View Full Version : Gear Teeth Question

01-20-2009, 06:51 PM
I am overhauling a 10" Standard Modern "Utilathe." The carriage is driven from the feed rod through a bevel gear arrangement. Through misuse, abuse or bad luck, the gears are a bit "mushed." The US Army parts manual says the gears are a 22-tooth and a 56-tooth.
Leblonde, who is the parts supplier for Standard Modern, are "not allowed" to give the specifications on the parts they sell, (that is a quote from their e-mail by the way.) They did quote me $337.00 for the 22-tooth gear and stated that they had no 55-tooth in stock so did not know the price.
I have since determined that that is a 28DP gear set. Now to the question. 22/55 is a ratio of 2.5:1, while 22/56 is 2.5454.../1! Somewhere I heard/read that for a set of gears that is repeatedly engaged/disengaged, it was considered "good practice" to add an extra "hunting tooth" to the larger of the two gears to equalize wear on the set. Is this what has been done here, or can someone not count?
I thought that $337.00 for a pokey little gear was a tad pricey, but Boston Gear lists nothing close, so I guess it is custom made and they DO have expenses!
Can someone explain this odd ratio, or did I accidentally get it right?

Spin Doctor
01-20-2009, 07:10 PM
This is just a guess so take it for what it's worth. The reason may have to do what fit in the available space in the apron

01-20-2009, 07:57 PM
Thanks Duffy (OP).

"Hunting" teeth is a very old practice to equalise wear. Tooth (teeth?) "numbers" and DP will be important as they must maintain the centre distances of the original gears as adjustment may be difficult is too far out or space is limited. Making any keyways will need to be considered too - although some are fixed with taper or roll pins. Any that slide on a shaft will/may need to be keyed or splined.

Machinery's Handbook has quite a good coverage of bevel gears.

I assume that you require "straight/spur" and not "spiral" teeth.

They can be very effectively cut in the HSM shop if you have a dividing head (with a tilting head axis) or a rotary table on a tilting table/angle-plate to mount the rotary table on.

As with spur gears, spiral gears can be made with "store-bought" or shop-made cutters (multi or single tooth). The usual cutters in "sets" (for a range of numbers of teeth for a set DP) should do the job.

In theory, the teeth should be generated/cut/made in a true conical shape so that all features melded or "disappeared" at the point of the cone. In practice this doesn't happen although some very ingenious machines come very close indeed.

So, back to the HSM shop environment -which I'd guess is where the gear/s will be made. Of course in this situation the milling cutter will cut the same profile through-out its cut, so a good compromise is required - and made - as is the case with spur gears too.

Making the bevel gear blanks is a bit more challenging than making a spur gear blank, but it is quite achievable in most HSM shops.

I'd suggest making three sets of "blanks". One to try the set-up and two good ones - one to use and test plus one set as a spare - just in case.

As a point of interest, when I was younger, the shop that I was in had a gear-making section (hobs, generators, shavers etc. - no grinders or lappers). The bevel gears were made on a shaping machine that had a tool with a cross-section similar to one edge of a (old-fashioned??) double bevel-edged Draftsman's ruler. The job not only rotated but "rolled" so as to very closely emulate (make?) and maintain a very good "involute curve" on the gear blank. I can't remember if the gear was cut one side/face at a time or whether it cut first one and then the other.

Gear cutting is not a job you'd want if you were tired or "hung-over" after a "heavy" night or week-end "out"!!

Mondays and the day after pay-days were a total PITA at times.

J Tiers
01-20-2009, 11:31 PM
They can be very effectively cut in the HSM shop if you have a dividing head (with a tilting head axis) or a rotary table on a tilting table/angle-plate to mount the rotary table on.

Or you just make a quickie fixture if your DH is inconvenient to use at an angle, as mine is due to daylight issues. The angle of the shaft is what sets the cone angle.
Gears are used to set the tooth indexing.... and are relatively easily available. I think, for instance, that both 22 and 56 are in my change gear set. The tail of this fixture swings to do the offsetting.


