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Estimation of acoustic source strength by inverse methods: Part I: Conditioning of the inverse problem
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Estimation of acoustic source strength by inverse methods: Part I, Conditioning of the inverse problem; Part II, experimental investigation of methods for choosing regularisation parameters
No full textThis paper deals with the discrete inverse problem in acoustics. It is assumed that a number of acoustic sources are located at known spatial positions and that the acoustic pressure is measured at a number of spatial positions in the radiated field. The transfer functions relating the strengths of the acoustic sources to the radiated pressures are also assumed known. In principle, the strengths of the acoustic sources can be deduced from the measured acoustic pressures by inversion of this matrix of transfer functions. The accuracy of source strength reconstruction (in the presence of noise which contaminates the measured pressures) is crucially dependent on the conditioning of the matrix to be inverted. This paper examines the conditioning of this inverse problem, particularly with regard to the geometry and number of sources and measurement positions and the non-dimensional frequency. A preliminary investigation is also presented of methods such as Tikhonov regularization and singular value discarding which can improve the accuracy of source strength reconstruction in poorly conditioned cases. Results are also presented which enable the solution of the inverse problem when the time histories of the acoustic sources are time-stationary random processes and the spectra and cross-spectra are measured at a number of positions in the radiated field. The paper illustrates the possibilities and limitations of the use of inverse methods in the deduction of acoustic source strength from radiated field measurements
A method for the efficient construction of acoustic pressure cross-spectral matrices
No full textA method is presented for constructing, with the minimum number of physical measurements, the full cross-spectral matrix of acoustic pressures associated with a number of measurement positions. It is necessary to evaluate the elements of the matrix in question when using inverse methods for the reconstruction of acoustic source strength spectra. The method presented uses the concept of "reference microphones". The relation between the rank of the cross-spectral matrix of acoustic pressures and the number of uncorrelated acoustic sources is discussed and used to determine the required number of reference microphones. A method is proposed for selecting this number in the inverse problem in which information regarding acoustic sources is unknown. The results of computer simulations are presented which explore the main features of the technique under various conditions. Experimental results are also presented which validate the technique
Rapid Laminated Tooling by a Brazing and Soldering Process
No full textLaminated tooling is a relatively fast and simple method to make metal tools directly for injection molding or resin transfer molding in the rapid prototyping field. Metal sheets are usually cut, stacked, aligned, and joined. Joining of metal sheets is usually accomplished by brazing or soldering. In the joining process, all the metal sheet layers should be rigidly joined, and thus heat should be applied to the whole volume of the laminate. Therefore, furnace brazing or diffusion bonding processes are considered suitable in laminated tooling. In this study, a rapid laminated tooling system composed of a CO 2 laser, a furnace, and a high-speed milling machine was developed. From the three-dimensional information of a product, slicing into two-dimensional contours was performed and low-carbon steel sheets were cut with the CO2 laser along the paths that were created from the slicing results. The metal sheets were joined by furnace brazing and by dip soldering. Furnace brazing was for relatively high-temperature tooling processes such as injection molding, and dip soldering was for low-temperature tooling processes such as reactive injection molding (RIM). Dip soldering was introduced as a new, simple, and fast joining process of steel laminates. In both joining methods, wetting experiments were performed to ensure the optimal values of the process parameters. Finally, laminate tools were machined with a high-speed milling machine to improve the surface quality
DEVELOPMENT AND REPAIR OF LAMINATE TOOLS BY JOINING PROCESS
No full textLaminate tooling process is a fast and simple method to make metal tools directly for various molding processes such as injection molding in rapid prototyping field. Metal sheets are usually cut, stacked, aligned and joined with brazing or soldering. Through the joining process, all of the metal sheet layers should be rigidly joined. When joining process parameters are not appropriate, there would be defects in the layers. Among various types of defects, non-bonded gaps of the tool surface are of great importance, because they directly affect the surface quality and dimensional accuracy of the final products. If a laminate tool with defects has to be abandoned, it could lead to great loss of time and cost. Therefore a repair method for non-bonded gaps of the surface is essential and has important meaning for rapid prototyping. In this study, a rapid laminate tooling system composed of a CO2 laser, a furnace, and a milling machine was developed. Metal sheets were joined by furnace brazing, dip soldering and adhesive bonding. Joined laminate tools were machined by a high-speed milling machine to improve surface quality. Also, repair brazing and soldering methods of the laminates using the CO₂ laser system have been investigated. ill laser repair process, the beam duration, beam power and beam profile were of great importance, and their effects were simulated by [mite element methods. The simulation results were compared with the experimental ones, and optimal parameters for laser repair process were investigated
A METHOD FOR THE EFFICIENT CONSTRUCTION OF ACOUSTIC PRESSURE CROSS-SPECTRAL MATRICES
No full textA method is presented for constructing, with the minimum number of physical measurements, the full cross-spectral matrix of acoustic pressures associated with a number of measurement positions. It is necessary to evaluate the elements of the matrix in question when using inverse methods for the reconstruction of acoustic source strength spectra. The method presented uses the concept of “reference microphones”. The relation between the rank of the cross-spectral matrix of acoustic pressures and the number of uncorrelated acoustic sources is discussed and used to determine the required number of reference microphones. A method is proposed for selecting this number in the inverse problem in which information regarding acoustic sources is unknown. The results of computer simulations are presented which explore the main features of the technique under various conditions. Experimental results are also presented which validate the technique
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