The Nano-K® vibration isolators used in Minus
K isolation platforms employ a revolutionary concept in low-frequency
vibration isolation. Vertical-motion isolation is provided by
a stiff spring that supports a weight load, combined with a negative-stiffness
mechanism (NSM). The net vertical stiffness is made very low without
affecting the static load-supporting capability of the spring.
Beam-columns connected in series with the vertical-motion isolator
provide horizontal-motion isolation. The horizontal stiffness
of the beam-columns is reduced by the "beam-column" effect. (A
beam-column behaves as a spring combined with an NSM.) The result
is a compact passive isolator capable of very low vertical and
horizontal natural frequencies and very high internal structural
frequencies.
Nano-K
isolators typically use three isolators stacked in series: a tilt-motion
isolator on top of a horizontal-motion isolator on top of a vertical-motion
isolator. A vertical-motion isolator is shown in Figure 1.
It uses a conventional spring connected to an NSM consisting of
two bars hinged at the center, supported at their outer ends on
pivots, and loaded in compression by forces P. The spring is compressed
by weight W to the operating position of the isolator, as shown
in Figure 1. The stiffness of the isolator is K=KS-KN
where KS is the spring stiffness and KN
is the magnitude of a negative stiffness which is a function of
the length of the bars and the load P. The isolator stiffness
can be made to approach zero while the spring supports the weight
W.
A horizontal-motion isolation system consisting of two beam-column
isolators is shown in Figure 2. Each isolator behaves like
two fixed-free beam columns loaded axially by a weight load W.
Without the weight load the beam-columns have horizontal stiffness
KS. With the weight load the lateral bending stiffness
is reduced by the "beam-column" effect. This behavior is equivalent
to a horizontal spring combined with an NSM so that the horizontal
stiffness is K=KS-KN, and KN
is the magnitude of the beam-column effect. Horizontal stiffness
can be made to approach zero by loading the beam-columns to approach
their critical buckling load.
Figure 3 shows a schematic of a Series SP-1 vibration
isolation platform consisting of a weighted platform supported
by a Series SM-1 vibration isolator incorporating the isolators
of Figures 1 and 2. Flexures are used in place of the hinged bars
shown in Figure 1. A tilt flexure serves as the tilt-motion isolator.
A vertical stiffness adjustment screw is used to adjust the compression
force on the negative-stiffness flexures thereby changing the
vertical stiffness. A vertical load adjustment screw is used to
adjust for varying weight loads by raising or lowering the base
of the support spring to keep the flexures in their straight,
unbent operating position. This feature is automated in single-isolator
systems and to achieve automatic leveling in multiple-isolator
systems.
Performance
Based on field testing and user evaluations, the Minus K 1/2-Hz
vibration isolation platforms and workstations perform about 10
to 100 times better than high-performance air tables depending
on the vibration isolation frequencies. They also perform better
than active or electronic-cancellation systems.
The transmissibility curves, which compare top-performing air
tables with the typical Minus K 1/2-Hz performance, are shown
below. Minus K isolators (adjusted to 1/2 Hz) achieve 93% isolation
efficiency at 2 Hz, 99% at 5 Hz, and 99.7% at 10 Hz. Isolation
performance closely follows that of an ideal undamped single DOF
system up to about 10 Hz and reaches a floor in the transmissibility
curve with some resonances at the higher frequencies.
The Minus K curve below is typical for any Minus K 1/2-Hz system,
horizontal or vertical.
Nano-K
isolators typically use three isolators stacked in series: a tilt-motion
isolator on top of a horizontal-motion isolator on top of a vertical-motion
isolator. A vertical-motion isolator is shown in Figure 1.
It uses a conventional spring connected to an NSM consisting of
two bars hinged at the center, supported at their outer ends on
pivots, and loaded in compression by forces P. The spring is compressed
by weight W to the operating position of the isolator, as shown
in Figure 1. The stiffness of the isolator is K=KS-KN
where KS is the spring stiffness and KN
is the magnitude of a negative stiffness which is a function of
the length of the bars and the load P. The isolator stiffness
can be made to approach zero while the spring supports the weight
W. 
