SJX426 

Mine is packed away or I would have looked it up��

jimmuller 

Oh, well, why didn't you say so?? Golly, that's my standard go-to book for light recreational reading. Somehow I missed those pages completely, must've jumped from 2200 to 2301 without realizing it. Though I did wonder how the redhead ended up with the captain's keychain in her glove compartment.

Thanks, Bill. I'll have to do some digging.

Just to fill in some blanks, I took a few pics. Here is a comparison of the cone I took out of the tandem (bottom) and one of the replacement cones (top).



Those profiles are clearly different. Of the four cones I got, one was visually a perfect match for the tandem, the other three like the top one. So I asked myself how those aftermarket replacement cones could work with the same races. The key issue seems to be whether the diameters are the same for that point on the cone where the balls run, which would also be where the angles are the same. They might be but I'd have to be clever to devise a way to measure that carefully. To my eye they don't look like it.

The second question is whether the radius at that point is the same or whether the radius is even critical as long as it is within some range. The shape of cone outside of that contact area really doesn't matter. What I don't know is whether machinists work with such standard curves that anyone could look at them and say "That's a such and such and it won't (or will) work" or "That was meant for 3/16" balls, not 1/4"."

So the jury is still out, so to speak. It just gets esotericer and esotericer, dunnit?

rootboy 

Bill,

After reading this thread, I also went and pulled out my copy of the Machinery's Handbook. Mine is an 18th edition. (didn't have to be current because I was never trained in, nor worked in, the field.) Bought it at one of the many estate sales I went to in the 90's.

So, yesterday I laid myself down to rest the back and delved through the anti-friction bearing chapters. Man, but I scoured the lengthy entries on ball bearings....and could find nothing that related to the relationship of the radius of the race to the size/radius of the ball. But it could be in there somewhere! It's a vast and detailed book. And I am certainly not a machinery-ist.

All the info I found in the book on ball bearings had mostly to do with those types of bearings used in assemblies like pressed races, sealed units, on machine and motor shaftings, etc.
So I decided not to write anything here about it.

You're right though. That is one very interesting and valuable reference book, if you're at all interested in things mechanical. My "Little Green Brick". I can't claim to understand most of it. But I love looking through it.

qcpmsame 

1. Mistake that kicked me into the gutter: I was wrongly assumed that the more knowledgeable people here, machinist and mechanical engineers would have suggested using Machinery's Handbook. (I am definitely not one of the knowledgeable people, we have some truly brilliant and experienced folks here.) Its my mentor's go to guide for getting the little details about materials and things like bearing specifications, he suggested back years ago that I purchase a copy, I kept trying to dig up things for our building projects when I had to check on the safety margins for things we had designed on the sites. Its well worth its price, IMHO. This was my first mistake, I assume now that a better way of answering the question is out there, I flat do not know the answer.

2. Jim, I only included the pages in case someone wanted to look into bearings on Machinery's, that is the TOC page to begin anti-friction bearings (balls, rollers, etc.) sorry of I was not clear or seemed to be shooting for the Mr Know it all award. something for me to watch out for on my part. Apparently there is a somewhat "governing body" for bearing criteria, the book has tables for bearing counts, size, hardness and other items, this will include the races. I never found any written standard for determining the angles in the race's faces, and the bearing diameter in relationship to each other.

3. Posting the citation to Machinery's was poorly timed on my part, the gentleman here didn't have much time to explain things to me, so he suggested I look in my handbook for the means that are used in determining what you are seeking. I rushed things to post a resource for use here, I know/knew better.

Bill

jimmuller 

Golly Bill, I was pulling your chain for the fun of it. Your answer about the machinery handbook was actually a great suggestion. I wouldn't know about such things otherwise and certainly don't have a copy. But Waltham has a great library which might.

Thanks to rootboy for looking through his too.

A few years ago a friend gave me a book published a zillion years ago and reprinted by MIT Press that claims to be all about the engineering and mechanical stuff of bicycles and tricycles. Reading through it puts me to sleep because so much of it is basic math stuff I know already like vector analysis, stress, geometry, etc. for an uninitiated inventor. But maybe it has a good section on bearings. After all, they were invented for bikes over 100 years ago, if I remember David(?) Herlihy's book Bicycle correctly.

The fact is, I don't have much time for that kind of research or self-education. So I was hoping to shortcut the education process. That never works of course, but what the heck, it's great entertainment anyway!

rootboy 

It certainly is an interesting subject, Jim.
BTW, the only thing I gleaned from my quick read through of the anti-friction bearing section of the Machinery's Handbook was something about how these assemblies, races and balls, I think, are designed as "self-centering".
Not that I understand it all that well. But, does it make sense that the ball will "automatically" find the center of the race concave radius when the three parts are assembled? Not sure. That may not stand up to mechanical theory, and I'm not sure it helps in your quest at any rate.

There is a lot to learn on subjects like this, for me. I'm going to peruse the section in the book again and see if there is anything in the numerous tables and charts.

