HOBBING VERSUS SHAPING, AND RESULTING UNDERCUT 1

[MRSSPOCK]

Hi. Can anyone verify if I have understood this correctly.

Having read this,

"Since addenda are standardized by a fixed value (ha = m), the interference
condition becomes more severe as the number of teeth on the mating gear increases. The
limit is reached when the gear becomes a rack. This is a realistic case since the hob is a
rack-type cutter. "

which can be found on page T36 here,

http://www.sdp-si.com/D805/D805_PDFS/Technical/8050T034.pdf

I am assuming that a gear cut using an arrangement as illustrated in the following image...

http://www.wzl.rwth-aachen.de/__C12...c1256f390032e1f0.htm/$FILE/W%E4lzsto%DFen.jpg

will generate less undercut than a rack type cutter?

If this is true, then, if let's say a gear of 12 teeth is to be mated with another gear of 12 teeth in service, is there any merit in using the tooth generation method which provides only the undercut required?

In other words, is there any reason to create such a large undercut using a rack cutter type geometry, if the gear being produced will never be mated with a rack in service?

(Please ignore production costs etc. I'm only thinking about the actual tooth geometry and its strength / weakness in service).

Thanks

 

[tbuelna]

You may not fully understand what that statement implies. Spur gear hobs are a generating type of rotary cutter that can have cutting edge profiles similar to rack teeth, but the cutter is not a rack shape. The shaping process also uses a circular cutter, but the cutting motion is linear for spur gears, followed by an indexing of the blank and radial travel of the cutter after each stroke.

As for undercutting, it is a result of the tooth design more than the process used to produce the gear teeth. Undercut is not necessary, and in fact it usually something to be avoided. Undercut becomes a problem with small numbers of teeth (<20T) and/or low pressure angles. The common approach used to eliminate/minimize undercutting is by modifying the tooth geometry (profile shift, increased PD, increased PA, etc). But with a gear mesh of two 12T spur gears you'll need lots of careful geometry tweaking to eliminate undercutting. With these gears I think you'd be better off using a shaping process.

I'd highly recommend taking a look at the AGMA standards to get a better understanding of how to modify your 12T/12T gear set to avoid undercutting, and also the effect of these modifications on gear efficiency and strength.

Good luck to you.
Terry

 

[MRSSPOCK]

Thanks Terry for taking the time to answer.

I agree with all your comments, but I still do deduce that a gear of let's say 9T can be made in a stronger way, if it is made specifically to run ONLY with another specific gear, let's say another 9T gear.

I have actually carried out a simulation to convince myself, using the 9T gear as an example.

Yes, I realise my cutter is a basic rack form, and doesn't necessarily illustrate a hob completely, but I still think it is adequate for the illustration.

My rack is MOD 2 with 20° P.A. and a radius on it's tip of (0.1875 x MOD = 0.375)

The rack was used to generate the purple gear, (with an offset of 0.3), in the manner you describe as a rotary indexing of the blank, followed by a linear translation of the cutter.

(I purposely left the generated gear with a pointed tooth, to better illustrate the clearance still available, which is shown in my animation video).

The root of the purple generated gear tooth would in theory have a constant tip contact, if this purple gear were to be meshed with a rack of identical geometry to my rack cutter.

The green gear in the animation is a replica of the purple gear, and is translated so as to have a centre distance of 19.016mm, i.e. the centre distance that two such gears require.

The animation clearly shows lots of tip clearance, which would be even greater if I had topped the teeth to reduce the outside diameter by 0.5mm, to match the actual physical gear I have in my hand.

So, in a nutshell, all I'm suggesting is that I deduce a small number tooth gear can be made stronger, if it is made to be dedicated to another specific gear, and not so that it can mate with any gear of the same MOD.

But getting back to my initial question regarding is there an advantage of shaping a gear, I can now see that if the shaping machine cutting tooth generates the involute by a series of straight edge cuts, similars to a rack form, then the end result will be the same.

The generated tooth profile I am suggesting, would actually mean the the cutting tool profile, would be very close to the tooth geometry of the gear that the gear being produced has to be mated with, but with the relevant clearances added.

See attached files.

Sorry if that sounds a bit confusing.

 

[MRSSPOCK]

sorry, forgot to attach the snapshot of the generation..

 

[MRSSPOCK]

I think I have figured it out now.

I wasn't trying to re-invent the wheel, but just wanted to know how to design the root area for a gear pump gear, so that it was built on some logic and not just a some random clearance geometry I decided upon.

I just created a totally pointed tooth, then once it crossed the base circle on its mating gear, plotted the path, as shown by the series of points. (The equation for this path is quite simple).

Once the two generated gears are meshed, the clearance at the root is zero, until the tooth is topped, then the topping becomes the clearance.

I realise I haven't even considered backlash or the finer details of the tooth geometry, but I was just trying to get a handle on the basic root generation initially.

http://i58.tinypic.com/24xl05g.jpg[/IMG]]

 

[Compositepro]

Don't overlook the fact that for a gear pump you need a bleed path for fluid that may get trapped in the pocket at the tooth tip.

 

[MRSSPOCK]

Thanks Co-Pro.

A friend pointed that one out to me also.

If you have experience of gear design, maybe you could answer this one.

Suppose you have a 20T and a 30T gear set, MOD 3, and you have a set centre distance of 76mm

Obviously some offset / profile shift needs introduced.

Is there a ratio of how / where that the offset gets applied?

e.g. 0.1 on 20T and 0.25 on 30T will do the job, but so will 0.2 on 20T and 0.15 on 30T

Or is just a case of choosing the offsets which provide the strongest solution?

Thanks