth method I have found is in American Machinist Gear Book 1910 by Charles H. Logue. He was one of the editors of the American Machinist and gives two early 1891 and 1892 references of the method but states that the first practical method was published in the American Machinist 14 Jan 1909 by S. K. Allen and that is the method used in the book.

I have a full set of mod 0.5 gear cutters and I will explain the method and give it a try.
 
The gear used for the Dulong S/N 2091 was gear #17, Shay gears used circular pitch rules as this was common in the days when wood patterns were made. The circular pitch is the distance along the pitch circle/cone from one tooth to the next tooth this can be measured with a ruler. It would be more complicated to use a ruler with the more modern diametrial pitch rules. If you have a dimetrial pitch gear the layout method is the same simply use the DP rules.


I will be using spur gear rules and a drafting board (CAD) to to draw the tooth cross-section. This eliminates a bunch of formulas and you can see the math on paper. I prefer this method over formulas or spreadsheets that in my opinion obscures the design process and the beauty of gears which are simply math in metal.

Spur gear rules can be found in machinist books gear books and catalogs and on the web. Normally bevel gears are designed and measured at the big end this makes it a lot simpler to use a gear pitch gage to measure the pitch of the gear. It is really hard to get an accurate measurement with a gear pitch gauge on the small end of a beval gear.

First step is to draw a rectangle with the sides equal to the number of teeth on the pinion and the top and botom with the number of teeth on the bull gear.
Then we scale the side of the box using circular pitch rules for the diameter of the pitch cone at the big end this is the pitch diameter. With CAD the pitch diameter of the bull gear should automatically scale to match the formula.



Now we draw the pitch cones. These are the theoretical cones that would work the same as the gear neglecting friction. This is the same as the pitch circle in a spur gear.



Now using the circular pitch rules for the addendum and the dedenum the parts of the gear above and below the pitch cone.



Cleanup and mirror the tooth profile and repete the process for the pinion.



In the next post I will scale the gear to 7/8" scale and design the parallel depth version.

If there are any questions or typos let me know.

Cheers Dan
ShaylocoDan

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Re: Shay gears (parallel depth bevel gears graphical tutorial)
« Reply #1 on: September 07, 2020, 08:17:00 PM »
Dan - wonderful to see this brought together in one tutorial like this!    :popcorn: :popcorn: :popcorn:
Couple questions on this first installment:
In the first step, you calculate the Circular Pitch C and Face Length - what are the formulas for that?
How does the DP or Module of the cutters factor in, or is that in a later installment?
 :popcorn: :popcorn: :popcorn:

Online Dan Rowe

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Re: Shay gears (parallel depth bevel gears graphical tutorial)
« Reply #2 on: September 07, 2020, 08:29:50 PM »
Wow Chris you are fast....The circular pitch (C') and face length (F) and number of teeth (N) are the know facts of Lima gear #17.

Circular pitch, diametral pitch and module are all different rule sets for gears. Module is usually metric but the system can be used for nonmetric measurements. These rules sets are in books or catalogs. I have a little folder and I am not really sure where all my rule sets came from. My favorite gear book is Gear Design Simplified by Franklin D. Jones and it covers everything in this topic.

Cheers Dan
« Last Edit: September 08, 2020, 01:48:54 AM by Dan Rowe »
ShaylocoDan

Online Dan Rowe

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Re: Shay gears (parallel depth bevel gears graphical tutorial)
« Reply #3 on: September 07, 2020, 08:35:53 PM »
My study of the Lima Shay gear drawings led me to finding drafting tools to draw gears. The first one is a Robinson's template odontograph. This was used to draw the shape of the side or flank of a gear tooth.



This next tool is a Boorman's Patent "Anglegraph" from the instructions "An instrument for ascertaining the correct Angles of Bevel Gears, without any drawings, templates or gauges, or calculations, beyond the diameter of the pitch line."  The small print on the book cover says "All Communications to be addressed J, A, Boorman c/o Greenwood & Bately, Ltd., Albion Works Leads," I think I am a bit late for that but a web search for this tool leads nowhere.



I think both tools could have been in the Lima works drafting room.

Back to gear #17... I scaled the drawing to 7/8" scale the red line is a 12" line. The calculations for a parallel depth gear are made at the small end so now we calculate the diametral pitch of the small end knowing the number of teeth and the pitch diameter of the small end. The answer is about 49.5 I was originally going to use 48 DP but I could not find all the cutters I needed on ebay. The price of a full set of Mod 0.5 gear cutters was about $60. 48 DP and Mod 0.5 are very close to the same size so next step is to convert the red line to metric.



