Implementation of Moving Magnet Actuation in Very Low Frequency Acoustic Transduction

Measuring the performance of hydrophones in submarine and surface ship towed arrays at low frequencies in the Leesburg test facility (Okahumpka, FL) is achieved using ambient noise as a calibration source. The preferred method of calibration that relies on a known, repeatable sound source is not implemented because the equipment capable of generating sound at such low frequencies does not currently exist. This project examines the feasibility of implementing a moving magnet actuator (MMA) as the motor force in a very low frequency (VLF) underwater acoustic projector. MMAs have the potential to advance low frequency projector technology by providing large linear displacements and large force outputs in a small package. To explore this potential, three methods of investigation are performed in this study: analytical modeling, numerical modeling, and experimental testing. Analytical modeling is performed in Matlab using fundamental equations for a simple acoustic point source. Numerical modeling is represented as a fluid-structure interaction (FSI) problem and is solved using the finite element program Abaqus. Experimental testing is conducted by placing a load on a Bose MMA to simulate the mass of the VLF projector’s water displacement. Analytical and numerical modeling efforts estimate a projector source level of over 125 dB// 1 μPa @1m at 1Hz and over 180 dB// 1 μPa @1m at 30Hz. The experimental efforts find that the Bose MMA operates at displacements necessary to achieve sound pressure levels calculated from the analytical and numerical models. This study indicates that an MMA is a suitable force generator for the VLF projector and explores future work necessary for VLF projector design, manufacture, and operation.

: A design of a hydraulically actuated transducer. In a hydraulically actuated transducer, an amplifier at the center of the device drives two opposing flexural disks. An electrically driven pump provides hydraulic power and a low-level electrical signal supplies the hydraulic amplifier with the signal (Image source: [8]   The low frequency (1-60Hz) performance tests conducted at LEFAC rely on ambient noise as a calibration signal. A spectrum of the ambient noise can be seen in Figure   2. A limitation of this passive method is the low signal-to-noise ratio of the hydrophones' outputs; the background electronic noise of the hydrophones may not be much less than the electronic signal produced by the acoustic noise in the spring [2]. With their large linear displacements and force outputs, moving magnet actuators (MMAs) have the potential to be implemented as the motor force in a very low frequency (VLF) underwater acoustic projector. A VLF projector can be used as the known sound source for LEFAC's calibration testing.
The objective of this study is to examine the feasibility of implementing an MMA as the motor force in a VLF underwater acoustic projector. Modeling of the acoustic output for the MMA is the first milestone in designing, manufacturing, and implementing a sound source to replace the ambient noise as the source of the calibration signal.

Thesis Content
Chapter 2 provides background information critical to the understanding of the research performed in this study. General knowledge of acoustics and sonar, a review of the U.S. Navy's current low frequency projectors, and an introduction to moving magnet actuation are covered in this chapter.
The research begins in Chapter 3 where two different engineering approaches to modeling a moving magnet low frequency projector are examined. The first is an analytical model using fundamental equations for a simple sound source. The second model is a finite element model using the software package Abaqus.
In addition to the modeling efforts, experimental testing is performed on a Bose LM2 MMA to validate that it can produce the forces and displacements necessary to implement the actuator in an underwater projector. The results of this experiment can be found in Chapter 4.
Although modeling and experimentation of the actuator are performed in this study, further analyses must still be completed in order to build a device. Chapter 5 discusses future design work required to build a functioning underwater acoustic projector.
Finally, the research concludes in Chapter 6. In this section, the significance of this study, the methods of analysis and experimentation, and key findings are all summarized.

Introduction to Acoustics
Acoustic waves are vibrational excitations traveling through an elastic medium. As illustrated in Figure Wavenumber ( ), also referred to as the special frequency, describes the number of waves per unit distance. It is expressed in this paper as radians per unit distance. From wavenumber, a value for wavelength (λ) can be derived.
Wavelength, λ, describes the length of the pressure wave cycle in meters.
Wavelength and frequency are related by the speed of sound in the medium c.
The speed of sound is defined by the modulus of elasticity and density of the medium. In this study, 1500 m/s is used as a sound speed in water.
Pressure amplitude ( 0 ) is the maximum value of a pressure wave above the hydrostatic pressure. Instead of listing a pressure in units of Pascals, acoustic wave amplitudes are often listed in decibel, representing the pressure with respect to a reference.
The sound pressure level (SPL) describes the amplitude of an acoustic wave and is represented as where is the root mean square (RMS) value of the pressure wave amplitude and is 1 in water. This is different from sound levels measured in air which are referenced to 20 .

