Document N28J1pwGEGQ1xpBJGODz5jyb

1936American Society of Heating and Ventilating Engineers Guide, natural frequency of. the 'machinery on the cork or felt is low in com parison with the frequency generated by the equipment, the cork or felt may be of little avail. The insulation of vibration can be accomplished by means of suitable elastic supports or suspensions, but the design of these elastic supports should be based upon calculation rather than guess-work. The theory of the. insulation of vibration was first worked out by Soderberg3. 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 com municated 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 r' + 4x*n*cs + (2xnm ~ db)2 (4) t1 = the so-called trdnsmissibility 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 objectionable vibrations. All the possible frequencies should be considered in the calcu lation. Sometimes beat effects are introduced by slight in-egularities 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 t1 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, \ind 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 50 vibrations per second, and for best results preferably 20. . When the forced frequency is low, it is frequently impossible to insulate for the fundamental forced frequency due to connecting pipe work and other relevant factors. In cases of this kind an effective installation of- *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. 334 18--Chapter Sound Control sound insulation may be obtained with a mounting which functions far above the fundamental forced frequency. For example, a compressor operating at 500 rpm has a forced frequency of 8.3 vibrations per second. By designing a mounting haying a natural frequency of 20 to 25 vibrations per second, it is possible to isolate practically all of the noise. 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 presents all frequencies Vabove about ine 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 staticmeasurements 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 thick ness 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 insu lation 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 335