# A Novel Drive Option for Piezoelectric Ultrasonic

Authors: Diana Engelke; Bernd Oehme; Jens Strackeljan
Journal: Modelling and Simulation in Engineering
 (2011)

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## Abstract

This paper concentrates on ultrasonic transducers, which are driven by
piezoelectric ceramic rings that are arranged in a stack. A novel drive option,
where the stack contains a new type of divided piezoelectric rings, is analyzed
using the finite element method, prototyped, and tested. To gain a better sense
of the vibration behavior, the studies focus initially on one ring and
subsequently on the different possibilities to assemble the transducer. The
investigations point out that natural bending frequencies can be excited at the
transducer. Thus, multiple vibration directions of the tip can be controlled,
what can be advantageous for instance in dental applications.


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## Body

## 1. Introduction

Piezoelectric actuators are applied in various engineering applications, for example,
in the fields of nanopositioning, ultrasonics (ultrasonic welding), ultrasonic
motors and diesel injection. These transducers use the piezoelectric effect for the
conversion of electrical energy to mechanical displacement. They have the advantage
to combine high speed and high positioning precision. An application example is the
sandwich or Langevin transducer. The transducer or parts of it have been analyzed
analytically in [1–3] and by means of the Finite Element Method
(FEM) in [4, 5] as well as by experimental studies in [6, 7]. This paper investigates a
dental ultrasonic scaler by means of the FEM and validates the data via
experiments.A dental ultrasonic scaler (Figure1) is a
hand-held instrument for the mechanical removal of dental plaque and calculus from
the teeth. It is driven by piezoelectric ceramic rings that are arranged in a stack
and that induce axial vibrations. These vibrations are transmitted through the
sonotrode (or horn), which amplifies them, to the tip. The tip is shaped in a way
that it increases the amplitudes further, so that the resulting oscillation can
remove the dental plaque. The resonator absorbs the reaction forces that emerge
during operation and the o-rings serve as bearing. The dentist uses the scaler
during the periodontal therapy or the professional dental cleaning. A laboratory
study [8] revealed that the tooth surface
takes little damage if the scaler tip oscillates in parallel to it (Figure 2 left).Figure 1
Dental ultrasonic scaler (upper view).Figure 2
Handling of the scaler.Today, there are two types of scaler probes on the market, the straight and the bent
probes. The straight probes are intended to vibrate with a linear movement in the
longitudinal direction (the x direction or 0° in Figure1) of the scaler. Recent studies [6, 9] showed that this
vibration behavior is not always ensured and the tips may oscillate elliptically and
with a lateral component. However, this is generally unintended [10]. By contrast, the bent probes are designed
to oscillate asymmetrically to the longitudinal plane, since the geometrically shape
is asymmetrical [9]. For both kinds of probes
an elliptical vibration pattern of the tip is possible, depending on the shape and
design of the probe. In this paper, the main vibration direction of the tip will be
evaluated, because previous measurements of the considered probe revealed that the
elliptical component is negligible.However, all of the above mentioned scalers oscillate in solely one main direction.
It is likely that the dentist cannot permanently ensure a parallel alignment between
the tip and the tooth (Figure2 middle),
because of the limited movement abilities in the patient's oral cavity. This harms
the dental substance unnecessarily. So it is desirable that the tip is able to
oscillate in multiple spatial directions, as indicated in Figure 1. Moreover, the vibration directions shall be
controlled individually, so that it is possible to predict the movement of the tip
precisely. Hence, with an appropriate control the tip is able to work permanently in
parallel to the tooth surface. A device that can provide such a control is presented
in [11]. The software of this system includes
a detection mode, which discriminates dental calculus deposits and clean tooth
surfaces [12, 13]. This algorithm can be upgraded to detect the angle between the
oscillating tip and the tooth surface and to control the drive frequency of the
scaler, so that the tip oscillates parallel to the tooth surface.One possibility to induce multidimensional vibration in multiple spatial directions
to the tip is the use of piezoceramic rings that consist of two segments which are
oppositely polarized. The idea to integrate divided rings into an ultrasonic
transducer comes up first in [14]. They
induce longitudinal-mode and flexural-mode vibrations in a one-dimensional
construction of a transducer system by means of two sets of piezoceramics. One set
consists of longitudinally polarized circular piezoceramic rings that are used to
generate the longitudinal oscillations. The other one comprises half rings, which
are polarized in opposite directions and thus generate the flexural-mode vibrations.
The physical dimensions of the transducer are varied so that both vibration modes
are at the same resonant frequency. The resulting vibrations are in the range of
some micrometers. An analytical solution for this problem is presented in [15] using the example of a slender rod.In the context of ultrasonic scalers, the idea to integrate divided piezoelectric
ceramic rings comes up first in [16]. The
generated vibrations result in a transverse movement of the tip. The scaler
transforms a longitudinal excitation to a perpendicular oscillation of the tip, but
it is still only one vibration direction. The idea to excite multidimensional
vibrations of a scaler tip by using divided piezoceramic rings is first risen in
[17].


