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

372 14. Machinery Noise ControlMechanical power, shaft speed, and torque are related as follows:P kW = 10 −6 T ω (14.13)whereP kW = transmitted power, kWT = torque, N mmω = πn/30—angular velocity, rad/sn = shaft speed, rpmIn English units, Equation (14.13) becomesP hp =Tn(14.14)63,025whereP hp = transmitted power, hpT = torque, lb-inn = shaft speed, rpmIt was observed by Hand (1982) that gear noise increases with speed at the rate of6–8 dB per doubling of speed. It was also observed that an increase of 2.5–4 dB ingear noise occurs for each doubling of load. Thus, according to Equation (14.13)or (14.14) a reduction in speed results in an increase in torque, if the transmittedpower is to be sustained, and so the noise effect of speed reduction is somewhatoffset by the increase in the torque.Meshing FrequenciesThe profile of most gear teeth is that of an involute curve. Force transmits throughthe driving gear to the driven gear along the line-of-action, which is fixed in space(excepting planetary gear trains). If the gears are ideal, perfectly fabricated, rigid,and transmitting constant torque, the power should be transmitted smoothly andwithout vibration or noise. Real gears, however, have tooth errors in spacing andtooth profile, and in some cases, an appreciable shaft eccentricity. Gear teeth doact elastically and flex slightly under load. Consequently, the driving gear teeththat are not in contact deflect ahead of their theoretical rigid-body positions, whilethe driven teeth that are not in contact lag behind their theoretical positions. Thisresults in a rather abrupt transfer of force when each pair of teeth comes intocontact, instantaneously accelerating the driven gear and decelerating the drivinggear. The fundamental frequency of the noise and vibration is given byf = nN(14.15)60wheref = the fundamental tooth meshing frequency, Hzn = rotational speed of the gear in questionN = the number of teeth in the gear in question