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Axle cone shapes?

Old 12-05-16, 07:44 AM
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Axle cone shapes?

I could post this in the Bicycle Mechanics forum but I'm betting I get a better answer here where people haven't completely gone over to the dark side to use cartridge bearings.

What are the general rules of thumb, if they exist at all outside esoteric mechanical engineering textbooks, for radius of curvature vs. bearing size vs axle and cone diameter?

I'm asking because I've seen different bearing cones for a non-bike application which have visibly different radii but for which one would expect the same ball size. So what is the general rule? Could it tolerate a range of radii as long as the balls fit? Does the hub race have to match the cone race to some degree? Does a visibly smaller radius imply it was necessarily meant for smaller balls or might it tolerate a larger size as long as the ball has a smaller radius than the cone?
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Old 12-05-16, 01:52 PM
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Hey Jim , I recently went through what you are talking about . As it worked out for me , the general rule that I think you are talking about is it needs to fit correctly . We are talking about 2 radii and a sphere (balls) so if it's not lining up you are going to have problems , like I did . I'm not a Engineer however I'm a retired machinist , I never tried to design (make ) anything like a loose ball bike hub but I have a pretty good idea that if any of it is out of line it's not going to work . On my hub re build I bought after market cones , balls and axle after a short distance it would loosen up wildly . I finally got OEM cones and have not had any problems . So my thought was that the aftermarket cones had some type of dimension problem
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Old 12-05-16, 02:15 PM
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Good question! I don't recall any instruction in my mechanical engineering education of how to design cup and cone bearings of the configuration used on bicycle hubs. I may not have signed up for that course or they didn't think it was important given it is a commodity design!


My suspicion is that the radii of the cup and cone are slightly larger than the bearing radius. this approach would allow for a point contact between the two surfaces. This may seam counter intuitive at first but if you think of the slight variations of the manufacturing process including tool wear, maybe not. So then you might think that a point contact would have incredible forces applied until you realize the hardness of the material, not to mention the number of balls that might be used in the assembly. More balls, greater distribution of force. Now, now, stay focused on the subject!


Most of the stuff we see, as the forum title might suggest, is worn surfaces that reflect either the contact patch path, or the area of the track of the ball during use. Don't know which or if it represents both.


If there is a ME being a bearing design SME on this forum? I would love to know the truth! How much if any of the race radii is the same as the ball radius? If it is not the same, is it a uniform radii or more parabola like? Of course you must answer the question of why the design is what it is!
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Old 12-05-16, 02:32 PM
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The contact area between balls and cones is surprisingly small, which suggests to me that you could have a range of radii without causing damage. If you are replacing cones and the new ones have a different radius, if it works, I would just ride it.
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Old 12-05-16, 03:10 PM
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Ideally, I think the bearings should ride at about the 45° point on both the cones and races.

If clearance is too low or too high, it may push the balls either further up or further down on the races.

I would think that radius as closely matching the actual bearing size would be preferable to increase the contact area. But, I'm not sure. Different parts of the ball will be moving at different speeds (middle vs outside edges), so friction may increase as contact area increases.

I have a wheel I built up with a generic set of cones last spring. About once a week the cones are loose and I have to retighten. Eventually I'll have to tear it down and see the damage. But, either the cones are very soft metal, or what I think happened is that the cones are too big in diameter, and the balls are rolling on the lower flat area. Then a minor amount of wear makes big changes, plus lateral stress puts extra stress on them.
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Old 12-05-16, 03:22 PM
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Originally Posted by SJX426 View Post
Good question! ...they didn't think it was important given it is a commodity design!

My suspicion is that the radii of the cup and cone are slightly larger than the bearing radius....

If there is a ME being a bearing design SME on this forum?
Thanks. There is a reason I asked the question. As for a commodity design, that problem is like "Googling is the new knowing" in that somebody somewhere, probably a Mech Eng professor or an academic journal reviewer, has to know so that we can rest assured the commodity is in fact correct. Otherwise how would Google know the right answer?? I guess I was sort of hoping an SME would chime in. All that being said...

