Gear Hobbing computations assistance requested

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Gear Hobbing computations assistance requested

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  • #523979
    Joseph Noci 1
    Participant
      @josephnoci1

      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

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      #33774
      Joseph Noci 1
      Participant
        @josephnoci1
        #523988
        Dave Halford
        Participant
          @davehalford22513

          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.

          #523991
          Joseph Noci 1
          Participant
            @josephnoci1

            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

            hobbing.jpg

            rotary table on mill table.jpg

            #524011
            Dave Halford
            Participant
              @davehalford22513

              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

              #524013
              John P
              Participant
                @johnp77052

                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

                #524016
                Joseph Noci 1
                Participant
                  @josephnoci1

                  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

                  #524022
                  John P
                  Participant
                    @johnp77052

                    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

                    #524026
                    Joseph Noci 1
                    Participant
                      @josephnoci1

                      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

                      #524028
                      Pete Rimmer
                      Participant
                        @peterimmer30576

                        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?

                        #524058
                        Joseph Noci 1
                        Participant
                          @josephnoci1

                          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

                          #524059
                          Joseph Noci 1
                          Participant
                            @josephnoci1

                            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.

                            bsw thread chart.jpg

                            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

                            #524063
                            JasonB
                            Moderator
                              @jasonb

                              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

                              #524066
                              Michael Gilligan
                              Participant
                                @michaelgilligan61133

                                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

                                #524073
                                Joseph Noci 1
                                Participant
                                  @josephnoci1

                                  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

                                  gear face.jpg

                                  112.5mm OD – ???

                                  od of gear.jpg

                                  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

                                  #524079
                                  Pete Rimmer
                                  Participant
                                    @peterimmer30576

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

                                    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.

                                    Joe

                                    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).

                                    #524083
                                    Joseph Noci 1
                                    Participant
                                      @josephnoci1
                                      Posted by Pete Rimmer on 01/02/2021 10:10:22:

                                      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..

                                      #524091
                                      John P
                                      Participant
                                        @johnp77052

                                        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.

                                        tap hob example.jpg

                                        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.
                                        internal 3.jpg
                                        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

                                        #524092
                                        Pete Rimmer
                                        Participant
                                          @peterimmer30576

                                          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

                                          #524103
                                          Joseph Noci 1
                                          Participant
                                            @josephnoci1

                                            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

                                            #524108
                                            Pete Rimmer
                                            Participant
                                              @peterimmer30576

                                              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.

                                              #524122
                                              Joseph Noci 1
                                              Participant
                                                @josephnoci1

                                                Pete, I believe I understand that. What I would like is achieve some level of agreement between the math and the 'gear' I hobbed. That is after all how commercial manufacturers make good gears! I don't need to be exact, but my gear at 112mm OD after hobbing seems that it should have been around 116mm – fudging is fine, but that is quite a difference. All I want is to obtain the calculated number of properly formed teeth on a sound PCD after machining. If that is a mm out from the calcs, OK, but 4mm is stretching it.

                                                The issue with adjusting the OD/PCD to 'suit' is that its done blind, ie, I start with a way oversize blank and hack away at the periphery till the teeth look good – not very scientific! And then I end up at 112.5mm OD, which is NOT what the maths says it should be – Rather what MY math says is should be – John intimated that my calcs were correct, but the result is not correct! So I was hoping someone can set me right with the math!

                                                Joe

                                                #524211
                                                John P
                                                Participant
                                                  @johnp77052

                                                  Hi Joe

                                                  Referring back to this here;
                                                  ———————————–
                                                  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 had made a small drawing of this gear the only important
                                                  features are the pcd which as calculated is 116.13 mm
                                                  which will have a normal od of 117.60mm

                                                  You can check this by the normal method for gears
                                                  by adding 2 teeth to the calculation.

                                                  For PCD

                                                  To recap 1 /11 = .0909090901 inch from my
                                                  calculator x 158 (tooth) = 14.36363636 inch
                                                  divide by Pi = 4.572087456 inches or 116.131 mm

                                                  For OD

                                                  Adding 2 teeth 1 /11 = .0909090901 inch from my
                                                  calculator x 160 (tooth) = 14.54545454 inches
                                                  divide by Pi = 4.62996198 inches or 117.60 mm

                                                  I have just left the numbers as the came off the calculator and
                                                  not rounded them off.

                                                  I think there is little doubt that this should be the size the
                                                  blank should be with no additions to increase the tooth depth.
                                                  The amount that i added ie (the blank od should be 118.87)
                                                  can really be any size within reason provided that you
                                                  ensure the cut depth is correct relative to the PCD and the
                                                  Normal OD.

                                                  Adding some extra material to the normal OD allows the
                                                  root of the tap to scallop out the extra diameter of the gear and
                                                  provides some extra material for the worm to work on.

                                                  You will continue to be able to cut the 158 tooth until that
                                                  you get to a point where the the tooth will eventually thin
                                                  out and completely vanish .I know i have done this
                                                  myself , i tried to cut just a few day's ago a 7 tooth
                                                  pinion but had not noticed that i had set 70 tooth,
                                                  i thought it was odd that i seemed to be cutting
                                                  a nice smooth groove where there should have
                                                  been teeth.

                                                  It has to be remembered that using a tap as a gear hob
                                                  will not produce a gear that will resemble a gear cut with
                                                  a proper gear cutting hob .

                                                  The 1 st photo here is a 90 tooth wheel cut with a 5/16 BSW
                                                  tap using the same calculation method it looks very similar
                                                  to your cut wheel.
                                                  These type of wheels are not well suited for power
                                                  transmission and may not be suitable for the application
                                                  you have in mind.

                                                  The 2nd photo here is a worm wheel that would be suitable to
                                                  transmit power cut with a 0.9 module hob and is overcut
                                                  the calculation for the size was about 53 1/2
                                                  tooth but was cut at 56 tooth ,the target tooth count was 60
                                                  but the tooth shape was becoming too degraded on a test piece
                                                  and 56 was about as far as i was prepared to go to be safe.
                                                  The difference in the shape of the teeth can clearly be seen
                                                  in comparison with a tap cut wheel.

                                                  John90 tooth  18 tpi tap.jpg

                                                  09 mod 56 tooth.jpg

                                                  #524214
                                                  Pete Rimmer
                                                  Participant
                                                    @peterimmer30576

                                                    To combat back-lash you could take two discs and fix them together. Hob your worm on the centre line then mill a couple of slots in the walls of the discs but make one slightly longer. Put springs in the pockets so that they try to rotate them relative to each other. That way both flanks of the worm will be loaded at all times regardless of the direction of rotation.

                                                    #524223
                                                    John Haine
                                                    Participant
                                                      @johnhaine32865

                                                      I'm just going to dive in here and probably hit my head on the bottom but…

                                                      If you were hobbing a gear you would set up the hob so its axis was parallel to the gear blank but not in the same plane, with the spacing between the hob axis and the blank axis such that when you feed the hob sideways, with both the hob and the blank rotating, the hob teeth will but to the full depth when the the hob has traversed right past the blank.

                                                      You can't do that with a worm wheel, but maybe you should be setting the hob axis co-planar with the blank and the axis spacing to get the required depth of cut, and feed the hob along its axis to engage with the blank? That way the hob should be cutting to the full depth in one pass and you should be able to avoid cutting away the teeth you just formed.

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