The use of Instantaneous Angular Speed (IAS) in condition monitoring of rotating machines is an appealing alternative to traditional approaches such as those based on accelerometers: the direct angular sampling characteristic of IAS measurements has proven to be a favoured framework to study mechanical phenomena involved in rotating machines. Physical models have been established to link the variations of IAS to torque disturbances in case of mechanical fault such as bearing failure. In this paper an original point of view is given on the IAS measurement by linking IAS variations and shaft vibrations. First the orbit of a rotating shaft is studied to show that it contains useful information about the health state of the bearing. Then angle position sensors traditionally used in IAS measurements are combined to reconstruct this orbit. It is shown that IAS measurements are sensitive to the shaft vibrations, which may be used advantageously to enhance the diagnosis possibilities. Finally the links between various defect sizes and the reconstructed orbits are investigated to propose a fault severity indicator.

Condition monitoring performed directly from the estimated instantaneous angular speed has found some interesting applications in industrial environments, going from bearing monitoring to gear failure detection. One common way to estimate the angular speed makes use of angular encoders linked to a rotating shaft. At the opposite of traditional time-sampled signals, encoders describe purely angular phenomena often encountered in rotating machines. However, rotating encoders suffer from various geometric defects, corrupting the measurement with an angular periodic signature. The angular synchronous average is a very popular tool to estimate this systematic error, but is only adapted to constant speed conditions, which is rarely the case in real applications. We propose here two different estimators to compute a robust estimation of the synchronous component in variable speed conditions. The former, as a data-driven approach, is based on a local weighted least squares method, while the latter is a model-based approach. We study the behaviour of our estimators with both simulations and experimental signals, and show the relevance of the proposed method in an industrial context.