I ran across this book, which can be downloaded in PDF format:

**LINK**

I am slowly learning the terms associated with helical gears (unfortunately I am a very slow learner).

The chapter on spiral (helical) gears begins on page 323.

From the above book, page 324:

the distance between two corresponding points of two adjoining teeth, measured in a direction at right angles to the direction of the teeth, is called the normal pitch. The normal section, which would give us the normal pitch, would show us the true section of the teeth. A section, taken at right angles to the axis, would give us the dis- torted view of the shape of the teeth as seen when looking at the end of a spiral gear. A section through the axis would also give a distorted view.

Perhaps I am overlooking it, but there does not seem to be an example anywhere that shows two gears of the same size, with shafts at 90 degrees, with helical angles at approximately 30 and 60 degrees, nor any explanation of the speed difference of the two shafts if configured this way. Is it suppose to be obvious? It is not to me.

I was under the assumption that a special gear cutter would be required for two of the same sized gears at 90 degrees, with varying helix angles, but apparently a stock gear cutter can be used?

The article referenced in the post above shows a relatively simple method of cutting helical gears using a lathe and a spiral ramp.

While I would like to be able to machine helical gears if required, I would much prefer to just design the gears in Solidworks, 3D print them, and then cast them (I believe I can make castings accurately enough to make this method work, and have seen the work of others recently that makes me believe this).

And as mentioned previously, 3D printing gear patterns frees me from having to use a specific gear cutter size.

I think Jason is on the right path (no pun intended).

I will give that method a try.

Since the gears can be 3D printed, then the correct mesh can be verified.

I am still hazy about the exact angle of the two gear helix.

If the angle is off slightly, does that mean that the two shafts will not remain synchronized? but instead one shaft will rotate slightly too fast, thus throwing off the engine timing?

I do think we are making progress, and thanks very much to those contributing to a solution for this gnarly problem. I am becoming more optimistic that a viable solution can be found.

.

Edited By PatJ on 31/01/2021 06:02:02

Edited By PatJ on 31/01/2021 06:03:12

Edited By PatJ on 31/01/2021 06:03:51

I attempted to cast a pair of full-sized gears for a windmill restoration, and was not successful due to mold failure, but I believe that if I had heated the 3D printed gear pattern to the point where it was soft, I could have successfully removed it from the bound sand.

This began a discussion on another forum about how it was done in the day, and so I looked at my photos from the Soule Museum in Meridian MS (USA), and there were a great number of gear patterns.

The question was raised , and I think it is a fair question "Why cast a gear? Why not just cut a blank and then use gear cutters to cut the teeth?".

My guess is that back in the day, it was far easier to cut gear teeth in wood, and then cast the gear.

A cast gear would probably only require minor cleanup and cutting to get it the exact size, and so a great deal of machining would be eliminated for every gear produced if a cast gear was used.

Back in 2012, I wanted to make castings in gray iron, and "they" said "you can't do that in a hobby setting".

"They" were wrong. Then they said "Well if you do make an iron casting, it will have inclusions, and will have chilled spots that are too hard to machine". "They" were wrong again.

I must admit I was a member of the "they" group, and I did not believe it could be done on a hobby level either.

But the proof is in the pudding, and as I have mentioned to some non-believers, come over to my house and I will demonstrate first hand how it is done, and you can drill and machine the parts yourself and see how easily they machine with no chills or inclusions. I can repeat that on any given day.

Then someone came up with the "lost-PLA" method, which is to 3D print a pattern using PLA filament, then coat it with multiple layers of ceramic slurry, burner out the PLA in an electric kiln, and then cast the part or parts in the same fashion as the lost-wax method.

I said "there is no way this will work". I was proven wrong, and someone sent me samples of a small part which had the surface finish and accuracy of a die-cast part, but in gray iron. I drilled the thin samples, and they drilled perfectly with no chills or inclusions.

I have not tried the lost-PLA method, since I think I can cast a sufficiently accurate gear with resin-bound sand.

The ceramic slurry has a given shelf life, and so that is another reason I have not tried it yet.

And the lost-filament (ceramic shell) method is a multi-step method (multiple layers of shell, burnout, etc), and so is far more time consuming than making a resin-bound mold, which takes perhaps 15 minutes total.

And there is 3D printer filament that supposedly will burn out very cleanly, and it is described in this video.

The accuracy of parts made using the lost filament method is phenomenal (in my opinion), and infinitely easier than the lost wax method (also in my opinion, not having done either though).

Edited By PatJ on 31/01/2021 06:56:55

Edited By PatJ on 31/01/2021 07:02:26

Gear patterns from the Soule museum (where the Speedy Twin steam engine was manufactured).

And here is my failed attempt to cast a pair of full sized windmill gears.

