Laser Doppler vibrometry (LDV) offers an attractive solution when radial vibration measurement directly from a rotor surface is required. Research to date has demonstrated application on polished-circular rotors and rotors coated with retro-reflective tape. In the latter case, however, a significant cross-sensitivity to the orthogonal radial vibration component occurs and post-processing is required to resolve individual radial vibration components. Until now, the fundamentally different behaviour observed between these cases has stood as an inconsistency in the published literature, symptomatic of the need to understand the effect of surface roughness. This paper offers the first consistent mathematical description of the polished-circular and rough rotor behaviours, combined with an experimental investigation of the relationship between surface roughness and cross-sensitivity. Rotors with surface roughness up to 10 nm satisfy the polished-circular rotor definition if vibration displacement is below 100% beam diameter, for a 90 μm beam, and below 40% beam diameter, for a 520 μm beam. On rotors with roughness between 10 nm and 50 nm, the polished-circular rotor definition is satisfied for vibration displacements up to 25% beam diameter, for a 90 μm beam, and up to 10% beam diameter, for a 520 μm beam. As roughness increases, cross-sensitivity increases but only rotors coated in retro-reflective tape satisfied the rough rotor definition fully. Consequently, when polished-circular surfaces are not available, rotor surfaces must be treated with retro-reflective tape and measurements post-processed to resolve individual vibration components. Through simulations, the value of the resolution and correction algorithms that form the post-processor has been demonstrated quantitatively. Simulations incorporating representative instrument misalignments and measurement noise have enabled quantification of likely error levels in radial vibration measurements. On a polished-circular rotor, errors around 0.2% for amplitude and 2 mrad for phase are likely, rising a little at the integer orders affected by pseudo-vibration. Higher pseudo-vibration levels and the need for resolution increase errors in the rough rotor measurements, especially around the synchronous frequency where errors reach 20% by amplitude and 100 mrad for phase. Outside a range of half an order either side of first order, errors are ten times lower and beyond fifth order errors are similar to those for the polished-circular rotor. Further simulations were performed to estimate sensitivities to axial vibration, speed variation and bending vibrations. © 2012 Elsevier Ltd.
Rothberg, S. J., Halkon, B. J., Tirabassi, M., & Pusey, C. (2012). Radial vibration measurements directly from rotors using laser vibrometry: The effects of surface roughness, instrument misalignments and pseudo-vibration. Mechanical Systems and Signal Processing, 33, 109–131. https://doi.org/10.1016/j.ymssp.2012.06.011