314: The Lateral Vibration of Loaded Shafts. 



maoy 2 k 2 



Then we have F 

 and F' 



m'acoH-' 2 



■K 



F' m' k'XP-co-) 

 so that ¥ - - X ffjjfZ&p 



If now Jc={l+p)co, k' = (l—p)(o, we find 



F _ m; ' 2- p(3-p 2 ) 

 F"~ m x 2 +/>(3 -/>*)' 



which is less than 1. 



Hence F' is less than F, or the centrifugal force is less 

 when the whirling speed is below the working speed rather 

 than the same amount above. 



11. To get a numerical idea of the degree of balance 

 desirable in any machine, we will consider the case of a 

 rotor consisting of a single heavy mass of 5 tons concen- 

 trated at the span centre. 



Further, suppose the working speed to be 1000 r.p.m. 

 and the critical speed 1250 r.p.m. 



Then 



Also F = mlc 2 u = 



a 1'25 2 -1 ' 



thusw = l'8a. If, therefore, the amplitude is to be limited 

 to say '0001 inch, a must be not more than about half that 

 figure. 



5 x 2240 /1250\ 2 1-8 

 32 X \»'5d) X V2 a 

 = 900,000 a, 



where a is inches, and F is lb. Putting a = '0001 inch, we 

 find F = 90 lb. 



If the rotor be out of balance to the extent of -^ oz. at a 

 radius of 10 inches, this corresponds to an eccentricity of 

 the mass centre of "00003 inch. Good balancing would realize 

 this figure. 