## 2. Materials and Methods

The starting point for the investigations is a conventional scaler with a straight
tip. In this scaler new, divided piezoceramic rings, which have the same dimensions
as the original ones, are integrated. These rings are diametrically separated by an
isolation bar and the halves are oppositely polarized. A model of one ring is shown
in Figure3. The directions of polarization
are indicated.Figure 3
Model of a new piezoceramic ring.


### 2.1. Finite Element Analysis

The behavior of a piezoceramic ring and the whole system of the ultrasonic scaler
is studied via a 3D FE model using ANSYS. The simulation model of the ultrasonic
scaler is presented in Figure4. The
material data is taken according to DIN specifications and adjusted to the
model. The potential difference at each piezoceramic is 130 V. The model
does not take into account the prestress of the piezostack during the assembly
or the temperature raise of the ceramics during operation, which could lead to a
variation of vibration amplitudes and a frequency shift. However, it will become
apparent that the model predicts well the behavior of the scaler.Figure 4
ANSYS model of the ultrasonic scaler.Furthermore the deformation of one piezoceramic will be simulated. The
manufacturer PI Ceramic GmbH provides the material data for the piezoceramic. A
voltage differential of 100 V is applied.An analysis is performed regarding the deformation of the new piezoceramic as
well as the vibration behavior of the scaler, meaning the amplitude at the
distal end in longitudinal and transverse direction. Thereby a scaler with two
original and two divided piezoceramic rings in the stack is examined, and the
influence of the position and rotation of the divided piezoceramics is pointed
out.


### 2.2. Displacement Measurement

The PSV-400 Scanning Laser Vibrometer (Polytec GmbH) is employed to characterize
the deformation of the original and the divided piezoceramics. This device
measures the vibration velocity at multiple points on the surface of a ceramic.
Figure5 shows the test setup. The
piezoceramic is excited with 100 V AC voltage at 10 kHz
frequency. The measurement of the vibration velocity takes place in the time
domain at ca. 40 points distributed over the periphery of the ring. The points
are predefined via the laser's data management system. This system takes the
control during the measurement.Figure 5
Displacement measurement of one piezoelectric ring.For quantifying the amplitude of the tip's distal end, different measuring
systems could be used. Measurements can be carried out for instance with a
Scanning Laser Vibrometer [7], which
contactlessly measures the motion of the tip. In this work, the measurements are
performed with an electrooptical displacement transducer, which is a noncontact
measuring system as well. For the frequencies that lie within the working range
of the scaler, the longitudinal and transversal vibration directions are
recorded.


## 2.1. Finite Element Analysis

The behavior of a piezoceramic ring and the whole system of the ultrasonic scaler
is studied via a 3D FE model using ANSYS. The simulation model of the ultrasonic
scaler is presented in Figure4. The
material data is taken according to DIN specifications and adjusted to the
model. The potential difference at each piezoceramic is 130 V. The model
does not take into account the prestress of the piezostack during the assembly
or the temperature raise of the ceramics during operation, which could lead to a
variation of vibration amplitudes and a frequency shift. However, it will become
apparent that the model predicts well the behavior of the scaler.Figure 4
ANSYS model of the ultrasonic scaler.Furthermore the deformation of one piezoceramic will be simulated. The
manufacturer PI Ceramic GmbH provides the material data for the piezoceramic. A
voltage differential of 100 V is applied.An analysis is performed regarding the deformation of the new piezoceramic as
well as the vibration behavior of the scaler, meaning the amplitude at the
distal end in longitudinal and transverse direction. Thereby a scaler with two
original and two divided piezoceramic rings in the stack is examined, and the
influence of the position and rotation of the divided piezoceramics is pointed
out.


