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Miter Gear Cutting

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Ray C

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Ok... Planning to do this in a few parts and am writing this as I go. The goal is to show the nitty-gritty basics about a miter gear and how to make one with a standard involute tooth surface. The intention is for folks to understand enough so when they open Machinery's Handbook and open the section on gears, you can follow along and then advance to more complicated gear types.

The tutorial on basic spur gears has most of the basic definitions and it's best to read that first before digging into this. https://www.hobby-machinist.com/threads/cutting-gears-diametral.69653/#post-584129 The format of this will be the about the same... A few "classroom lessons" with definitions and terms, followed by actually making the gear. I won't be able to start making the gear for a few days due to my FT job getting in the way of fun.

Part 1 ....

A miter gear is a special case of bevel gear. A miter gear connects shafts that are at right angles. A bevel gear can connect shafts at arbitrary angles (but there are some practical limitations).

FYI: For this example, we're talking about straight-tooth gears. The configuration of the teeth (curved etc) does not change the fact that the gear is a bevel-type gear.

A pair of mating miter gears can be different sizes but must be the same diametral pitch (for US sized gears) or modulus (for metric gears). This rule is true for all types of gears.

Diametral Pitch has the same meaning as for spur gears. If the gear is defined to be a 16 DP gear then, for every inch of diameter there will be 16 teeth. As diameter increases tooth count increases according to that ratio.

See the basic picture of the major features.

The yellow line is the Pitch Line. Since miter gears connect intersecting shafts, the Pitch Line of a miter gear is 45 degrees. The Pitch Line is with respect to the blue line which is the centerline of the gear and/or axis of the shaft. The Pitch Line does not correspond to any physical feature of the gear. Even though this could be called a 45 degree gear, there is no physical component that is 45 degrees.

The green line (surface line) is on top of the surface of the Addendum. The angle with respect to the pitch line is the "Addendum Angle" and everything above the yellow line up to the green line is the "Addendum" part of the tooth. The Addendum angle is usually a few degrees (we will calculate it later). The metal gear blank must have a "Surface Angle" that equals the pitch angle (45 degrees) plus the Addendum angle.

The red line is the "Cut Line" and rides at the bottom of the tooth. The angle between the pitch line and the cut line is called the Dedendum angle. This angle is not numerically the same as the Addendum angle. The milling cut angle will be "45 degrees minus the Dedendum angle".

Notice that all the lines intersect at an imaginary point at the top of the gear. The physical characteristics (defined by the surface and cut lines) have different angles. As a result of this, the tooth depth of a miter gear is not constant along its length. Look a the red circles and you can see tooth depth is different from top to bottom. The term tooth depth and "Whole Depth" will come-up later so be apprised, when measured, it is the depth at the deepest end of the tooth.
Pic1.JPG

Some definitions for Part 1:

Just like with the spur gear, the Addendum = 1 / Diametral Pitch. This is physically measured from the pitch line to the top of the tooth at the tallest part of the tooth (at the OD of the gear).

The Dedendum for bevel gears depends on which standards the gear is being made to. There are multiple variations and usually, gears made by different standards should still mesh but, the clearance at the root and addendum might not be suitable for a given application. In this example the dedendum is being assumed to be the classic model shown in Machinery Handbook. Dedendum = 1.157 / Diametral Pitch. This is measured from the pitch line at the tallest part of the tooth (at the OD of the gear).

If you stick to this standard (which is recommended when milling gears manually) the Whole Depth = 2.157/ Diametric Pitch or Whole Depth = Addendum + Dedendum. The values will come out the same if you stick with this convention.


Almost all of the physical features are now defined. Next, we will define a few intermediate terms that help make the math easier. After that, we'll show formulas to determine everything you need to make a gear. That is: the "Cutting Angle", "Stock Surface Angle", "Whole Depth", "Outside Diameter" and something called "Virtual Teeth" (which is used to determine which cutting gear to use).

Until we meet again...

