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

Problems for Chapter 14 407the noise and vibration frequencies that can occur as the result of imbalanceand defects.8. A ball-bearing is constructed as follows: it has twelve 15-mm-diameter balls,and the inner race diameter is 50 mm at the point of ball contact. The innerrace has a rotational speed of 1800 rpm and the outer race remains stationary.Find:(a) rotational speed of separator(b) speed of the balls relative to the separator(c) shaft imbalance frequency(d) outer race defect frequency(e) inner race defect frequency(f) frequency arising from damage to one ball(g) frequency attributable to imbalance in the separator.9. A roller bearing contains ten 16-mm-diameter rollers. The inner race diameteris 30 mm. The inner race rotates at 6000 rpm while the outer race remainsstationary. Find:(a) rotational speed of the separator(b) speed of the rollers relative to the separator(c) shaft imbalance frequency(d) outer race frequency(e) inner race frequency(f) frequency caused by a defect in one roller(g) frequency caused by imbalance of the separator.10. In a nonplanetary gear transmission, the input shaft gear has 40 teeth and rotatesat 1200 rpm. It meshes with another shaft through a 30-tooth gear. Predict allof the fundamental frequencies that are likely to arise in this transmission.11. The gears of a reverted gear train of Figure 14.8 carry the following specifications:gear 1 (driver), 50 teeth; gear 2, 90 teeth; gear 3, 46 teeth; and outputgear 4, 47 teeth. The input shaft rotates at 2400 rpm.(a) Determine the rotational speeds of the other shafts.(b) Compute each of the fundamental tooth-error and shaft frequencies andthe first three harmonics.(c) Find all of the fundamental tooth meshing frequencies and their first threeharmonics.(d) Determine the sideband frequencies.12. It is specified that a pair of spur gears is to be used to reduce shaft speed from2400 rpm to 1600 rpm. The driver has 18 teeth and a diametral pitch of 4. Thepressure angle is 20 ◦ in the stub teeth.(a) Predict the fundamental tooth-error frequencies.(b) Determine the fundamental tooth meshing frequency.(c) Find the contact ratio, on the basis of Equation (14.21) and discuss theresults in terms of noise. Assume that a = 0.25.13. Consider a chain drive system that contains a 15-tooth input sprocket thatrotates at 2500 rpm. The chain has 90 links, and it is specified that the outputsprocket rotates at 1500 rpm. Determine: