Order tracking with multiple shafts and crossing orders

Abstract

Transient sinusoids that cross in frequency exhibit interaction phenomena that defy conventional tracking filter techniques. The Vold–Kalman filter explicitly uses shaft speed information from multiple shafts to decouple interacting orders through a simultaneous estimation. The estimation uses energy constraints to distribute the total signal energy between the orders. The outputs of the filter are time histories of complex envelopes of the order functions, without beating interactions and with no phase bias. The estimation is also independent of slew rates, such that highly transient events may be tracked with high fidelity. By modulating the complex envelopes by suitable carrier waves, time histories of the individual orders are obtained which can be used for sound quality studies and sound synthesis. The phase information allows for the construction of operating deflection shapes as a function of shaft, order, and shaft speed. Examples will be shown for vibrations in continuous rate belt drive transmissions and sound synthesis for torque converters.