Gear Hobbing computations assistance requested

I kindly request some help in calculating gear blank diameters for a worm gear I am trying to cut.

I am still busy with my Polar arm 3D printer, which has as drive train a stepper with a 20 tooth gear, and the arms with a 170 tooth gear - 8.5:1 ratio, This is still way to high and the only practical way forward, due to structural implementation constraints on the machine, is to place the steppers at right angles and drive by means of a worm gear. The idea is to hob into the existing 170tooth gear and make a mating worm to drive said gear.

The 170tooth gear is a large model helicopter rotor drive gear, plastic, but tough as nails. The Hob is a re-purposed tap - a 5/6 BSW-11 tap, which I have re-ground on the T&C grinder, to have well raked cutting edges. It cuts the plastic beautifully..

The tap - 11 TPI 'almost' mates with the existing 170 tooth gear. That gear is 120mm OD. I am un-constrained in actual gear diameter as well as actual number of teeth on that diameter - that is taken care of in the printer software.

So, as I am not aiming for s specific number of teeth or gear diameter, this should be easy...Nope....

I have spent many hours trying to work out the match between what I have, the number of teeth I can fit, DP, Addendum, pitch and Base circles, Outside diameters, etc.....I came up with 168 teeth on a Gear blank OD of 118mm.

Some of the constants for the calcs were an intelligent guess though - I do not have such good data on the Tap teeth

I wish to use the existing gear and just hob it to size, so to speak, with the result hopefully being around 118mm OD, and 168 teeth - having cut away all the old 170teeth in the process.

I made test blanks, 200mm OD, and started to hobbit..I stopped with an OD of 112 mm, and lots of missing teeth...

I tried 5 more blanks - set the No teeth to 165, 166, 167, 169, 170 - still a disaster!

I expected to see teeth being obliterated with multiple full blank revolutions while the blank diameter was incorrect for that tooth qty selection, and that tooth erosion begin to cease the deeper I cut, ie, as the blank diameter supposedly approached the correct one. I all cases I approached a final blank diameter of 100 to 112mm (from 200mm!!) with no sign of anything looking to work.

I am not sure how to proceed!

Joe

Joseph,

The tap will never give you the correct profile to match your existing gear.

If you are free hobbing gashing the blank first is supposed to drive the blank at the right speed.

Dave,

Perhaps I have not explained correctly.

I am not truing to match the existing gear profile - forget that it has 170 gear teeth already on it - consider it to just be a blank disc into which I wish to hob teeth, the shape or profile of the 5/8 BSW hob. I want a final diameter between 110mm and 120mm, with tooth count between 150 and 170 - thats it...The profile will match my worm ' good enough' 'cause that I will cut to 5/8BSW.

I am not free hobbing - I am using a hobbing machine - well, my rotary table and my Hobber controller..

I will take photo's of the actual job and post tomorrow..

Joe

So you ran the mill at 146 rpm while your table went 1rpm and it still came out wrong. If you look at the link, the bottom left drawing shows the involute shape generated by the non involute shape of a hob. So you might be generating the correct tooth form for the tap

link

Hi Joe

Try 123.48 mm as the Pcd for 11 tpi tap and 168 tooth.

1.000 inch / 11 = 0.09090 inch x 168 = 15.272 inch
divided by Pi = 4.8614 inch = 123.468 mm
As this is is the pcd you would need to add
some extra about .059 inch or 1.5 mm for the OD size and
some additional material if you want the wheel to wrap
around the worm.

It is fairly close to your 118 mm size.

John

John, Thanks for your input. I think I am missing something though!

You indicate PCD=123.4mm +1.5mm for OD + wraparound : I understand your reasoning there, but that's not close to 118mm as you say it is ?( which I had worked out I need for my blank OD) -

If your reasoning is sound, I need to reduce the tooth count by a good few teeth to fit within my 118 to 120mm blank, it seems.

No teeth = (PCD x Pi)/ 1/11TPI .

So for PCD = say 118mm, and 11TPI = 2.30909mm

No teeth = 118 x Pi / 2.30909 = 160.5 teeth.

