Fully Supported Stress Concentration 1

[JakeAdkins]

I have a pin in bending with a transverse hole. Getting the stress concentration factor is pretty straight forward.


However the transverse hole is on a section of the pin that is fully supported (360 degrees) with a bushing. My gut feeling is that the bushing is going to 'cancel out' or change the stress concentration factor. I should still have a stress concentration but I don't think it will be as high as it would be without the bushing. I cannot find any thing to support this gut feeling. Any thoughts.




See pic:

http://files.engineering.com/getfile.aspx?folder=d110b22b-ed2c-4e45-9789-83

 

[EngineerTex]

Nothing comes up when you click on the file.

-T

Engineering is not the science behind building things. It is the science behind not building things.

 

[JakeAdkins]

OK lets try this one more time

 

[MotorVib]

It has been some time but take a look in Peterson book I know that there is something about it in there. My machine Design book by Robert L. Norton has it also.

Chris

"In this house, we obey the laws of thermodynamics." Homer Simpson

 

[rb1957]

i figure your pin is running left-to-right in your pic, and there is transverse load applied to the pin, reacted at the bush. wouldn't that mean that the transverse hole is in a section with a constant moment, sort of like a beam with two point loads (has constant moment between the loads).

 

[JakeAdkins]

Chris I have Norton's Design of Machinery (3rd) but it deals with statis and dynamics of Machines. It does not really deal with stress analysis.

 

[JakeAdkins]

rb1957 you are correct. The pin is under a bending condition. The transverse hole causes a stress concentration but the location of that stress concentration is supported with a bushing. I am wondering if the bushing support all the way around the pin effects the stress concentration.

The reason I am asking the question is when you go through the fatigue life calculations (treating the bushing as a distributed reaction load) the pin should not last very long ~1000 cycles but when it was tested it lasted 130K cycles and then had a fatigue failure at the transverse hole.

 

[rb1957]

is it a press-fit bushing ? then you could count it as part of the bending section ... also it would impose some (maybe small, maybe not) compression stress on the surface of the pin ... to be out by a factor of 100 is a bit much, even for fatigue calcs !

 

[desertfox]

Hi jakeAdkins

Can you give any sizes? from your drawing the proportions are such that using classical bending theory may not be applicable and the pin in that case would be in double shear.

regards

desertfox

 

[EngineerTex]

I don't think that you get much benefit from your bushing.

Look closely at what's happening in the bushing area. The end of the hole that sees tension is being pushed away from the bushing. The question would be how much?

It's going to happen one of two ways:

1) If the bushing material is much stiffer than the pin, then the pin will deflect to look something slightly bent compared to the much stiffer bushing which stays mainly straight. In this scenario, there's probably some certain amount of benefit that you get from the bushing, but only because the bending deflection of your pin has allowed the bushing to take up some of the bending load. But I don't think that's likely.

2) If the pin is as stiff as or more stiff than the bushing, then the pin moves out of contact with the bushing, and it's like there's no bushing there at all, rather it's being supported by a semi-circular seat. In that case, the stress concentration factor will be unchanged from your current calculation.

So, I'm going with number two, but you have to consider how you're calculating your stress distribution on the outside fibers of your member.

Your shear-moment diagrams will look one of two ways. You're either considering a point reaction in the center or that the bushing is carrying it as a distributed load. Neither of these is necessarily perfectly accurate, but you'll get the lowest calculated stresses if you consider the bushing to support the loads with a uniform stress. i.e., the moment diagram will look like a bell instead of a roof peak. HOWEVER, in order make certain that you are actually getting a uniform loading scenario from your bushing, you need to make certain that the deflection across the length of the bushing matches the deflection of the pin. Determine what cross-sectional shape you need for your bushing to achieve this and you can be sure of a uniformly-distributed load in the bushing.

Other than that, my gut tells me that if the pin you showed on your drawing is to scale with the bushing, then shear is the overriding factor while bending and stress concentration factors may be the least of your worries.

-T

Engineering is not the science behind building things. It is the science behind not building things.

 

[EngineerTex]

Dang. You beat me to the punch, desertfox.

-T


Engineering is not the science behind building things. It is the science behind not building things.

 

[desertfox]

Hi EngineerTex

Sorry about that, you must have been typing that fairly long
reply while I nipped in on your blind side.

regards

desertfox

 

[iainuts]

I'd agree with the fairly detailed responce by EngineerTex, but would also add the following for consideration.

Generally, there must be some amount of gap between the bushing and shaft. Let's assume first that the bushing is infinitely stiff such as if it were pressed into a housing of the same thickness as the bushing. In this case, the shaft's bending (ie: deflection) at the point where the transverse hole is, is restricted by how much clearance is available. Imagine a small clearnance and then imagine imposing a bending load (as you show in the picture) such that at first, only the two outer edges of the bushing are in contact at the top of the bushing as shown in the picture.

As the load is increased the shaft bends into a U shape with the center of the shaft coming down and contacting the opposite (lower inside surface) of the bushing. Further increase in load tends to flatten out the shaft in the center as it pushes against the lower surface shown in the picture - such that along this flattened, center section, stress is essentially zero (assuming the bearing is infinitely rigid). This probably won't happen, but by assuming a constant moment between the two edges, you can find the point where the deflection takes up all the gap between the bushing and shaft. An increase in the bending moment won't flatten it much, though you could continue this by assuming the shaft is cantalevered at some point just off center such that the imposed load causes the shaft to touch at the top of the bushing.

If you look at the stress created by this known deflection, you could then apply the stress concentration to that value. Note this is assuming the deflection calculated is less than the deflection as if it were a point load at each end of the bushing and a constant moment between them.

This all assumes an infinitely rigid bushing with no wear, so the next step would be to try and quantify how much additional deflection will result as the bushing material is compressed around the point loads. Also, as the bushing wears at the contact points, the shaft deflection will increase. So it could be that stresses are within the infinite life range for the material, but after some material is worn away from the bushing, deflection increases, resulting in increased stress and eventual fatigue failure.