Introduction

Complex Functions

As a maintenance engineer or technician, you’re already using complex numbers on a daily basis. You probably just did not remember it ! Look at any graph : it has TWO components, the X axis and the Y axis. In vibration, most of the time, this means X=amplitude and Y=frequency. Even entry level personnel goes beyond this : a waterfall display uses the same as above, plus a third component which is time related, whether expressed in minutes, days or date. X and Y remain the same, Z=time.

Any vector used in balancing is also composed of an X and a Y, but in this case, we use POLAR coordinates : X= amplitude and Y=angle to map out on a chart. Descartes would be all smiles to see just how much his mathematical musings influence our daily lives : TV, computers, spreadsheets, games, the Cartesian coordinates (X,Y) are everywhere !

2-channel functions imply complex functions. And the most obvious is the collection of a spectrum with simultaneous collection of PHASE components. This type of information may also be used to draw a Nyquist plot, where amplitude and phase VARY because the RPM is changing, and so, plotted on a polar graph and indicating the RPM at a given moment, we draw many conclusions to support our diagnostic work regarding machine behavior.

2-channel is important in bringing back structural information on the REACTIONS of a machine or a structure to the input of a KNOWN force : using a load cell hammer, we measure the force of the impact, the duration of the impact, the phase reaction and the waveform going through the structure, expressed in the frequency domain or FFT. In animating a structure, we may use roaming force, roaming sensor or a combination of both. In relying on rotational forces (and defects) to supply the energy, then we may animate a machine through its Operating Deflection Shapes aka ODS, but this is yet another application.

They are close, but ODS just requires FFT (or partial information thereof including but not necessarily limited to first order amplitude), 1X phase (and possibly other orders if more precision is desired and the capacity to collect and process the information is present), and a network of points which yield a descriptive array of what the machine and its structure may be doing.