So I need to choose 160 teeth and that should get me close to a PCD of 117.6mm, and therefore a blank of 120mm should be ok for wraparound, etc.

Somewhere it seems I just messed up the calculations and came up with 168 teeth, but what surprised me was that even in cutting down more and more on the blank - till 112mm OD, I still did not get a balance of teeth into the blank!

I think I need to do it again and be more observant to try see what is going on!

Joe

Hi Joe

I just picked out the 168 tooth as an example , i think that when you
try to hob down to a size and get a tooth count in the way that
you tried it is easy to run through and past the diameter you need.
The situation when hobbing with a tap is more critical than
when using a gear cutting hob because of the shape
of the thread profile .
I had cut a similar type of wormwheel only a few day's ago with a
5/16 unc tap using the same calculation method and it worked out ok.
You just need to know how far to feed in from your 120 mm diameter
to get the tap in the correct place for 117.6 Pcd.

John

Thanks John. That all makes sense. Since I have to cut away the existing teeth on the 120mm OD, I think its safest to go for 158 teeth, which gives me the 117.6mm PCD. I have to do some setup though to get my measurement references correct to know exactly where the tap cutting edge is in relation to the pitch line.

Thanks again!

Joe

Joe if you get a 35dp hob it will come very close indeed to your 90 thou pitch (It's one thou per pitch different). Then you can turn a proper acme screw to drive it.

What are you doing about removing backlash?

Hello Pete.

I am very new to hobbing so do suffer from lack of understanding! I built the electronic control for the rotary table and implemented a hobbing function which I believe works correctly - a duplicate of this setup was built by another member and he used it to successfully make some gears. At least that eliminated any underlying software issues!

So the problem lies just with my understanding!

Pete, if I extrapolate your 1 thou error, for a 158 tooth gear, it give a 4mm 'error; after once around the blank, so I would need to increase the blank diameter or reduce the number of teeth - the latter being no problem. The problem being obtaining said hob - complicated from where I live here in Namibia.. The forces and torque involved in the application are very low, speeds are very low indeed - the wheel max rpm is typically 1rpm, so the worm runs around 150 to 200rpm max. and accelerations are gentle.

The gear is either HDPE or Polyprop. and is quite slippery. I am hoping to achieve very low or no backlash simply by forcing the worm up hard against the driven gear and run it in so that they bed in and mate well, with a little of that very thick silicone 'oil' ( more like a 'solid' treacle!) on the gears.

Joe

In trying to have a better understanding of the formulae for gear cutting I used some of the various thread form charts for the BSW thread taps to determine thread pitch centerlines, etc. However, something is amiss in these charts - and this seems prevalent in ALL of the BSW charts.

The thread in question is 5/8BSW - the chart gives data in mm.

I am interested in dimension H1.

That should be equal to D minus d3 in the picture.

But D=15.876mm and d3=12.913mm - the difference being 2.96mm, NOT 1.479 as in the chart.

However, 2.96mm / 2 = 1.48mm, close to the chart H1. I do not understand the diagram reference as the dimensions d3 and D are from the thread axis and so the dimension H1 should just be the difference?

Where have I gone wrong?

Joe

Joe, D and d3 can't be from th ethread axis as D is shown as almost 5/8" it would be half that if taken from the axis.

Try this one which gives a formula for height of 0.640327 x pitch to get the height = 1.4785732mm

You may also want to look at Andrews post on worms and wheels, he also has another thread somewhere about using a tap as the hob

Edited By JasonB on 01/02/2021 08:19:59

This is the clearest diagram of the Whitworth thread form that I have yet seen:

https://en.wikipedia.org/wiki/British_Standard_Whitworth#/media/File:Whitworth_Thread.svg

**LINK**

MichaelG.

Edited By Michael Gilligan on 01/02/2021 08:23:20

Jason and Michael, thanks for that. Makes a lot more sense now.

I really thought cutting this worm wheel would be simple, but I am still battling.

I read Andrews post through prior to my post on this, and re-read it a few times this morning, re-looked at my calcs and went and cut another blank - not a success...

Cant see the wood for the trees now.

I hobbed another blank to test again, based on the following calcs, and with the results indicated.

