Bearing Assembly Contact Loads & Distribution - Free Body Diagram
Bearing Assembly Contact Loads & Distribution - Free Body Diagram
(OP)
Hey folks,
I'm designing an assembly that looks and behaves similarly to a cylindrical roller bearing and I'd like to get your help on the best approach to take in calculating some force loads. The "rollers" are cam followers that mount to a rotating center assembly. There is a stationary assembly that has an OD "race" for the cam followers to react loads against. A singular force is applied to the center of the assembly, radially loading the "bearing". I am trying to calculate the loads that pass through each of the cam followers for given rotational positions of the rotating assembly. Im assuming the assembly is stationary and frictionless, all bodies are rigid, and that the cam followers can only react forces in a radial direction. I attached a pdf that shows the simplified 2D representation for two different cases.
I first started with a free body diagram, summing forces and moments to identify loads on each of the cam followers. I came to the conclusion that the system is indeterminate because of the 5x support locations, and there are multiple solutions that meet the constraints of the sum of moments and forces equations. I proved it to myself with a simplified FBD for a rigid beam simply supported in 3 locations. Based on sum of forces and moments I could get any number of solutions that satisfied all of the constraints. Does this conclusion make sense? Or could I be missing something?
I think the equation that I am missing that could be the last piece in this puzzle would be a method to estimate/determine the load distribution across the multiple supports. Id guess this could be done possibly as a function of proximity to the applied load? Or possibly by making the assumption that the load is evenly divided among the contact points? I could imagine running across a similar problem in determining the loads on each axle of a vehicle with more than 2 axles, or as I mentioned above, determining the compressive loads on each roller or ball in a radially loaded bearing.
Any thoughts on how to estimate the load distribution across the 5x supports?
Thanks,
Jeff
I'm designing an assembly that looks and behaves similarly to a cylindrical roller bearing and I'd like to get your help on the best approach to take in calculating some force loads. The "rollers" are cam followers that mount to a rotating center assembly. There is a stationary assembly that has an OD "race" for the cam followers to react loads against. A singular force is applied to the center of the assembly, radially loading the "bearing". I am trying to calculate the loads that pass through each of the cam followers for given rotational positions of the rotating assembly. Im assuming the assembly is stationary and frictionless, all bodies are rigid, and that the cam followers can only react forces in a radial direction. I attached a pdf that shows the simplified 2D representation for two different cases.
I first started with a free body diagram, summing forces and moments to identify loads on each of the cam followers. I came to the conclusion that the system is indeterminate because of the 5x support locations, and there are multiple solutions that meet the constraints of the sum of moments and forces equations. I proved it to myself with a simplified FBD for a rigid beam simply supported in 3 locations. Based on sum of forces and moments I could get any number of solutions that satisfied all of the constraints. Does this conclusion make sense? Or could I be missing something?
I think the equation that I am missing that could be the last piece in this puzzle would be a method to estimate/determine the load distribution across the multiple supports. Id guess this could be done possibly as a function of proximity to the applied load? Or possibly by making the assumption that the load is evenly divided among the contact points? I could imagine running across a similar problem in determining the loads on each axle of a vehicle with more than 2 axles, or as I mentioned above, determining the compressive loads on each roller or ball in a radially loaded bearing.
Any thoughts on how to estimate the load distribution across the 5x supports?
Thanks,
Jeff





RE: Bearing Assembly Contact Loads & Distribution - Free Body Diagram
At least this should really simplify your equations!
Doug
RE: Bearing Assembly Contact Loads & Distribution - Free Body Diagram
RE: Bearing Assembly Contact Loads & Distribution - Free Body Diagram
You have a very complex problem that I would solve as Doug before me stated. Solve for the worst case.
RE: Bearing Assembly Contact Loads & Distribution - Free Body Diagram
For cam follower sizing and FOS considerations I will take the conservative route and assume the entire load passes through a single point in my 2D representation.
For the sake on discussion, if someone were trying to predict the real world loading case, does anyone know of a method to at least estimate what the distribution may be over the multiple contact points? This would require the big assumption that all 5 cam followers are in simultaneous contact with the body that reacts the forces. What I would love to find is any text book reference to a method for defining this type of load plot, shown in red here: http://qualitybearings.files.wordpress.com/2010/08/load.jpg
Like I said above, it seems like this might be a common calculation done in bearing design, or on other systems that have redundant supports and are indeterminate.