This was not my pattern, and I only had one pattern, so I could not heat it up to get it soft enough to get a clean removal from the sand.

I actually think I could have cast a gear with this mold, but there was some mold cracking, and so I did not feel the casting would be accurate enough, and I abandoned the attempt.

The bound sand does produce a dimensionaly accurate casting, since the sand sets prior to the pattern being extracted, so the mold is a dimensionaly exact replica of the pattern.

The fact that there is no draft angle on the gear pattern is the reason why it would need to be heated to get it soft for removal from the sand.  I would have most of the center part of the gear pattern removable (the center part could be wood), and thus only a thin outer section with the teeth would need to be removed.

I do think this is a viable method though if the pattern can be sacrificed.

Edited By PatJ on 31/01/2021 07:12:12

Edited By PatJ on 31/01/2021 07:14:26

On a side topic, this is a preliminary (not complete) 3D print and screen image of the 3D model for my Speedy Twin frame/cylinder pattern.

This would probably be a good candidate for the ceramic shell process, assuming the passages could be worked out somehow.  There are a number of complex steam/exhaust passages that run across the top of this engine.  The core makers for this engine were masters at what they did.

This was printed on my Prusa.

Last photo is a full-sized Speedy Twin, for reference.

This seems to be a very unique engine, with its semi-balanced multi-D valves, and almost instant reversing without using a Stephenson-style link, and only two eccentrics.

The pressure on the D-valves is reversed when the engine is reversed, but through an extremely clever arrangement, the D-valve does not lift off of its seat when the steam pressure is reversed on it.

Edited By PatJ on 31/01/2021 07:20:46

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Edited By PatJ on 31/01/2021 07:32:18

I'm fascinated by the history of technology too. Gears go back a long time, and the sophistication of the 2000 year old Antikythera Mechanism surprised everybody!

However, for centuries the main use of gear wheels was in windmills and watermills grinding flour. Millwrights were agricultural, metal expensive, and so the wheels and teeth were both made of wood.

At first simple round rods, later more accurately shaped teeth. Early gear makers didn't understand the mathematics, but overtime wear tends to shape the teeth more-or-less correctly, and fairly good gears can be made by rule of thumb methods.

As wooden gears wear quickly and aren't reliably strong, there was obvious advantage in metal, at first just copying wooden methods, but later casting them whole.

'Fairly good' isn't ideal, and clock-makers were first to develop gears on scientific principles, looking for the optimal curves needed for meshing gear wheels to roll over each other. Clock gear tooth shapes favour low friction rather than power transfer, so industry stuck to traditional methods for many more years. Cast gears made with teeth of nearly the right shape were common. Far from perfect in that they were noisy, inefficient and wore out relatively quickly, but they did the job provided rpm was low. However, as industry demanded more power and speed, cast gears became less popular. By this time, the maths needed for power transfer rolling curves was well understood, so industry moved to gear cutting. Understanding the maths also made it possible to develop special purpose precision gears, opening the door to all sorts of mechanisms. Cut teeth are all correctly curved, the gear is uniformly strong, and the metal is tougher and harder than cast-iron. And accurately shaped teeth wear slowly and are quieter.

Quieter, not quiet! When motor cars appeared, the appalling racket made by their gearboxes was a serious problem. No one cared if working people were deafened in factories, but rich people wanted better. This led to a second burst of research that slowly got rid of most of the whine and clatter made by plain gears. Again the answer is precision shapes, no simple cast gears in this gearbox:

I don't know if rough toothed gear blanks are ever cast in steel and then finished. It would reduce the amount of cutting, but it might be quicker and more structurally consistent to work with a round blank. Quicker because blanks don't need to be aligned in machines, and consistent because cast teeth aren't quite the same temper as the body. A Production Engineer would understand the trade-offs.

Excellent work by the way! Impressive mastery of several techniques. Thanks for sharing.

Dave

The angles need to add up to exactly 90 degrees (for a right angle drive). If they are 'off' the gears won't mesh correctly with the axes at 90° (think of trying to mesh spur gears with one axis tilted with respect to the other).

The diameter of each gear depends on the tooth count *and* helix angle for a given *normal* pitch. One is free to choose arbitrary angles (subject to them summing to 90° ) but the diameter of the resulting gears will vary. For the unique set of angles given previously, the gear sizes are identical with a 2:1 ratio.

Reduction ratio is set by the tooth count (only).

Edited By Andy_G on 31/01/2021 10:23:35

After encountering frustrations trying to get Fusion360 to draw a parametric involute, I've found this add-in by Ross Korsky which looks very promising:

Link

It also seems to include provision for adding clearance for 3D printed gears, etc.

