Wheel friction

[ipas]

Hi,

I'm calculating bearing loads for a turntable with wheels running on circular rails. The wheels are positioned vertically and they are not driven.

Does anyone know how to calculate axial bearing load?

 

[desertfox]

Hi ipas

Any chance of a sketch or drawing? I am a little confused as your title talks about friction forces, but your main question relate's to axial loads on bearings.
Here is a site that deals with rolling and sliding friction if that helps:-

http://www.roymech.co.uk/Useful_Tables/Tribology/co_of_frict.htm#Rolling

desertfox

 

[ipas]

I made a simplified sketch of the wheel/rail/turntable arrangement. There are other forces in the wheel/rail interface, but I left them out for simplicity.

In real life the turntable is a circular steel structure with 60 wheels evenly spaced on two concentric rails.

Hope it helps explaining my problem.

 

[desertfox]

hi ipas

Well that helps for starters well rolling friction coefficients for the wheel and track can be obtained from that site link I gave you earlier.
The axial force at the bearing are you looking for the centrifugal force due to the rotation of the turntable?
If so go to this link and scroll down till you come to
rotary motion.

http://www.roymech.co.uk/Useful_Tables/Form/Dynamics.html

desertfox

 

[MintJulep]

The axial load will be:

W * mu * sin(a)

mu is the coefficient of adhesion between wheel and rail (this is not the coefficient of friction).

a is the slip angle of the wheel.

a will be small, so axial load will be small.

 

[williedawg]

just a WAG, but if you're talking point contact, wouldn't the axial load be null as long as the axis or axes are located radially from the center of the table?

The problem comes in when using wheels that make contact on their width such as rubber or polyurethane. These will deform and "squirm" when forced along the track.
It still might be of minor concern, but if this is something you must quantify, it may require experimentation....perhaps the axes being canted.

If you're looking for power requirements to turn the table under load, there are a lot more variables to consider; the main one being rolling resistance of the wheels.

 

[williedawg]

..or what MintJulep said; I was slow on the typing

 

[desertfox]

Hi ipas

You might want to look round this site to:-

http://www.engineersedge.com/lubrication/laws_rolling_friction.htm

desertfox

 

[ipas]

Thank you guys!

MintJulep: Where can I find out more about these things? Can you please advise me a book or other recource. Thanks again!

 

[zekeman]

There will also be a slight slipping owing to the width of the bearing ,i.e. the inner and outer surfaces in contact with the rail have a slight mismatch in velocity.The associated forces should be minimal.
The major axial force, F, is the centripetal force on the bearing of mass m
F=mw^2
w= angular velocity of the turntable

 

[zekeman]

Correction
F=m*w^2*r
r radius of turntable

 

[MintJulep]

ipas,

Any statics and dynamics text book covers the fundamentals of this.

 

[Bobfromoh]

If roller/ball bearings were used, wouldn't it eliminate the slipping?

 

[Tmoose]

Will the turntable's rotational centering be provided by the rollers? A steel or urethane cylinder rolling on a flat surface will try (insist!) to travel in a straight line. To get it to "turn" or follow a curved path will require some axial load, and as others pointed out, the inner and outer edges to slip since they must travel slightly different distances but must rotate at the same rpm. Tapered roller bearings have their races and rollers designed as cones to reduce the sliding and create more perfect rolling.

http://www.ntn.ca/pics/roller_guidance_pic1.jpg

http://www.bearings.machinedesign.com/guiEdits/Content/BDE_6_4/images/fig17.jpg

It may be possible to "steer" each roller bearing to reduce the axial load, but some cylindrical roller and track wear will still occur due to slipping. It Maybe easier to provide centering with a bearing in the center of the table, and mount the rollers on casters, to avoid having to machine the roller axle seats with great precision, or go thru an elaborate alignment adjustment.

Unless there is resilience somewhere between track and turntable (flexible turntable relative to loads, etc) I don't picture many of the 60 rollers carrying their share of the load