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

380 14. Machinery Noise ControlBall or Roller Bearings with Stationary Outer RacesIn most bearing applications the outer race is stationary. Equation (14.22a)becomes0 − n C=− D I(14.23)n I − n C D Owhich yields the separator speedn C =n I D I(14.24)D O + D Iand the speed of the balls relative to the separator is given byn R B = n B − n C =− (n I − n C )D ID B=− n R I D ID B(14.25)Here n R Iis the speed of the inner race relative to separator speed. Equation (14.25)is obtained by eliminating n B through the use of relation (14.22b).Vibration and noise frequencies are related to the absolute speeds n, relativespeeds n R , and the number of balls or rollers ν B . For bearings with stationaryouter races, the following fundamental frequencies are likely to arise:1. Shaft imbalance:2. Outer race defect:f = n I60(14.26)3. Inner race defect:f O = n R O ν B60= n Cν B60(14.27)f I = n I Rν B60 = (n I − n C )ν B604. Defect or damage to one ball or roller:f B = 2n BR60 = n B − n C305. Imbalance or damage in the separator or cage:(14.28)(14.29)f C = n C(14.30)60With the appearance of the fundamentals as calculated above, harmonics 2 f ,3 f , ...are apt to occur.Example Problem 5Consider a ball bearing that uses twelve 8-mm-diameter balls. The inner andthe outer diameters are D I = 28 and D O = 44 mm, measured at the ball