Cheers Dan

« Last Edit: September 07, 2020, 08:48:52 PM by Dan Rowe »
ShaylocoDan

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Re: Shay gears (parallel depth bevel gears graphical tutorial)
« Reply #4 on: September 07, 2020, 08:37:35 PM »
The true gear #17 was a cycloid tooth gear with slightly different rules for the addendum and dedendum, which made it just a tad bigger at the tips of the gears. I have never even considered making a true cycloid form as the cutters would have to be made in the shop.

The gear is scaled to metric dimnensions.



The green lines add about 0.01" or .25mm to the face of the small end and. This is the exact Mod 0.5 dimensions which I will use for the calculations. This green section will not be on the finished gear.

I use a program to design gears and it will generate .dfx and g code the new version will do printer friendly outputs. It will also draw cycloid gears but the watchmaker's form not the power gear form. If you are working with gears a lot it really is helpful.
http://www.delphusa.com/index.htm

Here is a screenshot for a Module (metric) 0.5 spur gear with 15 teeth and a 20 degree pressure angle. This matches the cutters I have.



Here is the 37 tooth gear.



I could have used the metric spur gear rules to calculate the dimensions but the program is simpler and no stupid math errors.

The addendum line and the dedendum line are both parallel to the pitch line with a parallel depth gear so here it is.



The red lines are the old gear. The new version is a bit smaller which is good as the trucks parts are already made and the gear clearence is close.

The next step is to select the cutter.

Cheers Dan
ShaylocoDan

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Re: Shay gears (parallel depth bevel gears graphical tutorial)
« Reply #5 on: September 07, 2020, 08:38:51 PM »
The face length of a Shay gear is just about the most important dimension of a model Shay truck because it is always seen in a clear right hand photo.



The gear rules compare the face length (F) to the pitch cone length (E). The rule for the modern Gleason system state that the face length should be about 1/4 E, and it should never exceed 1/3 E. No wonder I can not find a sutiable gear set!

The Shay gear is 0.42E which clearly exceeds the Gleason rule. No fixed rule is given for parallel depth gears, but they should not exceed 1/3 E. The reason given is the cutter is selected by the small end dimensions so excessive face length will make the form of the tooth at the big end stubby.




The drawing in the book is similar to the above drawing except that there is no Z dimension, here the first parragraph.

"NUMBER OF CUTTER."
    "Note: To determine the number of cutter to use (shape or profile number), first find the radius X  at inner ends of teeth; then determine the number of teeth of equal pitch on a spur gear of radius X, and select cutter to suit this number. (Some prefer the radius Y from the center-line to mid-section of tooth.) This radius Y may be obtained, accurately enough for practical purposes, by measuring a fairly accurate drawing."

The book then gives a fromula for calculating the radius at X, but as we already have a very accurate drawing we can simply measure the radius at X, Y, and Z. I used my gear program to draw the form cutters for Module 0.5, they are just below the red scale line. The cutter number at X the small end is 3. The number at Y is 4, and the number at Z is 5. I drew the green hatch to show the range of cutter number 4. It is clear to me that cutter 4 is the best comprimise and the big end should not be stubby.

Now on to the bull gear.



The cutter at the small end is 7 and the cutter at the middle and big end is nmber 8. The green hatch for cutter 8 is bigger than the section for cutter 7 so the best choice is cutter 8.

The rules given in this post are all from Gear Design Simplified by Franklin D. Jones. The method given in American Machinist Gear Book 1910 by Charles H. Logue makes the cutter number calculation at the middle of the gear face or at Y. This is the original method and it would have been used for replacement Shay gears if proper gear machines were not avaialble.

The next post will be how to cut the gear on a milling machine.

Cheers Dan
ShaylocoDan


Online Dan Rowe

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Re: Shay gears (parallel depth bevel gears graphical tutorial)
« Reply #7 on: September 07, 2020, 09:20:33 PM »
John, Many thanks, I found the first link but not the second one, now I have patent numbers and dates which are important facts.

