SPHERES AND CYLINDERS 



129 



Thus, if the correction for ellipticity is denoted by C f l and the 

 correction for variation in thickness by (7 a , we have 



~ _ minimum outside diameter 



1 maximum outside diameter' 



_ minimum thickness 



2 average thickness 



and the correction constants C and K are therefore defined as 



By an experimental determination of C and C z the formulas can 

 therefore be applied to any given type of tube. 



82. Shrinkage and forced fits. In machine construction shrink- 

 age and forced, or pressed, fits are frequently employed for connect- 

 ing certain parts, such as crank disk and shaft, wheel and axle, etc. 

 To make such a connection the shaft is finished slightly larger than 

 the hole in the disk or ring in which it belongs. The shaft is then 

 either tapered slightly at the end and pressed into the ring cold, or 

 the ring is enlarged by heating until it will slip over the shaft, in 

 which case the shrinkage due 

 to cooling causes it to grip the 

 shaft. 



To analyze the stresses aris- 

 ing from shrinkage and forced 

 fits, let D l denote the diameter 

 of the hole in the ring or disk, 

 and D z the diameter of the 



shaft (Fig. 98). When shrunk or forced together, D v must increase 

 slightly and D 2 decrease slightly; that is, D x and D 2 must of necessity 

 take the same value D. Consequently, the circumference of the hole 

 changes from TT D^ to TT D, and hence the unit deformation % l of a 

 fiber on the inner surface of the hole is 



irD - 



D 



FIG. 