Andy

______________________________________________________________

Relevant notes for interest:

General Usage Instructions

Once the add-in is running its button can be found under the CREATE menu.

Description of inputs

Gear Standards:

The true involute pitch and involute geometry of a helical gear is in the plane of rotation (Radial System). However, because of the nature of tooth generation with a rack-type hob, a single tool can generate helical gears at all helix angles as well as standard spur gears. However, this means the normal pitch is the common denominator, and usually is taken as a standard value (e.g. 14.5 deg or most commonly 20 deg). In other words if you plan to have your gear manufactured with a standard hob you will likely want to use the "Normal System" and a pressure Angle of 20 degrees.

Normal System: Pressure angle and module are defined relative to the normal of the tooth (i.e. defined as if the tooth was rotated by the helix angle). When defining a gear in the normal system changes to the Helix Angle will cause the gears diameter to change as well as the working thickness (and therefore the strength) of the tooth.

Radial System: Pressure angle and module are defined relative to the plane of rotation. When defining a gear in the radial system changes to the Helix Angle does NOT affect the gear diameter but it does change the "normal pressure angle" which may require custom tooling to have the gear manufactured (obviously this is not an issue if 3D printing the part).

Sunderland: The Sunderland machine is commonly used to make a double helical gear, or herringbone, gear. The radial pressure angle and helix angle are fixed at 20° and 22.5°, respectively. The tooth profile of Sunderland gears is also slightly shorter (and therefore stronger) than equivalent gears defined in the radial system.

Handedness: Direction the tooth appears to lean when placed flat on a table.

Helical gears of opposite hand operate on parallel shafts.

Helical gears of the same hand operate at right angles.

Helix Angle: Angle of tooth twist. 0 degrees produces a standard spur gear. The higher the helix angle the more twist the gear has.

Pressure Angle: The pressure angle defines the angle of the line of action which is a common tangent between the two base circles of a pair of gears. The short of it is this: leave this value at 20 degrees until you have reason to do otherwise - but know that any pair of gears MUST have the same pressure angle.

Module: The module is the length of pitch diameter per tooth. Therefore m = d / z; where m is module, d is the pitch diameter of the gear, and z is the number of teeth.

Teeth: Number of teeth the gear has. The higher the helix angle, and to some extent pressure angle, are the fewer teeth the gear needs to have to avoid undercutting. It is possible to create a Helical gear with a single tooth given a high enough Helix Angle. CAUTION: due to performance reasons, do not make gears with several hundred teeth.

Backlash: [experimental] a positive value here causes each tooth to be slightly narrower than the ideal tooth. In the real world having a perfect tooth is not often desired, it is better to build in a little backlash to reduce friction, allowing room for lubricant between teeth, and to prevent jamming. Backlash is allowed to also be negative which has no real world application I'm aware of but may be useful for compensating for undersized teeth which were 3D printed, etc.]

Dave-

Thanks much for the kind works and the interesting information.

That Antikythera mechanism was quite the piece of work. I am not convinced we know more than the ancients knew. And it makes you wonder what they knew and how far back they knew it before they created this mechanism.

Very humbling indeed as I struggle (unsuccessfully so far) to try and create two gears with a $1,000 computer and expensive 3D software, LOL.

Andy G-

Thanks for the gear information.

I keep reading about helical gears over and over, so that the terms can begin to sink in.

I must say I am helical-gear-challenged for sure, but I have not thrown in the towel just yet.

I tried JasonB's method, and the first gear went pretty well.

The second gear did not go well.

Solidworks seems a bit quirky with the "swept cut" command, and the typical options that I am use to on many other commands is not present on the swept cut command, such as extract from midplane, and the ability to use either positive or negative angles.

I will rest a bit and then try another approach.

.

These are the two gears with the profile downloaded from a supply house, with a 45 degree angle.

They appear to mesh correctly when I insert them into an assembly at a 90 degree angle.

And this is one version of my attempt at a swept cut normal to the path.

I tried several versions of the gear with fewer teeth, but no mesh.

It is obvious I am lost in space on this gear thing, but I will keep on chugging.

I feel like I know more today about it than I did yesterday, so there is that.

.

Edited By PatJ on 01/02/2021 18:44:24

Edited By PatJ on 01/02/2021 18:51:48

Edited By PatJ on 01/02/2021 18:52:24

Edited By PatJ on 01/02/2021 18:53:47

Now I see the button for toggling the angle of the helix from positive to negative.

I needed that last night.

It is difficult to learn every aspect of 3D software, especially when you are plowing fresh (frozen) ground.

The only way I know to learn 3D is to create things with 3D.

With each complete model, the knowledge base improves significantly.

.