Eyeballing a bearing held up to a cone shows pretty clearly that the ball conventionally has a smaller radius. If it had a larger radius it would contact the race or cone in two tracks out along the edges. That might in fact add some stability but maybe there is some reason it isn't commonly done, like higher costs per benefit. It would require two machined radii on that surface.

So I was really wondering about a mismatch between the race and cone shapes. After some musing and drawing on a whiteboard I have convinced myself that, as noglider suggests, it may not matter much. Here is why, or perhaps I should say here are the conditions under which it doesn't matter.

As long as the race or cone is a good size to accommodate the ball at all near the center of the surface, as you tighten the cone on the axle the two surface move closer together. The point of nearest possible approach will always be where the tangents to the race and cone surfaces are parallel. If, say, a replacement cone's curvature isn't an exact match for an original, the ball will track along the race at a lightly different position but it will still be a point of stability because the race and cone will always be a fixed distance apart.

The primary difference then will be in the distribution of force components between horizontal and vertical. Eyeballing most cones shows that the contact surface seems to be slightly less than 45 degrees, indicating that the intent was to take more vertical load. The tangent of the new contact position would seem to be important but you can judge than by where the balls track when assembled with the correct size. If the balls seem to track in a good spot, then it would seem to be okay.

Here's why I asked. Some of you may know I've looked around for a source of cones for the rear axle of our tandem. Its threads are the later 11mm x 1mm as compared to the original 9.5mm x 1mm. I've looked at moped parts and our first trial ended up with failed cones after only about 35 miles. However it turns out that there was a Honda moped which used this size on the front wheel. I've installed a used cone on our tandem and after almost 50 miles it seems to have done well. I picked some up from a moped repair shop near us and I have several others on order as an experiment. But I noticed that the various cones I got locally had different radii. I used the one that was visually closest to the original, but I'm wondering whether the others would work just as well.

Details at 11...
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Old 12-05-16, 03:32 PM
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I think one of the Shimano generator hubs also had a 11mm cone, but had a bit of an odd shape to it.

Eventually I'll pull that wheel that I've been regularly re-adjusting apart. Maybe in the next week or so. But I believe its problem is the bearings riding too low on the cones. Perhaps that is part of your problem with some of the moped cones.

Thinking of the Shimano cones... maybe you could use undersized bearings to achieve the proper spacing.

Shimano DH-3N72, DH-2N72 Dynamo Hub Cone M11x12.1mm w/Dust Cover | eBay
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Old 12-05-16, 03:33 PM
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I'm a ME (but bearing design theory isn't my specialty). My take though: If we were dealing with very high speeds and/or heavy loads, there would be some benefit to optimizing the cup radius versus ball diameter. There's several angular contact designs out there. For the speeds and loads we are using, though, most anything will work.
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Old 12-05-16, 03:37 PM
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Aaron Goss * Showed a technique to grind a new surface in a pitted cone using 2 drill Motors ..

1 spins the cone, on an axle , the other has the Grinding tool spinning in it

Hint: Dont let it get Hot , or the heat treatment goes away.

*Aaron's Bike repair Seattle ..
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Old 12-05-16, 03:47 PM
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Originally Posted by fietsbob View Post
Aaron Goss * Showed a technique to grind a new surface in a pitted cone using 2 drill Motors ..

1 spins the cone, on an axle , the other has the Grinding tool spinning in it

Hint: Dont let it get Hot , or the heat treatment goes away.

*Aaron's Bike repair Seattle ..
I re-cut my Campy NR bottom bracket spindle cones on a lathe... whew.. that was HARD. So grinding stone might be preferable.

You will make the cones narrower, but you can make up for that with washers on an axle (not the BB).

