Helical Gears

[jadge]

I am taking a short sabbatical from building my traction engines to have a go at designing and machining some of the more intriguing types of gears, and looking at the mathematics behind them. I've been rabbitting on about helical gears, and the mathematics behind them for some while, so I thought it was about time I actually machined some.

I started with a couple of helical gears intended to run on parallel shafts, which means that one needs to be right hand and one left hand. I like sensible size gears; 6DP and 24 teeth seemed like a good place to start, and a 30° helix angle, as that is within the capabilities of my universal mill but large enough to be interesting. Although the gears are imperial my mill is metric so I had to translate the lead into metric to see if it was close to one listed in the dividing head manual. Setting up the mill by swivelling the table and adding the dividing head and gear train from table to dividing head proved fairly straightforward. I ran the HSS steel cutter at 117rpm. The initial feedrate based on 4 thou per tooth was a bit ambitous, not least because the cutter was somewhat eccentric and was only cutting on two or three teeth. I ended up with a feedrate equivalent to about 1.6 thou per tooth. Here is the basic setup:



The gear train can just be seen on the extreme left. And before any smartypants points it out I know the dividing head is the 'wrong' way round. But that's how it worked out with the kit I've got and the way the gear pickoff is orientated on the mill table feedscrew. The gear was cut in one pass; material is low carbon steel, EN1A in English money. I had a few fumbles with the first attempt, I was relying on the grip of the dividing head chuck to resist the cutting forces; it didn't.  Hence the rusty spacer that can be seen to the left of the gear blank. Another important point is that it helps to tighten up the milling cutter arbor before machining.  Shown here is a close up of the cutting process:



The machine has flood coolant, so I used it. It's been a while since I used the horizontal mill and the coolant was mostly water, which meant that the EN1A rusted as you looked at it. I had to add a few yoghurt tubs of coolant before the refractometer registered a sensible concentration of about 7%. This is the finished gear, the OD is a tad under 5" and the face width is 1":



For cutting the left hand gear it is, in theory, a simple case of swinging the table the other way and adding an idler gear to the gear train to reverse the rotation direction of the dividing head. However, as seen here it isn't that simple:



To get access to the dividing head I had to move it across one T-slot, and add the home made risers so that the dividing plate cleared the table. I also had to move the milling cutter to it's outermost position. When I bought the dividing head I got a lot of the accessories, including the full set of gears, but I was missing one keyed sleeve and some internally threaded collars to hold the gears. Once the thread (non-standard at 7/8" 16 tpi Whitworth) was established it was pretty quick to knock out the required parts. The two black knobs at the bottom of the picture are for the table feed gearbox. There are 18 feeds in total, nine due to combinations of the handles and the feed motor is two speed. If I recall the feed motor is 1hp induction. That's a bit odd because all the feedrates are in the ratio 3:2 between high and low ranges. All I can think of is that the induction motor is pole switching between 6 and 4. Finally here are the two finished gears:



They seem to mesh well and the action feels very smooth. Centre to centre distance agrees with the maths too, at least as measured with a rule.

So having done the low helix stuff, how about a high helix helical gear? Clearly I can't do this with the same set up, as the table only sviwels ±45°. I also don't have the universal vertical head for my horizontal mill that is needed for low lead (aka high helix angle) milling. However, I reckoned I could achieve the same thing on the Bridgeport with a right angle head. That needed more adaptors to be made so that the gear train could be connected to the table leadscrew. In deference to the less rigid set up I chose to use 14DP with a helix angle of 70°. I chose 17 teeth giving an OD of about 3.7". That allowed me to make the gear blank from the middle of the foul up that was maquerading as the first attempt at making a helical gear. Here's the basic setup, for convenience in the gear train there is an idler, so the resulting helical gear will be left hand:



And a close up of the gear cutting in action:



Note the felt tip pen numbers; I always check the indexing before cutting. Been there, done that, and set the dividing head up incorrectly. For low leads it is recommended to turn the dividing head plate, rather than the leadscrew. That way the dividing head is driving the leadscrew through a reducing gear train. I didn't have much choice, as the feed motor on the Bridgeport didn't step up to the plate. it just sat there stalled. To get proper leverage on the dividing head plate and handle I used a bit of plastic tube. If I was doing this for real, rather than just as a fun exercise, I'd make a handle that fitted properly. Here is the resultant high helix gear, I'm quite pleased with it:



I had intended to leave the helical gears there and move on to other things. But I've decided to make a mating gear for the high helix gear for shafts at right angles. So the horizontal mill is now set up to cut a 14DP, 36 tooth, 20° helix, left hand gear.

Overall this exercise has gone quite well and I feel that I can now make helical gears if required, and more importantly to me I also have a basic understanding of the mathematics behind them. If I get really bored in the future I'll have a go at making a helical gear on the CNC mill. Milling helical features is not a problem, so it's just a matter of ploughing through the trigonometry to work out the toolpath for a normal endmill to form the tooth (space) shape in multiple paths.

