Design - May 2009
Negative stiffness a big positive for Vibration
systems shield delicate electronics from low-frequency vibrations
and require less space, investment, and maintenance.
- Negative-stiffness isolators use mechanical components
to keep vibrations from sensitive equipment.
- Negative-stiffness systems 0.5-Hz resonant frequencies
give them better low-frequency isolation efficiency
than pneumatic systems.
- Equipment that detects features on the atomic scale
benefits from the lower-noise environment negative-stiffness
Minus K Technology, minusk.com
"Smoothing out bad vibes"
Machine Design, Feb 26, 1993, has a detailed discussion
of the mechanics of negative stiffness isolators.
Minus K Technology
Edited by Jessica Shapiro
If you're trying to isolate sensitive equipment from vibrations,
air tables and other pneumatic systems come to mind. The low-frequency
vibration isolation and precise control needed to support state-of-the-art
instruments for microelectronics fabrication, industrial laser
and optical systems, biological research, and other areas may
seem to call for expensive active vibration isolators, but negative-stiffness
vibration isolators can provide the necessary protection at
a reasonable cost.
Vibration isolators keep incidental vibrations in the environment
from damaging or otherwise disturbing equipment. These environmental
vibrations come from many sources, according to Dr. David Platus,
president and founder of Minus K Technology, Inglewood,
Calif., and principal inventor of negative-stiffness vibration-isolation
| "One source of vibrations in a
building is HVAC equipment mounted on the roof. People
walking around in the building generate vibrations, too.
In taller buildings, wind can cause movement, particularly
horizontal oscillations. Vehicle traffic is another vibration
source," Platus says.
Environmental vibrations like these can have frequencies
as low as 2 Hz. Pneumatic systems typically have a resonant
frequency around 2.3 Hz, so they are not effective at
isolating equipment from low-frequency vibrations of this
nature. Negative-stiffness isolators, on the other hand,
with a resonant frequency at 0.4 to 0.5 Hz, can screen
out these lower-end frequencies. Vibrations under 1 Hz
are rare; when they do occur they carry little energy
that can affect the payload.
While users need to consider the range of frequencies
in the environment and which frequencies will most severely
effect the equipment being isolated, the vibration-isolation
efficiency is another consideration.
Isolation efficiency is the percentage of vibration energy that
gets past an isolation system into the equipment and is inversely
related to the transmissibility. Negative stiffness systems'
low resonant frequency means they exhibit lower transmissibility
at lower frequencies than pneumatic systems can. They also transmit
less vibration energy over the entire range of building vibration
frequencies of concern. A system with a 0.5-Hz natural frequency
has a 93% isolation efficiency at 2 Hz. The efficiency grows
to 99% at 5 Hz and 99.7% at 10 Hz.
The positives of negative stiffness
So how do negative-stiffness isolators produce their high isolation
efficiencies? And what exactly is negative stiffness?
Negative-stiffness isolators use one system to isolate payloads
from vertical motions and a different one to protect equipment
from horizontal motions. Both systems use a negative-stiffness
mechanism to keep overall stiffness and, therefore, resonant
frequency low. The mechanisms differ slightly for each direction
of movement. In the vertical direction, a stiff spring supports
the payload weight. Stiff systems have higher resonant frequencies
and tend to transmit more vibrations to the load, so a negative-stiffness
mechanism perpendicular to the spring's axis lowers overall
Horizontal flexures attach to the top of the spring. The flexures
are preloaded in compression so that the horizontal position
represents an unstable equilibrium when the preload compresses
the spring. This unstable equilibrium has the same effect as
a negative stiffness in the vertical direction.
The spring's positive stiffness, defined by its spring constant,
Ks, means that it compresses a given amount under a given weight
load and resists further compression. The flexures, on the other
hand, provide less resistance to deflection the more their position
departs from horizontal. This contrary behavior can be represented
by a negative stiffness, Kn.
Engineers setting up the system adjust the horizontal compression
preload and spring position so Kn approaches Ks. The result
is a low overall stiffness, which translates to low-resonant
In the horizontal direction, vertically oriented beam-columns
provide vibration isolation. Classic beam-column behavior dictates
that as the load on the end of a beam-column approaches the
critical buckling load, the beam column's horizontal stiffness
approaches zero with a corresponding drop in resonant frequency.