I now routinely polish my cones by hand with sandpaper (320 to 600) and a small drill press before installing.
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Old 12-05-16, 04:26 PM
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Not in a mechanical engineering field, different type of discipline here, but I will present this to a master machinist and former mechanical systems development lab manager, in the now defunct Westinghouse NCD, in Pensacola, he has experience in design and machining races and balls as well as roller bearing assemblies. Hopefully I can find out something for you Jim.

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Old 12-05-16, 06:57 PM
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I didn't see this site mentioned yet. A good resource, if you need something specific.
I've also used it to determine what I think I need, then go find it on Ebay.
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Old 12-06-16, 05:52 AM
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Originally Posted by CliffordK View Post
I think one of the Shimano generator hubs also had a 11mm cone, but had a bit of an odd shape to it...

Shimano DH-3N72, DH-2N72 Dynamo Hub Cone M11x12.1mm w/Dust Cover | eBay
Interesting idea. That cone with dust cover doesn't look quite right but one can't really tell from a pic like that.

Originally Posted by nashvillebill View Post
For the speeds and loads we are using, though, most anything will work.
Thanks. That's what I'm thinking but there's no harm in asking.

Originally Posted by qcpmsame View Post
... but I will present this to a master machinist and former mechanical systems development lab manager, in the now defunct Westinghouse NCD, in Pensacola, he has experience in design and machining races and balls as well as roller bearing assemblies.
Thank you!

Originally Posted by old's'cool View Post
I didn't see this site mentioned yet.
I've looked more than once on WheelsMfg's website. Alas they don't do 11mm. Maybe if I paid them enough money...

A few more backstory bits - When I tried the moped parts last year the shape was seemingly an exact match to the original and called for the same size balls. Apparently it wasn't case-hardened well enough. These Honda cones (OEM vs. aftermarket) are maybe just fine but that fact that I saw two different shapes made me wonder. If they nominally were for the same application could they be different and still work? One never knows about aftermarket parts though.
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Old 12-06-16, 05:58 AM
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Originally Posted by jimmuller View Post
I could post this in the Bicycle Mechanics forum but I'm betting I get a better answer here where people haven't completely gone over to the dark side to use cartridge bearings.
I don't consider cartridge bearings going over to the "Dark Side". Some of the Suntour Sprint and Superbe reviled or bettered anything by Campy or Shimano.
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Old 12-06-16, 08:08 AM
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I believe, could be wrong but can't see it, that the force will always end up with the cone and race contacting the ball at the ends of the diameter of the ball. that is why there are variations in where the wear pattern is from cone to cone.


Typically it is found near the "center" of the radius curvature of the cup/cone. So it really doesn't matter what the radius is as long as the force ends up allowing the ball to be somewhere near the middle of the radius curvature regardless of the radius dimensions relative to the ball. if I were to design the bearing assembly, the radii of the cup and cone would be very slightly larger than the ball radius as confirmed.


Hardness of the surface is the key to longevity along with lubrication, of course.
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Old 12-06-16, 08:55 AM
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Originally Posted by Wileyone View Post
I don't consider cartridge bearings going over to the "Dark Side". Some of the Suntour Sprint and Superbe reviled or bettered anything by Campy or Shimano.
AH, but it is when the intent is Dark Side Humor.

I have a pair of Mavic 501 hubs with cartridge bearings and they have been quite wonderful and maintenance-free for a long time.
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Old 12-06-16, 09:28 AM
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Originally Posted by jimmuller View Post
I have a pair of Mavic 501 hubs with cartridge bearings and they have been quite wonderful and maintenance-free for a long time.

