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LXXV. The Whirling Speeds of a Loaded Shaft supported 

 in Three Bearings. By H. H. Jeffcott *. 



§ 1. Introductory. 



THE problem of the mechanical support of the rotor of a 

 turbo-generator may be solved in two or more ways. 

 Some designers arrange the turbine and generator each 

 separately with two bearings, and connect the shafts of the 

 machines by a flexible coupling, thus permitting each to 

 preserve its own alignment. On the other hand, many 

 machines are built with three bearings and a continuous 

 shaft. In some instances the main rotor is supported in two 

 bearings, and the third bearing is of the nature of an 

 outboard one supporting the overhanging rotor. Other 

 machines too. besides turbo-generators, are designed with 

 three bearings, for example, turbo-blowers, motor driven 

 pumps, etc. 



On account of the high speeds at which turbines operate 

 it is important that the designer should determine the 

 whirling speeds, and in many cases it is necessary that at 

 -least the first two whirling speeds should be calculated. It 

 is true that by the use of a very stiff and heavy shaft the 

 lowest whirling speed may in many cases be kept above the 

 normal working speed of the machine. But in other cases, 

 where very high efficiency is essential, a smaller shaft will 

 give a lighter rotor, and with smaller journal dimensions, it 

 will lead to reduced friction loss in the bearings and a more 

 economic performance. Also it is probably well known 

 that, in the design of high-speed electric generators for 

 direct coupling to steam turbines, the shaft must sometimes 

 be kept somewhat small in diameter, and as a consequence 

 the working speed usually lies somewhere between the first 

 and second whirling speeds, at all events in the higher speed 

 machines. In this case the size of the shaft is limited by 

 magnetic considerations. The machine being designed for 

 a high rate of revolutions, in order to limit the centrifugal 

 stresses in the windings the outside diameter of the rotor 

 must be kept low. This restricts the depth of core through 

 which the magnetic flux is carried, and in order to avoid too 

 high a flux density in the core-plates the shaft diameter must 

 be kept small. 



It will be seen therefore that, both from the point of view 

 of securing high efficiency and of providing adequately For 

 the magnetic circuit of the rotor of the electric generator. 

 * Communicated by the Author. 



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