Request for advice regarding cantilever mounted housing, deflections and stresses

Hello everyone,
I would like to ask for some advice regarding a cantilever mounted bearing housing.
Due to various design constraints, I have two choices as to how I
implement a cantilevered mounted bearing housing. I have uploaded two simple dimensioned jpeg images for reference, at the following site. You can Save or print the images as needed.
http://www.ice9.zoomshare.com
The housing has two drawn-cup needle roller bearings pressed into it, and the housing oscillates on a stationary shaft (i.e., a hardened steel dowel pin). As shown in the drawings, I can use a 7/16" OD dowel with the bearings spaced closer together, or I can use a 3/8" OD dowel with the bearings spaced further apart.
1. I mainly need to know the correct way to model the forces on the shaft, due to the housing load, so I can determine how far the end of the shaft & housing will deflect, and whether the dowel can withstand the stresses without taking a permanent set.
The maximum load on the housing will probably be about 130 pounds, but I would like for the dowel to be able to withstand a 200 pound housing load if possible, for a safety factor.
It seems to me that the load on the bearings will almost be a torque moment, where the the shaft is being bent between the contact points of the two bearings, with bearing #2 pushing down, and bearing #1 pushing almost upwardly.
Here is the formula I used to calculate the bearing loads, the letters are shown with the corresponding dimensions, on the two drawings.
Where (LA) = the housing load
Load on bearing #1 = (LA) * B / A
Load on bearing #2 = (LA) * C / A
2. The bearing shaft is a hardened steel pull dowel pin, made from C1541, 4037, or 4140 steel (thats all the info I can get from Mcmaster Carr). The single shear strength for the pin is 130,000 PSI. The pins have a core hardness of Rockwell C47-58, and a surface hardness of C60 (they meet ASME B18.8.2 standards).
Since the dowel is hardened I am not sure what the maximum yield strength is, I know tensile goes up with hardening but I don't have any information on the yield strength of the hardened dowel pin. I am hoping someone can shed some light on this issue.
I have a beam design program I can use to help determine stress and deflection of the dowel, but I am not sure If I should put a torque moment between the two bearings, or perhaps a combination of a torque moment and vertical forces.
Using a housing load of 130 pounds, the formula given above, and a downward force on both bearing #1 & #2, it seems the 3/8" OD dowel has slightly less stress than the 7/16" dowel, but it deflects about .001" further.
The end of the dowel is 1.26" from the cantilever support. The loaded end of the housing is 1.48" from the cantilever support, and there is a .031" space between the housing and the cantilever support.
I have a 3/8" OD, lever "connection socket" that screws into the bearing housing, perpendicular to the housing, right next to the cantilever steel support. The advantage of housing #1 is that I can "step" the bearing bore in the housing so that I have a little more housing material to thread the connection socket into, since bearing # 1 is moved out from under the connection socket, and closer to the load end of the housing.
The advantage of housing #2 is that the bearings are spaced further apart, and this helps reduce housing deflection due to bearing misalignment. The trade off is that I have a little less housing material to thread the connection socket into, since the socket threads in, right on top of bearing #1.
The housing is oscillated by hand, and never gets hot. The radial clearance between the bearing ID and the shaft OD will be .0002" Min. to .002" maximum.
If there is no way to model this to get a close estimate, I would appreciate your gut feelings as to which method is best, as far keeping the deflections at the load end of the housing to a minimum, and avoiding overloading the dowel so that it does not incur a permanent set due to the housing load. Obviously, if the dowels had the same OD in each case, then housing #2 would be best, since the bearings are spaced further apart.
I think that either arrangement could take 130 pounds, but I am not sure about 200 pounds. I would like to be able to estimate the maximum housing load the dowel pin could withstand without taking a permanent set, and make a close estimate on the deflection of the dowel and housing.
Thanks for your help. John
Add pictures here
<% if( /^image/.test(type) ){ %>
<% } %>
<%-name%>
Add image file
Upload
wrote:

Let me put a simpler question to you: what is the stress at the root of a 3/8 in dowel 1.5 inch long, with a side load at the end of 200 lb? And a 7/16 in dowel? And what is the tip deflection in each case?
Your beam program answers this. That speaks to the pin max stress.
Brian Whatcott Altus OK
Add pictures here
<% if( /^image/.test(type) ){ %>
<% } %>
<%-name%>
Add image file
Upload
Hi Brian,
Thanks for your message.

