# Shaft. Application of full spectrum to rotating machinery diagnostics. Centerlines. Paul Goldman, Ph.D. and Agnes Muszynska, Ph.D.

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2 Figure 1. Half spectrum data-processing sequence: spectrums are obtained independently using the data from each probe. One process for obtaining a full spectrum, which demonstrates the correlation between the orbit and full spectrum, includes an expansion of the direct orbit into a sum of filtered orbits (Figure 2). Each filtered orbit has, in general, an elliptical shape. An elliptical orbit can be presented as a sum of two circular orbits: one is the locus of the vector rotating in the direction of rotation (forward), and the other is the locus of the vector rotating in the opposite direction (reverse). Both vectors rotate at the same frequency (the frequency of the filtered orbit). What is the correlation of full spectrum with filtered orbits and half spectrum? Since such a presentation of the filtered orbit can be done in only one way, forward and reverse circles are completely determined by the filtered orbit. An instantaneous position of the rotor on its filtered orbit can be presented as a sum of vectors of the instantaneous positions on the forward and reverse orbits: R ω e j(ωtα ω ) R ω e j(ωtβ ω ). Here R ω and R ω are the radiuses of the forward and reverse orbits, ω is the frequency of filtering, and α ω and β ω are phases of forward and reverse responses. In Figure 2, ω = Ω. Since Ω is the rotative speed, ω can, therefore, be equal to Ω or to 2Ω. (1X or 2X). Note that the major axis of the filtered orbit ellipse is R ω R ω, while its minor axis is R ω R ω. Forward precession of the filtered elliptical orbit (in the direction of the rotor rotation) means that R ω > R ω, while reverse precession means that R ω < R ω. To completely define an ellipse, the major axis orientation is needed. The angle between the horizontal probe and the ellipse major axis, (β ω α ω )/2, is determined by the relative phase of the forward and reverse components. In two important cases, the ellipse degenerates into a simpler form: 1. If the filtered orbit is circular and forward, then the reverse component does not exist. If the filtered orbit is circular and reverse, then the forward component does not exist. There is no relative phase, and the major axis equals the minor axis. 2. If the filtered orbit is a straight line, then the amplitude of the forward component is equal to the amplitude of the reverse component. Relative phase is still important to defining the orientation of the line. A full spectrum is constructed from the radiuses of the 18 Orbit First Quarter 1999

3 Figure 2. Full spectrum data-processing sequence: the spectrum obtained from the data from two probes. Orbit First Quarter

4 Figure 3. Mathematical procedure for obtaining a full spectrum. forward and reverse components of the filtered orbits. The horizontal coordinate equals ± frequency ( for the forward and for the reverse components), and the vertical coordinate equals the peak to peak amplitude of the corresponding forward or reverse component. In ADRE for Windows, the full spectrum is obtained as the result of an FFT transformation of the sampled signals. The X component is the direct input, and the Y component is the quadrature input (Figure 3). Half spectrums are obtained independently from X and Y sampled signals. Each of them is considered as the direct input to the FFT, while the quadrature input is zero. It is important to note that the full spectrum forward and reverse component amplitudes can be used to recover the shape of the corresponding filtered orbit. Determining the orientation of the orbit is not possible in the full spectrum without the relative phase information, however. There is no way to make any judgment on the shape of the filtered orbit using half spectrums. The full spectrum is unaffected by probe orientation or probe rotation, as is the orbit. The X and Y half spectrums are dependent on the actual probe locations and can change dramatically with changes in their orientation. These characteristics, along with the enhanced applications of the full spectrum, make it superior to the half spectrum. Periodicity of irregularities Major frequency components Once 1X forward (can include mechanical bow) What can it do for me? So, now that we know how a full spectrum is created, and what additional information it contains in comparison to a half spectrum, the question is, how can it be used? In order to perform reliable diagnostics, all possible information has to be extracted from the available data. Since full spectrum contains more information than the half spectrum, it has an advantage from that perspective. It can be used for steady state analysis (full spectrum, full spectrum waterfall) or for transient analysis (full spectrum cascade). One of the possible applications of full spectrum is for analysis of the rotor runout caused by mechanical, electrical, or magnetic irregularities. Depending on the periodicity of such irregularities observed by the XY proximity probes, different combinations of forward and reverse components are observed. The rules for such an analysis are summarized in Table 1. The amplitude and frequency components generated by the irregularities of the rotor do not change with rotative speed, unless there is a change in the rotor axial position. In that case, a new pattern will emerge, but it will follow the same rules. Twice 2X forward and 2X reverse, with the same magnitudes Three times 3X reverse Table 1. Runout signature analysis. Four times 4X forward and 4X reverse, with the same magnitudes Five times 5X forward 20 Orbit First Quarter 1999

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