The design of high-sensitive hydrophones is one of the research interests in ... the bandwidth of the transducer at the expanse of the maximum response ...
PHENMA 2014
TWO‐STEPS PARETO‐BASED OPTIMIZATION OF BROADBAND pMUT HYDROPHONE
KKU-IENC 2014
1 1 1 S.‐H. Chang , J.‐C. Liu , J.‐K. Wu , 2 Shevtsov S.
2 , Zhilyaev I.
1National Kaohsiung Marine University
Kaohsiung city, Taiwan R.O.C.
Khon Kaen, Tailand March 27-29, 2014
2 2 Shevtsova M. , Oganesyan P. 2Southern Scientific Center of Russian Academy
Rostov on Don, Russia
1. Introduction. The design of high-sensitive hydrophones is one of the research interests in underwater acoustics. Due to progress of micro- and nanotechnology the most attention of researchers is attracted the transducers that use the micro-electromechanical system (MEMS) concept. Piezoelectric micro-machined ultrasonic transducers (pMUTs) present a new approach to sound detection and generation that can overcome the shortcomings of conventional transducers. For accurate ultrasound field measurement, small size hydrophones which have smaller than the acoustic wavelength are required for providing an omnidirectional response and avoid spatial averaging.position. In pMUTs, the sound-sensoring element is a micromachined multi-layered membrane with a piezoactive layer, typically a thin lead-zirconate-titanate (PZT) film. Such film can be formed by a batch-mode fabrication technology for integration of bulk piezoelectric layers on silicon substrate and then to form a desired smart structure with the piezoelectric layer by using micromachining. Typical fabrication techniques include a lowtemperature bonding technique using a spin-on polymer (Cytop), design of electrode interconnect, chemical mechanical polishing (CMP) for thinning down the bulk PZT, and Deep-Reactive-Ion-Etching (DRIE) of silicon [1 - 4]. The latest designs of MEMS based acoustic transducer utilized perforated damping backplate [5 - 7]. The purpose of such design was to flatten the frequency response spectra thus providing wider bandwidth with increasing damping factor of the diaphragm. The small vacuum gap between the backplate and the upper diaphragm, and also set of holes with diameters ~5 μm alters the damping characteristic and thus broaden the bandwidth of the transducer at the expanse of the maximum response strengths, and the receiving sensitivity. However, the physical mechanism of the influence of holes on the acoustic characteristics of the sensors remains unclear. An example of the studied hydrophone design is shown in Figure 1.
Receiving response of acoustic transducer, which represents how much voltage will be produced by the transducer corresponds to every Pascal (Pa) of sound pressure received at the surface of transducer was calculated according to the relationship. S R dB 10 log V Vref ; Vref 1V Before time-harmonic analysis the modal analysis has been carried out to confirm the first flexural mode of the diaphragm oscillations and its eigenfrequency. Obviously, hydrophone with the circular active diaphragm can operates only near first natural bending mode.
3. Multiobjective Pareto‐based hydrophone optimization By restricting attention to the set of choices that are Pareto-efficient, we can make trade-offs within this set, rather than considering the full range of every parameter. In the considered system we have a design space with 6 real variables: Young module Yw, Poisson ratio νw, density ρw, and two Rayleigh damping parameters (mass damping αdM and stiffness damping βdK parameters) of the polymeric protective layer; and also the relative perforation area pw. These design variables were enclosed within the own intervals. Our first numerical simulations have been demonstrated a very high sensitivity of all objectives to changes of such hydrophone’s parameters as relative degree of perforation and first flexural vibration eigenfrequency of thick protective layer. Hence, these parameters have been used to solve the optimization problem. To calculate this eigenfrequency we used the relationships (4, 5) for the flexural stiffness D of the protective plate and first eigenfrequency f0, where dependence of eigenvalue Λ0 has been borrowed from [7], assuming the Mindlin plate model (see Fig. 5). To determine the Y h3 D permissible parameters of perforation and Young D (4) f 0 (5) 2 2 12 1 2 R h module of protective plate that allow to eliminate very high deflection of active plate we simulate the underwater lowering test, whose results are presented in Fig.6.