Introduction to Sonar and Transducers
The U.S. Navy has applied the physics of underwater sound described in Section 2.1 for generations through the use of sonar. Sonar, derived originally as an acronym for SOund NAvigation and Ranging, is a technique that uses sound propagation to navigate, communicate, or detect objects underwater.
There are two fundamental classes of sonar systems. The first is a passive system, where sound propagates from a target to a receiver. The receiver in a passive system is called a hydrophone: a transducer that converts sound waves to electrical signals. The second is an active system, where acoustic energy radiates from a transmitter to a target and back to a receiver. The transmitter in an active system is called a projector. When an electrical signal is applied to a projector, a sound that radiates in the acoustic medium is produced.
Hydrophones and projectors are designed for different frequencies based on their application. A hydrophone designed to monitor the sound produced by an earthquake or explosion where the majority of acoustic energy is below 100Hz is designed differently than a sensor developed to monitor marine mammals that communicate at frequencies up to 100kHz. Likewise, a projector intended to transmit a low frequency wave that can travel long distances is designed much differently than the high frequency transmitter use for acoustic homing on a target.

Current Low Frequency Projector Technologies
Designing an underwater acoustic projector that is low frequency, has a high power output, and has a high efficiency has been a challenge since the mid-1900s. This section of the thesis discusses three sonic and infrasonic projector types: moving coil, bender bar, and hydraulic actuation. Each subsection will provide an example of this projector type along with key disadvantages.

Moving coil projector
Moving coil underwater acoustic projectors (also called electrodynamic projectors or voice coil projectors) use the same transduction principles commonly seen in traditional loudspeakers. Lorentz force, a force that is exerted by a magnetic field on a moving electric charge, is the physical principle behind electrodynamic transducers. Lorentz force can be expressed as [7] = × where is current and is magnetic field.

Hydraulically Actuated Transducers
In a hydraulically actuated transducer, seen in Figure 9, an amplifier at the center of the device drives two opposing flexural disks. An electrically driven pump provides hydraulic power and a low-level electrical signal supplies the hydraulic amplifier with the acoustic waveform.
Hydraulic projectors are appropriate for low frequency applications where high sound pressure levels are required. Unlike moving coil projectors, hydraulic projectors provide large force outputs. Unfortunately, these devices are massive. The HLF-1D, Figure   10, weighs 1066 kgs and has a frequency range of 20-1500Hz. They are also unreliable and require regular maintenance [8].

Moving Magnet Actuation
Moving coil actuation, bender bar, and hydraulic actuation are all transduction methods that the Navy has implemented in underwater acoustics for decades. With the advancement in the lightweight rare earth magnets, MMAs appear to be a promising motor for underwater acoustic projectors due to their large linear displacements, large force outputs, and compact size.
A simple schematic for an MMA can be seen in Figure 11. As with the moving coil projector in Section 2.3.1, the motor force employed by this actuator is Lorentz force.
However, the permanent magnet is mobile and a stationary coil is mounted on the outside of the housing which has two advantages. First, the static coil mounted to the back iron allows for improved heat dissipation over moving coil. Heat generated due to resistive losses is further away from the motion stage [9]. Second, in the moving coil case, coil size is limited because its mass contributes to the moving mass of the system. Since the coils are now the stationary piece, they can be designed with high gauge wires to drive greater currents. A greater current will result in a larger Lorentz force.

Bose Electroforce Moving Magnet Actuator
Instead of designing an actuator, USRD purchased an off the shelf MMA to implement in the VLF projector. USRD purchased the LM3000-25 MMA (also referred to as the LM2) which is shown in Figure 12. Table 1 summarizes key specifications of the LM2. Figure 13 and Figure 14 are performance curves of the actuator [10] [11].   A preliminary design of the VLF projector is shown in Figure 15. The LM2's radiating face is attached to a larger radiating face to increase the volume of water displaced by the moving piston. A cavity behind the radiating face will be gas-filled in order to compensate for hydrostatic pressure. Since the plan is to utilize the VLF projector as a sound source at a constant test depth for array testing at LEFAC, it only has to be compensated for the specific pressure at that depth. A rubber suspension will couple the radiating face to the housing and allow for the 25mm displacement.