Ray
 

benmychree

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I have cut bevel gears, it takes a special cutter made for bevel gears, and it takes a minimum of three cuts to form each teeth, a central cut is taken through all the teeth, then the blank is offset to one side and the cutter is realigned with the small end of the tooth and a cut taken through all the teeth in turn, then the blank is offset to the other side of the central cut, and the process repeated until the tooth is the correct dimension at both ends. When the central cut is made, the tooth is way too thick at the big end. A standard involute cutter of the correct pitch will make a tooth space that is too wide at the small end, hence the need for a special cutter, made more narrow than the standard cutters. The amount of offset is a matter of experimentation , but a formula approximates it; even then, Brown & Sharpe's book on gearing says that some filing of the teeth may be necessary for satisfactory work. See Brown & Sharpe's book "Practical Treatise on Gearing".
 

Ray C

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I have cut bevel gears, it takes a special cutter made for bevel gears, and it takes a minimum of three cuts to form each teeth, a central cut is taken through all the teeth, then the blank is offset to one side and the cutter is realigned with the small end of the tooth and a cut taken through all the teeth in turn, then the blank is offset to the other side of the central cut, and the process repeated until the tooth is the correct dimension at both ends. When the central cut is made, the tooth is way too thick at the big end. A standard involute cutter of the correct pitch will make a tooth space that is too wide at the small end, hence the need for a special cutter, made more narrow than the standard cutters. The amount of offset is a matter of experimentation , but a formula approximates it; even then, Brown & Sharpe's book on gearing says that some filing of the teeth may be necessary for satisfactory work. See Brown & Sharpe's book "Practical Treatise on Gearing".
For manual cutting on a mill, here's a couple methods I'm aware of. One is a 2-pass method where the first pass is made with the cutter raised 1/2 of the chordal distance and the second pass with the indexer advanced to a half-angle followed by lowering the cutter 1/2 chordal distance.

There is also the 3 pass method where you take a center cut then 2 more passes (similar to the 2 pass method) moving the cutter 1/3 chordal distance up then down and 1/3 the angle offset. 2 Pass vs 3 pass is done depending on having indexing values that can accommodate all the angle settings.

Ray

EDIT: Fixed misspelling.
 
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benmychree

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Yes, the two pass method is mentioned in B&S, but it seems that until the amount of offset that is necessary is established, the 3 pass is used as a starting point to establish that dimension. And then, the milling method can only create an approximate gear tooth shape, as opposed to generating methods, such as a bevel gear generator.
 
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tertiaryjim

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Have you looked at the use of a shaper setup to "Generate" the gears?
I think with some effort it could be done on a vertical mill but probably wouldn't be a good use of time. Too much effort to determine and connect the gearing.
I'm sure someone has done it on a horizontal mill.
Nice wright-up.
 

benmychree

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I am sure that it is not possible to "generate" a bevel or miter gear by any "common" process by any common milling machine, whether horizontal or vertical orientation.
 

Ray C

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Have you looked at the use of a shaper setup to "Generate" the gears?
I think with some effort it could be done on a vertical mill but probably wouldn't be a good use of time. Too much effort to determine and connect the gearing.
I'm sure someone has done it on a horizontal mill.
Nice wright-up.
Hi there Tertiaryjim. Thanks...

Well, I don't have a shaper so that settles that... These gears are for a table-top project and I wanted to tackle making them myself.

Ray

PS: I did have a misspelling and will go back and correct it.
 

Ray C

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All,

Be apprised that many gears commercially available are approximations of the ideal tooth configuration. For example, if someone makes spur gears using cutters like the ones shown, you are not producing an ideal gear. Since each of those cutters can make a range of sizes, compromises are being made. The fact remains, such gears are commonplace yet, world keeps spinning. Same is true for bevel/miter gears.

The techniques I'm outlining and some of the terms I'm using come from very old books dating back to the late 30's and 40's. Regarding days-gone-by... The overwhelming majority of the lathes and mills people talk about on this website have "imperfect" gears in them.

Gear cutters.jpg

Ray
 

benmychree

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Yes, that is correct for the usual type of "range type" cutters; although I have never seen one, the old books say that for closer work, "half number" cutters were available to more closely approximate "perfection".
I don't see how machining a bevel gear on a shaper could be any different than milling, the cutter moves in a straight path with either machine, so unless some convoluted accessory device was made to roll the blank, there would be no difference.
Later, I may post how I made a foundry pattern for a cast tooth miter gear, it is about 12" in diameter and about 1 DP, I made it for a local historic grist mill that dates back to the mid 1840s.
 

tertiaryjim

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benmychree
Your right about rolling the blank. Some people have posted information about it in the past.
 