Degree of perforation
Fig.1 – Cross-section of the studied hydrophone design
Fig. 2 - Sketch of the modeled pMUT hydrophone design
We present the coupled acoustic-piezoelectric problem for the frequency response sensitivity of the hydrophone interacted with a fluid medium, and demonstrate its finite element implementation. In the final part the Pareto – based optimization approach for the FRF of hydrophone’s sensitivity is proposed and discussed. Three objectives were investigated, the transmitting voltage response averaged over the frequency range 40…200 kHz (in dB/Pa), the maximum and averaged variation of sensitivity inside this frequency band. The emphasize of the proposed approach is using the first eigenfrequency of flexural vibration the protective plate and a Rayleigh stiffness damping of its material as the design variables. Such solution allowed to sufficiently diminish the number of design variables. To describe the effective mechanical, electromechanical properties of active PZT and intermediate SiO2 layers we used the relationships for their effective dependencies on the relative perforated area, which were presented in [6, 7].
Fig.5 – The dependence of circular Mindlin plate first eigenvalue on the material Poisson ratio
Fig. 6 – The dependencies of the maximum diaphragm deflection at the water depth 200m
The optimization algorithm includes calculation of all objectives at the varying design variables, the reconstruction of design and objective space, next discarding of infeasible designs, and finally selection of the feasible designs that satisfy the constraints on the properties of active diaphragm (see Figs. 7, 8).
2. FE model of pMUT hydrophone in the fluid medium
The forward problem of the hydrophone modeling has been solved using FE soft package Comsol Multiphysics operated in the coupling Structural Mechanics/Piezoelectricity – Acoustics 2D axially symmetric mode. The geometry of modeled system together with the boundary conditions and FEM mesh are presented in Figures 3, 4. Multilayered circular plate of the hydrophone is clamped on the lateral cylindrical surface, whereas the lower surface is free assuming the existence of the vacuum cavity. Upper surface experienced the acoustic pressure from the fluid, and upper surface of the fluid volume is the source of the sound pressure. To eliminate reflection of sound waves the fluid volume is surrounded by the perfectly matched layer (PML).
Fig. 7 – 3D view on the objective space Dark green – multyobjective optimum area Green and yellow – Pareto frontier area
Fig. 8 – Two projections of objectives (sensitivity – left and its maximum FRF non-uniformity - right) on the design subspace for all simulated designs
Fig. 10 – The superimposed projections of objectives for constrained designs
Fig.3 – The geometry and boundary conditions for the modeled hydrophone – fluid medium interaction
Fig.4 – The finite element meshing of fluid (above) and mechanic-piezoelectric domains
At the time‐harmonic analysis when pressure varies with the time as
p x, t p x expit
(1)
the governing equation for the acoustic medium is the homogeneous Helmholtz equation where ρ0 is the density, cs denotes the speed of sound, and ω is the sound p 2 p (2) angular frequency. This equation is active both in the fluid domain and PML. 0 2 The piezoelectric phenomena are governed by the piezoelectricity equations 0 0 cs in the strain-charge form (Eq. 3), where [d] and [d]T are the matrices of E T S [ s ] T [ d ]E; piezoelectric effect, s is the compliance matrix, S and T are the mrchanical strain and stress respectively, E is the electric field, and D is the charge (3) T D [d ]T [ ]E, density. All material constants in Eq. (3) are the empiric functions of degree of perforations (see [6, 7]). On the boundaries between piezoelectric and other layers the continuity of strains is supplied. The lower surface of the perforated piezoelectric layer is grounded whereas the upper surface is connected to the electric resistance R=1 MOhm, which simulates an input impedance of the electronic amplifier. Electric potential on this electric load is calculated according the Ohm law using a value of electric current, which is determined by integration of the current density over the upper conductive surface of the piezoelectric layer.
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Fig. 9 – Two projections of objectives on the design subspace for the feasible designs
The contour lines presented in Fig. 10 are the levels of objectives from the objective subspace, which were built at the constraining the degree of perforation and Young module of protective layer to eliminate the diaphragm deflection above 0.25 mm at the water depth 200 m. As one can see from the Fig. 10, the area where averaged hydrophone sensitivity in the operatin frequency range and its FRF non-uniformity have satisfactory values (dark green region), is rather small. But using this diagrams we can decide the best design taking into account the most important operating requirements. Moreover, on the second optimization step (design of the real structure) we can choose the most appropriate materials that provide the frequency and damping parameters, which were defined at the first optimization step presented above. Such optimal choice of material can also includes a moisture absorption and other necessary parameters for underwater applications. In the presented work we used the the relative area of the perforated holes and also protective plate’s elastic and viscous properties as the auxiliaries intermediate design variables, to optimize together the sensitivity’s frequency response to broadening and equalizes the operating frequency band of the hydrophone. These key parameters have been optimized using the Pareto approach and the finite element model of coupled piezoelectric-acoustic problem, which includes hydrophone structure placed inside the fluid medium and interacting with it.
References
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