Cheers Dan
ShaylocoDan

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Re: Shay gears (parallel depth bevel gears graphical tutorial)
« Reply #8 on: September 07, 2020, 10:39:27 PM »
Chris, when you were asking about bevel gears on your Mann Wagon build, I had an answer the next day but you had already cut the gears, so I took a bit more time to cover the subject. Here is a link to CP, DP  and Module rules.
http://www.linngear.com/wp-content/uploads/2013/06/Gear-dimension-calculation-tips_DP_CP_Mod.pdf

Cheers Dan
ShaylocoDan

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Re: Shay gears (parallel depth bevel gears graphical tutorial)
« Reply #9 on: September 07, 2020, 11:36:09 PM »
Chris, when you were asking about bevel gears on your Mann Wagon build, I had an answer the next day but you had already cut the gears, so I took a bit more time to cover the subject. Here is a link to CP, DP  and Module rules.
http://www.linngear.com/wp-content/uploads/2013/06/Gear-dimension-calculation-tips_DP_CP_Mod.pdf

Cheers Dan
Great - thanks! Just saved that one away.  Like I probably will with this whole thread!   :cheers:

Offline jadge

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Re: Shay gears (parallel depth bevel gears graphical tutorial)
« Reply #10 on: September 08, 2020, 11:10:33 AM »
Interesting exposition; thanks Don. I'm pleased to note that you mentioned Tregold's approximation.

There's nothing fundamental about the limits on the face width of a bevel gear. But there are some practical limits. In design terms as the tooth form gets smaller the load carrying capability also gets smaller and at some point extra face width simply doesn't add anything in terms of power transmission. In terms of manufacture whatever method is used the cutter must be able to pass through the small end. With a Gleason shaper that would be possible for relative large face widths although the tool would be fairly delicate. I've seen a Gleason bevel gear planer in action and had the details described at RAE Farnborough, but never used one in anger. In theory the parallel depth method shouldn't be bothered about face width, although I've never used the method. However the smaller the tooth form at the inner edge the greater the error in curvature at the outer end which would ultimately defeat the point of the large face width. I have cut bevel gears using involute cutters specifically for bevel gears, albeit some 45 years ago. The special cutters are designed to go through the small end of the bevel gear while having the curvature associated with the outer edge. There must be a limit on how small the inner edge tooth form can be, but I don't know what the cutter design limit is.

I'd second the book "Gear Design Simplified". When I designed the gears at RAE I borrowed a copy from the library, but have subsequently bought my own version.

These days I design in 3D CAD using pen, paper and formulae to derive the numbers. I'm no mathematician but even I can see elegance in the formulae. Once the planes are set up the design is fairly straightforward:



I design at 1DP and scale the drawing as a last operation. While I could make my own special involute cutters I find it easier to use the CNC mill to make the bevel gears in the first place. So it wouldn't be a problem having a large face width.

Andrew

RAE = Royal Aircraft Establishment

Offline PJPickard

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Re: Shay gears (parallel depth bevel gears graphical tutorial)
« Reply #11 on: September 08, 2020, 11:55:30 AM »
Dan,
Nice discussion and I have ordered a copy of the book. As for the real engines, I think it is mentioned in the Climax book that they were used as cast. Years ago I was at Cass (back when they let you walk around the shops and yard) and WM #6 was outside the shops. I guy was using and angle grinder to shape a gear that they had just built up with weld. That surprised me, but on further reflection I knew that the Cass shop had no way(well ,no easy way) to machine the gears. Still seemed kinda undignified to be using an angle grinder on the last Shay ever built!

Online Dan Rowe

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Re: Shay gears (parallel depth bevel gears graphical tutorial)
« Reply #12 on: September 12, 2020, 09:12:10 PM »
I'm pleased to note that you mentioned Tregold's approximation.

Andrew, there is no mention of Tredgold's approximation in the text!!!! I have read more than several books about bevel gears and I remember that some of them mentioned Tredgold's approximation but even after a reread I did not really understand it. Old textbooks can sometimes be a bit hard to wade through.

I checked the web and found a better explination.

"The form of teeth formed based on Tredgold's Approximation depends upon the slant height of the back cone (not on the radius R). A sphere is approximated between the back cone and pitch cone as shown in the figure below. The back cone is forming the teeth of the equivalent spur gear."



https://www.ques10.com/p/47776/virtual-no-of-teeth-of-bevel-gear-by-tredgolds-a-1/

Now I see that the method I used to find the number of the gear form cutter was Tredgold's approximation.

This makes me question my method for drawing 3D bevel gears. I think I should be using Tredgold's approximation to choose the form of the involute curve and apply it to the back cone.

