Document 5LQ5b6KzkKxgzbDB8wwXQVxQD

American Society of Heating and Ventilating Engineers Guide, 1934 Soderberg*. If a machine of mass m be supported by an elastic pad the amount of vibratory force communicated by the machine to the floor or foundation upon which it rests will be determined by the elastic and viscous properties of the pad. The ratio of the vibratory force communicated to the floor or foundation with the machine resting upon the pad, and with the machine resting directly upon the floor, is given by the following equation: where + 4*!n,* --Y2inm 2ime ) (4) c1 = the so-called transmissibility of the support, c = the compliance (that is, the reciprocal of the force constant). r = the mechanical resistance owing to the viscous forces within the support, n = the frequency of vibration generated by the machine which is to be insulated, such as the commutation frequency of a motor or the blade frequency of a fan. m =' the mass of the machine to be insulated. It should be noted that not only must vibrations within the audible range of fre quencies be considered, but those in the sub-audible range as well, since these may cause objectional vibrations. All the possible frequencies should be considered in the calcu lation. Sometimes beat effects are introduced by slight irregularities of belts or pulleys that have much lower frequencies than those of the rotating elements. If the pad is to be of any value in the prevention of solid-borne vibra tions; the value of t' must be considerably smaller than unity. If the fundamental frequency of vibration generated by the machine happens to coincide with the natural frequency of the mass of the machine resting on the elastic pad, a condition of resonance will be established, and the machine will exert a greater force upon the foundation than it would if the pad were completely removed. It is necessary, therefore, that the elastic support be sufficiently compliant, and the mass of the machine sufficiently heavy, that the natural frequency of the mass m upon its elastic support will be low in comparison with the frequencies which are generated by the machine. Thus, if the principal vibrations in the machine be of the order of 100 vibrations per second, the natural frequency of the machine mounted on its elastic support should not exceed about 20 vibrations per second. If a slab of insulating material be placed under the entire foundation of a machine, as is often done in practice, it may happen that the natural frequency of the machine on its elastic support will be nearly the same as the frequencies which are to be insulated, in which case the elastic support will be worse than nothing. In general, as Equation 4 shows, both m and c should be as large as possible if the vibrations of the machine are to be effectively insulated from the solid structure of the building. Further more, the machine should rest upon a rigid floor so that the elastic yielding of the floor is prevented from communicating the machinery vibrations to the solid structure of the building. The elastic support under the machine acts as a low-pass filter which passes all frequencies below about two times the natural frequency of the machine mounted on its elastic support, but prevents all frequencies C. R. Soderberg, The Electric Journal (January, 1924). and succeeding articles. See also V. O. Knudsen, Physical Review, Vol. 32, 1928, p. 324. and A. L. Kimball, journal Acoustical Society of America, Vol 2. 1930. p. 297. 250 Chapter 18--Sound Control above about */from reaching the solid structure of the building. The principal influence of the internal mechanical resistance r is to limit the vibration at the resonant frequency. It is generally advisable, therefore, to use materials which have an appreciable internal resistance. The values of c and r can be determined for any specimen of flexible material and, when known, can be used to determine the insulation value of any particular set-up. The value of c can be obtained by making static measurements of the amount of displacement of the compressed support for each additional unit of the compressing force. If this be done for a specimen of the flexible material of a certain thickness and area of cross section, the compliance can be determined for any other thickness or area from the relation that c will be directly proportional to the thickness and inversely proportional to the area of the flexible support. When the internal resistance r is not too large, it can be determined by observing the successive amplitudes of the free vibrations of a mass m which rests upon a specimen of the flexible material, and solving for r by the usual logdecrement method. Or, if the damping be so great that the free motion of m is non-oscillatory, r can be obtained from measurements on the experi mentally-determined resonance curve of the forced vibrations of m, or from measurements of the rate of return of m when it is given an initial displacement. If the resistance of a certain specimen of material, as cork, felt, or rubber, has been determined by any of these methods, the resistance for any other thickness or area of the material can be determined approxi mately because the resistance will be inversely proportional to the thickness and directly proportional to the area of cross section of the .flexible support. Thus, if the values of c and r for a flexible material be known, it is possible to calculate, by means of Equation 4, the amount of insulation that will be obtained from the use of this material as a flexible support for a piece of equipment having a mass m. For the routine calculations in practice, r may be neglected with only a slight sacrifice of accuracy. Table 4 gives the values of c and r for a number of commonly used flexible materials. In general, there are two principal points to observe in the design of a flexible support for any piece of equipment, namely, the material should have a relatively large compliance and it should be loaded to nearly the upper safe limit of loading. Several flexible metallic supports have recently been developed. Example 2. A machine weighing 1000 lb has a base area of 20 sq ft. Assume that the principal vibration of the machine has a frequency of 100 cycles per second (most machinery vibrations are less than 150 vibrations per second, and the assumed frequency of 100 is cjuite representative of typical machines). Suppose that a 1-in. slab-of corkboard weighing 1.10 lb per board foot be placed between the machine and the floor. The loading on the cork will then be only 50 lb per square foot, or slightly more than A lb per square inch. (It is assumed that the compliance c in centimeters per dyne for a specimen 1 in. thick and 1 sq cm in cross-section is 0.25 X 10^ and the resistance-r in mechanical ohms is 0.15 X 10s). - The transmissibility is calculated in the following manner: Mass of machine in grams = 1000 X 454 = 4.54 X 10s. Area of base in square centimeters = 20 X 144 X 2.54 X 2.54 = 1.86 X 10*. 251