Analytical Method
The first method for modeling the acoustic performance of the VLF projector uses fundamental equations for radiation impedance from Kinsler and Fry [12]. Radiation impedance quantitatively links a drive with an acoustic field. For a circular piston, radiation impedance is defined as where 0 is the density of water, c is sound speed of water, S is the area of the radiating face, k is the wavenumber, a is the radius of the radiating face, and 1 and 1 are the piston resistance and reactive functions where J1 is the Bessel function of the first kind and H1 is the Struve function expressed as The expression for radiation impedance can be simplified for sufficiently low frequency. This is done using the criteria <<1, where k is the acoustic wavenumber and a is the radiating surface. For this study, the radiating face of the VLF projector is modeled as a 30cm diameter circular piston. The wavenumbers are calculated using Equation 13 where f is the frequency (in Hertz) and c is the speed of sound in water, approximately 1500 m/s. The quantity is calculated for the upper and lower limits of the frequencies of interest.
For f = 1Hz: For f = 100Hz: For the low frequency assumption, the radiation impedance can be approximated using only the first terms in the expansions for the Struve and Bessel functions. This reduces the equation for impedance to Since ka is small, the resistive term can be neglected in comparison to the reactive term. The equation for radiation impedance can be further simplified to The mechanical impedance of a mass is Therefore, the radiation impedance of a low frequency can be simplified to an added mass.
This radiation mass is added to the mass of the piston radiating face to calculate the total added mass being pushed by the LM2: Using the total mass and the LM2's performance curves, a displacement curve for the VLF projector is generated, as shown in Figure 16. Figure 16: A plot of displacement amplitude for an added mass of 14.1 kg. This curve was generated using the total mass (piston and radiation mass) and the Bose performance curves of the LM2 MMA.
The peak displacement amplitude, 0 , is integrated to calculate peak velocity 0 .
A plot of the modeled source level can be seen in Figure 17. Figure 17: A plot of expected source level for the VLF projector using equations for a simple point source. The shape is defined by a displacement limited region where the acoustic performance is limited by the peak displacement of the MMA and the force limited region where the acoustic performance is limited by the peak force of the MMA.

Displacement
Limited Region

Force Limited Region
The source level response takes a linear shape to about 18.5Hz where it begins to curl down and decrease. The region below 18.5Hz is referred to as the displacement limited region. Source level is limited by the 0.025m displacement of the MMA's radiating face.
The region above 18.5Hz is known as the force limited region. Source level is limited by the force output of the MMA, where the actuator is no longer getting the full 0.025m displacement. The force limitation is due to the added mass of the water displaced by the radiating face. Figure 18 shows how the displacement region changes as a function of piston size. A larger piston (r = 0.25 m) has a smaller displacement limited region with higher acoustic output. A smaller piston (r = .05m) has a larger displacement limited region with lower acoustic output. Elements are connected to each other at nodes. A set of connected elements is called a mesh. Figure 19 shows examples of meshes containing 2D elements with three nodes (triangular mesh) and four nodes (quadrilateral mesh).   Once all the geometries for the model are defined, the next step is to mesh the model. The structure is defined using CAX4R elements. These are continuum (C), or solid, axisymmetric (AX) quadrilateral (4 node) elements that use a reduced (R) integration method for calculating the stiffness matrix. There are two active degrees of freedom for the nodes of these elements: displacement in the x and displacement in the y in meters (m).

