Hindawi Publishing Corporation
Advances in Mechanical Engineering
Volume , Article ID , pages
http://dx.doi.org/.//
Research Article
Synthetic Amplitude Spectrum and Its Extensions
for Analyzing the Two Perpendicular Directional Vibration
Displacement Signals of a Rotating Rotor
Liang Yonggang, Liu Tiebing, Liu Hongxing, Si Junfeng, Huang Xiaolin, and Wang Rui
School of Electronic Science and Engineering, Nanjing University, Nanjing 210093, China
Correspondence should be addressed to Liu Hongxing; njhxliu@nju.edu.cn
Received July ; Revised January ; Accepted January
Academic Editor: A. Seshadri Sekhar
Copyright © Liang Yonggang et al. is is an open access article distributed under the Creative Commons Attribution License,
which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Classical Amplitude Spectrum analysis and Full Amplitude Spectrum analysis exhibit deciencies in analyzing the two per-
pendicular directional vibration displacement signals of a rotating rotor. e shape of Classical Amplitude Spectrum is inuenced
by the installing position of its sensor. Neither Classical Amplitude Spectrum nor Full Amplitude Spectrum can indicate the
actual radial rotor vibration amplitude on every frequency. erefore, the previous two methods are not convenient to be used in
rotating machine diagnoses. To solve these problems, this paper proposes a new rotor vibration analyzing tool here called Synthetic
Amplitude Spectrum (SAS). e paper discusses the principle of SAS analysis, provides the specic making process of SAS, and
applies it to two other current important analyzing methods in rotating machine diagnoses, resulting in two SAS extensions. e
two extensions include a short-time SAS array tool for rotor vibration time-frequency analysis and a SAS waterfall plot tool for
analyzing rotor vibration during machine startup or shutdown. e experiments and theoretical analysis showed that SAS and its
two extension methods are not inuenced by the installation position of the two sensors, and each amplitude of the spectrums can
represent the actual radial rotor vibration amplitude on the frequency.
1. Introduction
Large rotating rotors found in large motors and centrifugal
compressors, and so on, are usually supported on various
forms of sliding bearings. ey oen have two vibration
displacement sensors placed at each sliding bearing with
angle of degrees between each other, as in Figure ,called
Sensor 𝑋 and Sensor 𝑌, respectively. e two displacement
sensors are set up to measure the running condition of the
rotor so that the conclusion on whether the whole machine
is healthy can be drawn. e two discretized displacement
signals from sensors 𝑋 and 𝑌,herecalled𝑥 and 𝑦 signal
sequences, respectively, are always acquired synchronously.
e most basic tools used in analyzing the 𝑥 and 𝑦 signal
sequences are amplitude spectrums.
e most well-known amplitude spectrum, here called
Classical Amplitude Spectrum (CAS), is usually obtained as
follows: process 𝑥 and 𝑦 signal sequences using FFT, respec-
tively, get two corresponding Fourier series of them, and then
take the amplitudes and the frequencies of the two series to
plot their respective amplitude spectrums. e shortcoming
of Classical Amplitude Spectrum is that if the installation
mode of two sensors changes from Figure (a) to Figure (b),
the obtained spectrums will show large dierences even for
same rotor and bearing conditions. erefore, it is not easy
for us to establish the relationship between the spectrum
characteristics and the machine conditions.
Full Amplitude Spectrum (FAS) is another amplitude
spectrum [–], and it can be obtained as follows: construct
a complex signal sequence 𝑧,letting𝑧 = 𝑥+𝑖𝑦,make
FFT of 𝑧, and then calculate its Fourier series and plot the
Fourier amplitude spectrum. Since Full Amplitude Spectrum
contains the information of both signals 𝑥 and 𝑦,itisnot
inuenced by the installation mode of sensors 𝑋 and 𝑌 any-
more. us, it is more convenient than Classical Amplitude
Spectrum to establish the relationship between the spectrum
characteristics and the machine conditions. However, in the
Full Amplitude Spectrum, each original actual frequency