## 2.2. Displacement Measurement

The PSV-400 Scanning Laser Vibrometer (Polytec GmbH) is employed to characterize
the deformation of the original and the divided piezoceramics. This device
measures the vibration velocity at multiple points on the surface of a ceramic.
Figure5 shows the test setup. The
piezoceramic is excited with 100 V AC voltage at 10 kHz
frequency. The measurement of the vibration velocity takes place in the time
domain at ca. 40 points distributed over the periphery of the ring. The points
are predefined via the laser's data management system. This system takes the
control during the measurement.Figure 5
Displacement measurement of one piezoelectric ring.For quantifying the amplitude of the tip's distal end, different measuring
systems could be used. Measurements can be carried out for instance with a
Scanning Laser Vibrometer [7], which
contactlessly measures the motion of the tip. In this work, the measurements are
performed with an electrooptical displacement transducer, which is a noncontact
measuring system as well. For the frequencies that lie within the working range
of the scaler, the longitudinal and transversal vibration directions are
recorded.


## 3. Results and Discussion

### 3.1. Deformation of the Piezoceramic Ring

Figure6 shows the measured vibration
velocities of the new type of piezoceramics. Each colored point represents one
measured data point. The displacement of the ceramic is obtained by integrating
these values. It is well to see that the halves extend in phase opposition. The
half left to the isolation bar contracts while the other one extends with
respect to the zero level of the ceramic. This is entirely logical, since the
oppositely polarized halves are controlled by the same signal. The absolute
values of the vibration velocity are the same but of opposite signs. The
displacement of the conventional piezoceramic is uniform in all measuring
points, what means that the upper surface moves evenly. This deformation is
obvious and not plotted here.Figure 6
Displacement of one new piezoceramic ring.Figure7 shows the deformation of a
divided piezoceramic that is calculated numerically in ANSYS. The displacement
in the polarization direction is marked in color. One sees well that the halves
of the ceramic expand in opposite directions.Figure 7
FEM calculation of the divided piezoceramic ring.Figure8 compares the simulated and
measured displacements on the divided piezoceramic. The measuring point is
located as far apart as possible from the isolation bar, so that the deflection
is maximal. It is well to see that the measurement and simulation data match
very well. The maximum deviation of the displacements is less than 7%.Figure 8
Comparison of simulated and experimental displacement data of the divided
piezoceramic ring.With the understanding of the vibration behavior of a single divided piezoceramic
ring, the whole scaler assembly is studied next. Since the simulation and
experimental data of the single ring match well, the model of the new
piezoceramic is integrated in the model of the overall system. A good compliance
of the simulated and measured values is expected.