From Michael's reference, I calculate the tap should penetrate about 1.9mm into the blank - (H-H/6).

I chose to cut 158 teeth which gives a PCD of 116.13mm. That 'should' give a blank OD of around 117.6mm.

I prepared a blank off 120mm diameter and started hobbing. I fed in from the periphery , which I think has an inherent problem - the No of teeth cannot fit into the periphery, and can only be correct at the PCD, so teeth started to be over-cut...( see copied text from Neil's post in Andrew's post on worm gears..)

Then fed in to full depth ( which should leave me with an OD of 117.6mm, - in the trough- no?) , but the teeth were still being over-cut or overlapped.

I continued to feed in slowly, and got to a point where now the teeth stabilised and were neat and uniform. I let the hobbing continue so that the blank had done maybe 50 or so rotations - the teeth remained clean and intact.

I removed the blank and counted the teeth - 158 teeth!

That was good, BUT...

I measured the now new OD of the blank ( at the crest of the teeth, but at bottom of the radius as cut by the tap - see 2nd photo) and the blank measures 112.5mm !! Nowhere near what should have been an OD of around 117mm.

158 teeth - counted a few times.

The OD here, across the outer edge, is close to 115mm

112.5mm OD - ???

My tap is a 5/8 BSW for sure. Engraved on the body, and I count 11 teeth in an inch.

I am at a loss!

Joe

Copy of Neil's comment:

Edit: thinking about it when the hob first contacts the blank, it's 'natural pitch' will want to cut two extra teeth at the OD than it will cut when advanced to the PCD. Perhaps a way around this is to have the hob fully advanced from the start and make the cut from the side of the blank rather than in from the edge. That way the hob's PCD will remain constant at the required value. Does that make sense?

Edited By Joseph Noci 1 on 01/02/2021 09:37:06

With small errors you'll get a slight deviation in tooth form but you will always get the number of teeth you asked for and they will always be evenly spaced when hobbing (or dividing, so long as you don't mess up in your indexing).

Afraid I did not understand that...I realise that with the driven HOB process, you will get the number of teeth, but that number of teeth will only fit properly on a circumference if that circumference is correct...And that is the issue here - I am trying to calculate what my gear blank diameter should be. If the diameter is not correct you simple erode all the teeth down to naught eventually while hobbing..

Posted by Joseph Noci 1 01/02/2021 05:51:47

Pete, if I extrapolate your 1 thou error, for a 158 tooth gear, it give a 4 mm 'error; after once around the
blank, so I would need to increase the blank diameter or reduce the number of teeth - the latter being no
problem.

Hi Joe

You do not need to adjust the size of the blank to allow for the 1 thou error,
as your hobbing unit cuts the number of teeth that it is set at , the 1 thou is
removed as part of the cutting action but is not accumulative ,it would
be a different matter if you were "free hobbing" as the tap would be driving
the work and would then end up with more teeth than required.
It is for this reason that most attempts at free hobbing unless they are pre-gashed
end up failing.

I should have pointed this out in an earlier post ,the sketch here shows
the PCD of the gear blank , the distance between the top of the
tooth of the tap and the root is divided and used as the reference for the pitch
line for the tap and the calculation for the in feed made from this.

Aliexpress have a fairly large range of gear cutting hobs and free shipping to
Namibia .

From your later post at 10:22:41

Afraid I did not understand that...I realise that with the driven HOB process, you will get the number of
teeth, but that number of teeth will only fit properly on a circumference if that circumference is correct...And
that is the issue here - I am trying to calculate what my gear blank diameter should be. If the diameter is
not correct you simple erode all the teeth down to naught eventually while hobbing..
-------------
No that is not true ,within certain limitations the pitch circle diameter can be altered for instance
herein this photo ,the outer ring has 36 tooth in order to fit 3 equally spaced gears the sun
gear has to divide into the 36 by 3 in order to do this.This could be 6,9 or 12. As 9 was chosen the planet gears need to be 13 tooth .
Fitting these in diametrically opposite leaves a space for a 10 tooth gear,in order to fit in this
space the sun gear has 9 teeth cut on a 10 tooth blank ,the effective pcd has changed
along with the profile shape of the tooth which just uses a different part of the the same involute
curve.