Ray C

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Part 2:

Just like the discussion about spur gears, part II will define all the terms of the formulas to define the critical aspects of the gear. We’ll also plug-in the numbers to get values.

One important value is the Pitch Cone Radius (abbreviated PCR). From the picture in part 1, there was a pitch line. The PCR is the length of pitch line from the end of the thick part of the tooth to the imaginary point where it intersects the shaft axis. This has no real physical measurement but is needed to solve many other aspects of bevel gears.

Pitch Cone Radius = Pitch Diameter / 2x Sin Pitch Cone Angle. (hereon: Pitch cone radius abbreviated PCR)

Addendum Angle = Addendum Amount / PCR and similarly, Dedendum Angle = Dedendum Amount / PCR (Note that these values are expressed as a pure tangent; thus, arctan is needed to get the actual value of the angle). These are the angles above and below the pitch line that outlines the addendum and dedendum.



There is also “virtual teeth” but, we’re going to leave that until we talk about the setup before making the gear.

For a 30 tooth gear with a DP (Diametral Pitch) of 25.4 (aka. Module 1 gear) here are the bare minimum values needed. There are other values that can be calculated but, they are more heavily needed to verify the gear once it is made.

Some plug & chug…

Pitch Diameter PD = No of Teeth / DP = 30/25.4 = 1.1811
Addendum = 1/PD = 0.0394
Dedendum = 1.157/DP = 0.0456
PCR = PD/2xsin PCA = 1.1811/2x0.7071 = 0.8352
Addendum Angle = arctan 0.0394/0.8352 = 2.7010 (degrees)
Dedendum Angle = arctan 0.0456/0.8352 = 3.1251 (degrees)
Angular Addendum = Addendum x cos Pitch Cone Angle = 0.0394 x cos 45 = 0.0279


Now, for the physical characteristics that you can relate to:

Cutting Angle: This is the angle to setup the mill and corresponds to the line in part 1. Cutting angle = Dedendum Angle - Pitch Angle
Cutting Angle = 3.1251 – 45 = -41.8749 (degrees) [the minus means it’s a line that cuts below the pitch angle].

Surface Angle. When you cut the blank, this is the angle of the tapered surface of the stock. Surface Angle = Pitch Angle + Addendum Angle
Surface Angle = 45 + 2.7010 = 47.7010 (degrees)

Outside Diameter. This is the diameter of the blank at the wide part. Outside Diameter = PD + 2 x angular addendum
Outside Diameter = 1.1811 + 2 x 0.0279 = 1.2368

Tooth Thickness (this is the thickness of the tooth at the pitch line at the wide end of the OD): Tooth Thickness = 1.571 / DP
Tooth Thickness = 1.571/25.4 = 0.0619 BTW: Tooth thickness is good to know now but really needed when determining how to cut the tooth.

And finally…

Tooth Depth: Depth of tooth at the wide-end (base) of the gear. Tooth Depth = 2.157 / DP
Tooth Depth = 2.157/25.4 = 0.0849


So, let all this soak in. Also, keep in-mind this represents the techniques used for manual generation of bevel/miter gears when standard involute cutters are used. The end result will produce an approximation of an ideal gear (just like any other gear that is made with cutters that cut ranges of teeth). If you want a perfect gear, use a CNC machine or a special-purpose gear machine.

I have not decided yet if I'll include another part that talks about setup or, if I'll skip right to making the part and include comments. FWIW, I'm on a special project at work and need to get-up at obscene hours in the morning to speak with people on the other side of the earth. Sleep is going to be at a premium for a while. It's going to be a couple days before I have enough time to write-up more about this.

Ray
 

Ray C

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Alright then... I had a crazy week at work due to a crazy schedule and to make matters worse, several folks were away and all their work got funneled my way. Last night, I double-check all the calculations, calculated all the compound angles and trimmed the parts to size. Both of the blanks were heat treated to Rc 32. The mill table angles were also set.