For the purposes of this exercise I bought some cheap import involute cutters from a UK ME supplier. They're crapsky, although I can't say I'm surprised.  They all have eccentricities, and both the 14DP cutters have a noticable wobble as well as eccentricity. I haven't measured it, but it is very obvious visually, so probably 10 thou or so.  For the purposes of making these gears it didn't really matter, but I sure wouldn't use them to make gears for a proper project.

It is also entirely proper to make an acknowledgement. Although I sketched out the basics of the gears by hand I made extensive use of the Excel spreadsheet by 'Don1966' to quickly do trial and error calculations to get convenient lead values. I just added a couple of cells to convert the lead from imperial to metric. Thanks Don! 

Now onto internal gears. I've sorted out the mathematics of the internal gear tooth shapes and have designed an internal gear and pinion in 3D CAD. I 3D printed these last weekend and all seems to work as expected. I have a quick play with them every time I pass the dining room table.  I also have a measure of the interference problems that can afflict internal gears, and the mathematics behind it, but that needs a bit more work. I'm now designing from scratch an internal gear and pinion, but with a 20°PA. Once done I'll 3D print them again and then make them in steel, just to prove I can do it.

Andrew

[steamer]

That is awesome!    I've read up on all of this done on the mill, but it's the first time I've actually seen someone do it!

Bravo!

Dave

[Jo]

Well done,

Now onto internal gears. I've sorted out the mathematics of the internal gear tooth shapes and have designed an internal gear and pinion in 3D CAD. I 3D printed these last weekend and all seems to work as expected. I have a quick play with them every time I pass the dining room table. 

Another who has found an alternative use for the dining room table 


Andrew, you will have to bring them along with you to Stratfield Saye so I can have a little fondle 

Jo

[BillTodd]

Very nice (must have a go at cutting some spirals on my haighton someday )

Have you seen this use for a helical gear?

<a href="https://www.youtube.com/watch?v=KP-5OLpI9cg" target="_blank">http://www.youtube.com/watch?v=KP-5OLpI9cg</a>

[jadge]

Andrew, you will have to bring them along with you to Stratfield Saye so I can have a little fondle 

That's the plan; I've already mentioned to Clive that one table won't be sufficient. I'll have to let him know I also need space for a fondle section. 

Bill: I hadn't seen that video. I'm not convinced; I don't see how it is a worm drive? If it is treated as two high helix gears then it may transmit motion but I would think that tooth loads would be high for a given torque. I wonder if he's managed to patent it?

Andrew

[jadge]

Just for completeless I've knocked out a mating helical gear for the previous high helix gear. It's a small gear, less than 3" OD.  It is 14DP, has 36 teeth, is left hand and has a helix angle of 20° so that it mates with the high helix (70°) gear with shafts at right angles. Here's the gear:



And the two gears carefully balanced:



That's it for helical gears; on to internal gears. I've designed a 20°PA internal gear and pinion from scratch, including the involute form. I 3D printed them yesterday and all seems well, so the task now is to make them in steel.

Andrew

[BillTodd]

Just wondering...

if you designed a helical internal gear the helix angle might allow you to get in side the ciicle of the gear with a hob or cutter

[Don1966]

Very nice set of gears Jadge and I did enjoy the setup photos of how it was done. Thanks for sharing that with us........

Don

[Kim]

Hey Andrew, that's some really nice gear work there!  I'm barely getting spur gears to work right and you're off doing these fancy helical!   I had to go through your post several times to understand it, but that is supper cool!

Thanks for posting all your 'making of' pictures.  It really helped me see what was going on.  I doubt there are any helical gears in my near future!
Kim

[PStechPaul]

The mechanism in the video might work for very light loads, strictly by friction, but under load the drive gear would tend to drive the driven gears apart or together.

I think the smaller of the two 90 degree helical gears (driven by the larger high helix angle gear, which is like a worm), should have a concave tooth form similar to the worm gear of a lathe screw-cutting dial. It will probably work OK as is, but perhaps better with the profile to match the "worm" which is like a leadscrew. It may be possible to make a gear cutter (hob) by milling flutes on the teeth of the high helix gear and using the "free hobbing" method.

[Jasonb]

Nice work as usual Andrew

The Helical gears do not need to be shaped like a worm & Wheel they work just fine as they are, it is unlikely that the high helix angled gear would drive a worm anyway. These gears are often found on side shaft engine where they have been used for 100yrs or more. Andrew has another good thread on cutting worms & wheels with a home made hob.

I'm just waiting to see the size of the model side shaft Andrew has planned for these gears

[Zephyrin]

Thanks for showing all these setups !
very informative and pleasant thread, I learned a lot, even if I dont have the tooling to do that !

