Machining Bevels.

[Archie]

Art,

Gleason's use of a double cutter is a very inexpensi ve way to double productio n. It cuts two tooth faces for the price of one and since the tool shape is simple, the cost is low. In the case of a rotating cutter, a double spindle machine would be necessary and, because the two spindles would have to be very close together, this would be difficult or expensive to accomplis h. Just ignore the second cutter for your purposes.

When you mention the "root angle", are you perhaps thinking of the base circle of the involute? At the point where the involute intersect s the baser circle of the involute, the involute is radial and then, as it moves out, the involute "bends over". One issue is how GM defines the tooth profile in cases where the working depth of the tooth profile exists inside the base circle. Form cutters "cheat" and use a cycloid form in the tips and roots, while using an involute for most of the working tooth in between. Generated gears with small numbers of teeth have an undercut generated by the interfere nce of the tips of the teeth when they operate below the base circle. I suggest that for most gears with PA's of 20 or more and larger numbers of teeth this is not an issue, although it will have to be addressed for 14-1/2 PA gears and pinions of any PA.

In order to understan d the generatio n of a straight-toothed bevel gear, the key is to see that a crown gear replaces the rack as the generatin g form. The crown gear has planar teeth(!) -- just as a rack is a degenerat e involute form that has planar tooth profiles, so is the crown gear. You may wonder how a crown gear can have lines that intersect at the common point of the cone, just observe that the lines that meet at the common point all lie on the surface of a cone that has degenerat ed into a plane. The tapered involute gear teeth of the gear being generated rolls its form on the planar surface of the crown gear. I'll see if I can find a decent graphic that shows this clearly -- if I have to make it myself, there may be a slight delay. (If someone beats me to it, my feelings will not be hurt . . .)

Archie

[John S]

When we say root angle and base angle i think we are talking the same, quite a few post back I said cut on the base angle so no Z movement was needed.

John S.

[Archie]

One more thing:

The Gleason cutters and any approach that is similarly applied to bevel gears must use a tapered form that has a small end that will pass through the small end of the root of the bevel gear. So long as this is the case, the tool, which could be a tapered end mill, will be able to generate the tapered involute tooth form in the same manner as the Gleason (& other) gear planers that is to move a straight-edged cutter in a set of straight line motions as the gear blank is rolled with the involute tooth surface tangent to the plane establish ed by the linear cutting edge and its feed motion.

Archie

[ArtF]

Hi Guys:

   Chuck explained this well to me offlist. I hadnt considere d properly a crown gear.. makes perfect sense when Chuck finally beat that into me. , I think I understan d what needs to be done now to make it work on a PA tapered bit. Im in the middle of some cutter creation routines, but I may switch to a new bevel Gcode maker using this theory as discussed here. Takes a bit to get your head around it all properly. But I think I have it firmly in head enough to code it. It will mean that cutting a bevel MUST be done with a PA taper as the code ( at least initially ) will be written with that in mind.

>>When you mention the "root angle", are you perhaps thinking of the base circle of the involute?

  No, I meant as opposed to the pitchcone angle vs the tip angle vs the rooth angle. Sometimes called dedendum angle. If tilted to pitchcode, the initial passes are at changing Z.. if tilted to the root angle, the initial passes have no Z motion.

>> At the point where the involute intersect s the baser circle of the involute, the involute is radial and then, as it moves out, the >>involute "bends over". One issue is how GM defines the tooth profile in cases where the working depth of the tooth profile exists inside >>the base circle. Form cutters "cheat" and use a cycloid form in the tips and roots


   The proper method is a trochoida l cut.The trochoid is the shape the edge of a rack will make when rolled under the base .. GM has a dual trochoid generator for low PA's with few teeth. Always best to eliminate undercut, but if it senses one is needed , it generates a trochoid for the root curve. Isnt perfect but does a pretty good job.


Thx
Art

[Archie]

Art,

Thanks for your patience regarding the clarifica tions of the cone angles and how tooth profiles inside the base cone are handled. I am glad to see the latter seems to be well under control. Undercut is a problem if significa nt power is being transmitt ed, but there are a lot of cases where this is not an issue and proper undercuts are satisfact ory. In my own primitive investiga tions into using a ball end mill & 3-axis contourin g I avoided undercuts by using a high PA because I thought that this was a necessary simplific ation because that the undercuts could not be machined. I am glad to see that your 4-axis approach handles them.