John2005: For a cantilevered mounted 7/16" OD dowel, 1.48" long, with a 200 pound load at the very end of the dowel, the deflection at the very end of the dowel is .004" and the maximum bending stress at the cantilever support is 36 KSI.
For a cantilevered mounted 3/8" OD dowel, 1.48" long, with a 200 pound load at the very end of the dowel, the deflection at the very end of the dowel is .007" and the maximum bending stress at the cantilever support is 57.2 KSI.
However, I think the problem might be little more complex, due to the way the housing distributes the loads on the bearings, and thus the dowel, as shown in the drawings at the website link in my previous message.
The actual dowel length is 1.26" from the cantilever support to the end of the dowel. The length from the cantilever support to the end of the housing is 1.48".
Referring to Housing #1 as shown in drawings:
For a 1.26" long cantilevered mounted 7/6" OD dowel, a 1.48" long housing, with a 200 pound load at the very end of the housing, there is a 212 pound load on bearing #1 at .638" from the cantilever support to the center of the bearing. There will be a 412 pound load on bearing #2 at 1.05" from the cantilever support to the center of the bearing. The deflection at the very end of the dowel is .0047" and the maximum bending stress at the cantilever support is 69.1 KSI. The moment at the cantilever support is 568 lb-in.
Referring to Housing #2 as shown in drawings:
For a 1.26" long cantilevered mounted 3/8" OD dowel, a 1.48" long housing, with a 200 pound load at the very end of the housing, there is a 105 pound load on bearing #1 at .219" from the cantilever support to the center of the bearing. There will be a 305 pound load on bearing #2 at 1.05" from the cantilever support to the center of the bearing. The deflection at the very end of the dowel is .0054" and the maximum bending stress at the cantilever support is 66.3 KSI. The moment at the cantilever support is 343 lb-in
However, the above figures are valid "only" if both bearing loads (bearings # 1 & #2) are acting vertically and downwardly on the dowel. I don't think this will actually be the case, and I would like to learn the correct way to model the force the bearings are exerting on the dowel, i.e., it seems it will be a torque moment to some extent, where the dowel is almost being bent between the contact points of the two bearings.
Do I model the bearing loads as a torque moment, with the rotation axis in the middle of the two bearings ? Or do I use a combination of vertical forces and a torque moment ?
I also need to get a close estimate on the yield strength of the hardened dowel pins, so I can determine if they can take the stresses and still spring back to their original position after the housing load is removed.
I want to keep any deviations of the end of the housing from it's longitudinal axis to a minimum, whether this comes from shaft deflection or bearing misalignment.
My best guess is that housing #2 will be best. The 3/8" dowel may defect a little further than the 7/16" dowel as seen above, but the bearings will be spaced further apart, which keeps problems from bearing misalignment to a minimum. This may mean that the total deviation of the end of the housing from it's longitudinal axis, is just about identical regardless of which arrangement is used. The stresses seem close whether a 3/8" or 7/16" dowel is used. If the dowel stresses and the total deviation of the end of the housing from it's longitudinal axis is practically the same in either case, then it seems that housing #2 would provide better bearing wear, but the trade off is that I will have a little less material to thread my lever connection socket into, as mentioned in my previous message.
I just want to learn the correct way to model the bearing forces in regards to how they act on the dowel, which will then give me a close estimate on deflection and stress. I then need to know the maximum housing load the dowels can handle without going past their yield points, and taking a permanent set. However, I don't know the yield strength of the hardened dowels.
Thanks again, John
Add pictures here
<% if( /^image/.test(type) ){ %>
<% } %>
<%-name%>
Add image file
Upload

Polytechforum.com is a website by engineers for engineers. It is not affiliated with any of manufacturers or vendors discussed here. All logos and trade names are the property of their respective owners.