Here's a quick pick of one of the blanks. I'm going to write-up another post on how to set the compound and mill angles because, it's very easy to make a mistake.

IMG_20180519_055248[1].jpg

I'm going to make the actual parts now, then come back for the write-up and finish this off. See you in a couple hours or so....

Ray
 

Ray C

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Home stretch. -No spoiler alert till we get to the end.


The gear blank has to be the proper size before cutting the teeth. The critical areas are the face width and the angle of the surface.

Earlier, the surface angle was defined to be the pitch angle plus the addendum angle which was 45 + 2.7010 = 47.7010 (degrees). That angle is with respect to the blue and green lines in the first post. This is NOT what you set your compound to because the compound angle is normal to the surface of what is being cut. The compound angle that’s needed is 45 – 2.7010 which is 42.299 degrees. Be really careful about this because it’s very hard to eye-ball the difference between 42 and 47 degrees and it’s an easy mistake to make.

The compound is nowhere near accurate but, after going through the triangle method of setting it up, it shows roughly 42.3 degrees. If someone needs to see the triangle method (again) let know. It's my cheap and dirty way of setting the compound. I'm sure I posted somewhere here at least a couple times over the years.
IMG_20180519_122453.jpg


Double check! When measuring the part this way, you should get twice the value of the “textbook” calculated value (2 x 47.7010 = 95.4). Believe it or not, that protractor is amazingly accurate for the $20 it cost.
IMG_20180519_122341 - Copy.jpg


In order for a miter gear to function properly, the face has to fall within a certain range. The range is the smaller of:

Pitch Cone Radius / 3 OR 8 / Diametral Pitch. In this case the optimal face was 0.278. Here's the catch. The face length is not with respect to the surface of the part, its in relation to the pitch line. In this case, the actual linear distance was solved as a trig problem and because the angle is just a few degrees, it's only a few thou different. Anyhow, I cut the Z length down to preserve the OD and get the desired face length. This was done while it was in the lathe.

IMG_20180519_055248.jpg


Part dimension are good. Now for the mill…

The cutting angle defined earlier was 3.1251 – 45 = 41.8749 degrees.



If you look at the top picture of the diagram, this time, the axis of measurement is the same as the axis of cutting so, you don’t need to “flip” the angle around as was done with the lathe. This is a top view of the mill table. The table moves back/forth in the Y direction to make the cut.
MillSetup.JPG

There are lots of ways to set angles on a mill. Here’s how I when a critical setting is needed. I’m all ears if anyone has a easier/faster and more accurate way of doing it.

Look at the second picture in the image above. To setup the angle, put a straight shaft in the rotary table and eye-ball it to 41.x degrees. Touch an indicator to the shaft at point A then, zero your DRO (or dials) then, move back to point B exactly 0.5000 inches. Then, move to point C just until the indicator touches. Since 0.5/tan 41.8749 is 0.5578, if the angle is perfect, the Y axis will read 0.5578 just when the indicator touches at point C. Adjust the angle and repeat as necessary. Last night, I had to do this about 10 or 12 times and then check it a couple more times after that. Things are going good if the process is repeated and the DRO is showing values within a thou of calculated.


IMG_20180519_123008.jpg


For this, the gear the bore ID’s are 3/8” and I made a special “arbor” to hold them. Just a piece of junk out of the junk pile but, it was a very precise fit. Last thing I do is indicate and make sure it spins true. In this case, TIR was surprisingly good and within 1 thou (you get lucky sometimes).
IMG_20180519_065732.jpg


In this case, with 30 teeth, it was just 3 cranks w/no extra holes. -How nice!


Here is something absolutely critical: The "Virtual" tooth gear cutter must be determined. This is a 30 tooth gear but, you cannot use the cutter for a 30 tooth spur gear. Virtual Gear Cutter = #Teeth / cos (pitch angle) in this case: 30/cos 45 = 42.4. Round-up the number properly then you must use the gear cutter for a 42 tooth spur gear even though this gear has only 30 teeth.

The centerline of the cutter was found using the same technique shown in how to cut spur gears. Before really cutting, I make a light test cut to make sure the line gets wider. It's hard to see in this picture, but it does get wider. This verifies the angle is set in the right orientation.
IMG_20180519_124012.jpg

The table is cranked in until the cut depth is reached which was calculated in the first part as 0.0849.

