ArticleStructural Dynamics of Mechanical Systems Using Spring Isolators
by Robert J. Sayer
This paper is a good read for anyone wanting to learn more about isolation of rotating machinery. It begins with a theoretical discussion of isolation and later presents the different types of isolators available today (elastomeric, spring, air, etc). Three real examples of isolated machinery are given (fan & two feeders). Throughout the paper, the inaccuracies of a single degree of freedom isolation model are stressed with an awareness of the flexural & torsional modes of the supported machines & bases above the isolators being emphasized. The structural dynamics of the foundation or floor supporting the isolators is also stressed.
There are three basic components to an isolated mechanical system; the equipment and structural base upon which the equipment is mounted, the isolator springs, and the foundation or structure that supports the isolator springs. The isolator spring can reduce the amount of dynamic force produced by the equipment from being transmitted into the foundation or supporting structure. An example would be a rooftop air handling fan and motor mounted on an isolator base supported by isolator springs. In this case, the springs minimize the amount of dynamic force produced by the motor and fan from being transmitted into the roof structure, thus, reducing building vibration.
Isolator springs can also reduce the transmission of foundation motion into equipment. An example would be an atomic force microscope mounted upon an isolator. The microscope does not produce dynamic forces that require isolation. However, the motion of the foundation upon which the microscope is supported could adversely affect it’s operation. In this case, the springs minimize the transmission of foundation vibration into the microscope.
It is important to understand that isolators do not eliminate the transmission of dynamic force or motion. Isolators simply reduce the transmission of dynamic force or motion. There will always be some amount of dynamic force that will be transmitted across the isolation springs.
Isolation design is commonly based upon the theoretical transmission equation for a single-degree-of-freedom (SDOF) vibrating system illustrated in Figure 1. The machine and isolator base are treated as a single rigid mass. The spring is assumed to be massless. The foundation upon which the spring and damper are supported is assumed be infinitely rigid.
The damper is assumed to be viscous and rigidly connected to the foundation. For the SDOF system illustrated in Figure 1, horizontal motion perpendicular to the major resisting direction of the spring is assumed to be constrained. The mass can only move in the vertical direction. The natural frequency of the simple spring-mass-damper system is given by Equation (1).
ωn = [k/m]1/2 [1-ζ2]1/2 Equation (1)
where k is the stiffness of the spring, m is the mass supported by the spring, and is the amount of damping (c) expressed as a percentage of critical damping (cc). For a lightly damped single-degree-of-freedom system, the damping term can be neglected and the natural frequency can be simplified using Equation (2).
ωn = [k/m]1/2 Equation (2)”
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