The ITD mode-shape coherence and confidence factor and its application to separating eigenvalue positions in the Z-plane

The properties of a newly defined mode-shape coherence and confidence factor are discussed in detail in connection with the Ibrahim time domain method. It has been found that this Factor is able to distinguish three kinds of modes, true physical modes within the frequency range (0 similar to f(pi)) (corresponding to an angular range (0 similar to pi) of eigenvalue positions in the Z-plane), frequency folded and/or overlapped modes and computational (noise) ones. Making use of this ability gives at least two benefits;(a) it releases the limitation on the user's constant Delta t(1) and increases the flexibility in use of all the user's constant combinations, and (b) it extends the angular range of eigenvalue positions to a multiple of 2 pi by using a large value of Delta t(1) and makes the identification of eigenvalue positions in the Z-plane more accurate by a sort of zoom process. Digital simulation and measurements on a gearbox were chosen as application examples to illustrate the above advantages. (C) 2000 Academic Press.