Document RpvxVwzo1qY1nmz07DQ2GYjbn

HEATING VENTILATING AIR CONDITIONING CUIDE 1944 where T = transmissibility of the support. to = frequency of the vibratory force. ten = natural frequency of the machine unit on its support (Damping = 0). Equation 12 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 = wB 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 -- 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 wn the isolation is effective enough for practical application, and experience and economical design have shown that a ratio of 5 to 1 is good. For high speeds, higher ratios for w to wn 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. The value of wa can be controlled by the flexibility of the machine support, and when the deflection of the machine support is proportional, to the load applied (such as springs or nearly so with rubber in shear) the value of wa can be determined by Equation 13. Wn = (13) where g = gravitational constant. d = static deflection of supporting material. to = radians per second and may be converted to frequency (/) expressed in cycles per second by Equation 14. ,' <i4> By the use of Equation 13 a set of curves may be plotted as shown in Fig. 7. The first line AB plotted as the critical frequencies for the various 636 CHAPTER 33. SOUND CONTROL static deflections, is a curve showing the worst possible conditions or resonant conditions. Plotting another curve CD, which is y/~2- 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 EGIJF which represents efficient and eco nomical isolation. Area GPOH is excellent isolation but for all except the highest speeds becomes rather uneconomical because of the large deflec tions required. .- Example S. An 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 is 1160 rpm and is belt connected to the compressor." Total weight of the compressor and motor is 4500 lb. 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 5 is desired. The desired natural frequency of the mounting is 360 + 5 = 72 cycles per minute. From Fig. 7 a deflection of 7 in. is required to attain a natural frequency of 72 cycles 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 would be 2.5 in. The next step is to determine the total weight to be supported by the springs. For low speed partially balanced compressors, it has been found necessary to add a founda- 637