Reference book on plain bearing design?

Does anyone know of a good treatise on plain bearing design that treats bearings which must take both radial and axial loads?

Much to my dismay, a survey of 10 ft of machine design books failed to turn up a single book which treated the design of conical plain bearings. Just cylindrical and pure thrust bearings. Nothing such as one would use for a lathe spindle. Obviously a great deal was written about the topic during the first half of the 20th century.

Searches for books on Amazon and general searches with google turned up nothing relevant. I've not tried google scholar yet, but will shortly. However, I'd really like to have a comprehensive treatise on the topic rather than a slew of papers.

Project is a replacement spindle bearing for a small lathe which currently has ABEC 1 deep groove bearings. Intended use makes rolling contact bearings undesirable because of the inherent periodic errors.

As a last resort I can copy the geometry of my Clausing 4902 or a Southbend, but I'd really like to understand the design issues rather than make a "Chinese copy".

Thanks,
Reg

Dumb question- can you not add the 2 concepts together like 2 vectors and arrive at a reasonable desired angle and surface area?

Sent from my SM-G973U using Tapatalk

You should be able to generalize the plain bearing design formulas in Shigley's Mechanical Engineering Design book to conical bearings. It would take some trig to account for the angles and some calculus to integrate up the oil film pressure to match the applied load. This would be a good homework problem for a senior undergrad ME.

Are you refering to the the dual cone bearings used in watchmakers lathes? If so, that's 19th, not 20th century technology.

Not just conical,but hard steel running on hard steel.

No. Everybody knows one should use dissimilar materials for bearings of this type. Hardened steel & synthetic ruby are better.

This is for a metal lathe, so sensible materials are bronze and steel.

The issue I'm trying to resolve is the best shape for keeping the axis of rotation constant as the bearing surfaces wear and minimizing deviations of the axis of rotation.

I have old books on lathe design which mention various configurations such as an involute curve and double tapers. The "Schiele" or "tractrix" curve is supposed to be optimal. But there are no mathematical details as they were written for machine operators, not designers.

As the diameter changes the surface speed changes and with it the wear on the surfaces. There is a daft claim that the Schiele curve is "frictionless". I have no idea what the basis for that claim is, but it's obviously not true for a lathe spindle.

The front and rear cone bearings of a watchmaker's lathe are precisely what I want to use, but larger. So the fundamental design is very old, although I doubt there was a detailed mathematical analysis of it before 1900. As important as it is, I'm sure it has been analyzed in exquisite detail. I'm lazy. I'd rather read about the solution than derive it. The derivation is trivial relative to verifying the result.

I'm looking for wall to wall math on mechanical engineering. I doubt that most of the members here want such things, but I'm a retired research scientist, so I have already paid the price to be able to read such things. I also know there are other forum members who routinely dabble in such things for entertainment. I'm hoping one of them will say, "You need to find a copy of...."

Hydrostatic and aerostatic bearings are closely related, but the construction is more complex than hydrodynamic bearings and the mathematical physics rather different.

Many of us old timers only had the Machinery Hand Book before computers.
http://www.nashua.edu/paradisem1/Machinery's Handbook 27th/27_Mach_11A.pdf

Not sure if this has the conical bearing info you are looking for but it has a lot of plain bearing info

Theory and Practice of Lubrication
By Fuller
ISBN 978-0471047032

MrStretch said:

Are you refering to the the dual cone bearings used in watchmakers lathes? If so, that's 19th, not 20th century technology.

Click to expand...

The old " Richards " PRT style horizontal boring machines used a big double taper bearing at the front on the facing slide spindle arrangement.

Regards Tyrone.

MrStretch said:

No. Everybody knows one should use dissimilar materials for bearings of this type.

Click to expand...

Who is this everyone? Like Mssrs Scahublin, Rivett, Boley, Bergeon, Lienen etc? Have you worked on disassembled one these lathes? The bearings are almost always in perfect condition, even after a century of service. The are so well made that with the smallest amount of oil, there is never metal to metal contact. The well made double concal hardened steel bearing is one best spindle designs there is, that's why it lasted so long. I have several 100 year hold machines that are perfect with no measurable runout. The bearings last and perform in application they were design for: small precision lathes.

Not just conical,but hard steel running on hard steel.

Click to expand...

The double cone makes them a real challenge to make, but curious why you want just conical. The 45 and 3 (or was it 2) degree set was so successful it achieve almost universal acceptance as they work so well

One book that has a lot of plane bearing engineering and design stuff is Stolarski's Tribology in Machine Design.

