DETECTOR OF DEFECTS FOR ROTATING MACHINERY
"Technical Field"
This invention refers to a tool of diagnostics for industrial rotating machine. Rotating
machines are those like fluid pumps, air compressors, blowers, electrical generators, gas turbine
machines etc., used in most industrial facilities. The primary function of the tool is to collect sound
wave emitted by rotating machine and then to analyze numerically the frequency of collected sound.
Thus, mechanic defects of rotating machine such as wearing of bearings, distortion of spindle shafts,
mass unbalance, etc. can be detected by the tool. The frequency analysis of sound data is performed
by mnning an application software on a general-purpose microcomputer. The frequency analysis is
carried using a mathematical logic of digital-filter to recognize malfimctions and mechanical defects
of machines.
"Background Art"
There are many kinds of tools for the diagnostic of rotating machine. One of most popular is that of
the type of mechanical vibration sensor (seismic-type accelerometer) accompanied by a computer
program based on the algorithm of Fast Fourier Transform (FFT) running on a specific-developed
board-computer. From the point of view of tool operators, this FFT technique presents some
technical inconveniences. These inconveniences are, first, a need to approximate and attain the
accelerometer sensor to a plain face of rotating machine and, second, a difficulty to pick up an
"instantaneous and repetitive variation" of the vibration signal. This "instantaneous and repetitive
variation" is considered as being one of primary causes of fatigue of mechanical components of
rotating machine. The inconveniences arise because of the FFT algorithm examines only the mean
distribution of vibration signal in a determined range of frequency. Therefore, the objective of the
invention is to find out a solution for these inconveniences and to propose a simple tool of easy
operation.
"Disclosure of Invention"
The utilization of sound wave avoids physical contact between microphone and target
rotating machine. The adoption of a digital-filter based on the theory of linear prediction by
auto-regression, being different from that of FFT, permits to detect malfunctions and defects at a
shorter interval of time (less than 1 second) and also with higher accuracy. Digital-filter is a numeric
equation based on the theory of linear prediction analysis (equation of auto-regression) used to
separate and extract an undesired white-noise from the collected sound data. The logic of
recognition of malfunctions and defects is constituted by a system of equations which determine a
power spectrum and a spectrum of moving-average of the white-noise. The power spectrum of the
white-noise is determined by transforming the sound data from the domain of time representation to
the domain of frequency representation. The spectrum of moving-average is an arithmetic average
taken dynamically along the axis of time. Therefore, the power spectrum and the spectrum of
moving-average of white-noise are quantities to visualize the existence of machine ma-fiinctions and
defects of mechanical components (bearing, spindle shaft, bush, etc.). The tool is characterized by
the following items:
(a) Collection of sound wave emitted by rotating machine.
(b) Collector having a parabolic-shape covering.
(c) No physical contact between microphone and target machine.
(d) Easy operation and wearable by technicians.
(e) Application software that can be run on any general-purpose microcomputer.
(f) Algorithm of digital-filter based on the theory of linear prediction analysis (equation of
auto-regression), and the numerical method to solve this equation is of Levmson-Durbin
method,
(g) Frequency analysis based on the spectrum of moving-average and the power spectrum.
"Brief Description of Drawings"
FIGURE 1 represents a schema of the present invention and FIGURE 2 is a view of the
covering of the collector. FIGURE 3 is a basic concept of the digital-filter and FIGURE 4 represents
its theoretical algorithm. FIGURE 5 shows a matrix of the Levinson-Durbin method for the
numerical analysis. FIGURE 6 gives is a basic concept of the apphcation software. FIGURE 7 to
FIGURE 10 show the data sample of sound emitted by machines "without defects" and results of
numerical analysis. FIGURE 11 to FIGURE 14 show the data sample of sound emitted by machines
"with defects" and results of numerical analysis. FIGURE 15 shows the numeric comparison of
moving-average between machines "with defects" and "without defects".
"Modes for Carrying Out the Invention"
The sound collector of the tool could be made by a molded plastic or molding a plate of
aluminum alloy, and all the application software could be developed using any computer
programming language. The details of the invention are explained by the following figures:
FIGURE 1 represents a schema of the tool. It is composed by a collector (1) of sound wave,
a microphone (2), an electronic amplifier (3), an analog digital converter (4), an general-purpose
microcomputer (5) and an application software.
FIGURE 2 is a view of the covering of the collector (1). The parabolic curve is represented
by the equation Y = (X * X) / (4*f), where f is the focal distance, and X and Y are Cartesian
coordinates. The distance between point P(X, Y) and the directive line is equal. The microphone is
of the condenser-type characterized by a high stability and sensibility along the entire range of
frequency (20 E-z to 20,000 Hz). The microphone is located on the geometrical focus of the
parabolic-shape covering.
FIGURE 3 is a basic concept of the digital-filter (6). The digital-filter is designed in such a
manner that when a data sample of sound (7) of the machine "without defects" is applied onto the
digital-filter, the output is a white-noise (8). The white-noise is a random signal where the arithmetic
average is equal to zero along the entire range of frequency. When a data sample of sound (9) of
machines "with defects" is applied onto the digital-filter, the output is a sum of white-noise (10) and
other characteristics, so that the arithmetic average is different of zero, suggesting therefore an
existence of some machine malfunctions and mechanical defects.
FIGURE 4 represents the algorithm of the digital-filter based on the theory of linear
prediction analysis. The function of the algorithm is to estimate intensity of sound wave
corresponding to a time instant n, in such a way that the difference between the estimated intensity
and the actual intensity x(n) (11) of the collected data sample (both collected at the same instant of
time) become minimum. The estimated intensity is obtained by a numerical summation of the
product of linear coefficients (12) and sound intensity (13). The arithmetic difference is called as
"prevision error" e(n), or simply "white-noise" (14). The upper limit M of the summation index is
order of auto-regression. In the present invention, the algorithm is solved by the numerical method
known as Levinson-Durbin method ("Digital Signal Processing", Second Edition., E. C. Ifeachor
and B. W. Jervis, Prentice Hall, 2002).