[jadge]

if you designed a helical internal gear the helix angle might allow you to get in side the ciicle of the gear with a hob or cutter

I don't think a hob would fit as the internal gear slopes the wrong way, into the hob. However I have seen pictures of internal spur gears being cut using an involute cutter mounted on a spindle that can reach inside the gear. With the correct linking of cutter and blank there's no reason why one shouldn't be able to cut an internal helical gear using such a system. As far as my setups go I should be able to do that using the right angle head on the Bridgeport. I would guess that the practicality would depend on gear size and helix angle, plus how far out the cutter could be on the arbor. Probably easier to suck it and see, rather than try and calculate anything. I'll put it on the list of things to try at some point. I think one would need to make a special cutter, as the standard involute cutters are not the correct shape, especially for small (<60) numbers of teeth.

Superficially the high helix gear looks like a worm, but it isn't and the mating gear does not need to be concave like a worm wheel. The ratio is 36:17, roughly 2:1, which is a lot lower than one would normally expect from a worm drive. If one views the high helix gear as a worm it is essentially a 17 start one. I've not seen a 17 start worm. The multiple start worms I have seen have a relatively low helix angle, so they look a little like a helical tooth slab mill, and are driven by the worm wheel not vice versa. Of course worms can engage with helical gears for low power and positioning systems, so I'm not sure where the distinction between a worm and worm wheel system and a helical gear system would be drawn.

I am happy to add a few practical notes that I learnt while making these gears. I centred the cutter over the gear blank by the time honoured method of trapping a ruler between cutter and blank and moving in Y until the ruler was adjudged to be horizontal. If I needed to be more accurate I'd touch off the side of the cutter on the side of the blank and then move the Y axis dial by half the cutter width, plus the blank radius, plus the thickness of the rod used to touch off. Of course that assumes that the cutter is ground symmetrically, but a quality one should be.

After cutting each tooth the process of getting ready to cut the next tooth is a bit of a palaver. Once a tooth has been cut the cutter needs to be reversed back to the start. The advice is to lift the cutter as otherwise backlash will cause the cutter to cut a different path on the way back. I can confirm that is the case if you don't lift the cutter.  When the dividing head is being driven by the table the division plate rotates along with the indent arm and fingers. In order to index to the next tooth independent of the table drive the division plate needs to be locked. To this end my dividing head has a small spring loaded spigot that engages with the division plate. The next tooth is then indexed in the standard way and the spigot pulled back to allow the division plate to rotate again.

If you don't remove the spigot before engaging the table feed something has to give, and I suspect that the spigot will break. Which is probably preferable to something expensive within the dividing head. Partly because it was quicker once I was ready to cut a tooth I advanced the table by hand until the cutter was almost engaged. This also gave a handy indication, ie, the table handle wouldn't move, if I'd forgotten to disengage the spigot.

Once I've set the cutter central on the blank I then touch of against the blank and set the Z axis dial to zero. I then wind on the calculated depth of cut, and set the dial to zero again. When I started to cut the helical gears I used to wind the handle exactly one turn back when reversing the cutter and then add one turn. But sadly I got confused and cut some teeth too shallow, which is retrievable, and some too deep, which isn't. So I got into the habit of turning the handle back just less than one turn to 0.2mm, one complete turn is 2.5mm. That way a quick glance would tell me whether I had the correct tooth depth set before cutting. If the dial reading was zero I'd put the cut back on, but if it was 0.2 I'd forgotten.

Andrew

[jadge]

Here's an exercise for the reader.

The two helical gears with axes that intersect at right angles are the same hand, both LH in my case. For the two helical gears where the axes are in the same plane one has to be LH and one RH. As the axes intersection angle reduces from 90º to 0º at what point do the gears change from the same hand to needing to be one LH and one RH?

Andrew

[gbritnell]

Hi Andrew,

 I don't think that question has an answer that you think it would. Ok, two gears with a 45 degree helix running either parallel or at right angles. As shown by the two gears that you have already cut as the helical intersection angle changes, 50/40, 60/30, etc. the limiting factor or should we say practical factor is when the steep helical gear has so many teeth that it becomes in itself a disc with parallel teeth. It never really reaches the point that it changes from parallel to right angle or vise versa.

 Two helical gears with an equal intersection angle will be able to drive each other, in other words one gear will be able to drive or be driven with equal loading. As the intersection angle gets steeper only one gear can be the driver because much like a worm and wheel the driven gear isn't able to (I don't know exactly how to say it) exert the proper angular pressure to make the driver turn.

 The original intent of helical gears was to eliminate the cogging action of spur gears (I believe that's what it's called) Although properly designed gears (involute curves) have a smooth transition form, tooth to tooth, they still only have (depending on the diameter) one or a couple of teeth engaging at any one time and that generates noise while helical gears with greater tooth contact are much quieter, even with tooth clearance. The down side to helicals is that they produce axial loads which must be addressed in the bearing loading. This loading also produces more heat.

 When I was building my model transmission I studied up on helical gearing and one of the unique things I discovered is that by changing the helical angle the ratio of two gear in mesh could be changed while still maintaining the same shaft spacing while with spur gearing when you want to change the ratio You have to add or subtract teeth which would alter the pitch to maintain the same shaft spacing, or give an undesirable ratio.

gbritnell