Isolation Techniques
For 2.5-Inch
Hard Disk Drives
By Peter A. Masterson
Senior Applications Engineer
E-A-R Specialty Composites
Indianapolis, Indiana
This equation models the motion of a
linear single degree of freedom system
(1DOF) and forms the basis for much
shock and vibration analysis. The vibration transmissibility of a 1DOF system as
a function of excitation frequency is
shown in Figure 2. The peak represents
the natural frequency of the system and
is called resonance.
Introduction
The development of the 2.5-inch hard
disk drive is one of the primary reasons
behind the success of notebook computers.
But the increased portability that made
the computers so popular also made
them more vulnerable to shock. It also
increased the need for relatively quiet,
unobtrusive operation.
Elastomeric grommets have provided
the necessary isolation that many miniature hard drives need when packaged
in component-dense designs. They can
help design engineers achieve quieter
sound levels and improve durability and
shock protection.
Amplification Region
Transmissibility
Isolation Region
What is isolation?
Isolation is the decoupling of one mass
from another by using a spring or isolator.
Decoupling two masses reduces the
effect of one on the other. How much
vibration is transmitted depends upon
the stiffness and damping of the isolator
between the masses.
Fn
√ 2 Fn
Frequency (Hz)
Figure 2: Typical Transmissibility Curve
Head/disk
assembly
for hard
disk drive
The graph is indicative of a system with
light damping. If there were no damping
in the system the response at resonance
would be infinite. A highly damped system would have a lower amplitude peak.
This effect is represented in Figure 3. The
natural frequency Fn (in Hz) is given by:
MASS
Km
Isolator
Frame
Kf
Fn =
n = 0.16 √
k
m
= 3.13
√
k (lb/in)
weight (lb)
2
When a system is designed utilizing
isolators, the forcing frequency must be
out in the isolation region indicated in
Figure 2. This situation benefits the
acoustic characteristics of the system.
Isolation removes the structureborne
sound that would have been radiated
into the chassis. When there are occasional but unavoidable forcing frequencies
that agree with resonance, high damping
keeps the amplification to a minimum.
Figure 1: Frame-Isolator-Mass System: Sketch
and Model
Usually the larger mass is considered to
be the isolator’s foundation —ground—
such as the chassis of a computer. The
hard drive would have mass m and the
isolator would have stiffness k and
damping c as found in the differential
equation:
mx + cx + kx = F0
Page 2
Elastomeric materials used for isolation
do not actually exhibit viscous damping.
Instead they are characterized by hysteretic
damping, which is a displacement-dependant term usually called loss factor ( ) or
tan . The “rule of thumb” used to equate
viscous damping to loss factor is:
Low Damping
Transmissibility
High Damping
= 2
1
This relationship is most accurate for low
damping levels, but out of necessity it
must be used for basic modeling of high
damping levels as well.
Fn
√ 2 Fn
Frequency (Hz)
Figure 3: Effect of Damping on Transmissibility
Transmissibility is the ratio of the force
applied to the system Fo to the force
transferred to ground Ft. Another
common term for transmissibility is percent
isolation, which is equal to 1-T. (Note:
Transmissibility can also be determined
for acceleration, velocity and displacement in the system). The equation for
vibration force transmissibility T is:
n
((
√
( 1- ( (
Fo
( + 2 ( n
2
(
T = Ft =
1+ 2
In addition to the benefits for vibration
isolation, damping also benefits shock
isolation, by minimizing the G level
experienced and the sway space requirements. Additional information about
shock and damping can be found in the
E-A-R Specialty Composites white paper
called, “Shock Control for Portable
Electronics” available online at
www.earshockandvibe.com.
Chassis Design Advice
When designing an isolation system, it is
important to consider the support structure used to hold the isolation mount(s).
When a mount placed into a soft bracket,
its ability to damp shock and vibration is
compromised. The relationship of two
springs in series is:
n
Ks =
where is the critical damping ratio, n
is the natural frequency (in rad/sec) and
is the forcing frequency (again in
rad/sec) acting upon the system. The
symbol is defined as the ratio of the
viscous damping coefficient to the critical
damping coefficient.
Kf Km
(Kf + Km )
Ks is the effective system stiffness, Km is
the stiffness of the mount and Kf is the
stiffness of the frame. This equation
shows is that when the frame stiffness is
low, the effective spring rate is significantly reduced. As a consequence, there
is more deflection in the frame and less
deflection going into the isolator causing
its ability to damp vibration or shock to
be dramatically reduced. Specifically, the
effective damping can be calculated by
the following equations:
= cccr
Critical damping ccr is that damping level
which will return a disturbed mass back
to equilibrium in the shortest amount
of time.
Page 3
Ks
Km
= Ks
(
s
1 + s2
(
[
m +
(
Ks
Kf
(
s
m
+
Km (1 + m2 )
f
for
m < 0.5
f
Kf (1 + f2 )
]
for
m > 0.5
As a rule of thumb, frame stiffness
should be at least 10 times the isolator
stiffness. When this condition is met, the
isolator has the dominant effect and
controls the motion of the mass. Systems
with flimsy rails or beams will allow
vibration to propagate into or out of the
hard drive, and the highly damped isolators will provide only a small benefit.
CONFOR foam can offer shock-protection
solutions when there is little available
space for any isolation. CONFOR foam is
highly damped, and it exhibits that
damping capability even in sheets as thin
as 1.5 mm. The semi-closed-celled foam
can be compressed to 50 percent of its
thickness without dramatically impacting
its stiffness properties. Figure 5 depicts a
pad of CONFOR foam cut to cushion a
2.5-inch hard drive.
E-A-R Solutions
E-A-R Specialty Composites has developed
numerous shock reduction techniques
for electronic devices. The solutions
typically involve the use of highly
damped elastomers — ISODAMP®
thermoplastics and VersaDamp™ TPEs —
in the form of grommets, snubbers and
sleeves, or the use of our highly damped
CONFOR® foam.
E-A-R has engineered numerous styles
and sizes of ISODAMP and VersaDamp
grommets that provide isolation and
high damping. (See Figure 4.) Custom
designs can be easily molded as well.
Figure 5: CONFOR Cushion for 2.5-inch Hard Drive
Figure 4: E-A-R Specialty Composites Grommets for 2.5-inch
Hard Drives
7911 Zionsville Road
Indianapolis, IN 46268
Phone (317) 692-1111
Fax (317) 692-3111
Website: www.earsc.com
Electronics Website: www.earshockandvibe.com