If you do all the setup properly you only need to make one pass. When using the proper cutter and when setting the addendum and dedendum angle properly, you only make one pass. If the gear does not fit when done, you did something wrong.

So, buzz, buzz, buzz... It took about 55 minutes to actually cut both these gears.

IMG_20180519_111623.jpg

When done, they needed just a little deburring. As expected, the HSS cutters had no problem at all cutting Rc32 metal.

IMG_20180519_151850.jpg

Even though the outer faces of the gears are NOT 45 degrees, they press together perfectly and make a perfect 90 degree angle. That's because the outer edges (defined by the cut line) are resting on the axis defined by the addendum and dedendum line. In this picture, if I were to remove the square, the gears would stay locked together in a perfect 90 degree angle.

IMG_20180519_132935.jpg

So, the only drawback to using generalized cutters for miter gears, is the very tops/edges of the gears endure some friction. If the gears were cut with cutters dedicated for that number of teeth, friction would be at it's theoretical lowest value.

So, that was fun... Hope you enjoyed the show. I wanted to get this over with and may have forgotten something. Let me know if I did.

Ray

IMG_20180519_111623.jpg

IMG_20180519_112745.jpg
 
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Ray C

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Oops... I just realized that a small detail was left out regarding cutting depth. As mentioned, the calculated tooth depth is 0.0849". That is measured at the rear of the tooth but, you have no real way to measure it because the physical geometry is somewhat abstract. Once setup, the tooth depth is generated by motion in the Y direction, influenced by a position set in the X direction. Solution: Math. This was not mentioned in the Machinery's Handbook because physical implementation is left up to operator. After a few minutes with pen and paper, it's obvious, the amount of X Feed once the part is touched off at the back end = Tooth Depth x Cos Pitch Angle. In this case: 0.0849 x cos 45 = 0.0600".

This, BTW, is just as critical as all the other precise measurements and setups in doing this. If you start messing around with manually tweaking the depth, it will be game-over and the gear won't hold the 90 degree angle when simply rested and balanced like this.

Those 2 gears have a happy spot where one just perfectly interlocks and rests on the other. When in-use of course, a couple thou of backlash space is needed.
IMG_20180519_205637.jpg

Earlier, there was a discussion about off-setting the angle and making 2 or 3 passes. Upon digging into this and reaching back into the memory bank, those techniques are used mainly when hand-ground "fly-cutter" like shaping tools are used. Because the tools are usually cut at 60 or 75 degree angles (similar to a HSS threading tool), the offsets and multiple passes are needed for cutting gears.

You don't need to do that when using rotary DP or Module-type cutters.

Ray
 

benmychree

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Read Brown Sharpe's book "Practical Treatise on Gearing" You will find that there is no mention of using fly cutters to cut bevel gears, and that special bevel gear cutters of the multi tooth type are used, and have a narrower point than ordinary involute gear cutters due to the geometry of a bevel gear as opposed to a spur gear, and that the only method set out is the rolling method to arrive at a shape of tooth that in usable, even then, filing the teeth must sometimes be resorted to for a smooth running gear. What you state in the last paragraphs is simply not true, do some reading by the people and companies who were the basis of the industry that we have today, not one's "memory bank".
 

macardoso

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Ray,

Thanks for the amazing write up. I may have to venture into gear cutting yet!

Benmychree, I'd be interested in the 3 pass method you desribed, can you explain how to do this? Also is filing required for commercially made bevel gears? That seems expensive and labor intensive.

-Mike
 

benmychree

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The best thing to do in reading about the three pass method is to resort to Brown & Sharpe's book that I referred to above, I think you could access it on line. As to filing regarding commercially available gears, it is not necessary, as they are made by a generating method that generates a correct tooth shape, something that a milling cutter can only approximate. Try searching "bevel gear generator".
 

