Document Vj2ZEZQvY7eYZEEkQyZEa37Eo

HEATINC VENTILATING AIR CONDITIONING GUIDE 1943 CHAPTER 33. SOUND CONTROL there is one basic law which is important in the solution of the problem. That is the law of transmissibility as governed by the equation: where . T = transmissibility of the support. w = frequency of the, vibratory force. tn = natural frequency of the machine unit on its support (Damping -- 0). By the use of Equation 14 a set of curves may be plotted as shown in Fig. 7. The first line AB plotted as the critical frequencies for the various static deflections, is a curve showing the worst possible conditions or, resonant conditions. Plotting another curve CD, which is times curve AB, shows the area MCDN in which the resilient material or mounting does more harm than good. Plotting two more curves EF, 3 times curve AB, and GH, 5 times curve AB, shows area EGHF which represents efficient and eco nomical isolation. Area GPOH is excellent isolation but for all except the Equation 13 shows that the transmissibility approaches unity for disturbing frequencies considerably lower than the natural frequency of the mounting. As the disturbing frequency is increased the transmis sibility is also increased until at the resonant frequency, where w = wa the transmissibility becomes infinite. This is not true in practice because all materials have some internal damping effect. However, operating at or very close to the resonant frequency is always serious as forces and stresses may be multiplied 10 to 100 times. As the disturbing frequency becomes greater than the natural frequency the transmissibility becomes a smaller quantity and at the value of w/wa = V~2 it again has the value of unity. Beyond this point true isolation is first accomplished. At a ratio of 3 to 1 for w to w,, the isolation is effective enough for practical application, and experience and economical design has shown that a ratio of 5 to 1 is good. For high speeds, higher ratios for w to ien are easily attained and give better results for effective vibration control but for the lower speeds as experienced with compressor work the higher ratios become uneconomical. For a given installation the speed of the compressor is fixed by the specifications, therefore the value of w is fixed. That leaves only wa to be determined and that is accomplished by the choice of mounting material and design for the support of the machine. It is well to keep in mind that/ when trying to isolate vibration, no attempt should be made'to isolate the driving and driven piece of equipment separately. The two should be mounted on a rigid frame and then the entire assembly isolated according to the rules presented in this chapter. Fig. 7. Static Deflection for Various Frequencies The value of wn can be controlled by the flexibility of the machine highest speeds becomes rather uneconomical because of the large deflec support, and when the deflection of thd- machine support is proportional to the load applied (such as springs or nearly so with rubber in shear) the tions required. value of wa can be determined by Equation 14. Example S. Air electric motor driven compressor unit is to be isolated. The com pressor is partially balanced and operates at a speed of 360 rpm. The speed of the motor %= JjL- . (14) is 1160 rpm and is belt connected to the compressor. Total weight of the. compressor " d and motor is 4500 lb. where Solution: The minimum disturbing frequency to be isolated is 360 cycles per minute. Assume that the desired ratio of forced to natural frequency is 3 as a minimum and that 1 g -- gravitational constant. 5 is desired.. The desired natural frequency of the mounting is 360 4- 5 = 72 cycles 1 d = static deflection of supporting material. to = radiants per second and may be converted to frequency (J) expressed in cycles per minute. From Fig. 7 a deflection of 7 in. is required to attain a natural frequency of 72 cycles per second by Equation 15. per minute. This value may be obtained from critical curve AB for 72 cycles or from curve GH (5 times critical) for 360 cycles. For the minimum ratio of 3 the deflection (15) would be 2.5 in. The next step is to determine the total weight to be supported by the springs. For 642