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Ball seal calcualtions

Ball seal calcualtions

Ball seal calcualtions

(OP)
I'm looking for a formula or reference on how to calculate the amount of preloading a ball seal would need to withstand a large amount for pressure.

I want to use a 3/8" bearing to seal a volume. the bearing is held in place by a 7/16"  hollow set screw. See the picture.

I can calculate the preloading of the ball. I'm having a hard time on modeling stresses.

is the situation like this or:
     (a)                          (b)
____________             _____________
  <        <                    <        <
  >        >                    >        >   
Ball       <                  Ball      BODY  
  >        >                    >        >
  <        <                    <        <
_____   BODY             ______________          
  ▲        <                         ▲
  |         >                         |
  P         <                         P
  |         >
  ▼        <
____________

I think it is more like (a)

but I don't know how to put that into an equation that.
 

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