The template used for a Gleason template planer should also use Tredgold's approximation calculated at the location of the template if my thinking is correct.

Did you have to file the teeth when using the special thin bevel gear cutter? My books on the subject say the method requires filling.

Thanks for the tip.

Cheers Dan
« Last Edit: September 13, 2020, 02:11:28 PM by Dan Rowe »
ShaylocoDan

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Re: Shay gears (parallel depth bevel gears graphical tutorial)
« Reply #13 on: September 12, 2020, 09:19:09 PM »
Years ago I was at Cass (back when they let you walk around the shops and yard) and WM #6 was outside the shops. I guy was using and angle grinder to shape a gear that they had just built up with weld. That surprised me, but on further reflection I knew that the Cass shop had no way(well ,no easy way) to machine the gears. Still seemed kinda undignified to be using an angle grinder on the last Shay ever built!
Good story about Cass. I did not know that the shops were off limits these days. I have not been there for several years. My favorite visit was when the #5 was being overhauled. There were Shay parts all over the place and the steam engine was in a bunch of pieces. This was before cell phones so I rushed to the gift shop to buy a disposable camera, unfortunately I am not good with photography and not one photo in the whole roll was any good just a blur.

Cheers Dan
ShaylocoDan

Offline jadge

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Re: Shay gears (parallel depth bevel gears graphical tutorial)
« Reply #14 on: September 13, 2020, 08:18:02 PM »
Did you have to file the teeth when using the special thin bevel gear cutter?

Yes, I did have to file the small end of the teeth to make them curve a bit more. The gears are quite small, 20 teeth and 20DP. So only a quick pass with a file was needed. I also ran the gears in with grinding paste after case hardening, driving them with an electric drill. It got rather exciting when the sliver of aluminium I was using to spread the paste got caught in the teeth.

You are correct, the pattern for a Gleason bevel planer should take into account Tregold's approximation.

When I create a bevel gear in CAD I place the involute profile as modified by Tregold's approximation on the back cone. The sketch is then lofted to a point at the origin to get the tooth, which can then be replicated in a circular pattern.

Andrew

Online Dan Rowe

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Re: Shay gears (parallel depth bevel gears graphical tutorial)
« Reply #15 on: September 18, 2020, 07:59:23 PM »
Thanks to Andrew, I now realize that I did not use the correct tooth curve for all the 3D bevel gears I drew and had made by Shapeways and other printed sources. They seem to run fine so I will use some of them because they are in the shop. Now that I understand Tredgold's approximation I know which gear curve to choose.

Here is a link to an explanition of Tredgold's approximation and it is still hard to follow and I understand the theory. There is also some of the early bevel gear machinery that dates to around 1910 in the US. I have copied the photos for this thread.
https://archive.org/details/bevelgearing00flanrich/page/32/mode/2up?q=Machinery%27s+Reference+37



This is a small Gleason template bevel gear planer. The template for finish cutting uses Tredgold's approximation.



This one is a specilized milling machine for automatically cutting bevel gears. It uses a special thin bevel gear cutter and the small ends of the teeth will have to be filed to a bit more curve, just like doing this on a standard milling machine and an index head.


Bilgram's bevel gear generator a modified shaper.



Gleason's bevel gear generating machine. It uses two rotary cutters to cut both sides of a single tooth at the same time. This is much quicker than a Bilgram machine.

Cheers Dan

 

ShaylocoDan

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Re: Shay gears (parallel depth bevel gears graphical tutorial)
« Reply #16 on: September 18, 2020, 08:22:14 PM »
Love the pictures of the old machines - be a fun model to make...! 

Online Dan Rowe

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Re: Shay gears (parallel depth bevel gears graphical tutorial)
« Reply #17 on: September 18, 2020, 10:44:31 PM »
Chris, Lima made the gears here is a photo of the gear testing machine.



The gear machines at Lima.



The machine on the left with the upside down bull gear is a radial planer or milling machine to face and drill the gear flange. The machine on the right with the operator is the gear cutting machine. I am not certain what principle the machine uses but I am leaning to a Gleason template planer. If anyone can identify the machine or even point out the operating principle I would be pleased to know.

Now those machnes would make cool models.

Cheers Dan
ShaylocoDan

Offline jadge

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Re: Shay gears (parallel depth bevel gears graphical tutorial)
« Reply #18 on: September 20, 2020, 11:29:48 AM »
Interesting pictures, thanks for posting.