Ray C

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Read Brown Sharpe's book "Practical Treatise on Gearing" You will find that there is no mention of using fly cutters to cut bevel gears, and that special bevel gear cutters of the multi tooth type are used, and have a narrower point than ordinary involute gear cutters due to the geometry of a bevel gear as opposed to a spur gear, and that the only method set out is the rolling method to arrive at a shape of tooth that in usable, even then, filing the teeth must sometimes be resorted to for a smooth running gear. What you state in the last paragraphs is simply not true, do some reading by the people and companies who were the basis of the industry that we have today, not one's "memory bank".
Please read more carefully, I did not say fly cutters. -Read carefully!. Also, you are simply wrong about the only method set out is the rolling method -Period. Also, the technique I outlined is customized for the case of miter gears -not the generalized case of bevel gears. Once again, please think before commenting. If you are concerned this is coming from my memory bank, you'll be happy to know that absolutely everything outlined in these techniques comes from the 28th edition of Machinery's Handbook particularly the pages between 2086 thru 2090 and 2211 thru 2144. Rather than taking unsubstantiated reckless pot-shot statements about gear making, I took the time to take credible resources and distill the information down to a format understandable by someone interested in the topic. -And I urge you... please read the very first paragraph of the first post of this thread.

The implication that these gears are all wrong is amusing. The proof is in the pudding, the techniques outlined in my thread produced gears that work -and work very well. They were used in a test setup last week which is the beginning of another long term thread I'm working on that will outline how to make spirals and other forms. When I finally produce those spirals, show how they're made -and show them in operation, I guess I'll have to put-up with another post with wild pot-shots about how it's all wrong.

Ray
 
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benmychree

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I stand by all that I have stated, and quote from authority, you might do well to read their book.
 

Ray C

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I stand by all that I have stated, and quote from authority, you might do well to read their book.

Likewise -and rather than just making farting noises in the back of the classroom followed by stating the names of some books, please take 10-15 hours of your personal time, to execute, photograph and write-up a live demonstration. And maybe it will be my turn to embarrass myself with some pot-shot statements at someone else's expense.

Ray
 

benmychree

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Personally, I feel no embarrassment regarding anything that I have stated; I have worked at the machinist trade all my working life, nearly 55 years, served a state supervised apprenticeship and have operated a successful machine shop business for about forty years, and believe that my statements have been well informed and substantiated by written authority. I have never been good with documenting a project, I'd rather just get the job done with and out the door, and get paid for it!
I am going to re read the book, and urge you to read it as well. There is nothing wrong with disagreement, as long as civility is observed, as it has been thus far.
 

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Personally, I feel no embarrassment regarding anything that I have stated; I have worked at the machinist trade all my working life, nearly 55 years, served a state supervised apprenticeship and have operated a successful machine shop business for about forty years, and believe that my statements have been well informed and substantiated by written authority. I have never been good with documenting a project, I'd rather just get the job done with and out the door, and get paid for it!
I am going to re read the book, and urge you to read it as well. There is nothing wrong with disagreement, as long as civility is observed, as it has been thus far.
Be apprised, I come from a family of tradesmen and respect their lifetime of hard work -as well as yours. In the context of this exchange, your work experience is totally irrelevant. So far, I have posted and documented a process that describes the basics of miter gears and how to make a basic miter gear. The process is outlined in a book precisely cited numerous times. You have made statements indicating what I have presented is wrong but, you have not cited specifically what it wrong. -That's because nothing is wrong. The objectives, boundaries and limitations were stated up-front. In this regard, you are clearly demonstrating you don't actually read what is written. And in my world of professional engineering, you're allowed to make that mistake only once. This is getting old... Please... If you wish to convey different information about gears, do it in a thread of your own. You infer constructive criticism... Please point-out to me what is constructive about what you said. -And perhaps I should "undelete" some of your posts that the other administrators deleted. Please think before you post.

Ray
 

Ray C

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All,

Enclosed is the PDF of "Practical Treatise on Gearing" that has been mentioned in the preceding posts. It is indeed a good read, very short of about 130 pages discounting the appendices of trig constants etc. I just finished reading the sections on spur and miter gears. The beginning parts of the book pertaining to spur and miter gears, appear to be similar in nature to the abbreviated/simplified content written here.