You missed the point i was making.
I bet all the lathes that use this type of bearing have bronze cones in the headstock and hardened steel cones on the spindle, thus using dissimilar materials. I am a clock restorer, so yes I've taken the spindles apart on my Lorch watchmakers lathe and my Stark #4 bench lathe. As you said, the design is simple & robust.
The desirability of using dissimilar materials for bearings has been known for centuries. Clockmakers switched to brass plates as soon a brass became commonly available, which happened in Europe sometime in the 16th century.

MrStretch said:

You missed the point i was making.
I bet all the lathes that use this type of bearing have bronze cones in the headstock and hardened steel cones on the spindle, thus using dissimilar materials. I am a clock restorer, so yes I've taken the spindles apart on my Lorch watchmakers lathe and my Stark #4 bench lathe. As you said, the design is simple & robust.
The desirability of using dissimilar materials for bearings has been known for centuries. Clockmakers switched to brass plates as soon a brass became commonly available, which happened in Europe sometime in the 16th century.

Click to expand...

Southbend made the 9" lathes with plain iron bearings as a cost cutting measure during the Depression. They performed very well.

Hardened steel on hardened steel demands very high accuracy and extremely good surface finish. To make that I suspect I'd need to recondition my Clausing 4902 first.

I'm using "conical" to distinguish from "cylindrical" bearings. I'm assuming I'll make double taper bearings. The 45 & 2-3 degree taper design is almost certainly what I want to use, but I want to know more about it than just the angles. The surface loading of each taper is an important consideration.

This book has been suggested to me in an another forum:

Bearing Design in Machinery; Engineering Tribology and Lubrication.
Avraham Harnoy. 2005. ISBN 0-203-90907-0

though at the moment I can only find an edition from 2002 on Amazon. I'd been looking at it before I posted my question. It looked very promising, but Amazon would not let me read the section on combined radial and axial loads.

I have several old copies of both Machinery's and American Machinist's handbooks. I never thought to look in those. I'd expected that the various mechanical engineering handbooks and machine design books would cover the subject much better than they did. Back to the bookshelf ;-)

Edit:

The 15th ed (1956) of Machinery's handbook has no discussion of plain bearing design, just the materials. The 15th (1970) has a section which appears in very similar form in the 25th (1996). Unfortunately, except for collars, there is no discussion of combined radial and axial loading.

I found a PDF of Harnoy's book, but it does not treat conical or taper bearings. So I'm still looking. Nice book though.

MrStretch said:

You missed the point i was making.
I bet all the lathes that use this type of bearing have bronze cones in the headstock and hardened steel cones on the spindle, thus using dissimilar materials. I am a clock restorer, so yes I've taken the spindles apart on my Lorch watchmakers lathe and my Stark #4 bench lathe. As you said, the design is simple & robust.
The desirability of using dissimilar materials for bearings has been known for centuries. Clockmakers switched to brass plates as soon a brass became commonly available, which happened in Europe sometime in the 16th century.

Click to expand...

How much are we betting? I'll go all in. You're taking a little of knowledge (dissimilar metals) and extrapolating into areas you don't know. A Stark 4 is hardly a watchmaker lathe (I have owned two of them) and don't know what Lorch model you are talking about. Having had all the brands I mentioned apart and probably a dozen more, they are universally from hardened steel shafts in hardened steel bearings as are the few still made (Bergeon and Star (also had to of those apart) come to mind)

Stating that these bearings and shafts both from hardened steel either aren't workable or inferior is just erroneous. They are by far the most common format for watchmakers lathes and do not show wear even after a century of use. They are hydrodynamic bearings made to a level of accuracy and finish such that there is never metal on metal contact so the concerns of similar metals galling is a not the issue you imagine it to be.

Math-head as you are, you will not feel warm and fuzzy about an old adage such as, "When in doubt, make it stout".

But it is relevant to your task because the load on an machine spindle is constantly changing, not only between drilling a large hole from solid with the tailstock (almost pure thrust and low speed) and turning a firing pin (high speed and negligible radial load) and some miscellaneous heavy turning job, or knurling (heavy radial load and no thrust). I said, not only between different types of turning, but from milliecond to millisecond as the tool chatters, as speed varies, as material inhomogeneities pass under the tool, and as tool dulls, or crashes.

Any design will be a complete compromise. Many machines have used tapered plain bearings with great success...Hendey lathes and my old US Machine Tool #1 Hand Mill come to mind.

It is an interesting fact of how the world is made, that if you design a spindle to be large enough to be stiff in itself and to accommodate certain tools or workpieces, it seems to automatically be large enough to have the necessary journals cut on it to carry service loads.

