Design of the Body

 

 

Select a suitable material for the body from table E-24

 

When two cylindrical parts are assembled by shrinking or press-fitting one part upon another, a contact pressure is created between the two parts.

 

A contact pressure  exists between the members at the transition radius R, causing radial stresses  in each member at the contacting surfaces.

 

The tangential stress at the inner surface of the outer member is found to be

 

                               Eqn. ( 3-61 )

 

where

 

  and 

 

Specify a suitable class of force fit from Table 19.6 and get the value of coefficient C from Table 19.7 (Standard Handbook of Machine Design, Shigley, Chapter 19 ).

 

Calculate the limit, L in thousandths of an inch corresponding to coefficient C and basic size D in inches

 

 

Take the worst case of minimum hole and maximum shaft.

 

This will give us the radial interference,  and is the radial deformation which the two members must experience.

 

Calculate  using Equ. ( 3-62 )

 

                Equ. ( 3-62 )

 

where

 

 

The body will also be subjected to compression as well as torsion.

 

 

 

,              

 

Calculate principal stresses with , , , and

 

.

 

Apply maximum normal stress theory to calculate factor of safety.

 

Determine the base dimensions

 

Check base for buckling.

 

 

Consider body as an equivalent column of inner diameter,  and outer diameter of .

 

 ,                                 

 

 

              

 

Calculate  by considering compressive stresses on the equivalent column

 

 

 

 

where  is ultimate compressive strength of the body material.

Take length of the column as .

 

 and .

 

                                                       

Calculate  ,  where     and      

 

 

If  , then it is a Johnson’s column, otherwise Euler’s column.

 

Calculate service factor, n. It should be greater than 3.5.

 

Calculate base seat outer diameter by considering bearing (compression) stress

 

 

 

Determine thickness ‘t’ of the base:

 

Assume a uniformly distributed load over the entire base seat at circumference i.e. at the center

 

 

  and

 

 

 

Calculate  and in terms of t.

 

Calculate t by applying appropriate failure theory for brittle material.