Beam columns can be modeled by two cantilevered beams meeting
at their free ends. Each cantilevered beam behaves as a horizontal
spring comparable with the spring in the vertical-vibration
isolator. The beam-column effect provides the negative-stiffness
For horizontal isolation, the pay-load itself is the preload
that gets the overall system's stiffness to approach zero. Systems
are sized for a range of payload weights, with the best isolation
performance toward the top of the weight range.
The horizontal and vertical-isolation systems combine for an
overall vibration-isolation product that is purely mechanical
in nature. This simplicity gives negative-stiffness systems
several advantages over pneumatic systems, in addition to the
ability to isolate at frequencies pneumatic systems find problematic.
The negative-stiffness vibration-isolation
system uses three subsystems to isolate the payload
from vibrations. The support spring, combined with the
vertical negative-stiffness flexures, clamp, compression
spring, and vertical-load and stiffness-adjustment screws,
isolates the system from vertical vibrations. The beam-columns
perform horizontal isolation. And the tilt flexure and
damper isolate tilt vibrations from the payload.
Negative-stiffness isolators can be designed for use in adverse
environments such as vacuum and high and low temperatures, due
to their all-metal construction. By contrast, pneumatic systems
run into problems when users need vibration isolation in such
"Pneumatic isolators can be used in vacuum chambers, but
they require very special seals and there is a risk they can
leak," says Platus. "High-performance pneumatic isolators
have sensors, valves, and pumps that keep them level. If the
payload mass is redistributing, the system wants to add or release
air to keep the table level."
In addition, pneumatic systems require compressed air that can
be tricky to feed into the sealed vacuum chamber. The need for
a compressed-air supply means users must have a dedicated compressed-air
line, a tank of pressurized gas, or a small compressor on hand.
Compressors generate their own mechanical and acoustic noise,
sometimes defeating the purpose of the vibration-isolation system.
Tanks of compressed gas can be costly and dangerous if not mounted
properly. Finally, dedicated lines can limit where in a room
users can place isolation systems.
Pneumatic systems can also be bulky,
further limiting where equipment can be housed in the
lab. Negative-stiffness systems vary in size by payload,
but can be much more compact. In many cases, better
isolation efficiency means a benchtop negative-stiffness
unit is sufficient to isolate a piece of equipment from
Simplicity can mean less maintenance and longer life,
too. Negative-stiffness isolators are designed for repeated
elastic deformation. The components do not deform plastically
or fatigue over time.
Cost-wise, negative-stiffness isolators are comparably
priced to air isolators. For many applications, they
can represent a lower-cost way to isolate sensitive
"Active vibration-isolation systems cost two to
three times what negative-stiffness isolators do,"
says Platus. "Negative-stiffness units' cost can
be comparable or even less than passive pneumatic units,
especially if users can replace big, freestanding air
tables with better-performing negative-stiffness benchtop
have resonant frequencies at 0.4 to 0.5 Hz, compared to
2.3 Hz for pneumatic systems. They transmit less energy
from low-frequency vibrations to the payload than do pneumatic
systems, and maintain better isolation performance through
building frequencies to about 100 Hz.
Researchers and engineers have found negative-stiffness vibration
isolation to be useful in sensitive analyses like atomic force
microscopy (AFM). Noise in AFM signals can be cut down by a
factor of two to three with negative-stiffness units when compared
with top-performance air tables. Reducing noise levels in the
sub-Angstrom range in particular brings clearer images that
let researchers see features the noise otherwise obscures.
Scanning-probe microscopes (SPMs) require unparalleled vibration
isolation, especially in the vertical axis, although they can
also be quite sensitive to horizontal vibrations. To achieve
the lowest possible noise floor, on the order of 1 A, isolation
is always used. Negative-stiffness isolators let users tailor
the system's resonant frequencies vertically and horizontally
without increasing complexity or facilities requirements.
Laser and optical systems are also extremely susceptible to
vibrations from the environment. Traditionally, large air tables
have been preferred for optical systems, but negative-stiffness
isolators are becoming a more common choice, especially since
they can provide 10 to l00x better isolation efficiency, depending
on vibration frequency.
Laser-based interferometers can resolve nanometer scale motions
and features. The sophisticated modern ellipsometry techniques
that allow this high performance rely on low noise for fringe-movement
detection. Properly isolating an interferometer improves resolution.
Optical profilers have similar sensitivity to vibrations due
to their complexity. Long optical paths can lead to angular
magnification of vibrations.
version of this article