### 3.2. Vibration Behavior of the Ultrasonic Scaler

The analysis of the scaler's natural frequencies in the working range returns two
longitudinal mode shapes and two bending frequencies. The investigated
conventional scaler with its symmetric structure in regard to the longitudinal
plane oscillates solely in longitudinal direction (disregarding possible
elliptical movements), whereas the scaler with the divided and conventional
piezoceramics excites the system in addition asymmetrically in regard to the
longitudinal plane and thus the 2 longitudinal and the 2 bending frequencies can
be induced, so that the tip oscillates in multiple directions, depending on the
driving frequency.Figure9 shows a schematic representation
of the piezostack. Each piezoceramic is either original or divided. The divided
piezoceramic rings are characterized by the position as well as the rotation
angle θ. These two parameters will be varied later, when
different configurations of the piezostack are studied.Figure 9
Scheme of the piezostack.Figure10 shows the measured and
simulated amplitudes of the distal end for one new scaler (2 divided
piezoceramics at positions 2 and 3, θ = 0° for
both). In that diagram x′ designates the longitudinal and z the
transversal movement of the tip. The qualitative amplitudes are plotted. The tip
of the investigated scaler oscillates during normal operation with amplitudes of
90 μm or more. Internal tests showed that the
output of the scaler is still satisfactory, even if the amplitude amounts to
only 30% of the initial value. This knowledge is used to determine the
limit (black dotted line). All amplitudes above this value are considered during
the evaluation of an amplitude response. The amplitudes below the limit are not
of interest, since they induce a low output.Figure 10
Experimental and simulated displacement of one new scaler.The difference between the simulated and measured data regarding the
eigenfrequencies amounts to maximum 2.1% (Figure10). Internal tests showed that the variations of the
measured eigenfrequencies of scalers stemming from one series are of the same
order of magnitude. Hence the simulation model represents very well the real
scaler.The scaler is simulated at a fixed off-resonance frequency. At this frequency,
the calculated deformation of the piezostack depends mainly on the excitation
and is not influenced by the resonance effects of the other components. Figure11 shows the translation of the
scaler in longitudinal direction. The deformed piezostack is shown enlarged.
Figure 12 illustrates the translation of
the outer surfaces of the four piezoceramics in the stack. The plot is derived
from the simulation results in ANSYS. The values for the nodal displacement on
the outer surface of each piezoceramic are read out and plotted enlarged.Figure 11
Deformation of the piezostack.Figure 12
Surfaces of the deformed piezoceramics.It can be seen clearly that the two divided piezoceramic rings deform
asymmetrically in regard to the longitudinal plane (z = 0). This
is the same behavior that the single piezoceramic ring has displayed (Figure7). The original piezoceramic rings
extend, as expected, in only one direction. The above comment implies that the
use of divided ceramics leads to an asymmetric excitation, which induces
flexural vibrations at the associated eigenfrequencies. The original
piezoceramics induce longitudinal vibrations. As a consequence, the tip performs
longitudinal and transversal movements, depending on the excitation frequency of
the scaler.The results show that the simulated and measured data match very well for a
single divided piezoceramic ring as well as for the new scaler assembly. Hence,
further studies can be performed on the simulation model without the need for
immediate experimental validation.Based on the obtained results for the scaler assembly the influence of the
position and the rotation angleθ of the divided
piezoceramic rings (Figure 9) are
studied. Calculations are performed on scalers, the stacks of which contain 2
divided piezoceramics at various positions and rotation angles. The results of
these calculations provide the information that it is worthwhile to study the
rotation angles 0° and 180°. For these configurations the application
tip oscillates with maximum amplitudes in the longitudinal and transversal
direction. An exemplary plot of the oscillations that the scaler from Figure
10 performs is shown in Figure 13. The diagram shows the vibration
amplitudes and the corresponding angles. It is well to see that the tip
oscillates in more than one direction depending on the driving frequency. This
is an improvement compared with the scalers, which are on the market today. The
new scaler is able to oscillate in two directions perpendicular to each other.
Hence, if the worst were to happen, that is, the longitudinally oscillating tip
is positioned perpendicular to the tooth (see Figure 2), the new scaler will be driven at frequency
fR3, so that the tip oscillates in parallel to the tooth
surface.Figure 13
Plotted oscillation of one new scaler.However, since the tip should oscillate in as many angles as possible, these two
directions are not satisfactory. A solution might be to control the
piezoceramics independently, so that the resulting vibrations can be superposed.
For that purpose, a redesign of the structure will be necessary.A possible redesign (Figure14) is
simulated in ANSYS. The two piezostacks can be controlled independently, that
is, with different frequencies and voltages. The simulation returns the
amplitude response (Figure 15). If the
stack with the standard piezoceramics is excited, the considered structure
vibrates only in the longitudinal direction. Otherwise, if the stack with the
divided piezoceramics is excited, the tip performs transversal oscillations.
These two amplitude responses can be superposed, when both stacks are controlled
with the same frequency. The amplitudes of each vibration direction depend on
the applied voltages. In the example, the frequencies for the longitudinal
(fR2) and flexural vibrations (fR3) are very close.
For driving the structure, the frequency fD is chosen, because it
allows to superpose the oscillation directions. The amplitudes are scaled with
the factors ax,
az ∈  [0,1]. An example of the resulting oscillations of
the application tip is plotted in Figure 16. It is well to see that all vibration angles between 0° and
90° can be controlled if the excitation frequencies are in phase. If they
are out of phase, the oscillations cover the angles between 0° and
−90°. Consequently, this new generator adjusts the vibration
direction of the tip in a way that the tip is able to oscillate always in
parallel to the tooth surface, no matter how the scaler is positioned with
respect to that surface.Figure 14
Layout of the redesigned structure with two piezostacks.Figure 15
Amplitude response of the redesigned structure.Figure 16
Plotted oscillations of the redesigned structure.


