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Vibration-excitation Method for Measuring the Mass Sensitivity of a Macro-scale PZT Bimorph Cantilever


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The micro g/Hz mass sensitivity of a macro-scale PZT bimorph cantilever has been measured by using a vibration-excitation method in its second mode of resonance by using experimental and numerical methods.
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Vibration-excitation Method for Measuring the Mass
Sensitivity of a Macro-scale PZT Bimorph Cantilever
Faezeh Arab Hassani*, and Chengkuo Lee
Dept. Electrical and Computer Engineering
National University of Singapore
Abstract The micro g/Hz mass sensitivity of a macro-scale
PZT bimorph cantilever has been measured by using a vibration-
excitation method in its second mode of resonance by using
experimental and numerical methods.
Keywords PZT bimorph cantilever; mass sensitivity;
vibration-excitation; second mode resonance; numerical and
Piezoelectric cantilevers can be used as high sensitive mass
sensors with the help of a coating layer for sensing various
types of biological and chemical molecules [1,2]. The
vibration-excitation provides a simple but accurate method for
the excitation of piezoelectric cantilevers for characterizing the
changes in the resonance frequency [3-5]. The usage of the
higher resonance modes of cantilevers improves the sensitivity
of the cantilever sensors for sensing small change in the
adsorbed mass [1,6,7]. The second mode resonance frequency,
f1, of the out-of-plane cantilever is calculated by using [8]:
!=1.012 !
where meff is the effective mass, km is the mechanical spring
stiffness, t is thickness, L is the length, E is Young’s modulus,
and ρ is the density of the cantilever. Considering,
meff=0.235ρwtL [8] in eq. (1), km, is calculated by:
!)! (2)
In this paper, we first model the uncoated PZT bimorph
cantilever by using the COMSOL software. The resonance
modes of cantilevers in various lengths are measured next, to
find out the mass sensitivity in the second resonance mode for
the comparison with the numerical result.
Commercial bimorph cantilevers with the length of 40 mm,
width of 10 mm, and thickness of 0.5 mm are purchased from
STEMiNIC Inc. By changing the clamping point of the
cantilevers, two effective lengths of 35, and 36.5 mm are used
for the experiments. The cantilevers consists of a thin layer of
Copper sandwiched between two layers of Lead Zirconate
Titanate (PZT) layers. The PZT layers are connected in series
and are oppositely polarized in the z-axis direction. By
applying acceleration in z-axis direction, a voltage will be
induced in the PZT layers that is picked from the Copper layer.
A. Numerical Modeling
COMSOL software is used for modeling the cantilevers.
The thickness of 0.2 mm is considered for the PZT layers, tPZT,
while the thickness of the Copper layer, tCu, is 0.1 mm. A force
of 1.568 mN is applied to the tip of cantilever to model the
acceleration of 0.5g (g=9.8 m/s2) used for the following
experiments. Fig. 1, shows the z-axis displacement of 35 mm-
and 36.5 mm-length cantilevers versus frequency in the first
two resonance modes. A frequency change, f, of 21 Hz for the
first mode and 105 Hz for the second mode is calculated in Fig.
1 by increasing the length from 35 mm to 36.5 mm. The out-of-
plane movement of the resonance modes of cantilevers are
shown in inset to Fig. 1. The mechanical properties of the
materials are given in Table I.
B. Experimental setup and results
The cantilever is clamped on top of a vibration exciter (type
4809 Brüel & Kjær) and various accelerations of 0.5g, g, 1.5g,
and 2 g are applied to the cantilever that causes the out-of-
plane resonance. Fig. 2 shows the experiment setup. The
attached accelerometer on top of the exciter, the amplifier, and
the vibration controller manage the acceleration applied to the
exciter and consequently the cantilever.
Fig. 1. The z-axis displacement versus frequency for the PZT bimorph
cantilevers with the length of 35 mm and 36.5 mm.
2016 International Conference on Optical Mems and Nanophotonics (OMN)
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Young’s Modulus (GPa)
Density (g/m3)
Elasticity constants
C11=C22=138.5 GPa
C12=77.4 GPa
C13=C23=73.6 GPa
C33=114.7 GPa
C44=30 GPa
C55=C66=25.6 GPa
Fig. 2. The measurement setup for PZT bimorph cantilevers.
The root mean square (RMS) value of the induced piezo
potential in the PZT layers versus frequency is then measured.
Fig. 3 presents the output voltage versus frequency for the first
two resonance modes for lengths of 35 and 36.5 mm in the
presence of 0.5g acceleration. f of 16 Hz for the first mode
and 30 Hz for the second mode is measured in Fig. 3 by
increasing the length from 35 mm to 36.5 mm. The inset to Fig.
3, shows how the increase of acceleration results in the
reduction of double peaks at the first mode to a single peak.
The dual peak is due to the not perfect bonding between the
Copper and PZT layers [9], and it will vanish by increasing the
acceleration due to the spring hardening effect [10].
The mass change, m, of the cantilevers due to the increase
of length and coating of polymer will cause changes in the
resonance frequency, f. However, the frequency change can
be negative or positive due to the stronger effect of changes in
the mass or spring stiffness [10]. Since, the changes in the
frequency for a higher mode of resonance is larger [6,11], the
calculations for the mass sensitivity in this paper has been
conducted for the second resonance mode.
Fig. 3. The output voltage versus frequency for PZT cantilevers with
the length of 35 and 36.5 mm.
The mass change, m, between 35 and 36.5 mm-length
cantilevers is calculated by using the following equation:
𝑚=0.235(2𝜌!"#𝑡!"# + 𝜌!"𝑡!" )𝑤𝐿
where ρPZT and ρCu are the density of the PZT and Copper
layers respectively. A m of 14.1564 mg is calculated by using
eq. (3). The increase in the length of cantilever will reduce km
by using the eq. (2), and increase the mass. Thus the resonance
frequency is reduced by referring to the eq. (1). This effect is
consistent with the numerical result in Fig. 1. By considering
the frequency change of 30 Hz in Fig. 3 for the second
resonance mode of the cantilever, a mass sensitivity of 0.47
mg/Hz is calculated. Similarly, by considering f=105 Hz in
Fig. 1, a mass sensitivity of 0.13 mg/Hz will be achieved.
Polymer coated PZT bimorph cantilevers will be used for
sensing chemical targets in liquid. For this reason, the micro
g/Hz sensitivity of the cantilevers before coating has been
calculated by using a vibration-based setup at the second
resonance mode. The achieved sensitivity value will be used
for investigating the properties of the polymer coating in the
future. A good consistency between the numerical and
experimental result has been observed for the mass sensitivity.
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