In the picture of the erecting shop the machine on the left looks like a vertical borer, not sure it has a drilling capability? The machine on the right looks like a vertical borer too, although I don't know what the gear train is for. It could be for machining conical surfaces as opposed to simple facing and cylinders?

With regards to the Gleason bevel gear generator I have seen one in action. I don't recall it using rotary cutters? It has two tools that reciprocate, one cutting and one being retracted alternately. As the cut progresses the gear being cut rotates and the whole cutter head also rotates about the axis of what would be the mating gear. So the cutters stay in sync with the tooh being cut, but effectively move outwards. As Dan says it is quicker than other types of machine as it cuts both sides of a tooth in each pass. It generates the tooth form as a series of lines in a similar way to hobbing of spur gears.

Andrew

Offline PJPickard

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Re: Shay gears (parallel depth bevel gears graphical tutorial)
« Reply #19 on: September 20, 2020, 12:46:35 PM »
Dan, great picture of the Lima shop! Where did you locate that?

Offline Millwright

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Re: Shay gears (parallel depth bevel gears graphical tutorial)
« Reply #20 on: September 20, 2020, 08:43:22 PM »
The machines look to me like early Webster and Bennett double column vertical borers.
John.

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Re: Shay gears (parallel depth bevel gears graphical tutorial)
« Reply #21 on: September 20, 2020, 09:00:48 PM »
I found an image of the other side of a Gleason template bevel gear planer.



Now the templates can be seen, there are curved templates for both sides of a tooth and a straight template for the roughing cut. These are all bolted to a plate that can rotate each template to the top to guide the cam follower.

This is a 24 inch machine which is big enough for gear #17 but not the larger Shay gears. I did find a larger Gleason planer large enough to do all the Shay gears and it looks nothing like the one in the Shay shop.



Gleason Model 54 Date built 1939

"Specification:
Straight Bevel Gear Planner, Model 54 capable to Produced Bevels up to 60"-1, 524 mm with a Face Width 14"-55.6 mm, comes equipped with a full set of change gears, full set of 14°30´ and 20° P.A. Forms, tool gauge, Arm Rest, assorted gear arbors, coolant pump and under power for inspection."

Back to the Shay shop......
The machine on the left with the gear flange getting cut true is a vertical boring mill sometimes called a vertical boring lathe. Most folks that have researched US railroad shops have heard of the Niles Tool Works of Hamilton Ohio. I knew they were not far from Lima so I looked for Niles vertical boring mills. I was hoping to find the half circle opening that is on the base of both machines but this was not the case.

Here is the smallest Niles vertical boring mill.


There is a list of special attachments for a Niles boring mill these are a cylinder boring bar, a slotting and key-setting attachment, a pulley turning attachment, and a thread cutting attachment.

The links are catalogs the first one has engravings and the second one has photographs, very interesting stuff.
Niles Tool Works Hamilton Ohio 1891
https://babel.hathitrust.org/cgi/pt?id=coo1.ark:/13960/t2c82vp12&view=1up&seq=1
https://babel.hathitrust.org/cgi/pt?id=wu.89089664148&view=1up&seq=7

I was think I was wrong about the machine on the left drilling the flange. The flange has to be drilled and two radial keyways need to be cut. These operations must have used a normal vertical milling machine unless there was a seperate attachment that could be added.

Here are both gears to compare.


The one with the gear facing up has a rough cast flange. This must mean that the teeth were cut first then the second machine faced and turned the diameter of the flange.

Cheers Dan
ShaylocoDan

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Re: Shay gears (parallel depth bevel gears graphical tutorial)
« Reply #22 on: September 20, 2020, 09:15:30 PM »
Dan, great picture of the Lima shop! Where did you locate that?

The photos are from George Kadelak's Shay Photo CD.
https://shaylocomotives.com/

For some unknown reason my name is not on the front page as a Shay contributor you have to go here to spot my work on the mechanical database.
https://shaylocomotives.com/links/Links.htm

Cheers Dan
ShaylocoDan

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Re: Shay gears (parallel depth bevel gears graphical tutorial)
« Reply #23 on: September 20, 2020, 09:21:07 PM »
There are a couple more photos here, on Gleasons website, towards the bottom of the page, along with a picture of the Gleason Works - they are cross town from me. A friend of mine works there, have to see if he knows of any other picture sources...


https://www.gleason.com/en/operations/the-gleason-works-rochester-ny-usa/this-is-our-story



Online Dan Rowe

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Re: Shay gears (parallel depth bevel gears graphical tutorial)
« Reply #24 on: September 20, 2020, 10:23:19 PM »
Chris the history of the Gleason works is not really clear to me.

