Laser Vibrometry-Based Precise Measurement of Tape-Shaped Tethers Damping Ratio Toward Space Applications

To mitigate the growing problem of space debris, current international guidelines require spacecraft in low Earth orbit (LEO) to implement post-mission disposal strategies to be deorbited within 25 years from the end of their operative life. Electrodynamic tethers (EDTs) are an effective and promising option for deorbiting as they do not require fuel consumption. However, the success of this new technology also depends on the dynamic stability of thin tape-shaped tethers during both deployment and deorbiting phases. This is where precise measurement of damping characteristics of thin tape-shaped tethers comes in. This article presents an innovative experimental setup and analysis methods for precisely measuring the damping ratio of a thin (thickness 50 $\mu \text{m}$ ) tape-shaped tether made of polyether ether ketone (PEEK) intended for use in EDT applications. To capture longitudinal oscillations during dynamic tests, we employed a laser vibrometer and explored four different methods of experimental data analysis, comparing and describing them in detail in this article. We also conducted an uncertainty analysis in line with the International Organization for Standardization (ISO) guide to the expression of uncertainty in measurement (GUM). The experimental results show good agreement among the four methods used to estimate the damping ratio with the most precise method involving nonlinear regression applied to all the experimental data. A Monte Carlo (MC) analysis was carried out considering the most significant sources of uncertainty. The smallest uncertainty interval is ±1% of the estimated damping ratio, with a 95% confidence level, using this method.