THE SCIENCE AND APPLICATIONS OF ACOUSTICS - H. H. Arnold ...

14.10 Ball and Roller Bearings 381contact points. The outer race is stationary and the inner race rotates at speedn I = 4500 rpm clockwise. Determine (a) the rotational speeds and (b) the noiseand vibration frequencies which will occur if there are defects and imbalancepresent.SolutionIt should be obvious that D I + 2D B = D O.(a) Use Equation (14.24) to find the separator speedn C =n I D I= 4500 × 28 = 1750 rpmD O + D I 28 + 44and, from Equation (14.25), the speed of the balls relative to the separatorisn B R = n B − n C =− (n I − n C )D I=−(4500 − 1750) × 28D B 8=−9625 rpm (counterclockwise)(b) We find the fundamental frequencies as follows:1. Shaft imbalance:2. Outer race defect:f O = n O R ν B603. Inner race defect:f I = (n I − n C )ν B04. Defect or damage to one ball:f = n I60 = 4500 = 75 Hz60= n Cν B60=f B = 2n BR60 = n B − n C30=1750 × 1260(4500 − 1750) × 1260= 350 Hz= 550 Hz=− 962530 = 320.8HzNotice that the negative sign is ignored in this answer.5. Imbalance or damage in the separator or cage:f C = n C60 = 175060 = 29.2HzHarmonics of all of the above frequencies are likely to occur.Ball or Roller Bearings with Nonstationary Outer RacesFor some applications, the shaft attached to the inner race of a bearing remainsstationary while the outer race rotates. In this case, n I = 0 and we obtain the