Have two sets, one set part of the GL330 pic above. Great hubs premium price when you can find them and often without the original skewers
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Old 12-06-16, 10:28 AM
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For what it's worth, Shimano hubs still use cup and cone bearings. And they're good hubs, too.
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Old 12-06-16, 10:55 AM
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In my experience, matching cones to the hub is critical, As noted the the balls should track in the middle of the race, which should provide slightly more radial loading than axial. If the balls track too high or low, there will be too much axial and radial loading respectively. Both situations can cause excessive wear and make it difficult to pre-load the bearings for proper performance.
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Old 12-06-16, 11:23 AM
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Originally Posted by jimmuller View Post
...Eyeballing a bearing held up to a cone shows pretty clearly that the ball conventionally has a smaller radius. If it had a larger radius it would contact the race or cone in two tracks out along the edges. That might in fact add some stability but maybe there is some reason it isn't commonly done, like higher costs per benefit. It would require two machined radii on that surface...
Most cartridge bearings are four point bearings. Also, three and four point bearings were used in the bicycle industry in the late 1890s. The marketing hype was typically focused on the lower loading and superior longevity. I guess that may have been a big deal at the time, with lower technology bearings and dirt dirt roads. Regardless, here is an advertisement for the E &D () four point hubs. You can't see the construction very well, so I've included the patent, which depicts a four point bottom bracket. The big drawback is the more complex, two part cup. It would have been difficult to install the bearings and the design totally prevents the use of caged bearings, which were a huge factor in reducing the labour costs of hub and bottom bracket assembly.

Edit: The Dodge name refers the Dodge brothers of automobile fame. Prior to venturing into cars, they worked for Canadian Typograph manufacturer Evans, who went into the bicycle business with them, after Horace Dodge invented the four point bicycle bearing.
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E&D four poit bearing a.jpg (68.2 KB, 138 views)
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Old 12-06-16, 02:47 PM
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Originally Posted by T-Mar View Post
In my experience, matching cones to the hub is critical, As noted the the balls should track in the middle of the race, which should provide slightly more radial loading than axial. If the balls track too high or low, there will be too much axial and radial loading respectively. Both situations can cause excessive wear and make it difficult to pre-load the bearings for proper performance.
This, in my experience too.
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Old 12-07-16, 09:57 AM
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Originally Posted by T-Mar View Post
In my experience, matching cones to the hub is critical, As noted the the balls should track in the middle of the race, which should provide slightly more radial loading than axial. If the balls track too high or low, there will be too much axial and radial loading respectively. Both situations can cause excessive wear and make it difficult to pre-load the bearings for proper performance.
Simple and elegant answer, T-Mar.

This may be slightly, or completely un-related...but matching cones to the hub can be important in another aspect.
Remember discussing the Nuovo Record vs. Nuovo Tipo cones, Jim? Gave me fits, as the dimensions of the N. Tipo cones were, apparently, different than the N. Record cones. And not inter changeable, as a result. A shorter length cone led to the cone wrench flats ending up being slightly "buried" inside the hub dust caps, thus not allowing adjustment of the hub.

An interesting, if esoteric topic, Jim.
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Old 12-07-16, 12:21 PM
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Originally Posted by rootboy View Post
....An interesting, if esoteric topic, Jim.

Esoteric topics is why I continue to come back to this forum!
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Old 12-07-16, 06:21 PM
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Same here! I love 'em.
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Old 12-07-16, 08:12 PM
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Jim,
I contacted our machinist/superintendent about bearings and races, he referred me to "Machinery's Handbook, 27th Edition, Industrial Press" This manual has all of the charts and in depth criteria for bearings, races and cartridge bearings, among a whole slew of other information about these type of things, about 4000 pages all total. One of the best investments in a reference book I have made fro my professional library.

Way too much to try and type in here and scanning is more than I have time to do right now, unfortunately. This book is pretty much the bible for anything related to materials, engineering specifications, mathematics applications for machinist operations, etc. Bearings begin on page 2203, just pass by the surface bearings, and start with anti-friction bearings, as ball and roller type bearings are called, as opposed to bushings and such. The criteria for size, number of balls or rollers, and race details as well.

Hope you have access to a copy, try any machinist shop or probably a mechanical engineering department for a manufacturing and fabrication concern, if you wish to pursue this. T-mar and the others seem to have pretty well filled in the blanks, this would be digging much further in to the fine print. Best of luck.

Bill
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