Cylindrical Piezoelectric PZT Transducers for Sensing and Actuation: Comparison
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Please note this is a comparison between Version 2 by Sirius Huang and Version 1 by Ata Meshkinzar.

Piezoelectric transducers have numerous applications in a wide range of sensing and actuation applications. Such a variety has resulted in continuous research into the design and development of these transducers, including but not limited to their geometry, material and configuration. Among these, cylindrical-shaped piezoelectric (PZT) transducers with superior features are suitable for various sensor or actuator applications.

  • sensing
  • actuation
  • piezoelectric PZT transducers
  • cylindrical transducers
  • stepped-thickness transducers
  • biomedical transducers
  • food industry transducers

1. Uniform-Thickness Transducers

Cylindrical transducers can be used as an actuator for ultrasonic particle separation for various purposes. The hollow geometry of a cylinder makes it an attractive choice for particle separation in a dynamic flow. Additionally, the curved cylinder surface subject to a suitable vibration mode shape can result in a focused, stronger acoustic field inside the transducer. However, limited literature has investigated the use of cylindrical ultrasound transducers for particle separation. A cylindrical PZT-4 transducer with an outer diameter of 19 mm, inner diameter of 16 mm and length of 28 mm was employed for separating microparticles in a continuous flow system [38][1]. A water-based and a blood-resembling fluid were considered in the study. At 202 kHz, the transducer generated a flow instability, mixing the suspension instead of separating it. However, at 345 kHz, separation was achieved successfully. This verifies that the implementation of cylindrical transducers for acoustic separation requires identifying a suitable frequency and acoustic pressure level commensurate with the medium and particle properties. The separation of particles is achieved through the acoustic standing wave applied by the transducer to the fluid that is created from the interaction of the incident and reflected waves in a medium [39][2]. The standing wave has a region of maximum displacement (pressure nodes) and a region of minimal displacement (pressure antinodes). The particles are aligned depending on their acoustic contrast factor, which is a function of the particles’ density, medium (fluid) density, particle compressibility and fluid compressibility [40][3]. When the particles have a positive acoustic contrast factor, they move towards a pressure node and a negative acoustic contrast factor causes them to move towards pressure antinodes [41][4]. The extraction of microparticles can be performed through a customized collector in-line with the nodal and/or anti-nodal circles where particles gather depending on the acoustic contrast factor.
The PZT4A piezoelectric transducer, with 30 mm length, 3 mm thickness, 1.5 mm width and a thickness mode resonance, was driven at 417 kHz, 10–12 Vpp and 80 mA at approximately 0.8–0.9 W. The polystyrene particles were 10 µm in diameter when diluted in water and were successfully concentrated within approximately 5 s along the central axis of the cylinder with an inner diameter of 2.2 mm, outer diameter of 3.97 mm and 15 mm of length.
In another application for fruit drying, an aluminum cylindrical shell (with an internal diameter of 100 mm, height of 310 mm and thickness of 10 mm) was excited at 21.8 kHz by a piezoelectric shaker at a suitable mode shape, generating a focused and stronger acoustic field at 155 dB using 75 W of electrical power, which is relatively high [8][5]. Although it was proven successful in improving the drying rate, a bulky and expensive power supply was required [43][6]. Reducing the power requirements and further amplifying the acoustic field are necessary for enhancing the uptake of such cylindrical transducers for various applications. One approach to achieving this is by making modifications to the shape and geometry of the transducer, as investigated in some studies using different methods, which will be elaborated on in the subsequent sections.

2. Modified Transducer Configurations

This section covers approaches available in the literature for modifying the cylindrical transducer configuration to improve performance. For instance, for the levitation of water droplets in the air, cylindrical transducers can be employed. The selection of the vibration frequency of the transducers strongly affects the generation of the acoustic standing wave inside the transducer with pressure nodes. To match the resonance frequency of the hollow cylindrical transducer with that of the cavity inside, two methods were proposed and investigated: (1) a physical change in the transducer geometry, and (2) a change in the resonance frequency of the cavity within the transducer [44,45,46][7][8][9]. These are elaborated on in the following sections.

