Ultrasonic measurements and modelling of attenuation and phase velocity in pulp suspensions

Abstract

Abstract-In the manufacturing process of paper the mass fraction and material properties of the fibres in the pulp suspension are important for the quality of the finished product. This study presents two different methods of pulp characterisation. The first is based on phase velocity, which we use to investigate the composition of the pulp. Here a method is presented where the optimal number of circular shifts within the sampling window of the signal is determined which gives, in a weakly dispersive medium, a continuous phase spectrum and minimizes the likelihood of discontinuities within the bandwidth. Hence, the ambiguity in phase unwrapping is avoided. The results from phase velocity measurements show that the phase velocity weakly increases with increasing amount of fines in the suspension. The dispersion is caused by the fibres and it correlates with fibre mass fraction. The second method is based on attenuation and is used to characterise the wood fibres. The results of the attenuation experiments show that it is possible to inversely calculate wood fibre properties by fitting the model to the experimental data, if the fibre diameter distribution is known. However, the accuracy of these calculation is difficult to determined and more work in this area is required.

Ultrasound characterization of the viscoelastic properties of additively manufactured photopolymer materials

“…Third, a fast Fourier transform was then applied to each signal u i ðtÞ over the total acquisition time length, thereby including zero padding as a typical way to improve the spectrum resolution. Fourth, to reduce the 2p-ambiguity due to the phase unwrapping, the absolute phase was calculated as in Niemi et al (2005) and He and Zheng (2001). In this way, each signal u i ðtÞ was circularly shifted to the beginning of the window, so that the total phase spectrum can be written as…”

Model-based phase velocity and attenuation estimation in wideband ultrasonic measurement systems

“…However, a good estimate of the attenuation is still needed. The phase unwrapping problem is well-known and has been addressed using other approaches [3], [5], [6].…”

“…Although different approaches exist to cope with wrapped phases [3]- [6], they all are based on nonparametric spectral estimates and, hence, suffer from bias and high uncertainties in low SNR frequency regions. In [7], the authors investigate errors generated by nonlin- earities when estimating phase velocity and attenuation, including also the timing jitter in a through-transmission setup.…”

2D-2 Ultrasonic Methods in Determining Elastic Material Properties of Fibres in Suspension

“…Its construction and the measurement principles are described in detail in Löfqvist [6] and Niemi [7]. The theory of pulse-echo measurements of attenuation and sound speed can be found in McClements [8].…”