By the way, if you love things mechanical, Jim, that book in older editions can sometimes be found quite cheap.
Mine is a 1968 edition and was probably considered to be out of date by guys in the trade who really need it to be up to date. I just keep it because it's full of all manner of interesting stuff.

SJX426 

Not to sound like "I told you so," but I did. the forces will cause the ball to align such that they are opposite each other. My statement was supposition but now is referenced. I tired to make this statement humbly, but couldn't figure it out so just spit it out!


So yeah, those two radii are different. I don't think the diameter difference is an issue as long as the radius keeps the ball so it will "center" some where along the curve of the profile. The OAL of the assembly might differ very slightly due to the difference in the "centering" with a different cone radius, but not noticeably (comment without calculation).


If the "centering" causes the ball to impinge on another part of the assembly, like the internal surface that the cup is positioned, then it wouldn't center and you would have contact at three points, not desirable. The only way to know is to use the blue stuff that mechanics use for adjusting ring gears in differentials to ensure proper tooth engagement with pinion teeth. Assemble and disassemble and look at the results. Measurements aren't going to happen, but indicators can.

fietsbob

Yes the Radius of a Front Cone is smaller than that of a Rear Cone, the axles tend to be smaller too ..
smaller balls in the front, than rear Too...

rootboy 

No need to be humble, SJX! ;>
Just spit it out. heh.

I have to humbly admit to not reading every part of every post.

Yes!, ****m Blue. I was thinking of that stuff. It'd be an interesting test.
In a pinch, I've used black or blue magic marker. But that dye stuff works better.

jimmuller 

Seein' as how I had to go to work today I didn't have time to look for Machinist's Handbook or anything else in the library. But I did dig up the other book I mentioned, Bicycles & Tricycles - An Elementary Treatise on Their Design and Construction by Archibald Sharp, B.Sc., originally published in 1896. Archibald Sharp is listed as Whitworth Scholar, Associate Member of the Institute of Civil Engineers, Instructor in Engineering Design at the Central Technical College, South Kensington. So it appears he probably knew what he was writing about.

It has a chapter on bearings and some interesting analysis of ball bearing behavior. As I had gleaned, the points of contact with cone and race will always be at opposite ends of a diameter, and at those points the cone and race surfaces will be parallel. If you mismatch race and cone the balls will simply adjust to a different position as you tighten the cone. The operative question would seem to be how much.

As T-Mar pointed out, the radial load is much greater than the axial load so you would like those contact points to be at a place on the surface where the tangent to the surface is closer to the spindle axis than 45 degrees. Mr. Sharp doesn't give a preferred figure. However you can judge that simply by where the contact happens.

Mr. Sharp's analysis did have one surprising result. The axis of rotation where the ball rolls around the spindle is different for the cone surface than for the race surface. The net result is that the ball necessarily spins as it rolls. That spinning action produces friction at the surfaces so that, contrary to popular opinion, ball bearings do not have zero friction. It also explains how either the bearing race or the cone will eventually end up with galling that produces grooves. He said that the more similar were the radii of the cone and race to the bearing radius the greater the friction would be, but they would also be able to sustain greater loads. He did not do any math to support that conclusion but it appears to be based on the premise that the contact points are not true points in the geometric sense but instead are surfaces of contact due to deformation at the stress points.

Fascinating stuff but doesn't really answer my questions. The best way to tell whether cones will work is to put everything together and see where the balls lay, so to speak.

jzink0883

T-Mar,

Stumbling on this made my morning; it’s 5 AM here. My four-wheeled vehicle is a Dodge Challenger named Horace to honor of the “techie” Dodge brother. (First time in my 72 years that I’ve named a vehicle.)

SJX426 

@jimmuller - Ran across this post from nearly 5 years ago due to the one in front of this one! Thanks for closing the discussion. I hope you found a resolution to your problem.

jimmuller 

Hi, SJX426. Thanks for the note. It so happens that there is an appendix to the story, or at least I think there is.

This fall we had been having trouble with the chain skipping on the tandem's FW, clearly from worn teeth and a stretched chain documented in another thread. I installed a new chain and FW, and two new chain rings. The Suntour FW tool will not fit over the big axle so I had to unpack the bearings whether I wanted to or not. I liked what I saw.

When I posted that note long ago I had picked up some moped and other replacement cones, the key feature being the axle diameter, 11mm IIRC, and then did that bearing research trying decided if they would work. I vaguely remember thinkin' I'd try them and if they didn't, well I would know eventually. I remember now that I tried the moped cones first when we did a ride of about 60 miles. At about the halfway point I discovered that the rear wheel had developed way too much lateral play. We made it home safely and when I pulled the bearings out discovered that the cones were toast. (I wondered how a moped, or its rider, would have survived.) I must have replaced them with the other aftermarket bearings I had found.

When I pulled the axle out a few weeks ago I didn't recognize the cones at first, as the size was slightly different from what I remembered. The races were smooth as silk, clean as a whistle without the slight pitting the origin cones had had. Then I remembered, or was pretty sure I did, that they were not the originals. The bearings looked good too and the wheel had been spinning easily. So it seems I had tried them after all and so far they have worked just fine. Problem solved and a lesson learned!