Copy a good old one. Make it a little bigger, journal hard and well-finished, and box of CDA 932 bronze tightly fitted in housing. Make it adjustable, and feed it lots of clean oil and it will run true and outlast us all.

For a plane bearing which must account for loads in any direction I would look toward a spherical type rather than opposing cones. I think that would be more on the order of 20th century tech than the conical types of yore.

As far as math... Well if you can't find the research material then build a couple different types and put them under load til they break. Gather your own data. I'm would hypothesize that the spherical type would improve more dramatically and under more varied conditions as opposed to the conical type as material increases.

I haven't seen it explicitly mentioned yet, but many of the later dual cone designs were engineered as explicit (simple) approximations to the Schiele curve.

sfriedberg said:

I haven't seen it explicitly mentioned yet, but many of the later dual cone designs were engineered as explicit (simple) approximations to the Schiele curve.

Click to expand...

The references I've found suggest that it was shown by experiment that the Schiele curve aka traktrix does not have the properties claimed. However, that doesn't mean that such an approximation is bad. The 45 & 2-3 degree taper seems pretty sound conceptually. But I plan to analyze the problem properly once I have collected the needed references and had time to study them.

I have finally found the magic phrase for finding references, "conical hydrodynamic bearings". That turned up a bunch of papers from ASME Tribology using google scholar, so now I need to figure out how to get copies of those and choose some tribology references.

Generally steel on steel for hydrodynamic bearings is frowned on, but the loads on a horologist's lathe are very light and the precision required high. For a general purpose instrument maker's lathe, bronze and steel has a very long and well respected track record, so I shall use that combination.

In any case, I want a properly engineered design. Compared to the labor of rescraping the ways to a tenth, the spindle bearing labor is minor.

I spent a couple of days going over rolling contact bearing designs to satisfy myself that the OEM deep groove Conrad spindle bearings were sensible choices. A popular amusement for some is replacing them with taper or angular contact bearings. For the maximum axial (65 lb) and radial (130 lb) loads possible with the OEM motor, a set of quality deep groove bearings have an L10 life of 100,000 hours. That pretty much confirmed my hunch that making changes by imitation rather than engineering was a fool's enterprise.

I am rebuilding an unmentionable new machine to do high precision instrument work. I expect to be designing and making other hydrodynamic or possibly hydrostatic or aerostatic bearings, so the learning experience required to engineer a hydrodynamic bearing for the spindle is well worth the trouble.

This is driven by amateur science in it's purest form. Purely done for love. I'm an unemployable old research scientist. I'd much rather have a few TB of oil and gas data to analyze, but that's not ever going to happen again. So it's on to personally funded science projects. I need to be learning something new to keep sane. Undertaking difficult projects has proven a good way to feed the need to learn. And one of these projects might actually result in a viable product if it's good enough someone else wants to manufacture it.

rhb said:

In any case, I want a properly engineered design. Compared to the labor of rescraping the ways to a tenth, the spindle bearing labor is minor.

.

Click to expand...

ok, I remember you now from the scraping forum. Same stance there. What do you expect to master with these spindles? Why reinvent the wheel? Just use the geometry the best makes do, its tried and true for 100+ years. Do what Schaublin does....or do you expect make a better machine ? From someone who's scraped machines to a 10th and made spindles, I say BS to your suggestion the spindle is minor bit of work in comparison. Have you scraped a machine or built a spindle before?

Good luck on the project and please post lots of pics

my southbend 9 spindle is operated so far out of the usual range of plain bearings that the books hardly have graphs that cover it. (yes i tried to work the numbers out)
the clearance is .001" to .0015" depending on how much force and the direction the force is applied to the spindle (bolt is not really all that tight on the shim stack).

when i put a 56 pound shaft with a center of gravity about 2 feet out from the chuck (which put about 150 pounds downward force on the spindle, and 100 pounds upward at the rear bearing, it took maybe 50 rpm to keep the oil film going. and that's with low viscosity atf which is about half the viscosity the velocite #10 is.

and my lathe runs fine at 1400 rpm without overheating the bearing. 150 pound upward forces at the spindle would be consistent with the heaviest cuts you would ever take with a southbend 9 and its relatively floppy spindle. you would have to be in back gear as low as 40 rpm to get that much force. so yes they can work for a hundred years, if run with adaquate lubrication.


" Compared to the labor of rescraping the ways to a tenth, the spindle bearing labor is minor."

i'll go against the grain here and say i agree with you. but if you're chasing roundness then you won't get roundness any better than the spindle is. so, you may be better off just buying good bearings. they may end up averaging out the spindle out of roundness errors.