title: Duct acoustics for air-coupled ultrasonic phased arrays
Creators: name: Rutsch, Matthias
Publisher: name: UNSPECIFIED
Year: 2023

description: Air-coupled ultrasound is used in many applications such as range inding, tactile feedback, flow metering or non-destructive testing. The transducers directivity is a crucial acoustic property for all these applications. For instance, a narrow beam width allows for higher angular resolutions, whereas a wider beam width allows for emitting the sound wave in a bigger area for obstacle detection. However, the transducers dimensions influence its directivity and its resonance frequency. In order to decouple the acoustic aperture from transducer, acoustic waveguides are investigated in this work. This way, grating lobe free phased arrays can be built for unambiguous beamforming. In this thesis, the wave propagation inside these waveguides, including coupling mechanisms from the transducer till the free-field, are investigated. First, the state of the art of duct acoustics applications in the audible range and the ultrasound range are presented. Afterwards, different duct acoustics models are derived and compared. Each model is validated for 40 kHz, a duct length of 80 mm and an aperture between 10 mm and 3.4 mm. The challenge of the simulations is to take higher modes into account while reducing the calculation times. Therefore, analytical and numerical models were investigated. As a result, the boundary element method is the most efficient approach for the given geometry wavelength ratio using the commercial software COMSOL Multiphysics. With this method, free-field calculations on a single Xeon E5-2660 v3 CPU and 256 GB RAM without the need of a cluster are possible. The model is validated with calibrated measurements in an anechoic chamber. Therefore, an automated measurement system is established where a calibrated measurement microphone moves relative to the transducer, thus characterizing the sound field in front of the transducer. This setup can measure a hemisphere with a radius of up to 6 m and has a dynamic range of 111 dB. After the validation of the numerical model, waveguide geometry optimizations were conducted. The analyzed properties were: the influence of a perpendicular output and input surface on the wave propagation inside the waveguide; the size of the output aperture; length variations of the waveguide including temperature dependence; the position of tapering and types of losses due to the waveguide. As a result, the perpendicular input is crucial for fundamental mode propagation, otherwise higher modes occur, because the input diameter is bigger compared to the wavelength. The size of the output surface can be increased for line arrays with an SPL gain of +10 dB. However, the limit of the aperture size is 3.7 × λ, otherwise higher modes occur at the output which lead to defocusing of the main lobe. The length of the waveguide can increase the SPL. However, the industrial temperature demands of −25◦C to 75◦C have the same influence on the SPL as the length optimization (±4.8 dB), and, thus, are not investigated in more detail. The positioning of the tapering has just a minor influence of ±0.4 dB. The losses of the waveguide are −10 dB with diffraction loss as the dominant part. The losses inside the waveguide (reflection and thermoviscous losses) could not be validated with measurements due to the narrow bandwidth of the transducers, since the incident and reflected wave superposed. The derived results of the geometry optimization were used to build four line arrays. First, a waveguide with equal length ducts was built as a reference. Second, a Bézier waveguide with plane input surfaces for the transducers was designed. Third, the output aperture was changed from round outputs to rectangular shapes to increase the SPL and sensitivity. Last, a shortened version of the Bézier waveguide was built which has a reduced length of 65%. All four waveguides were simulated using the boundary element method and validated with the measurement etup. As a result, in both simulation and measurement the shorten waveguide has an increased SPL of +5 dB compared to the reference waveguide with equal length ducts. Thus, it is possible to build compact waveguides for air-coupled phased arrays. Next, the influence of different duct lengths in an acoustic waveguide is analyzed in more detail. Using ducts of different length offers more design freedom for the entire waveguide for compact design, easier assembly and reduced assembly time. However, different lengths must be compensated with additional time delays. Therefore, two waveguides were compared. First, an equal length waveguide was used. Second, a waveguide with Bézier-shaped ducts was used. The time delays, due to varying duct lengths, were measured and simulated with analytic and numerical methods. Afterwards, the directivity patterns of both waveguides were compared. As a result, the time compensation has no significant impact on the beam profile regarding side lobe level and half power beam width. In addition, SPL deviation of the waveguides are within the manufacturing tolerances of the transducers. The last aspect investigated in this thesis is the water resistance of the waveguide. Since it is designed for air-coupled ultrasound, it can be clogged due to dirt, dust or liquid. Two commonly known solutions for this issue is the use of hydrophobic fabrics or thin films. Therefore, both solutions were compared. First, these two approaches showed no significant impact on the beamforming capabilities of the phased array. In addition, the IP class of the fabric reached IPX7 and the thin film achieved even IPX8. Furthermore, the fabric has a minor insertion loss of just −1.8 dB. In contrast, the film reduces the SPL by −7.5 dB. This loss can be further reduced with special effort to +0.4 dB by changing the waveguide geometry and tuning the system to the correct resonance frequency. However, this shows that the film has a high temperature dependence compared to the fabric. In conclusion, acoustic waveguides enhance the acoustic properties of ultrasonic sensors. The directivity can be decoupled from the transducer and customized for a certain application.