When two springs are better than one.
Wire-rope vibration isolators protect equipment from shock and vibration in a variety of commercial, industrial, military, and aerospace applications. A problem with such isolators, as well as with many other types, is an inability to mitigate high-vibration frequencies (at or above about 100 Hz). The reason is isolator transmissibility slowly falls off with rising frequency. Transmissibility is defined as the ratio of transmitted force to applied force.
But the addition of an undamped, stiff, solid-wire spring in series with and about two to three-times stiffer than the wire-rope spring effectively decouples the isolator and payload at high-vibration frequencies. Then transmissibility rolls off with increasingfrequency at double the rate (log scale) and is just slightly higher at resonance than conventional designs.
Of course, separate decoupling springs add complexity and cost. But the design of wire-rope isolators makes it fairly straightforward to integrate the devices during manufacture.
WIRE-ROPE ISOLATORS BY THE NUMBERS
Wire-rope isolators can be modeled as a single-degree-of-freedom, mass-spring-damper system. For a conventional wire-rope isolator, transmissibility, T between an isolator base and attached payload is given in complex notation by:
T=(As + B) / (Cs2 + As + B)
For isolators with an additional solid-wire spring in series, the expression is:
T=(As + B) / (Ds3 + Es2 + As + B).