FIGURE 5 shows a matrix of the Levinson-Durbin method. This method calculates linear
coefficients of the digital-filter. The sequence of values r(0), r(l), r(2), ... r(M-l) represents
auto-regression (15) of order M. The linear coefficients (12) are fitted in such a manner that the
digital-filter reproduces with good accuracy the intensity of the collected sound data (11).
FIGURE 6 is a basic concept of the application software. The software is constituted by
five modules necessary to calculate the graphs of auto-regression (15), of linear coefficients (12) of
the digital-filter, of white-noise (8, 10), of the moving-average spectrum (16, 17), and of power
spectrum (18, 19).
FIGURE 7 shows a data sample of sound wave collected from the machine "without
defects". For convenience, the condition "without defects" is adopted as an initial "new state" of the
machine. This condition "without defects" will be used as a "condition of reference" in order to
evaluate the sound data emitted by target machines "with defects". TABLE 1 is a list of coefficients
of the digital-filter, of order M = 30, calculated for the sound data of the machine "without defects"
("new state" of the machine).
FIGURE 8 is the spectrum of white-noise corresponding to the data sample of FIGURE 7.
Once the white-noise represents a prevision error, the arithmetic average of its amplitude is equal to
zero along all frequency.
FIGURE 9 shows the power spectrum of the white-noise for the machine "without
defects".
This corresponds to the case of FIGURE 8. The intensity of power spectrum is in the unit
decibel and the frequency in the unit Hz.
FIGURE 10 is the spectrum of moving-average of white-noise for machine "without
defects". The moving-average is defined as an arithmetic average taken on certain instants of time
before and after the time instant centered on the instant of time of reference. The instant of time of
reference is that where one wishes to calculate the value of moving-average. As the instant of
reference varies from time equivalent to zero until the time equivalent to (L— 1) along the data
sequence, the moving-average is a value which depends on the location of the instant of reference.
In other words, the moving-average is movable or "moving" along the axis of time.
FIGURE 11 shows the data sample of sound emitted by machines "with defects". Eventual
defects could be hidden in this data sample. The digital-filter described by the coefficients ("new
state" of the machine) shown on TABLE 1 is applied to this data sample.
FIGURE 12 is the spectrum of white-noise corresponding to the data sample of FIGURE
11. The characteristics of this white-noise are different from that of the machine "without defects"
shown on FIGURE 8. Remarkable variation of the amplitude suggests an existence of any
malfunctions and mechanical defects.
FIGURE 13 is the power spectrum of the white-noise of machines "with defects". This
corresponds to the case of FIGURE 12. The peaks appeared on the graph indicate an existence of
any malfunctions and mechanical defects for that specific frequency.
FIGURE 14 shows the spectrum of moving-average for machines "with defects". The
characteristics of this moving-average are different from that of the machine "without defects"
shown on FIGURE 10. The result of numerical comparison of height and width of moving-average
(that is, between FIGURE 10 and FIGURE 14) characterizes the appeared malfunctions and defects.
FIGURE 15 shows the numeric difference of moving-average between machines "with
defects" and "without defects". The vertical coordinate is a numeric subtraction of moving-average.
The location of peaks (with positive and negative values) and the height and width of peaks
characterize and specify the appeared malfunctions and defects.
The tool should be operated in the following way:
(a) The sound wave of a target machine is collected using the collector (1). First, the sound
emitted by the machine "without defects" is collected. The parabolic-shape covering of the
collector collects only the sound coming just from the target machine, and blocking out all
undesired sound unnecessary for the present analysis. The collected sound is reflected and
directed to the focus, and then the microphone (2) transforms the acoustic signal to an
analog electrical signal.
(b) The electronic amplifier (3) augments the intensity of analog signal up to a level sufficient to
convert it into a digital signal,
(c) The analog digital converter (4) makes a data sampling of analog signal and constructs a
temporal sequence of values, such as x(0), x(l), x(2), ... x(L-l), where L is the number of
data elements contained in the sample.
(d) The microcomputer (5) takes the data sample and loads to the working memory. The
application software solves a system of linear equations to calculate coefficients (12) of the
digital-filter,
(e) The digital-filter (6) is applied to the data sample (7) to calculate the white-noise of the
machine "without defects". The calculated white-noise (8) is a "condition of reference"
necessary to estimate next collected data (those emitted by machines "with defect").
(f) Thus, the new sound wave is collected by pointing out the collector to the direction of
machines "with defect". A temporal sequence of values (9) is constructed.
(g) The digital-filter is applied again to the data sequence (9), and the white-noise (10) is
estimated.
(h) The software calculates the spectrum of moving-average (16, 17) and the power spectrum
(18, 19). These two kinds of spectra are calculated based on the data sequence coming from
machines "without defects" and "with defects".
(i) The software compares the results of two kinds of spectra by noting on the shape and
location of peaks of graphs. The shape and location of peaks suggest the existence of
malfunctions and defects on target rotating machine.
"Industrial Applicability"
The tool described by this invention can substitute the human ear perception of
experimented "technicians" of diagnostics. The diagnostics of rotating machine are performed based
on the numerical quantity derived from the frequency analysis (moving-average spectrum and
power spectrum). This quantitative information is utilized during the planning study of maintenance
services in most industrial facilities, such as chemical and petrochemical plant, steel plant, paper and
cellulose, energy, cement, automobile, foods etc.