Edited By PatJ on 01/02/2021 19:13:36

Pat your helix angles in the last image look wrong. The gear with the fewer number of teeth wants the 26.6deg helix and the one with double the teeth needs the 53.4deg helix which should get them looking better.

Jason-

Thanks. Looks like there are at least two methods for creating helical gears in Solidworks, and I have been using the more difficult method, and this has created some problems.

I am getting ready to try the second method, and I think it will work better.

(26.4 and 63.4)

.

26.6

I mis-typed.

26.6 and 63.4

The 45 degree gears will mesh because they both have the same helix angle, and hence the relationship between the normal and transverse modules will be the same for each. It looks like you're on the right path now - just getting the handedness & pitch angles the right way around.

If you appreciate the Antikythera mechanism, and have a day to spare....

Clickspring Antikythera Construction

Andy-

I showed my wife the Antikythera mechanism, and asked her some questions, such as "where did they get the metal to begin with, where did they get the tools such as hacksaws, files, drill bits, etc., and then where did they get the knowledge base (by direct observation of celestial events I guess).

We are spoiled these days. There are perhaps 10 hardware stores just in the city that I live in, and what cannot be had there can be purchased online from around the world.

Jason-

I am inching closer to a solution on the helical gears.

I have the handedness correct (both gears are the same direction).

The second Solidworks method works much better than the initial one that I tried, however, the second method does not give an option about rotation angle, but rather length of the path, with 1 being a 360 degree rotation around the part.

I have proportioned the length to the angle, but that does not give the correct result, but I can manually manipulate the path length, and it looks like I am getting close to a mesh, so that is good.

I will rest a day, and then verify that the gear with the fewer number of teeth has the 26.6 degree angle.

I may have the wrong angles on the gears.

I must say this is a good exercise in helical gear cutting in 3D, and would be very useful for cutting actual gears also. Too bad all 3D programs are not exactly the same, but most are pretty close, and close enough to generally follow how a part is created.

The Solidworks "helix/spiral" command has the options "Height and Revolution", "Height and Pitch", "Spiral", "Constant Pitch", and "Variable Pitch". I vaguely recall using this function to create IC engine spring models, using a variable pitch on the helix, and a circular section.

For "Cut-Sweeping" the gear tooth section along the helix/spiral path, I have the following options:

"Orientation/Twist type":

1. Follow path.

2. Keep normal constant.

3. Follow path and 1st guide curve.

4. Follow 1st and 2nd guide curves.

5. Twist along path.

6. Twist along path with normal constant.

I am using selection No.6 for this item.

I have tried each of these items, and it seems like No.06 is the only one that comes close to working, but I need to look at this further, and understand exactly what I am doing here.

There there is "Define By":

1. Degrees.

2. Radians.

3. Turns.

I am using degrees, and if the circular arrow button to the left of the degrees box is pressed, the angle is flipped to the opposite hand.

Lots of options, which is typical of Solidworks, and all very confusing at first, but once you make a part using the methods needed, then it is just a matter of making note of the exact settings that were used, or pulling up a previously made part and duplicating those settings (I don't have any previously made helical gear models, yet).

Better to have many options and not use them all than to have too few options and not have something that you may need.

I can see that this can most likely be worked out in 3D (by me).

Its always easy to watch someone else do things, and not so easy to duplicate that effort sometimes.  This seems to be true with metal casting also.

Looks like I used the 26.6 degrees for the gear with the larger number of teeth, so I will rework the angles, and try again tomorrow.

I owe you folks for all the hand-holding through this effort. Hats off to all of you.

I appreciate it.

.

Edited By PatJ on 02/02/2021 05:51:27

Edited By PatJ on 02/02/2021 05:52:07

Edited By PatJ on 02/02/2021 05:54:03

Edited By PatJ on 02/02/2021 05:54:57

A quick Google last night found a free app for Fusion360 that will generate helical gears and it's dead easy to use simply enter the few items in the box one of which is the helix angle and if the Module (or DP) is left the same it will produce two gears of the same diameter if you halve the number of teeth with teeth running at the two angles - you need to do it once for each gear. I'm not good enough at the CAD side of F360 to move them into mesh!

This could be very useful for those building small IC engines where the old sources of helical timing gears have dried up and it would be easy to generate a pair of gears and have them metal printed or investment cast for a reasonable sum

If doing the helical cut the pitch can be calculated quite easily with a bit of Trig as the circumference can be calculated and we know from rod the helix angles so the pitch can be worked out see image here

I got them to mesh and polished them up a bit while I was at it. The silver 15T gear on the crankshaft will drive the 30T gold cam gear giving the correct ratio.

Hi Jason - that’s the same one as I found (above). It does seem to work very well!

off topic: If you explore the Clickspring channel, he makes the metal, drill bits, files, etc. using contemporary technology. It really is remarkable.