EXAMPLE OF ALTERNATOR DESIGN 327 



tance in the design of high-speed machinery is the particular 

 speed at which vibration becomes excessive. Without attempt- 

 ing to go into the mechanical design of shaft and bearings, it 

 should be pointed out that the size of shaft in turbo-alternators 

 is determined mainly by what is known as the whirling speed, 

 which, in turn, depends upon the deflection of the rotor considered 

 as a beam with the points of support at the centers of the two 

 bearings. There will be one or more critical speeds at which 

 the frequency of the bending due to the weight of the rotating 

 part will correspond exactly with the natural frequency of vi- 

 bration of the shaft considered as a deflected spring. The vibra- 

 tion will then be excessive, causing chattering in the bearings 

 and abnormal stresses which may lead to fracture of the shaft. 



The maximum deflection of the rotor due to its own weight 

 together with the unbalanced magnetic pull (if any) can be 

 calculated within a fair degree of accuracy when the position of 

 the bearings and the cross-section of the shaft are known. The 

 whirling speed of a rotor with steel shaft, in revolutions per min- 

 ute, can then be calculated, because it is approximately 



190 



V Deflection in inches 



In turbo-alternators the whirling speed is generally, higher 

 than the running speed; but this is not a necessary condition' 

 of design; and in direct-current steam-turbine-driven dynamos, 

 where the provision of a commutator calls for the smallest possible 

 diameter of shaft, the whirling speed is commonly lower than the 

 normal running speed. In such cases it is necessary to pass 

 through the critical speed, causing vibration of the rotor, every 

 time the machine is started or stopped; but this is not a serious 

 objection. A good rule is to arrange for the whirling speed to 

 be either 25 per cent, above, or 25 per cent, below, the running 

 speed. Taking as an example the design under consideration, 

 the whirling speed should be either 1,800 + 25 per cent. = 2,250; 

 or 1,800 25 per cent. = 1,350. In the first place the permis- 

 sible deflection would be (2255) = - 00714 m -J anc * m tne 



(190 \ 2 

 j ocn) = 0.0198 in. 



By making a very rough estimate of the rotor weight and the 

 span between bearings, it will be seen that the smaller deflection 



