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An Accurate Measurement of Rotation Velocity-Eliminating Measurement Errors Caused by Gear Tooth Shape Unevenness
Abstract:
It is very important to accurately measure rotation frequencies and fluctuations of rotating systems since they cause vibrations and noises, and since they sometimes indicate system malfunctions. Most rotating systems are equipped with electro- or magneto-conductive gears as their components, and rotation pulses are very commonly obtained by installing electromagnetic or electrostatic type sensors closely to target gears, and time dependent (instantaneous) rotation frequencies are obtained from intervals between adjacent pulses. However, since the number of pulses per revolution is relatively small, a method of obtaining instantaneous frequencies from adjacent pulse intervals is not adequate. For these kinds of pulses, instantaneous rotation frequencies are typically derived using the analytic signal (or Hilbert transform) method. In either case, there is an inherent limitation in using rotation pulses obtained from gears. Individual shapes of teeth may slightly differ from each other and this unevenness of the tooth shape causes errors in the instantaneous rotation frequency estimation.
In order to solve the above mentioned problem, this paper proposes a method that uses two sensors closely located to each other. Information regarding the true rotation frequencies of the gear is contained in the two sensor signals without delay. On the other hand, the errors (spurious instantaneous frequencies) caused by the unevenness of the tooth shapes are contained with a time delay corresponding to the angle difference between the sensors. The subtraction of the instantaneous frequencies obtained from the two rotation pulses gives an instantaneous rotation frequency signal that contains only the spurious instantaneous frequencies. Since the time delay can be known from the phase measurement of the two pulses, the spurious instantaneous frequencies (and then the true instantaneous frequencies) can be calculated. This paper includes numerical discussions of the effectiveness of the method and some experimental results.
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