Stress Analysis for a groove in a cylinder

[feajob]

Hi,

I am trying to find out how stress analysis was performed for a groove in a cylinder? Unfortunately, there is no reference for the equations used in this analysis. I have attached this analysis.

I know that there is a ring, which goes into contact with the cylinder through a groove. So, contact stresses are involved. I checked chapter 13 of Roark's Formulas 6th edition. But, I am not able to find a reference for Parameters to calculate the moments, radial shear, and radial deflection shown on second page of the attached analysis. I appreciate to know if anyone already worked with this type of analysis. If so, please let me know what is the reference for all equations provided on the second page of analysis?

Thanks,
A.A.Y.

 

[rb1957]

are you troubled that the ring is not balanced ?

the two forces shown don't react the radial component of the ring's pressure distribution, and even if there isn't one (theta = 0) then the two forces are off-set.

maybe it's only in the picture ? what's loading the ring ? impact ? (this looks like a small actuator, <2"OD) the "ring" is not truly a ring, is it; 'cause it has to be open somewhere (how does it fit into the groove)

there are just so many failure modes ...
shear tear-out of the ring
collapse of the ring
bearing in the cyclinder
bending of the cyclinder walls

but the math looks very impressive !

 

[rb1957]

looking at the calc in detail, it's just a pic thing ... the calc has P applied and reacted on the ID of the cyclinder (X=A) ... so what's the fancy looking pressure distribution for ?

 

[rb1957]

but is that because R = 0 ??

but ti doesn't equal T ...

and what i said in my 2nd post isn't quite right, X = A 'cause R = 0; the calc shows the reaction offset from the load (Lb not equal to 0) ... so i'm back to an incomplete FBD ...

 

[rb1957]

seems odd that there's no check for bearing,

and why is Lb = 1/2 of T-t1 ? where is the centroid of a cosine pressure dist'n ?

in case you didn't figure, it's a slow day !

 

[feajob]

rb1957,

Thanks for your replies. All of your questions are good. I don't have any answer yet. I am trying to find out why?

A.A.Y.

 

[feajob]

rb1957,

I think that there is problem with Figure. In reality, two components of loads are applied to the ring (or groove). If you consider the resultant then they are in equilirium. This is spring type ring, that's why they can put it in the groove. In fact, its material is a music wire alloy.

Now, I believe that the sources of all those terms are Table 29 of Roark's 6th edition. Probably, superposition is used for considering the impact of radial and axial load components at groove.


Thanks for your remarks,
A.A.Y.

 

[rb1957]

the way i read the pic, the flange reaction is inclined, but the load applied to ring isn't (does show a radial load component).

but i think the equations are messed, with R=0 ...