## 3.1. Deformation of the Piezoceramic Ring

Figure6 shows the measured vibration
velocities of the new type of piezoceramics. Each colored point represents one
measured data point. The displacement of the ceramic is obtained by integrating
these values. It is well to see that the halves extend in phase opposition. The
half left to the isolation bar contracts while the other one extends with
respect to the zero level of the ceramic. This is entirely logical, since the
oppositely polarized halves are controlled by the same signal. The absolute
values of the vibration velocity are the same but of opposite signs. The
displacement of the conventional piezoceramic is uniform in all measuring
points, what means that the upper surface moves evenly. This deformation is
obvious and not plotted here.Figure 6
Displacement of one new piezoceramic ring.Figure7 shows the deformation of a
divided piezoceramic that is calculated numerically in ANSYS. The displacement
in the polarization direction is marked in color. One sees well that the halves
of the ceramic expand in opposite directions.Figure 7
FEM calculation of the divided piezoceramic ring.Figure8 compares the simulated and
measured displacements on the divided piezoceramic. The measuring point is
located as far apart as possible from the isolation bar, so that the deflection
is maximal. It is well to see that the measurement and simulation data match
very well. The maximum deviation of the displacements is less than 7%.Figure 8
Comparison of simulated and experimental displacement data of the divided
piezoceramic ring.With the understanding of the vibration behavior of a single divided piezoceramic
ring, the whole scaler assembly is studied next. Since the simulation and
experimental data of the single ring match well, the model of the new
piezoceramic is integrated in the model of the overall system. A good compliance
of the simulated and measured values is expected.