Interesting pictures, thanks for posting.

With regards to the Gleason bevel gear generator I have seen one in action. I don't recall it using rotary cutters? It has two tools that reciprocate, one cutting and one being retracted alternately. As the cut progresses the gear being cut rotates and the whole cutter head also rotates about the axis of what would be the mating gear. So the cutters stay in sync with the tooh being cut, but effectively move outwards. As Dan says it is quicker than other types of machine as it cuts both sides of a tooth in each pass. It generates the tooth form as a series of lines in a similar way to hobbing of spur gears.

Andrew

James Gleason son of William Gleason patented a bevel gear generator with two rotary cutters in 1898 US patent 605249 June 7. 1898. This machine has two rotary cutters acting on both sides of a tooth.
https://patents.google.com/patent/US605249A/en?oq=605249

This is not the same machine as the image of the Gleason bevel gear generator I posted. I can see two cutters in the image the top one is closer that the lower one.

Here is an image showing the operating principle with a confusing date of 1905.



Cheers Dan
ShaylocoDan

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Re: Shay gears (parallel depth bevel gears graphical tutorial)
« Reply #25 on: September 20, 2020, 11:07:58 PM »
Dan, my friend who worked there is getting some info for me, he has a video and booklet that was produced ror the Gleason company 100 year mark. I'll put up more when I get it...

Online Dan Rowe

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Re: Shay gears (parallel depth bevel gears graphical tutorial)
« Reply #26 on: September 21, 2020, 01:45:27 AM »
Hi Chris that might fill a few holes....

I reread my copy of Studies in the History of Machine Tools by Robert S. Woodbury. The first section is the History of the Gear Cutting Machine.

Pg. 87
"Two other describing-generating machines deserve mention.... One is described in an Austrian patent of 1879 issued to C. Dengg & Company of Vienna.35 This machine (Fig. 31) generates only epicycloidal teeth and only bevel gears. The tool is guided along an element of the tracing curve, but the machine could not form hypocycloidal flanks. It is shown here as an example of the highly specialized types of gear-cutting machines sometimes developed."

"35. Austrian Patent No. 657 of July 1879."



I had dismissed this machine because of where it was built, but the machine in the Shay shop has a stricking similarity to the patent drawing. The vertical shaft with 3 bevel gears is on the top and there are a bunch more gears but patent drawings often differ from the actual machine. The Shay gears were epicycloidal bevel gears so that matches. I am not sure that Gleason machines ever made epicycloidal gears.

I tried to find the patent and Dengg & Company but did not find anything. I am now thinking that the photo is very possibly the extremely rare Dengg bevel gear machine.

Cheers Dan
« Last Edit: September 21, 2020, 02:23:40 AM by Dan Rowe »
ShaylocoDan

Offline Don1966

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Re: Shay gears (parallel depth bevel gears graphical tutorial)
« Reply #27 on: September 21, 2020, 01:54:20 AM »
Hey Dan, have you ever thought of modeling one of these machines. Making it a working model. Bet it would make a great project. Just me rambling.....


 :cheers:
Don

Offline john mills

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Re: Shay gears (parallel depth bevel gears graphical tutorial)
« Reply #28 on: September 21, 2020, 10:08:16 AM »
Hi Dan
I'm following with interest i have only been told of
Gleason type generating machines using 2 reciprocating cutters wondering how they worked .
interesting you mentioned  nile vertical borer   i new some one how had one a 48"  table in his shed at home

latter i had a job were they were using one .I said at the time i' new some one that had one of these .latter when i
saw that person he confirmed it was his machine he had changed it for a bigger machine.
  How small did they make these bevell gear generators  ,in stead of a model  you could probably just build a small one.that would be an interesting project.
       John

Online Dan Rowe

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Re: Shay gears (parallel depth bevel gears graphical tutorial)
« Reply #29 on: September 22, 2020, 10:44:21 PM »
John, wow they guy who had a Niles vertical boring machine only to trade up to a larger machine does not have a shed.... he has a machine Palace  :cartwheel:

I forgot to mention that the Niles Works build 31% of the engines for Liberty ships. I have only seen one which is at the Merchant Marine Academy where it was no longer part of the curriculum when I was an engineering cadet but we asked and asked until they let us run it on steam. That was very cool to see.