I realize a crown gear approach will require some re-think, but I think the end result will be well worth the trouble. Not only will the generatio n work properly, but tool life should be higher and total cutting time should be much lower due to the advantage s of the tapered end mill.

Thanks,

Archie

[ArtF]

Archie:

   Actually, it's you guys that are owed a thank you. I started this forum for that very reason. As with Mach3 when I began, I was not very knowledga ble in CNC,
the CNC group taught me what I needed to know. Same is happening here.

  Not being an expert on gears, its invaluabl e to have it explained at times. For Spur and bevel, I was generatin g an involute and matching the tool to the curve.. I can see now thats inefficen t , more so in bevels than spurs. I suspect Spur code could be sped up by tapers around 20% or so as the Y motion is the predomina nt saving. Less Y and a bit less rotation will be necessary .

  On bevels, a much larger saving shoudl be able to be done. Not huge in time, but vastly better in complexit y. As an example, my bevels cut so far, ( which do look and run nicely together, are very complex to calculate . An involute is generated, selected point by point, and then rotated on a pitch cone plane increment ally to find a point where the next involute point is above the current one, this indicated a tangental sweet spot and confirms the pass as a proper shaving pass. Very inefficen t, but the only way I could think of at the time. I hadnt considere d crowns at all.. my mistake.

   My thanks to all of you..codi ng continues ..

Art

[ArtF]

OK, I have a quick question. .

  TO use a taper to generate or simulate the Crown gear, is the taper actually double the PA?
Ive never used a tapered bit, but it appears to me the included angle of the PA must be used, that woudl imply
a taper of 40 degrees for a 20 degree gear.. the PA is always at right angles to one side of the rack, so while the
racks sides angle is for example 20 degrees, a taper that makes that rack wouidl be a 40 degree taper would it not?

  This is more a question about the specs of a taper bit, is a 40degree taper , 20 degrees on each side, or is a 20 degree
taper 20 degree's on each side.. Makes a bit of a differenc e in the calculati ons.

   I also see that with this method, to be done properly, a double sweep must be performed, that is that the tapered bit must be swept
coming into the tooth from base to root ( if undercut exists ), in order to create a proper trochoid. ( I suspected this ). In all cases it must be swepth from base to tip on the other side.

 see http://www.brockeng.com/mechanism/RackNPinion.htm for an example, watch carefully and you can see the necessity of the sweep below base circle on the opposing side as the rack comes into the tooth. ( again, only necessary if the base diamter is larger than the root diamter.

   I figure you guys know the taper question quicker than I can find the damn spec ..

Art

 

Art

[Archie]

Art,

Whether a taper is the angle from the axis or the whole (included) angle can be a source of confusion and different folks prefer one or the other. A direct analog is radius vs diameter: one can measure a diameter directly if the part is round, while a radius is a distance to an imaginary center. If one is working with an arc, then a radius would seem to be the correct term. I recommend not making assumptio ns, but always stating what you are using and asking what the other person is using.

In our case, the tapered tool is replacing the tapered crown gear tooth, so it would be the same half-angle (the pressure angle) and would also be the same included angle. I would expect that most tapered cutters you buy from stock would be specified at the included (whole) angle because it can be measured directly. (When one uses such a tool, it actually only generates a bevel at the half-angle.) If the cutter was expensive I would always confirm that the seller was using the same reference as I was before laying down $$$.

I am not certain that you need to separate the cuts below and above the base circle, but it seems that this is the way you attacked spur and helical gears, so as long as the two paths are stitched together so that the whole working surface of the tooth is cut without lost motion, it should work fine.

