4 Wilson, Faihn-c of ccrtam Cast Steel Dies. 



moment. The above solution substitutes for these con- 

 ditions no total radial pressure and no total moment of 

 radial pressure on any strip of rim parallel to the axis. 

 The surface of zero pressure is therefore sometimes 

 slightly without and sometimes slightly within the rim. 



At the inner face the manner of the distribution of 

 the pressure between the tube and the die is unknown, 

 but it may reasonably be taken that the pressure at the 

 emission edge is zero, since the hole is cylindrical at 

 that edge. 



It is, therefore, necessary to assume that the total 

 radial pressure over the inner face is proportional to the 

 pull on the tube, the average slope of the face, and the 

 friction between the tube and the die. The law of variation 

 of pressure over the inner face between the die and tube, 

 as given by these assumptions, seems sufficiently reason- 

 able to justify their adoption. 



If / = safe stress in the material of the die, and the 

 ratio of external to internal radii be taken as 2, formula 

 (i) gives 



(2) ^=yi-46i8|^ 



By recasting the dimensions of the dies in this way, it 

 was found that in some cases the strength could have been 

 increased, and the weight of metal reduced at the same 

 time. 



Determination of T. 



The value of T may be taken as the maximum pull 

 which the machine is capable of exerting, or it may be 

 obtained as follows : — Imagine the tube solid and its ends 

 firmly gripped and then pulled apart. The force necessary 

 to produce the required reduction of area would be 



(3) T=^r9i{^o-A,YA-'* 



* Mancli. Memoirs, \o\. 43, No. 10. 