I quoted everything Woodbury had to say about the Dengg machine but the sentance "The tool is guided along an element of the tracing curve, but the machine could not form hypocycloidal flanks." is really a bit confusing to say the least.

To make sense ot that statment we need to know how a epicycloidal or cycloidal gear is constructed. Here is a link to a few very short video clips that show how construct a cycloidal gear.

https://www.tec-science.com/mechanical-power-transmission/cycloidal-gear/geometry-of-cycloidal-gears/

Be sure to watch the last one also to learn how an involute curve the more modern gear curve relates to a cycloid gear curve.

Now it should be clear why Woodbury's statment is troubling. The curve above the pitch line or addendum is an epicycloidal curve and the dedendum curve is a hypocycloidal curve. So Woodbury is saying that a Dengg machine could not cut the lower part of the gear. Well that would make it a very useless machine.

The special case where the rolling circle is half of the pitch circle giving a straight line got me thinking....what if the dedendum was a straight line or a nearly straight line?



The tooth form is shown on the pinion drawing and the dedendum curve is nearly straight it only varies 0.011" from straight. I checked my old gear books and the construction looks like it is Grant's odontograph. I have this method in at least two books so I will go through the example drawings then see if it works on #17 pinion. If it works I can draw the bull gear tooth using the same method to see the dedendum curve and see how straight it is.

The Dengg machine is really a powered Spirograph that cuts bevel gears!!!!

Cheers Dan
ShaylocoDan

Online Dan Rowe

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Re: Shay gears (parallel depth bevel gears graphical tutorial)
« Reply #30 on: September 25, 2020, 10:37:18 PM »
William Ripper in his 1914 book Machine Drawing & Design has a helpful image to show the relationship between the pitch circle and the generating circle of a cycloid gear.



Tooth A has a generating circle with the diameter equal to the radius of the pitch circle, this gives a straight line for the dedendum flank.

Tooth B has a generating circle that has a diameter less then the radius of the pitch circle, this has the dedendum curves make the root of the gear thicker.

Tooth C has a generating circle that has a diameter larger than the pitch circle radius, this causes undercutting at the root and should never be used.

I looked at all the Lima Shay drawings in my collection and the ones that had  tooth forms shown there was a mix of A and B tooth forms.

I wish Woodbury had given the American Machinist issue information for the image of the Dengg machine, as he did for several other machines..... That research will have to wait.

The link that has the process of generating cycloid gears had a good overview of the pros and cons of cycloid gears.
https://www.tec-science.com/mechanical-power-transmission/cycloidal-gear/geometry-of-cycloidal-gears/

"Pros and cons of cycloidal gears
The cycloidal shape of a tooth leads to less wear of the tooth flanks during meshing and thus to lower friction losses in comparison to the involute shape. The reason for this is the lower contact pressure (lower hertzian contact stress), since a convex and a concave flank always meet in mesh and “nestle” up against each other, so to speak."

"Furthermore, cycloidal gears can be produced with a significantly lower number of teeth without undercutting compared to involute gears. In this way, gears with only three or even two teeth can theoretically be produced."

"The lower friction and the low number of minimum teeth are the main reasons why cycloidal gears are/were often found in clocks."

"Despite the mentioned advantages of cycloidal gears, involute gears are still the most commonly used type of gears in mechanical engineering! The reason is the relatively simple production of an involute shape (straight tool flanks) compared to a cycloidal shape (curved tool flanks)."

"Furthermore, cycloidal gears are very sensitive to an inaccurate adjustment of the centre distance, which then leads to a change in the transmission ratio. For these reasons, cycloidal gears are hardly found in mechanical engineering but are only used in special cases such as in the watch industry, for roots type blowers or for the drive of gear racks."

The first sentence of the last parragraph is the reason that cycloid gears are a bad idea with a Shay locomotives. Almost all of the Shay trucks were equalized or had springs on the left side. This will cause pitch errors on the bevel gears as the left side moves up and down. The curve changes at the pitch line so this makes the wrong curves run together, add some grease and dirt and this will lead to gear wear. So yes there is an engineering reason why the tales of gears wearing out are true. At some point Lima switched to involute gears and I have seen a 1922 Lima ad stating that the gears now had a two year guarantee.

Cheers Dan
ShaylocoDan