2.1. Structurally Tuned Transducer Configuration

The first approach involves structural tuning of the cylinder by creating a cut along its length. This causes the breathing resonance frequency of the transducer to match one of the resonance frequencies of the cavity with a certain number of nodal circles inside the transducer.
The PZT transducer was radially poled with nickel electrodes on the outer and inner surfaces. The inner diameter was 16.9 mm, the outer diameter was 19.0 mm and the length was 17.0 mm, with the transducer being driven at 66.7 kHz, close to the third cavity mode of 65.7 kHz. The drive voltage was approximately 1 Vpp at approximately 100 mW of input power. The initial breathing mode frequency of the transducer was 61 kHz, which was altered to 66.7 kHz by adding the axial cut to match that of the cavity at its third mode of 65.7 kHz. The results revealed that the concentration of water droplets at the nodal circles can be achieved.

2.2. Cavity-Tuned Transducer Configuration

The second approach, cavity tuning, involves altering the resonance frequency of the cavity inside the transducer to match the breathing resonance frequency of the transducer. To do this, various approaches were investigated, such as coaxially inserting an elliptical or circular metallic rod inside the transducer cavity [44,45,46][7][8][9]. The rod diameter in the case of a circular insert is chosen to have one coaxial circular pressure node in the cavity. For a radially poled cylindrical PZT of inner radius 1.96 cm, length 5.06 cm and outer radius 2.22 cm, operating at a breathing mode resonance of 23.2 kHz, the resonance in air occurs at R = 1.224 cm. The difference between this radius and the inner radius is approximately 0.73 cm, which is close to half the wavelength in the air at that frequency, leading to the formation of one circular node.
The second case involved employing an elliptical cross-section with major and minor diameters of 25.3 mm and 24 mm, respectively, to break the axial symmetry of the cavity, which results in the formation of two localized pressure nodes (rather than circles) in line with the minor axis of the ellipse.
For collection purposes, a tube was placed at the end of the cavity around and in line with the localized pressure nodes and/or circles to collect water droplets.

3. Stepped-Thickness Transducer Configurations

As stated earlier, to employ the benefits of the curved and focused geometry of a cylindrical transducer as well as stepped-thickness characteristics for flat plates, which had shown advantages over uniform-thickness plates, previous work investigated both circumferentially and axially stepped-thickness piezoelectric PZT cylindrical transducers in an effort to amplify the generated acoustic field inside the transducer without the need to increase the input power [2,4,5][10][11][12]. This required a suitable constructive interference of the radiated waves inside the transducer and minimized the counter-phase vibrations at any cross-section along the length. This required a vibration mode shape with suitable circumferential and axial mode numbers to eliminate or diminish out-of-phase vibrations and radiations. To achieve this, steps were introduced at equal intervals around the circumference to excite certain vibration mode shapes and create localized high vibration amplitudes.
It is also worth mentioning that these thickness variations can lead to stress concentration, which needs to be considered in the design of these transducers to eliminate design problems while having strong acoustic fields. The authors employed FEM analysis to investigate the stress distribution, vibration and acoustic response of these transducers. Both externally and internally stepped transducers with odd and even numbers of steps were investigated. Those with an even number of steps showed better constructive interference of the radiated waves and a more symmetrical acoustic field inside the transducer. It was also concluded that the uniformity of the acoustic field along the length of the transducer was favorable, with slight variations in the sound pressure level. This was attributed to the suitable vibration mode shape identified with an axial wave number of one leading to the whole length to vibrate in-phase longitudinally. Another observation was that the frequency of operation at the intended mode shape was lower than that of the uniform-thickness or axially stepped one. This is also favorable for the long-term performance of the transducers. In fact, as a general rule, higher frequencies tend to cause overheating or gradual depolarization of the material [47][13] and possibly fatigue failure [20][14] (particularly in sharp edges, such as in stepped-thickness structures). Thus, a lower frequency is desirable to minimize overheating and depolarization.
Axially stepped cylindrical transducers were also investigated in the literature [4,5][11][12]. To identify the step configuration and frequency range, the authors first investigated the mode shapes and corresponding frequencies that have regions in counter-phase axially, i.e., modes with axial wave numbers of three and five. The stepped regions were introduced at the counter-phase region between each two consecutive in-phase regions. As an example, for the mode with an axial wave number of three, there was one region in counter-phase with the other two regions. Hence, one stepped-thickness region was introduced. Accordingly, this clarified the width of the stepped region. Similar to the circumferential stepped transducers, the aim was to have mode shapes without or with minimal out-of-phase vibrations and to localize higher amplitude vibrations to achieve an amplified acoustic field. 
Both the axially and circumferentially stepped transducers previously investigated [2,4,5][10][11][12] were designed for biomedical applications and humidification in lung therapies where it is preferable to have an in-line humidifier fitting in a breathing tube of approximately 2 cm diameter, such as those used in continuous positive airway pressure (CPAP) devices [1,48][15][16]. Accordingly, the authors investigated the effect of the focused acoustic field from these stepped-thickness transducers on a stream of polydisperse microwater droplets generated by a nebulizer [3][17]. 
The underlying mechanism exposed the droplets to the acoustic field while they passed through the transducer. This improved the relative movement between water droplets and air, leading to enhanced heat transfer and evaporation. Larger droplets in the stream were found to be affected more than small ones by the acoustic field. A noticeable reduction in the size of 90% of the droplets was observed, which improved the droplet size distribution in the stream. This was reported to be of particular and practical importance for some drug delivery applications or humidification in lung-supportive devices.

