Make a 72 tooth worm gear without indexing?

[tornitore45]

What Chriske said makes perfect sense. Because: For a given pitch P there is an arithmetic series of diameters accommodating an integer number of teeth.
The diameters corresponding to 1 tooth increment differ P/pie.
Since the 1/2 depth of the tooth (from pitch diameter to top or bottom)
is P x Sqrt(3)/4 < 0.5 x P/pie there is no way that the process can be "confused" and start off with the "wrong" number of teeth.

Starting with a pitch diameter Dp = N x P/pie
and adding the tooth depth H = 0.5 x P x Sqrt(3) will give the blank diameter Db

As the cutting starts on the Db it is bound to generate N + a fraction of tooth but less than N+1 teeth. At the end the hobbing will try to overrun the previously cut teeth but that is OK because on the Db the teeth have plenty of space (as long as we are not trying to cut too many teeth above N.

As the hob penetrates the blank it will reach a point where the hob pitch radius touches the gear pitch radius, that radius that allow exactly N teeth.

If you stop here you got perfect teeth and a concave groove on top of the worm gear.

Now the question is: But how do we manage to have the same N at the bottom of the groove, at the pitch diameter and at the Blank diameter?

Visualizing the engagement between the Hob and the worm gear as a snug fit at the pitch-to pitch diameters, the gash at the bottom of the groove has zero width and is spaced exactly 360*/N, the spaces at the blank diameter can not be = P but must be larger. When we were just starting out the Hob was overrunning the teeth at the Db cutting a bit larger space but never enough to fit one more tooth, ad the process continues the hob will continue to widen the opening at the Db above and beyond P but by then the drive contact is nearing the pitch to pitch point where the drive set exactly N tooth.

The secret is to start with a blank that is not oversized to the point of starting N+1 teeth. If the number of teeth is not important but you only want full shape nice teeth then any old blank will do if you stop at the right spot before starting to chew up the N? teeth in an effort to place N?-1 teeth on a smaller diameter. This will not work very well because however many N? teeth are there are not going to go away and allow a new set of N?-1 teeth to synchronize on the next allowable diameter.

 

[Chriske]

Mauro,

I think my brain will be pleased to hear someone cracked it, I'll pass on the message.
Thanks...

Chris

 

[Chriske]

On the other hand...
Suppose I make a wormwheel like I did for my project and end up with a 1:156 ratio.
Suppose The wormwheel is just under 6 mm thick, say 5.5mm.
Suppose I stay on it and keep pushing the tap further and further in the wormwheel.
Suppose I keep pushing the tap until the wormwheel has become nothing more than a rod with a few teeth(So it has become a hobbed bolt for my 3D-printer) Meaning the tap has 'consumed' most of the wormwheel, and I'm left with a 'wormwheel' diameter 7 mm and ratio 1:18
My brain is puzzled again...! Sorry Mauro...

My question : what will happen with the number of teeth while decreasing the diameter of the wormwheel as described here. How would it look like while milling...??

Chris

 

[tornitore45]

I am responding with a guess because I never tried and an analysis is really difficult.
Since this is basically a geometry problem, pictures are essential.
I have placed my thoughts into the attached spreadsheet.

In my previous post

Since the 1/2 depth of the tooth (from pitch diameter to top or bottom)
is P x Sqrt(3)/4 < 0.5 x P/pie there is no way that the process can be "confused" and start off with the "wrong" number of teeth.

Wrong! the sign should be >
Still the conclusion is not invalidated since the start involves a very small depth of cut. The problem arises when N teeth are set and we force the hobbing beyond expecting to find a new happy spot at N-1 teeth. Once N teeth are established there is no way to transition smoothly to N-1, the N-1 "potential" locations have already been compromised.

View attachment Hobbing.xlsx

 

[TSutrina]

I have been looking at hobbing gears since I do not have a rotary or index table. I first calculated if I could cut a hob on my Atlas 10" lathe. Atlas cast pot metal gears have a 16/in pitch diameter, module 0.0625 in, and (rack) 5.093/in circular pitch and pressure angle 14.5 deg the same as an ACME thread. I adding to the tool steel lathe tool rounds of 0.25 of the module to the 2 module high rack thus 0.156 in tool. The hob would be created as others have shown and the gears on the lathe set as close as possible to the rack, 5.0 TPI. To create a spur rack the axis of gear blank to the hob axis is 168.975 deg pitch diameter (center of tooth) is 0.327 ", rood diameter is 0.171 ", and OD is 0.483. Obvious deflection and potential breakage of this hob would be a problem.

To make a Hob an odd pitch thread speed in needed which is not with possible with standard lathe threads. Thus a means of making an odd pitch is needed. The Reference below is such an approach. We know that if you gash a gear blank a hob will automatic follow it gashes. Thus that approach below create in effect a helix gash by adding material. This material can be totally machined away or removed once a cut gash of the forming tool tooth shape is made. Spur Gear add 'V' face on side point PD so that the hob will create gashes properly spaced. May need to taper front of Hob to PD of hob at the lead angle.
Ref:http://www.opensourcemachinetools.org/archive-manuals/lindsay_thread_follower.pdf
I chose the hob diameter at 1.65". Thus pitch diameter (-1.25 Module) is 1.4937" and the root diameter is 1.337". The hob circular pitch is PI x Pitch Dia / sqroot( (PI x PD / Circ Pitch) squared - 1) thus 0.197 in . Inverse is the Hob TPI of the attached follower spiral thus 15.986/in. A little trig the lead angle is 0.764 deg which is the angle that the hob or blank need to be placed at to cut a spur gear. The Diametral pitch is the hob TPI and the module is the inverse thus 0.0626".

 

[JCSteam]

It's an old thread I know, but I thought to show how I made a wormwheel to be used in a startracker I designed.
The assembly runs very slow, the wormwheel itself runs at a whoping1 rpday. So I choose SS for the worm. A SS bolt(M6) that has been cleaned up a bit serves as worm.
To make the wormwheel is basically nothing more than a M6 tap pushing against a brass's disk perimeter. I made(3D printed) two brackets that will hold two ball bearings(8x22x7). The wormwheel has the same size hole as the bearings. Once the assembly is fixed on the milling machine, the wormwheel can rotate freely around the 8 mm axis.
Then the rotating tap is pushed very gently against the perimeter of the wormwheel. If you go for it, again go slow..!
As you see there's no indexing involved, yet it turned out to be a perfect wormwheel, very sharp and clean teeth.

EDIT : forgot to mention diameter of the wormwheel : 50mm (2") Ratio : 1:156

A LOT of what is discussed in this thread is well over the top of my head, however....
Seeing this has made me have an idea, which may work, I want to make a worm and pinion for a small traction engines steering, the engine will be around 3/4" scale, would making a small diameter wheel, and a brass bolt work using the method shown above? Essentially using something like a M4 tap on the wheel and a M4 bolt shortened and fastened to a steel rod?

Simple answers for a simple mind please

 

[Chriske]

First of all I would consider using a thicker tap, say M6 like I did. M4 is to thin imo, it cannot handle that kind of strain. Keep in mind to use brass for the wormwheel. There's no way you can make a steel wormwheel using the technique mentioned above. Maybe if you can find a way to support the tap at the very top, I suppose it can be done using steel.
Feeding the tap into the wormwheel, go slow, very slow..!