Direction of actuation
Designing a mesh requires a compromise between accuracy of the results and computational time to run the analysis. In FEA, the DOF is calculated for each node. A course mesh with large elements will contain a small number of nodes resulting in a small number of equations to solve. An analysis with a course mesh will have a short computation time but numerical approximations may not be accurate. A fine mesh with small elements will contain a large number of nodes resulting in a large number of equations to solve. An analysis with a fine mesh should yield high resolution results, but may take more time to compute.
In order to create a mesh that is both accurate and computationally efficient, a method of mesh refinement is used once the model is constructed. In this method, the model is first made with a course mesh, then reran with finer and finer meshes, comparing the results between models of different meshes until there is a point of diminishing returns on the accuracy. To begin, the mesh is designed using three elements through the thickness of the thinnest wall of the structure. The structure meshed can be seen in Figure 22. Once the structure is finished, the acoustic domain is meshed. The acoustic domain is defined using ACAX3 elements. These are acoustic (AC) axisymmetric (AX) triangular (3 node) elements. The nodes of these elements only record one active degree of freedom: acoustic pressure (POR) in Pascals.
It is difficult to perform a finite element modeling on acoustics of SONAR transducers for two reasons. One reason is that mesh must be small such that there are multiple nodes per wavelength. Equation 5 shows for a constant speed of sound, frequency is inversely proportional to wavelength. Higher frequency SONAR means shorter wavelength and a finer mesh.
The second reason is acoustic measurements must be taken in the far field, defined as [16] = where is the transition region between the near field and the far field, is wavelength, and is the area of the circular piston. For a transducer of constant size, as wavelength is decreased (frequency increased), the distance to the far field increases, demanding a larger acoustic domain for the model.
An FEA analysis that requires both a large acoustic domain and a fine mesh can become very computationally demanding due to the number of equations that must be solved. This is not an issue as this application is low frequency (long wavelength).
Source level is recorded one meter from the radiating face. A node is created one meter from the projector's radiating face in the fluid domain. For the shortest wavelength, Since 1 meter is greater than r, pressure recorded is in the far field.
Mesh must be small such that there are multiple elements per wavelength. The minimum number is two elements per wavelength, but the recommended is three to five [17]. This results in about six to ten nodes per wavelength. While the criteria would be difficult to meet for a high frequency applications, the shortest wavelength in this study is 15 meters long. The meshed acoustic domain is shown in Figure 23. The elements grow from the center of the domain with the largest elements at the outer edge of the acoustic domain. These large elements are 1/25 th the size of the smallest wavelength, making the domain more than suitable for this application.
. Figure 23: The meshed acoustic domain. This fluid is meshed with ACAX3 elements and element size grows as it approaches the outer boundary of the domain.
Material properties are defined for all parts of the structure and the fluid. Table 2 shows properties for the butyl rubber suspension pieces and the stainless steel housing. Table 3 shows the material properties for the acoustic domain water [18].   Table 3: Material properties of the fluid in the numerical model. The fluid refers to the acoustic domain.
Loads and boundary conditions are then defined in HyperMesh. The model is designed to solve for acoustic pressure in the fluid domain due to actuation of the projector's radiating face. In order to study the interactions between the fluid and structure, a tie constraint (Abaqus keyword TIE) [19] is applied at the surface. This is the continuity constraint that ties all nodes on the interface between the fluid and structure together.
Abaqus computes the coupling matrices from Equations 32 and 33 for these nodes. The structure is set as the "master" and the fluid is set at the "slave." Therefore, the motion of all nodal values on the fluid-structure interface is due to the motion of the structure.   The calculated SL shows the Abaqus output of the model having a greater value for acoustic pressure than the analytical model. One hypothesis for the discrepancy is "effective radius." The radius of the piston is 0.15 m, but the radius of the piston plus the suspension is 0.175 m. The suspension contributing to a larger surface area than just the piston itself could account for the higher SL. In Figure 26, the analytical model is rerun for the effective radius of 0.175m.  The equipment used to drive the actuator is pictured in Figure 28. A signal generator is used to apply a +/-10 V command signal to the Bose amplifier. The Bose amplifier drives the MMA with a current proportional to the command voltage (4.7A/V).

Experimental Analysis
From acceleration data and frequency information, the displacement 0 of the MMA is calculated using the equation where ω is the angular frequency and is acceleration.
where is the mean value based on sample mean ̅ and standard deviation s from sample size N. The critical value depends on the degrees of freedom in the study ( ) and an alpha value ( ). The degree of freedom is the number of independent pieces of information within the statistical analysis. For confidence interval, the degree of freedom is one less than the sample size. Alpha is the percentage of confidence subtracted from one.
Mean values and confidence intervals are plotted in Figure 30 and can be seen in tabular form in Table 4. Figure 31 plots the experimental data against the theoretical displacements from Figure 16.   A regression curve is constructed from the experimental data (as illustrated in Figure 31). The regression is a piecewise function with a constant displacement from 1Hz to 18.5Hz and a decreasing exponential from 18.5Hz to 100Hz. Figure 31: Plot of a regression fit to the experimental data (green). The regression is a piecewise function that is constant below 18.5 kHz and a decreasing exponential above 18.5 kHz. The regression fit is plotted against the theatrical displacements for a 14.1kg added mass based on the Bose performance curves.
The analytical acoustic analysis was rerun using the experimental data regression curve from Figure 31. Figure 32 shows that source levels calculated using the experimental data and source levels calculated using the Bose performance curves are within half a decibel in the displacement limited region (below 18.5Hz) and within one decibel in the force limited region (above 18.5Hz). Comparing source level based on the Bose specification curves for displacement with source level based on the displacement curve constructed from the experimental data validates the results of the two models that are based on the Bose performance curves.
Figure 32: Plot of acoustic source level using the experimental fit of displacement (green) against the source level estimated in the analytical analysis using the Bose specifications for displacement.