I believe in my write-up of spur gears, or perhaps somewhere earlier in this thread, it was mentioned there are many techniques and standards which may be used to modify the shape of a basic, involute gear. The paper "Practical Treatise on Gearing" appears to go into some of the early methods being considered on how to improve the shape of a gear tooth. Be apprised, the book has publish dates ranging from 1886 to 1911 and thus, the final version was written long before the SAE (and later AGMA) finalized the standards on gear tooth shape. In that timeframe for example, Whitworth threads (introduced in 1844 and ending about 1955) were still in use. I would be hesitant to recommend "Practical Treatise on Gearing" to learn about the now-advisable ways of modifying gear teeth. -And to be perfectly honest, I am not conversant on the latest developments there. I am a member of the IEEE and ASME -but there is only so many hours in the day to keep up on things.

To clarify once again, the techniques I conveyed in my thread were about basic miter gear geometry with a basic involute tooth surface. It makes a technically correct and perfectly functional gear for low speed use -much the same quality and efficiency as the change gears on your manual lathe.

Finally, my hat goes off to all the engineers of over a century ago, who sweat their brains out figuring this stuff out. I also respect the folks who toiled behind machinery trying to actually make the darn things.

Regards

Ray
 

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Eddyde

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Ray, Thanks for the excellent write up. I would have never thought possible to make such gears but after reading this I feel confident I could, if the need should ever arise.
 

Ray C

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Ray, Thanks for the excellent write up. I would have never thought possible to make such gears but after reading this I feel confident I could, if the need should ever arise.
LOL: I don't normally give professional advice on public websites. My PE insurance underwriter doesn't appreciate it. For you Eddy, I'll break my own rule.

Here you go: McMaster-Carr https://www.mcmaster.com/#miter-gears/=1d0bpi1 Same exact gears...

Ray
 

benmychree

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All,

Enclosed is the PDF of "Practical Treatise on Gearing" that has been mentioned in the preceding posts. It is indeed a good read, very short of about 130 pages discounting the appendices of trig constants etc. I just finished reading the sections on spur and miter gears. The beginning parts of the book pertaining to spur and miter gears, appear to be similar in nature to the abbreviated/simplified content written here.

I believe in my write-up of spur gears, or perhaps somewhere earlier in this thread, it was mentioned there are many techniques and standards which may be used to modify the shape of a basic, involute gear. The paper "Practical Treatise on Gearing" appears to go into some of the early methods being considered on how to improve the shape of a gear tooth. Be apprised, the book has publish dates ranging from 1886 to 1911 and thus, the final version was written long before the SAE (and later AGMA) finalized the standards on gear tooth shape. In that timeframe for example, Whitworth threads (introduced in 1844 and ending about 1955) were still in use. I would be hesitant to recommend "Practical Treatise on Gearing" to learn about the now-advisable ways of modifying gear teeth. -And to be perfectly honest, I am not conversant on the latest developments there. I am a member of the IEEE and ASME -but there is only so many hours in the day to keep up on things.

To clarify once again, the techniques I conveyed in my thread were about basic miter gear geometry with a basic involute tooth surface. It makes a technically correct and perfectly functional gear for low speed use -much the same quality and efficiency as the change gears on your manual lathe.

Finally, my hat goes off to all the engineers of over a century ago, who sweat their brains out figuring this stuff out. I also respect the folks who toiled behind machinery trying to actually make the darn things.

Regards

Ray
My copy of "Practical Treatise on Gearing" is dated 1920, and my Copy of "Practical Treatise on Milling and Milling Machines" from my apprenticeship days, dated 1963 ( $ 1.25 paper cover, $1.75 cloth cover), lists other publications by Brown & Sharpe, including the Practical Treatise on Gearing as still being published at that time "Contains tables and illustrations, and is written for those who wish to obtain practical explanations and descriptions for making gears". The price at that time is $1.25 for paper cover and $1.75 for cloth cover. Also listed is "Formulas in Gearing" a supplement to "Practical Treatise", cloth $1.75. I have not seen a up to date copy of either of the two to know if they were updated or not in the later editions.
 

rdean

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I made a set of gears using your write up and even though they did not turn out as well as yours they will be just fine. I have tried several different ways of making them over the years and these are the best yet.

GEDC3613.JPG

Thanks
Ray
 
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