(On the other hand . . .) Machines that cut gears by the generatin g process always have some sort of gear train that couples the motion of the tool to the motion of the gear blank. In the case of bevel gear generatio n one can think of this gear train as two cones with infinitel y fine teeth that represent the meshing of an ideal model of the gear to be cut and the crown gear that would mesh with that gear. Because of the high number of teeth, these gears would mesh and rotate with no undercut or interfere nce. If the real gear being cut had a base circle that was above the bottom of the working surface of the gear's teeth, the undercut would automatic ally be cut by the cutting tool edge (near its tip) -- the tool edge would always lie in the extended plane of a tooth face on the crown gear. The end (tip) of the tool edge would always lie on a line which would be an extension of the tip of the same crown gear tooth that the cutter edge was coplanar with. In the case of a tapered end mill, the edge we are discussin g is a line that lies on the cone of the cutter's taper and is where the cutting occurs. I think you could dispense with calculati ng the trochoid, but I am not telling you that this is necessary -- you have already done the work and the computer can handle the work.


Archie

[ArtF]

Archie:

  So then to cut a PA 20 gear, the taper would bne a whole angle of 40 degree's if Im correct. ( Just to make sure we're on the same page ).

 As to computing the trochoid, its not a computati on, its actually just what happens when the tip of the rack is under the base circle. BUT, it means in our case, if the base circle IS larger than the root, the cutter must rotate into thew tooth as well as rotate out.

 By that I mean we have always used a mill in spurs to basically go to the edge of a tooth and rotate out.. we then move to the other edge and rotate out in the other direction . In the case where the base circle is larger than the rooth, we have to both rotate the tool into the tooth as well as rotate it out. The rotation in only needs to be done from base circle inwards, as opposed to the rotation out which occurs from base circle outwards.

 
   Anyway.. thats not difficult, its the angle I questione d, I just wanted to make sure.. A taper normally speced at 40 degrees' ( whole ) woudl be necessary to cut a 20PA gear...

Art
 

[Archie]

Art,

I think we are on the same page . . . You have control over the model of the tool inside your software -- it is only in the real world that someone might try to cut a 20 PA gear with a 20 included angle cutter. I recommend you call the cutter angle out as: "20-degree angle from tool axis, 40-degree total included angle."

I am glad to hear that you are letting the tool calculate the trochoid. A mechanica l  gear generator does the whole operation by rolling the tool in from the tip of the gear to the root on one side and then rolling out root to tip on the other. This action seems normal to me, but none of my projects requires such motion or much focus on efficienc y. All tool-paths take the tool off the work, so dwell marks should not be a problem.

Archie

P.S.: I am working on getting Windows 7 on my Mac so I can get your software running locally and hence be more aware of what is going on. Thanks for your patience.

[John S]

Yup, 40 degrees included, imagine you are using one rack tooth but its rotating as a cutter.

John S.

[ArtF]

Good, thats what I figured.. .just wanted to make sure.. I couldnt seem to find any suplliers of 40degree tapered mills.. didnt look hard though..

Art

[Chuck]

Art,

You are on track,  I wonder if you will be back to point to point calculati ons on spiral bevels?  The compound angle may mess up the "simple" rack generatio n method when you start rotating the gear. I have been thinking about it and can't get my head screwed up enough to visualize it!  Oh well get the strait cut bevels working and then we can discuss spirals.  I can see how the helical spur gears will work but that is a much simpler setup.


And yes 40 degrees included or 20 per side,  here is a catalog link:
3-Flute 15 deg. Per Side End Cutting Tapered End Mills
http://www.wttool.com/index/page/category/category_id/13820/

Chuck

[Chuck]

Looking for 20 degree stock taper endmills.  not much out there!
I have been grinding single flute taper endmills,  I will put together a program to generate the Gcode.

I did find an interesti ng link:
http://www.homemodelenginemachinist.com/index.php?topic=9759.0

Side not I am building a 1/4 scale Shay Loco.

Chuck

[ArtF]

Thats kinda what I was concerned about, I didnt see any 40 degree tapers out there.. Though I guess its easy enough to make one..

  However, 30 degree woudl give a 15PA..not too bad I guess..

 As to zerol and spiral bevels, I already made the code to compute the offset angles involved. . ( Helical bevels are quite a bitch to calculate really.. at least the way I do it.. We'll see.

  Im into the code for Bevel2 so we'll see how that works for straight, then Ill hook in the helical generator to see hwo that works, in theory, it shoudl work alraight under all the assumptio ns we discussed .

  Art