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

14.8 Gears 371fromwheref BRC = N r × N s60 K BRC× n Hz (14.11)f BRC = blade-rate component frequency, HzN r = number of rotating bladesN s = number of stationary bladesK RBC = greatest common factor of N r and N sn = rotational speed, rpmExample Problem 3Find the frequency of the blade rate component of a diffuser-type compressor withN r = 16 and N s = 24 and operating at a speed of 6000 rpm.SolutionUsing Equation (14.11) we find thatf BRC = N r × N s 16 × 24× n = × 6000 = 4800 Hz60 K BRC 60 × 8If the blade-rate component frequency falls within the audio range, we shouldexpect an increase of several decibels in the octave-band sound power level inwhich it occurs.The total sound power level in the four octave bands with center frequencies of500, 1000, 2000, and 4000 can be roughly estimated for both reciprocating andcentrifugal compressors from the expressionL w = 10 log hp + K c dB (14.12)where K c = air compressor constant = 86 dB for the 1–100 hp range. Equation(14.12) is very similar to Equation (14.10) for pumps, and either expression willyield a straight line in a semi-log plot. Also, it is not unreasonable to estimate thatthe sound power is equally divided among the four octave bands. Thus, each bandlevel is 6 dB below the total estimated from Equation (4.12).14.8 GearsInternal combustion engines and electric motors generally operate at speeds of oneto several thousand revolutions per minute. These high speeds help maximize thepower-to-weight and power-to-initial cost ratios. Gearing and other speed reducersare applied when the driven machinery requires high torque and low speeds.