Getting back to your gear for 158 tooth on a pcd of 116.13 mm the normal od 117.60 mm
the blank od should be 118.87 and the tap/hob should in feed from this diameter by 2.159 mm.
The cut width across the face of the gear at this should be as measured 10.80 mm .

I think that these measurements agree with what you have ,the sides of the teeth will always
be degraded to some extent but should be clean within the working zone

John

That's the point you will not erode all of the teeth because you're not relying on spacing but on indexing. The 4mm error is spread between the teeth but it's not added together to leave a gap at the end. On the first turn you have 158 indexes, on the second turn you have 158 indexes, and so-on. After ten turns you'll still have 158 indexes and each one will be in the exact same place as all the other turns.

This is how profile-shifting is used to reduce under-cut on low tooth-count gears. You increase the diameter to change the tooth form.

EDIT: John beat me to it.

Edited By Pete Rimmer on 01/02/2021 11:43:08

Wow, thats all way to much for me! I need to read all that a few times and try understand - I think I have a problem in grasping some fundamental issue here, and so the rest will not fall into place.

I dont quite follow the concept of the 'index' position - If this was a single point cutter, and I indexed the rotary table 158 times around the blank, spending time at each index position to cut the tooth, then I agree, the cutter can only fit into a slot that is one of the 158 index positions.

But in hobbing with a helical hob ( the tap) there are no 'individual' index positions. The only criteria is that a gear tooth crest must always line up with a hob trough as both rotate. Now if the gear blank diameter is too large, the 158 teeth will fit into a shorter periphery ( since the pitch of the hob did not change), and although the hob tooth should then mate with the periphery tooth 1 again, it actually cuts fresh blank - ie, putting more teeth on the blank, in the extra circumference. The chance that when the hob meets the original tooth 1 in the blank, that it mates with it, is pot luck...and so the teeth begin to be cut on top of each other and erode.

That does happen, I watched it many times over 5 or 6 blanks, and only ceases when the blank diameter is correct for that pitch hob.

I believe I understand your comment John:

,the effective pcd has changed along with the profile shape of the tooth which just uses a different part of the the same involute
curve.

But does that not only apply if you are changing by one or two teeth, sort of thing, ie, a small change to fiddle the result?

John, then what gets me is - refer your comment:

Getting back to your gear for 158 tooth on a pcd of 116.13 mm the normal od 117.60 mm
the blank od should be 118.87 and the tap/hob should in feed from this diameter by 2.159 mm.
The cut width across the face of the gear at this should be as measured 10.80 mm .

I think that these measurements agree with what you have

If those measurements are correct, why did my final gear, with 158 teeth around it, apparently neatly spaced and formed, result in a final blank OD of 112.5mm?

Should that not have been 118.87mm - 2.159mm, ie = 116.71mm??

112.5mm is quite some ways from 116.7mm!

Also, can you please explain where this dimension is taken:

The cut width across the face of the gear at this should be as measured 10.80 mm .

I am battling with this indexing versus spacing thing!

Pete, you said -

That's the point you will not erode all of the teeth because you're not relying on spacing but on indexing. The 4mm error is spread between the teeth but it's not added together to leave a gap at the end. On the first turn you have 158 indexes, on the second turn you have 158 indexes, and so-on. After ten turns you'll still have 158 indexes and each one will be in the exact same place as all the other turns.

Surely that is only possible if the gear blank periphery is divided into 158 equal spaces ( the teeth)? And since these spaces are directly related to the pitch of the hob, we surely have little room to fiddle the space size? And then, to fit 158 indexed positions , related to the hob pitch, equally around the blank, we need to have the blank the correct diameter.

I am sure I will see the light soon..!

Joe

All that happens is that the profile of each tooth is slightly different. If you go bigger on th e OD you get more tooth and less gap, smaller you get less tooth and more gap. This is why gears are specified at PCD - the tooth and gap are equal there.

If fairness, because you have the facility the best thing to do is what you say - adjust the OD/PCD to suit your cutter's pitch. Then you don't have to worry about it.