Angular (pitch and yaw) vibration measurements directly from rotors using laser vibrometry

Parallel beam laser vibrometers offer direct measurement of pitch and yaw vibration directly from rotors. This paper, intended as an essential guide for the practical parallel beam laser vibrometer practioner, presents exact mathematical expressions for measured angular velocity in the presence of inevitable misalignments and estimates the likely measurement error levels due to such misalignments as well as to other sources of uncertainty through numerical simulation. Cross-sensitivity to the orthogonal vibration component, i.e. cross-sensitivity in a pitch measurement to yaw motion and vice-versa, is confirmed for rough rotors whereas it is shown not to be present when rotors are polished-circular. A complementary experimental investigation of the relationship between surface roughness and cross-sensitivity confirms the identification of two preferred measurement configurations: from the side of a polished-circular rotor and from the end face of a (rough) rotor coated in retro-reflective tape. Rotors with surface roughness up to 50 nm satisfy the former case provided the vibration displacement at the rotor surface does not exceed 20% beam diameter. For surfaces with roughness of 10 nm this can be extended to 50%. For rough rotor end face measurements, post-processing is required to resolve the inherent cross-sensitivity; the need for post-processing is justified quantitatively through numerical simulation. Further simulations incorporating typical levels of instrument misalignment and measurement noise are used to enable quantification of the likely errors in such angular vibration measurements. For measurements from the side of a polished-circular rotor, errors are around 1% for amplitude and 10 mrad at integer orders affected by pseudo-vibration and around one-third of these levels elsewhere. For measurements from a rough rotor end face, errors will be similar at integer orders (from 2). Errors in the rotational speed measurement, required for post-processing, must be minimised in order to limit errors up to 2nd order while misalignments determine errors at around 0.4% amplitude and 4 mrad phase at orders above 2 other than at the integer orders.