## 3.2. Vibration Behavior of the Ultrasonic Scaler

The analysis of the scaler's natural frequencies in the working range returns two
longitudinal mode shapes and two bending frequencies. The investigated
conventional scaler with its symmetric structure in regard to the longitudinal
plane oscillates solely in longitudinal direction (disregarding possible
elliptical movements), whereas the scaler with the divided and conventional
piezoceramics excites the system in addition asymmetrically in regard to the
longitudinal plane and thus the 2 longitudinal and the 2 bending frequencies can
be induced, so that the tip oscillates in multiple directions, depending on the
driving frequency.Figure9 shows a schematic representation
of the piezostack. Each piezoceramic is either original or divided. The divided
piezoceramic rings are characterized by the position as well as the rotation
angle θ. These two parameters will be varied later, when
different configurations of the piezostack are studied.Figure 9
Scheme of the piezostack.Figure10 shows the measured and
simulated amplitudes of the distal end for one new scaler (2 divided
piezoceramics at positions 2 and 3, θ = 0° for
both). In that diagram x′ designates the longitudinal and z the
transversal movement of the tip. The qualitative amplitudes are plotted. The tip
of the investigated scaler oscillates during normal operation with amplitudes of
90 μm or more. Internal tests showed that the
output of the scaler is still satisfactory, even if the amplitude amounts to
only 30% of the initial value. This knowledge is used to determine the
limit (black dotted line). All amplitudes above this value are considered during
the evaluation of an amplitude response. The amplitudes below the limit are not
of interest, since they induce a low output.Figure 10
Experimental and simulated displacement of one new scaler.The difference between the simulated and measured data regarding the
eigenfrequencies amounts to maximum 2.1% (Figure10). Internal tests showed that the variations of the
measured eigenfrequencies of scalers stemming from one series are of the same
order of magnitude. Hence the simulation model represents very well the real
scaler.The scaler is simulated at a fixed off-resonance frequency. At this frequency,
the calculated deformation of the piezostack depends mainly on the excitation
and is not influenced by the resonance effects of the other components. Figure11 shows the translation of the
scaler in longitudinal direction. The deformed piezostack is shown enlarged.
Figure 12 illustrates the translation of
the outer surfaces of the four piezoceramics in the stack. The plot is derived
from the simulation results in ANSYS. The values for the nodal displacement on
the outer surface of each piezoceramic are read out and plotted enlarged.Figure 11
Deformation of the piezostack.Figure 12
Surfaces of the deformed piezoceramics.It can be seen clearly that the two divided piezoceramic rings deform
asymmetrically in regard to the longitudinal plane (z = 0). This
is the same behavior that the single piezoceramic ring has displayed (Figure7). The original piezoceramic rings
extend, as expected, in only one direction. The above comment implies that the
use of divided ceramics leads to an asymmetric excitation, which induces
flexural vibrations at the associated eigenfrequencies. The original
piezoceramics induce longitudinal vibrations. As a consequence, the tip performs
longitudinal and transversal movements, depending on the excitation frequency of
the scaler.The results show that the simulated and measured data match very well for a
single divided piezoceramic ring as well as for the new scaler assembly. Hence,
further studies can be performed on the simulation model without the need for
immediate experimental validation.Based on the obtained results for the scaler assembly the influence of the
position and the rotation angleθ of the divided
piezoceramic rings (Figure 9) are
studied. Calculations are performed on scalers, the stacks of which contain 2
divided piezoceramics at various positions and rotation angles. The results of
these calculations provide the information that it is worthwhile to study the
rotation angles 0° and 180°. For these configurations the application
tip oscillates with maximum amplitudes in the longitudinal and transversal
direction. An exemplary plot of the oscillations that the scaler from Figure
10 performs is shown in Figure 13. The diagram shows the vibration
amplitudes and the corresponding angles. It is well to see that the tip
oscillates in more than one direction depending on the driving frequency. This
is an improvement compared with the scalers, which are on the market today. The
new scaler is able to oscillate in two directions perpendicular to each other.
Hence, if the worst were to happen, that is, the longitudinally oscillating tip
is positioned perpendicular to the tooth (see Figure 2), the new scaler will be driven at frequency
fR3, so that the tip oscillates in parallel to the tooth
surface.Figure 13
Plotted oscillation of one new scaler.However, since the tip should oscillate in as many angles as possible, these two
directions are not satisfactory. A solution might be to control the
piezoceramics independently, so that the resulting vibrations can be superposed.
For that purpose, a redesign of the structure will be necessary.A possible redesign (Figure14) is
simulated in ANSYS. The two piezostacks can be controlled independently, that
is, with different frequencies and voltages. The simulation returns the
amplitude response (Figure 15). If the
stack with the standard piezoceramics is excited, the considered structure
vibrates only in the longitudinal direction. Otherwise, if the stack with the
divided piezoceramics is excited, the tip performs transversal oscillations.
These two amplitude responses can be superposed, when both stacks are controlled
with the same frequency. The amplitudes of each vibration direction depend on
the applied voltages. In the example, the frequencies for the longitudinal
(fR2) and flexural vibrations (fR3) are very close.
For driving the structure, the frequency fD is chosen, because it
allows to superpose the oscillation directions. The amplitudes are scaled with
the factors ax,
az ∈  [0,1]. An example of the resulting oscillations of
the application tip is plotted in Figure 16. It is well to see that all vibration angles between 0° and
90° can be controlled if the excitation frequencies are in phase. If they
are out of phase, the oscillations cover the angles between 0° and
−90°. Consequently, this new generator adjusts the vibration
direction of the tip in a way that the tip is able to oscillate always in
parallel to the tooth surface, no matter how the scaler is positioned with
respect to that surface.Figure 14
Layout of the redesigned structure with two piezostacks.Figure 15
Amplitude response of the redesigned structure.Figure 16
Plotted oscillations of the redesigned structure.


## 4. Conclusion

This paper demonstrates the benefits to simulate an ultrasonic dental scaler by means
of the FEM. The simulated and measured frequency responses match very well. On this
basis investigations of new versions are performed. They reveal that the tip is able
to oscillate in multiple vibration directions, which can be controlled individually,
if the scaler is excited asymmetrically, for example, by means of divided
piezoceramics. A redesign of the original transducer shows the potentialities of the
divided piezoceramics. By driving the ceramics of the transducer independently, the
tip is able to oscillate in all spatial directions. This allows a gentle and
painless treatment, because the vibration direction of the tip can be adjusted
precisely, depending on the present angle between the tip and the tooth surface.



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*Source: 910876-2011-07-21.xml*