Would any FEA users be able to comment on the feasibility and confidence/accuracy level of analyzing a model like this and getting simulated loads on the contact points?
Its interesting to me that the freebody diagram method is contradictory in the sense that it assumes, and actually requires a perfectly rigid body, but cannot accept the assumption of perfect geometry of more than 2x support points contacting the body.
RE: Bearing Assembly Contact Loads & Distribution - Free Body Diagram
Once you have an accurate analysis result of the deflections at each roller contact under load, you can adjust the installed position of each roller to give a better load distribution under operating conditions.
Hope that helps.
Terry
RE: Bearing Assembly Contact Loads & Distribution - Free Body Diagram
for me if the substrate is a significant, stiff, and reasonably uniform hunk of metal i'd assume 5 equal radial forces react the normal component of the load. the side component would be reacted by the two rollers on the right side, and finally you've got the off-set couple (of the side forces) increasing the vertical loads on one side, reducing them on the other.
another choice for the horizontal component (possibly the same, but a different way of thinking about it) would be to assume four rollers have radial loads (two positive, two negative) so that their resultant balances the horizontal component with no nett vertical. you could try the same magnitude for these four, or 1/3:2/3, ... the "problems" for the rollers is when the outer one starts to lift (if the applied force is outside the rollers).
Quando Omni Flunkus Moritati
RE: Bearing Assembly Contact Loads & Distribution - Free Body Diagram
rb1957, The rollers contact a very significant & uniform seamless forged-then-turned ring that acts as an outer race. When I first started on this design I took a similar approach to the one you've outlined - I'd started with the assumption that the vertical component was evenly distributed among the 5 rollers. This even 1/5 reaction load was applied to each roller as the vertical component. I then found the radial resultant on each of the rollers (assuming no friction, they can only react loads radially). I noticed 2 problems with these results:
1. The forces in the "horizontal" direction did not sum to zero in cases where the rollers were positioned asymmetrically.
2. The radial loads on the outermost rollers were highest, the load on the bottom-most roller were lowest. By playing with the geometry, and sending the outermost rollers to near-90° locations, the radial loads on these rollers approached infinity.
I attached a pdf with figures that show this approach. The large orange/brown arrow is the input force. Ignore the yellow arrow. The red construction lines show the "vertical" and "horizontal" load components for each roller. Its plain to see that the horizontal loads do not sum to zero in these figures.
Your suggestion of assuming the radial forces on each roller are equal sounds like a good one. I will try it out and see what it looks like.
BTW this is all just for discussion. The rollers have been sized to carry the entire load through one set, along with a generous FOS.
Thanks for the input.
RE: Bearing Assembly Contact Loads & Distribution - Free Body Diagram
RE: Bearing Assembly Contact Loads & Distribution - Free Body Diagram
can you resolve the applied force along (and normal to) the CL on the middle fastener. now you'll have two force components to balance. the radial one ... maybe 5 equal radial loads produces an unlikely result ... maybe 4:2:1 distribution (ie the CL fastener reacts 40&, the inner two 20% each, the outer two 10% each; a more numberical way to describe this would be to say the radial forces are proportional to cos(theta), the angle off the CL of the group. The normal component would be reacted by 4 radial forces.
Quando Omni Flunkus Moritati
RE: Bearing Assembly Contact Loads & Distribution - Free Body Diagram
"On the human scale, the laws of Newtonian Physics are non-negotiable"
RE: Bearing Assembly Contact Loads & Distribution - Free Body Diagram
if the line of action is not through the centre of the radial forces, or if the radial forces don't converge to a center, then you've got three equations.
Quando Omni Flunkus Moritati
RE: Bearing Assembly Contact Loads & Distribution - Free Body Diagram
The fit and bending stiffness of the cantilevered cam followers means heavy loads will tend to distribute the loading on a few followers at the bottom. The followers' rollers may even be edge loaded
The stiffness of the outer race support may modify the distribution significantly. I'm picturing a hammock.
One of the things FEA has "taught" me is there aren't many structures or components that are remotely resemble "rigid".
RE: Bearing Assembly Contact Loads & Distribution - Free Body Diagram
Stefano