01-21-2009, 12:43 AM
Thanks for those replies Tiffie and JT. I should add that a colleague and I studied the problem, pontificated a lot, scratched our heads and finally concluded that, since it STILL worked, if I cleaned up all the "fuzzy" edges on the gear teeth, then the chances are pretty good that it will continue to work. That is, as long as I dont try any "crashbox" gear shifting. After all, I am a hobbyist, not a production machinist and it is VERY doubtful that I will ever really "load her up." If it should crash in the future, then I now know what to do. By my calculations, I can buy a pair of cutters AND a dividing head for about the price of the small gear and 10 or 15 teeth on the large one!

The Fixer
01-21-2009, 12:47 AM
I bought a used offshore machine (Goodway 16-40) that had the same setup behind the apron that u described. same tooth #'s too. It has a plastic/nylon 56t bevel gear running on a 22 t steel gear. Apperently it is considered a 'sacrificial gear' which is designed to be the weak link in case of "disaster" in the drive train, so something less replaceable doesn't break. eg the apron housing.
It was the first gear I ever made so I was quite pleased when it worked out. I made my own gear cutter out of a 1/4 x2" washer which I free handed on the lathe to the gear profile and then used the zip-cut to cut 4 cutter teeth. I filed some back clearance on the cutter teeth and mounted on a quicky made arbor and I was all set.
The gear was obsolete from Goodway but the factory actually emailled me the blueprints for the gear!! I was stunned when when I got the reply to my email requesting a new gear!!!
I went up the street to the local plastics shop and for $20 bucks I got a 10" long piece of "Nylarod" 6" in dia. In retrospect I wish I would have made 3 of them at the time but I was very unsure of being successful first time around.
Here's a link to some pics of the adventure.


01-21-2009, 01:16 AM
Thanks for that post and pic JT as it just about says it all.

As said, the angle between the shafts (on which the bevel gears run - and the centres of those shafts must intersect) is what determines the angle subtended by the axis/centres of the involute cone pitch circle cones centres (usually but by no means always, 90 degree, as it can be any angle within practical limits (where/how fitted and made).

The angle between the two involute cones (which are touching at their pitch circle through-out their length) is divided in the same ratio as the ratio between the meshing teeth in each pair of bevel gears.

For instance, same numbers of teeth is ratio of 1:1 and 1+1 =2 so, the say 90 degree angle between the gears is divided into two equal parts ie 90/2 = 45 which is half the included angle at the involute cone at the pitch cone of each gear, so each gear has a 90 degree involute pitch cone.


Tooth ratio is 3:1 and 3 + 1 = 4 of which 3 parts (of say 120 shaft angle) is on the gear with the larger number of teeth and one part is on the gear with the least number of teeth.

Assume the angle between shaft centres is 120 degree, each 1/4 part = 120/4 = 30 degree. So the involute pitch cones will have angles within that 120 degree of (1 x 30 = 30 degree) and (3 x 30 = 90 degree). So the cones will have included angles of 60 and 180 degree.

Normal - well almost - terms and quantities apply for DP, PCD, PA circular pitch etc. etc.

Same applies for modular (Metric) bevel gearing.

This may all seem too difficult, but it isn't. If you can manage spur gears you are more than half way there with bevel gears. All the same terms are there.

Just don't get over-awed by the stuff in Machinery's Handbook.

I am quite deliberately keeping this to the practical day-to-day level of Machinist and machines in an average HSM shop.

There is no need for high-fallutin' theorising or copious posts of text, tables etc. etc. It may well happen. Read it if you will, but just sift or chuck out or ignore anything that is not relevant to you in your shop at your level.

In the next month or more I will post a different approach to gear cutting and measurement than has generally been the case here in the past. It is in Machinery's Handbook. It is quite easy and no gear calipers are required. It can all be done quite accurately with a good set and "feel" with the common old much-maligned digital caliper. Back-lash and clearances will be dealt with as well - and not a micrometer needed either as at a pinch your digital caliper will do the job. All the cutters will be the same "store-bought" ones most of us know about and some have used.

So, in the meantime, get beavering away with those bevel gears.