Future work
This thesis investigates the feasibility of implementing a moving magnet actuator (MMA) as the motor driver for a low frequency underwater acoustic projector. The analysis was based on displacement and force outputs provided in the product technical specifications and was verified experimentally. This analysis is only the first step in the design, fabrication, and calibration of an underwater transducer.
The next step for building the projector would be a detailed design for a housing.
The SolidWorks designs delivered in this report were simplified solid models intended only to be used for the FEA modeling. When the housing is designed for manufacturing of parts, the designer will have to focus on designing a watertight housing. The Bose MMA is an expensive piece of equipment; precautions must be taken to ensure the housing will not flood when placed in the water.
Another design parameter to investigate is how the projector will compensate for hydrostatic pressure. Since the primary intention of this projector is to use it as a sound source for calibrating a towed array, the projector only needs to be pressure compensated to a specific test depth of about 15 meters.
The design of the operational projector will also have to factor in designing cabling.
The current model of the MMA came with a 5 foot cable from the Bose amplifier to the actuator. If the MMA is to be used as a projector at a test depth, a new set of cabling must be designed.
Another design factor for the mechanical design of the projector is how the heat generated from the MMA is dissipated. Currently, fans cool heat sinks attached to the coils of the actuator. When the MMA is placed inside a housing, a new heat dissipation system must be designed. This could be as simple as designing heat sinks that span to the wall of the housing.
Once the projector is built, it must then be calibrated. Since the frequency range is 1-100Hz, long wavelengths will make it difficult to get an accurate transmitting voltage response (TVR) of the projector due to any reflections of sound in the Leesburg test facility.
It may be necessary to imbed an accelerometer in the radiating face of the projector as a feedback for how the projector is operating at depth.

Conclusion
The U.S. Navy has developed a passive calibration method at the Leesburg test facility for frequencies below 60Hz. In the passive method, ambient noise in the facility is used as the calibration sound source. The Navy is looking to replace this method with a reference projector calibration method. Unfortunately, the Navy does not currently have a reliable sound source at this frequency.
The data presented in this work shows the feasibility of implementing a moving magnet actuator (MMA) as the motor force in an underwater acoustic transducer. Based on the MMA's force and displacement specifications, a sound pressure level was calculated using two methods. The first method was an analytical method using equations for a simple sound source. This analysis was done using the software program Matlab. The second analysis was a numerical analysis: a fluid-structure interaction model where the acoustic medium was the fluid and the projector was the structure. Modeling efforts estimate a source level of over 125dB re 1 @1m at 1Hz and over 180 dB re 1 @1m at 30Hz.
These numbers can be compared to spectrum levels of the spring at thesis frequencies which are 91 dB re 1 / √ at 1 Hz and 87 dB re / √ at 30 Hz.
This thesis also covered experimentally testing the Bose moving magnet actuator.
The experimental efforts found the MMA operates at displacements necessary to achieve sound pressure levels calculated from the analytical and numerical models.
Lastly, future work was discussed. This thesis is just the preliminary study on what kind of acoustic output can be achieved using a moving magnet actuator. There are still many factors that will play a role in building a transducer. These factors include building APPENDIX This Appendix contains a list of the MATLAB scripts and the HyperMesh input deck used in the thesis, along with a brief description of what each one does.

AnalyticalandNumericalCode.m
This script is used to calculate the analytical solution from fundamental equations for an acoustic point source. The script also loads numerical outputs from Abaqus to compare to the numerical results.

DataCollection.m
This script is used to record the experimental data on the PXI chassis.

MMA_processing.m
This script is used to process the experimental data and compare it to the analytical results.

VLF_FEAInputFile.inp
Input file exported from HyperMesh and input into Abaqus to solve the FEA problem.