References

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  2. Leong, T.; Juliano, P.; Johansson, L.; Mawson, R.; McArthur, S.; Manasseh, R. Continuous Flow Ultrasonic Skimming of Whole Milk in a Liter-Scale Vessel. Ind. Eng. Chem. Res. 2015, 54, 12671–12681.
  3. Leong, T.; Johansson, L.; Juliano, P.; McArthur, S.L.; Manasseh, R. Ultrasonic Separation of Particulate Fluids in Small and Large Scale Systems: A Review. Ind. Eng. Chem. Res. 2013, 52, 16555–16576.
  4. Trippa, G.; Ventikos, Y.; Taggart, D.P.; Coussios, C.C. CFD modeling of an ultrasonic separator for the removal of lipid particles from pericardial suction blood. IEEE Trans. Biomed. Eng. 2011, 58, 282–290.
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  6. Protheroe, M. An Investigation of Droplet Evaporation Characteristics in an Ultrasound Environment. Ph.D. Thesis, Auckland University of Technology, Auckland, New Zealand, 2014.
  7. Kogan, S.; Kaduchak, G.; Sinha, D.N. Acoustic concentration of particles in piezoelectric tubes: Theoretical modeling of the effect of cavity shape and symmetry breaking. J. Acoust. Soc. Am. 2004, 116, 1967–1974.
  8. Kaduchak, G.; Sinha, D.N.; Lizon, D.C. Novel cylindrical, air-coupled acoustic levitation/concentration devices. Rev. Sci. Instrum. 2002, 73, 1332–1336.
  9. Kaduchak, G.; Sinha, D.N. Low-power acoustic harvesting of aerosols. In Proceedings of the 2001 IEEE Ultrasonics Symposium, Atlanta, GA, USA, 7–10 October 2001.
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  11. Al-Jumaily, A.M.; Meshkinzar, A.; Harris, P.D.; Huang, L. Acoustic radiation characteristics of piezoelectric shells with internal and external axial stepped-thickness configurations. Sens. Actuators A Phys. 2020, 302, 111819.
  12. Meshkinzar, A.; Al-Jumaily, A.M.; Harris, P.D. Acoustic Amplification Utilizing Stepped-Thickness Piezoelectric Circular Cylindrical Shells. J. Sound Vib. 2018, 437, 110–118.
  13. Lozano, A.; Amaveda, H.; Barreras, F.; Jordaà, X.; Lozano, M. High-Frequency Ultrasonic Atomization with Pulsed Excitation. J. Fluids Eng. 2004, 125, 941–945.
  14. Gallego-Juárez, J.A.; Rodríguez-Corral, G.; Sarabia, E.R.-F.D.; Vázquez-Martínez, F.; Acosta-Aparicio, V.M.; Campos-Pozuelo, C. Development of Industrial Models of High-Power Stepped-Plate Sonic And Ultrasonic Transducers For Use in Fluids. In Proceedings of the 2001 IEEE Ultrasonics Symposium (Cat. No.01CH37263), Atlanta, GA, USA, 7–10 October 2001; pp. 571–578.
  15. Al-Jumaily, A.M.; Meshkinzar, A. On the Development of Focused Ultrasound Liquid Atomizers. Adv. Acoust. Vib. 2017, 2017, 7861726.
  16. Al-Jumaily, A.; Reddy, P. Medical Devices For Respiratory Dysfunction: Principles and Modeling of Continuous Airway Pressure (CPAP); ASME Press: New York, NY, USA, 2012.
  17. Meshkinzar, A.; Al-Jumaily, A.M. Acoustically enhanced evaporation of a polydisperse stream of micro water droplets. J. Aerosol Sci. 2020, 139, 105466.
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