Continuous Stiffness Measurement A
Agilent Nano Indenter G200 User’s Guide
A-11
(41)
and
(42)
In a CSM experiment, the excitation frequency, w, is set. You measure
the displacement amplitude (z
o
), phase angle (f), and excitation
amplitude (F
o
).
Therefore, using
, you can easily calculate
S
and
D
s
w
if you know the machine parameters K
f
, m, K
s
, and D
i
. The
parameters m, K
s
, and D
i
are determined by analyzing the dynamic
response of the system when the indenter is hanging free. This
calibration is performed in the factory, so you do not need to ever repeat
it. Details on determining the load-frame stiffness, K
f
, are provided in
, "NanoSuite" of this manual.
It is important to note that the reduced spring constant
(43)
continually changes over the course of a single indentation experiment.
Usually when one considers an oscillating system, the characteristics of
the components are fixed and the system response is examined by
changing the excitation frequency. However, during a CSM experiment,
the excitation frequency is fixed. The natural frequency, defined as
(K/m)
1/2
, continually increases because the contact stiffness,
S
, is
continually increasing. Resonance occurs when the natural frequency
passes through the excitation frequency. Because the system is
over-critically damped, no peak is observed in the displacement
amplitude at resonance.
S
1
F
o
z
o
------
cos
K
s
m
2
–
–
-----------------------------------------------------
1
K
f
-----
–
1
–
=
D
s
F
o
z
o
------
sin
D
i
–
=
K
1
S
---
1
K
f
-----
+
1
–
K
s
+
=
