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.

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The housing has two drawn-cup needle roller bearings pressed into it, and the housing oscillates rotationally 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 how the bearing forces act 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.

I can calculate the force at each bearing, but I am not sure exactly how the force actually acts on the dowel. 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 model a torque moment with the rotation axis 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.

However, if I model the bearing loads as a torque moment with the rotation axis in the middle of the two bearings, the 7/16" dowel deflects about .002" less than the 3/8" dowel, and with about 10 KSI less bending stress.

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 radialclearance 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.

I want to keep the deviations of the housing end from it's longitudinal axis to a minimum, whether the deviation comes from shaft deflection or bearing misalignment. However, I need to be sure that the dowel is not going to be stressed past it's yield point, so that it springs back to it's original position when the housing load is removed, and does not
take a permanent set.