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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

Singapore

*faezeh.arabhassani@gmail.com

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

experimental

I. INTRODUCTION

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]:

𝑓

!=1.012 !

!!

!

!

=!

!!

!!

!!""

(1)

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:

𝑘!=9.50𝐸𝑤(!

!)! (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.

II. PZT BIMORPH CANTILEVERS

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)

Po1.11-1

978-1-5090-1035-6/16/$31.00 ©2016 IEEE

Authorized licensed use limited to: UNIVERSITY OF BRISTOL. Downloaded on November 25,2020 at 08:15:30 UTC from IEEE Xplore. Restrictions apply.

TABLE I. PROPERTIES OF PZT CANTILEVERS’ MATERIALS

Material

Young’s Modulus (GPa)

Density (g/m3)

PZT

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

7.8

Copper

120

8.96

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].

III. MASS SENSITIVITY

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!" )𝑤∆𝐿

(3)

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.

IV. CONCLUSION

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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2016 International Conference on Optical Mems and Nanophotonics (OMN)

Po1.11-2

978-1-5090-1035-6/16/$31.00 ©2016 IEEE

Authorized licensed use limited to: UNIVERSITY OF BRISTOL. Downloaded on November 25,2020 at 08:15:30 UTC from IEEE Xplore. Restrictions apply.