Machinery placed on Upper Floors of Buildings. 401 



the motor at about this speed until the position of: worst 

 vibration is found accurately. If the vibrations with the 

 badly balanced motor become too great, remove the weight 

 and allow the ordinary unbalance to create the resonant 

 vibrations. 



I£ the point of: maximum vibration is not easily perceptible 

 to the feel, one might use an indicator of vibrations such as 

 Digby's Vibragraph as made by Sieinen's Bros., and watch 

 its indications during the test (Electrician, vol. vii. p. ' 8, 

 1912). Suppose, now, we have found n 6 = 1400, and that 

 m/M = 0*l, and that the motor to be installed will run at 

 1800 r.p.m., what sort of elastic support shall we use to 

 avoid communication of vibration? Here n/n b = 1*285 ; to 

 get a good result the motor speed should lie midway between 

 the critical speeds, so make n a /n b — l'0 ; n a then =2100 and 

 the support should deflect 0*2 mm. under the weight of the 

 motor. The critical speeds are 1280 and 2340 approxi- 

 mately. Another good result would be obtained if 

 n a /n b = 0'4z or less; n a <560 ; the deflexion of the support 

 should be 3 mm. or more; the critical speeds would be 550 

 and 1420, which lie well away from 1800 r.p.m. If the 

 normal speed of the motor is the same as that of the floor, 

 viz. n = n b , then one should try to get ?i a = n b and the critical 

 speeds of the motor would be 1*17 and 0'86 n b . 



The conclusions to be drawn are : — 



(1) The critical frequency of rotation of a motor, mass ??i, 

 joined by an elastic support S to a body, mass M, resting 

 on another elastic support S', differs from the natural fre- 

 quency n a of m oscillating on S, and from the natural 

 frequency n b of M oscillating on S' ; unless the ratio m/M 

 is very small. 



(2) The critical speeds n u n 2 , or the critical angular 

 velocities a*!, &> 2 °£ the motor are related to the natural 

 frequencies, n a of the motor on spring S and n b of the floor 

 on spring S', thus 



n x n 2 = n a n b . 



(3) If the ratio of weights m/M < 0*1 and also n a /n b <0'2, 

 then ?i 1 = n a and n 2 = n b . 



(4) Fig. 4 shows how >*, and n 2 are related to n a and n b . 

 ni and n 2 always lie outside the range between n a and >i b . 



(5) Usually the mass of the floor M and the stiffness of 

 the floor represented by b, and the mass of the motor m are 

 fixed, but the elasticity of the support represented by a is 



